Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(289,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.r (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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.5 | ||
Root | \(0.583700 + 2.17840i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.289 |
Dual form | 1728.2.r.f.1441.5 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80664 | − | 3.12920i | 0.682846 | − | 1.18272i | −0.291262 | − | 0.956643i | \(-0.594075\pi\) |
0.974108 | − | 0.226081i | \(-0.0725915\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.635828 | + | 0.367095i | 0.191709 | + | 0.110683i | 0.592783 | − | 0.805363i | \(-0.298029\pi\) |
−0.401073 | + | 0.916046i | \(0.631363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.527909 | − | 0.304788i | 0.146416 | − | 0.0845331i | −0.425003 | − | 0.905192i | \(-0.639727\pi\) |
0.571418 | + | 0.820659i | \(0.306393\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52420 | 1.33982 | 0.669908 | − | 0.742444i | \(-0.266334\pi\) | ||||
0.669908 | + | 0.742444i | \(0.266334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.36788 | + | 4.10129i | 0.493737 | + | 0.855177i | 0.999974 | − | 0.00721700i | \(-0.00229726\pi\) |
−0.506237 | + | 0.862394i | \(0.668964\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.78630 | + | 3.91807i | 1.26018 | + | 0.727568i | 0.973110 | − | 0.230341i | \(-0.0739841\pi\) |
0.287074 | + | 0.957908i | \(0.407317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.70951 | − | 8.15710i | −0.845852 | − | 1.46506i | −0.884879 | − | 0.465821i | \(-0.845759\pi\) |
0.0390267 | − | 0.999238i | \(-0.487574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 6.25839i | − | 1.05786i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.34163i | − | 0.384961i | −0.981301 | − | 0.192481i | \(-0.938347\pi\) | ||
0.981301 | − | 0.192481i | \(-0.0616532\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.26210 | − | 7.38217i | −0.665628 | − | 1.15290i | −0.979115 | − | 0.203309i | \(-0.934830\pi\) |
0.313486 | − | 0.949593i | \(-0.398503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.88403 | − | 5.12920i | −1.35480 | − | 0.782195i | −0.365884 | − | 0.930661i | \(-0.619233\pi\) |
−0.988918 | + | 0.148466i | \(0.952567\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.88032 | − | 10.1850i | 0.857733 | − | 1.48564i | −0.0163535 | − | 0.999866i | \(-0.505206\pi\) |
0.874086 | − | 0.485771i | \(-0.161461\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.02791 | − | 5.24449i | −0.432558 | − | 0.749213i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0323i | 1.79012i | 0.445942 | + | 0.895062i | \(0.352869\pi\) | ||||
−0.445942 | + | 0.895062i | \(0.647131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.27166 | 0.171470 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.04788 | − | 0.604996i | 0.136423 | − | 0.0787637i | −0.430235 | − | 0.902717i | \(-0.641569\pi\) |
0.566658 | + | 0.823953i | \(0.308236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.78630 | + | 5.65012i | 1.25301 | + | 0.723424i | 0.971706 | − | 0.236195i | \(-0.0759005\pi\) |
0.281302 | + | 0.959619i | \(0.409234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.527909 | − | 0.914365i | 0.0654790 | − | 0.113413i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.46826 | + | 3.15710i | −0.668055 | + | 0.385702i | −0.795339 | − | 0.606165i | \(-0.792707\pi\) |
0.127284 | + | 0.991866i | \(0.459374\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.63999 | 0.313309 | 0.156655 | − | 0.987653i | \(-0.449929\pi\) | ||||
0.156655 | + | 0.987653i | \(0.449929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.05582 | −0.240615 | −0.120308 | − | 0.992737i | \(-0.538388\pi\) | ||||
−0.120308 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.29743 | − | 1.32642i | 0.261816 | − | 0.151160i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.24540 | − | 2.15710i | 0.140119 | − | 0.242693i | −0.787422 | − | 0.616414i | \(-0.788585\pi\) |
0.927541 | + | 0.373721i | \(0.121918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6161 | − | 6.12920i | −1.16527 | − | 0.672767i | −0.212706 | − | 0.977116i | \(-0.568228\pi\) |
−0.952560 | + | 0.304350i | \(0.901561\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.28630 | − | 4.78410i | 0.898775 | − | 0.518908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.94418 | 0.206083 | 0.103041 | − | 0.994677i | \(-0.467143\pi\) | ||||
0.103041 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.20257i | − | 0.230892i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73205 | + | 3.00000i | 0.177705 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.78630 | − | 13.4863i | 0.790579 | − | 1.36932i | −0.135030 | − | 0.990842i | \(-0.543113\pi\) |
0.925609 | − | 0.378481i | \(-0.123554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.70257 | − | 5.60178i | −0.965442 | − | 0.557398i | −0.0675984 | − | 0.997713i | \(-0.521534\pi\) |
−0.897844 | + | 0.440314i | \(0.854867\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.684168 | − | 1.18501i | −0.0674130 | − | 0.116763i | 0.830349 | − | 0.557244i | \(-0.188141\pi\) |
−0.897762 | + | 0.440481i | \(0.854808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4684i | 1.30204i | 0.759062 | + | 0.651019i | \(0.225658\pi\) | ||||
−0.759062 | + | 0.651019i | \(0.774342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.42084i | 0.136092i | 0.997682 | + | 0.0680458i | \(0.0216764\pi\) | ||||
−0.997682 | + | 0.0680458i | \(0.978324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.75839 | + | 8.24177i | 0.447632 | + | 0.775321i | 0.998231 | − | 0.0594485i | \(-0.0189342\pi\) |
