Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3564,2,Mod(1189,3564)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3564, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3564.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3564.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.4586832804\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2377.2 | ||
Root | \(1.81730 + 1.81730i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3564.2377 |
Dual form | 3564.2.i.t.1189.2 |
$q$-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 \(\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times\).
\(n\) | \(1541\) | \(1783\) | \(2917\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.665179 | + | 1.15212i | −0.297477 | + | 0.515246i | −0.975558 | − | 0.219742i | \(-0.929479\pi\) |
0.678081 | + | 0.734987i | \(0.262812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41905 | + | 4.18992i | 0.914315 | + | 1.58364i | 0.807901 | + | 0.589318i | \(0.200603\pi\) |
0.106414 | + | 0.994322i | \(0.466063\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.299154 | − | 0.518150i | 0.0829704 | − | 0.143709i | −0.821554 | − | 0.570130i | \(-0.806893\pi\) |
0.904525 | + | 0.426422i | \(0.140226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.47271 | 1.81240 | 0.906199 | − | 0.422852i | \(-0.138971\pi\) | ||||
0.906199 | + | 0.422852i | \(0.138971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.41487 | 0.554009 | 0.277004 | − | 0.960869i | \(-0.410658\pi\) | ||||
0.277004 | + | 0.960869i | \(0.410658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.764279 | − | 1.32377i | 0.159363 | − | 0.276025i | −0.775276 | − | 0.631623i | \(-0.782389\pi\) |
0.934639 | + | 0.355597i | \(0.115723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.61507 | + | 2.79739i | 0.323015 | + | 0.559478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.43428 | − | 2.48425i | −0.266339 | − | 0.461313i | 0.701574 | − | 0.712596i | \(-0.252481\pi\) |
−0.967914 | + | 0.251283i | \(0.919148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.98907 | − | 5.17722i | 0.536853 | − | 0.929857i | −0.462218 | − | 0.886766i | \(-0.652946\pi\) |
0.999071 | − | 0.0430905i | \(-0.0137204\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.43641 | −1.08795 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.73332 | 1.60015 | 0.800074 | − | 0.599902i | \(-0.204794\pi\) | ||||
0.800074 | + | 0.599902i | \(0.204794\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.01471 | − | 5.22163i | 0.470819 | − | 0.815482i | −0.528624 | − | 0.848856i | \(-0.677292\pi\) |
0.999443 | + | 0.0333739i | \(0.0106252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.64336 | + | 2.84638i | 0.250610 | + | 0.434069i | 0.963694 | − | 0.267009i | \(-0.0860355\pi\) |
−0.713084 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.30866 | − | 3.99872i | −0.336753 | − | 0.583273i | 0.647067 | − | 0.762433i | \(-0.275995\pi\) |
−0.983820 | + | 0.179160i | \(0.942662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.20360 | + | 14.2091i | −1.17194 | + | 2.02987i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.59097 | −0.630618 | −0.315309 | − | 0.948989i | \(-0.602108\pi\) | ||||
−0.315309 | + | 0.948989i | \(0.602108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.33036 | −0.179386 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.74346 | − | 8.21592i | 0.617546 | − | 1.06962i | −0.372386 | − | 0.928078i | \(-0.621460\pi\) |
0.989932 | − | 0.141543i | \(-0.0452065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.73320 | + | 8.19815i | 0.606025 | + | 1.04967i | 0.991889 | + | 0.127110i | \(0.0405701\pi\) |
−0.385864 | + | 0.922556i | \(0.626097\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.397982 | + | 0.689325i | 0.0493636 | + | 0.0855002i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.25043 | − | 2.16581i | 0.152765 | − | 0.264596i | −0.779478 | − | 0.626429i | \(-0.784516\pi\) |
0.932243 | + | 0.361833i | \(0.117849\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.142348 | 0.0168937 | 0.00844683 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844683 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6564 | −1.36428 | −0.682139 | − | 0.731223i | \(-0.738950\pi\) | ||||
−0.682139 | + | 0.731223i | \(0.738950\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.41905 | + | 4.18992i | −0.275676 | + | 0.477485i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.309059 | + | 0.535306i | 0.0347719 | + | 0.0602266i | 0.882888 | − | 0.469584i | \(-0.155596\pi\) |
−0.848116 | + | 0.529811i | \(0.822263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.04948 | + | 12.2101i | 0.773781 | + | 1.34023i | 0.935477 | + | 0.353387i | \(0.114970\pi\) |
−0.161697 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97069 | + | 8.60949i | −0.539147 | + | 0.933830i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.35318 | −0.779436 | −0.389718 | − | 0.920934i | \(-0.627427\pi\) | ||||
−0.389718 | + | 0.920934i | \(0.627427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.89467 | 0.303444 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.60632 | + | 2.78223i | −0.164805 | + | 0.285451i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.33724 | + | 2.31616i | 0.135776 | + | 0.235170i | 0.925894 | − | 0.377785i | \(-0.123314\pi\) |
−0.790118 | + | 0.612955i | \(0.789981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.52028 | + | 9.56140i | 0.549288 | + | 0.951395i | 0.998324 | + | 0.0578808i | \(0.0184343\pi\) |
−0.449036 | + | 0.893514i | \(0.648232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.17709 | − | 3.77084i | 0.214515 | − | 0.371552i | −0.738607 | − | 0.674136i | \(-0.764516\pi\) |
