Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
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: | yes |
Analytic conductor: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 19 x^{9} + 33 x^{8} + 120 x^{7} - 178 x^{6} - 296 x^{5} + 380 x^{4} + 280 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.979305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0.979305 | 0.565402 | 0.282701 | − | 0.959208i | \(-0.408770\pi\) | ||||
0.282701 | + | 0.959208i | \(0.408770\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.33286 | 1.04329 | 0.521644 | − | 0.853163i | \(-0.325319\pi\) | ||||
0.521644 | + | 0.853163i | \(0.325319\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.04096 | −0.680320 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.28458 | 0.589877 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.60681 | −0.632244 | −0.316122 | − | 0.948719i | \(-0.602381\pi\) | ||||
−0.316122 | + | 0.948719i | \(0.602381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89553 | 0.664280 | 0.332140 | − | 0.943230i | \(-0.392229\pi\) | ||||
0.332140 | + | 0.943230i | \(0.392229\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.979305 | −0.213702 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.81847 | 0.796205 | 0.398103 | − | 0.917341i | \(-0.369669\pi\) | ||||
0.398103 | + | 0.917341i | \(0.369669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.442245 | 0.0884490 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.93664 | −0.950057 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10856 | −0.577245 | −0.288623 | − | 0.957443i | \(-0.593197\pi\) | ||||
−0.288623 | + | 0.957443i | \(0.593197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.32534 | −1.31567 | −0.657835 | − | 0.753162i | \(-0.728527\pi\) | ||||
−0.657835 | + | 0.753162i | \(0.728527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.979305 | 0.170475 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.33286 | −0.394326 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.46215 | −0.240376 | −0.120188 | − | 0.992751i | \(-0.538350\pi\) | ||||
−0.120188 | + | 0.992751i | \(0.538350\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.979305 | −0.156814 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.286060 | −0.0446750 | −0.0223375 | − | 0.999750i | \(-0.507111\pi\) | ||||
−0.0223375 | + | 0.999750i | \(0.507111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.21304 | −1.40497 | −0.702487 | − | 0.711696i | \(-0.747927\pi\) | ||||
−0.702487 | + | 0.711696i | \(0.747927\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.76128 | −0.709770 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.81847 | 0.556981 | 0.278490 | − | 0.960439i | \(-0.410166\pi\) | ||||
0.278490 | + | 0.960439i | \(0.410166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.55286 | −0.357472 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8763 | −1.63133 | −0.815666 | − | 0.578523i | \(-0.803629\pi\) | ||||
−0.815666 | + | 0.578523i | \(0.803629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.33286 | 0.314563 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.83561 | 0.375585 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.80563 | −1.27658 | −0.638292 | − | 0.769794i | \(-0.720359\pi\) | ||||
−0.638292 | + | 0.769794i | \(0.720359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26111 | 0.161469 | 0.0807343 | − | 0.996736i | \(-0.474273\pi\) | ||||
0.0807343 | + | 0.996736i | \(0.474273\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.04096 | 0.257137 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.33286 | −0.289356 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.93124 | −0.602447 | −0.301224 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301224 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.73944 | 0.450176 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2180 | 1.92472 | 0.962360 | − | 0.271780i | \(-0.0876122\pi\) | ||||
0.962360 | + | 0.271780i | \(0.0876122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.183169 | 0.0214383 | 0.0107191 | − | 0.999943i | \(-0.496588\pi\) | ||||
0.0107191 | + | 0.999943i | \(0.496588\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.433093 | 0.0500092 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7288 | −1.76963 | −0.884813 | − | 0.465947i | \(-0.845714\pi\) | ||||
−0.884813 | + | 0.465947i | \(0.845714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.28841 | 0.143156 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3290 | 1.68257 | 0.841286 | − | 0.540591i | \(-0.181799\pi\) | ||||
0.841286 | + | 0.540591i | \(0.181799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.08133 | −0.659612 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.04423 | −0.326376 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.7996 | −1.14476 | −0.572379 | − | 0.819989i | \(-0.693979\pi\) | ||||
−0.572379 | + | 0.819989i | \(0.693979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.17374 | −0.743882 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.75487 | 0.693035 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.70388 | 0.477606 | 0.238803 | − | 0.971068i | \(-0.423245\pi\) | ||||
0.238803 | + | 0.971068i | \(0.423245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.04096 | −0.205124 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6825 | −1.06294 | −0.531472 | − | 0.847076i | \(-0.678361\pi\) | ||||
−0.531472 | + | 0.847076i | \(0.678361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1224 | −1.29299 | −0.646494 | − | 0.762919i | \(-0.723766\pi\) | ||||
−0.646494 | + | 0.762919i | \(0.723766\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.28458 | −0.222953 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.16009 | −0.208824 | −0.104412 | − | 0.994534i | \(-0.533296\pi\) | ||||
−0.104412 | + | 0.994534i | \(0.533296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2998 | 1.27389 | 0.636945 | − | 0.770909i | \(-0.280198\pi\) | ||||
0.636945 | + | 0.770909i | \(0.280198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.43189 | −0.135909 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1758 | 1.14540 | 0.572701 | − | 0.819764i | \(-0.305895\pi\) | ||||
