Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 16x^{14} + 174x^{12} + 1012x^{10} + 4243x^{8} + 9708x^{6} + 15858x^{4} + 12150x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(-1.38883 - 2.40552i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.449 |
Dual form | 2736.2.dc.c.1889.6 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00395 | − | 1.15698i | 0.896195 | − | 0.517418i | 0.0202309 | − | 0.999795i | \(-0.493560\pi\) |
0.875964 | + | 0.482377i | \(0.160227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.442911 | 0.167405 | 0.0837023 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0837023 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.35455i | 1.31295i | 0.754350 | + | 0.656473i | \(0.227952\pi\) | ||||
−0.754350 | + | 0.656473i | \(0.772048\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.90192 | + | 1.09807i | 0.527496 | + | 0.304550i | 0.739996 | − | 0.672611i | \(-0.234827\pi\) |
−0.212500 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.76720 | − | 1.02029i | 0.428608 | − | 0.247457i | −0.270145 | − | 0.962820i | \(-0.587072\pi\) |
0.698754 | + | 0.715362i | \(0.253738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76570 | − | 3.36911i | 0.634494 | − | 0.772928i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0969149 | − | 0.0559538i | −0.0202082 | − | 0.0116672i | 0.489862 | − | 0.871800i | \(-0.337047\pi\) |
−0.510070 | + | 0.860133i | \(0.670381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.177216 | − | 0.306946i | 0.0354431 | − | 0.0613893i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.77765 | − | 4.81103i | 0.515797 | − | 0.893387i | −0.484035 | − | 0.875049i | \(-0.660829\pi\) |
0.999832 | − | 0.0183379i | \(-0.00583747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50698i | 0.450267i | 0.974328 | + | 0.225134i | \(0.0722819\pi\) | ||||
−0.974328 | + | 0.225134i | \(0.927718\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.887572 | − | 0.512440i | 0.150027 | − | 0.0866181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93598i | 0.647071i | 0.946216 | + | 0.323536i | \(0.104872\pi\) | ||||
−0.946216 | + | 0.323536i | \(0.895128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.99745 | + | 5.19173i | 0.468123 | + | 0.810813i | 0.999336 | − | 0.0364253i | \(-0.0115971\pi\) |
−0.531213 | + | 0.847238i | \(0.678264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.54424 | − | 2.67470i | −0.235494 | − | 0.407888i | 0.723922 | − | 0.689882i | \(-0.242338\pi\) |
−0.959416 | + | 0.281994i | \(0.909004\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.99929 | + | 4.61839i | 1.16682 | + | 0.673661i | 0.952928 | − | 0.303197i | \(-0.0980539\pi\) |
0.213888 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80383 | −0.971976 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.77115 | + | 6.53182i | −0.518007 | + | 0.897215i | 0.481774 | + | 0.876296i | \(0.339993\pi\) |
−0.999781 | + | 0.0209193i | \(0.993341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.03813 | + | 8.72631i | 0.679342 | + | 1.17665i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.993498 | + | 1.72079i | 0.129342 | + | 0.224028i | 0.923422 | − | 0.383786i | \(-0.125380\pi\) |
−0.794080 | + | 0.607814i | \(0.792047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.98105 | − | 5.16332i | 0.381684 | − | 0.661096i | −0.609619 | − | 0.792694i | \(-0.708678\pi\) |
0.991303 | + | 0.131599i | \(0.0420110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.08180 | 0.630319 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.09793 | + | 1.78859i | 0.378472 | + | 0.218511i | 0.677153 | − | 0.735842i | \(-0.263213\pi\) |
−0.298681 | + | 0.954353i | \(0.596547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.86806 | + | 6.69968i | 0.459055 | + | 0.795106i | 0.998911 | − | 0.0466509i | \(-0.0148548\pi\) |
−0.539856 | + | 0.841757i | \(0.681521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.78179 | − | 8.28230i | −0.559666 | − | 0.969370i | −0.997524 | − | 0.0703259i | \(-0.977596\pi\) |
0.437858 | − | 0.899044i | \(-0.355737\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.92868i | 0.219793i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.17111 | − | 2.98554i | 0.581795 | − | 0.335900i | −0.180051 | − | 0.983657i | \(-0.557626\pi\) |
0.761847 | + | 0.647758i | \(0.224293\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.81116i | 0.308565i | 0.988027 | + | 0.154282i | \(0.0493066\pi\) | ||||
−0.988027 | + | 0.154282i | \(0.950693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.36092 | − | 4.08923i | 0.256078 | − | 0.443540i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.87202 | + | 10.1706i | −0.622432 | + | 1.07808i | 0.366599 | + | 0.930379i | \(0.380522\pi\) |
−0.989031 | + | 0.147706i | \(0.952811\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.842379 | + | 0.486348i | 0.0883053 | + | 0.0509831i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.64431 | − | 9.95140i | 0.168703 | − | 1.02099i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7441 | − | 6.20313i | 1.09090 | − | 0.629832i | 0.157085 | − | 0.987585i | \(-0.449790\pi\) |
0.933816 | + | 0.357753i | \(0.116457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.31021 | − | 0.756450i | −0.130371 | − | 0.0752696i | 0.433396 | − | 0.901203i | \(-0.357315\pi\) |
−0.563767 | + | 0.825934i | \(0.690648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.2916i | − | 1.40819i | −0.710106 | − | 0.704095i | \(-0.751353\pi\) | ||
0.710106 | − | 0.704095i | \(-0.248647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.20173 | −0.406197 | −0.203098 | − | 0.979158i | \(-0.565101\pi\) | ||||
−0.203098 | + | 0.979158i | \(0.565101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.49326 | − | 4.32623i | 0.717724 | − | 0.414378i | −0.0961906 | − | 0.995363i | \(-0.530666\pi\) |
