Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1727.3 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1727 |
Dual form | 2592.2.s.g.863.3 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.896575 | − | 0.517638i | 0.400961 | − | 0.231495i | −0.285938 | − | 0.958248i | \(-0.592305\pi\) |
0.686898 | + | 0.726753i | \(0.258972\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.232051 | − | 0.133975i | −0.0877070 | − | 0.0506376i | 0.455505 | − | 0.890233i | \(-0.349459\pi\) |
−0.543212 | + | 0.839596i | \(0.682792\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.93185 | − | 3.34607i | 0.582475 | − | 1.00888i | −0.412710 | − | 0.910863i | \(-0.635418\pi\) |
0.995185 | − | 0.0980141i | \(-0.0312490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23205 | + | 2.13397i | 0.341709 | + | 0.591858i | 0.984750 | − | 0.173974i | \(-0.0556608\pi\) |
−0.643041 | + | 0.765832i | \(0.722327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.69213i | 1.62308i | 0.584297 | + | 0.811540i | \(0.301370\pi\) | ||||
−0.584297 | + | 0.811540i | \(0.698630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.96713 | + | 5.13922i | 0.618689 | + | 1.07160i | 0.989725 | + | 0.142982i | \(0.0456692\pi\) |
−0.371036 | + | 0.928618i | \(0.620997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.96410 | + | 3.40192i | −0.392820 | + | 0.680385i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.79315 | − | 1.03528i | −0.332980 | − | 0.192246i | 0.324184 | − | 0.945994i | \(-0.394910\pi\) |
−0.657163 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.464102 | + | 0.267949i | −0.0833551 | + | 0.0481251i | −0.541098 | − | 0.840959i | \(-0.681991\pi\) |
0.457743 | + | 0.889085i | \(0.348658\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.277401 | −0.0468894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.46410 | −1.06269 | −0.531346 | − | 0.847155i | \(-0.678314\pi\) | ||||
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79315 | − | 1.03528i | 0.280043 | − | 0.161683i | −0.353400 | − | 0.935472i | \(-0.614974\pi\) |
0.633443 | + | 0.773789i | \(0.281641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.46410 | + | 3.73205i | 0.985766 | + | 0.569132i | 0.904006 | − | 0.427520i | \(-0.140613\pi\) |
0.0817602 | + | 0.996652i | \(0.473946\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.76028 | − | 8.24504i | 0.694358 | − | 1.20266i | −0.276039 | − | 0.961147i | \(-0.589022\pi\) |
0.970397 | − | 0.241517i | \(-0.0776449\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.46410 | − | 6.00000i | −0.494872 | − | 0.857143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3843i | 1.83847i | 0.393710 | + | 0.919235i | \(0.371192\pi\) | ||||
−0.393710 | + | 0.919235i | \(0.628808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.72500 | + | 6.45189i | 0.484954 | + | 0.839965i | 0.999851 | − | 0.0172873i | \(-0.00550300\pi\) |
−0.514897 | + | 0.857252i | \(0.672170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.69615 | − | 8.13397i | 0.601281 | − | 1.04145i | −0.391347 | − | 0.920243i | \(-0.627991\pi\) |
0.992627 | − | 0.121205i | \(-0.0386760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.20925 | + | 1.27551i | 0.274024 | + | 0.158208i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.42820 | − | 4.86603i | 1.02967 | − | 0.594480i | 0.112779 | − | 0.993620i | \(-0.464025\pi\) |
0.916890 | + | 0.399140i | \(0.130691\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.92820 | 1.16201 | 0.581004 | − | 0.813901i | \(-0.302660\pi\) | ||||
0.581004 | + | 0.813901i | \(0.302660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.896575 | + | 0.517638i | −0.102174 | + | 0.0589903i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1603 | − | 7.59808i | −1.48064 | − | 0.854850i | −0.480885 | − | 0.876784i | \(-0.659684\pi\) |
−0.999759 | + | 0.0219334i | \(0.993018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.86370 | − | 6.69213i | 0.424097 | − | 0.734557i | −0.572239 | − | 0.820087i | \(-0.693925\pi\) |
0.996336 | + | 0.0855301i | \(0.0272584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | + | 6.00000i | 0.375735 | + | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.69213i | 0.709364i | 0.934987 | + | 0.354682i | \(0.115411\pi\) | ||||
−0.934987 | + | 0.354682i | \(0.884589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.660254i | − | 0.0692134i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.896575 | + | 1.55291i | 0.0919867 | + | 0.159326i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | + | 6.06218i | −0.355371 | + | 0.615521i | −0.987181 | − | 0.159602i | \(-0.948979\pi\) |
0.631810 | + | 0.775123i | \(0.282312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3843 | + | 7.72741i | 1.33178 | + | 0.768906i | 0.985573 | − | 0.169251i | \(-0.0541349\pi\) |
0.346211 | + | 0.938157i | \(0.387468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2321 | + | 8.79423i | −1.50086 | + | 0.866521i | −0.500859 | + | 0.865529i | \(0.666983\pi\) |
−1.00000 | 0.000992235i | \(0.999684\pi\) | ||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1774 | 1.46726 | 0.733628 | − | 0.679551i | \(-0.237826\pi\) | ||||
0.733628 | + | 0.679551i | \(0.237826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.928203 | −0.0889057 | −0.0444529 | − | 0.999011i | \(-0.514154\pi\) | ||||
−0.0444529 | + | 0.999011i | \(0.514154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.58871 | + | 4.38134i | −0.713885 | + | 0.412162i | −0.812498 | − | 0.582964i | \(-0.801893\pi\) |
