Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), 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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.7 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.8 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.10949 | −1.21792 | −0.608958 | − | 0.793203i | \(-0.708412\pi\) | ||||
−0.608958 | + | 0.793203i | \(0.708412\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.39046i | − | 1.51626i | −0.652103 | − | 0.758130i | \(-0.726113\pi\) | ||
0.652103 | − | 0.758130i | \(-0.273887\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.44995 | 0.483317 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.53014 | + | 0.733543i | −0.979086 | + | 0.203448i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.15215i | 1.84668i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.05719 | 1.46908 | 0.734542 | − | 0.678563i | \(-0.237397\pi\) | ||||
0.734542 | + | 0.678563i | \(0.237397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.08356i | − | 0.248587i | −0.992246 | − | 0.124293i | \(-0.960334\pi\) | ||
0.992246 | − | 0.124293i | \(-0.0396664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.10949i | − | 0.460329i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.38895 | −1.33219 | −0.666094 | − | 0.745867i | \(-0.732035\pi\) | ||||
−0.666094 | + | 0.745867i | \(0.732035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.49523 | −1.29905 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.26981 | 0.629276 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.88226 | −0.349528 | −0.174764 | − | 0.984610i | \(-0.555916\pi\) | ||||
−0.174764 | + | 0.984610i | \(0.555916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.69756i | 1.02331i | 0.859191 | + | 0.511656i | \(0.170968\pi\) | ||||
−0.859191 | + | 0.511656i | \(0.829032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.10949i | 0.367215i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.39046 | 0.573093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.35035i | 0.879592i | 0.898098 | + | 0.439796i | \(0.144949\pi\) | ||||
−0.898098 | + | 0.439796i | \(0.855051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.44681 | − | 1.54740i | 1.19244 | − | 0.247783i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.69745i | − | 0.265098i | −0.991176 | − | 0.132549i | \(-0.957684\pi\) | ||
0.991176 | − | 0.132549i | \(-0.0423162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.15280 | 1.24329 | 0.621645 | − | 0.783299i | \(-0.286465\pi\) | ||||
0.621645 | + | 0.783299i | \(0.286465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 4.91601i | − | 0.732835i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.26952i | 0.331044i | 0.986206 | + | 0.165522i | \(0.0529308\pi\) | ||||
−0.986206 | + | 0.165522i | \(0.947069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.7776 | −1.78922 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.6554 | −1.73835 | −0.869176 | − | 0.494503i | \(-0.835350\pi\) | ||||
−0.869176 | + | 0.494503i | \(0.835350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.39046 | −0.457170 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.28577i | 0.302758i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.70115i | 1.26298i | 0.775383 | + | 0.631491i | \(0.217557\pi\) | ||||
−0.775383 | + | 0.631491i | \(0.782443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04222 | 0.133442 | 0.0667211 | − | 0.997772i | \(-0.478746\pi\) | ||||
0.0667211 | + | 0.997772i | \(0.478746\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.44995i | 0.182677i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.48705 | + | 11.9688i | 0.308480 | + | 1.48455i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.67103i | − | 0.814996i | −0.913206 | − | 0.407498i | \(-0.866401\pi\) | ||
0.913206 | − | 0.407498i | \(-0.133599\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.4774 | 1.62249 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9085i | 1.65063i | 0.564671 | + | 0.825316i | \(0.309003\pi\) | ||||
−0.564671 | + | 0.825316i | \(0.690997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.29126i | − | 0.970419i | −0.874398 | − | 0.485209i | \(-0.838743\pi\) | ||
0.874398 | − | 0.485209i | \(-0.161257\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.7016 | 1.58213 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.23170 | −0.138577 | −0.0692883 | − | 0.997597i | \(-0.522073\pi\) | ||||
−0.0692883 | + | 0.997597i | \(0.522073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2475 | −1.24972 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9980i | 1.20719i | 0.797291 | + | 0.603595i | \(0.206266\pi\) | ||||
−0.797291 | + | 0.603595i | \(0.793734\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 20.5367i | − | 2.22751i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.97062 | 0.425695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.96113i | 0.313879i | 0.987608 | + | 0.156940i | \(0.0501628\pi\) | ||||
−0.987608 | + | 0.156940i | \(0.949837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.733543 | − | 3.53014i | −0.0768962 | − | 0.370060i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 12.0189i | − | 1.24631i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67379 | −0.376922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.535647i | − | 0.0543867i | −0.999630 | − | 0.0271933i | \(-0.991343\pi\) | ||
0.999630 | − | 0.0271933i | \(-0.00865698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.44995i | − | 0.145726i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.46249 | −0.941553 | −0.470776 | − | 0.882253i | \(-0.656026\pi\) | ||||
−0.470776 | + | 0.882253i | \(0.656026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0615 | −1.58259 | −0.791294 | − | 0.611436i | \(-0.790592\pi\) | ||||
−0.791294 | + | 0.611436i | \(0.790592\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.15215 | −0.697978 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.7042 | 1.80820 | 0.904100 | − | 0.427321i | \(-0.140543\pi\) | ||||
0.904100 | + | 0.427321i | \(0.140543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.9856i | − | 1.24380i | −0.783097 | − | 0.621899i | \(-0.786361\pi\) | ||
0.783097 | − | 0.621899i | \(-0.213639\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.2865i | − | 1.07127i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94235 | 0.182721 | 0.0913605 | − | 0.995818i | \(-0.470878\pi\) | ||||
