Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (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: | \(25.8715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.2 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.1081 |
Dual form | 3240.2.q.be.2161.2 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63746 | + | 2.83616i | 0.618901 | + | 1.07197i | 0.989687 | + | 0.143250i | \(0.0457552\pi\) |
−0.370785 | + | 0.928719i | \(0.620911\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.13746 | + | 5.43424i | 0.945979 | + | 1.63848i | 0.753778 | + | 0.657129i | \(0.228229\pi\) |
0.192201 | + | 0.981356i | \(0.438437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.637459 | − | 1.10411i | 0.176799 | − | 0.306225i | −0.763983 | − | 0.645236i | \(-0.776759\pi\) |
0.940782 | + | 0.339011i | \(0.110092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.63746 | + | 6.30026i | −0.758463 | + | 1.31370i | 0.185172 | + | 0.982706i | \(0.440716\pi\) |
−0.943634 | + | 0.330990i | \(0.892618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.13746 | + | 5.43424i | 0.582611 | + | 1.00911i | 0.995169 | + | 0.0981809i | \(0.0313024\pi\) |
−0.412557 | + | 0.910932i | \(0.635364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13746 | + | 5.43424i | −0.563504 | + | 0.976018i | 0.433683 | + | 0.901066i | \(0.357214\pi\) |
−0.997187 | + | 0.0749524i | \(0.976120\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.27492 | 0.553562 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5498 | −1.73438 | −0.867191 | − | 0.497976i | \(-0.834077\pi\) | ||||
−0.867191 | + | 0.497976i | \(0.834077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77492 | − | 6.53835i | 0.589543 | − | 1.02112i | −0.404749 | − | 0.914428i | \(-0.632641\pi\) |
0.994292 | − | 0.106691i | \(-0.0340255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 3.46410i | −0.304997 | − | 0.528271i | 0.672264 | − | 0.740312i | \(-0.265322\pi\) |
−0.977261 | + | 0.212041i | \(0.931989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.637459 | − | 1.10411i | −0.0929829 | − | 0.161051i | 0.815782 | − | 0.578359i | \(-0.196307\pi\) |
−0.908765 | + | 0.417308i | \(0.862974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.86254 | + | 3.22602i | −0.266077 | + | 0.460859i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.725083 | −0.0995978 | −0.0497989 | − | 0.998759i | \(-0.515858\pi\) | ||||
−0.0497989 | + | 0.998759i | \(0.515858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.27492 | 0.846110 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.50000 | + | 11.2583i | −0.846228 | + | 1.46571i | 0.0383226 | + | 0.999265i | \(0.487799\pi\) |
−0.884551 | + | 0.466444i | \(0.845535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.27492 | − | 7.40437i | −0.547347 | − | 0.948033i | −0.998455 | − | 0.0555636i | \(-0.982304\pi\) |
0.451108 | − | 0.892469i | \(-0.351029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.637459 | − | 1.10411i | −0.0790670 | − | 0.136948i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.274917 | + | 0.476171i | −0.0335865 | + | 0.0581735i | −0.882330 | − | 0.470631i | \(-0.844026\pi\) |
0.848744 | + | 0.528805i | \(0.177360\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.27492 | 0.982052 | 0.491026 | − | 0.871145i | \(-0.336622\pi\) | ||||
0.491026 | + | 0.871145i | \(0.336622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0997 | 1.76728 | 0.883641 | − | 0.468165i | \(-0.155085\pi\) | ||||
0.883641 | + | 0.468165i | \(0.155085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.2749 | + | 17.7967i | −1.17094 | + | 2.02812i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.27492 | − | 9.13642i | −0.593475 | − | 1.02793i | −0.993760 | − | 0.111538i | \(-0.964422\pi\) |
0.400286 | − | 0.916390i | \(-0.368911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.27492 | − | 2.20822i | −0.139940 | − | 0.242384i | 0.787533 | − | 0.616272i | \(-0.211358\pi\) |
−0.927474 | + | 0.373888i | \(0.878024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | + | 1.73205i | −0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.8248 | −1.35942 | −0.679710 | − | 0.733481i | \(-0.737895\pi\) | ||||