0.0986126 | + | 0.995126i | \(0.468560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.32051 | + | 3.07180i | 0.496140 | + | 0.286447i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.896575 | − | 1.55291i | 0.0821889 | − | 0.142355i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.96410 | − | 3.40192i | −0.178555 | − | 0.309266i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.24316i | 0.826733i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.46410i | 0.307389i | 0.988118 | + | 0.153695i | \(0.0491172\pi\) | ||||
−0.988118 | + | 0.153695i | \(0.950883\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.86370 | − | 6.69213i | −0.337573 | − | 0.584694i | 0.646402 | − | 0.762997i | \(-0.276273\pi\) |
−0.983976 | + | 0.178303i | \(0.942939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.232051 | − | 0.401924i | 0.0201214 | − | 0.0348512i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.38186 | + | 5.41662i | 0.801546 | + | 0.462773i | 0.844012 | − | 0.536325i | \(-0.180188\pi\) |
−0.0424654 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.03590 | + | 0.598076i | −0.0878638 | + | 0.0507282i | −0.543288 | − | 0.839546i | \(-0.682821\pi\) |
0.455424 | + | 0.890274i | \(0.349488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.52056 | 0.796149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.14359 | −0.178016 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.79796 | + | 5.65685i | −0.802680 | + | 0.463428i | −0.844407 | − | 0.535701i | \(-0.820047\pi\) |
0.0417274 | + | 0.999129i | \(0.486714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.16025 | − | 4.13397i | −0.582693 | − | 0.336418i | 0.179510 | − | 0.983756i | \(-0.442549\pi\) |
−0.762203 | + | 0.647338i | \(0.775882\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.277401 | + | 0.480473i | −0.0222814 | + | 0.0385925i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.53590 | + | 2.66025i | 0.122578 | + | 0.212311i | 0.920784 | − | 0.390074i | \(-0.127550\pi\) |
−0.798206 | + | 0.602385i | \(0.794217\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.59008i | − | 0.125316i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5885i | 1.22098i | 0.792023 | + | 0.610491i | \(0.209028\pi\) | ||||
−0.792023 | + | 0.610491i | \(0.790972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.17398 | − | 2.03339i | −0.0908451 | − | 0.157348i | 0.817022 | − | 0.576607i | \(-0.195623\pi\) |
−0.907867 | + | 0.419258i | \(0.862290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.46410 | − | 6.00000i | 0.266469 | − | 0.461538i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.00481 | + | 4.62158i | 0.608594 | + | 0.351372i | 0.772415 | − | 0.635118i | \(-0.219049\pi\) |
−0.163821 | + | 0.986490i | \(0.552382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.911543 | − | 0.526279i | 0.0689062 | − | 0.0397830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5959 | 1.46467 | 0.732334 | − | 0.680946i | \(-0.238431\pi\) | ||||
0.732334 | + | 0.680946i | \(0.238431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.46410 | −0.480473 | −0.240236 | − | 0.970714i | \(-0.577225\pi\) | ||||
−0.240236 | + | 0.970714i | \(0.577225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.79555 | + | 3.34607i | −0.426098 | + | 0.246008i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.3923 | + | 12.9282i | 1.63749 | + | 0.945404i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.83083 | + | 11.8313i | −0.494262 | + | 0.856086i | −0.999978 | − | 0.00661351i | \(-0.997895\pi\) |
0.505717 | + | 0.862700i | \(0.331228\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0358984 | − | 0.0621778i | −0.00258402 | − | 0.00447566i | 0.864731 | − | 0.502236i | \(-0.167489\pi\) |
−0.867315 | + | 0.497761i | \(0.834156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.4195i | − | 1.02735i | −0.857985 | − | 0.513675i | \(-0.828284\pi\) | ||
0.857985 | − | 0.513675i | \(-0.171716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25.5885i | − | 1.81392i | −0.421219 | − | 0.906959i | \(-0.638398\pi\) | ||
0.421219 | − | 0.906959i | \(-0.361602\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.277401 | + | 0.480473i | 0.0194698 | + | 0.0337226i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.07180 | − | 1.85641i | 0.0748575 | − | 0.129657i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.79555 | + | 3.34607i | 0.400887 | + | 0.231452i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.8205 | − | 10.8660i | 1.29566 | − | 0.748048i | 0.316006 | − | 0.948757i | \(-0.397658\pi\) |
0.979651 | + | 0.200709i | \(0.0643246\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.72741 | 0.527005 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.143594 | 0.00974776 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2808 | + | 8.24504i | −0.960633 | + | 0.554622i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3205 | − | 11.7321i | −1.36076 | − | 0.785636i | −0.371037 | − | 0.928618i | \(-0.620998\pi\) |
−0.989725 | + | 0.142982i | \(0.954331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.07055 | + | 3.58630i | −0.137427 | + | 0.238031i | −0.926522 | − | 0.376240i | \(-0.877217\pi\) |
0.789095 | + | 0.614272i | \(0.210550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3137i | 0.741186i | 0.928795 | + | 0.370593i | \(0.120845\pi\) | ||||
−0.928795 | + | 0.370593i | \(0.879155\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.85641i | − | 0.642961i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.72741 | − | 13.3843i | −0.499844 | − | 0.865756i | 0.500156 | − | 0.865936i | \(-0.333276\pi\) |
−1.00000 | 0.000179684i | \(0.999943\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.96410 | + | 5.13397i | −0.190935 | + | 0.330708i | −0.945560 | − | 0.325447i | \(-0.894485\pi\) |
