Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(431,2592)]
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, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.p (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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.534694406811304329216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2159.8 | ||
Root | \(-1.40501 - 0.161069i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.2159 |
Dual form | 2592.2.p.f.431.8 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | 1.53819 | − | 2.66422i | 0.687899 | − | 1.19148i | −0.284617 | − | 0.958641i | \(-0.591867\pi\) |
0.972516 | − | 0.232835i | \(-0.0748002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.45632 | − | 1.99551i | 1.30637 | − | 0.754231i | 0.324879 | − | 0.945756i | \(-0.394677\pi\) |
0.981488 | + | 0.191525i | \(0.0613432\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64492 | + | 0.949697i | −0.495963 | + | 0.286344i | −0.727045 | − | 0.686590i | \(-0.759107\pi\) |
0.231082 | + | 0.972934i | \(0.425773\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.926118 | + | 0.534695i | 0.256859 | + | 0.148298i | 0.622901 | − | 0.782301i | \(-0.285954\pi\) |
−0.366042 | + | 0.930598i | \(0.619287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.08863i | − | 1.71925i | −0.510929 | − | 0.859623i | \(-0.670698\pi\) | ||
0.510929 | − | 0.859623i | \(-0.329302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.73205 | −0.856191 | −0.428096 | − | 0.903733i | \(-0.640815\pi\) | ||||
−0.428096 | + | 0.903733i | \(0.640815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.412157 | − | 0.713876i | 0.0859406 | − | 0.148853i | −0.819851 | − | 0.572577i | \(-0.805944\pi\) |
0.905792 | + | 0.423723i | \(0.139277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23205 | − | 3.86603i | −0.446410 | − | 0.773205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.25207 | − | 3.90069i | −0.418198 | − | 0.724340i | 0.577560 | − | 0.816348i | \(-0.304005\pi\) |
−0.995758 | + | 0.0920079i | \(0.970672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.06040 | + | 2.92163i | 0.908876 | + | 0.524740i | 0.880069 | − | 0.474845i | \(-0.157496\pi\) |
0.0288063 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 12.2779i | − | 2.07534i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.91264i | − | 1.13643i | −0.822880 | − | 0.568216i | \(-0.807634\pi\) | ||
0.822880 | − | 0.568216i | \(-0.192366\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.28985 | + | 1.89939i | 0.513788 | + | 0.296635i | 0.734389 | − | 0.678729i | \(-0.237469\pi\) |
−0.220602 | + | 0.975364i | \(0.570802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.48853 | + | 6.04232i | 0.508855 | + | 0.881363i | 0.999947 | + | 0.0102553i | \(0.00326442\pi\) |
−0.491092 | + | 0.871108i | \(0.663402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.46410 | − | 7.73205i | 0.637729 | − | 1.10458i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.6569 | −1.46384 | −0.731918 | − | 0.681393i | \(-0.761375\pi\) | ||||
−0.731918 | + | 0.681393i | \(0.761375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.84325i | 0.787904i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.64492 | + | 0.949697i | 0.214151 | + | 0.123640i | 0.603239 | − | 0.797561i | \(-0.293877\pi\) |
−0.389088 | + | 0.921201i | \(0.627210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.926118 | − | 0.534695i | 0.118577 | − | 0.0684606i | −0.439538 | − | 0.898224i | \(-0.644858\pi\) |
0.558116 | + | 0.829763i | \(0.311525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.84909 | − | 1.64492i | 0.353386 | − | 0.204028i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.59808 | + | 7.96410i | −0.561744 | + | 0.972970i | 0.435600 | + | 0.900140i | \(0.356536\pi\) |
−0.997344 | + | 0.0728295i | \(0.976797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6569 | −1.26474 | −0.632370 | − | 0.774667i | \(-0.717918\pi\) | ||||
−0.632370 | + | 0.774667i | \(0.717918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.92820 | 0.693844 | 0.346922 | − | 0.937894i | \(-0.387227\pi\) | ||||
0.346922 | + | 0.937894i | \(0.387227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.79025 | + | 6.56491i | −0.431940 | + | 0.748141i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.30856 | + | 3.06490i | −0.597259 | + | 0.344828i | −0.767963 | − | 0.640495i | \(-0.778729\pi\) |
0.170703 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.98803 | − | 5.18924i | 0.986564 | − | 0.569593i | 0.0823186 | − | 0.996606i | \(-0.473768\pi\) |
0.904245 | + | 0.427013i | \(0.140434\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.8857 | − | 10.9037i | −2.04844 | − | 1.18267i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.6683i | − | 1.44884i | −0.689359 | − | 0.724420i | \(-0.742108\pi\) | ||
0.689359 | − | 0.724420i | \(-0.257892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.26795 | 0.447403 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.74060 | + | 9.94301i | −0.588973 | + | 1.02013i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.69615 | + | 9.86603i | 0.578357 | + | 1.00174i | 0.995668 | + | 0.0929795i | \(0.0296391\pi\) |
−0.417311 | + | 0.908764i | \(0.637028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.07638 | + | 5.32844i | 0.306111 | + | 0.530200i | 0.977508 | − | 0.210898i | \(-0.0676388\pi\) |
−0.671397 | + | 0.741098i | \(0.734305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.45632 | + | 1.99551i | 0.340561 | + | 0.196623i | 0.660520 | − | 0.750808i | \(-0.270336\pi\) |
−0.319959 | + | 0.947431i | \(0.603669\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.47908i | − | 0.819704i | −0.912152 | − | 0.409852i | \(-0.865580\pi\) | ||
0.912152 | − | 0.409852i | \(-0.134420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1208i | 0.969398i | 0.874681 | + | 0.484699i | \(0.161071\pi\) | ||||