0.572701 | + | 0.819764i | \(0.305895\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.90795 | 0.830671 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.04096 | 0.188687 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.60681 | 0.238966 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.280140 | −0.0252593 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6326 | −0.951010 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.59695 | −0.141707 | −0.0708533 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708533 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.02237 | −0.794376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.72718 | 0.500386 | 0.250193 | − | 0.968196i | \(-0.419506\pi\) | ||||
0.250193 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89553 | −0.251074 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.5165 | −0.991182 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7036 | 1.17078 | 0.585390 | − | 0.810752i | \(-0.300941\pi\) | ||||
0.585390 | + | 0.810752i | \(0.300941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.16193 | −0.522648 | −0.261324 | − | 0.965251i | \(-0.584159\pi\) | ||||
−0.261324 | + | 0.965251i | \(0.584159\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.73944 | 0.314918 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.25185 | −0.602233 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.979305 | 0.0807717 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.66700 | 0.300413 | 0.150206 | − | 0.988655i | \(-0.452006\pi\) | ||||
0.150206 | + | 0.988655i | \(0.452006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4743 | −1.34066 | −0.670331 | − | 0.742062i | \(-0.733848\pi\) | ||||
−0.670331 | + | 0.742062i | \(0.733848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.32040 | 0.430129 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.0890 | −1.37262 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.898098 | −0.0716760 | −0.0358380 | − | 0.999358i | \(-0.511410\pi\) | ||||
−0.0358380 | + | 0.999358i | \(0.511410\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6305 | −0.922359 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.81847 | −0.300937 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.05949 | 0.474616 | 0.237308 | − | 0.971435i | \(-0.423735\pi\) | ||||
0.237308 | + | 0.971435i | \(0.423735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.28458 | 0.177855 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.96978 | −0.229809 | −0.114904 | − | 0.993377i | \(-0.536656\pi\) | ||||
−0.114904 | + | 0.993377i | \(0.536656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.90966 | −0.451923 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.79498 | −0.364556 | −0.182278 | − | 0.983247i | \(-0.558347\pi\) | ||||
−0.182278 | + | 0.983247i | \(0.558347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.442245 | −0.0334306 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.60271 | −0.721784 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6819 | −1.17212 | −0.586060 | − | 0.810268i | \(-0.699322\pi\) | ||||
−0.586060 | + | 0.810268i | \(0.699322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.5030 | 1.59830 | 0.799152 | − | 0.601129i | \(-0.205282\pi\) | ||||
0.799152 | + | 0.601129i | \(0.205282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.23501 | 0.0912946 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.41100 | −0.250782 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.60681 | −0.190629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.93664 | 0.359088 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9627 | −0.937951 | −0.468975 | − | 0.883211i | \(-0.655377\pi\) | ||||
−0.468975 | + | 0.883211i | \(0.655377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8808 | −0.783214 | −0.391607 | − | 0.920133i | \(-0.628081\pi\) | ||||
−0.391607 | + | 0.920133i | \(0.628081\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.28458 | −0.163602 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8956 | −1.06127 | −0.530635 | − | 0.847600i | \(-0.678046\pi\) | ||||
−0.530635 | + | 0.847600i | \(0.678046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.66656 | 0.118139 | 0.0590696 | − | 0.998254i | \(-0.481187\pi\) | ||||
0.0590696 | + | 0.998254i | \(0.481187\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.82919 | −0.340625 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.10856 | 0.218178 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.667338 | −0.0466089 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.79334 | −0.541675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.89553 | 0.200288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.7614 | −1.15390 | −0.576950 | − | 0.816780i | \(-0.695757\pi\) | ||||
−0.576950 | + | 0.816780i | \(0.695757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.8823 | 1.08824 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.4927 | −1.46579 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.32534 | 0.497276 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.179378 | 0.0121212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.60681 | 0.175353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.79512 | −0.321105 | −0.160552 | − | 0.987027i | \(-0.551328\pi\) | ||||
−0.160552 | + | 0.987027i | \(0.551328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.902605 | −0.0601736 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5168 | −0.764397 | −0.382199 | − | 0.924080i | \(-0.624833\pi\) | ||||
−0.382199 | + | 0.924080i | \(0.624833\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.1605 | 0.935754 | 0.467877 | − | 0.883794i | \(-0.345019\pi\) | ||||
0.467877 | + | 0.883794i | \(0.345019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.979305 | −0.0644335 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.8496 | −1.16936 | −0.584682 | − | 0.811263i | \(-0.698781\pi\) | ||||
−0.584682 | + | 0.811263i | \(0.698781\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.90795 | 0.581091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.4033 | −1.00055 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0009 | −1.61717 | −0.808587 | − | 0.588377i | \(-0.799767\pi\) | ||||