−0.679710 | + | 0.733481i | \(0.737895\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17525 | 0.437685 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.500000 | − | 0.866025i | 0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | − | 13.8564i | −0.812277 | − | 1.40690i | −0.911267 | − | 0.411816i | \(-0.864894\pi\) |
0.0989899 | − | 0.995088i | \(-0.468439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.86254 | + | 8.42217i | 0.483841 | + | 0.838037i | 0.999828 | − | 0.0185594i | \(-0.00590799\pi\) |
−0.515987 | + | 0.856597i | \(0.672575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.91238 | − | 5.04438i | 0.286965 | − | 0.497038i | −0.686119 | − | 0.727489i | \(-0.740687\pi\) |
0.973084 | + | 0.230452i | \(0.0740204\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.0997 | −1.45974 | −0.729870 | − | 0.683586i | \(-0.760419\pi\) | ||||
−0.729870 | + | 0.683586i | \(0.760419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.27492 | −0.601028 | −0.300514 | − | 0.953777i | \(-0.597158\pi\) | ||||
−0.300514 | + | 0.953777i | \(0.597158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.63746 | + | 6.30026i | 0.339195 | + | 0.587503i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.27492 | − | 5.67232i | −0.300211 | − | 0.519981i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.1873 | + | 24.5731i | −1.28975 | + | 2.23392i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2749 | 1.00049 | 0.500244 | − | 0.865885i | \(-0.333244\pi\) | ||||
0.500244 | + | 0.865885i | \(0.333244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.774917 | − | 1.34220i | 0.0677048 | − | 0.117268i | −0.830186 | − | 0.557487i | \(-0.811766\pi\) |
0.897891 | + | 0.440219i | \(0.145099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.63746 | + | 2.83616i | 0.141986 | + | 0.245926i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.27492 | + | 12.6005i | 0.621538 | + | 1.07654i | 0.989199 | + | 0.146576i | \(0.0468252\pi\) |
−0.367661 | + | 0.929960i | \(0.619841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.27492 | 0.521104 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.00000 | − | 1.73205i | 0.0819232 | − | 0.141895i | −0.822153 | − | 0.569267i | \(-0.807227\pi\) |
0.904076 | + | 0.427372i | \(0.140560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.13746 | + | 10.6304i | 0.499459 | + | 0.865089i | 1.00000 | 0.000624236i | \(-0.000198701\pi\) | |
−0.500541 | + | 0.865713i | \(0.666865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.13746 | + | 5.43424i | 0.252007 | + | 0.436488i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.36254 | + | 9.28819i | −0.427977 | + | 0.741279i | −0.996693 | − | 0.0812554i | \(-0.974107\pi\) |
0.568716 | + | 0.822534i | \(0.307440\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.8248 | −1.87765 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5498 | 1.60959 | 0.804794 | − | 0.593555i | \(-0.202276\pi\) | ||||
0.804794 | + | 0.593555i | \(0.202276\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.72508 | + | 6.45203i | −0.288256 | + | 0.499273i | −0.973393 | − | 0.229140i | \(-0.926409\pi\) |
0.685138 | + | 0.728413i | \(0.259742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.68729 | + | 9.85068i | 0.437484 | + | 0.757745i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.36254 | + | 7.55614i | 0.331678 | + | 0.574483i | 0.982841 | − | 0.184455i | \(-0.0590520\pi\) |
−0.651163 | + | 0.758938i | \(0.725719\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63746 | − | 2.83616i | 0.123780 | − | 0.214394i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5498 | 0.863275 | 0.431638 | − | 0.902047i | \(-0.357936\pi\) | ||||
0.431638 | + | 0.902047i | \(0.357936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2749 | 1.20971 | 0.604853 | − | 0.796337i | \(-0.293232\pi\) | ||||
0.604853 | + | 0.796337i | \(0.293232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.27492 | + | 9.13642i | −0.387820 | + | 0.671723i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.27492 | − | 10.8685i | −0.458867 | − | 0.794782i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.68729 | + | 16.7789i | 0.700948 | + | 1.21408i | 0.968134 | + | 0.250432i | \(0.0805728\pi\) |