−0.874681 | + | 0.484699i | \(0.838929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.42878 | − | 5.44371i | −0.886985 | − | 0.512101i | −0.0140300 | − | 0.999902i | \(-0.504466\pi\) |
−0.872955 | + | 0.487800i | \(0.837799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.26795 | − | 2.19615i | −0.118237 | − | 0.204792i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1454 | − | 24.5006i | −1.29671 | − | 2.24597i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.69615 | + | 6.40192i | −0.336014 | + | 0.581993i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.64863 | 0.147458 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.98803 | − | 5.18924i | −0.785287 | − | 0.453386i | 0.0530134 | − | 0.998594i | \(-0.483117\pi\) |
−0.838301 | + | 0.545208i | \(0.816451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.8992 | + | 7.44734i | −1.11850 | + | 0.645766i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1270 | − | 8.73356i | 1.29238 | − | 0.746158i | 0.313307 | − | 0.949652i | \(-0.398563\pi\) |
0.979076 | + | 0.203494i | \(0.0652297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.59808 | + | 2.76795i | −0.135547 | + | 0.234774i | −0.925806 | − | 0.377998i | \(-0.876613\pi\) |
0.790259 | + | 0.612773i | \(0.209946\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.03119 | −0.169857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.8564 | −1.15071 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.07638 | + | 5.32844i | −0.252027 | + | 0.436523i | −0.964084 | − | 0.265599i | \(-0.914430\pi\) |
0.712057 | + | 0.702122i | \(0.247764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.51673 | + | 4.91713i | −0.693081 | + | 0.400151i | −0.804765 | − | 0.593593i | \(-0.797709\pi\) |
0.111684 | + | 0.993744i | \(0.464376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.5677 | − | 8.98803i | 1.25043 | − | 0.721936i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8857 | + | 10.9037i | 1.50724 | + | 0.870207i | 0.999965 | + | 0.00842371i | \(0.00268138\pi\) |
0.507277 | + | 0.861783i | \(0.330652\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.28985i | − | 0.259276i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.80385 | −0.689571 | −0.344785 | − | 0.938682i | \(-0.612048\pi\) | ||||
−0.344785 | + | 0.938682i | \(0.612048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0690 | − | 19.1721i | 0.856548 | − | 1.48359i | −0.0186530 | − | 0.999826i | \(-0.505938\pi\) |
0.875201 | − | 0.483759i | \(-0.160729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.92820 | − | 10.2679i | −0.456016 | − | 0.789842i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.824313 | − | 1.42775i | −0.0626714 | − | 0.108550i | 0.832987 | − | 0.553292i | \(-0.186629\pi\) |
−0.895659 | + | 0.444742i | \(0.853295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4294 | − | 8.90815i | −1.16635 | − | 0.673393i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.79879i | 0.283935i | 0.989871 | + | 0.141967i | \(0.0453428\pi\) | ||||
−0.989871 | + | 0.141967i | \(0.954657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.20817i | − | 0.238461i | −0.992867 | − | 0.119231i | \(-0.961957\pi\) | ||
0.992867 | − | 0.119231i | \(-0.0380428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.4168 | − | 10.6329i | −1.35403 | − | 0.781750i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.73205 | + | 11.6603i | 0.492296 | + | 0.852682i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.48853 | + | 6.04232i | 0.252421 | + | 0.437207i | 0.964192 | − | 0.265205i | \(-0.0854397\pi\) |
−0.711770 | + | 0.702412i | \(0.752106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.69615 | − | 4.66987i | 0.194073 | − | 0.336145i | −0.752523 | − | 0.658566i | \(-0.771163\pi\) |
0.946596 | + | 0.322421i | \(0.104497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.0305 | 1.21337 | 0.606687 | − | 0.794941i | \(-0.292498\pi\) | ||||
0.606687 | + | 0.794941i | \(0.292498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.6775i | − | 1.11135i | −0.831400 | − | 0.555675i | \(-0.812460\pi\) | ||
0.831400 | − | 0.555675i | \(-0.187540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.5677 | − | 8.98803i | −1.09264 | − | 0.630836i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.1208 | − | 5.84325i | 0.706868 | − | 0.408110i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.13894 | − | 3.54432i | 0.424639 | − | 0.245165i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5263 | − | 18.2321i | 0.724659 | − | 1.25515i | −0.234455 | − | 0.972127i | \(-0.575331\pi\) |
0.959114 | − | 0.283019i | \(-0.0913360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.15276 | 0.419614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.3205 | 1.58310 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.79025 | − | 6.56491i | 0.254960 | − | 0.441604i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5902 | − | 13.0424i | 1.51275 | − | 0.873386i | 0.512860 | − | 0.858472i | \(-0.328586\pi\) |
0.999889 | − | 0.0149140i | \(-0.00474744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.28985 | − | 1.89939i | 0.218355 | − | 0.126067i | −0.386833 | − | 0.922150i | \(-0.626431\pi\) |
0.605188 | + | 0.796082i | \(0.293098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1208 | + | 5.84325i | 0.668802 | + | 0.386133i | 0.795623 | − | 0.605793i | \(-0.207144\pi\) |
−0.126821 | + | 0.991926i | \(0.540477\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1773i | 0.928784i | 0.885630 | + | 0.464392i | \(0.153727\pi\) | ||||
−0.885630 | + | 0.464392i | \(0.846273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.4641 | 1.40016 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.15276 | + | 10.6569i | −0.397989 | + | 0.689337i | −0.993478 | − | 0.114027i | \(-0.963625\pi\) |