0.813914 | + | 0.580985i | \(0.197333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9168 | 1.02696 | 0.513482 | − | 0.858100i | \(-0.328355\pi\) | ||||
0.513482 | + | 0.858100i | \(0.328355\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.258950 | −0.0241472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.782711 | − | 0.451898i | 0.0717510 | − | 0.0414254i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.96209 | −0.723826 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7497i | 0.961481i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.90866 | − | 2.83402i | −0.435573 | − | 0.251478i | 0.266145 | − | 0.963933i | \(-0.414250\pi\) |
−0.701718 | + | 0.712455i | \(0.747583\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.66663 | − | 5.00368i | 0.757207 | − | 0.437173i | −0.0710853 | − | 0.997470i | \(-0.522646\pi\) |
0.828292 | + | 0.560297i | \(0.189313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22496 | − | 1.49222i | 0.106217 | − | 0.129392i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.06189 | + | 2.34514i | 0.347031 | + | 0.200358i | 0.663377 | − | 0.748285i | \(-0.269123\pi\) |
−0.316346 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.89581 | − | 13.6759i | 0.669714 | − | 1.15998i | −0.308270 | − | 0.951299i | \(-0.599750\pi\) |
0.977984 | − | 0.208680i | \(-0.0669166\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78160 | + | 8.28198i | −0.399858 | + | 0.692574i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 12.8548i | − | 1.06753i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.31416 | + | 1.91343i | −0.271507 | + | 0.156754i | −0.629572 | − | 0.776942i | \(-0.716770\pi\) |
0.358065 | + | 0.933696i | \(0.383436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.5228i | − | 1.50736i | −0.657239 | − | 0.753682i | \(-0.728276\pi\) | ||
0.657239 | − | 0.753682i | \(-0.271724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.90053 | + | 5.02387i | 0.232977 | + | 0.403527i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1897 | + | 21.1131i | 0.972840 | + | 1.68501i | 0.686886 | + | 0.726765i | \(0.258977\pi\) |
0.285954 | + | 0.958243i | \(0.407690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0429246 | − | 0.0247826i | −0.00338294 | − | 0.00195314i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.4185 | −1.44265 | −0.721324 | − | 0.692598i | \(-0.756466\pi\) | ||||
−0.721324 | + | 0.692598i | \(0.756466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.78160 | − | 8.28198i | 0.370012 | − | 0.640879i | −0.619555 | − | 0.784953i | \(-0.712687\pi\) |
0.989567 | + | 0.144074i | \(0.0460204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.08848 | − | 7.08145i | −0.314498 | − | 0.544727i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.56321 | − | 16.5640i | −0.727077 | − | 1.25933i | −0.958113 | − | 0.286390i | \(-0.907545\pi\) |
0.231036 | − | 0.972945i | \(-0.425788\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0784907 | − | 0.135950i | 0.00593334 | − | 0.0102768i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.84289 | −0.735692 | −0.367846 | − | 0.929887i | \(-0.619905\pi\) | ||||
−0.367846 | + | 0.929887i | \(0.619905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6805 | + | 11.3626i | 1.46284 | + | 0.844572i | 0.999142 | − | 0.0414197i | \(-0.0131881\pi\) |
0.463700 | + | 0.885992i | \(0.346521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.55386 | + | 7.88752i | 0.334806 | + | 0.579902i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44291 | + | 7.69535i | 0.324898 | + | 0.562740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.9342i | 1.58710i | 0.608502 | + | 0.793552i | \(0.291771\pi\) | ||||
−0.608502 | + | 0.793552i | \(0.708229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.23065 | − | 5.32932i | 0.664437 | − | 0.383613i | −0.129529 | − | 0.991576i | \(-0.541346\pi\) |
0.793965 | + | 0.607963i | \(0.208013\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4637i | 0.888003i | 0.896026 | + | 0.444002i | \(0.146442\pi\) | ||||
−0.896026 | + | 0.444002i | \(0.853558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.64907 | − | 2.85627i | 0.116899 | − | 0.202476i | −0.801638 | − | 0.597810i | \(-0.796038\pi\) |
0.918537 | + | 0.395334i | \(0.129371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.23025 | − | 2.13086i | 0.0863468 | − | 0.149557i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0135 | + | 6.93599i | 0.839059 | + | 0.484431i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.6710 | + | 12.0434i | 1.01481 | + | 0.833056i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.10782 | + | 4.10370i | −0.489322 | + | 0.282510i | −0.724293 | − | 0.689492i | \(-0.757834\pi\) |
0.234971 | + | 0.972002i | \(0.424500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.18916 | − | 3.57332i | −0.422098 | − | 0.243698i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.11037i | 0.0753768i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.48141 | 0.301452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.3452 | + | 12.9010i | −1.49635 | + | 0.863916i | −0.999991 | − | 0.00420411i | \(-0.998662\pi\) |
−0.496355 | + | 0.868120i | \(0.665328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.4461 | 1.35705 | 0.678527 | − | 0.734576i | \(-0.262619\pi\) | ||||
0.678527 | + | 0.734576i | \(0.262619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.8292 | −1.11211 | −0.556053 | − | 0.831147i | \(-0.687685\pi\) | ||||
−0.556053 | + | 0.831147i | \(0.687685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7589 | − | 8.52104i | 0.966886 | − | 0.558232i | 0.0686005 | − | 0.997644i | \(-0.478147\pi\) |