−0.808587 | + | 0.588377i | \(0.799767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.85076 | −0.248049 | −0.124025 | − | 0.992279i | \(-0.539580\pi\) | ||||
−0.124025 | + | 0.992279i | \(0.539580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0717 | 1.03100 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.33286 | 0.149041 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.89553 | −0.184238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0117 | 0.951329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6235 | 0.986144 | 0.493072 | − | 0.869989i | \(-0.335874\pi\) | ||||
0.493072 | + | 0.869989i | \(0.335874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.81847 | 0.240065 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.95547 | −0.372946 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.79105 | 0.236479 | 0.118239 | − | 0.992985i | \(-0.462275\pi\) | ||||
0.118239 | + | 0.992985i | \(0.462275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.46215 | 0.0908537 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.34445 | 0.392712 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8208 | 0.790563 | 0.395282 | − | 0.918560i | \(-0.370647\pi\) | ||||
0.395282 | + | 0.918560i | \(0.370647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.7057 | −1.70195 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.5761 | −0.647249 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.2682 | 1.05286 | 0.526430 | − | 0.850218i | \(-0.323530\pi\) | ||||
0.526430 | + | 0.850218i | \(0.323530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.99630 | 0.424995 | 0.212497 | − | 0.977162i | \(-0.431840\pi\) | ||||
0.212497 | + | 0.977162i | \(0.431840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.979305 | 0.0592702 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.442245 | 0.0266684 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.5108 | 1.29246 | 0.646228 | − | 0.763144i | \(-0.276345\pi\) | ||||
0.646228 | + | 0.763144i | \(0.276345\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.9507 | 0.895077 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7124 | 0.818013 | 0.409007 | − | 0.912531i | \(-0.365875\pi\) | ||||
0.409007 | + | 0.912531i | \(0.365875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.2520 | −1.56052 | −0.780259 | − | 0.625457i | \(-0.784913\pi\) | ||||
−0.780259 | + | 0.625457i | \(0.784913\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.61508 | 0.391844 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.286060 | 0.0168856 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2045 | −0.600267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.60653 | 0.270040 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.63462 | −0.153916 | −0.0769581 | − | 0.997034i | \(-0.524521\pi\) | ||||
−0.0769581 | + | 0.997034i | \(0.524521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.8752 | −1.33185 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.93664 | −0.286453 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.81847 | −0.220828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.21304 | 0.531031 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4614 | −0.600991 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.94199 | 0.168458 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6740 | −0.894565 | −0.447282 | − | 0.894393i | \(-0.647608\pi\) | ||||
−0.447282 | + | 0.894393i | \(0.647608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8508 | −0.731058 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.412463 | 0.0233886 | 0.0116943 | − | 0.999932i | \(-0.496277\pi\) | ||||
0.0116943 | + | 0.999932i | \(0.496277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1735 | −0.631563 | −0.315782 | − | 0.948832i | \(-0.602267\pi\) | ||||
−0.315782 | + | 0.948832i | \(0.602267\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.76128 | 0.268268 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.4553 | 1.03655 | 0.518276 | − | 0.855214i | \(-0.326574\pi\) | ||||
0.518276 | + | 0.855214i | \(0.326574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.10856 | −0.174046 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.11539 | −0.118070 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.54810 | −0.419987 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.442245 | −0.0245313 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.0246 | 0.720260 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.81847 | −0.210519 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1894 | −0.944815 | −0.472407 | − | 0.881380i | \(-0.656615\pi\) | ||||
−0.472407 | + | 0.881380i | \(0.656615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.98420 | 0.163533 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.5039 | −0.628526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.5406 | −1.17339 | −0.586697 | − | 0.809807i | \(-0.699572\pi\) | ||||
−0.586697 | + | 0.809807i | \(0.699572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9238 | 0.647613 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.32534 | −0.396689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.72361 | 0.469663 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.68411 | 0.412505 | 0.206252 | − | 0.978499i | \(-0.433873\pi\) | ||||
0.206252 | + | 0.978499i | \(0.433873\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8842 | −0.636145 | −0.318073 | − | 0.948066i | \(-0.603036\pi\) | ||||
−0.318073 | + | 0.948066i | \(0.603036\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.93664 | 0.263498 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.68606 | 0.249414 | 0.124707 | − | 0.992194i | \(-0.460201\pi\) | ||||
0.124707 | + | 0.992194i | \(0.460201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.8343 | 2.00804 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.55286 | 0.135112 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1521 | 0.746918 | 0.373459 | − | 0.927647i | \(-0.378172\pi\) | ||||