−0.267186 | + | 0.963645i | \(0.586094\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3746 | 1.59412 | 0.797062 | − | 0.603898i | \(-0.206387\pi\) | ||||
0.797062 | + | 0.603898i | \(0.206387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2749 | + | 17.7967i | −0.721158 | + | 1.24908i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.77492 | − | 6.53835i | −0.263652 | − | 0.456658i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.13746 | + | 5.43424i | 0.217023 | + | 0.375894i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.04983 | − | 13.9427i | 0.554173 | − | 0.959857i | −0.443794 | − | 0.896129i | \(-0.646368\pi\) |
0.997967 | − | 0.0637277i | \(-0.0202989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.5498 | −1.39501 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.27492 | + | 2.20822i | −0.0857602 | + | 0.148541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.72508 | − | 6.45203i | −0.247242 | − | 0.428236i | 0.715517 | − | 0.698595i | \(-0.246191\pi\) |
−0.962760 | + | 0.270359i | \(0.912858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.27492 | + | 7.40437i | −0.282494 | + | 0.489295i | −0.971998 | − | 0.234987i | \(-0.924495\pi\) |
0.689504 | + | 0.724282i | \(0.257829\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.09967 | 0.596139 | 0.298070 | − | 0.954544i | \(-0.403657\pi\) | ||||
0.298070 | + | 0.954544i | \(0.403657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.27492 | −0.0831664 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.72508 | + | 11.6482i | −0.435009 | + | 0.753458i | −0.997296 | − | 0.0734837i | \(-0.976588\pi\) |
0.562287 | + | 0.826942i | \(0.309922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1375 | + | 21.0227i | 0.781842 | + | 1.35419i | 0.930867 | + | 0.365357i | \(0.119053\pi\) |
−0.149025 | + | 0.988833i | \(0.547613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.86254 | + | 3.22602i | 0.118993 | + | 0.206103i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.637459 | − | 1.10411i | 0.0405605 | − | 0.0702529i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7251 | −1.18192 | −0.590958 | − | 0.806702i | \(-0.701250\pi\) | ||||
−0.590958 | + | 0.806702i | \(0.701250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −45.6495 | −2.86996 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.54983 | − | 2.68439i | 0.0966760 | − | 0.167448i | −0.813631 | − | 0.581382i | \(-0.802512\pi\) |
0.910307 | + | 0.413934i | \(0.135846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.2749 | − | 29.9210i | −1.07341 | − | 1.85920i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.362541 | − | 0.627940i | −0.0223553 | − | 0.0387204i | 0.854631 | − | 0.519235i | \(-0.173783\pi\) |
−0.876987 | + | 0.480515i | \(0.840450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.362541 | + | 0.627940i | −0.0222707 | + | 0.0385741i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.9244 | 1.58064 | 0.790320 | − | 0.612694i | \(-0.209914\pi\) | ||||
0.790320 | + | 0.612694i | \(0.209914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4502 | 0.817039 | 0.408520 | − | 0.912750i | \(-0.366045\pi\) | ||||
0.408520 | + | 0.912750i | \(0.366045\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.13746 | − | 5.43424i | 0.189196 | − | 0.327697i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6375 | − | 21.8887i | −0.759311 | − | 1.31517i | −0.943202 | − | 0.332219i | \(-0.892203\pi\) |
0.183891 | − | 0.982947i | \(-0.441131\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.08762 | + | 5.34792i | 0.184192 | + | 0.319030i | 0.943304 | − | 0.331930i | \(-0.107700\pi\) |
−0.759112 | + | 0.650960i | \(0.774366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.72508 | − | 9.91613i | 0.340321 | − | 0.589453i | −0.644171 | − | 0.764881i | \(-0.722798\pi\) |
0.984492 | + | 0.175428i | \(0.0561310\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.7251 | 1.45948 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.36254 | − | 9.28819i | 0.313283 | − | 0.542622i | −0.665788 | − | 0.746141i | \(-0.731904\pi\) |