0.898285 | + | 0.439412i | \(0.144813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3736 | 1.39426 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.873308i | 0.0564896i | 0.999601 | + | 0.0282448i | \(0.00899180\pi\) | ||||
−0.999601 | + | 0.0282448i | \(0.991008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8703 | − | 6.85330i | −0.764631 | − | 0.441460i | 0.0663249 | − | 0.997798i | \(-0.478873\pi\) |
−0.830956 | + | 0.556338i | \(0.812206\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.6345 | + | 7.87191i | −0.871079 | + | 0.502918i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.95964 | − | 3.37084i | 0.570089 | − | 0.214481i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.7744 | + | 7.95265i | 0.869432 | + | 0.501967i | 0.867159 | − | 0.498031i | \(-0.165943\pi\) |
0.00227233 | + | 0.999997i | \(0.499277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.243654 | − | 0.422021i | 0.0153184 | − | 0.0265322i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.34197 | − | 14.4487i | 0.520358 | − | 0.901286i | −0.479362 | − | 0.877617i | \(-0.659132\pi\) |
0.999720 | − | 0.0236687i | \(-0.00753467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.74329i | 0.108323i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.01480 | + | 4.05000i | −0.432551 | + | 0.249733i | −0.700433 | − | 0.713718i | \(-0.747010\pi\) |
0.267882 | + | 0.963452i | \(0.413676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.4526i | 1.07211i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.70165 | + | 8.14349i | 0.286664 | + | 0.496517i | 0.973011 | − | 0.230757i | \(-0.0741202\pi\) |
−0.686347 | + | 0.727274i | \(0.740787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.04408 | + | 7.00456i | 0.245661 | + | 0.425497i | 0.962317 | − | 0.271930i | \(-0.0876618\pi\) |
−0.716657 | + | 0.697426i | \(0.754328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.33661 | + | 0.771694i | 0.0806008 | + | 0.0465349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.6025 | −1.23788 | −0.618941 | − | 0.785438i | \(-0.712438\pi\) | ||||
−0.618941 | + | 0.785438i | \(0.712438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.75309 | − | 13.4287i | 0.462510 | − | 0.801091i | −0.536575 | − | 0.843853i | \(-0.680282\pi\) |
0.999085 | + | 0.0427613i | \(0.0136155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4307 | + | 23.2627i | 0.798372 | + | 1.38282i | 0.920676 | + | 0.390329i | \(0.127639\pi\) |
−0.122303 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.32760 | + | 2.29948i | 0.0783659 | + | 0.135734i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.41801 | + | 11.1163i | −0.377530 | + | 0.653901i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.25367 | −0.248502 | −0.124251 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124251 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.98184 | + | 2.29892i | 0.231832 | + | 0.133848i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.122883 | − | 0.212839i | −0.00710648 | − | 0.0123088i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.683960 | − | 1.18465i | −0.0394228 | − | 0.0682823i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13.7961i | − | 0.789961i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.9950 | + | 8.08003i | −0.798738 | + | 0.461152i | −0.843030 | − | 0.537867i | \(-0.819230\pi\) |
0.0442918 | + | 0.999019i | \(0.485897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.4966i | − | 1.67260i | −0.548272 | − | 0.836300i | \(-0.684714\pi\) | ||
0.548272 | − | 0.836300i | \(-0.315286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8233 | − | 20.4785i | 0.668291 | − | 1.15751i | −0.310091 | − | 0.950707i | \(-0.600360\pi\) |
0.978382 | − | 0.206806i | \(-0.0663070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.33946 | + | 12.7123i | −0.412225 | + | 0.713995i | −0.995133 | − | 0.0985437i | \(-0.968582\pi\) |
0.582908 | + | 0.812538i | \(0.301915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.9499 | + | 12.0954i | 1.17297 | + | 0.677214i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.45005 | − | 8.77571i | 0.0806829 | − | 0.488293i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.674098 | − | 0.389191i | 0.0373922 | − | 0.0215884i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.54297 | + | 2.04553i | 0.195330 | + | 0.112774i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 27.0043i | − | 1.48429i | −0.670238 | − | 0.742146i | \(-0.733808\pi\) | ||
0.670238 | − | 0.742146i | \(-0.266192\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.27747 | 0.452246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.27218 | − | 3.62125i | 0.341668 | − | 0.197262i | −0.319342 | − | 0.947640i | \(-0.603462\pi\) |
0.661009 | + | 0.750378i | \(0.270128\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.9168 | −0.591177 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.11386 | −0.330118 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.1501 | + | 7.01489i | −0.652254 | + | 0.376579i | −0.789319 | − | 0.613983i | \(-0.789566\pi\) |
0.137065 | + | 0.990562i | \(0.456233\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.7540 | −1.32505 | −0.662526 | − | 0.749039i | \(-0.730516\pi\) | ||||
−0.662526 | + | 0.749039i | \(0.730516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.21215i | 0.224190i | 0.993697 | + | 0.112095i | \(0.0357561\pi\) | ||||
−0.993697 | + | 0.112095i | \(0.964244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.5028 | + | 8.95056i | 0.822805 | + | 0.475047i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.82959 | + | 1.63366i | −0.149340 | + | 0.0862214i | −0.572808 | − | 0.819690i | \(-0.694146\pi\) |