0.373459 | + | 0.927647i | \(0.378172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.6159 | −0.558732 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.979305 | 0.0514002 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.427307 | 0.0223663 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9661 | −0.885625 | −0.442813 | − | 0.896614i | \(-0.646019\pi\) | ||||
−0.442813 | + | 0.896614i | \(0.646019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.583837 | 0.0303933 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.8763 | 0.616586 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.89452 | 0.305206 | 0.152603 | − | 0.988288i | \(-0.451234\pi\) | ||||
0.152603 | + | 0.988288i | \(0.451234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.4126 | −0.537703 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.10856 | 0.160099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.354818 | 0.0182258 | 0.00911289 | − | 0.999958i | \(-0.497099\pi\) | ||||
0.00911289 | + | 0.999958i | \(0.497099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.56390 | −0.0801212 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.1046 | −1.28279 | −0.641393 | − | 0.767213i | \(-0.721643\pi\) | ||||
−0.641393 | + | 0.767213i | \(0.721643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.33286 | −0.118894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.8034 | 0.955833 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4783 | 0.886187 | 0.443094 | − | 0.896475i | \(-0.353881\pi\) | ||||
0.443094 | + | 0.896475i | \(0.353881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.95401 | −0.503396 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.60866 | 0.282919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.6931 | −1.84623 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1899 | 1.11368 | 0.556840 | − | 0.830620i | \(-0.312014\pi\) | ||||
0.556840 | + | 0.830620i | \(0.312014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.83561 | −0.141958 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.8152 | 1.83846 | 0.919230 | − | 0.393720i | \(-0.128812\pi\) | ||||
0.919230 | + | 0.393720i | \(0.128812\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.32534 | 0.364901 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.00568 | 0.149353 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.46215 | −0.0724762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59380 | −0.227149 | −0.113574 | − | 0.993529i | \(-0.536230\pi\) | ||||
−0.113574 | + | 0.993529i | \(0.536230\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4200 | 0.661961 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.80563 | 0.482504 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.7603 | 1.75541 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.03441 | −0.295506 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.4748 | 1.73306 | 0.866528 | − | 0.499129i | \(-0.166347\pi\) | ||||
0.866528 | + | 0.499129i | \(0.166347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7158 | −0.522254 | −0.261127 | − | 0.965304i | \(-0.584094\pi\) | ||||
−0.261127 | + | 0.965304i | \(0.584094\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.79334 | −0.378925 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.15285 | −0.0559214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.26111 | −0.0610294 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.979305 | −0.0472813 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.3325 | 1.26839 | 0.634197 | − | 0.773172i | \(-0.281331\pi\) | ||||
0.634197 | + | 0.773172i | \(0.281331\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.8589 | −1.00242 | −0.501208 | − | 0.865327i | \(-0.667111\pi\) | ||||
−0.501208 | + | 0.865327i | \(0.667111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.10177 | −0.340504 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.0565 | 0.528903 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7517 | −0.608606 | −0.304303 | − | 0.952575i | \(-0.598424\pi\) | ||||
−0.304303 | + | 0.952575i | \(0.598424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.04096 | −0.0971886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.9295 | −0.566789 | −0.283395 | − | 0.959003i | \(-0.591461\pi\) | ||||
−0.283395 | + | 0.959003i | \(0.591461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.1940 | −1.19431 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.59112 | 0.169854 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.651619 | 0.0307518 | 0.0153759 | − | 0.999882i | \(-0.495106\pi\) | ||||
0.0153759 | + | 0.999882i | \(0.495106\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.286060 | −0.0134700 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1334 | −0.758013 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.33286 | 0.109366 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.3642 | 1.60749 | 0.803745 | − | 0.594974i | \(-0.202838\pi\) | ||||
0.803745 | + | 0.594974i | \(0.202838\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.8689 | 0.600668 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1979 | −0.474966 | −0.237483 | − | 0.971392i | \(-0.576322\pi\) | ||||
−0.237483 | + | 0.971392i | \(0.576322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.6391 | 1.37745 | 0.688723 | − | 0.725025i | \(-0.258172\pi\) | ||||
0.688723 | + | 0.725025i | \(0.258172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.7353 | −0.776083 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.97904 | 0.276677 | 0.138338 | − | 0.990385i | \(-0.455824\pi\) | ||||
0.138338 | + | 0.990385i | \(0.455824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.93124 | 0.227704 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.879512 | −0.0405258 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.21304 | −0.423616 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.28053 | 0.0587549 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.2390 | 1.10983 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.3925 | −1.38867 | −0.694334 | − | 0.719653i | \(-0.744301\pi\) | ||||
−0.694334 | + | 0.719653i | \(0.744301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.46215 | 0.0666684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.73944 | −0.170151 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9735 | 0.498281 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6920 | 1.48141 | 0.740707 | − | 0.671828i | \(-0.234490\pi\) | ||||