0.0913605 | + | 0.995818i | \(0.470878\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.6615i | 2.01995i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.11854 | + | 1.06360i | −0.473209 | + | 0.0983300i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.05719i | 0.555262i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.58077i | 0.322867i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.06952i | 0.453432i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.2352 | 1.79558 | 0.897791 | − | 0.440422i | \(-0.145171\pi\) | ||||
0.897791 | + | 0.440422i | \(0.145171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.1983 | −1.51422 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1914 | 1.32728 | 0.663640 | − | 0.748052i | \(-0.269011\pi\) | ||||
0.663640 | + | 0.748052i | \(0.269011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.08356 | 0.0939570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 11.0862i | − | 0.954146i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.51302i | 0.556445i | 0.960517 | + | 0.278222i | \(0.0897452\pi\) | ||||
−0.960517 | + | 0.278222i | \(0.910255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.47873 | 0.803975 | 0.401988 | − | 0.915645i | \(-0.368319\pi\) | ||||
0.401988 | + | 0.915645i | \(0.368319\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.78753i | − | 0.403183i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.733543 | + | 3.53014i | 0.0613419 | + | 0.295205i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.38175i | 0.529975i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.10949 | 0.173988 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.14389i | − | 0.667173i | −0.942719 | − | 0.333587i | \(-0.891741\pi\) | ||
0.942719 | − | 0.333587i | \(-0.108259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.6160i | − | 0.863918i | −0.901893 | − | 0.431959i | \(-0.857822\pi\) | ||
0.901893 | − | 0.431959i | \(-0.142178\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.78263 | 0.710034 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.3173 | 1.55161 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6183 | 1.16667 | 0.583335 | − | 0.812232i | \(-0.301748\pi\) | ||||
0.583335 | + | 0.812232i | \(0.301748\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.6964 | 2.11717 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.38895i | − | 0.503520i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.3167i | − | 1.51300i | −0.653994 | − | 0.756500i | \(-0.726908\pi\) | ||
0.653994 | − | 0.756500i | \(-0.273092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.15215 | 0.556794 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.4575i | 1.19614i | 0.801444 | + | 0.598070i | \(0.204065\pi\) | ||||
−0.801444 | + | 0.598070i | \(0.795935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9238 | − | 5.17902i | 0.917218 | − | 0.398386i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.57112i | − | 0.120146i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.7061 | 0.966026 | 0.483013 | − | 0.875613i | \(-0.339542\pi\) | ||||
0.483013 | + | 0.875613i | \(0.339542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.49523i | − | 0.490993i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 20.4645i | − | 1.53821i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8917 | 0.814086 | 0.407043 | − | 0.913409i | \(-0.366560\pi\) | ||||
0.407043 | + | 0.913409i | \(0.366560\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5373 | 0.931887 | 0.465944 | − | 0.884814i | \(-0.345715\pi\) | ||||
0.465944 | + | 0.884814i | \(0.345715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.19855 | −0.162521 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.1402 | 1.33369 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.05719i | − | 0.442946i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.26981i | 0.237844i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.4529 | −1.11813 | −0.559065 | − | 0.829124i | \(-0.688840\pi\) | ||||
−0.559065 | + | 0.829124i | \(0.688840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.6057i | 1.48323i | 0.670825 | + | 0.741616i | \(0.265940\pi\) | ||||
−0.670825 | + | 0.741616i | \(0.734060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.24641 | − | 25.2481i | −0.375703 | − | 1.80805i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.80816i | − | 0.128826i | −0.997923 | − | 0.0644131i | \(-0.979482\pi\) | ||
0.997923 | − | 0.0644131i | \(-0.0205175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.9470 | −1.05956 | −0.529782 | − | 0.848134i | \(-0.677726\pi\) | ||||
−0.529782 | + | 0.848134i | \(0.677726\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0725i | 0.992596i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.88226i | − | 0.132109i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.75516 | −0.401958 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.26368 | −0.643870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.08356 | −0.0749518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.27173 | −0.431764 | −0.215882 | − | 0.976420i | \(-0.569263\pi\) | ||||
−0.215882 | + | 0.976420i | \(0.569263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 29.3398i | − | 2.01033i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 27.6417i | − | 1.88515i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.69756 | −0.386775 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.4903i | 1.18189i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.3827 | + | 4.44321i | −1.43836 | + | 0.298882i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7143i | 1.58802i | 0.607902 | + | 0.794012i | \(0.292011\pi\) | ||||
−0.607902 | + | 0.794012i | \(0.707989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.41778 | −0.627852 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.3569i | 1.81574i | 0.419254 | + | 0.907869i | \(0.362292\pi\) | ||||
−0.419254 | + | 0.907869i | \(0.637708\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.97069i | − | 0.196309i | −0.995171 | − | 0.0981543i | \(-0.968706\pi\) | ||
0.995171 | − | 0.0981543i | \(-0.0312939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.10949 | −0.138794 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.47412 | −0.0965731 | −0.0482865 | − | 0.998834i | \(-0.515376\pi\) | ||||
−0.0482865 | + | 0.998834i | \(0.515376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.69473 | 0.501949 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.59825 | 0.168774 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.7293i | − | 0.758706i | −0.925252 | − | 0.379353i | \(-0.876147\pi\) | ||