−0.550600 | + | 0.834769i | \(0.685601\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.10364 | + | 4.10129i | 0.662418 | + | 0.382447i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.98025 | − | 17.2863i | 0.914888 | − | 1.58463i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.23048 | − | 9.05946i | −0.475498 | − | 0.823587i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24495 | 0.199207 | 0.0996035 | − | 0.995027i | \(-0.468243\pi\) | ||||
0.0996035 | + | 0.995027i | \(0.468243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.223773 | − | 0.129195i | 0.0195511 | − | 0.0112878i | −0.490193 | − | 0.871614i | \(-0.663074\pi\) |
0.509744 | + | 0.860326i | \(0.329740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25839 | + | 3.61328i | 0.542671 | + | 0.313311i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00371 | + | 1.73848i | −0.0857527 | + | 0.148528i | −0.905712 | − | 0.423894i | \(-0.860663\pi\) |
0.819959 | + | 0.572422i | \(0.193996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.95582 | − | 1.12920i | 0.165891 | − | 0.0957771i | −0.414756 | − | 0.909933i | \(-0.636133\pi\) |
0.580647 | + | 0.814156i | \(0.302800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.447546 | 0.0374256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5726 | 1.12714 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7863 | − | 7.38217i | 1.04749 | − | 0.604771i | 0.125548 | − | 0.992088i | \(-0.459931\pi\) |
0.921947 | + | 0.387316i | \(0.126598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.82827 | − | 4.89871i | 0.230162 | − | 0.398652i | −0.727694 | − | 0.685902i | \(-0.759408\pi\) |
0.957856 | + | 0.287250i | \(0.0927412\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.1285 | − | 8.15710i | −1.13483 | − | 0.655194i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7584 | − | 7.94341i | 1.09804 | − | 0.633953i | 0.162334 | − | 0.986736i | \(-0.448098\pi\) |
0.935705 | + | 0.352783i | \(0.114765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.1116 | 1.34859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.51678i | 0.667086i | 0.942735 | + | 0.333543i | \(0.108244\pi\) | ||||
−0.942735 | + | 0.333543i | \(0.891756\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.95582 | − | 3.38759i | −0.151346 | − | 0.262139i | 0.780376 | − | 0.625310i | \(-0.215027\pi\) |
−0.931723 | + | 0.363171i | \(0.881694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31421 | + | 10.9365i | −0.485708 | + | 0.841271i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5000 | − | 6.06218i | −0.798300 | − | 0.460899i | 0.0445762 | − | 0.999006i | \(-0.485806\pi\) |
−0.842876 | + | 0.538107i | \(0.819140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.61328 | + | 6.25839i | 0.273139 | + | 0.473090i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34163i | 0.174052i | 0.996206 | + | 0.0870259i | \(0.0277363\pi\) | ||||
−0.996206 | + | 0.0870259i | \(0.972264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.02791 | − | 3.51244i | −0.149095 | − | 0.258240i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.51244 | + | 2.02791i | 0.256855 | + | 0.148295i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.684168 | + | 1.18501i | −0.0495046 | + | 0.0857445i | −0.889716 | − | 0.456515i | \(-0.849098\pi\) |
0.840211 | + | 0.542259i | \(0.182431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.73048 | + | 13.3896i | 0.556452 | + | 0.963804i | 0.997789 | + | 0.0664620i | \(0.0211711\pi\) |
−0.441337 | + | 0.897342i | \(0.645496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9356i | 0.921625i | 0.887498 | + | 0.460812i | \(0.152442\pi\) | ||||
−0.887498 | + | 0.460812i | \(0.847558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7413 | −1.32854 | −0.664269 | − | 0.747493i | \(-0.731257\pi\) | ||||
−0.664269 | + | 0.747493i | \(0.731257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.5208 | − | 14.1571i | 1.72102 | − | 0.993634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7863 | − | 7.38217i | −0.893034 | − | 0.515593i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.734191 | + | 1.27166i | −0.0507851 | + | 0.0879623i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.20032 | − | 4.15710i | 0.495690 | − | 0.286187i | −0.231242 | − | 0.972896i | \(-0.574279\pi\) |
0.726932 | + | 0.686709i | \(0.240946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.7681 | −1.21177 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.0336 | −2.31035 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.91627 | − | 1.68371i | 0.196170 | − | 0.113259i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.99909 | + | 6.92662i | −0.267799 | + | 0.463841i | −0.968293 | − | 0.249817i | \(-0.919630\pi\) |
0.700494 | + | 0.713658i | \(0.252963\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.56032 | + | 2.63290i | 0.302679 | + | 0.174752i | 0.643646 | − | 0.765323i | \(-0.277421\pi\) |
−0.340967 | + | 0.940075i | \(0.610754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0168 | + | 8.09259i | −0.926255 | + | 0.534774i | −0.885625 | − | 0.464401i | \(-0.846270\pi\) |
−0.0406298 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.0968 | −1.84068 | −0.920341 | − | 0.391116i | \(-0.872089\pi\) | ||||
−0.920341 | + | 0.391116i | \(0.872089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 20.3700i | − | 1.32879i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.29608 | + | 16.1013i | 0.601314 | + | 1.04151i | 0.992622 | + | 0.121246i | \(0.0386891\pi\) |
−0.391309 | + | 0.920259i | \(0.627978\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.55582 | − | 7.89091i | 0.293466 | − | 0.508298i | −0.681161 | − | 0.732134i | \(-0.738525\pi\) |
0.974627 | + | 0.223836i | \(0.0718579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.08373 | − | 5.24449i | −0.580338 | − | 0.335058i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.609577 | + | 1.05582i | 0.0387864 | + | 0.0671801i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5800i | 1.36212i | 0.732228 | + | 0.681059i | \(0.238480\pi\) | ||||