0.953123 | + | 0.302584i | \(0.0978494\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4796 | −1.39979 | −0.699897 | − | 0.714244i | \(-0.746771\pi\) | ||||
−0.699897 | + | 0.714244i | \(0.746771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.98019 | −0.381233 | −0.190617 | − | 0.981665i | \(-0.561049\pi\) | ||||
−0.190617 | + | 0.981665i | \(0.561049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.48158 | − | 14.6905i | 0.797880 | − | 1.38197i | −0.123114 | − | 0.992393i | \(-0.539288\pi\) |
0.920994 | − | 0.389576i | \(-0.127379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.01677 | + | 1.76109i | 0.0948138 | + | 0.164222i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.0769 | + | 31.3100i | 1.65710 | + | 2.87019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9490 | −0.979312 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.48257 | −0.663971 | −0.331985 | − | 0.943285i | \(-0.607718\pi\) | ||||
−0.331985 | + | 0.943285i | \(0.607718\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.72987 | − | 8.19238i | 0.413251 | − | 0.715772i | −0.581992 | − | 0.813194i | \(-0.697727\pi\) |
0.995243 | + | 0.0974227i | \(0.0310599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.84169 | + | 10.1181i | 0.506539 | + | 0.877351i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.07989 | − | 13.9948i | −0.690311 | − | 1.19565i | −0.971736 | − | 0.236071i | \(-0.924140\pi\) |
0.281424 | − | 0.959583i | \(-0.409193\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7634 | + | 18.6427i | −0.912937 | + | 1.58125i | −0.103043 | + | 0.994677i | \(0.532858\pi\) |
−0.809894 | + | 0.586576i | \(0.800475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.598308 | 0.0500330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.81622 | 0.316920 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.09460 | + | 14.0203i | −0.663135 | + | 1.14858i | 0.316652 | + | 0.948542i | \(0.397441\pi\) |
−0.979787 | + | 0.200042i | \(0.935892\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.58143 | − | 7.93527i | −0.372832 | − | 0.645763i | 0.617168 | − | 0.786831i | \(-0.288280\pi\) |
−0.990000 | + | 0.141068i | \(0.954946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.97654 | + | 6.88756i | 0.319403 | + | 0.553222i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5000 | + | 19.9185i | −0.917798 | + | 1.58967i | −0.115044 | + | 0.993360i | \(0.536701\pi\) |
−0.802753 | + | 0.596312i | \(0.796632\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.39532 | 0.582833 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.30655 | −0.180663 | −0.0903316 | − | 0.995912i | \(-0.528793\pi\) | ||||
−0.0903316 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.56951 | − | 14.8428i | 0.663128 | − | 1.14857i | −0.316661 | − | 0.948539i | \(-0.602562\pi\) |
0.979789 | − | 0.200033i | \(-0.0641050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.32101 | + | 10.9483i | 0.486232 | + | 0.842178i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.54604 | − | 6.14192i | −0.269600 | − | 0.466961i | 0.699158 | − | 0.714967i | \(-0.253558\pi\) |
−0.968759 | + | 0.248006i | \(0.920225\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.81388 | + | 13.5340i | −0.590674 | + | 1.02308i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.7442 | −1.32626 | −0.663131 | − | 0.748503i | \(-0.730773\pi\) | ||||
−0.663131 | + | 0.748503i | \(0.730773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1753 | 0.830656 | 0.415328 | − | 0.909672i | \(-0.363667\pi\) | ||||
0.415328 | + | 0.909672i | \(0.363667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.47440 | + | 11.2140i | −0.476007 | + | 0.824469i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.73635 | + | 6.47155i | 0.273229 | + | 0.473247i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0795 | − | 20.9223i | −0.874042 | − | 1.51388i | −0.857780 | − | 0.514017i | \(-0.828157\pi\) |
−0.0162618 | − | 0.999868i | \(-0.505177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2172 | − | 17.6967i | 0.735450 | − | 1.27384i | −0.219076 | − | 0.975708i | \(-0.570304\pi\) |
0.954526 | − | 0.298128i | \(-0.0963623\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.28776 | 0.0917491 | 0.0458745 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458745 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0157 | 0.993547 | 0.496774 | − | 0.867880i | \(-0.334518\pi\) | ||||
0.496774 | + | 0.867880i | \(0.334518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.93920 | − | 12.0190i | 0.487036 | − | 0.843571i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.01065 | + | 6.94664i | 0.280116 | + | 0.485175i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.20743 | + | 2.09134i | 0.0835200 | + | 0.144661i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.37400 | − | 4.11189i | 0.163433 | − | 0.283074i | −0.772665 | − | 0.634814i | \(-0.781077\pi\) |
0.936098 | + | 0.351740i | \(0.114410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.37251 | −0.298203 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.9229 | 1.96341 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23549 | − | 3.87198i | 0.150375 | − | 0.260458i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1674 | − | 17.6105i | −0.680861 | − | 1.17929i | −0.974719 | − | 0.223436i | \(-0.928273\pi\) |
0.293858 | − | 0.955849i | \(-0.405061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9589 | + | 25.9095i | 0.992854 | + | 1.71967i | 0.599772 | + | 0.800171i | \(0.295258\pi\) |
0.393083 | + | 0.919503i | \(0.371409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.05997 | − | 3.56798i | 0.136127 | − | 0.235779i | −0.789900 | − | 0.613235i | \(-0.789868\pi\) |