0.595489 | + | 0.803363i | \(0.296958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.69615 | + | 4.66987i | 0.173674 | + | 0.300813i | 0.939702 | − | 0.341995i | \(-0.111103\pi\) |
−0.766027 | + | 0.642808i | \(0.777769\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.7333 | − | 23.7867i | −0.877386 | − | 1.51968i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.45632 | − | 1.99551i | −0.219920 | − | 0.126971i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.1773i | − | 0.894861i | −0.894319 | − | 0.447431i | \(-0.852339\pi\) | ||
0.894319 | − | 0.447431i | \(-0.147661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.56569i | 0.0984344i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.28985 | + | 1.89939i | 0.205215 | + | 0.118481i | 0.599086 | − | 0.800685i | \(-0.295531\pi\) |
−0.393871 | + | 0.919166i | \(0.628864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.7942 | − | 23.8923i | −0.857132 | − | 1.48460i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.64863 | − | 2.85550i | −0.101659 | − | 0.176078i | 0.810710 | − | 0.585449i | \(-0.199082\pi\) |
−0.912368 | + | 0.409371i | \(0.865748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.3923 | + | 28.3923i | −1.00697 | + | 1.74413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.8860 | −1.21247 | −0.606236 | − | 0.795285i | \(-0.707321\pi\) | ||||
−0.606236 | + | 0.795285i | \(0.707321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9730i | 0.727311i | 0.931534 | + | 0.363655i | \(0.118471\pi\) | ||||
−0.931534 | + | 0.363655i | \(0.881529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.34310 | + | 4.23954i | 0.442806 | + | 0.255654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8857 | − | 10.9037i | 1.13473 | − | 0.655137i | 0.189611 | − | 0.981859i | \(-0.439277\pi\) |
0.945120 | + | 0.326722i | \(0.105944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.98803 | + | 5.18924i | −0.536181 | + | 0.309564i | −0.743530 | − | 0.668703i | \(-0.766850\pi\) |
0.207349 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.9282 | − | 24.1244i | 0.827946 | − | 1.43404i | −0.0717013 | − | 0.997426i | \(-0.522843\pi\) |
0.899647 | − | 0.436618i | \(-0.143824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.1610 | 0.894926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.2487 | −1.95581 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.79025 | + | 6.56491i | −0.221429 | + | 0.383526i | −0.955242 | − | 0.295825i | \(-0.904405\pi\) |
0.733813 | + | 0.679351i | \(0.237739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.06040 | − | 2.92163i | 0.294628 | − | 0.170104i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.763411 | − | 0.440756i | 0.0441492 | − | 0.0254896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.91264 | + | 3.99102i | 0.398438 | + | 0.230038i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.28985i | − | 0.188376i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9282 | −1.19444 | −0.597218 | − | 0.802079i | \(-0.703727\pi\) | ||||
−0.597218 | + | 0.802079i | \(0.703727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2447 | + | 17.7444i | −0.580925 | + | 1.00619i | 0.414445 | + | 0.910075i | \(0.363976\pi\) |
−0.995370 | + | 0.0961176i | \(0.969357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.69615 | − | 8.13397i | −0.265442 | − | 0.459759i | 0.702237 | − | 0.711943i | \(-0.252185\pi\) |
−0.967679 | + | 0.252184i | \(0.918851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.40482 | + | 14.5576i | 0.472062 | + | 0.817635i | 0.999489 | − | 0.0319652i | \(-0.0101766\pi\) |
−0.527427 | + | 0.849600i | \(0.676843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.40895 | + | 4.27756i | 0.414821 | + | 0.239497i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.4551i | 1.47200i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.77386i | − | 0.264806i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.1150 | + | 13.9228i | 1.32950 | + | 0.767589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.937822 | + | 1.62436i | 0.0515474 | + | 0.0892827i | 0.890648 | − | 0.454694i | \(-0.150251\pi\) |
−0.839100 | + | 0.543977i | \(0.816918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.1454 | + | 24.5006i | 0.772847 | + | 1.33861i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.69615 | − | 9.86603i | 0.310289 | − | 0.537437i | −0.668136 | − | 0.744039i | \(-0.732907\pi\) |
0.978425 | + | 0.206603i | \(0.0662408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0986 | −0.601025 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.69549i | − | 0.415517i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.57969 | + | 3.79879i | 0.353216 | + | 0.203930i | 0.666101 | − | 0.745862i | \(-0.267962\pi\) |
−0.312885 | + | 0.949791i | \(0.601295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.28205 | + | 1.31754i | −0.122155 | + | 0.0705264i | −0.559833 | − | 0.828606i | \(-0.689135\pi\) |
0.437677 | + | 0.899132i | \(0.355801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.57969 | − | 3.79879i | 0.350202 | − | 0.202189i | −0.314572 | − | 0.949233i | \(-0.601861\pi\) |
0.664774 | + | 0.747044i | \(0.268528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3923 | + | 28.3923i | −0.870013 | + | 1.50691i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.7867 | −1.25541 | −0.627707 | − | 0.778449i | \(-0.716007\pi\) | ||||
−0.627707 | + | 0.778449i | \(0.716007\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07180 | −0.266937 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.11870 | − | 15.7940i | 0.477294 | − | 0.826698i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.4628 | + | 18.7424i | −1.69455 | + | 0.978346i | −0.743785 | + | 0.668419i | \(0.766971\pi\) |