0.979071 | + | 0.203519i | \(0.0652378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.50000 | + | 11.2583i | 0.378445 | + | 0.655485i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.63746 | + | 8.03231i | 0.268191 | + | 0.464521i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.54983 | − | 11.3446i | 0.377526 | − | 0.653895i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.54983 | −0.489562 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.09967 | 0.0627614 | 0.0313807 | − | 0.999508i | \(-0.490010\pi\) | ||||
0.0313807 | + | 0.999508i | \(0.490010\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9622 | + | 22.4512i | −0.735020 | + | 1.27309i | 0.219695 | + | 0.975569i | \(0.429494\pi\) |
−0.954715 | + | 0.297523i | \(0.903840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | − | 6.92820i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.63746 | + | 4.56821i | 0.148134 | + | 0.256576i | 0.930538 | − | 0.366195i | \(-0.119340\pi\) |
−0.782404 | + | 0.622772i | \(0.786007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.6873 | + | 34.0994i | −1.10228 | + | 1.90920i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | −0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.27492 | −0.0707197 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.08762 | − | 3.61587i | 0.115094 | − | 0.199349i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.41238 | + | 16.3027i | 0.517351 | + | 0.896078i | 0.999797 | + | 0.0201524i | \(0.00641515\pi\) |
−0.482446 | + | 0.875926i | \(0.660252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.274917 | + | 0.476171i | 0.0150203 | + | 0.0260160i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.72508 | + | 4.71998i | −0.148445 | + | 0.257114i | −0.930653 | − | 0.365903i | \(-0.880760\pi\) |
0.782208 | + | 0.623017i | \(0.214093\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.3746 | −2.13225 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.7251 | 0.579100 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.00000 | − | 12.1244i | 0.375780 | − | 0.650870i | −0.614664 | − | 0.788789i | \(-0.710708\pi\) |
0.990443 | + | 0.137920i | \(0.0440416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.41238 | − | 11.1066i | −0.343247 | − | 0.594521i | 0.641787 | − | 0.766883i | \(-0.278193\pi\) |
−0.985034 | + | 0.172362i | \(0.944860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.27492 | + | 5.67232i | 0.174306 | + | 0.301907i | 0.939921 | − | 0.341392i | \(-0.110898\pi\) |
−0.765615 | + | 0.643299i | \(0.777565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.13746 | − | 7.16629i | 0.219594 | − | 0.380347i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.824752 | −0.0435287 | −0.0217644 | − | 0.999763i | \(-0.506928\pi\) | ||||
−0.0217644 | + | 0.999763i | \(0.506928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.54983 | − | 13.0767i | 0.395176 | − | 0.684466i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.27492 | − | 10.8685i | −0.327548 | − | 0.567330i | 0.654477 | − | 0.756082i | \(-0.272889\pi\) |
−0.982025 | + | 0.188752i | \(0.939556\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.18729 | − | 2.05645i | −0.0616412 | − | 0.106766i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5498 | + | 26.9331i | −0.805140 | + | 1.39454i | 0.111057 | + | 0.993814i | \(0.464576\pi\) |
−0.916197 | + | 0.400729i | \(0.868757\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.27492 | 0.476420 | 0.238210 | − | 0.971214i | \(-0.423439\pi\) | ||||
0.238210 | + | 0.971214i | \(0.423439\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.18729 | − | 2.05645i | 0.0606678 | − | 0.105080i | −0.834096 | − | 0.551619i | \(-0.814010\pi\) |
0.894764 | + | 0.446539i | \(0.147344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.2749 | + | 17.7967i | 0.523658 | + | 0.907003i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.27492 | − | 14.3326i | −0.419555 | − | 0.726691i | 0.576340 | − | 0.817210i | \(-0.304481\pi\) |
−0.995895 | + | 0.0905197i | \(0.971147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.27492 | − | 12.6005i | 0.367908 | − | 0.637236i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.5498 | −0.530820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.09967 | 0.356322 | 0.178161 | − | 0.984001i | \(-0.442985\pi\) | ||||
