Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(17,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bj (of order \(4\), 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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.17 | ||
Character | \(\chi\) | \(=\) | 1440.593 |
Dual form | 1440.2.bj.a.17.17 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.42597 | − | 1.72238i | 0.637714 | − | 0.770273i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.11972 | + | 3.11972i | −1.17914 | + | 1.17914i | −0.199179 | + | 0.979963i | \(0.563828\pi\) |
−0.979963 | + | 0.199179i | \(0.936172\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17794 | 0.355163 | 0.177581 | − | 0.984106i | \(-0.443173\pi\) | ||||
0.177581 | + | 0.984106i | \(0.443173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.15100 | + | 2.15100i | −0.596579 | + | 0.596579i | −0.939401 | − | 0.342822i | \(-0.888617\pi\) |
0.342822 | + | 0.939401i | \(0.388617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.33507 | − | 1.33507i | −0.323803 | − | 0.323803i | 0.526421 | − | 0.850224i | \(-0.323534\pi\) |
−0.850224 | + | 0.526421i | \(0.823534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.322444 | 0.0739738 | 0.0369869 | − | 0.999316i | \(-0.488224\pi\) | ||||
0.0369869 | + | 0.999316i | \(0.488224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.71347 | + | 4.71347i | −0.982826 | + | 0.982826i | −0.999855 | − | 0.0170294i | \(-0.994579\pi\) |
0.0170294 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.933209 | − | 4.91214i | −0.186642 | − | 0.982428i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.63043i | 1.23124i | 0.788043 | + | 0.615620i | \(0.211094\pi\) | ||||
−0.788043 | + | 0.615620i | \(0.788906\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0675826 | 0.0121382 | 0.00606909 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00606909 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.924721 | + | 9.82198i | 0.156306 | + | 1.66022i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.60938 | − | 7.60938i | −1.25097 | − | 1.25097i | −0.955284 | − | 0.295690i | \(-0.904450\pi\) |
−0.295690 | − | 0.955284i | \(-0.595550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.19684i | 0.499262i | 0.968341 | + | 0.249631i | \(0.0803093\pi\) | ||||
−0.968341 | + | 0.249631i | \(0.919691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.70505 | + | 6.70505i | −1.02251 | + | 1.02251i | −0.0227703 | + | 0.999741i | \(0.507249\pi\) |
−0.999741 | + | 0.0227703i | \(0.992751\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.34279 | − | 7.34279i | −1.07106 | − | 1.07106i | −0.997274 | − | 0.0737817i | \(-0.976493\pi\) |
−0.0737817 | − | 0.997274i | \(-0.523507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12.4653i | − | 1.78075i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73432 | + | 5.73432i | 0.787669 | + | 0.787669i | 0.981112 | − | 0.193442i | \(-0.0619653\pi\) |
−0.193442 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.67971 | − | 2.02887i | 0.226492 | − | 0.273572i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.68448i | 1.13062i | 0.824877 | + | 0.565312i | \(0.191244\pi\) | ||||
−0.824877 | + | 0.565312i | \(0.808756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5620i | 1.60840i | 0.594359 | + | 0.804199i | \(0.297406\pi\) | ||||
−0.594359 | + | 0.804199i | \(0.702594\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.637580 | + | 6.77210i | 0.0790821 | + | 0.839976i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87740 | + | 1.87740i | 0.229360 | + | 0.229360i | 0.812425 | − | 0.583065i | \(-0.198147\pi\) |
−0.583065 | + | 0.812425i | \(0.698147\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.18221i | 0.496337i | 0.968717 | + | 0.248168i | \(0.0798286\pi\) | ||||
−0.968717 | + | 0.248168i | \(0.920171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97893 | + | 3.97893i | 0.465699 | + | 0.465699i | 0.900518 | − | 0.434819i | \(-0.143188\pi\) |
−0.434819 | + | 0.900518i | \(0.643188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.67485 | + | 3.67485i | −0.418788 | + | 0.418788i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.66644i | − | 1.08756i | −0.839228 | − | 0.543780i | \(-0.816993\pi\) | ||
0.839228 | − | 0.543780i | \(-0.183007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.585119 | + | 0.585119i | 0.0642251 | + | 0.0642251i | 0.738490 | − | 0.674265i | \(-0.235539\pi\) |