0.754626 | + | 0.656156i | \(0.227818\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.21166 | − | 3.58630i | −0.396848 | − | 0.229120i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.69615 | + | 2.13397i | −0.235181 | + | 0.135782i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.58630 | −0.226365 | −0.113183 | − | 0.993574i | \(-0.536105\pi\) | ||||
−0.113183 | + | 0.993574i | \(0.536105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.9282 | 1.44148 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.79315 | + | 1.03528i | −0.111854 | + | 0.0645788i | −0.554883 | − | 0.831928i | \(-0.687237\pi\) |
0.443029 | + | 0.896507i | \(0.353904\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50000 | + | 0.866025i | 0.0932055 | + | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.72741 | − | 13.3843i | 0.476492 | − | 0.825309i | −0.523145 | − | 0.852244i | \(-0.675241\pi\) |
0.999637 | + | 0.0269349i | \(0.00857468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820 | + | 12.0000i | 0.425596 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.10583i | − | 0.189366i | −0.995507 | − | 0.0946829i | \(-0.969816\pi\) | ||
0.995507 | − | 0.0946829i | \(-0.0301837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0526i | 0.792886i | 0.918059 | + | 0.396443i | \(0.129756\pi\) | ||||
−0.918059 | + | 0.396443i | \(0.870244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.58871 | + | 13.1440i | 0.457616 | + | 0.792614i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4641 | + | 18.1244i | −0.628727 | + | 1.08899i | 0.359081 | + | 0.933307i | \(0.383090\pi\) |
−0.987807 | + | 0.155680i | \(0.950243\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1774 | + | 8.76268i | 0.905408 | + | 0.522738i | 0.878951 | − | 0.476912i | \(-0.158244\pi\) |
0.0264575 | + | 0.999650i | \(0.491577\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.464102 | − | 0.267949i | 0.0275880 | − | 0.0159279i | −0.486143 | − | 0.873880i | \(-0.661596\pi\) |
0.513731 | + | 0.857952i | \(0.328263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.554803 | −0.0327490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.7846 | −1.63439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0788 | − | 13.9019i | 1.40670 | − | 0.812158i | 0.411630 | − | 0.911351i | \(-0.364960\pi\) |
0.995068 | + | 0.0991934i | \(0.0316263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.67949 | + | 3.85641i | 0.388895 | + | 0.224529i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.31130 | + | 12.6636i | −0.422824 | + | 0.732352i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 1.73205i | −0.0576390 | − | 0.0998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.72363i | − | 0.556773i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3923i | 1.27800i | 0.769208 | + | 0.638998i | \(0.220651\pi\) | ||||
−0.769208 | + | 0.638998i | \(0.779349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.03768 | − | 8.72552i | −0.285661 | − | 0.494779i | 0.687109 | − | 0.726555i | \(-0.258880\pi\) |
−0.972769 | + | 0.231776i | \(0.925546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.96410 | − | 17.2583i | 0.563204 | − | 0.975499i | −0.434010 | − | 0.900908i | \(-0.642902\pi\) |
0.997214 | − | 0.0745904i | \(-0.0237649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.79315 | − | 1.03528i | −0.100713 | − | 0.0581469i | 0.448797 | − | 0.893634i | \(-0.351853\pi\) |
−0.549511 | + | 0.835487i | \(0.685186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.92820 | + | 4.00000i | −0.387905 | + | 0.223957i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5911 | −0.644947 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.67949 | −0.536922 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.20925 | + | 1.27551i | −0.121800 | + | 0.0703213i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8205 | + | 12.5981i | 1.19936 | + | 0.692453i | 0.960413 | − | 0.278579i | \(-0.0898634\pi\) |
0.238950 | + | 0.971032i | \(0.423197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.03768 | − | 8.72552i | 0.275238 | − | 0.476726i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.42820 | + | 12.8660i | 0.404640 | + | 0.700857i | 0.994280 | − | 0.106809i | \(-0.0340635\pi\) |
−0.589639 | + | 0.807667i | \(0.700730\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.07055i | 0.112127i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.73205i | 0.201512i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.72741 | − | 13.3843i | −0.414829 | − | 0.718505i | 0.580582 | − | 0.814202i | \(-0.302825\pi\) |
−0.995410 | + | 0.0956973i | \(0.969492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.16025 | + | 8.93782i | −0.276222 | + | 0.478431i | −0.970443 | − | 0.241332i | \(-0.922416\pi\) |
0.694221 | + | 0.719762i | \(0.255749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.3548 | − | 17.5254i | −1.61562 | − | 0.932781i | −0.988034 | − | 0.154237i | \(-0.950708\pi\) |
−0.627590 | − | 0.778544i | \(-0.715959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1436 | − | 5.85641i | 0.538366 | − | 0.310826i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.1480 | −1.69671 | −0.848353 | − | 0.529432i | \(-0.822405\pi\) | ||||
−0.848353 | + | 0.529432i | \(0.822405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.90138 | − | 5.13922i | 0.465920 | − | 0.268999i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7679 | − | 8.52628i | −0.770881 | − | 0.445068i | 0.0623080 | − | 0.998057i | \(-0.480154\pi\) |
−0.833189 | + | 0.552989i | \(0.813487\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79315 | − | 3.10583i | 0.0930958 | − | 0.161247i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.62436 | − | 11.4737i | −0.342996 | − | 0.594087i | 0.641991 | − | 0.766712i | \(-0.278108\pi\) |