0.423468 | + | 0.905911i | \(0.360813\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.70186 | − | 18.6359i | −0.194835 | − | 0.980836i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.1649 | − | 11.0649i | −1.00314 | − | 0.579163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.26245 | − | 2.18663i | 0.0658994 | − | 0.114141i | −0.831193 | − | 0.555984i | \(-0.812342\pi\) |
0.897093 | + | 0.441843i | \(0.145675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.67028 | + | 2.89301i | −0.0867168 | + | 0.150198i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.46572i | − | 0.0758922i | −0.999280 | − | 0.0379461i | \(-0.987918\pi\) | ||
0.999280 | − | 0.0379461i | \(-0.0120815\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5657 | − | 6.10012i | 0.544162 | − | 0.314172i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.0737i | − | 0.517450i | −0.965951 | − | 0.258725i | \(-0.916698\pi\) | ||
0.965951 | − | 0.258725i | \(-0.0833023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.807614 | + | 1.39883i | 0.0412671 | + | 0.0714768i | 0.885921 | − | 0.463836i | \(-0.153527\pi\) |
−0.844654 | + | 0.535312i | \(0.820194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.23144 | + | 3.86497i | 0.113725 | + | 0.196977i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.9026 | − | 12.0681i | −1.05981 | − | 0.611879i | −0.134427 | − | 0.990924i | \(-0.542919\pi\) |
−0.925378 | + | 0.379045i | \(0.876253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.228357 | −0.0115485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.90844 | − | 11.9658i | 0.347601 | − | 0.602063i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.61727 | − | 2.80119i | −0.0811682 | − | 0.140588i | 0.822584 | − | 0.568644i | \(-0.192532\pi\) |
−0.903752 | + | 0.428056i | \(0.859198\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5950 | − | 28.7433i | −0.828713 | − | 1.43537i | −0.899048 | − | 0.437850i | \(-0.855740\pi\) |
0.0703352 | − | 0.997523i | \(-0.477593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.75285 | + | 4.76807i | −0.137129 | + | 0.237514i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.1394 | −0.849570 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.9680 | − | 9.79650i | −0.839016 | − | 0.484406i | 0.0179139 | − | 0.999840i | \(-0.494298\pi\) |
−0.856929 | + | 0.515434i | \(0.827631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.440031 | + | 0.762156i | 0.0216525 | + | 0.0375032i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.25246 | + | 5.63343i | 0.159657 | + | 0.276534i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0352i | 0.587956i | 0.955812 | + | 0.293978i | \(0.0949793\pi\) | ||||
−0.955812 | + | 0.293978i | \(0.905021\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1141 | + | 7.57142i | −0.639142 | + | 0.369009i | −0.784284 | − | 0.620402i | \(-0.786969\pi\) |
0.145142 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 0.723247i | − | 0.0350826i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.32034 | − | 2.28689i | 0.0638956 | − | 0.110670i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.08531 | + | 12.2721i | −0.341287 | + | 0.591127i | −0.984672 | − | 0.174416i | \(-0.944196\pi\) |
0.643385 | + | 0.765543i | \(0.277530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4317 | + | 15.2604i | 1.27023 | + | 0.733366i | 0.975031 | − | 0.222070i | \(-0.0712814\pi\) |
0.295197 | + | 0.955436i | \(0.404615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.456552 | + | 0.171766i | −0.0218398 | + | 0.00821669i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.25778 | − | 2.45823i | 0.203213 | − | 0.117325i | −0.394940 | − | 0.918707i | \(-0.629235\pi\) |
0.598153 | + | 0.801382i | \(0.295901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.3646 | − | 14.0669i | −1.15760 | − | 0.668338i | −0.206869 | − | 0.978369i | \(-0.566327\pi\) |
−0.950727 | + | 0.310030i | \(0.899661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.1753i | 1.28823i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.56032 | 0.356794 | 0.178397 | − | 0.983959i | \(-0.442909\pi\) | ||||
0.178397 | + | 0.983959i | \(0.442909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.6077 | + | 13.0525i | −1.06455 | + | 0.614620i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.25078 | 0.105518 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8749 | 0.976486 | 0.488243 | − | 0.872708i | \(-0.337638\pi\) | ||||
0.488243 | + | 0.872708i | \(0.337638\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3048 | + | 8.83625i | −0.712817 | + | 0.411545i | −0.812103 | − | 0.583514i | \(-0.801677\pi\) |
0.0992862 | + | 0.995059i | \(0.468344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3998 | −1.13395 | −0.566977 | − | 0.823733i | \(-0.691887\pi\) | ||||
−0.566977 | + | 0.823733i | \(0.691887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.00332i | 0.231526i | 0.993277 | + | 0.115763i | \(0.0369313\pi\) | ||||
−0.993277 | + | 0.115763i | \(0.963069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.37211 | + | 0.792186i | 0.0633580 | + | 0.0365797i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6471 | − | 6.72447i | 0.535535 | − | 0.309191i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.544013 | − | 1.44598i | −0.0249610 | − | 0.0663461i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.8134 | − | 6.82045i | −0.539766 | − | 0.311634i | 0.205218 | − | 0.978716i | \(-0.434210\pi\) |
−0.744984 | + | 0.667082i | \(0.767543\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.32199 | + | 7.48590i | −0.197066 | + | 0.341328i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3538 | − | 24.8616i | 0.651774 | − | 1.12890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4543i | 0.972185i | 0.873907 | + | 0.486092i | \(0.161578\pi\) | ||||