0.926027 | + | 0.377456i | \(0.123201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6559 | 1.09117 | 0.545583 | − | 0.838057i | \(-0.316308\pi\) | ||||
0.545583 | + | 0.838057i | \(0.316308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.14269 | 0.400705 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.63409 | + | 14.9547i | −0.558493 | + | 0.967339i | 0.439129 | + | 0.898424i | \(0.355287\pi\) |
−0.997623 | + | 0.0689147i | \(0.978046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.65375 | + | 14.9887i | 0.557437 | + | 0.965509i | 0.997709 | + | 0.0676448i | \(0.0215485\pi\) |
−0.440273 | + | 0.897864i | \(0.645118\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.9137 | − | 18.9031i | −0.697253 | − | 1.20768i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.722417 | − | 1.25126i | 0.0459663 | − | 0.0796160i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.50545 | −0.410620 | −0.205310 | − | 0.978697i | \(-0.565820\pi\) | ||||
−0.205310 | + | 0.978697i | \(0.565820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.52856 | 0.0960996 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.00358 | − | 1.73825i | 0.0626017 | − | 0.108429i | −0.833026 | − | 0.553234i | \(-0.813394\pi\) |
0.895628 | + | 0.444805i | \(0.146727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.5454 | + | 40.7818i | 1.46304 | + | 2.53406i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.95990 | − | 8.59080i | −0.305841 | − | 0.529731i | 0.671608 | − | 0.740907i | \(-0.265604\pi\) |
−0.977448 | + | 0.211176i | \(0.932271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.05382 | − | 5.28937i | 0.187594 | − | 0.324923i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2380 | −0.990048 | −0.495024 | − | 0.868879i | \(-0.664841\pi\) | ||||
−0.495024 | + | 0.868879i | \(0.664841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.22363 | −0.256567 | −0.128284 | − | 0.991738i | \(-0.540947\pi\) | ||||
−0.128284 | + | 0.991738i | \(0.540947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.61507 | + | 2.79739i | −0.0973926 | + | 0.168689i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.74664 | + | 8.22142i | 0.285198 | + | 0.493977i | 0.972657 | − | 0.232246i | \(-0.0746073\pi\) |
−0.687459 | + | 0.726223i | \(0.741274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4056 | + | 21.4871i | 0.740056 | + | 1.28181i | 0.952469 | + | 0.304634i | \(0.0985343\pi\) |
−0.212414 | + | 0.977180i | \(0.568132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.00231 | + | 15.5925i | −0.535132 | + | 0.926875i | 0.464025 | + | 0.885822i | \(0.346405\pi\) |
−0.999157 | + | 0.0410531i | \(0.986929\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.1709 | 1.72191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.8414 | 2.28479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.35498 | + | 7.54305i | −0.254421 | + | 0.440670i | −0.964738 | − | 0.263212i | \(-0.915218\pi\) |
0.710317 | + | 0.703882i | \(0.248552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.31051 | + | 10.9301i | 0.367412 | + | 0.636376i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.457274 | − | 0.792022i | −0.0264448 | − | 0.0458038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.95074 | + | 13.7711i | −0.458273 | + | 0.793752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.5937 | −0.721114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4202 | −0.880080 | −0.440040 | − | 0.897978i | \(-0.645036\pi\) | ||||
−0.440040 | + | 0.897978i | \(0.645036\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.53325 | − | 4.38772i | 0.143648 | − | 0.248805i | −0.785220 | − | 0.619217i | \(-0.787450\pi\) |
0.928868 | + | 0.370412i | \(0.120784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.413716 | − | 0.716577i | −0.0233846 | − | 0.0405033i | 0.854096 | − | 0.520115i | \(-0.174111\pi\) |
−0.877481 | + | 0.479612i | \(0.840778\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.57902 | + | 6.19905i | 0.201018 | + | 0.348173i | 0.948857 | − | 0.315707i | \(-0.102242\pi\) |
−0.747839 | + | 0.663881i | \(0.768908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.43428 | − | 2.48425i | 0.0803043 | − | 0.139091i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.0456 | 1.00408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.93262 | 0.107203 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1695 | − | 19.3462i | 0.615796 | − | 1.06659i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.212128 | + | 0.367417i | 0.0116596 | + | 0.0201950i | 0.871796 | − | 0.489868i | \(-0.162955\pi\) |
−0.860137 | + | 0.510064i | \(0.829622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.66352 | + | 2.88131i | 0.0908880 | + | 0.157423i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8431 | − | 30.9052i | 0.971977 | − | 1.68351i | 0.282409 | − | 0.959294i | \(-0.408867\pi\) |
0.689569 | − | 0.724220i | \(-0.257800\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.97814 | 0.323735 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.5130 | −2.45747 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.877257 | + | 1.51945i | −0.0470936 | + | 0.0815686i | −0.888611 | − | 0.458661i | \(-0.848329\pi\) |
0.841518 | + | 0.540230i | \(0.181663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.47728 | + | 4.29077i | 0.132606 | + | 0.229680i | 0.924680 | − | 0.380745i | \(-0.124332\pi\) |
−0.792075 | + | 0.610424i | \(0.790999\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.17126 | − | 12.4210i | −0.381688 | − | 0.661103i | 0.609616 | − | 0.792697i | \(-0.291324\pi\) |
−0.991304 | + | 0.131594i | \(0.957990\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0946873 | + | 0.164003i | −0.00502548 | + | 0.00870438i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.4052 | −0.654719 | −0.327360 | − | 0.944900i | \(-0.606159\pi\) | ||||