0.925252 | − | 0.379353i | \(-0.123853\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11251i | 0.0716628i | 0.999358 | + | 0.0358314i | \(0.0114079\pi\) | ||||
−0.999358 | + | 0.0358314i | \(0.988592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9171 | 0.892779 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.39046i | 0.216609i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.794841 | + | 3.82514i | 0.0505745 | + | 0.243388i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 23.2002i | − | 1.47025i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.3845 | 1.85473 | 0.927366 | − | 0.374156i | \(-0.122068\pi\) | ||||
0.927366 | + | 0.374156i | \(0.122068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.38895i | 0.401670i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 43.3219i | 2.71292i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.21605 | −0.200612 | −0.100306 | − | 0.994957i | \(-0.531982\pi\) | ||||
−0.100306 | + | 0.994957i | \(0.531982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.35035 | −0.332455 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.72919 | −0.168933 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9637 | 1.10769 | 0.553844 | − | 0.832621i | \(-0.313160\pi\) | ||||
0.553844 | + | 0.832621i | \(0.313160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 42.9076i | 2.63579i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.24648i | − | 0.382278i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.53047 | −0.581083 | −0.290541 | − | 0.956862i | \(-0.593835\pi\) | ||||
−0.290541 | + | 0.956862i | \(0.593835\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.9006i | − | 1.26962i | −0.772669 | − | 0.634810i | \(-0.781079\pi\) | ||
0.772669 | − | 0.634810i | \(-0.218921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.54740 | + | 7.44681i | 0.0936530 | + | 0.450701i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.49523i | 0.391677i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.3475 | 0.801975 | 0.400987 | − | 0.916084i | \(-0.368667\pi\) | ||||
0.400987 | + | 0.916084i | \(0.368667\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.26118i | 0.494584i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.183295i | 0.0109345i | 0.999985 | + | 0.00546724i | \(0.00174028\pi\) | ||||
−0.999985 | + | 0.00546724i | \(0.998260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.80597 | 0.226241 | 0.113121 | − | 0.993581i | \(-0.463915\pi\) | ||||
0.113121 | + | 0.993581i | \(0.463915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.74982 | 0.459060 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.69745 | 0.100198 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.6895 | 1.15821 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.12994i | 0.0662384i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.4190i | 1.30973i | 0.755744 | + | 0.654867i | \(0.227275\pi\) | ||||
−0.755744 | + | 0.654867i | \(0.772725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.8914 | 1.91501 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.26981i | − | 0.189734i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.5539 | − | 4.68657i | 1.30433 | − | 0.271031i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.15280i | 0.469919i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9610 | 1.14673 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.53360i | − | 0.202333i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4548i | 1.68107i | 0.541755 | + | 0.840537i | \(0.317760\pi\) | ||||
−0.541755 | + | 0.840537i | \(0.682240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.8816 | 1.92746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.68743 | 0.0956851 | 0.0478426 | − | 0.998855i | \(-0.484765\pi\) | ||||
0.0478426 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3653 | 0.811974 | 0.405987 | − | 0.913879i | \(-0.366928\pi\) | ||||
0.405987 | + | 0.913879i | \(0.366928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.91601 | 0.276986 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.0176i | − | 1.34896i | −0.738293 | − | 0.674480i | \(-0.764368\pi\) | ||
0.738293 | − | 0.674480i | \(-0.235632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.88226i | 0.105387i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.4563 | −2.20223 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.56336i | − | 0.365195i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.9291 | − | 4.76453i | 1.27188 | − | 0.264289i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.3931i | 1.51484i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.26952 | −0.125123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.4829i | − | 1.45563i | −0.685772 | − | 0.727816i | \(-0.740535\pi\) | ||
0.685772 | − | 0.727816i | \(-0.259465\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.75775i | 0.425122i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.6179 | −1.23575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7375 | 0.584907 | 0.292453 | − | 0.956280i | \(-0.405528\pi\) | ||||
0.292453 | + | 0.956280i | \(0.405528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.09737 | −0.222539 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.69756 | 0.308540 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 45.6947i | − | 2.46012i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.38449 | 0.289055 | 0.144527 | − | 0.989501i | \(-0.453834\pi\) | ||||
0.144527 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2633i | 1.29879i | 0.760453 | + | 0.649393i | \(0.224977\pi\) | ||||
−0.760453 | + | 0.649393i | \(0.775023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.5429 | + | 2.39855i | −0.616115 | + | 0.128025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.61034i | 0.511507i | 0.966742 | + | 0.255753i | \(0.0823235\pi\) | ||||
−0.966742 | + | 0.255753i | \(0.917676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 47.1562 | 2.50279 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 12.7776i | − | 0.676262i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.6139i | 0.665736i | 0.942973 | + | 0.332868i | \(0.108016\pi\) | ||||
−0.942973 | + | 0.332868i | \(0.891984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8259 | 0.938205 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.10949 | 0.110720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.1112 | −1.47141 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7005 | 1.60255 | 0.801276 | − | 0.598294i | \(-0.204155\pi\) | ||||