−0.674265 | + | 0.738490i | \(0.735539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.20329 | + | 0.395732i | −0.455911 | + | 0.0429231i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.557322 | 0.0590760 | 0.0295380 | − | 0.999564i | \(-0.490596\pi\) | ||||
0.0295380 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.4210i | − | 1.40690i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.459796 | − | 0.555372i | 0.0471741 | − | 0.0569800i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5772 | + | 10.5772i | −1.07395 | + | 1.07395i | −0.0769138 | + | 0.997038i | \(0.524507\pi\) |
−0.997038 | + | 0.0769138i | \(0.975493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.52870 | 0.948141 | 0.474071 | − | 0.880487i | \(-0.342784\pi\) | ||||
0.474071 | + | 0.880487i | \(0.342784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.162450 | + | 0.162450i | 0.0160066 | + | 0.0160066i | 0.715065 | − | 0.699058i | \(-0.246397\pi\) |
−0.699058 | + | 0.715065i | \(0.746397\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.7955 | − | 11.7955i | 1.14032 | − | 1.14032i | 0.151925 | − | 0.988392i | \(-0.451453\pi\) |
0.988392 | − | 0.151925i | \(-0.0485471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8601 | 1.04021 | 0.520105 | − | 0.854102i | \(-0.325893\pi\) | ||||
0.520105 | + | 0.854102i | \(0.325893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.74476 | + | 8.74476i | −0.822637 | + | 0.822637i | −0.986486 | − | 0.163848i | \(-0.947609\pi\) |
0.163848 | + | 0.986486i | \(0.447609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.39713 | + | 14.8397i | 0.130283 | + | 1.38381i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.33011 | 0.763620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.61245 | −0.873859 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.79132 | − | 5.39723i | −0.875762 | − | 0.482743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.83755 | − | 3.83755i | 0.340528 | − | 0.340528i | −0.516038 | − | 0.856566i | \(-0.672594\pi\) |
0.856566 | + | 0.516038i | \(0.172594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.85715 | −0.162260 | −0.0811298 | − | 0.996704i | \(-0.525853\pi\) | ||||
−0.0811298 | + | 0.996704i | \(0.525853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00593 | + | 1.00593i | −0.0872256 | + | 0.0872256i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.89240 | − | 1.89240i | −0.161678 | − | 0.161678i | 0.621631 | − | 0.783310i | \(-0.286470\pi\) |
−0.783310 | + | 0.621631i | \(0.786470\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4370 | −1.56380 | −0.781902 | − | 0.623401i | \(-0.785750\pi\) | ||||
−0.781902 | + | 0.623401i | \(0.785750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.53375 | + | 2.53375i | −0.211883 | + | 0.211883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4201 | + | 9.45481i | 0.948392 | + | 0.785179i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.24573i | 0.102054i | 0.998697 | + | 0.0510272i | \(0.0162495\pi\) | ||||
−0.998697 | + | 0.0510272i | \(0.983750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7587 | −1.36380 | −0.681902 | − | 0.731444i | \(-0.738847\pi\) | ||||
−0.681902 | + | 0.731444i | \(0.738847\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0963708 | − | 0.116403i | 0.00774069 | − | 0.00934972i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.90784 | − | 6.90784i | −0.551306 | − | 0.551306i | 0.375512 | − | 0.926818i | \(-0.377467\pi\) |
−0.926818 | + | 0.375512i | \(0.877467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 29.4094i | − | 2.31778i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.07821 | − | 6.07821i | 0.476082 | − | 0.476082i | −0.427794 | − | 0.903876i | \(-0.640709\pi\) |
0.903876 | + | 0.427794i | \(0.140709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.82159 | + | 2.82159i | 0.218341 | + | 0.218341i | 0.807799 | − | 0.589458i | \(-0.200659\pi\) |
−0.589458 | + | 0.807799i | \(0.700659\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.74643i | 0.288187i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.27921 | + | 7.27921i | 0.553428 | + | 0.553428i | 0.927428 | − | 0.374001i | \(-0.122014\pi\) |
−0.374001 | + | 0.927428i | \(0.622014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.2358 | + | 12.4131i | 1.37850 | + | 0.938345i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.56604i | 0.714999i | 0.933913 | + | 0.357500i | \(0.116371\pi\) | ||||
−0.933913 | + | 0.357500i | \(0.883629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.44857i | − | 0.330659i | −0.986238 | − | 0.165330i | \(-0.947131\pi\) | ||