−0.950760 | + | 0.309927i | \(0.899695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.8336 | + | 21.2659i | −1.91231 | + | 1.10407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1073 | + | 9.29957i | 0.834006 | + | 0.481514i | 0.855222 | − | 0.518261i | \(-0.173421\pi\) |
−0.0212163 | + | 0.999775i | \(0.506754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.81667i | − | 0.248071i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2679 | 1.34929 | 0.674647 | − | 0.738141i | \(-0.264296\pi\) | ||||
0.674647 | + | 0.738141i | \(0.264296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.824313 | + | 1.42775i | −0.0421204 | + | 0.0729547i | −0.886317 | − | 0.463079i | \(-0.846745\pi\) |
0.844197 | + | 0.536034i | \(0.180078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.6603 | + | 20.1962i | 0.594262 | + | 1.02929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.69095 | + | 13.3211i | 0.389946 | + | 0.675407i | 0.992442 | − | 0.122715i | \(-0.0391602\pi\) |
−0.602496 | + | 0.798122i | \(0.705827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.06040 | − | 2.92163i | −0.255916 | − | 0.147753i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.8576i | 0.948827i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.1208i | 0.507949i | 0.967211 | + | 0.253974i | \(0.0817379\pi\) | ||||
−0.967211 | + | 0.253974i | \(0.918262\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.1594 | + | 7.59757i | 0.657148 | + | 0.379405i | 0.791190 | − | 0.611571i | \(-0.209462\pi\) |
−0.134041 | + | 0.990976i | \(0.542795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12436 | + | 5.41154i | 0.155635 | + | 0.269568i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.56491 | + | 11.3708i | 0.325411 | + | 0.563628i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.30385 | − | 7.45448i | 0.212812 | − | 0.368600i | −0.739782 | − | 0.672847i | \(-0.765071\pi\) |
0.952593 | + | 0.304246i | \(0.0984046\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.58051 | 0.373012 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 31.9281i | − | 1.56729i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.9108 | + | 13.2276i | 1.11927 | + | 0.646209i | 0.941214 | − | 0.337812i | \(-0.109687\pi\) |
0.178053 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.13429 | − | 2.38693i | 0.201493 | − | 0.116332i | −0.395859 | − | 0.918311i | \(-0.629553\pi\) |
0.597352 | + | 0.801979i | \(0.296220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.4048 | + | 15.8222i | −1.32933 | + | 0.767489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.13397 | − | 3.69615i | 0.103270 | − | 0.178869i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.382565 | 0.0184275 | 0.00921375 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921375 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53590 | 0.217981 | 0.108991 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108991 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.53819 | + | 2.66422i | −0.0735816 | + | 0.127447i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.4694 | + | 7.19918i | −0.595130 | + | 0.343598i | −0.767123 | − | 0.641500i | \(-0.778313\pi\) |
0.171994 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.6742 | + | 13.6683i | −1.12480 | + | 0.649402i | −0.942621 | − | 0.333864i | \(-0.891647\pi\) |
−0.182176 | + | 0.983266i | \(0.558314\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.4154 | − | 21.0245i | −1.72626 | − | 0.996655i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0468i | 1.13484i | 0.823429 | + | 0.567419i | \(0.192058\pi\) | ||||
−0.823429 | + | 0.567419i | \(0.807942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.21539 | −0.339759 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.56491 | − | 11.3708i | 0.307768 | − | 0.533070i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.19615 | − | 5.53590i | −0.149510 | − | 0.258958i | 0.781537 | − | 0.623859i | \(-0.214436\pi\) |
−0.931046 | + | 0.364901i | \(0.881103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.96594 | − | 5.13716i | −0.138138 | − | 0.239261i | 0.788654 | − | 0.614837i | \(-0.210778\pi\) |
−0.926792 | + | 0.375576i | \(0.877445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.10039 | − | 1.21266i | −0.0976134 | − | 0.0563571i | 0.450399 | − | 0.892828i | \(-0.351282\pi\) |
−0.548012 | + | 0.836470i | \(0.684615\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 19.8754i | − | 0.919726i | −0.887990 | − | 0.459863i | \(-0.847899\pi\) | ||
0.887990 | − | 0.459863i | \(-0.152101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.7020i | 1.69474i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.28985 | − | 1.89939i | −0.151267 | − | 0.0873342i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.33013 | + | 14.4282i | 0.382212 | + | 0.662011i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.07638 | − | 5.32844i | −0.140563 | − | 0.243463i | 0.787146 | − | 0.616767i | \(-0.211558\pi\) |
−0.927709 | + | 0.373304i | \(0.878225\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.69615 | − | 6.40192i | 0.168530 | − | 0.291903i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.0470 | 1.59140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.2073i | 1.50477i | 0.658726 | + | 0.752383i | \(0.271096\pi\) | ||||
−0.658726 | + | 0.752383i | \(0.728904\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6090 | + | 16.5174i | 1.29111 | + | 0.745420i | 0.978850 | − | 0.204578i | \(-0.0655821\pi\) |
0.312256 | + | 0.949998i | \(0.398915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.6506 | + | 15.9641i | −1.24532 | + | 0.718985i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.8336 | + | 21.2659i | −1.65221 | + | 0.953906i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.80385 | + | 4.85641i | −0.125517 | + | 0.217403i | −0.921935 | − | 0.387344i | \(-0.873392\pi\) |