−0.327360 | + | 0.944900i | \(0.606159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1684 | −0.693074 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.75359 | − | 13.4296i | 0.405841 | − | 0.702938i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.91167 | − | 11.9714i | −0.360786 | − | 0.624900i | 0.627304 | − | 0.778774i | \(-0.284158\pi\) |
−0.988090 | + | 0.153874i | \(0.950825\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.1058 | − | 19.2358i | −0.576583 | − | 0.998672i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0460 | − | 22.5964i | 0.675497 | − | 1.17000i | −0.300826 | − | 0.953679i | \(-0.597262\pi\) |
0.976323 | − | 0.216316i | \(-0.0694043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.71628 | −0.0883931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0276 | 0.566451 | 0.283225 | − | 0.959053i | \(-0.408596\pi\) | ||||
0.283225 | + | 0.959053i | \(0.408596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.9756 | + | 32.8668i | −0.969610 | + | 1.67941i | −0.272925 | + | 0.962035i | \(0.587991\pi\) |
−0.696685 | + | 0.717378i | \(0.745342\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.21820 | − | 5.57409i | −0.164015 | − | 0.284082i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0487514 | + | 0.0844398i | 0.00247179 | + | 0.00428127i | 0.867259 | − | 0.497858i | \(-0.165880\pi\) |
−0.864787 | + | 0.502139i | \(0.832547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.71123 | − | 9.89215i | 0.288830 | − | 0.500267i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.822319 | −0.0413753 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.9953 | −0.752594 | −0.376297 | − | 0.926499i | \(-0.622803\pi\) | ||||
−0.376297 | + | 0.926499i | \(0.622803\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.774675 | + | 1.34178i | −0.0386854 | + | 0.0670051i | −0.884720 | − | 0.466123i | \(-0.845650\pi\) |
0.846034 | + | 0.533128i | \(0.178984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.78838 | − | 3.09757i | −0.0890858 | − | 0.154301i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.86666 | + | 8.42930i | 0.241231 | + | 0.417825i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.26896 | + | 9.12610i | −0.260533 | + | 0.451257i | −0.966384 | − | 0.257104i | \(-0.917232\pi\) |
0.705851 | + | 0.708361i | \(0.250565\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.8987 | 2.25853 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.7567 | −0.920728 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9759 | − | 29.4031i | 0.829328 | − | 1.43644i | −0.0692388 | − | 0.997600i | \(-0.522057\pi\) |
0.898566 | − | 0.438838i | \(-0.144610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.61751 | − | 9.72981i | −0.273781 | − | 0.474202i | 0.696046 | − | 0.717997i | \(-0.254941\pi\) |
−0.969827 | + | 0.243795i | \(0.921608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0690 | + | 20.9041i | 0.585431 | + | 1.01400i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.8997 | + | 39.6635i | −1.10819 | + | 1.91945i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.2229 | −1.55212 | −0.776061 | − | 0.630658i | \(-0.782785\pi\) | ||||
−0.776061 | + | 0.630658i | \(0.782785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.2169 | 1.25991 | 0.629953 | − | 0.776633i | \(-0.283074\pi\) | ||||
0.629953 | + | 0.776633i | \(0.283074\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.84563 | − | 3.19673i | 0.0882886 | − | 0.152920i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.1053 | − | 24.4310i | −0.673208 | − | 1.16603i | −0.976989 | − | 0.213288i | \(-0.931583\pi\) |
0.303782 | − | 0.952742i | \(-0.401751\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.0190 | − | 19.0854i | −0.523527 | − | 0.906776i | −0.999625 | − | 0.0273836i | \(-0.991282\pi\) |
0.476098 | − | 0.879392i | \(-0.342051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89118 | − | 8.47178i | 0.231864 | − | 0.401601i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.6704 | −0.692338 | −0.346169 | − | 0.938172i | \(-0.612518\pi\) | ||||
−0.346169 | + | 0.938172i | \(0.612518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.02942 | 0.283914 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.92548 | + | 3.33502i | −0.0902677 | + | 0.156348i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3679 | − | 19.6897i | −0.531767 | − | 0.921048i | −0.999312 | − | 0.0370785i | \(-0.988195\pi\) |
0.467545 | − | 0.883969i | \(-0.345138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.11156 | − | 14.0496i | −0.377793 | − | 0.654357i | 0.612948 | − | 0.790123i | \(-0.289984\pi\) |
−0.990741 | + | 0.135767i | \(0.956650\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.39403 | + | 14.5389i | −0.390104 | + | 0.675680i | −0.992463 | − | 0.122546i | \(-0.960894\pi\) |
0.602359 | + | 0.798225i | \(0.294228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.9741 | −0.507822 | −0.253911 | − | 0.967228i | \(-0.581717\pi\) | ||||
−0.253911 | + | 0.967228i | \(0.581717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0994 | 0.558700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.64336 | + | 2.84638i | −0.0755617 | + | 0.130877i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.90019 | + | 6.75533i | 0.178953 | + | 0.309956i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.95307 | + | 3.38282i | 0.0892382 | + | 0.154565i | 0.907189 | − | 0.420723i | \(-0.138223\pi\) |
−0.817951 | + | 0.575288i | \(0.804890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.91176 | − | 5.04332i | 0.132765 | − | 0.229955i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.55801 | −0.161561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.4163 | −1.87675 | −0.938376 | − | 0.345615i | \(-0.887670\pi\) | ||||