−0.873907 | + | 0.486092i | \(0.838422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.7044 | + | 20.6140i | −1.61132 | + | 0.930295i | −0.622253 | + | 0.782816i | \(0.713782\pi\) |
−0.989065 | + | 0.147479i | \(0.952884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.3361i | − | 0.510551i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.71321 | + | 2.96736i | 0.0768479 | + | 0.133104i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.3512 | − | 31.7851i | −0.821511 | − | 1.42290i | −0.904557 | − | 0.426352i | \(-0.859798\pi\) |
0.0830465 | − | 0.996546i | \(-0.473535\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1080 | + | 10.4547i | 0.807396 | + | 0.466151i | 0.846051 | − | 0.533102i | \(-0.178974\pi\) |
−0.0386545 | + | 0.999253i | \(0.512307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.50080 | −0.155783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3608 | + | 23.1415i | −0.592205 | + | 1.02573i | 0.401729 | + | 0.915758i | \(0.368409\pi\) |
−0.993935 | + | 0.109971i | \(0.964924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.11791 | − | 3.66832i | −0.0936906 | − | 0.162277i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.5351 | − | 28.6396i | −0.728623 | − | 1.26201i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.1110 | + | 34.8333i | −0.884481 | + | 1.53197i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.78016 | −0.165612 | −0.0828059 | − | 0.996566i | \(-0.526388\pi\) | ||||
−0.0828059 | + | 0.996566i | \(0.526388\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.9565 | − | 6.32572i | −0.479093 | − | 0.276604i | 0.240945 | − | 0.970539i | \(-0.422543\pi\) |
−0.720038 | + | 0.693934i | \(0.755876\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.55785 | + | 4.43033i | 0.111422 | + | 0.192988i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4937 | − | 19.9077i | −0.499728 | − | 0.865554i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.1657i | 0.570268i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.42007 | + | 4.86133i | −0.364031 | + | 0.210174i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 29.6276i | − | 1.27615i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.87282 | + | 11.9041i | −0.295485 | + | 0.511796i | −0.975098 | − | 0.221776i | \(-0.928815\pi\) |
0.679612 | + | 0.733571i | \(0.262148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0107 | − | 17.3391i | 0.428813 | − | 0.742727i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3538 | − | 5.97776i | −0.442696 | − | 0.255591i | 0.262044 | − | 0.965056i | \(-0.415603\pi\) |
−0.704741 | + | 0.709465i | \(0.748937\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.52679 | − | 22.6641i | −0.363253 | − | 0.965522i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.29034 | − | 1.32233i | 0.0973952 | − | 0.0562311i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.5342 | − | 21.6704i | −1.59037 | − | 0.918203i | −0.993242 | − | 0.116060i | \(-0.962973\pi\) |
−0.597132 | − | 0.802143i | \(-0.703693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.78274i | − | 0.286879i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.49961 | 0.147491 | 0.0737455 | − | 0.997277i | \(-0.476505\pi\) | ||||
0.0737455 | + | 0.997277i | \(0.476505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.8767 | − | 12.6305i | 0.920360 | − | 0.531370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.6088 | 1.28319 | 0.641594 | − | 0.767045i | \(-0.278274\pi\) | ||||
0.641594 | + | 0.767045i | \(0.278274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.03663 | 0.0433816 | 0.0216908 | − | 0.999765i | \(-0.493095\pi\) | ||||
0.0216908 | + | 0.999765i | \(0.493095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0343497 | + | 0.0198318i | −0.00143248 | + | 0.000827043i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.8235 | −1.40809 | −0.704045 | − | 0.710155i | \(-0.748625\pi\) | ||||
−0.704045 | + | 0.710155i | \(0.748625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24509i | 0.0516552i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.4431 | − | 16.4217i | −1.17799 | − | 0.680115i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.5448 | + | 14.7483i | −1.05435 | + | 0.608728i | −0.923863 | − | 0.382722i | \(-0.874987\pi\) |
−0.130484 | + | 0.991450i | \(0.541653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.44631 | + | 6.93355i | 0.348024 | + | 0.285692i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.793776 | + | 0.458287i | 0.0325965 | + | 0.0188196i | 0.516210 | − | 0.856462i | \(-0.327343\pi\) |
−0.483613 | + | 0.875282i | \(0.660676\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.04568 | − | 1.81116i | 0.0428686 | − | 0.0742505i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.45145 | − | 11.1742i | 0.263599 | − | 0.456567i | −0.703597 | − | 0.710600i | \(-0.748424\pi\) |
0.967196 | + | 0.254033i | \(0.0817571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.13260i | − | 0.0869908i | −0.999054 | − | 0.0434954i | \(-0.986151\pi\) | ||
0.999054 | − | 0.0434954i | \(-0.0138494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.9556 | + | 9.21200i | −0.648689 | + | 0.374521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8985i | 1.09178i | 0.837858 | + | 0.545888i | \(0.183808\pi\) | ||||
−0.837858 | + | 0.545888i | \(0.816192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.1426 | + | 17.5676i | 0.410327 | + | 0.710708i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.19926 | + | 9.00538i | 0.209996 | + | 0.363724i | 0.951713 | − | 0.306989i | \(-0.0993216\pi\) |
−0.741717 | + | 0.670713i | \(0.765988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.3209 | − | 18.6605i | −1.30119 | − | 0.751243i | −0.320583 | − | 0.947220i | \(-0.603879\pi\) |
−0.980609 | + | 0.195977i | \(0.937212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.38013 | −0.0554721 | −0.0277361 | − | 0.999615i | \(-0.508830\pi\) | ||||