0.740707 | + | 0.671828i | \(0.234490\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.93409 | 0.268349 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.6634 | 1.38382 | 0.691911 | − | 0.721983i | \(-0.256769\pi\) | ||||
0.691911 | + | 0.721983i | \(0.256769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.10343 | 0.364960 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.76128 | −0.214004 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.2180 | −0.727475 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0432 | 1.16586 | 0.582928 | − | 0.812524i | \(-0.301907\pi\) | ||||
0.582928 | + | 0.812524i | \(0.301907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.90832 | −0.129934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0360 | −1.60677 | −0.803384 | − | 0.595462i | \(-0.796969\pi\) | ||||
−0.803384 | + | 0.595462i | \(0.796969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.9207 | −1.10896 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.979305 | 0.0434925 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.9584 | −0.973290 | −0.486645 | − | 0.873600i | \(-0.661780\pi\) | ||||
−0.486645 | + | 0.873600i | \(0.661780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.183169 | −0.00810291 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2942 | −0.631104 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.6127 | −1.34896 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.81847 | 0.167936 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.69575 | −0.206120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5117 | −0.854825 | −0.427412 | − | 0.904057i | \(-0.640575\pi\) | ||||
−0.427412 | + | 0.904057i | \(0.640575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8683 | −1.21859 | −0.609297 | − | 0.792942i | \(-0.708548\pi\) | ||||
−0.609297 | + | 0.792942i | \(0.708548\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.433093 | −0.0189017 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.0958 | 0.831824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.41931 | −0.366057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0129 | 0.868487 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.286060 | 0.0123906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.03920 | −0.217864 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.3574 | −0.662719 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9951 | −0.687684 | −0.343842 | − | 0.939027i | \(-0.611728\pi\) | ||||
−0.343842 | + | 0.939027i | \(0.611728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.0580 | 0.903685 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.0266 | 1.32903 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.3080 | −1.68069 | −0.840345 | − | 0.542053i | \(-0.817647\pi\) | ||||
−0.840345 | + | 0.542053i | \(0.817647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.57388 | −0.109850 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.00093 | −0.383453 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.7288 | 0.668856 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.34041 | −0.141792 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.9317 | −1.60722 | −0.803608 | − | 0.595159i | \(-0.797089\pi\) | ||||
−0.803608 | + | 0.595159i | \(0.797089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.21304 | 0.389670 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.55286 | −0.107782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.9013 | −1.47091 | −0.735457 | − | 0.677571i | \(-0.763032\pi\) | ||||
−0.735457 | + | 0.677571i | \(0.763032\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.4045 | 1.19498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.28841 | −0.0541080 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.3620 | 0.979384 | 0.489692 | − | 0.871895i | \(-0.337109\pi\) | ||||
0.489692 | + | 0.871895i | \(0.337109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0498 | 0.629815 | 0.314907 | − | 0.949122i | \(-0.398027\pi\) | ||||
0.314907 | + | 0.949122i | \(0.398027\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6945 | −0.530319 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.68870 | 0.0704235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.8152 | 0.741656 | 0.370828 | − | 0.928702i | \(-0.379074\pi\) | ||||
0.370828 | + | 0.928702i | \(0.379074\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.6556 | −0.442831 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.3290 | −0.635952 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.8763 | −0.491865 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.76128 | 0.196855 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4425 | 1.17395 | 0.586974 | − | 0.809606i | \(-0.300319\pi\) | ||||
0.586974 | + | 0.809606i | \(0.300319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.2107 | −0.873973 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.5874 | −0.600044 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.3548 | 1.41078 | 0.705392 | − | 0.708818i | \(-0.250771\pi\) | ||||
0.705392 | + | 0.708818i | \(0.250771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.08133 | 0.249310 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.63207 | 0.0667961 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.93947 | −0.0792447 | −0.0396223 | − | 0.999215i | \(-0.512615\pi\) | ||||
−0.0396223 | + | 0.999215i | \(0.512615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9317 | −0.813032 | −0.406516 | − | 0.913644i | \(-0.633256\pi\) | ||||
−0.406516 | + | 0.913644i | \(0.633256\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0645 | 0.409857 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.33286 | 0.0948443 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.52805 | −0.102611 | −0.0513053 | − | 0.998683i | \(-0.516338\pi\) | ||||
−0.0513053 | + | 0.998683i | \(0.516338\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.04423 | 0.123358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.81847 | −0.154479 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.3609 | 0.539641 | 0.269821 | − | 0.962911i | \(-0.413036\pi\) | ||||