0.178161 | + | 0.984001i | \(0.442985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6375 | − | 20.1567i | 0.581147 | − | 1.00658i | −0.414197 | − | 0.910187i | \(-0.635937\pi\) |
0.995344 | − | 0.0963887i | \(-0.0307292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 6.92820i | 0.199254 | + | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.0997 | − | 57.3303i | −1.64069 | − | 2.84176i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9124 | − | 25.8290i | 0.737370 | − | 1.27716i | −0.216306 | − | 0.976326i | \(-0.569401\pi\) |
0.953676 | − | 0.300836i | \(-0.0972657\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −42.5739 | −2.09493 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.54983 | −0.125166 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.54983 | + | 7.88054i | −0.222274 | + | 0.384990i | −0.955498 | − | 0.294997i | \(-0.904681\pi\) |
0.733224 | + | 0.679987i | \(0.238015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1375 | + | 27.9509i | 0.786492 | + | 1.36224i | 0.928104 | + | 0.372321i | \(0.121438\pi\) |
−0.141612 | + | 0.989922i | \(0.545229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | + | 1.73205i | 0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0000 | − | 24.2487i | 0.677507 | − | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.27492 | 0.302252 | 0.151126 | − | 0.988514i | \(-0.451710\pi\) | ||||
0.151126 | + | 0.988514i | \(0.451710\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5498 | 0.603107 | 0.301553 | − | 0.953449i | \(-0.402495\pi\) | ||||
0.301553 | + | 0.953449i | \(0.402495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.63746 | + | 6.30026i | −0.174003 | + | 0.301382i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6873 | + | 21.9750i | 0.605531 | + | 1.04881i | 0.991967 | + | 0.126495i | \(0.0403727\pi\) |
−0.386436 | + | 0.922316i | \(0.626294\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.27492 | + | 9.13642i | 0.250619 | + | 0.434085i | 0.963696 | − | 0.267001i | \(-0.0860326\pi\) |
−0.713077 | + | 0.701085i | \(0.752699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.41238 | + | 11.1066i | −0.303976 | + | 0.526501i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.54983 | −0.0731412 | −0.0365706 | − | 0.999331i | \(-0.511643\pi\) | ||||
−0.0365706 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.3746 | 2.23078 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.08762 | − | 3.61587i | 0.0978693 | − | 0.169515i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.00000 | − | 13.8564i | −0.374224 | − | 0.648175i | 0.615986 | − | 0.787757i | \(-0.288758\pi\) |
−0.990211 | + | 0.139581i | \(0.955424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6873 | − | 20.2430i | −0.544332 | − | 0.942810i | −0.998649 | − | 0.0519698i | \(-0.983450\pi\) |
0.454317 | − | 0.890840i | \(-0.349883\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7371 | + | 35.9178i | −0.963736 | + | 1.66924i | −0.250763 | + | 0.968049i | \(0.580681\pi\) |
−0.712973 | + | 0.701191i | \(0.752652\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.1993 | 1.86020 | 0.930102 | − | 0.367302i | \(-0.119718\pi\) | ||||
0.930102 | + | 0.367302i | \(0.119718\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80066 | −0.0831469 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.5498 | − | 21.7370i | 0.577042 | − | 0.999466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500000 | − | 0.866025i | −0.0229416 | − | 0.0397360i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.13746 | − | 3.70219i | −0.0976630 | − | 0.169157i | 0.813054 | − | 0.582188i | \(-0.197803\pi\) |
−0.910717 | + | 0.413031i | \(0.864470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.72508 | + | 11.6482i | −0.306637 | + | 0.531112i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | −0.726523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.2749 | −1.68909 | −0.844544 | − | 0.535486i | \(-0.820128\pi\) | ||||
−0.844544 | + | 0.535486i | \(0.820128\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50000 | − | 12.9904i | 0.338470 | − | 0.586248i | −0.645675 | − | 0.763612i | \(-0.723424\pi\) |