−0.0277361 | + | 0.999615i | \(0.508830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.60078 | + | 4.50468i | −0.104198 | + | 0.180476i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3233 | + | 23.0766i | 0.532931 | + | 0.923063i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.01585 | + | 6.95566i | 0.160122 | + | 0.277340i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.59458 | + | 11.4222i | −0.262526 | + | 0.454709i | −0.966913 | − | 0.255108i | \(-0.917889\pi\) |
0.704386 | + | 0.709817i | \(0.251222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.1156 | −0.520478 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.9403 | − | 7.47109i | −0.512714 | − | 0.296015i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.14519 | + | 12.3758i | 0.282218 | + | 0.488816i | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) |
−0.689713 | + | 0.724083i | \(0.742263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.69241 | + | 8.12750i | 0.185051 | + | 0.320517i | 0.943594 | − | 0.331106i | \(-0.107422\pi\) |
−0.758543 | + | 0.651623i | \(0.774088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 31.2028i | − | 1.22671i | −0.789807 | − | 0.613355i | \(-0.789819\pi\) | ||
0.789807 | − | 0.613355i | \(-0.210181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.49326 | + | 4.32623i | −0.294136 | + | 0.169819i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.50143i | 0.293554i | 0.989170 | + | 0.146777i | \(0.0468899\pi\) | ||||
−0.989170 | + | 0.146777i | \(0.953110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5783 | − | 20.0543i | 0.452403 | − | 0.783585i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4317 | − | 30.1925i | 0.679041 | − | 1.17613i | −0.296229 | − | 0.955117i | \(-0.595729\pi\) |
0.975270 | − | 0.221017i | \(-0.0709376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1329 | + | 7.58227i | 0.510810 | + | 0.294916i | 0.733166 | − | 0.680049i | \(-0.238042\pi\) |
−0.222357 | + | 0.974965i | \(0.571375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.728285 | − | 4.40758i | 0.0282417 | − | 0.170919i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.538392 | + | 0.310841i | −0.0208466 | + | 0.0120358i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4839 | + | 12.9811i | 0.867983 | + | 0.501130i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 37.6595i | − | 1.45167i | −0.687870 | − | 0.725834i | \(-0.741454\pi\) | ||
0.687870 | − | 0.725834i | \(-0.258546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.3032 | −1.01091 | −0.505457 | − | 0.862852i | \(-0.668676\pi\) | ||||
−0.505457 | + | 0.862852i | \(0.668676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.75869 | − | 2.74743i | 0.182622 | − | 0.105437i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.0314 | 0.651690 | 0.325845 | − | 0.945423i | \(-0.394351\pi\) | ||||
0.325845 | + | 0.945423i | \(0.394351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8531 | 0.414676 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.3448 | + | 8.28198i | −0.546494 | + | 0.315518i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.8728 | −0.984247 | −0.492124 | − | 0.870525i | \(-0.663779\pi\) | ||||
−0.492124 | + | 0.870525i | \(0.663779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 36.5412i | − | 1.38609i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.5942 | + | 6.11655i | 0.401283 | + | 0.231681i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8947 | + | 9.75417i | −0.638105 | + | 0.368410i | −0.783884 | − | 0.620907i | \(-0.786764\pi\) |
0.145779 | + | 0.989317i | \(0.453431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2608 | + | 10.8857i | 0.500139 | + | 0.410563i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.580306 | − | 0.335040i | −0.0218247 | − | 0.0126005i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.39305 | − | 16.2692i | 0.352763 | − | 0.611004i | −0.633969 | − | 0.773358i | \(-0.718575\pi\) |
0.986733 | + | 0.162354i | \(0.0519087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.140275 | − | 0.242964i | 0.00525335 | − | 0.00909907i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.1289i | 0.827575i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.42192 | + | 4.86240i | −0.314085 | + | 0.181337i | −0.648753 | − | 0.760999i | \(-0.724709\pi\) |
0.334668 | + | 0.942336i | \(0.391376\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.32989i | − | 0.235737i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.984487 | − | 1.70518i | −0.0365629 | − | 0.0633288i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.51333 | − | 14.7455i | −0.315742 | − | 0.546881i | 0.663853 | − | 0.747863i | \(-0.268920\pi\) |
−0.979595 | + | 0.200982i | \(0.935587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.45795 | − | 3.15115i | −0.201870 | − | 0.116550i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.2345 | −0.968995 | −0.484497 | − | 0.874793i | \(-0.660997\pi\) | ||||
−0.484497 | + | 0.874793i | \(0.660997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.78850 | + | 13.4901i | −0.286893 | + | 0.496913i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0102 | + | 34.6587i | 0.736088 | + | 1.27494i | 0.954244 | + | 0.299028i | \(0.0966622\pi\) |
−0.218157 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.38094 | − | 11.0521i | −0.234094 | − | 0.405463i | 0.724915 | − | 0.688838i | \(-0.241879\pi\) |
−0.959009 | + | 0.283376i | \(0.908546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.42761 | + | 7.66885i | −0.162215 | + | 0.280965i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.86099 | −0.0679992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.1942 | + | 12.8138i | 0.809877 | + | 0.467583i | 0.846913 | − | 0.531731i | \(-0.178458\pi\) |