−0.732228 | + | 0.681059i | \(0.761520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.47695i | 0.218594i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.70999 | − | 4.69384i | −0.169045 | − | 0.292794i | 0.769040 | − | 0.639201i | \(-0.220735\pi\) |
−0.938084 | + | 0.346407i | \(0.887402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.32741 | − | 4.23048i | −0.455303 | − | 0.262869i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00787 | + | 8.67389i | −0.308798 | + | 0.534855i | −0.978100 | − | 0.208136i | \(-0.933260\pi\) |
0.669301 | + | 0.742991i | \(0.266594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.2863 | + | 19.5484i | 0.693312 | + | 1.20085i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 12.1115i | − | 0.738452i | −0.929340 | − | 0.369226i | \(-0.879623\pi\) | ||
0.929340 | − | 0.369226i | \(-0.120377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0572 | 1.21839 | 0.609193 | − | 0.793022i | \(-0.291493\pi\) | ||||
0.609193 | + | 0.793022i | \(0.291493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.27166 | + | 0.734191i | −0.0766837 | + | 0.0442734i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.75839 | − | 2.74726i | −0.285904 | − | 0.165067i | 0.350189 | − | 0.936679i | \(-0.386117\pi\) |
−0.636093 | + | 0.771612i | \(0.719451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.58373 | + | 7.93925i | −0.273442 | + | 0.473616i | −0.969741 | − | 0.244136i | \(-0.921496\pi\) |
0.696299 | + | 0.717752i | \(0.254829\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.7239 | + | 11.3876i | −1.17246 | + | 0.676922i | −0.954259 | − | 0.298981i | \(-0.903353\pi\) |
−0.218204 | + | 0.975903i | \(0.570020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.8003 | −1.81809 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5168 | 0.795105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.7026 | − | 10.7979i | 1.09262 | − | 0.630822i | 0.158344 | − | 0.987384i | \(-0.449384\pi\) |
0.934272 | + | 0.356562i | \(0.116051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.04788 | − | 1.81499i | 0.0610101 | − | 0.105673i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.50005 | + | 1.44340i | 0.144582 | + | 0.0834742i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.1005 | + | 18.5332i | −1.85024 | + | 1.06824i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5726 | 1.12072 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.51678i | − | 0.486078i | −0.970016 | − | 0.243039i | \(-0.921856\pi\) | ||
0.970016 | − | 0.243039i | \(-0.0781444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3965 | + | 21.4713i | 0.702939 | + | 1.21753i | 0.967430 | + | 0.253138i | \(0.0814628\pi\) |
−0.264491 | + | 0.964388i | \(0.585204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.55582 | + | 13.0871i | −0.427080 | + | 0.739724i | −0.996612 | − | 0.0822447i | \(-0.973791\pi\) |
0.569532 | + | 0.821969i | \(0.307124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5837 | − | 6.11052i | −0.594441 | − | 0.343201i | 0.172410 | − | 0.985025i | \(-0.444844\pi\) |
−0.766852 | + | 0.641824i | \(0.778178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.87661 | + | 4.98244i | 0.161059 | + | 0.278963i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.0484i | 0.614749i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.21915i | 0.0676264i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.2473 | − | 36.8013i | −1.17140 | − | 2.02892i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.4076 | + | 12.3597i | 1.17667 | + | 0.679349i | 0.955241 | − | 0.295828i | \(-0.0955955\pi\) |
0.221426 | + | 0.975177i | \(0.428929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.46826 | + | 9.47131i | −0.298763 | + | 0.517473i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.75839 | − | 11.7059i | −0.368153 | − | 0.637660i | 0.621124 | − | 0.783712i | \(-0.286676\pi\) |
−0.989277 | + | 0.146053i | \(0.953343\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.91535i | − | 0.374487i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.41160 | 0.184209 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.3044 | + | 7.68130i | −0.714218 | + | 0.412354i | −0.812621 | − | 0.582793i | \(-0.801960\pi\) |
0.0984028 | + | 0.995147i | \(0.468627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.3310 | − | 15.7796i | −1.46299 | − | 0.844660i | −0.463846 | − | 0.885916i | \(-0.653531\pi\) |
−0.999149 | + | 0.0412558i | \(0.986864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.9963 | + | 24.2423i | −0.744947 | + | 1.29029i | 0.205272 | + | 0.978705i | \(0.434192\pi\) |
−0.950219 | + | 0.311582i | \(0.899141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.95999 | − | 2.28630i | 0.210174 | − | 0.121344i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1290 | −0.692921 | −0.346460 | − | 0.938065i | \(-0.612616\pi\) | ||||
−0.346460 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.08373 | + | 1.78039i | −0.161410 | + | 0.0931899i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.73992 | + | 11.6739i | −0.351821 | + | 0.609372i | −0.986569 | − | 0.163348i | \(-0.947771\pi\) |
0.634748 | + | 0.772720i | \(0.281104\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.7806 | + | 23.5447i | 2.11722 | + | 1.22238i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.84212 | + | 2.79560i | −0.250715 | + | 0.144751i | −0.620092 | − | 0.784529i | \(-0.712905\pi\) |
0.369376 | + | 0.929280i | \(0.379571\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.77673 | 0.246014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.0894i | 1.69969i | 0.527035 | + | 0.849844i | \(0.323304\pi\) | ||||