−0.938376 | + | 0.345615i | \(0.887670\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.70955 | − | 16.8174i | 0.438186 | − | 0.758960i | −0.559364 | − | 0.828922i | \(-0.688954\pi\) |
0.997550 | + | 0.0699620i | \(0.0222878\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.7180 | − | 18.5641i | −0.482713 | − | 0.836083i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.344348 | + | 0.596428i | 0.0154461 | + | 0.0267535i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.14534 | + | 14.1081i | −0.364635 | + | 0.631567i | −0.988718 | − | 0.149792i | \(-0.952140\pi\) |
0.624082 | + | 0.781359i | \(0.285473\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.89003 | 0.396387 | 0.198193 | − | 0.980163i | \(-0.436493\pi\) | ||||
0.198193 | + | 0.980163i | \(0.436493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6879 | −0.653603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.46378 | − | 9.46355i | 0.242178 | − | 0.419464i | −0.719156 | − | 0.694848i | \(-0.755472\pi\) |
0.961334 | + | 0.275384i | \(0.0888049\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1974 | − | 48.8393i | −1.24738 | − | 2.16052i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.89632 | + | 5.01657i | 0.127627 | + | 0.221056i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.30866 | − | 3.99872i | 0.101535 | − | 0.175863i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.3814 | 1.06817 | 0.534084 | − | 0.845431i | \(-0.320657\pi\) | ||||
0.534084 | + | 0.845431i | \(0.320657\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.8100 | −0.997412 | −0.498706 | − | 0.866771i | \(-0.666191\pi\) | ||||
−0.498706 | + | 0.866771i | \(0.666191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.3365 | − | 38.6879i | 0.972991 | − | 1.68527i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.3318 | + | 17.8951i | 0.449207 | + | 0.778049i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.80373 | − | 3.12414i | −0.0781280 | − | 0.135322i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.63152 | − | 16.6823i | 0.416407 | − | 0.721238i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.4072 | −0.706709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8424 | −0.724112 | −0.362056 | − | 0.932156i | \(-0.617925\pi\) | ||||
−0.362056 | + | 0.932156i | \(0.617925\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.64754 | − | 4.58567i | 0.113408 | − | 0.196429i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.2323 | − | 28.1151i | −0.694042 | − | 1.20212i | −0.970503 | − | 0.241091i | \(-0.922495\pi\) |
0.276460 | − | 0.961025i | \(-0.410839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46360 | − | 5.99913i | −0.147554 | − | 0.255572i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.49526 | + | 2.58986i | −0.0635849 | + | 0.110132i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.7403 | −0.963537 | −0.481769 | − | 0.876298i | \(-0.660005\pi\) | ||||
−0.481769 | + | 0.876298i | \(0.660005\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.96647 | 0.0831728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0171 | + | 20.8142i | −0.506460 | + | 0.877214i | 0.493512 | + | 0.869739i | \(0.335713\pi\) |
−0.999972 | + | 0.00747504i | \(0.997621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.2835 | + | 19.5437i | 0.474702 | + | 0.822208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8496 | + | 32.6485i | 0.790218 | + | 1.36870i | 0.925832 | + | 0.377936i | \(0.123366\pi\) |
−0.135614 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7610 | − | 27.2989i | 0.659578 | − | 1.14242i | −0.321147 | − | 0.947029i | \(-0.604068\pi\) |
0.980725 | − | 0.195393i | \(-0.0625982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.93747 | 0.205907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.3431 | 1.13831 | 0.569153 | − | 0.822232i | \(-0.307271\pi\) | ||||
0.569153 | + | 0.822232i | \(0.307271\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.1061 | + | 59.0734i | −1.41496 | + | 2.45078i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.29548 | − | 3.97589i | −0.0950692 | − | 0.164665i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.16685 | − | 7.21720i | −0.171984 | − | 0.297886i | 0.767129 | − | 0.641493i | \(-0.221685\pi\) |
−0.939114 | + | 0.343607i | \(0.888351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.21822 | − | 12.5023i | 0.297421 | − | 0.515149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.73195 | 0.317513 | 0.158757 | − | 0.987318i | \(-0.449252\pi\) | ||||
0.158757 | + | 0.987318i | \(0.449252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.0974 | −1.97180 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4097 | + | 30.1544i | −0.711340 | + | 1.23208i | 0.253014 | + | 0.967463i | \(0.418578\pi\) |
−0.964354 | + | 0.264615i | \(0.914755\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9241 | − | 22.3853i | −0.527186 | − | 0.913114i | −0.999498 | − | 0.0316820i | \(-0.989914\pi\) |
0.472312 | − | 0.881432i | \(-0.343420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.665179 | − | 1.15212i | −0.0270434 | − | 0.0468405i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.64647 | − | 9.77997i | 0.229183 | − | 0.396957i | −0.728383 | − | 0.685170i | \(-0.759728\pi\) |
0.957566 | + | 0.288213i | \(0.0930612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.76258 | −0.111762 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9140 | 0.521590 | 0.260795 | − | 0.965394i | \(-0.416015\pi\) | ||||
0.260795 | + | 0.965394i | \(0.416015\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8911 | + | 25.7922i | −0.599494 | + | 1.03835i | 0.393402 | + | 0.919367i | \(0.371298\pi\) |