0.796418 | + | 0.604747i | \(0.206726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.4977 | 1.31524 | 0.657619 | − | 0.753351i | \(-0.271564\pi\) | ||||
0.657619 | + | 0.753351i | \(0.271564\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.9282 | 0.842294 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.110437 | − | 0.191282i | 0.00489503 | − | 0.00847845i | −0.863568 | − | 0.504233i | \(-0.831775\pi\) |
0.868463 | + | 0.495755i | \(0.165109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4898 | − | 11.8298i | 0.906414 | − | 0.523318i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6329 | − | 6.13894i | 0.468544 | − | 0.270514i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4767 | − | 6.62610i | −0.504746 | − | 0.291416i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.08863i | − | 0.310559i | −0.987871 | − | 0.155279i | \(-0.950372\pi\) | ||
0.987871 | − | 0.155279i | \(-0.0496278\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5885 | 1.64363 | 0.821814 | − | 0.569756i | \(-0.192962\pi\) | ||||
0.821814 | + | 0.569756i | \(0.192962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7103 | − | 35.8713i | 0.902156 | − | 1.56258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1603 | + | 19.3301i | 0.485228 | + | 0.840440i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.03119 | + | 3.51813i | 0.0879806 | + | 0.152387i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.5902 | − | 13.0424i | −0.976658 | − | 0.563874i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.9582i | 0.730440i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.5632i | − | 1.48599i | −0.669298 | − | 0.742994i | \(-0.733405\pi\) | ||
0.669298 | − | 0.742994i | \(-0.266595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.9641 | + | 15.5677i | 1.15501 | + | 0.666848i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7942 | − | 27.3564i | −0.675312 | − | 1.16968i | −0.976377 | − | 0.216072i | \(-0.930675\pi\) |
0.301065 | − | 0.953604i | \(-0.402658\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.40482 | + | 14.5576i | 0.358057 | + | 0.620174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2321 | + | 21.1865i | −0.520160 | + | 0.900943i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.9401 | 0.633034 | 0.316517 | − | 0.948587i | \(-0.397487\pi\) | ||||
0.316517 | + | 0.948587i | \(0.397487\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.13878i | 0.0904607i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.2539 | − | 17.4671i | −1.27505 | − | 0.736151i | −0.299117 | − | 0.954217i | \(-0.596692\pi\) |
−0.975934 | + | 0.218066i | \(0.930025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.0065 | + | 16.7469i | −1.22031 | + | 0.704548i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.25742 | − | 3.03538i | 0.220403 | − | 0.127250i | −0.385734 | − | 0.922610i | \(-0.626052\pi\) |
0.606137 | + | 0.795360i | \(0.292718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.59808 | + | 2.76795i | −0.0668774 | + | 0.115835i | −0.897525 | − | 0.440963i | \(-0.854637\pi\) |
0.830648 | + | 0.556798i | \(0.187970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.67982 | −0.153459 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9282 | 0.496578 | 0.248289 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248289 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7103 | − | 35.8713i | 0.859209 | − | 1.48819i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.5298 | − | 10.1208i | 0.726008 | − | 0.419161i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.6090 | + | 16.5174i | −1.18082 | + | 0.681747i | −0.956204 | − | 0.292701i | \(-0.905446\pi\) |
−0.224616 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.8857 | − | 10.9037i | −0.778171 | − | 0.449277i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.7330i | 1.59057i | 0.606233 | + | 0.795287i | \(0.292680\pi\) | ||||
−0.606233 | + | 0.795287i | \(0.707320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −87.0333 | −3.56802 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2603 | − | 19.5035i | 0.460084 | − | 0.796890i | −0.538880 | − | 0.842382i | \(-0.681152\pi\) |
0.998965 | + | 0.0454928i | \(0.0144858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1962 | − | 26.3205i | −0.619864 | − | 1.07364i | −0.989510 | − | 0.144463i | \(-0.953854\pi\) |
0.369646 | − | 0.929173i | \(-0.379479\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3708 | + | 19.6947i | 0.462287 | + | 0.800705i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6106 | + | 17.6730i | 1.24245 | + | 0.717326i | 0.969591 | − | 0.244729i | \(-0.0786992\pi\) |
0.272854 | + | 0.962056i | \(0.412032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.46120i | 0.301848i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.91264i | 0.279199i | 0.990208 | + | 0.139599i | \(0.0445815\pi\) | ||||
−0.990208 | + | 0.139599i | \(0.955418\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.9965 | − | 14.4317i | −1.00632 | − | 0.581000i | −0.0962087 | − | 0.995361i | \(-0.530672\pi\) |
−0.910112 | + | 0.414361i | \(0.864005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5981 | + | 32.2128i | 0.747520 | + | 1.29474i | 0.949008 | + | 0.315251i | \(0.102089\pi\) |
−0.201488 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.2752 | − | 47.2421i | −1.09276 | − | 1.89272i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.6962 | − | 23.7224i | 0.547846 | − | 0.948897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.0012 | −1.95380 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0939i | 0.879542i | 0.898110 | + | 0.439771i | \(0.144940\pi\) | ||||
−0.898110 | + | 0.439771i | \(0.855060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.26857 | − | 4.77386i | 0.327613 | − | 0.189147i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.2539 | + | 17.4671i | −1.19496 | + | 0.689909i | −0.959427 | − | 0.281957i | \(-0.909016\pi\) |