−0.984988 | + | 0.172625i | \(0.944775\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.10205i | − | 0.262769i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.19615i | − | 0.472375i | −0.971708 | − | 0.236187i | \(-0.924102\pi\) | ||
0.971708 | − | 0.236187i | \(-0.0758979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5254 | + | 30.3548i | 0.895504 | + | 1.55106i | 0.833179 | + | 0.553003i | \(0.186518\pi\) |
0.0623252 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.535898 | + | 0.928203i | −0.0273119 | + | 0.0473056i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.4877 | − | 7.20977i | −0.633151 | − | 0.365550i | 0.148821 | − | 0.988864i | \(-0.452452\pi\) |
−0.781971 | + | 0.623314i | \(0.785786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.3923 | + | 19.8564i | −1.73929 | + | 1.00418i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.7322 | −0.791574 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7846 | 1.34428 | 0.672141 | − | 0.740424i | \(-0.265375\pi\) | ||||
0.672141 | + | 0.740424i | \(0.265375\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5959 | − | 11.3137i | 0.978573 | − | 0.564980i | 0.0767343 | − | 0.997052i | \(-0.475551\pi\) |
0.901839 | + | 0.432072i | \(0.142217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.14359 | − | 0.660254i | −0.0569665 | − | 0.0328896i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.4877 | + | 21.6293i | −0.618992 | + | 1.07212i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.99622i | − | 0.0982277i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.00000i | − | 0.392705i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.86611 | + | 13.6245i | 0.384284 | + | 0.665600i | 0.991670 | − | 0.128807i | \(-0.0411148\pi\) |
−0.607385 | + | 0.794407i | \(0.707782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.76795 | + | 8.25833i | −0.232376 | + | 0.402486i | −0.958507 | − | 0.285070i | \(-0.907983\pi\) |
0.726131 | + | 0.687556i | \(0.241317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.7661 | − | 13.1440i | −1.10432 | − | 0.637579i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.17949 | + | 1.25833i | −0.105473 | + | 0.0608949i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.37945 | −0.259119 | −0.129560 | − | 0.991572i | \(-0.541356\pi\) | ||||
−0.129560 | + | 0.991572i | \(0.541356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.7846 | −1.28719 | −0.643593 | − | 0.765368i | \(-0.722557\pi\) | ||||
−0.643593 | + | 0.765368i | \(0.722557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.90138 | + | 5.13922i | −0.425811 | + | 0.245842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4641 | − | 10.6603i | −0.881243 | − | 0.508786i | −0.0101753 | − | 0.999948i | \(-0.503239\pi\) |
−0.871068 | + | 0.491162i | \(0.836572\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6617 | − | 23.6627i | 0.649085 | − | 1.12425i | −0.334257 | − | 0.942482i | \(-0.608485\pi\) |
0.983342 | − | 0.181766i | \(-0.0581815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.46410 | + | 6.00000i | 0.164214 | + | 0.284427i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.9038i | − | 0.608967i | −0.952518 | − | 0.304484i | \(-0.901516\pi\) | ||
0.952518 | − | 0.304484i | \(-0.0984839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8.00000i | − | 0.376705i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.341773 | − | 0.591968i | −0.0160225 | − | 0.0277519i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3923 | − | 30.1244i | 0.813578 | − | 1.40916i | −0.0967670 | − | 0.995307i | \(-0.530850\pi\) |
0.910345 | − | 0.413851i | \(-0.135817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.2856 | − | 12.8666i | −1.03795 | − | 0.599258i | −0.118695 | − | 0.992931i | \(-0.537871\pi\) |
−0.919251 | + | 0.393672i | \(0.871204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0167 | − | 15.5981i | 1.25557 | − | 0.724904i | 0.283360 | − | 0.959013i | \(-0.408551\pi\) |
0.972210 | + | 0.234109i | \(0.0752174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.3596 | −1.77507 | −0.887536 | − | 0.460738i | \(-0.847585\pi\) | ||||
−0.887536 | + | 0.460738i | \(0.847585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.60770 | −0.120412 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.9754 | − | 14.4195i | 1.14837 | − | 0.663011i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.89230 | − | 3.40192i | −0.270357 | − | 0.156091i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.45001 | + | 12.9038i | −0.340399 | + | 0.589589i | −0.984507 | − | 0.175346i | \(-0.943896\pi\) |
0.644107 | + | 0.764935i | \(0.277229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.96410 | − | 13.7942i | −0.363132 | − | 0.628963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.24693i | 0.329066i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 23.4449i | − | 1.06239i | −0.847250 | − | 0.531194i | \(-0.821743\pi\) | ||
0.847250 | − | 0.531194i | \(-0.178257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.86611 | − | 13.6245i | −0.354992 | − | 0.614865i | 0.632124 | − | 0.774867i | \(-0.282183\pi\) |
−0.987117 | + | 0.160002i | \(0.948850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.92820 | − | 12.0000i | 0.312031 | − | 0.540453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.62536 | − | 1.51575i | −0.117763 | − | 0.0679907i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8564 | − | 6.26795i | 0.485999 | − | 0.280592i | −0.236914 | − | 0.971531i | \(-0.576136\pi\) |
0.722913 | + | 0.690939i | \(0.242803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1165 | −1.29824 | −0.649120 | − | 0.760686i | \(-0.724863\pi\) | ||||
−0.649120 | + | 0.760686i | \(0.724863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | 0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.0740 | − | 9.28032i | 0.712467 | − | 0.411343i | −0.0995068 | − | 0.995037i | \(-0.531727\pi\) |