0.269821 | + | 0.962911i | \(0.413036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.653527 | −0.0263528 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.81741 | 0.314717 | 0.157359 | − | 0.987542i | \(-0.449702\pi\) | ||||
0.157359 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8668 | 0.959288 | 0.479644 | − | 0.877463i | \(-0.340766\pi\) | ||||
0.479644 | + | 0.877463i | \(0.340766\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.8504 | −0.756440 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.7996 | 0.432678 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.0156 | −1.08063 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83561 | 0.113243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.81155 | 0.151977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6974 | −0.704523 | −0.352262 | − | 0.935902i | \(-0.614587\pi\) | ||||
−0.352262 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.4145 | −0.652417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.72547 | −0.147841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.1003 | −1.30943 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.6388 | 1.32865 | 0.664327 | − | 0.747442i | \(-0.268718\pi\) | ||||
0.664327 | + | 0.747442i | \(0.268718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5558 | 0.731770 | 0.365885 | − | 0.930660i | \(-0.380766\pi\) | ||||
0.365885 | + | 0.930660i | \(0.380766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.0480 | −0.828762 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.2113 | 1.22704 | 0.613521 | − | 0.789678i | \(-0.289752\pi\) | ||||
0.613521 | + | 0.789678i | \(0.289752\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.80563 | −0.384905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.17374 | 0.281161 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.4228 | −1.58186 | −0.790932 | − | 0.611903i | \(-0.790404\pi\) | ||||
−0.790932 | + | 0.611903i | \(0.790404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.3607 | 0.522046 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.373840 | −0.0145849 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.56349 | −0.177768 | −0.0888841 | − | 0.996042i | \(-0.528330\pi\) | ||||
−0.0888841 | + | 0.996042i | \(0.528330\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.3024 | −1.45090 | −0.725448 | − | 0.688277i | \(-0.758367\pi\) | ||||
−0.725448 | + | 0.688277i | \(0.758367\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.55286 | 0.0991449 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.75487 | −0.261943 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8699 | −0.459606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.69588 | −0.181553 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.26111 | 0.0486846 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.2640 | 1.47497 | 0.737484 | − | 0.675365i | \(-0.236014\pi\) | ||||
0.737484 | + | 0.675365i | \(0.236014\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.18320 | −0.0840315 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.4686 | 0.978839 | 0.489419 | − | 0.872049i | \(-0.337209\pi\) | ||||
0.489419 | + | 0.872049i | \(0.337209\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.70388 | −0.180518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2785 | −0.432192 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6773 | −0.485082 | −0.242541 | − | 0.970141i | \(-0.577981\pi\) | ||||
−0.242541 | + | 0.970141i | \(0.577981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.9687 | 1.22146 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8675 | 0.529077 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.8763 | 0.452450 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.9122 | −1.29008 | −0.645041 | − | 0.764148i | \(-0.723160\pi\) | ||||
−0.645041 | + | 0.764148i | \(0.723160\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.04096 | 0.0775297 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.3749 | −0.545272 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.745703 | 0.0282455 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.4802 | −0.661161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.5469 | 1.64474 | 0.822371 | − | 0.568951i | \(-0.192651\pi\) | ||||
0.822371 | + | 0.568951i | \(0.192651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.23371 | −0.159677 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.72361 | 0.328550 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.6825 | 0.401755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.5607 | 1.67351 | 0.836757 | − | 0.547574i | \(-0.184449\pi\) | ||||
0.836757 | + | 0.547574i | \(0.184449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.1018 | 1.20391 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.9716 | −1.04754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.33286 | −0.0872441 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.4835 | −0.914353 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7805 | −1.29709 | −0.648546 | − | 0.761175i | \(-0.724623\pi\) | ||||
−0.648546 | + | 0.761175i | \(0.724623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1224 | 0.488704 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.77107 | −0.140248 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.37475 | −0.0510568 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.7891 | 1.06773 | 0.533864 | − | 0.845571i | \(-0.320740\pi\) | ||||
0.533864 | + | 0.845571i | \(0.320740\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.8738 | 0.439772 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0166 | 0.888287 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.49094 | 0.276684 | 0.138342 | − | 0.990385i | \(-0.455823\pi\) | ||||
0.138342 | + | 0.990385i | \(0.455823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.28458 | 0.0842681 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.93124 | −0.181645 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.5073 | −1.26937 | −0.634686 | − | 0.772770i | \(-0.718871\pi\) | ||||
−0.634686 | + | 0.772770i | \(0.718871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.83561 | −0.104169 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.7560 | −1.86206 | −0.931028 | − | 0.364948i | \(-0.881087\pi\) | ||||