0.986238 | − | 0.165330i | \(-0.0528688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.9570 | + | 2.25551i | −1.76136 | + | 0.165828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.57264 | − | 1.57264i | −0.115003 | − | 0.115003i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.16704i | − | 0.229159i | −0.993414 | − | 0.114579i | \(-0.963448\pi\) | ||
0.993414 | − | 0.114579i | \(-0.0365521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07726 | + | 1.07726i | 0.0775426 | + | 0.0775426i | 0.744814 | − | 0.667272i | \(-0.232538\pi\) |
−0.667272 | + | 0.744814i | \(0.732538\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.59062 | + | 5.59062i | −0.398315 | + | 0.398315i | −0.877638 | − | 0.479323i | \(-0.840882\pi\) |
0.479323 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.7707i | − | 1.11796i | −0.829182 | − | 0.558978i | \(-0.811194\pi\) | ||
0.829182 | − | 0.558978i | \(-0.188806\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.6851 | − | 20.6851i | −1.45181 | − | 1.45181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.50618 | + | 4.55860i | 0.384568 | + | 0.318386i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.379820 | 0.0262727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.9274i | − | 0.752273i | −0.926564 | − | 0.376137i | \(-0.877252\pi\) | ||
0.926564 | − | 0.376137i | \(-0.122748\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98746 | + | 21.1099i | 0.135543 | + | 1.43968i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.210839 | + | 0.210839i | −0.0143127 | + | 0.0143127i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.74348 | 0.386348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.947865 | − | 0.947865i | −0.0634737 | − | 0.0634737i | 0.674657 | − | 0.738131i | \(-0.264291\pi\) |
−0.738131 | + | 0.674657i | \(0.764291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.87410 | + | 4.87410i | −0.323506 | + | 0.323506i | −0.850110 | − | 0.526605i | \(-0.823465\pi\) |
0.526605 | + | 0.850110i | \(0.323465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1740 | 1.13489 | 0.567444 | − | 0.823412i | \(-0.307932\pi\) | ||||
0.567444 | + | 0.823412i | \(0.307932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.1696 | − | 17.1696i | 1.12482 | − | 1.12482i | 0.133811 | − | 0.991007i | \(-0.457278\pi\) |
0.991007 | − | 0.133811i | \(-0.0427216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.1177 | + | 2.17649i | −1.50803 | + | 0.141978i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8347 | 1.28300 | 0.641501 | − | 0.767122i | \(-0.278312\pi\) | ||||
0.641501 | + | 0.767122i | \(0.278312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.89615 | −0.186557 | −0.0932787 | − | 0.995640i | \(-0.529735\pi\) | ||||
−0.0932787 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.4700 | − | 17.7751i | −1.37167 | − | 1.13561i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.693576 | + | 0.693576i | −0.0441312 | + | 0.0441312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.93270 | 0.563827 | 0.281914 | − | 0.959440i | \(-0.409031\pi\) | ||||
0.281914 | + | 0.959440i | \(0.409031\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.55219 | + | 5.55219i | −0.349063 | + | 0.349063i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.4301 | + | 12.4301i | 0.775367 | + | 0.775367i | 0.979039 | − | 0.203672i | \(-0.0652877\pi\) |
−0.203672 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 47.4782 | 2.95015 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1529 | − | 12.1529i | 0.749383 | − | 0.749383i | −0.224981 | − | 0.974363i | \(-0.572232\pi\) |
0.974363 | + | 0.224981i | \(0.0722319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0537 | − | 1.69972i | 1.10903 | − | 0.104413i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 19.0912i | − | 1.16401i | −0.813185 | − | 0.582005i | \(-0.802268\pi\) | ||
0.813185 | − | 0.582005i | \(-0.197732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6087 | −0.826670 | −0.413335 | − | 0.910579i | \(-0.635636\pi\) | ||||
−0.413335 | + | 0.910579i | \(0.635636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.09927 | − | 5.78622i | −0.0662882 | − | 0.348922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9103 | + | 13.9103i | 0.835788 | + | 0.835788i | 0.988301 | − | 0.152514i | \(-0.0487368\pi\) |
−0.152514 | + | 0.988301i | \(0.548737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9435i | 0.831799i | 0.909411 | + | 0.415899i | \(0.136533\pi\) | ||||