0.984145 | + | 0.177365i | \(0.0567572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.27492 | − | 10.8685i | −0.282608 | − | 0.489492i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5498 | + | 23.4690i | 0.607793 | + | 1.05273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7749 | − | 25.5909i | 0.661416 | − | 1.14561i | −0.318828 | − | 0.947813i | \(-0.603289\pi\) |
0.980244 | − | 0.197794i | \(-0.0633776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.72508 | 0.432761 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0997 | − | 24.4213i | 0.624957 | − | 1.08246i | −0.363592 | − | 0.931558i | \(-0.618450\pi\) |
0.988549 | − | 0.150899i | \(-0.0482168\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.7251 | + | 42.8251i | 1.09377 | + | 1.89447i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.91238 | − | 5.04438i | −0.128335 | − | 0.222282i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | − | 6.92820i | 0.175920 | − | 0.304702i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9244 | 1.17958 | 0.589790 | − | 0.807557i | \(-0.299210\pi\) | ||||
0.589790 | + | 0.807557i | \(0.299210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.6495 | −1.73375 | −0.866876 | − | 0.498524i | \(-0.833876\pi\) | ||||
−0.866876 | + | 0.498524i | \(0.833876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.27492 | − | 10.8685i | 0.273340 | − | 0.473438i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.9622 | − | 25.9153i | −0.650531 | − | 1.12675i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.81271 | − | 8.33585i | −0.208461 | − | 0.361066i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.54983 | + | 13.0767i | −0.326408 | + | 0.565355i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.3746 | −1.00681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.9244 | 1.88846 | 0.944229 | − | 0.329289i | \(-0.106809\pi\) | ||||
0.944229 | + | 0.329289i | \(0.106809\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.13746 | + | 5.43424i | −0.134394 | + | 0.232777i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0000 | − | 17.3205i | −0.427569 | − | 0.740571i | 0.569087 | − | 0.822277i | \(-0.307297\pi\) |
−0.996657 | + | 0.0817056i | \(0.973963\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.13746 | + | 5.43424i | 0.133660 | + | 0.231506i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2749 | − | 29.9210i | 0.734604 | − | 1.27237i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.9244 | −1.39505 | −0.697526 | − | 0.716559i | \(-0.745716\pi\) | ||||
−0.697526 | + | 0.716559i | \(0.745716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.09967 | −0.215693 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.5498 | − | 32.1293i | 0.781782 | − | 1.35409i | −0.149120 | − | 0.988819i | \(-0.547644\pi\) |
0.930903 | − | 0.365268i | \(-0.119023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.2251 | − | 22.9065i | −0.554424 | − | 0.960291i | −0.997948 | − | 0.0640285i | \(-0.979605\pi\) |
0.443524 | − | 0.896263i | \(-0.353728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.587624 | − | 1.01779i | 0.0245913 | − | 0.0425934i | −0.853468 | − | 0.521145i | \(-0.825505\pi\) |
0.878059 | + | 0.478552i | \(0.158838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.27492 | 0.303385 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.4502 | −0.476677 | −0.238338 | − | 0.971182i | \(-0.576603\pi\) | ||||
−0.238338 | + | 0.971182i | \(0.576603\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.17525 | − | 7.23174i | 0.173218 | − | 0.300023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.27492 | − | 3.94027i | −0.0942174 | − | 0.163189i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.2749 | − | 29.9210i | −0.713012 | − | 1.23497i | −0.963721 | − | 0.266911i | \(-0.913997\pi\) |
0.250709 | − | 0.968062i | \(-0.419336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.13746 | + | 5.43424i | −0.129277 | + | 0.223914i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.1993 | 1.97931 | 0.989655 | − | 0.143469i | \(-0.0458258\pi\) | ||||
0.989655 | + | 0.143469i | \(0.0458258\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.54983 | −0.268517 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.86254 | + | 13.6183i | −0.321255 | + | 0.556430i | −0.980747 | − | 0.195282i | \(-0.937438\pi\) |