−0.992896 | + | 0.118987i | \(0.962035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.31714 | + | 5.74545i | 0.133327 | + | 0.230929i | 0.924957 | − | 0.380072i | \(-0.124101\pi\) |
−0.791630 | + | 0.611001i | \(0.790767\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.7877 | − | 30.8092i | −0.712650 | − | 1.23435i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.792287 | + | 1.37228i | −0.0316915 | + | 0.0548912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 72.7342 | 2.90010 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.68229 | −0.385446 | −0.192723 | − | 0.981253i | \(-0.561732\pi\) | ||||
−0.192723 | + | 0.981253i | \(0.561732\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.97725 | − | 8.62085i | 0.197516 | − | 0.342108i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.90828 | + | 8.50139i | 0.194473 | + | 0.336837i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3286 | + | 19.6217i | 0.447452 | + | 0.775009i | 0.998219 | − | 0.0596497i | \(-0.0189984\pi\) |
−0.550768 | + | 0.834658i | \(0.685665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.53510 | + | 13.0512i | −0.297155 | + | 0.514688i | −0.975484 | − | 0.220070i | \(-0.929371\pi\) |
0.678329 | + | 0.734759i | \(0.262705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.19177 | 0.164795 | 0.0823977 | − | 0.996600i | \(-0.473742\pi\) | ||||
0.0823977 | + | 0.996600i | \(0.473742\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.48692 | 0.372394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.7483 | + | 34.2050i | −0.772809 | + | 1.33854i | 0.163209 | + | 0.986592i | \(0.447816\pi\) |
−0.936018 | + | 0.351953i | \(0.885518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.29243 | + | 10.8988i | 0.245866 | + | 0.425852i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9623 | + | 36.3078i | 0.816575 | + | 1.41435i | 0.908191 | + | 0.418556i | \(0.137463\pi\) |
−0.0916159 | + | 0.995794i | \(0.529203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9531 | − | 34.5599i | 0.776087 | − | 1.34422i | −0.158094 | − | 0.987424i | \(-0.550535\pi\) |
0.934181 | − | 0.356799i | \(-0.116132\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.5431 | −0.602735 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.38477 | −0.169779 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.73320 | + | 8.19815i | −0.182723 | + | 0.316486i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4626 | − | 21.5859i | −0.480400 | − | 0.832077i | 0.519347 | − | 0.854563i | \(-0.326175\pi\) |
−0.999747 | + | 0.0224863i | \(0.992842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.3324 | − | 42.1449i | −0.935170 | − | 1.61976i | −0.774331 | − | 0.632781i | \(-0.781913\pi\) |
−0.160839 | − | 0.986981i | \(-0.551420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.46968 | + | 11.2058i | −0.248284 | + | 0.430040i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.3086 | 1.38931 | 0.694654 | − | 0.719344i | \(-0.255557\pi\) | ||||
0.694654 | + | 0.719344i | \(0.255557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.4983 | 0.821408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.37341 | + | 2.37881i | −0.0523226 | + | 0.0906254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.6896 | − | 41.0316i | −0.901196 | − | 1.56092i | −0.825943 | − | 0.563753i | \(-0.809357\pi\) |
−0.0752527 | − | 0.997164i | \(-0.523976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.3191 | − | 24.8015i | −0.543156 | − | 0.940774i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.5281 | − | 39.0197i | 0.853311 | − | 1.47798i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5991 | −0.551401 | −0.275701 | − | 0.961244i | \(-0.588910\pi\) | ||||
−0.275701 | + | 0.961244i | \(0.588910\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.5047 | 0.886496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.7076 | + | 46.2590i | −1.00444 | + | 1.73975i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.1599 | + | 34.9180i | 0.757121 | + | 1.31137i | 0.944313 | + | 0.329048i | \(0.106728\pi\) |
−0.187193 | + | 0.982323i | \(0.559939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.56897 | − | 7.91369i | −0.171109 | − | 0.296370i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.397982 | + | 0.689325i | −0.0148837 | + | 0.0257793i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.7901 | −1.59580 | −0.797900 | − | 0.602790i | \(-0.794056\pi\) | ||||
−0.797900 | + | 0.602790i | \(0.794056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.0660 | 0.784539 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.63294 | − | 8.02448i | 0.172063 | − | 0.298022i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.26214 | − | 7.38224i | −0.158074 | − | 0.273792i | 0.776100 | − | 0.630610i | \(-0.217195\pi\) |
−0.934174 | + | 0.356818i | \(0.883862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.2803 | + | 21.2702i | 0.454205 | + | 0.786706i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.29471 | − | 5.70661i | 0.121693 | − | 0.210779i | −0.798742 | − | 0.601673i | \(-0.794501\pi\) |
0.920435 | + | 0.390895i | \(0.127834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.50086 | 0.0921205 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1577 | 0.410444 | 0.205222 | − | 0.978715i | \(-0.434208\pi\) | ||||
0.205222 | + | 0.978715i | \(0.434208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.4893 | − | 26.8283i | 0.568249 | − | 0.984236i | −0.428490 | − | 0.903546i | \(-0.640954\pi\) |