−0.909411 | + | 0.415899i | \(0.863467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3526 | − | 14.3526i | 0.853174 | − | 0.853174i | −0.137349 | − | 0.990523i | \(-0.543858\pi\) |
0.990523 | + | 0.137349i | \(0.0438582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.97323 | − | 9.97323i | −0.588701 | − | 0.588701i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.4352i | − | 0.790303i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.4180 | − | 12.4180i | −0.725465 | − | 0.725465i | 0.244248 | − | 0.969713i | \(-0.421459\pi\) |
−0.969713 | + | 0.244248i | \(0.921459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.9580 | + | 12.3838i | 0.870889 | + | 0.721014i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 20.2773i | − | 1.17267i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 41.8357i | − | 2.41137i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.6366 | + | 17.9131i | 1.23891 | + | 1.02570i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9940 | + | 14.9940i | 0.855753 | + | 0.855753i | 0.990834 | − | 0.135082i | \(-0.0431297\pi\) |
−0.135082 | + | 0.990834i | \(0.543130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.7316i | − | 1.85604i | −0.372534 | − | 0.928019i | \(-0.621511\pi\) | ||
0.372534 | − | 0.928019i | \(-0.378489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.25286 | + | 8.25286i | 0.466479 | + | 0.466479i | 0.900772 | − | 0.434293i | \(-0.143002\pi\) |
−0.434293 | + | 0.900772i | \(0.643002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.30940 | − | 8.30940i | 0.466702 | − | 0.466702i | −0.434142 | − | 0.900844i | \(-0.642948\pi\) |
0.900844 | + | 0.434142i | \(0.142948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.81027i | 0.437291i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.430487 | − | 0.430487i | −0.0239529 | − | 0.0239529i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5733 | + | 8.55867i | 0.697443 | + | 0.474749i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 45.8149 | 2.52586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.43429i | 0.408626i | 0.978906 | + | 0.204313i | \(0.0654960\pi\) | ||||
−0.978906 | + | 0.204313i | \(0.934504\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.91071 | − | 0.556482i | 0.322936 | − | 0.0304038i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.88868 | + | 3.88868i | −0.211830 | + | 0.211830i | −0.805044 | − | 0.593215i | \(-0.797859\pi\) |
0.593215 | + | 0.805044i | \(0.297859\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0796083 | 0.00431103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0501 | + | 17.0501i | 0.920620 | + | 0.920620i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7432 | − | 20.7432i | 1.11355 | − | 1.11355i | 0.120889 | − | 0.992666i | \(-0.461426\pi\) |
0.992666 | − | 0.120889i | \(-0.0385744\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.04055 | 0.162757 | 0.0813783 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813783 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.46489 | + | 3.46489i | −0.184417 | + | 0.184417i | −0.793278 | − | 0.608860i | \(-0.791627\pi\) |
0.608860 | + | 0.793278i | \(0.291627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.20337 | + | 5.96371i | 0.382315 | + | 0.316521i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.63299 | −0.455632 | −0.227816 | − | 0.973704i | \(-0.573158\pi\) | ||||
−0.227816 | + | 0.973704i | \(0.573158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8960 | −0.994528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.5271 | − | 1.17940i | 0.655698 | − | 0.0617327i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.3844 | + | 15.3844i | −0.803060 | + | 0.803060i | −0.983573 | − | 0.180512i | \(-0.942224\pi\) |
0.180512 | + | 0.983573i | \(0.442224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.7789 | −1.85755 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.40616 | + | 7.40616i | −0.383476 | + | 0.383476i | −0.872353 | − | 0.488877i | \(-0.837407\pi\) |
0.488877 | + | 0.872353i | \(0.337407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.2620 | − | 14.2620i | −0.734532 | − | 0.734532i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.54952 | 0.336426 | 0.168213 | − | 0.985751i | \(-0.446200\pi\) | ||||
0.168213 | + | 0.985751i | \(0.446200\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.8778 | + | 14.8778i | −0.760222 | + | 0.760222i | −0.976362 | − | 0.216140i | \(-0.930653\pi\) |