0.801276 | + | 0.598294i | \(0.204155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.46123i | − | 0.128126i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 12.6554i | − | 0.657035i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.9676 | −0.671435 | −0.335717 | − | 0.941963i | \(-0.608979\pi\) | ||||
−0.335717 | + | 0.941963i | \(0.608979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 10.6941i | − | 0.552242i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.64466 | − | 1.38072i | 0.342218 | − | 0.0711108i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.9438i | − | 1.12718i | −0.826056 | − | 0.563588i | \(-0.809421\pi\) | ||
0.826056 | − | 0.563588i | \(-0.190579\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42.6859 | −2.18687 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3287i | 1.14094i | 0.821317 | + | 0.570472i | \(0.193240\pi\) | ||||
−0.821317 | + | 0.570472i | \(0.806760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.39046i | − | 0.172794i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.8212 | 0.600904 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.7973 | 0.547445 | 0.273723 | − | 0.961809i | \(-0.411745\pi\) | ||||
0.273723 | + | 0.961809i | \(0.411745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −38.6991 | −1.95710 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.0462 | −1.61652 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.17602i | 0.210118i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.71532i | − | 0.487598i | −0.969826 | − | 0.243799i | \(-0.921606\pi\) | ||
0.969826 | − | 0.243799i | \(-0.0783937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.28577 | −0.114432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3367i | 0.865754i | 0.901453 | + | 0.432877i | \(0.142501\pi\) | ||||
−0.901453 | + | 0.432877i | \(0.857499\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.17940 | − | 20.1132i | −0.208191 | − | 1.00191i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.1342i | 1.89490i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.35035 | 0.265207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.64721i | − | 0.229790i | −0.993378 | − | 0.114895i | \(-0.963347\pi\) | ||
0.993378 | − | 0.114895i | \(-0.0366532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 13.7392i | − | 0.677703i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.70115 | −0.477362 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37.2884 | 1.83041 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.9953 | −0.979174 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.8602 | 0.725967 | 0.362983 | − | 0.931796i | \(-0.381758\pi\) | ||||
0.362983 | + | 0.931796i | \(0.381758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 13.4579i | − | 0.655896i | −0.944696 | − | 0.327948i | \(-0.893643\pi\) | ||
0.944696 | − | 0.327948i | \(-0.106357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.29070i | 0.159999i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −39.3428 | −1.90841 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.04222i | 0.0504364i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.54740 | − | 7.44681i | −0.0747093 | − | 0.359535i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.9138i | 1.48906i | 0.667587 | + | 0.744532i | \(0.267327\pi\) | ||||
−0.667587 | + | 0.744532i | \(0.732673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.08516 | 0.148263 | 0.0741316 | − | 0.997248i | \(-0.476382\pi\) | ||||
0.0741316 | + | 0.997248i | \(0.476382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.4622i | − | 0.645465i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.92285i | 0.331165i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.5908 | 1.26911 | 0.634555 | − | 0.772878i | \(-0.281183\pi\) | ||||
0.634555 | + | 0.772878i | \(0.281183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.44995 | −0.0690453 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8072 | 0.655999 | 0.328000 | − | 0.944678i | \(-0.393625\pi\) | ||||
0.328000 | + | 0.944678i | \(0.393625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0396 | 0.475923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.1795i | 0.812560i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1115i | 1.56263i | 0.624138 | + | 0.781314i | \(0.285450\pi\) | ||||
−0.624138 | + | 0.781314i | \(0.714550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69745 | −0.0799300 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.3944i | 1.05218i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.9688 | + | 2.48705i | −0.561107 | + | 0.116595i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.7724i | − | 1.39269i | −0.717705 | − | 0.696347i | \(-0.754807\pi\) | ||
0.717705 | − | 0.696347i | \(-0.245193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.8059 | 0.924459 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.8433i | − | 0.924194i | −0.886829 | − | 0.462097i | \(-0.847097\pi\) | ||
0.886829 | − | 0.462097i | \(-0.152903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.00306i | − | 0.232512i | −0.993219 | − | 0.116256i | \(-0.962911\pi\) | ||
0.993219 | − | 0.116256i | \(-0.0370893\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −40.7498 | −1.88973 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.849550 | 0.0393125 | 0.0196563 | − | 0.999807i | \(-0.493743\pi\) | ||||
0.0196563 | + | 0.999807i | \(0.493743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.67103 | 0.308040 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.8372 | −1.42090 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.15280i | − | 0.374866i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.03801i | 0.322926i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.3497 | −0.840176 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4.54583i | − | 0.207704i | −0.994593 | − | 0.103852i | \(-0.966883\pi\) | ||
0.994593 | − | 0.103852i | \(-0.0331168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.92471 | − | 18.8875i | −0.178951 | − | 0.861196i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.4774i | 0.613245i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.81609 | −0.0824644 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.20647i | − | 0.190613i | −0.995448 | − | 0.0953066i | \(-0.969617\pi\) | ||