0.659492 | + | 0.751711i | \(0.270771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.950166 | + | 1.64574i | 0.0387581 | + | 0.0671309i | 0.884754 | − | 0.466059i | \(-0.154327\pi\) |
−0.845996 | + | 0.533190i | \(0.820993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.1873 | + | 24.5731i | 0.576795 | + | 0.999039i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | − | 20.7846i | 0.487065 | − | 0.843621i | −0.512824 | − | 0.858494i | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.62541 | −0.0657572 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.0241 | −1.85890 | −0.929448 | − | 0.368954i | \(-0.879716\pi\) | ||||
−0.929448 | + | 0.368954i | \(0.879716\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8248 | + | 37.8016i | −0.878631 | + | 1.52183i | −0.0257881 | + | 0.999667i | \(0.508210\pi\) |
−0.852843 | + | 0.522167i | \(0.825124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.18729 | + | 15.9129i | 0.369268 | + | 0.639592i | 0.989451 | − | 0.144865i | \(-0.0462749\pi\) |
−0.620183 | + | 0.784457i | \(0.712942\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.0000 | − | 36.3731i | −0.841347 | − | 1.45726i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0997 | 0.841299 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4743 | 0.974305 | 0.487152 | − | 0.873317i | \(-0.338036\pi\) | ||||
0.487152 | + | 0.873317i | \(0.338036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.63746 | − | 9.76436i | 0.223716 | − | 0.387487i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.37459 | + | 4.11290i | 0.0940845 | + | 0.162959i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9622 | + | 29.3794i | 0.669967 | + | 1.16042i | 0.977913 | + | 0.209013i | \(0.0670251\pi\) |
−0.307946 | + | 0.951404i | \(0.599642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5498 | − | 28.6652i | 0.652662 | − | 1.13044i | −0.329813 | − | 0.944046i | \(-0.606986\pi\) |
0.982475 | − | 0.186397i | \(-0.0596811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.5498 | 1.12241 | 0.561205 | − | 0.827677i | \(-0.310338\pi\) | ||||
0.561205 | + | 0.827677i | \(0.310338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −81.5739 | −3.20206 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.72508 | − | 8.18408i | 0.184907 | − | 0.320268i | −0.758638 | − | 0.651512i | \(-0.774135\pi\) |
0.943545 | + | 0.331244i | \(0.107468\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.774917 | − | 1.34220i | −0.0302785 | − | 0.0524439i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.63746 | − | 14.9605i | −0.336468 | − | 0.582779i | 0.647298 | − | 0.762237i | \(-0.275899\pi\) |
−0.983766 | + | 0.179458i | \(0.942566\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9622 | − | 34.5756i | 0.776440 | − | 1.34483i | −0.157542 | − | 0.987512i | \(-0.550357\pi\) |
0.933982 | − | 0.357321i | \(-0.116310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.27492 | 0.126996 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.6495 | −1.76756 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8248 | − | 46.4618i | 1.03556 | − | 1.79364i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.45017 | + | 7.70791i | 0.171541 | + | 0.297118i | 0.938959 | − | 0.344029i | \(-0.111792\pi\) |
−0.767418 | + | 0.641148i | \(0.778459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.4622 | − | 23.3172i | −0.517395 | − | 0.896154i | −0.999796 | − | 0.0202036i | \(-0.993569\pi\) |
0.482401 | − | 0.875950i | \(-0.339765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.1993 | − | 45.3786i | 1.00544 | − | 1.74147i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.45017 | 0.0554890 | 0.0277445 | − | 0.999615i | \(-0.491168\pi\) | ||||
0.0277445 | + | 0.999615i | \(0.491168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.5498 | 0.555921 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.462210 | + | 0.800572i | −0.0176088 | + | 0.0304994i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.91238 | + | 6.77643i | 0.148834 | + | 0.257788i | 0.930797 | − | 0.365537i | \(-0.119115\pi\) |