−0.527035 | + | 0.849844i | \(0.676696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.61237 | + | 13.1850i | 0.388974 | + | 0.673723i | 0.992312 | − | 0.123763i | \(-0.0394963\pi\) |
−0.603338 | + | 0.797486i | \(0.706163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.29743 | − | 3.97926i | 0.117088 | − | 0.202802i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.29743 | − | 3.05847i | −0.268590 | − | 0.155071i | 0.359657 | − | 0.933085i | \(-0.382894\pi\) |
−0.628247 | + | 0.778014i | \(0.716227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.0806 | + | 22.6563i | 0.661516 | + | 1.14578i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 4.31421i | − | 0.217071i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.2054i | − | 1.11446i | −0.830358 | − | 0.557230i | \(-0.811864\pi\) | ||
0.830358 | − | 0.557230i | \(-0.188136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0521 | + | 26.0710i | 0.751666 | + | 1.30192i | 0.947015 | + | 0.321190i | \(0.104083\pi\) |
−0.195348 | + | 0.980734i | \(0.562584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.97238 | − | 2.87080i | −0.247692 | − | 0.143005i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.859601 | − | 1.48887i | 0.0426088 | − | 0.0738007i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.55582 | + | 7.89091i | 0.225271 | + | 0.390180i | 0.956401 | − | 0.292058i | \(-0.0943400\pi\) |
−0.731130 | + | 0.682238i | \(0.761007\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 4.37204i | − | 0.215134i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.2322 | −1.04225 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.7722 | + | 11.4155i | −0.965936 | + | 0.557683i | −0.897995 | − | 0.440006i | \(-0.854976\pi\) |
−0.0679411 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.2473 | − | 12.2671i | −1.03553 | − | 0.597863i | −0.116965 | − | 0.993136i | \(-0.537316\pi\) |
−0.918563 | + | 0.395274i | \(0.870650\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.52420 | + | 9.56819i | −0.267963 | + | 0.464126i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.3607 | − | 20.4155i | 1.71122 | − | 0.987975i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.920789 | 0.0443529 | 0.0221764 | − | 0.999754i | \(-0.492940\pi\) | ||||
0.0221764 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.05582 | 0.0987963 | 0.0493981 | − | 0.998779i | \(-0.484270\pi\) | ||||
0.0493981 | + | 0.998779i | \(0.484270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.20257 | + | 4.73576i | −0.392382 | + | 0.226542i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0281 | + | 19.1013i | −0.526344 | + | 0.911655i | 0.473185 | + | 0.880963i | \(0.343104\pi\) |
−0.999529 | + | 0.0306915i | \(0.990229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5517 | − | 13.5976i | −1.11897 | − | 0.646040i | −0.177836 | − | 0.984060i | \(-0.556910\pi\) |
−0.941139 | + | 0.338020i | \(0.890243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.91627 | − | 1.68371i | 0.138245 | − | 0.0798156i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.10422 | 0.429655 | 0.214827 | − | 0.976652i | \(-0.431081\pi\) | ||||
0.214827 | + | 0.976652i | \(0.431081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.25839i | − | 0.294696i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.90748 | − | 3.30386i | −0.0894242 | − | 0.154887i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.8421 | + | 25.7073i | −0.694285 | + | 1.20254i | 0.276136 | + | 0.961119i | \(0.410946\pi\) |
−0.970421 | + | 0.241418i | \(0.922387\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.3589 | − | 11.7542i | −0.948208 | − | 0.547448i | −0.0556845 | − | 0.998448i | \(-0.517734\pi\) |
−0.892524 | + | 0.451000i | \(0.851067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.95075 | − | 6.84290i | −0.183607 | − | 0.318016i | 0.759499 | − | 0.650508i | \(-0.225444\pi\) |
−0.943106 | + | 0.332492i | \(0.892111\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3.06324i | − | 0.141750i | −0.997485 | − | 0.0708748i | \(-0.977421\pi\) | ||
0.997485 | − | 0.0708748i | \(-0.0225791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.8150i | 1.05350i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.76581 | − | 6.52257i | −0.173152 | − | 0.299908i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.46410 | − | 2.00000i | −0.158944 | − | 0.0917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.10364 | − | 12.3039i | 0.324573 | − | 0.562178i | −0.656852 | − | 0.754019i | \(-0.728113\pi\) |
0.981426 | + | 0.191841i | \(0.0614459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.713701 | − | 1.23617i | −0.0325419 | − | 0.0563643i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 26.9725i | − | 1.22476i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.1088 | 1.00184 | 0.500922 | − | 0.865492i | \(-0.332994\pi\) | ||||
0.500922 | + | 0.865492i | \(0.332994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.2340 | − | 19.7650i | 1.54496 | − | 0.891983i | 0.546446 | − | 0.837494i | \(-0.315980\pi\) |
0.998514 | − | 0.0544890i | \(-0.0173530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.4889 | + | 21.6442i | 1.68841 | + | 0.974806i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.76952 | − | 8.26105i | 0.213942 | − | 0.370559i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2652 | − | 5.92662i | 0.459534 | − | 0.265312i | −0.252314 | − | 0.967645i | \(-0.581192\pi\) |
0.711848 | + | 0.702333i | \(0.247858\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.4246 | −1.04445 | −0.522226 | − | 0.852807i | \(-0.674898\pi\) | ||||
−0.522226 | + | 0.852807i | \(0.674898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.4051 | −0.863518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.78630 | − | 3.91807i | 0.300797 | − | 0.173665i | −0.342004 | − | 0.939699i | \(-0.611106\pi\) |