0.995448 | − | 0.0953066i | \(-0.0303832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.7484i | 1.84271i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.33800 | 0.105513 | 0.0527563 | − | 0.998607i | \(-0.483199\pi\) | ||||
0.0527563 | + | 0.998607i | \(0.483199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.4012 | −0.513486 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.91601 | −0.220958 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.9085 | −0.623880 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.93176i | − | 0.131244i | −0.997845 | − | 0.0656218i | \(-0.979097\pi\) | ||
0.997845 | − | 0.0656218i | \(-0.0209031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 32.6075i | − | 1.45680i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.9960 | −1.24828 | −0.624140 | − | 0.781312i | \(-0.714551\pi\) | ||||
−0.624140 | + | 0.781312i | \(0.714551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.0822i | 1.42764i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.1532 | + | 10.9251i | −1.11709 | + | 0.485201i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 41.9840i | − | 1.86091i | −0.366411 | − | 0.930453i | \(-0.619414\pi\) | ||
0.366411 | − | 0.930453i | \(-0.380586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.29126 | 0.366784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.54305i | − | 0.156430i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 54.4560i | 2.39962i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.26952 | 0.0998134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.8034 | −1.17654 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.6736 | −1.03716 | −0.518581 | − | 0.855029i | \(-0.673539\pi\) | ||||
−0.518581 | + | 0.855029i | \(0.673539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.8305 | 0.735945 | 0.367973 | − | 0.929837i | \(-0.380052\pi\) | ||||
0.367973 | + | 0.929837i | \(0.380052\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.7016i | 0.597988i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.5112i | 1.50333i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8187 | 0.774727 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0662i | 0.610421i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24516 | + | 5.99226i | 0.0539337 | + | 0.259554i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 63.4158i | − | 2.74170i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.9760 | −0.991488 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.8116i | − | 0.464826i | −0.972617 | − | 0.232413i | \(-0.925338\pi\) | ||
0.972617 | − | 0.232413i | \(-0.0746621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.4472 | −1.13496 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.0273 | −1.88592 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0580 | −0.729349 | −0.364675 | − | 0.931135i | \(-0.618820\pi\) | ||||
−0.364675 | + | 0.931135i | \(0.618820\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.51116 | 0.0644949 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.03956i | 0.0868880i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.23170i | − | 0.0523770i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −38.2665 | −1.62432 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.5401i | 1.80248i | 0.433319 | + | 0.901241i | \(0.357342\pi\) | ||||
−0.433319 | + | 0.901241i | \(0.642658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.7805 | + | 5.98043i | −1.21729 | + | 0.252945i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7776i | 0.539470i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.44992 | 0.356122 | 0.178061 | − | 0.984019i | \(-0.443018\pi\) | ||||
0.178061 | + | 0.984019i | \(0.443018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.58546i | − | 0.277053i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 11.2475i | − | 0.472350i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.5192 | −1.40520 | −0.702599 | − | 0.711586i | \(-0.747977\pi\) | ||||
−0.702599 | + | 0.711586i | \(0.747977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8664 | −0.873233 | −0.436617 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436617 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.5977 | 1.36179 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 41.4977 | 1.73058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.23241i | − | 0.134567i | −0.997734 | − | 0.0672836i | \(-0.978567\pi\) | ||
0.997734 | − | 0.0672836i | \(-0.0214332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 43.4676i | − | 1.80645i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9980 | −0.456275 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.6554i | 0.524133i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.60610 | + | 17.3542i | 0.149094 | + | 0.717508i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 31.4601i | − | 1.29850i | −0.760575 | − | 0.649250i | \(-0.775083\pi\) | ||
0.760575 | − | 0.649250i | \(-0.224917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.17367 | 0.254382 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.81430i | 0.156899i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 5.56692i | − | 0.228606i | −0.993446 | − | 0.114303i | \(-0.963537\pi\) | ||
0.993446 | − | 0.114303i | \(-0.0364635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.5367 | 0.841921 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.5305 | 1.29046 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.8832 | −1.22099 | −0.610497 | − | 0.792018i | \(-0.709030\pi\) | ||||
−0.610497 | + | 0.792018i | \(0.709030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2407 | −0.417727 | −0.208864 | − | 0.977945i | \(-0.566977\pi\) | ||||
−0.208864 | + | 0.977945i | \(0.566977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.67267i | − | 0.393902i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.39046i | 0.137842i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.65268 | −0.188846 | −0.0944232 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944232 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.97062i | 0.160898i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.66479 | − | 8.01174i | −0.0673502 | − | 0.324120i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.25496i | 0.212246i | 0.994353 | + | 0.106123i | \(0.0338437\pi\) | ||||
−0.994353 | + | 0.106123i | \(0.966156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.1404 | 0.489550 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.6452i | − | 0.790884i | −0.918491 | − | 0.395442i | \(-0.870591\pi\) | ||