−0.0370362 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.4306 | − | 37.1188i | −0.779938 | − | 1.35089i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.13282 | + | 10.6224i | 0.222901 | + | 0.386076i | 0.955688 | − | 0.294383i | \(-0.0951140\pi\) |
−0.732787 | + | 0.680459i | \(0.761781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.1024i | − | 0.909962i | −0.890501 | − | 0.454981i | \(-0.849646\pi\) | ||
0.890501 | − | 0.454981i | \(-0.150354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.31884 | − | 1.91614i | 0.120150 | − | 0.0693687i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.36372i | 0.157565i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.18965 | − | 5.52464i | 0.115022 | − | 0.199224i | −0.802767 | − | 0.596293i | \(-0.796640\pi\) |
0.917788 | + | 0.397070i | \(0.129973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.50637 | + | 6.07322i | −0.126115 | + | 0.218438i | −0.922168 | − | 0.386789i | \(-0.873584\pi\) |
0.796053 | + | 0.605227i | \(0.206918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.769510 | + | 0.444277i | 0.0276416 | + | 0.0159589i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.7816 | + | 4.26001i | 0.923721 | + | 0.152631i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.1741 | + | 16.8437i | −1.04393 | + | 0.602714i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.8550 | + | 28.2064i | 1.74371 | + | 1.00673i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.2645i | 1.32834i | 0.747583 | + | 0.664168i | \(0.231214\pi\) | ||||
−0.747583 | + | 0.664168i | \(0.768786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.83516 | 0.171918 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3394 | − | 6.54680i | 0.402674 | − | 0.232484i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.90386 | 0.173704 | 0.0868518 | − | 0.996221i | \(-0.472319\pi\) | ||||
0.0868518 | + | 0.996221i | \(0.472319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8484 | 0.666809 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.0657 | − | 20.8225i | 1.27273 | − | 0.734811i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.114692 | −0.00404236 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 37.0689i | − | 1.30327i | −0.758531 | − | 0.651637i | \(-0.774083\pi\) | ||
0.758531 | − | 0.651637i | \(-0.225917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.2641 | + | 7.65801i | 0.465764 | + | 0.268909i | 0.714465 | − | 0.699671i | \(-0.246670\pi\) |
−0.248701 | + | 0.968580i | \(0.580004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.9098 | + | 21.3099i | −1.29289 | + | 0.746452i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2823 | − | 2.19469i | −0.464688 | − | 0.0767825i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.4866 | − | 22.7976i | −1.37809 | − | 0.795642i | −0.386163 | − | 0.922430i | \(-0.626200\pi\) |
−0.991930 | + | 0.126788i | \(0.959533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.1367 | + | 17.5573i | −0.353343 | + | 0.612008i | −0.986833 | − | 0.161743i | \(-0.948289\pi\) |
0.633490 | + | 0.773751i | \(0.281622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.03132 | + | 12.1786i | −0.244503 | + | 0.423492i | −0.961992 | − | 0.273078i | \(-0.911958\pi\) |
0.717489 | + | 0.696570i | \(0.245291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.5594i | 1.92966i | 0.262879 | + | 0.964829i | \(0.415328\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0237 | + | 6.94189i | −0.416597 | + | 0.240522i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 22.1289i | − | 0.765803i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.23353 | − | 12.5288i | −0.249729 | − | 0.432544i | 0.713721 | − | 0.700430i | \(-0.247008\pi\) |
−0.963451 | + | 0.267886i | \(0.913675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.930701 | − | 1.61202i | −0.0320931 | − | 0.0555870i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.3862 | − | 9.46060i | −0.563704 | − | 0.325454i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.52650 | −0.121172 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.220233 | − | 0.381455i | 0.00754950 | − | 0.0130761i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.25689 | + | 9.10519i | 0.179992 | + | 0.311756i | 0.941878 | − | 0.335956i | \(-0.109059\pi\) |
−0.761885 | + | 0.647712i | \(0.775726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.44649 | − | 5.96950i | −0.117730 | − | 0.203914i | 0.801138 | − | 0.598480i | \(-0.204228\pi\) |
−0.918868 | + | 0.394566i | \(0.870895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14881 | − | 1.98980i | 0.0391970 | − | 0.0678912i | −0.845761 | − | 0.533561i | \(-0.820853\pi\) |
0.884958 | + | 0.465670i | \(0.154187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.8213 | −1.38957 | −0.694787 | − | 0.719216i | \(-0.744501\pi\) | ||||
−0.694787 | + | 0.719216i | \(0.744501\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.3284 | − | 22.1289i | −1.30321 | − | 0.752406i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0007 | + | 22.5179i | 0.441018 | + | 0.763866i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92800 | + | 6.80349i | 0.133095 | + | 0.230527i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.76115i | 0.160956i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6606 | − | 15.9699i | 0.934032 | − | 0.539264i | 0.0459478 | − | 0.998944i | \(-0.485369\pi\) |
0.888085 | + | 0.459680i | \(0.152036\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.3540i | − | 1.12372i | −0.827231 | − | 0.561862i | \(-0.810085\pi\) | ||
0.827231 | − | 0.561862i | \(-0.189915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.8620 | − | 27.4739i | 0.533800 | − | 0.924569i | −0.465420 | − | 0.885090i | \(-0.654097\pi\) |