−0.931028 | + | 0.364948i | \(0.881087\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.55462 | 0.313417 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.2858 | −1.14469 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.16009 | 0.0789281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.7913 | −0.831666 | −0.415833 | − | 0.909441i | \(-0.636510\pi\) | ||||
−0.415833 | + | 0.909441i | \(0.636510\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.3001 | 0.557568 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.4323 | −1.39870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.70078 | −0.279889 | −0.139945 | − | 0.990159i | \(-0.544692\pi\) | ||||
−0.139945 | + | 0.990159i | \(0.544692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.73944 | 0.135733 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.329560 | 0.0119465 | 0.00597327 | − | 0.999982i | \(-0.498099\pi\) | ||||
0.00597327 | + | 0.999982i | \(0.498099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2998 | −0.481485 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.4118 | 0.448748 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.80563 | 0.354061 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.9152 | 0.898465 | 0.449233 | − | 0.893415i | \(-0.351697\pi\) | ||||
0.449233 | + | 0.893415i | \(0.351697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.71259 | 0.133706 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.0350 | 1.29609 | 0.648044 | − | 0.761603i | \(-0.275587\pi\) | ||||
0.648044 | + | 0.761603i | \(0.275587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.23959 | −0.116370 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.43189 | 0.0513689 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.828294 | −0.0296767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2180 | 0.580325 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.3458 | 0.548416 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.09514 | −0.0747787 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.0281 | −1.31991 | −0.659955 | − | 0.751305i | \(-0.729425\pi\) | ||||
−0.659955 | + | 0.751305i | \(0.729425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.5555 | 0.446986 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1758 | −0.432922 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.26111 | −0.0447833 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.1324 | −0.962285 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.8666 | −0.880820 | −0.440410 | − | 0.897797i | \(-0.645167\pi\) | ||||
−0.440410 | + | 0.897797i | \(0.645167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.95401 | −0.352148 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.0416 | 0.778803 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.183169 | 0.00646388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.90795 | −0.313964 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.9108 | 0.595290 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.9534 | −1.36953 | −0.684764 | − | 0.728765i | \(-0.740095\pi\) | ||||
−0.684764 | + | 0.728765i | \(0.740095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.20179 | −0.147545 | −0.0737724 | − | 0.997275i | \(-0.523504\pi\) | ||||
−0.0737724 | + | 0.997275i | \(0.523504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.85151 | 0.240293 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.1359 | 0.495161 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.6766 | −0.933297 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.04096 | −0.0713170 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8090 | 0.865842 | 0.432921 | − | 0.901432i | \(-0.357483\pi\) | ||||
0.432921 | + | 0.901432i | \(0.357483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1090 | 0.491809 | 0.245905 | − | 0.969294i | \(-0.420915\pi\) | ||||
0.245905 | + | 0.969294i | \(0.420915\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.433093 | 0.0150784 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.9753 | 1.32053 | 0.660266 | − | 0.751032i | \(-0.270444\pi\) | ||||
0.660266 | + | 0.751032i | \(0.270444\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.8367 | 0.376374 | 0.188187 | − | 0.982133i | \(-0.439739\pi\) | ||||
0.188187 | + | 0.982133i | \(0.439739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.0656 | 0.730757 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.60681 | −0.0903206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.92809 | −0.239757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.1626 | 1.24996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.9990 | 1.65711 | 0.828555 | − | 0.559908i | \(-0.189163\pi\) | ||||
0.828555 | + | 0.559908i | \(0.189163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3368 | −0.666788 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4286 | 0.462506 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.33286 | 0.0802529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.7087 | −0.882320 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.58318 | −0.191389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.6149 | −1.18519 | −0.592595 | − | 0.805500i | \(-0.701897\pi\) | ||||
−0.592595 | + | 0.805500i | \(0.701897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.7864 | −0.471486 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.3956 | −0.901656 | −0.450828 | − | 0.892611i | \(-0.648871\pi\) | ||||
−0.450828 | + | 0.892611i | \(0.648871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.1458 | −0.960323 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.280140 | 0.00954714 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.08423 | −0.0369077 | −0.0184539 | − | 0.999830i | \(-0.505874\pi\) | ||||