0.811974 | + | 0.583694i | \(0.198393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.30385 | − | 1.33013i | −0.101916 | − | 0.0588414i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.10446 | + | 15.7694i | −0.401190 | + | 0.694882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.3923 | − | 31.8564i | −0.808893 | − | 1.40104i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 37.6018i | − | 1.64736i | −0.567053 | − | 0.823681i | \(-0.691916\pi\) | ||
0.567053 | − | 0.823681i | \(-0.308084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8038i | 0.472419i | 0.971702 | + | 0.236210i | \(0.0759052\pi\) | ||||
−0.971702 | + | 0.236210i | \(0.924095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.79315 | − | 3.10583i | −0.0781109 | − | 0.135292i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.10770 | + | 10.5788i | −0.265552 | + | 0.459949i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.41851 | + | 2.55103i | 0.191387 | + | 0.110497i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6077 | − | 7.85641i | 0.588312 | − | 0.339662i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.7685 | −1.15300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6077 | 0.628034 | 0.314017 | − | 0.949417i | \(-0.398325\pi\) | ||||
0.314017 | + | 0.949417i | \(0.398325\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.832204 | + | 0.480473i | −0.0356477 | + | 0.0205812i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.96410 | − | 2.86603i | −0.212250 | − | 0.122542i | 0.390107 | − | 0.920770i | \(-0.372438\pi\) |
−0.602356 | + | 0.798227i | \(0.705771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.79315 | − | 3.10583i | 0.0763908 | − | 0.132313i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.03590 | + | 3.52628i | 0.0865752 | + | 0.149953i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 10.2784i | − | 0.435511i | −0.976003 | − | 0.217756i | \(-0.930126\pi\) | ||
0.976003 | − | 0.217756i | \(-0.0698736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3923i | 0.777912i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.52056 | − | 16.4901i | −0.401244 | − | 0.694974i | 0.592633 | − | 0.805473i | \(-0.298089\pi\) |
−0.993876 | + | 0.110498i | \(0.964755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.53590 | + | 7.85641i | −0.190827 | + | 0.330522i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.3963 | − | 19.2814i | −1.40004 | − | 0.808316i | −0.405648 | − | 0.914029i | \(-0.632954\pi\) |
−0.994397 | + | 0.105713i | \(0.966288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9641 | + | 11.5263i | −0.835472 | + | 0.482360i | −0.855722 | − | 0.517435i | \(-0.826887\pi\) |
0.0202508 | + | 0.999795i | \(0.493554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3110 | −0.972134 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0718 | −1.08538 | −0.542692 | − | 0.839932i | \(-0.682595\pi\) | ||||
−0.542692 | + | 0.839932i | \(0.682595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.79315 | + | 1.03528i | −0.0743924 | + | 0.0429505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.7846 | + | 25.8564i | 1.85479 | + | 1.07086i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.138701 | + | 0.240237i | −0.00572479 | + | 0.00991563i | −0.868874 | − | 0.495034i | \(-0.835156\pi\) |
0.863149 | + | 0.504950i | \(0.168489\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.464102 | − | 0.803848i | −0.0191230 | − | 0.0331220i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.8076i | 1.05979i | 0.848063 | + | 0.529895i | \(0.177769\pi\) | ||||
−0.848063 | + | 0.529895i | \(0.822231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.85641i | − | 0.0761052i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.93426 | + | 10.2784i | 0.242467 | + | 0.419965i | 0.961416 | − | 0.275097i | \(-0.0887100\pi\) |
−0.718949 | + | 0.695062i | \(0.755377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.39230 | + | 5.87564i | −0.138375 | + | 0.239673i | −0.926882 | − | 0.375354i | \(-0.877521\pi\) |
0.788507 | + | 0.615026i | \(0.210855\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.52193 | − | 2.03339i | −0.143187 | − | 0.0826690i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.23205 | + | 5.33013i | −0.374717 | + | 0.216343i | −0.675517 | − | 0.737344i | \(-0.736080\pi\) |
0.300800 | + | 0.953687i | \(0.402746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4596 | 0.949075 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.3923 | −1.51026 | −0.755130 | − | 0.655575i | \(-0.772427\pi\) | ||||
−0.755130 | + | 0.655575i | \(0.772427\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.42091 | − | 4.86181i | 0.339013 | − | 0.195729i | −0.320822 | − | 0.947139i | \(-0.603959\pi\) |
0.659836 | + | 0.751410i | \(0.270626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.571797 | − | 0.330127i | −0.0229825 | − | 0.0132689i | 0.488465 | − | 0.872584i | \(-0.337557\pi\) |
−0.511447 | + | 0.859315i | \(0.670890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.896575 | − | 1.55291i | 0.0359205 | − | 0.0622162i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.03590 | − | 8.72243i | −0.201436 | − | 0.348897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 43.2586i | − | 1.72483i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9808i | 0.795422i | 0.917511 | + | 0.397711i | \(0.130195\pi\) | ||||
−0.917511 | + | 0.397711i | \(0.869805\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.79315 | + | 3.10583i | 0.0711590 | + | 0.123251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.53590 | − | 14.7846i | 0.338205 | − | 0.585788i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.5665 | + | 21.1117i | 1.44429 | + | 0.833861i | 0.998132 | − | 0.0610939i | \(-0.0194589\pi\) |