0.642801 | + | 0.766033i | \(0.277772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.71413 | + | 6.43305i | −0.164303 | + | 0.284582i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.05250 | − | 1.18501i | −0.0904441 | − | 0.0522179i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.47774 | − | 4.31728i | 0.328871 | − | 0.189874i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4535 | −1.20276 | −0.601381 | − | 0.798963i | \(-0.705383\pi\) | ||||
−0.601381 | + | 0.798963i | \(0.705383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.83255i | 0.167586i | 0.996483 | + | 0.0837928i | \(0.0267034\pi\) | ||||
−0.996483 | + | 0.0837928i | \(0.973297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.0163 | − | 45.0615i | −1.13329 | − | 1.96291i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.286299 | − | 0.495885i | 0.0124478 | − | 0.0215602i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.50000 | − | 2.59808i | −0.194917 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.6640 | + | 20.2026i | 0.504277 | + | 0.873433i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.44613i | − | 0.191508i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9707i | 0.686632i | 0.939220 | + | 0.343316i | \(0.111550\pi\) | ||||
−0.939220 | + | 0.343316i | \(0.888450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.23048 | + | 2.13126i | 0.0527080 | + | 0.0912930i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.02905 | + | 5.21292i | 0.386054 | + | 0.222888i | 0.680449 | − | 0.732795i | \(-0.261785\pi\) |
−0.294395 | + | 0.955684i | \(0.595118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.83614 | + | 13.5726i | −0.333831 | + | 0.578212i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 7.79423i | −0.191359 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0471i | 1.06128i | 0.847597 | + | 0.530640i | \(0.178049\pi\) | ||||
−0.847597 | + | 0.530640i | \(0.821951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.25327 | −0.264485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.28405 | + | 1.31870i | −0.0962612 | + | 0.0555764i | −0.547358 | − | 0.836899i | \(-0.684366\pi\) |
0.451097 | + | 0.892475i | \(0.351033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.2752 | + | 8.24177i | 0.600561 | + | 0.346734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.0242 | + | 17.3624i | −0.420236 | + | 0.727871i | −0.995962 | − | 0.0897720i | \(-0.971386\pi\) |
0.575726 | + | 0.817643i | \(0.304719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00416 | + | 1.15710i | −0.0838716 | + | 0.0484233i | −0.541349 | − | 0.840798i | \(-0.682086\pi\) |
0.457478 | + | 0.889221i | \(0.348753\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.47152 | −0.394989 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4610 | 1.01832 | 0.509162 | − | 0.860671i | \(-0.329956\pi\) | ||||
0.509162 | + | 0.860671i | \(0.329956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.3589 | + | 22.1465i | −1.59140 | + | 0.918792i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.78410 | + | 8.28630i | −0.198137 | + | 0.343183i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.0839 | − | 9.86339i | −0.705127 | − | 0.407106i | 0.104127 | − | 0.994564i | \(-0.466795\pi\) |
−0.809254 | + | 0.587459i | \(0.800129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.3142 | − | 9.41901i | 0.672215 | − | 0.388104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.46096 | −0.347450 | −0.173725 | − | 0.984794i | \(-0.555580\pi\) | ||||
−0.173725 | + | 0.984794i | \(0.555580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 34.5726i | − | 1.41734i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.22748 | + | 5.59016i | 0.131871 | + | 0.228408i | 0.924398 | − | 0.381430i | \(-0.124568\pi\) |
−0.792527 | + | 0.609837i | \(0.791235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.52791 | − | 4.37847i | 0.103116 | − | 0.178601i | −0.809851 | − | 0.586635i | \(-0.800452\pi\) |
0.912967 | + | 0.408034i | \(0.133786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.6914 | − | 9.05946i | −0.637948 | − | 0.368319i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0220880 | − | 0.0382575i | −0.000896524 | − | 0.00155282i | 0.865577 | − | 0.500776i | \(-0.166952\pi\) |
−0.866473 | + | 0.499223i | \(0.833619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.16901i | − | 0.290027i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.8887i | − | 1.08602i | −0.839725 | − | 0.543012i | \(-0.817284\pi\) | ||
0.839725 | − | 0.543012i | \(-0.182716\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.20628 | + | 15.9457i | 0.370631 | + | 0.641952i | 0.989663 | − | 0.143414i | \(-0.0458081\pi\) |
−0.619032 | + | 0.785366i | \(0.712475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.65330 | − | 0.954531i | −0.0664516 | − | 0.0383658i | 0.466406 | − | 0.884571i | \(-0.345549\pi\) |
−0.532858 | + | 0.846205i | \(0.678882\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.51244 | − | 6.08373i | 0.140723 | − | 0.243739i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12.9356i | − | 0.515777i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51752 | 0.0604114 | 0.0302057 | − | 0.999544i | \(-0.490384\pi\) | ||||
0.0302057 | + | 0.999544i | \(0.490384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.36742 | − | 1.94418i | 0.133632 | − | 0.0771525i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.19692 | − | 1.84574i | −0.126667 | − | 0.0731310i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.49258 | − | 14.7096i | 0.335437 | − | 0.580994i | −0.648132 | − | 0.761528i | \(-0.724449\pi\) |
0.983569 | + | 0.180535i | \(0.0577828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.02905 | + | 5.21292i | −0.356071 | + | 0.205578i | −0.667356 | − | 0.744739i | \(-0.732574\pi\) |