−0.235531 | + | 0.971867i | \(0.575683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.39230 | + | 16.2679i | −0.370396 | + | 0.641545i | −0.989626 | − | 0.143664i | \(-0.954111\pi\) |
0.619230 | + | 0.785210i | \(0.287445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.7720 | 1.56360 | 0.781800 | − | 0.623529i | \(-0.214302\pi\) | ||||
0.781800 | + | 0.623529i | \(0.214302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60770 | −0.141614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2062 | + | 28.0700i | −0.634198 | + | 1.09846i | 0.352487 | + | 0.935817i | \(0.385336\pi\) |
−0.986685 | + | 0.162646i | \(0.947997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.6506 | + | 15.9641i | −1.08040 | + | 0.623767i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8576 | − | 10.8874i | 0.734586 | − | 0.424114i | −0.0855113 | − | 0.996337i | \(-0.527252\pi\) |
0.820098 | + | 0.572224i | \(0.193919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1938 | + | 22.6285i | 1.52446 | + | 0.880149i | 0.999580 | + | 0.0289735i | \(0.00922385\pi\) |
0.524882 | + | 0.851175i | \(0.324109\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.8216i | 1.77689i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.71281 | −0.143761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.01560 | + | 1.75906i | −0.0392066 | + | 0.0679079i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.6244 | − | 30.5263i | −0.679369 | − | 1.17670i | −0.975171 | − | 0.221452i | \(-0.928920\pi\) |
0.295802 | − | 0.955249i | \(-0.404413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.2485 | + | 38.5356i | 0.855080 | + | 1.48104i | 0.876571 | + | 0.481273i | \(0.159826\pi\) |
−0.0214905 | + | 0.999769i | \(0.506841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.3755 | + | 22.7334i | 1.51109 | + | 0.872429i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.7509i | 1.52103i | 0.649323 | + | 0.760513i | \(0.275052\pi\) | ||||
−0.649323 | + | 0.760513i | \(0.724948\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 53.7354i | − | 2.05313i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.86954 | − | 5.69818i | −0.375999 | − | 0.217083i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.92820 | + | 3.33975i | 0.0733523 | + | 0.127050i | 0.900369 | − | 0.435128i | \(-0.143297\pi\) |
−0.827016 | + | 0.562178i | \(0.809964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.91629 | + | 8.51526i | 0.186485 | + | 0.323002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4641 | − | 23.3205i | 0.509989 | − | 0.883327i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 51.8567 | 1.95860 | 0.979300 | − | 0.202415i | \(-0.0648790\pi\) | ||||
0.979300 | + | 0.202415i | \(0.0648790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7983i | 0.973002i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.2659 | + | 12.2779i | 0.799786 | + | 0.461757i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.4289 | − | 17.5681i | 1.14278 | − | 0.659786i | 0.195664 | − | 0.980671i | \(-0.437314\pi\) |
0.947118 | + | 0.320885i | \(0.103980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.17136 | − | 2.40833i | 0.156219 | − | 0.0901928i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.12436 | + | 5.41154i | −0.116844 | + | 0.202380i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.80138 | −0.290942 | −0.145471 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9282 | 0.593197 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0534 | + | 17.4131i | −0.373376 | + | 0.646706i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5902 | − | 13.0424i | 0.837823 | − | 0.483717i | −0.0187009 | − | 0.999825i | \(-0.505953\pi\) |
0.856524 | + | 0.516108i | \(0.172620\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.2779 | − | 7.08863i | 0.454113 | − | 0.262183i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4767 | − | 6.62610i | −0.423903 | − | 0.244741i | 0.272843 | − | 0.962059i | \(-0.412036\pi\) |
−0.696746 | + | 0.717318i | \(0.745369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 17.4671i | − | 0.643409i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6410 | 0.759292 | 0.379646 | − | 0.925132i | \(-0.376046\pi\) | ||||
0.379646 | + | 0.925132i | \(0.376046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.8475 | + | 44.7692i | −0.948253 | + | 1.64242i | −0.199148 | + | 0.979969i | \(0.563818\pi\) |
−0.749104 | + | 0.662452i | \(0.769516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.46410 | + | 16.3923i | 0.346738 | + | 0.600568i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9201 | − | 29.3064i | −0.618246 | − | 1.07083i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2816 | − | 9.97754i | −0.630615 | − | 0.364086i | 0.150375 | − | 0.988629i | \(-0.451952\pi\) |
−0.780990 | + | 0.624543i | \(0.785285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.2539i | 1.10105i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 52.0930i | − | 1.89335i | −0.322189 | − | 0.946675i | \(-0.604419\pi\) | ||
0.322189 | − | 0.946675i | \(-0.395581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.2744 | + | 21.5204i | 1.35119 | + | 0.780113i | 0.988417 | − | 0.151763i | \(-0.0484950\pi\) |
0.362778 | + | 0.931876i | \(0.381828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.1962 | + | 34.9808i | 0.731150 | + | 1.26639i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.01560 | + | 1.75906i | 0.0366710 | + | 0.0635161i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.03590 | + | 3.52628i | −0.0734164 | + | 0.127161i | −0.900397 | − | 0.435070i | \(-0.856724\pi\) |
0.826980 | + | 0.562231i | \(0.190057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.7179 | 1.60839 | 0.804196 | − | 0.594364i | \(-0.202596\pi\) | ||||