0.446157 | + | 0.894955i | \(0.352792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2487 | + | 8.80385i | −0.601350 | + | 0.347190i | −0.769573 | − | 0.638559i | \(-0.779531\pi\) |
0.168222 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1822 | 0.911387 | 0.455694 | − | 0.890137i | \(-0.349391\pi\) | ||||
0.455694 | + | 0.890137i | \(0.349391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.7846 | 1.12989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.96575 | − | 5.17638i | 0.350857 | − | 0.202567i | −0.314206 | − | 0.949355i | \(-0.601738\pi\) |
0.665063 | + | 0.746788i | \(0.268405\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.92820 | − | 4.00000i | −0.270707 | − | 0.156293i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2480 | + | 29.8744i | −0.671885 | + | 1.16374i | 0.305484 | + | 0.952197i | \(0.401182\pi\) |
−0.977369 | + | 0.211542i | \(0.932151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6244 | + | 37.4545i | 0.841090 | + | 1.45681i | 0.888974 | + | 0.457958i | \(0.151419\pi\) |
−0.0478841 | + | 0.998853i | \(0.515248\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.480473i | − | 0.0186320i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.2872i | − | 0.475762i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.1445 | − | 31.4273i | −0.700462 | − | 1.21324i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4282 | + | 18.0622i | −0.401978 | + | 0.696246i | −0.993965 | − | 0.109702i | \(-0.965010\pi\) |
0.591987 | + | 0.805948i | \(0.298344\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.6993 | − | 10.7961i | −0.718674 | − | 0.414927i | 0.0955904 | − | 0.995421i | \(-0.469526\pi\) |
−0.814264 | + | 0.580494i | \(0.802859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.62436 | − | 0.937822i | 0.0623370 | − | 0.0359903i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | −1.29872 | −0.649361 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649361 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2154 | 0.428518 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.5617 | + | 16.4901i | −1.08811 | + | 0.628222i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3205 | − | 15.1962i | −1.00128 | − | 0.578089i | −0.0926528 | − | 0.995698i | \(-0.529535\pi\) |
−0.908627 | + | 0.417610i | \(0.862868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.619174 | + | 1.07244i | −0.0234866 | + | 0.0406800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.92820 | + | 12.0000i | 0.262424 | + | 0.454532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 49.4703i | − | 1.86847i | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||
0.356663 | − | 0.934233i | \(-0.383914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.1962i | − | 0.422271i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.07055 | − | 3.58630i | −0.0778711 | − | 0.134877i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.08846 | + | 10.5455i | −0.228657 | + | 0.396045i | −0.957410 | − | 0.288731i | \(-0.906767\pi\) |
0.728753 | + | 0.684776i | \(0.240100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.75410 | − | 1.59008i | −0.103142 | − | 0.0595489i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.53590 | − | 4.92820i | 0.319225 | − | 0.184304i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.58630 | 0.133746 | 0.0668732 | − | 0.997761i | \(-0.478698\pi\) | ||||
0.0668732 | + | 0.997761i | \(0.478698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.71281 | 0.175514 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.04386 | − | 4.06678i | 0.261602 | − | 0.151036i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.4641 | − | 10.6603i | −0.684796 | − | 0.395367i | 0.116864 | − | 0.993148i | \(-0.462716\pi\) |
−0.801659 | + | 0.597781i | \(0.796049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9754 | + | 43.2586i | −0.923747 | + | 1.59998i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4641 | + | 28.5167i | 0.608115 | + | 1.05329i | 0.991551 | + | 0.129719i | \(0.0414076\pi\) |
−0.383435 | + | 0.923568i | \(0.625259\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 37.6018i | − | 1.38508i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3923i | 0.529429i | 0.964327 | + | 0.264715i | \(0.0852778\pi\) | ||||
−0.964327 | + | 0.264715i | \(0.914722\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7651 | − | 22.1098i | −0.468306 | − | 0.811129i | 0.531038 | − | 0.847348i | \(-0.321802\pi\) |
−0.999344 | + | 0.0362187i | \(0.988469\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.85641 | + | 10.1436i | −0.214562 | + | 0.371633i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.52193 | − | 2.03339i | −0.128689 | − | 0.0742984i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.76795 | − | 1.59808i | 0.101004 | − | 0.0583146i | −0.448647 | − | 0.893709i | \(-0.648094\pi\) |
0.549651 | + | 0.835394i | \(0.314761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.55961 | −0.311516 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.39230 | −0.195987 | −0.0979933 | − | 0.995187i | \(-0.531242\pi\) | ||||
−0.0979933 | + | 0.995187i | \(0.531242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.9435 | + | 21.9067i | −1.37545 | + | 0.794118i | −0.991608 | − | 0.129281i | \(-0.958733\pi\) |
−0.383844 | + | 0.923398i | \(0.625400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.215390 | + | 0.124356i | 0.00779765 | + | 0.00450198i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.17878 | + | 15.8981i | −0.331427 | + | 0.574048i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.42820 | − | 11.1340i | −0.231807 | − | 0.401501i | 0.726533 | − | 0.687132i | \(-0.241130\pi\) |