0.918491 | − | 0.395442i | \(-0.129409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5124i | 0.623497i | 0.950165 | + | 0.311748i | \(0.100915\pi\) | ||||
−0.950165 | + | 0.311748i | \(0.899085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.8907 | −0.838314 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.96113 | −0.118635 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.2881 | −0.611525 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.28577 | 0.0912849 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.4081i | 1.29219i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.7412i | 1.50246i | 0.660043 | + | 0.751228i | \(0.270538\pi\) | ||||
−0.660043 | + | 0.751228i | \(0.729462\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2302 | 0.525851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 68.6066i | − | 2.72257i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53014 | − | 0.733543i | 0.139869 | − | 0.0290640i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20.1666i | 0.797779i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2744 | −0.484811 | −0.242406 | − | 0.970175i | \(-0.577936\pi\) | ||||
−0.242406 | + | 0.970175i | \(0.577936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.5059i | 1.55796i | 0.627048 | + | 0.778980i | \(0.284263\pi\) | ||||
−0.627048 | + | 0.778980i | \(0.715737\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 58.3100i | 2.29595i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.5680 | 0.454786 | 0.227393 | − | 0.973803i | \(-0.426980\pi\) | ||||
0.227393 | + | 0.973803i | \(0.426980\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.70115 | 0.380803 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0189 | 0.471060 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.4016 | 0.798375 | 0.399188 | − | 0.916869i | \(-0.369292\pi\) | ||||
0.399188 | + | 0.916869i | \(0.369292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 51.5059i | − | 2.01250i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0219i | − | 0.469020i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1249 | −1.40723 | −0.703614 | − | 0.710582i | \(-0.748432\pi\) | ||||
−0.703614 | + | 0.710582i | \(0.748432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8050i | 1.23707i | 0.785757 | + | 0.618535i | \(0.212274\pi\) | ||||
−0.785757 | + | 0.618535i | \(0.787726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 45.1067 | − | 9.37290i | 1.75180 | − | 0.364013i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3.67379i | − | 0.142463i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0257 | 0.465637 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 50.0250i | − | 1.93408i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.04222i | − | 0.0402343i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.5632 | −1.48650 | −0.743251 | − | 0.669013i | \(-0.766717\pi\) | ||||
−0.743251 | + | 0.669013i | \(0.766717\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.2382 | −0.817458 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.8742 | 1.22503 | 0.612513 | − | 0.790460i | \(-0.290159\pi\) | ||||
0.612513 | + | 0.790460i | \(0.290159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.535647 | 0.0205562 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 57.7090i | − | 2.21142i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.9904i | − | 0.611856i | −0.952055 | − | 0.305928i | \(-0.901033\pi\) | ||
0.952055 | − | 0.305928i | \(-0.0989666\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.0821 | 0.843715 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.26664i | 0.239087i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.6754 | − | 9.28327i | 1.70200 | − | 0.353664i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.6269i | 1.20314i | 0.798819 | + | 0.601572i | \(0.205459\pi\) | ||||
−0.798819 | + | 0.601572i | \(0.794541\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.44995 | 0.0550791 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 32.1373i | − | 1.21904i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.2818i | − | 0.389451i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.10965 | 0.117618 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8564 | −0.901044 | −0.450522 | − | 0.892765i | \(-0.648762\pi\) | ||||
−0.450522 | + | 0.892765i | \(0.648762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.79745 | 0.218655 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.2320 | −0.611331 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 9.46249i | − | 0.355873i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2315i | 1.51093i | 0.655192 | + | 0.755463i | \(0.272588\pi\) | ||||
−0.655192 | + | 0.755463i | \(0.727412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.78590 | −0.0669765 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.4014i | − | 1.36324i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.9688 | − | 2.48705i | 0.447608 | − | 0.0930103i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.7429i | 0.924039i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.9884 | −1.41673 | −0.708363 | − | 0.705848i | \(-0.750566\pi\) | ||||
−0.708363 | + | 0.705848i | \(0.750566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.0615i | − | 0.598162i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.34682i | − | 0.0872792i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.2257 | 0.454053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.83158 | 0.327545 | 0.163773 | − | 0.986498i | \(-0.447634\pi\) | ||||
0.163773 | + | 0.986498i | \(0.447634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.38458 | 0.162392 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.3830 | 1.82650 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 41.0304i | − | 1.51549i | −0.652550 | − | 0.757746i | \(-0.726301\pi\) | ||
0.652550 | − | 0.757746i | \(-0.273699\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 7.15215i | − | 0.263811i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.67103 | −0.245731 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.90919i | 0.107016i | 0.998567 | + | 0.0535081i | \(0.0170403\pi\) | ||||
−0.998567 | + | 0.0535081i | \(0.982960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.67671 | − | 8.06910i | −0.0615955 | − | 0.296426i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31.5498i | − | 1.15745i | −0.815523 | − | 0.578724i | \(-0.803551\pi\) | ||