−0.0184539 | + | 0.999830i | \(0.505874\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1860 | −0.380336 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.99336 | −0.339392 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.7288 | −0.533562 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.93124 | 0.167089 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.60043 | −0.324925 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.6326 | 0.359448 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7169 | 0.530723 | 0.265362 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265362 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.58010 | −0.0870245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.9150 | −1.14262 | −0.571312 | − | 0.820733i | \(-0.693566\pi\) | ||||
−0.571312 | + | 0.820733i | \(0.693566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.38111 | −0.181089 | −0.0905444 | − | 0.995892i | \(-0.528861\pi\) | ||||
−0.0905444 | + | 0.995892i | \(0.528861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.4018 | −0.753028 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0514 | 0.606107 | 0.303053 | − | 0.952974i | \(-0.401994\pi\) | ||||
0.303053 | + | 0.952974i | \(0.401994\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.59695 | 0.0535600 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.28841 | 0.0431633 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0565 | 0.369991 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.5837 | −1.22286 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.73944 | −0.124856 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7713 | 0.759464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.9592 | 1.03140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.02237 | 0.300246 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.1635 | 1.66749 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4949 | 0.580909 | 0.290454 | − | 0.956889i | \(-0.406194\pi\) | ||||
0.290454 | + | 0.956889i | \(0.406194\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.8025 | 0.723143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.7260 | −1.44871 | −0.724353 | − | 0.689429i | \(-0.757861\pi\) | ||||
−0.724353 | + | 0.689429i | \(0.757861\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3290 | 0.507314 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.88111 | 0.0952466 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.72718 | −0.189128 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.76629 | −0.190212 | −0.0951061 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951061 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3497 | −0.505789 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.2180 | −0.533821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.646629 | −0.0212610 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.7823 | 0.879646 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.993416 | 0.0325929 | 0.0162965 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162965 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.89553 | 0.0948972 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.403927 | 0.0132240 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.08133 | −0.198881 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.98084 | 0.260723 | 0.130361 | − | 0.991467i | \(-0.458386\pi\) | ||||
0.130361 | + | 0.991467i | \(0.458386\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9423 | −0.357087 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.46084 | 0.0802212 | 0.0401106 | − | 0.999195i | \(-0.487229\pi\) | ||||
0.0401106 | + | 0.999195i | \(0.487229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.09231 | −0.0355705 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.5165 | 0.374632 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5354 | −0.732301 | −0.366150 | − | 0.930556i | \(-0.619324\pi\) | ||||
−0.366150 | + | 0.930556i | \(0.619324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.183169 | −0.00594591 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0733 | 0.586068 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.811014 | −0.0262713 | −0.0131357 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131357 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.2403 | −0.978552 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.04423 | −0.0984060 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.7036 | −0.442513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6606 | 0.730986 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.40867 | 0.142067 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.3833 | −0.817118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.2075 | 1.58241 | 0.791203 | − | 0.611554i | \(-0.209455\pi\) | ||||
0.791203 | + | 0.611554i | \(0.209455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.39189 | −0.237462 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.9554 | 0.640398 | 0.320199 | − | 0.947350i | \(-0.396250\pi\) | ||||
0.320199 | + | 0.947350i | \(0.396250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.16193 | 0.197542 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.433093 | −0.0138701 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.0330 | −0.928849 | −0.464424 | − | 0.885613i | \(-0.653739\pi\) | ||||
−0.464424 | + | 0.885613i | \(0.653739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.7996 | −0.345158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.1444 | −0.866653 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.451059 | −0.0143866 | −0.00719328 | − | 0.999974i | \(-0.502290\pi\) | ||||
−0.00719328 | + | 0.999974i | \(0.502290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.7495 | −1.10721 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.73944 | −0.119028 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1797 | −1.11865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7744 | −0.405791 | −0.202896 | − | 0.979200i | \(-0.565035\pi\) | ||||
−0.202896 | + | 0.979200i | \(0.565035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.8337 | −0.534200 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.88785 | 0.123253 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.5482 | 0.460745 | 0.230373 | − | 0.973102i | \(-0.426006\pi\) | ||||
0.230373 | + | 0.973102i | \(0.426006\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.21812 | 0.228371 |
(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 | 8008.2.a.v.1.8 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.v.1.8 | ✓ | 11 | 1.1 | even | 1 | trivial |