0.311285 | + | 0.950317i | \(0.399241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.2802 | 1.74083 | 0.870417 | − | 0.492315i | \(-0.163849\pi\) | ||||
0.870417 | + | 0.492315i | \(0.163849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.888365 | 0.0348714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.6452 | − | 16.5383i | 1.12097 | − | 0.647194i | 0.179324 | − | 0.983790i | \(-0.442609\pi\) |
0.941649 | + | 0.336596i | \(0.109276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.223773 | − | 0.387586i | 0.00874353 | − | 0.0151442i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.8882 | + | 16.1013i | 1.08637 | + | 0.627217i | 0.932608 | − | 0.360891i | \(-0.117527\pi\) |
0.153764 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.2752 | + | 6.50972i | −0.438553 | + | 0.253199i | −0.702984 | − | 0.711206i | \(-0.748149\pi\) |
0.264430 | + | 0.964405i | \(0.414816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.5168 | 0.485380 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.1101i | 1.43691i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.14827 | + | 7.18501i | 0.160142 | + | 0.277374i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.73048 | − | 6.46138i | 0.143800 | − | 0.249068i | −0.785125 | − | 0.619337i | \(-0.787401\pi\) |
0.928924 | + | 0.370269i | \(0.120735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.8700 | + | 17.8228i | 1.18643 | + | 0.684987i | 0.957494 | − | 0.288455i | \(-0.0931414\pi\) |
0.228938 | + | 0.973441i | \(0.426475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.1341 | − | 48.7297i | −1.07969 | − | 1.87007i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4535i | 1.05048i | 0.850954 | + | 0.525240i | \(0.176025\pi\) | ||||
−0.850954 | + | 0.525240i | \(0.823975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.47695i | 0.132847i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.97209 | + | 6.87986i | 0.151325 | + | 0.262102i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3730 | − | 11.1850i | −0.736984 | − | 0.425498i | 0.0839877 | − | 0.996467i | \(-0.473234\pi\) |
−0.820972 | + | 0.570969i | \(0.806568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.95582 | − | 3.38759i | 0.0741886 | − | 0.128498i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.5447 | − | 40.7806i | −0.891819 | − | 1.54468i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.4633i | 0.395193i | 0.980283 | + | 0.197596i | \(0.0633136\pi\) | ||||
−0.980283 | + | 0.197596i | \(0.936686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.68325 | 0.176632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.0581 | + | 20.2408i | −1.31850 | + | 0.761235i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.3884 | + | 11.7712i | 0.765701 | + | 0.442078i | 0.831339 | − | 0.555766i | \(-0.187575\pi\) |
−0.0656378 | + | 0.997844i | \(0.520908\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.3031 | − | 38.6301i | 0.835257 | − | 1.44671i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.671318 | − | 0.387586i | 0.0251059 | − | 0.0144949i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0076 | 1.67850 | 0.839251 | − | 0.543745i | \(-0.182994\pi\) | ||||
0.839251 | + | 0.543745i | \(0.182994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.94418 | −0.184131 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.5726 | + | 7.83614i | −0.504074 | + | 0.291027i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.37529 | − | 14.5064i | 0.310622 | − | 0.538014i | −0.667875 | − | 0.744274i | \(-0.732796\pi\) |
0.978497 | + | 0.206260i | \(0.0661292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.0771 | − | 28.3347i | −1.81518 | − | 1.04800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0798 | + | 12.1704i | −0.778601 | + | 0.449525i | −0.835934 | − | 0.548830i | \(-0.815073\pi\) |
0.0573335 | + | 0.998355i | \(0.481740\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.63583 | −0.170763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0558i | 1.17919i | 0.807698 | + | 0.589596i | \(0.200713\pi\) | ||||
−0.807698 | + | 0.589596i | \(0.799287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.98071 | − | 15.5550i | −0.329470 | − | 0.570659i | 0.652937 | − | 0.757413i | \(-0.273537\pi\) |
−0.982407 | + | 0.186753i | \(0.940203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.7863 | − | 22.1465i | 0.468454 | − | 0.811386i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.1452 | + | 24.3325i | 1.53995 | + | 0.889092i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9273 | + | 18.9266i | 0.398742 | + | 0.690642i | 0.993571 | − | 0.113210i | \(-0.0361134\pi\) |
−0.594829 | + | 0.803853i | \(0.702780\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 9.79743i | − | 0.356565i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 52.1292i | − | 1.89467i | −0.320248 | − | 0.947334i | \(-0.603766\pi\) | ||
0.320248 | − | 0.947334i | \(-0.396234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.0447 | + | 27.7902i | 0.581620 | + | 1.00739i | 0.995288 | + | 0.0969668i | \(0.0309141\pi\) |
−0.413668 | + | 0.910428i | \(0.635753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.44608 | + | 2.56695i | 0.160959 | + | 0.0929297i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.368791 | − | 0.638765i | 0.0133163 | − | 0.0230645i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.61164 | − | 2.79143i | −0.0581171 | − | 0.100662i | 0.835503 | − | 0.549486i | \(-0.185176\pi\) |
−0.893620 | + | 0.448824i | \(0.851843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2331i | 0.691765i | 0.938278 | + | 0.345883i | \(0.112420\pi\) | ||||