0.815523 | − | 0.578724i | \(-0.196449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.6115 | −1.01161 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.9466i | 0.583456i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.7042i | 0.683435i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.2106 | −1.72274 | −0.861369 | − | 0.507979i | \(-0.830393\pi\) | ||||
−0.861369 | + | 0.507979i | \(0.830393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.9863 | −2.25891 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.9932 | −1.30993 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.3429 | 1.61167 | 0.805835 | − | 0.592140i | \(-0.201717\pi\) | ||||
0.805835 | + | 0.592140i | \(0.201717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 13.4774i | − | 0.489200i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.2642i | 1.38708i | 0.720420 | + | 0.693538i | \(0.243949\pi\) | ||||
−0.720420 | + | 0.693538i | \(0.756051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.9856 | 0.470112 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 29.7772i | − | 1.07660i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.11621 | − | 34.2465i | −0.256951 | − | 1.23657i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.0112i | 1.33466i | 0.744763 | + | 0.667329i | \(0.232563\pi\) | ||||
−0.744763 | + | 0.667329i | \(0.767437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.78423 | 0.244328 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 26.1438i | − | 0.940325i | −0.882580 | − | 0.470163i | \(-0.844195\pi\) | ||
0.882580 | − | 0.470163i | \(-0.155805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 37.0069i | − | 1.32933i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.2865 | 0.404902 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.83930 | −0.0658999 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.9085 | 0.497684 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.15465 | −0.219949 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 49.5629i | − | 1.76897i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.6164i | − | 1.02006i | −0.860155 | − | 0.510032i | \(-0.829634\pi\) | ||
0.860155 | − | 0.510032i | \(-0.170366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.8942 | −1.34907 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.94235i | 0.0690620i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.67918 | + | 0.764511i | −0.130651 | + | 0.0271486i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 90.5132i | − | 3.21017i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.2134 | −1.07022 | −0.535108 | − | 0.844784i | \(-0.679729\pi\) | ||||
−0.535108 | + | 0.844784i | \(0.679729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.7469i | 0.486331i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.29350i | 0.151703i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.29126 | −0.292592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.6615 | −0.763468 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.1044 | 0.707709 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.3543 | −1.38362 | −0.691811 | − | 0.722079i | \(-0.743187\pi\) | ||||
−0.691811 | + | 0.722079i | \(0.743187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.8199i | − | 0.766202i | −0.923707 | − | 0.383101i | \(-0.874856\pi\) | ||
0.923707 | − | 0.383101i | \(-0.125144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.0896i | 1.54629i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −65.4925 | −2.29410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.83409i | − | 0.309066i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06360 | − | 5.11854i | −0.0371653 | − | 0.178856i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8303i | 1.39009i | 0.718968 | + | 0.695044i | \(0.244615\pi\) | ||||
−0.718968 | + | 0.695044i | \(0.755385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7997 | 0.829605 | 0.414803 | − | 0.909911i | \(-0.363851\pi\) | ||||
0.414803 | + | 0.909911i | \(0.363851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 13.7016i | − | 0.477030i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.44588i | − | 0.154598i | −0.997008 | − | 0.0772992i | \(-0.975370\pi\) | ||
0.997008 | − | 0.0772992i | \(-0.0246297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.96779 | 0.103076 | 0.0515379 | − | 0.998671i | \(-0.483588\pi\) | ||||
0.0515379 | + | 0.998671i | \(0.483588\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.1565 | −0.976737 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.05719 | −0.209869 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.4082 | 1.81366 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.6299i | 0.643945i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.62600i | − | 0.228755i | −0.993437 | − | 0.114378i | \(-0.963513\pi\) | ||
0.993437 | − | 0.114378i | \(-0.0364874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.4571 | −0.877830 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.386660i | − | 0.0133173i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.5593 | − | 40.4273i | −0.604058 | − | 1.39074i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.02866 | −0.275543 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 34.1831i | − | 1.17178i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6224i | 0.432184i | 0.976373 | + | 0.216092i | \(0.0693311\pi\) | ||||
−0.976373 | + | 0.216092i | \(0.930669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.32681 | −0.182173 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.1596 | 0.483683 | 0.241841 | − | 0.970316i | \(-0.422249\pi\) | ||||
0.241841 | + | 0.970316i | \(0.422249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.3533 | −1.58156 | −0.790778 | − | 0.612104i | \(-0.790324\pi\) | ||||
−0.790778 | + | 0.612104i | \(0.790324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.58077 | −0.122032 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.2760i | 1.30293i | 0.758679 | + | 0.651465i | \(0.225845\pi\) | ||||
−0.758679 | + | 0.651465i | \(0.774155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 43.0795i | − | 1.46475i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.5349 | −1.41060 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.23170i | 0.0417824i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.89348 | + | 23.5497i | 0.165809 | + | 0.797951i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.776662i | − | 0.0262860i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.06952 | −0.171381 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5870i | 0.391266i | 0.980677 | + | 0.195633i | \(0.0626761\pi\) | ||||