0.999220 | − | 0.0394792i | \(-0.0125699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.202841 | − | 0.351330i | 0.00681072 | − | 0.0117965i | −0.862600 | − | 0.505887i | \(-0.831165\pi\) |
0.869411 | + | 0.494090i | \(0.164499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.17410 | − | 1.25522i | −0.0729169 | − | 0.0420986i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.6835 | − | 14.1775i | 1.26103 | − | 0.474430i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.7247 | + | 11.3880i | −0.659323 | + | 0.380660i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0612 | + | 6.96353i | 0.402263 | + | 0.232247i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3907i | 0.512738i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52.5851 | 1.74799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6077 | − | 13.0525i | 0.750675 | − | 0.433402i | −0.0752627 | − | 0.997164i | \(-0.523980\pi\) |
0.825938 | + | 0.563761i | \(0.190646\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6992 | 1.34842 | 0.674212 | − | 0.738538i | \(-0.264483\pi\) | ||||
0.674212 | + | 0.738538i | \(0.264483\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.2413 | −0.405129 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.83854 | − | 2.21618i | 0.126760 | − | 0.0731848i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.1092 | −1.65295 | −0.826475 | − | 0.562973i | \(-0.809658\pi\) | ||||
−0.826475 | + | 0.562973i | \(0.809658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.9896i | 0.559221i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.20814 | + | 0.697517i | 0.0397233 | + | 0.0229342i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.94942 | − | 5.16695i | 0.293621 | − | 0.169522i | −0.345953 | − | 0.938252i | \(-0.612444\pi\) |
0.639574 | + | 0.768730i | \(0.279111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.8173 | + | 22.9229i | −0.616713 | + | 0.751267i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8068 | + | 10.2807i | 0.582343 | + | 0.336216i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2882 | + | 23.0159i | −0.434107 | + | 0.751896i | −0.997222 | − | 0.0744827i | \(-0.976269\pi\) |
0.563115 | + | 0.826378i | \(0.309603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.53979 | + | 11.3272i | −0.213191 | + | 0.369258i | −0.952711 | − | 0.303876i | \(-0.901719\pi\) |
0.739520 | + | 0.673134i | \(0.235052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.670875i | − | 0.0218467i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.3231 | + | 26.1673i | −1.47280 | + | 0.850324i | −0.999532 | − | 0.0305930i | \(-0.990260\pi\) |
−0.473272 | + | 0.880917i | \(0.656927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 21.0030i | − | 0.681785i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.9642 | + | 27.6508i | 0.517132 | + | 0.895699i | 0.999802 | + | 0.0198965i | \(0.00633368\pi\) |
−0.482670 | + | 0.875802i | \(0.660333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.3775 | + | 43.9551i | 0.821196 | + | 1.42235i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.79906 | + | 1.03869i | 0.0580946 | + | 0.0335409i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.7150 | 0.797259 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.3318 | − | 21.3594i | 0.396976 | − | 0.687583i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6781 | − | 28.8873i | −0.536331 | − | 0.928952i | −0.999098 | − | 0.0424724i | \(-0.986477\pi\) |
0.462767 | − | 0.886480i | \(-0.346857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.86806 | + | 6.69968i | 0.124132 | + | 0.215003i | 0.921393 | − | 0.388631i | \(-0.127052\pi\) |
−0.797261 | + | 0.603634i | \(0.793719\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.49714 | − | 6.05722i | 0.112113 | − | 0.194186i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.2249 | −1.03097 | −0.515483 | − | 0.856900i | \(-0.672387\pi\) | ||||
−0.515483 | + | 0.856900i | \(0.672387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44.2885 | − | 25.5700i | −1.41547 | − | 0.817220i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.33406 | − | 7.50682i | −0.138235 | − | 0.239430i | 0.788594 | − | 0.614915i | \(-0.210810\pi\) |
−0.926829 | + | 0.375485i | \(0.877476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4203 | + | 24.9767i | 0.459469 | + | 0.795824i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.345625i | 0.0109902i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3953 | − | 12.9299i | 0.711411 | − | 0.410733i | −0.100172 | − | 0.994970i | \(-0.531939\pi\) |
0.811583 | + | 0.584237i | \(0.198606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.63178i | − | 0.241944i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.41801 | + | 7.65222i | −0.139920 | + | 0.242348i | −0.927466 | − | 0.373907i | \(-0.878018\pi\) |
0.787546 | + | 0.616255i | \(0.211351\pi\) | |||||||
\(998\) | 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 | 2736.2.dc.c.449.6 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.c.449.3 | 16 | ||
4.3 | odd | 2 | 171.2.m.a.107.8 | yes | 16 | ||
12.11 | even | 2 | 171.2.m.a.107.1 | yes | 16 | ||
19.8 | odd | 6 | inner | 2736.2.dc.c.1889.3 | 16 | ||
57.8 | even | 6 | inner | 2736.2.dc.c.1889.6 | 16 | ||
76.27 | even | 6 | 171.2.m.a.8.1 | ✓ | 16 | ||
228.179 | odd | 6 | 171.2.m.a.8.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.m.a.8.1 | ✓ | 16 | 76.27 | even | 6 | ||
171.2.m.a.8.8 | yes | 16 | 228.179 | odd | 6 | ||
171.2.m.a.107.1 | yes | 16 | 12.11 | even | 2 | ||
171.2.m.a.107.8 | yes | 16 | 4.3 | odd | 2 | ||
2736.2.dc.c.449.3 | 16 | 3.2 | odd | 2 | inner | ||
2736.2.dc.c.449.6 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.c.1889.3 | 16 | 19.8 | odd | 6 | inner | ||
2736.2.dc.c.1889.6 | 16 | 57.8 | even | 6 | inner |