−0.938278 | + | 0.345883i | \(0.887580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.8380 | 0.676682 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.7643 | − | 8.52420i | 0.528988 | − | 0.305411i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.67858 | + | 0.969129i | 0.0600643 | + | 0.0346782i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7584 | − | 23.8302i | 0.491058 | − | 0.850537i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.4974 | + | 18.1850i | −1.12276 | + | 0.648226i | −0.942104 | − | 0.335321i | \(-0.891155\pi\) |
−0.180656 | + | 0.983546i | \(0.557822\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.3868 | 1.22265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.88836 | 0.244613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.9538 | − | 7.47885i | 0.458845 | − | 0.264915i | −0.252713 | − | 0.967541i | \(-0.581323\pi\) |
0.711559 | + | 0.702627i | \(0.247990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.4841 | − | 56.2640i | 1.14920 | − | 1.99048i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.30715 | − | 0.754681i | −0.0461282 | − | 0.0266321i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.6675 | − | 14.8191i | 0.904659 | − | 0.522305i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0409808 | 0.00144081 | 0.000720404 | − | 1.00000i | \(-0.499771\pi\) | ||||
0.000720404 | 1.00000i | \(0.499771\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.2568i | − | 1.51895i | −0.650535 | − | 0.759476i | \(-0.725455\pi\) | ||
0.650535 | − | 0.759476i | \(-0.274545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.37575 | + | 12.7752i | 0.258361 | + | 0.447495i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2584 | − | 17.7681i | 0.358896 | − | 0.621626i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7863 | + | 14.3104i | 0.865048 | + | 0.499436i | 0.865699 | − | 0.500564i | \(-0.166874\pi\) |
−0.000651604 | 1.00000i | \(0.500207\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.2059 | − | 36.7297i | −0.739191 | − | 1.28032i | −0.952860 | − | 0.303411i | \(-0.901875\pi\) |
0.213669 | − | 0.976906i | \(-0.431459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1116i | 0.490710i | 0.969433 | + | 0.245355i | \(0.0789045\pi\) | ||||
−0.969433 | + | 0.245355i | \(0.921096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.6088i | 0.785237i | 0.919701 | + | 0.392618i | \(0.128431\pi\) | ||||
−0.919701 | + | 0.392618i | \(0.871569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.7268 | − | 28.9716i | −0.579548 | − | 1.00381i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.86747 | − | 3.38759i | −0.203052 | − | 0.117232i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.05530 | + | 12.2201i | −0.243576 | + | 0.421886i | −0.961730 | − | 0.273998i | \(-0.911654\pi\) |
0.718154 | + | 0.695884i | \(0.244987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.2026 | + | 28.0637i | 0.558709 | + | 0.967713i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.8731i | 0.752456i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.7984 | −1.29877 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.60368 | − | 5.54469i | 0.329210 | − | 0.190070i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.7863 | − | 21.2386i | −1.25954 | − | 0.727195i | −0.286554 | − | 0.958064i | \(-0.592510\pi\) |
−0.972985 | + | 0.230869i | \(0.925843\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.8421 | − | 29.1714i | 0.575316 | − | 0.996476i | −0.420691 | − | 0.907204i | \(-0.638213\pi\) |
0.996007 | − | 0.0892724i | \(-0.0284542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.8165 | + | 22.9881i | −1.35852 | + | 0.784344i | −0.989425 | − | 0.145047i | \(-0.953667\pi\) |
−0.369098 | + | 0.929390i | \(0.620333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.8786 | 1.08516 | 0.542581 | − | 0.840004i | \(-0.317447\pi\) | ||||
0.542581 | + | 0.840004i | \(0.317447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.58373 | − | 0.914365i | 0.0537242 | − | 0.0310177i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.92450 | + | 3.33333i | −0.0652091 | + | 0.112945i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 37.9395 | + | 21.9044i | 1.28259 | + | 0.740503i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.3925 | − | 26.2073i | 1.53279 | − | 0.884959i | 0.533563 | − | 0.845760i | \(-0.320853\pi\) |
0.999231 | − | 0.0391990i | \(-0.0124806\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.0558 | −1.14737 | −0.573685 | − | 0.819076i | \(-0.694487\pi\) | ||||
−0.573685 | + | 0.819076i | \(0.694487\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0530 | − | 31.2687i | −0.606161 | − | 1.04990i | −0.991867 | − | 0.127280i | \(-0.959375\pi\) |
0.385706 | − | 0.922622i | \(-0.373958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.05582 | − | 7.02488i | 0.136028 | − | 0.235607i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.3700 | + | 11.7606i | 0.681657 | + | 0.393555i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.19615 | − | 9.00000i | −0.173688 | − | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 73.8087i | − | 2.46166i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.9930i | 2.39843i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.02791 | + | 3.51244i | 0.0674100 | + | 0.116757i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.6935 | − | 21.1850i | −1.21839 | − | 0.703437i | −0.253815 | − | 0.967253i | \(-0.581686\pi\) |
−0.964573 | + | 0.263816i | \(0.915019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.3321 | + | 43.8765i | −0.839289 | + | 1.45369i | 0.0512002 | + | 0.998688i | \(0.483695\pi\) |
−0.890490 | + | 0.455004i | \(0.849638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | − | 7.79423i | −0.148928 | − | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.933638i | − | 0.0308315i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.3372 | −0.835796 | −0.417898 | − | 0.908494i | \(-0.637233\pi\) | ||||