−0.781963 | + | 0.623325i | \(0.785781\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.50000 | − | 7.79423i | −0.170695 | − | 0.295652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.54983 | + | 13.0767i | −0.285970 | + | 0.495315i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3746 | 1.26054 | 0.630270 | − | 0.776376i | \(-0.282944\pi\) | ||||
0.630270 | + | 0.776376i | \(0.282944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5498 | −0.397895 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9244 | + | 27.5819i | −0.598899 | + | 1.03732i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.450166 | + | 0.779710i | 0.0169063 | + | 0.0292826i | 0.874355 | − | 0.485287i | \(-0.161285\pi\) |
−0.857448 | + | 0.514570i | \(0.827952\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8248 | − | 39.5336i | −0.854794 | − | 1.48055i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | − | 6.92820i | 0.149592 | − | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.8248 | 1.67168 | 0.835841 | − | 0.548972i | \(-0.184981\pi\) | ||||
0.835841 | + | 0.548972i | \(0.184981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0756 | 0.710412 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.13746 | − | 5.43424i | 0.116522 | − | 0.201823i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1873 | + | 26.3052i | 0.563266 | + | 0.975604i | 0.997209 | + | 0.0746643i | \(0.0237885\pi\) |
−0.433943 | + | 0.900940i | \(0.642878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.00000 | − | 5.19615i | 0.110808 | − | 0.191924i | −0.805289 | − | 0.592883i | \(-0.797990\pi\) |
0.916096 | + | 0.400959i | \(0.131323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.45017 | −0.127088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9244 | 0.585789 | 0.292895 | − | 0.956145i | \(-0.405381\pi\) | ||||
0.292895 | + | 0.956145i | \(0.405381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2749 | + | 24.7249i | −0.523696 | + | 0.907068i | 0.475924 | + | 0.879487i | \(0.342114\pi\) |
−0.999620 | + | 0.0275813i | \(0.991219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00000 | − | 1.73205i | −0.0366372 | − | 0.0634574i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.7251 | − | 42.8251i | −0.903435 | − | 1.56480i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2749 | + | 29.9210i | −0.630371 | + | 1.09183i | 0.357105 | + | 0.934064i | \(0.383764\pi\) |
−0.987476 | + | 0.157770i | \(0.949570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.2749 | 0.446730 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3746 | 1.24937 | 0.624683 | − | 0.780879i | \(-0.285228\pi\) | ||||
0.624683 | + | 0.780879i | \(0.285228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.7749 | − | 42.9114i | 0.898090 | − | 1.55554i | 0.0681570 | − | 0.997675i | \(-0.478288\pi\) |
0.829933 | − | 0.557863i | \(-0.188379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.2749 | − | 17.7967i | −0.371977 | − | 0.644283i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.28696 | + | 14.3534i | 0.299225 | + | 0.518273i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.13746 | − | 14.0945i | 0.293444 | − | 0.508260i | −0.681178 | − | 0.732118i | \(-0.738532\pi\) |
0.974622 | + | 0.223858i | \(0.0718652\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6495 | −1.13835 | −0.569177 | − | 0.822215i | \(-0.692738\pi\) | ||||
−0.569177 | + | 0.822215i | \(0.692738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.27492 | 0.225402 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.77492 | − | 6.53835i | 0.135250 | − | 0.234261i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.9622 | + | 44.9679i | 0.929001 | + | 1.60908i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.36254 | + | 9.28819i | 0.191397 | + | 0.331510i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.0000 | − | 29.4449i | 0.605985 | − | 1.04960i | −0.385911 | − | 0.922536i | \(-0.626113\pi\) |
0.991895 | − | 0.127060i | \(-0.0405540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.6495 | −0.698656 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9003 | −0.387082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.7251 | + | 22.0405i | −0.450746 | + | 0.780714i | −0.998432 | − | 0.0559691i | \(-0.982175\pi\) |
0.547687 | + | 0.836683i |