0.996739 | − | 0.0806899i | \(-0.0257123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7687 | − | 18.6520i | −0.394535 | − | 0.683355i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.0268 | − | 60.6683i | −1.27985 | − | 2.21677i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2654 | − | 22.9763i | 0.484061 | − | 0.838418i | −0.515772 | − | 0.856726i | \(-0.672495\pi\) |
0.999832 | + | 0.0183084i | \(0.00582808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1899 | 0.443636 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.8731 | 1.01306 | 0.506532 | − | 0.862221i | \(-0.330927\pi\) | ||||
0.506532 | + | 0.862221i | \(0.330927\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.1092 | − | 22.7059i | 0.475210 | − | 0.823088i | −0.524387 | − | 0.851480i | \(-0.675705\pi\) |
0.999597 | + | 0.0283925i | \(0.00903882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.62828 | − | 16.6767i | −0.348567 | − | 0.603736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.83805 | − | 4.91565i | −0.102476 | − | 0.177494i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.144447 | + | 0.250190i | −0.00520889 | + | 0.00902207i | −0.868618 | − | 0.495482i | \(-0.834991\pi\) |
0.863409 | + | 0.504504i | \(0.168325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.498896 | 0.0179440 | 0.00897202 | − | 0.999960i | \(-0.497144\pi\) | ||||
0.00897202 | + | 0.999960i | \(0.497144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.3103 | 0.693645 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.28013 | − | 12.6096i | 0.260838 | − | 0.451784i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0711742 | + | 0.123277i | 0.00254681 | + | 0.00441121i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.2991 | − | 26.4988i | −0.546048 | − | 0.945782i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.73662 | − | 9.93612i | 0.204488 | − | 0.354184i | −0.745481 | − | 0.666527i | \(-0.767780\pi\) |
0.949970 | + | 0.312342i | \(0.101114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 82.0695 | 2.91805 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.66383 | 0.201128 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.7986 | + | 18.7038i | −0.382507 | + | 0.662522i | −0.991420 | − | 0.130715i | \(-0.958273\pi\) |
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.2519 | − | 29.8812i | −0.610330 | − | 1.05712i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.82819 | − | 10.0947i | −0.205673 | − | 0.356235i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.91921 | + | 8.52032i | −0.173379 | + | 0.300302i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.2898 | 0.361772 | 0.180886 | − | 0.983504i | \(-0.442104\pi\) | ||||
0.180886 | + | 0.983504i | \(0.442104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7751 | 0.869971 | 0.434986 | − | 0.900437i | \(-0.356753\pi\) | ||||
0.434986 | + | 0.900437i | \(0.356753\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.53427 | − | 2.65744i | 0.0537432 | − | 0.0930860i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.96850 | + | 6.87364i | 0.138840 | + | 0.240478i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.76652 | − | 8.25585i | −0.166353 | − | 0.288131i | 0.770782 | − | 0.637099i | \(-0.219866\pi\) |
−0.937135 | + | 0.348968i | \(0.886532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.4956 | + | 19.9109i | −0.400711 | + | 0.694051i | −0.993812 | − | 0.111077i | \(-0.964570\pi\) |
0.593101 | + | 0.805128i | \(0.297903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.43382 | −0.119406 | −0.0597028 | − | 0.998216i | \(-0.519015\pi\) | ||||
−0.0597028 | + | 0.998216i | \(0.519015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.9789 | −1.42326 | −0.711628 | − | 0.702556i | \(-0.752042\pi\) | ||||
−0.711628 | + | 0.702556i | \(0.752042\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −61.3031 | + | 106.180i | −2.12403 | + | 3.67892i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.4005 | + | 19.7463i | 0.394531 | + | 0.683348i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.1623 | + | 19.3337i | 0.385367 | + | 0.667475i | 0.991820 | − | 0.127644i | \(-0.0407416\pi\) |
−0.606453 | + | 0.795119i | \(0.707408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.3857 | − | 17.9885i | 0.358127 | − | 0.620294i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.8184 | −0.578572 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.83810 | −0.166239 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.43897 | − | 12.8847i | 0.255005 | − | 0.441681i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.1439 | − | 22.7658i | −0.450037 | − | 0.779487i | 0.548351 | − | 0.836248i | \(-0.315256\pi\) |
−0.998388 | + | 0.0567615i | \(0.981923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.9288 | − | 41.4459i | −0.817391 | − | 1.41576i | −0.907598 | − | 0.419840i | \(-0.862086\pi\) |
0.0902065 | − | 0.995923i | \(-0.471247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.74322 | − | 4.75140i | 0.0935975 | − | 0.162116i | −0.815425 | − | 0.578863i | \(-0.803497\pi\) |
0.909022 | + | 0.416747i | \(0.136830\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.1189 | 0.650815 | 0.325407 | − | 0.945574i | \(-0.394499\pi\) | ||||
0.325407 | + | 0.945574i | \(0.394499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.43500 | 0.320800 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.309059 | + | 0.535306i | −0.0104841 | + | 0.0181590i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.748143 | − | 1.29582i | −0.0253499 | − | 0.0439073i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.4863 | − | 45.8756i | −0.895400 | − | 1.55088i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.02078 | + | 3.50009i | −0.0682368 | + | 0.118190i | −0.898125 | − | 0.439740i | \(-0.855071\pi\) |