−0.417898 | + | 0.908494i | \(0.637233\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.39367 | − | 0.804638i | 0.0458734 | − | 0.0264850i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.05582 | + | 2.34163i | 0.133354 | + | 0.0769922i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.67466 | + | 13.2929i | −0.251798 | + | 0.436126i | −0.964021 | − | 0.265827i | \(-0.914355\pi\) |
0.712223 | + | 0.701953i | \(0.247688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4890 | − | 6.05582i | 0.343763 | − | 0.198471i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.02488 | 0.229738 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5390 | −0.376964 | −0.188482 | − | 0.982077i | \(-0.560357\pi\) | ||||
−0.188482 | + | 0.982077i | \(0.560357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.6675 | + | 16.5512i | −0.934532 | + | 0.539552i | −0.888242 | − | 0.459376i | \(-0.848073\pi\) |
−0.0462901 | + | 0.998928i | \(0.514740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.1843 | − | 34.9602i | 0.657290 | − | 1.13846i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.9526 | + | 8.63290i | 0.485895 | + | 0.280532i | 0.722870 | − | 0.690984i | \(-0.242823\pi\) |
−0.236975 | + | 0.971516i | \(0.576156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.08528 | + | 0.626589i | −0.0352298 | + | 0.0203399i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.2159 | 0.946394 | 0.473197 | − | 0.880957i | \(-0.343100\pi\) | ||||
0.473197 | + | 0.880957i | \(0.343100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.37003i | 0.0766922i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.62669 | + | 6.28160i | 0.117112 | + | 0.202844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.8589 | + | 49.9851i | −0.930932 | + | 1.61242i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.1914 | + | 13.3896i | 0.746559 | + | 0.431026i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.00416 | − | 3.47131i | −0.0644495 | − | 0.111630i | 0.832000 | − | 0.554775i | \(-0.187196\pi\) |
−0.896450 | + | 0.443146i | \(0.853862\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.2791i | − | 0.650787i | −0.945579 | − | 0.325393i | \(-0.894503\pi\) | ||
0.945579 | − | 0.325393i | \(-0.105497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.16021i | − | 0.261604i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.65417 | + | 2.86511i | 0.0529217 | + | 0.0916631i | 0.891273 | − | 0.453468i | \(-0.149813\pi\) |
−0.838351 | + | 0.545131i | \(0.816480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.23617 | + | 0.713701i | 0.0395080 | + | 0.0228100i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.5963 | − | 35.6739i | 0.656921 | − | 1.13782i | −0.324488 | − | 0.945890i | \(-0.605192\pi\) |
0.981409 | − | 0.191930i | \(-0.0614748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.2026 | + | 19.4034i | 0.356944 | + | 0.618245i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 48.5813i | − | 1.54479i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.2802 | 1.40661 | 0.703303 | − | 0.710890i | \(-0.251708\pi\) | ||||
0.703303 | + | 0.710890i | \(0.251708\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.1120 | + | 16.2305i | −0.891211 | + | 0.514541i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.8478 | + | 17.8100i | 0.976959 | + | 0.564047i | 0.901351 | − | 0.433090i | \(-0.142577\pi\) |
0.0756081 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.r.f.289.5 | 12 | ||
3.2 | odd | 2 | 576.2.r.e.97.1 | ✓ | 12 | ||
4.3 | odd | 2 | inner | 1728.2.r.f.289.2 | 12 | ||
8.3 | odd | 2 | 1728.2.r.e.289.2 | 12 | |||
8.5 | even | 2 | 1728.2.r.e.289.5 | 12 | |||
9.2 | odd | 6 | 5184.2.d.q.2593.2 | 12 | |||
9.4 | even | 3 | 1728.2.r.e.1441.5 | 12 | |||
9.5 | odd | 6 | 576.2.r.f.481.6 | yes | 12 | ||
9.7 | even | 3 | 5184.2.d.r.2593.8 | 12 | |||
12.11 | even | 2 | 576.2.r.e.97.6 | yes | 12 | ||
24.5 | odd | 2 | 576.2.r.f.97.6 | yes | 12 | ||
24.11 | even | 2 | 576.2.r.f.97.1 | yes | 12 | ||
36.7 | odd | 6 | 5184.2.d.r.2593.11 | 12 | |||
36.11 | even | 6 | 5184.2.d.q.2593.5 | 12 | |||
36.23 | even | 6 | 576.2.r.f.481.1 | yes | 12 | ||
36.31 | odd | 6 | 1728.2.r.e.1441.2 | 12 | |||
72.5 | odd | 6 | 576.2.r.e.481.1 | yes | 12 | ||
72.11 | even | 6 | 5184.2.d.q.2593.11 | 12 | |||
72.13 | even | 6 | inner | 1728.2.r.f.1441.5 | 12 | ||
72.29 | odd | 6 | 5184.2.d.q.2593.8 | 12 | |||
72.43 | odd | 6 | 5184.2.d.r.2593.5 | 12 | |||
72.59 | even | 6 | 576.2.r.e.481.6 | yes | 12 | ||
72.61 | even | 6 | 5184.2.d.r.2593.2 | 12 | |||
72.67 | odd | 6 | inner | 1728.2.r.f.1441.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.1 | ✓ | 12 | 3.2 | odd | 2 | ||
576.2.r.e.97.6 | yes | 12 | 12.11 | even | 2 | ||
576.2.r.e.481.1 | yes | 12 | 72.5 | odd | 6 | ||
576.2.r.e.481.6 | yes | 12 | 72.59 | even | 6 | ||
576.2.r.f.97.1 | yes | 12 | 24.11 | even | 2 | ||
576.2.r.f.97.6 | yes | 12 | 24.5 | odd | 2 | ||
576.2.r.f.481.1 | yes | 12 | 36.23 | even | 6 | ||
576.2.r.f.481.6 | yes | 12 | 9.5 | odd | 6 | ||
1728.2.r.e.289.2 | 12 | 8.3 | odd | 2 | |||
1728.2.r.e.289.5 | 12 | 8.5 | even | 2 | |||
1728.2.r.e.1441.2 | 12 | 36.31 | odd | 6 | |||
1728.2.r.e.1441.5 | 12 | 9.4 | even | 3 | |||
1728.2.r.f.289.2 | 12 | 4.3 | odd | 2 | inner | ||
1728.2.r.f.289.5 | 12 | 1.1 | even | 1 | trivial | ||
1728.2.r.f.1441.2 | 12 | 72.67 | odd | 6 | inner | ||
1728.2.r.f.1441.5 | 12 | 72.13 | even | 6 | inner | ||
5184.2.d.q.2593.2 | 12 | 9.2 | odd | 6 | |||
5184.2.d.q.2593.5 | 12 | 36.11 | even | 6 | |||
5184.2.d.q.2593.8 | 12 | 72.29 | odd | 6 | |||
5184.2.d.q.2593.11 | 12 | 72.11 | even | 6 | |||
5184.2.d.r.2593.2 | 12 | 72.61 | even | 6 | |||
5184.2.d.r.2593.5 | 12 | 72.43 | odd | 6 | |||
5184.2.d.r.2593.8 | 12 | 9.7 | even | 3 | |||
5184.2.d.r.2593.11 | 12 | 36.7 | odd | 6 |