−0.958340 | + | 0.285630i | \(0.907797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.5569i | 0.739379i | 0.929155 | + | 0.369690i | \(0.120536\pi\) | ||||
−0.929155 | + | 0.369690i | \(0.879464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.10512i | − | 0.0756181i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.79315 | + | 3.10583i | 0.0642463 | + | 0.111278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.8564 | − | 37.8564i | 0.782084 | − | 1.35461i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.75410 | + | 1.59008i | 0.0982980 | + | 0.0567524i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.2128 | + | 15.1340i | −0.934386 | + | 0.539468i | −0.888196 | − | 0.459465i | \(-0.848041\pi\) |
−0.0461899 | + | 0.998933i | \(0.514708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.34795 | 0.0834836 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1436 | 0.821853 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.62536 | − | 1.51575i | 0.0929949 | − | 0.0536906i | −0.452781 | − | 0.891622i | \(-0.649568\pi\) |
0.545776 | + | 0.837931i | \(0.316235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.1769 | + | 31.8564i | 1.95202 | + | 1.12700i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1798 | − | 33.2204i | 0.676841 | − | 1.17232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.823085 | − | 1.42563i | −0.0290100 | − | 0.0502467i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 19.5959i | − | 0.688956i | −0.938794 | − | 0.344478i | \(-0.888056\pi\) | ||
0.938794 | − | 0.344478i | \(-0.111944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.4641i | − | 0.543018i | −0.962436 | − | 0.271509i | \(-0.912477\pi\) | ||
0.962436 | − | 0.271509i | \(-0.0875227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.06918 | + | 13.9762i | 0.282651 | + | 0.489566i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.46410 | + | 11.1962i | −0.226150 | + | 0.391704i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.6993 | + | 10.7961i | 0.652612 | + | 0.376785i | 0.789456 | − | 0.613807i | \(-0.210363\pi\) |
−0.136845 | + | 0.990593i | \(0.543696\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.6244 | − | 19.9904i | 1.20693 | − | 0.696821i | 0.244842 | − | 0.969563i | \(-0.421264\pi\) |
0.962087 | + | 0.272742i | \(0.0879306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.3692 | 1.89060 | 0.945302 | − | 0.326196i | \(-0.105767\pi\) | ||||
0.945302 | + | 0.326196i | \(0.105767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6795 | 0.544571 | 0.272286 | − | 0.962216i | \(-0.412220\pi\) | ||||
0.272286 | + | 0.962216i | \(0.412220\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.1528 | − | 23.1822i | 1.39121 | − | 0.803216i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.10512 | − | 1.21539i | −0.0728506 | − | 0.0420603i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.4911 | + | 45.8840i | −0.914575 | + | 1.58409i | −0.107053 | + | 0.994253i | \(0.534141\pi\) |
−0.807522 | + | 0.589837i | \(0.799192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3564 | − | 21.4019i | −0.426083 | − | 0.737997i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.17260i | − | 0.246745i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.05256i | 0.0361664i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.1798 | − | 33.2204i | −0.657476 | − | 1.13878i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.3038 | + | 23.0429i | −0.455515 | + | 0.788975i | −0.998718 | − | 0.0506264i | \(-0.983878\pi\) |
0.543203 | + | 0.839602i | \(0.317212\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.9802 | + | 19.0411i | 1.12658 | + | 0.650432i | 0.943073 | − | 0.332586i | \(-0.107921\pi\) |
0.183509 | + | 0.983018i | \(0.441255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0359 | − | 9.25833i | 0.547138 | − | 0.315890i | −0.200829 | − | 0.979626i | \(-0.564364\pi\) |
0.747967 | + | 0.663736i | \(0.231030\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.6302 | −0.361855 | −0.180927 | − | 0.983496i | \(-0.557910\pi\) | ||||
−0.180927 | + | 0.983496i | \(0.557910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.56922 | 0.325363 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.8473 | + | 29.3567i | −1.72488 | + | 0.995858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.7679 | + | 11.9904i | 0.703695 | + | 0.406279i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.23835 | − | 2.14488i | 0.0418638 | − | 0.0725102i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.6244 | − | 21.8660i | −0.426294 | − | 0.738363i | 0.570246 | − | 0.821474i | \(-0.306848\pi\) |
−0.996540 | + | 0.0831107i | \(0.973514\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.9038i | 0.434740i | 0.976089 | + | 0.217370i | \(0.0697478\pi\) | ||||
−0.976089 | + | 0.217370i | \(0.930252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.1244i | − | 0.811849i | −0.913907 | − | 0.405925i | \(-0.866950\pi\) | ||
0.913907 | − | 0.405925i | \(-0.133050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.93426 | − | 10.2784i | −0.199253 | − | 0.345116i | 0.749034 | − | 0.662532i | \(-0.230518\pi\) |
−0.948286 | + | 0.317416i | \(0.897185\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.464102 | − | 0.803848i | 0.0155655 | − | 0.0269602i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.2808 | + | 8.24504i | 0.477890 | + | 0.275910i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.5692 | − | 10.1436i | 0.587274 | − | 0.339063i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.10961 | 0.0370074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −89.5692 | −2.98398 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.79555 | + | 3.34607i | −0.192651 | + | 0.111227i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2128 | − | 27.2583i | −1.56768 | − | 0.905098i | −0.996439 | − | 0.0843124i | \(-0.973131\pi\) |