0.804196 | + | 0.594364i | \(0.202596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.0849i | − | 0.936996i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.2779 | − | 7.08863i | −0.439900 | − | 0.253977i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5298 | − | 10.1208i | 0.627264 | − | 0.362151i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.0995 | − | 33.5438i | 2.07366 | − | 1.19723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.72243 | − | 6.44744i | 0.132690 | − | 0.229826i | −0.792022 | − | 0.610492i | \(-0.790972\pi\) |
0.924713 | + | 0.380666i | \(0.124305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.4519 | −1.54497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.7333 | + | 23.7867i | −0.486457 | + | 0.842569i | −0.999879 | − | 0.0155679i | \(-0.995044\pi\) |
0.513422 | + | 0.858136i | \(0.328378\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.8318 | − | 24.7289i | 1.51528 | − | 0.874847i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.75144 | + | 5.62999i | −0.344121 | + | 0.198678i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.76488 | − | 5.06040i | −0.308921 | − | 0.178356i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.1773i | 0.498446i | 0.968446 | + | 0.249223i | \(0.0801752\pi\) | ||||
−0.968446 | + | 0.249223i | \(0.919825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.0718 | 0.950619 | 0.475310 | − | 0.879819i | \(-0.342336\pi\) | ||||
0.475310 | + | 0.879819i | \(0.342336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5420 | + | 23.4554i | −0.474355 | + | 0.821607i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.73205 | − | 6.46410i | −0.130568 | − | 0.226150i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.43888 | − | 9.42042i | −0.189818 | − | 0.328775i | 0.755371 | − | 0.655297i | \(-0.227457\pi\) |
−0.945190 | + | 0.326522i | \(0.894123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9861 | + | 12.1163i | 0.731529 | + | 0.422348i | 0.818981 | − | 0.573820i | \(-0.194539\pi\) |
−0.0874525 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.6324i | 1.41293i | 0.707749 | + | 0.706464i | \(0.249711\pi\) | ||||
−0.707749 | + | 0.706464i | \(0.750289\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5632i | 1.20043i | 0.799839 | + | 0.600215i | \(0.204918\pi\) | ||||
−0.799839 | + | 0.600215i | \(0.795082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −54.8097 | − | 31.6444i | −1.89904 | − | 1.09641i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.0526 | − | 58.9808i | −1.17844 | − | 2.04111i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5264 | + | 21.6963i | 0.432459 | + | 0.749041i | 0.997084 | − | 0.0763065i | \(-0.0243127\pi\) |
−0.564626 | + | 0.825347i | \(0.690979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.35641 | − | 7.54552i | 0.150221 | − | 0.260190i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.4748 | −1.25477 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.5028i | 1.01373i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.93477 | − | 2.84909i | −0.169162 | − | 0.0976655i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.8992 | − | 7.44734i | 0.441659 | − | 0.254992i | −0.262642 | − | 0.964893i | \(-0.584594\pi\) |
0.704301 | + | 0.709901i | \(0.251261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.881512 | − | 0.508941i | 0.0301119 | − | 0.0173851i | −0.484869 | − | 0.874587i | \(-0.661133\pi\) |
0.514980 | + | 0.857202i | \(0.327799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.79423 | − | 10.0359i | 0.197697 | − | 0.342420i | −0.750085 | − | 0.661342i | \(-0.769987\pi\) |
0.947781 | + | 0.318921i | \(0.103321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.9853 | −0.544147 | −0.272073 | − | 0.962276i | \(-0.587709\pi\) | ||||
−0.272073 | + | 0.962276i | \(0.587709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07180 | −0.172446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.82145 | − | 10.0830i | 0.197479 | − | 0.342044i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.51673 | + | 4.91713i | −0.288578 | + | 0.166611i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.69818 | − | 3.28985i | 0.192634 | − | 0.111217i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6036 | − | 9.58611i | −0.560665 | − | 0.323700i | 0.192747 | − | 0.981248i | \(-0.438260\pi\) |
−0.753412 | + | 0.657548i | \(0.771594\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.07075i | 0.204529i | 0.994757 | + | 0.102264i | \(0.0326088\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.1244 | −1.48490 | −0.742451 | − | 0.669900i | \(-0.766337\pi\) | ||||
−0.742451 | + | 0.669900i | \(0.766337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9090 | + | 22.3590i | −0.433440 | + | 0.750740i | −0.997167 | − | 0.0752210i | \(-0.976034\pi\) |
0.563727 | + | 0.825961i | \(0.309367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0194 | − | 22.5502i | −0.435677 | − | 0.754615i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1208 | + | 5.84325i | 0.338301 | + | 0.195318i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 26.3188i | − | 0.877780i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.5427i | 2.51669i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.54727 | − | 4.93477i | −0.284121 | − | 0.164037i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.1865 | − | 40.1603i | −0.769896 | − | 1.33350i | −0.937619 | − | 0.347665i | \(-0.886975\pi\) |
0.167723 | − | 0.985834i | \(-0.446359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.220874 | − | 0.382565i | −0.00731788 | − | 0.0126749i | 0.862343 | − | 0.506324i | \(-0.168996\pi\) |
−0.869661 | + | 0.493649i | \(0.835663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.85641 | + | 17.0718i | −0.326199 | + | 0.564994i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.4207 | −1.36783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 58.0130i | − | 1.91367i | −0.290628 | − | 0.956836i | \(-0.593864\pi\) | ||