0.829888 | + | 0.557929i | \(0.188404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1415 | −0.510129 | −0.255065 | − | 0.966924i | \(-0.582097\pi\) | ||||
−0.255065 | + | 0.966924i | \(0.582097\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1342 | −1.18236 | −0.591181 | − | 0.806539i | \(-0.701338\pi\) | ||||
−0.591181 | + | 0.806539i | \(0.701338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.70152 | − | 4.67917i | 0.0907081 | − | 0.157111i | −0.817101 | − | 0.576494i | \(-0.804420\pi\) |
0.907809 | + | 0.419383i | \(0.137754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.1007 | − | 31.3514i | −0.607078 | − | 1.05149i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.57511 | − | 9.65638i | −0.186564 | − | 0.323138i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.8031 | − | 20.4435i | 0.394533 | − | 0.683351i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.1487 | −0.571940 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.3070 | −1.14293 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.43360 | + | 12.8754i | −0.247101 | + | 0.427992i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6509 | − | 28.8401i | −0.552882 | − | 0.957620i | −0.998065 | − | 0.0621806i | \(-0.980195\pi\) |
0.445182 | − | 0.895440i | \(-0.353139\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.25397 | + | 5.63604i | 0.107809 | + | 0.186730i | 0.914882 | − | 0.403721i | \(-0.132283\pi\) |
−0.807074 | + | 0.590451i | \(0.798950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.04948 | + | 12.2101i | −0.233304 | + | 0.404094i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.7672 | 1.51137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3385 | −0.505971 | −0.252985 | − | 0.967470i | \(-0.581412\pi\) | ||||
−0.252985 | + | 0.967470i | \(0.581412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0425841 | − | 0.0737578i | 0.00140167 | − | 0.00242777i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7200 | + | 27.2279i | 0.516871 | + | 0.895247i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.70797 | + | 9.88650i | 0.187273 | + | 0.324366i | 0.944340 | − | 0.328971i | \(-0.106702\pi\) |
−0.757067 | + | 0.653337i | \(0.773369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.8106 | + | 34.3130i | −0.649267 | + | 1.12456i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.94138 | −0.325118 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.1486 | 0.527552 | 0.263776 | − | 0.964584i | \(-0.415032\pi\) | ||||
0.263776 | + | 0.964584i | \(0.415032\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.4028 | − | 33.6066i | 0.632512 | − | 1.09554i | −0.354524 | − | 0.935047i | \(-0.615357\pi\) |
0.987036 | − | 0.160496i | \(-0.0513095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.60816 | − | 7.98157i | −0.150062 | − | 0.259916i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.3083 | + | 52.4956i | 0.984889 | + | 1.70588i | 0.642429 | + | 0.766345i | \(0.277927\pi\) |
0.342459 | + | 0.939533i | \(0.388740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.48705 | + | 6.03975i | −0.113195 | + | 0.196059i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7474 | 1.09318 | 0.546592 | − | 0.837399i | \(-0.315925\pi\) | ||||
0.546592 | + | 0.837399i | \(0.315925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.1401 | 1.04003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.0913 | − | 67.7081i | 1.26232 | − | 2.18641i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.36909 | − | 4.10339i | −0.0764224 | − | 0.132367i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.5925 | + | 23.5430i | 0.437559 | + | 0.757874i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.2027 | − | 38.4562i | 0.713991 | − | 1.23667i | −0.249356 | − | 0.968412i | \(-0.580219\pi\) |
0.963347 | − | 0.268257i | \(-0.0864476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.82990 | −0.315456 | −0.157728 | − | 0.987483i | \(-0.550417\pi\) | ||||
−0.157728 | + | 0.987483i | \(0.550417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −104.148 | −3.33885 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.36248 | + | 12.7522i | −0.235547 | + | 0.407979i | −0.959431 | − | 0.281942i | \(-0.909021\pi\) |
0.723885 | + | 0.689921i | \(0.242355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.67659 | − | 6.36804i | −0.117504 | − | 0.203523i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.8918 | + | 41.3818i | 0.762030 | + | 1.31987i | 0.941803 | + | 0.336166i | \(0.109130\pi\) |
−0.179773 | + | 0.983708i | \(0.557536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.856591 | + | 1.48366i | −0.0272933 | + | 0.0472733i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.02394 | 0.159752 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.1838 | 1.24471 | 0.622357 | − | 0.782733i | \(-0.286175\pi\) | ||||
0.622357 | + | 0.782733i | \(0.286175\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.32296 | + | 16.1478i | −0.295558 | + | 0.511921i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2299 | + | 21.1828i | 0.387324 | + | 0.670866i | 0.992089 | − | 0.125539i | \(-0.0400660\pi\) |
−0.604764 | + | 0.796405i | \(0.706733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3564.2.i.t.2377.2 | 12 | ||
3.2 | odd | 2 | 3564.2.i.s.2377.5 | 12 | |||
9.2 | odd | 6 | 3564.2.i.s.1189.5 | 12 | |||
9.4 | even | 3 | 3564.2.a.o.1.5 | ✓ | 6 | ||
9.5 | odd | 6 | 3564.2.a.p.1.2 | yes | 6 | ||
9.7 | even | 3 | inner | 3564.2.i.t.1189.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3564.2.a.o.1.5 | ✓ | 6 | 9.4 | even | 3 | ||
3564.2.a.p.1.2 | yes | 6 | 9.5 | odd | 6 | ||
3564.2.i.s.1189.5 | 12 | 9.2 | odd | 6 | |||
3564.2.i.s.2377.5 | 12 | 3.2 | odd | 2 | |||
3564.2.i.t.1189.2 | 12 | 9.7 | even | 3 | inner | ||
3564.2.i.t.2377.2 | 12 | 1.1 | even | 1 | trivial |