−0.980677 | + | 0.195633i | \(0.937324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 47.2928i | − | 1.59515i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.1642 | 1.69007 | 0.845037 | − | 0.534708i | \(-0.179578\pi\) | ||||
0.845037 | + | 0.534708i | \(0.179578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.0193 | −1.38041 | −0.690204 | − | 0.723615i | \(-0.742479\pi\) | ||||
−0.690204 | + | 0.723615i | \(0.742479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −69.3841 | −2.33232 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.42094 | −0.0812871 | −0.0406435 | − | 0.999174i | \(-0.512941\pi\) | ||||
−0.0406435 | + | 0.999174i | \(0.512941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2352i | 0.678666i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.2475i | 0.376805i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.45917 | 0.0822931 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 36.9280i | − | 1.23437i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.5773 | + | 9.88628i | −1.58856 | + | 0.330093i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 10.7243i | − | 0.357676i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.6561 | −2.55379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 17.1983i | − | 0.572322i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 42.5071i | − | 1.41298i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0320 | 1.19642 | 0.598211 | − | 0.801338i | \(-0.295878\pi\) | ||||
0.598211 | + | 0.801338i | \(0.295878\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7202 | −0.455069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.77033 | 0.158048 | 0.0790241 | − | 0.996873i | \(-0.474820\pi\) | ||||
0.0790241 | + | 0.996873i | \(0.474820\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9980 | 0.363981 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.45409i | 0.246425i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.1914i | 0.501665i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.1280 | −0.663961 | −0.331980 | − | 0.943286i | \(-0.607717\pi\) | ||||
−0.331980 | + | 0.943286i | \(0.607717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 62.1346i | − | 2.04740i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.2025 | − | 49.0989i | −0.335818 | − | 1.61611i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 34.7518i | − | 1.14263i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.2884 | −0.764893 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.1004i | − | 1.41408i | −0.707174 | − | 0.707040i | \(-0.750030\pi\) | ||
0.707174 | − | 0.707040i | \(-0.249970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.08356i | 0.0355124i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.55961 | −0.116536 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.5367 | −0.671621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.1060 | 1.66956 | 0.834781 | − | 0.550583i | \(-0.185594\pi\) | ||||
0.834781 | + | 0.550583i | \(0.185594\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.3034 | −0.988915 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.7070i | 1.49001i | 0.667061 | + | 0.745003i | \(0.267552\pi\) | ||||
−0.667061 | + | 0.745003i | \(0.732448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8450i | 0.353160i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.0862 | 0.360633 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 29.9119i | − | 0.972005i | −0.873957 | − | 0.486003i | \(-0.838455\pi\) | ||
0.873957 | − | 0.486003i | \(-0.161545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.08199 | + | 29.2693i | 0.197430 | + | 0.950123i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.6648i | 1.64292i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.8982 | 1.26004 | 0.630018 | − | 0.776580i | \(-0.283047\pi\) | ||||
0.630018 | + | 0.776580i | \(0.283047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.3924i | 1.69538i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.97062i | − | 0.128352i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.51302 | −0.210316 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.46215 | −0.0471660 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.1201 | 0.873934 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 69.8629 | 2.24897 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5034i | 0.498555i | 0.968432 | + | 0.249278i | \(0.0801932\pi\) | ||||
−0.968432 | + | 0.249278i | \(0.919807\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8453i | 0.444777i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.05075 | −0.0658117 | −0.0329059 | − | 0.999458i | \(-0.510476\pi\) | ||||
−0.0329059 | + | 0.999458i | \(0.510476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.47873i | 0.303874i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −48.3687 | + | 10.0507i | −1.54904 | + | 0.321881i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.12610i | 0.0680200i | 0.999421 | + | 0.0340100i | \(0.0108278\pi\) | ||||
−0.999421 | + | 0.0340100i | \(0.989172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.96113 | 0.0946381 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 18.8286i | − | 0.601149i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.5890i | 1.64543i | 0.568451 | + | 0.822717i | \(0.307543\pi\) | ||||
−0.568451 | + | 0.822717i | \(0.692457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.13051 | −0.195334 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.78753 | 0.152389 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.0878 | −1.65630 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.8263 | 1.45572 | 0.727861 | − | 0.685725i | \(-0.240515\pi\) | ||||
0.727861 | + | 0.685725i | \(0.240515\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 55.8655i | 1.77284i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.6772i | 1.60658i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9847 | 0.537912 | 0.268956 | − | 0.963152i | \(-0.413321\pi\) | ||||
0.268956 | + | 0.963152i | \(0.413321\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.4946i | 0.553506i |
(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 | 4004.2.m.c.2157.7 | ✓ | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.8 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.7 | ✓ | 36 | 1.1 | even | 1 | trivial | |
4004.2.m.c.2157.8 | yes | 36 | 13.12 | even | 2 | inner |