−0.571236 | − | 0.820786i | \(-0.693536\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.277401 | + | 0.480473i | −0.00919072 | + | 0.0159188i | −0.870584 | − | 0.492019i | \(-0.836259\pi\) |
0.861393 | + | 0.507938i | \(0.169592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.9282 | − | 25.8564i | −0.494051 | − | 0.855722i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.07055i | 0.0683757i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.0333i | 1.88136i | 0.339301 | + | 0.940678i | \(0.389809\pi\) | ||||
−0.339301 | + | 0.940678i | \(0.610191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.9391 | + | 24.1432i | 0.458810 | + | 0.794682i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.6962 | − | 21.9904i | 0.417447 | − | 0.723039i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5959 | − | 11.3137i | −0.642921 | − | 0.371191i | 0.142818 | − | 0.989749i | \(-0.454384\pi\) |
−0.785739 | + | 0.618558i | \(0.787717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3923 | − | 6.00000i | 0.340594 | − | 0.196642i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.7685 | 0.875424 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.21539 | 0.203048 | 0.101524 | − | 0.994833i | \(-0.467628\pi\) | ||||
0.101524 | + | 0.994833i | \(0.467628\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.6651 | + | 15.9725i | −0.901856 | + | 0.520687i | −0.877802 | − | 0.479024i | \(-0.840991\pi\) |
−0.0240544 | + | 0.999711i | \(0.507657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6410 | + | 6.14359i | 0.346519 | + | 0.200063i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.138701 | − | 0.240237i | 0.00450717 | − | 0.00780664i | −0.863763 | − | 0.503898i | \(-0.831899\pi\) |
0.868270 | + | 0.496092i | \(0.165232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2321 | + | 21.1865i | 0.397069 | + | 0.687744i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.9038i | − | 0.417995i | −0.977916 | − | 0.208997i | \(-0.932980\pi\) | ||
0.977916 | − | 0.208997i | \(-0.0670200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.1436i | 0.457676i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.45138 | − | 2.51386i | −0.0468674 | − | 0.0811768i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.3564 | + | 26.5981i | −0.495368 | + | 0.858002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0643712 | − | 0.0371647i | −0.00207218 | − | 0.00119638i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.1603 | + | 5.86603i | −0.326732 | + | 0.188639i | −0.654389 | − | 0.756158i | \(-0.727074\pi\) |
0.327657 | + | 0.944797i | \(0.393741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.6418 | 1.49681 | 0.748404 | − | 0.663243i | \(-0.230820\pi\) | ||||
0.748404 | + | 0.663243i | \(0.230820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.320508 | 0.0102750 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.00481 | + | 4.62158i | −0.256096 | + | 0.147857i | −0.622553 | − | 0.782578i | \(-0.713904\pi\) |
0.366456 | + | 0.930435i | \(0.380571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.3923 | + | 12.9282i | 0.715661 | + | 0.413187i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.0082 | − | 38.1194i | 0.701954 | − | 1.21582i | −0.265826 | − | 0.964021i | \(-0.585645\pi\) |
0.967780 | − | 0.251799i | \(-0.0810221\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.46410 | − | 12.9282i | −0.237826 | − | 0.411927i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.2939i | 1.40846i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.48334i | 0.237716i | 0.992911 | + | 0.118858i | \(0.0379233\pi\) | ||||
−0.992911 | + | 0.118858i | \(0.962077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.2456 | − | 22.9420i | −0.419912 | − | 0.727310i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.39230 | − | 5.87564i | 0.107435 | − | 0.186084i | −0.807295 | − | 0.590148i | \(-0.799069\pi\) |
0.914731 | + | 0.404064i | \(0.132403\pi\) | |||||||
\(998\) | 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 | 2592.2.s.g.1727.3 | 8 | ||
3.2 | odd | 2 | inner | 2592.2.s.g.1727.2 | 8 | ||
4.3 | odd | 2 | 2592.2.s.c.1727.3 | 8 | |||
9.2 | odd | 6 | 864.2.c.b.863.4 | yes | 8 | ||
9.4 | even | 3 | 2592.2.s.c.863.2 | 8 | |||
9.5 | odd | 6 | 2592.2.s.c.863.3 | 8 | |||
9.7 | even | 3 | 864.2.c.b.863.6 | yes | 8 | ||
12.11 | even | 2 | 2592.2.s.c.1727.2 | 8 | |||
36.7 | odd | 6 | 864.2.c.b.863.5 | yes | 8 | ||
36.11 | even | 6 | 864.2.c.b.863.3 | ✓ | 8 | ||
36.23 | even | 6 | inner | 2592.2.s.g.863.3 | 8 | ||
36.31 | odd | 6 | inner | 2592.2.s.g.863.2 | 8 | ||
72.11 | even | 6 | 1728.2.c.f.1727.5 | 8 | |||
72.29 | odd | 6 | 1728.2.c.f.1727.6 | 8 | |||
72.43 | odd | 6 | 1728.2.c.f.1727.3 | 8 | |||
72.61 | even | 6 | 1728.2.c.f.1727.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.b.863.3 | ✓ | 8 | 36.11 | even | 6 | ||
864.2.c.b.863.4 | yes | 8 | 9.2 | odd | 6 | ||
864.2.c.b.863.5 | yes | 8 | 36.7 | odd | 6 | ||
864.2.c.b.863.6 | yes | 8 | 9.7 | even | 3 | ||
1728.2.c.f.1727.3 | 8 | 72.43 | odd | 6 | |||
1728.2.c.f.1727.4 | 8 | 72.61 | even | 6 | |||
1728.2.c.f.1727.5 | 8 | 72.11 | even | 6 | |||
1728.2.c.f.1727.6 | 8 | 72.29 | odd | 6 | |||
2592.2.s.c.863.2 | 8 | 9.4 | even | 3 | |||
2592.2.s.c.863.3 | 8 | 9.5 | odd | 6 | |||
2592.2.s.c.1727.2 | 8 | 12.11 | even | 2 | |||
2592.2.s.c.1727.3 | 8 | 4.3 | odd | 2 | |||
2592.2.s.g.863.2 | 8 | 36.31 | odd | 6 | inner | ||
2592.2.s.g.863.3 | 8 | 36.23 | even | 6 | inner | ||
2592.2.s.g.1727.2 | 8 | 3.2 | odd | 2 | inner | ||
2592.2.s.g.1727.3 | 8 | 1.1 | even | 1 | trivial |