0.290628 | − | 0.956836i | \(-0.406136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.86954 | − | 5.69818i | −0.324860 | − | 0.187558i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.7244 | + | 15.4294i | −0.878694 | + | 0.507314i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.9761 | − | 10.3785i | 0.589775 | − | 0.340507i | −0.175233 | − | 0.984527i | \(-0.556068\pi\) |
0.765009 | + | 0.644020i | \(0.222735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.6603 | + | 28.8564i | −0.546018 | + | 0.945731i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.4207 | 1.35460 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3923 | −0.764193 | −0.382097 | − | 0.924122i | \(-0.624798\pi\) | ||||
−0.382097 | + | 0.924122i | \(0.624798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.33957 | − | 16.1766i | 0.304461 | − | 0.527342i | −0.672680 | − | 0.739934i | \(-0.734857\pi\) |
0.977141 | + | 0.212591i | \(0.0681902\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.71186 | − | 1.56569i | 0.0883104 | − | 0.0509860i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.3192 | − | 14.6180i | 0.822762 | − | 0.475022i | −0.0286060 | − | 0.999591i | \(-0.509107\pi\) |
0.851368 | + | 0.524569i | \(0.175773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.49022 | + | 3.16978i | 0.178220 | + | 0.102895i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.7041i | 0.508705i | 0.967112 | + | 0.254353i | \(0.0818624\pi\) | ||||
−0.967112 | + | 0.254353i | \(0.918138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4641 | 0.694562 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.8558 | − | 60.3719i | 1.12555 | − | 1.94951i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.57180 | + | 2.72243i | 0.0507031 | + | 0.0878204i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.29438 | − | 14.3663i | −0.267006 | − | 0.462467i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.51673 | − | 4.91713i | −0.273879 | − | 0.158124i | 0.356770 | − | 0.934192i | \(-0.383878\pi\) |
−0.630649 | + | 0.776068i | \(0.717211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 55.8275i | − | 1.79159i | −0.444466 | − | 0.895796i | \(-0.646607\pi\) | ||
0.444466 | − | 0.895796i | \(-0.353393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.7559i | 0.408935i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.3844 | + | 11.7689i | 0.652154 | + | 0.376521i | 0.789281 | − | 0.614032i | \(-0.210453\pi\) |
−0.137127 | + | 0.990554i | \(0.543787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9808 | + | 22.4833i | 0.414867 | + | 0.718571i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.6578 | + | 47.9047i | 0.882147 | + | 1.52792i | 0.848949 | + | 0.528475i | \(0.177236\pi\) |
0.0331982 | + | 0.999449i | \(0.489431\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.1962 | − | 45.3731i | 0.834679 | − | 1.44571i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.64863 | 0.0524233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 25.7983i | − | 0.819511i | −0.912195 | − | 0.409755i | \(-0.865614\pi\) | ||
0.912195 | − | 0.409755i | \(-0.134386\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.7684 | − | 24.1150i | −1.32415 | − | 0.764497i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.35593 | − | 0.782847i | 0.0429428 | − | 0.0247930i | −0.478375 | − | 0.878156i | \(-0.658774\pi\) |
0.521318 | + | 0.853363i | \(0.325441\pi\) | |||||||
\(998\) | 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.p.f.2159.8 | 16 | ||
3.2 | odd | 2 | inner | 2592.2.p.f.2159.2 | 16 | ||
4.3 | odd | 2 | 648.2.l.f.539.1 | 16 | |||
8.3 | odd | 2 | inner | 2592.2.p.f.2159.1 | 16 | ||
8.5 | even | 2 | 648.2.l.f.539.3 | 16 | |||
9.2 | odd | 6 | inner | 2592.2.p.f.431.1 | 16 | ||
9.4 | even | 3 | 864.2.f.a.431.2 | 8 | |||
9.5 | odd | 6 | 864.2.f.a.431.8 | 8 | |||
9.7 | even | 3 | inner | 2592.2.p.f.431.7 | 16 | ||
12.11 | even | 2 | 648.2.l.f.539.8 | 16 | |||
24.5 | odd | 2 | 648.2.l.f.539.6 | 16 | |||
24.11 | even | 2 | inner | 2592.2.p.f.2159.7 | 16 | ||
36.7 | odd | 6 | 648.2.l.f.107.6 | 16 | |||
36.11 | even | 6 | 648.2.l.f.107.3 | 16 | |||
36.23 | even | 6 | 216.2.f.a.107.4 | yes | 8 | ||
36.31 | odd | 6 | 216.2.f.a.107.5 | yes | 8 | ||
72.5 | odd | 6 | 216.2.f.a.107.6 | yes | 8 | ||
72.11 | even | 6 | inner | 2592.2.p.f.431.8 | 16 | ||
72.13 | even | 6 | 216.2.f.a.107.3 | ✓ | 8 | ||
72.29 | odd | 6 | 648.2.l.f.107.1 | 16 | |||
72.43 | odd | 6 | inner | 2592.2.p.f.431.2 | 16 | ||
72.59 | even | 6 | 864.2.f.a.431.1 | 8 | |||
72.61 | even | 6 | 648.2.l.f.107.8 | 16 | |||
72.67 | odd | 6 | 864.2.f.a.431.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.a.107.3 | ✓ | 8 | 72.13 | even | 6 | ||
216.2.f.a.107.4 | yes | 8 | 36.23 | even | 6 | ||
216.2.f.a.107.5 | yes | 8 | 36.31 | odd | 6 | ||
216.2.f.a.107.6 | yes | 8 | 72.5 | odd | 6 | ||
648.2.l.f.107.1 | 16 | 72.29 | odd | 6 | |||
648.2.l.f.107.3 | 16 | 36.11 | even | 6 | |||
648.2.l.f.107.6 | 16 | 36.7 | odd | 6 | |||
648.2.l.f.107.8 | 16 | 72.61 | even | 6 | |||
648.2.l.f.539.1 | 16 | 4.3 | odd | 2 | |||
648.2.l.f.539.3 | 16 | 8.5 | even | 2 | |||
648.2.l.f.539.6 | 16 | 24.5 | odd | 2 | |||
648.2.l.f.539.8 | 16 | 12.11 | even | 2 | |||
864.2.f.a.431.1 | 8 | 72.59 | even | 6 | |||
864.2.f.a.431.2 | 8 | 9.4 | even | 3 | |||
864.2.f.a.431.7 | 8 | 72.67 | odd | 6 | |||
864.2.f.a.431.8 | 8 | 9.5 | odd | 6 | |||
2592.2.p.f.431.1 | 16 | 9.2 | odd | 6 | inner | ||
2592.2.p.f.431.2 | 16 | 72.43 | odd | 6 | inner | ||
2592.2.p.f.431.7 | 16 | 9.7 | even | 3 | inner | ||
2592.2.p.f.431.8 | 16 | 72.11 | even | 6 | inner | ||
2592.2.p.f.2159.1 | 16 | 8.3 | odd | 2 | inner | ||
2592.2.p.f.2159.2 | 16 | 3.2 | odd | 2 | inner | ||
2592.2.p.f.2159.7 | 16 | 24.11 | even | 2 | inner | ||
2592.2.p.f.2159.8 | 16 | 1.1 | even | 1 | trivial |