0.216140 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.08927 | + | 11.5697i | 0.0555142 | + | 0.589648i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 0.254115i | − | 0.0128842i | −0.999979 | − | 0.00644208i | \(-0.997949\pi\) | ||
0.999979 | − | 0.00644208i | \(-0.00205059\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.5857 | 0.636484 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.6493 | − | 13.7841i | −0.837718 | − | 0.693552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6584 | − | 20.6584i | −1.03682 | − | 1.03682i | −0.999296 | − | 0.0375215i | \(-0.988054\pi\) |
−0.0375215 | − | 0.999296i | \(-0.511946\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 20.6863i | − | 1.03303i | −0.856279 | − | 0.516513i | \(-0.827230\pi\) | ||
0.856279 | − | 0.516513i | \(-0.172770\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.145370 | + | 0.145370i | −0.00724139 | + | 0.00724139i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.96340 | − | 8.96340i | −0.444299 | − | 0.444299i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 26.9787i | − | 1.33401i | −0.745053 | − | 0.667005i | \(-0.767576\pi\) | ||
0.745053 | − | 0.667005i | \(-0.232424\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.0931 | − | 27.0931i | −1.33317 | − | 1.33317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.84216 | − | 0.173436i | 0.0904282 | − | 0.00851364i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.3778i | 1.67946i | 0.543001 | + | 0.839732i | \(0.317288\pi\) | ||||
−0.543001 | + | 0.839732i | \(0.682712\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.05773i | 0.197762i | 0.995099 | + | 0.0988809i | \(0.0315263\pi\) | ||||
−0.995099 | + | 0.0988809i | \(0.968474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.31217 | + | 7.80398i | −0.257678 | + | 0.378549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.1899 | − | 39.1899i | −1.89653 | − | 1.89653i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0853i | 0.774800i | 0.921912 | + | 0.387400i | \(0.126627\pi\) | ||||
−0.921912 | + | 0.387400i | \(0.873373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.04812 | − | 3.04812i | −0.146483 | − | 0.146483i | 0.630062 | − | 0.776545i | \(-0.283030\pi\) |
−0.776545 | + | 0.630062i | \(0.783030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.51983 | + | 1.51983i | −0.0727033 | + | 0.0727033i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.78470i | 0.228361i | 0.993460 | + | 0.114181i | \(0.0364243\pi\) | ||||
−0.993460 | + | 0.114181i | \(0.963576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.2608 | + | 11.2608i | 0.535019 | + | 0.535019i | 0.922062 | − | 0.387043i | \(-0.126503\pi\) |
−0.387043 | + | 0.922062i | \(0.626503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.794726 | − | 0.959922i | 0.0376736 | − | 0.0455047i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.49133 | −0.353538 | −0.176769 | − | 0.984252i | \(-0.556565\pi\) | ||||
−0.176769 | + | 0.984252i | \(0.556565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.76569i | 0.177319i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.1161 | − | 19.1380i | −1.08370 | − | 0.897202i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2198 | + | 14.2198i | −0.665173 | + | 0.665173i | −0.956595 | − | 0.291422i | \(-0.905872\pi\) |
0.291422 | + | 0.956595i | \(0.405872\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4366 | 0.905254 | 0.452627 | − | 0.891700i | \(-0.350487\pi\) | ||||
0.452627 | + | 0.891700i | \(0.350487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.18789 | + | 2.18789i | 0.101680 | + | 0.101680i | 0.756117 | − | 0.654437i | \(-0.227094\pi\) |
−0.654437 | + | 0.756117i | \(0.727094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.06992 | + | 2.06992i | −0.0957845 | + | 0.0957845i | −0.753375 | − | 0.657591i | \(-0.771576\pi\) |
0.657591 | + | 0.753375i | \(0.271576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7139 | −0.540897 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.89816 | + | 7.89816i | −0.363158 | + | 0.363158i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.300908 | − | 1.58389i | −0.0138066 | − | 0.0726739i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.5481 | 1.25871 | 0.629353 | − | 0.777120i | \(-0.283320\pi\) | ||||
0.629353 | + | 0.777120i | \(0.283320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.7355 | 1.49261 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.13520 | + | 33.3008i | 0.142362 | + | 1.51211i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7336 | + | 27.7336i | −1.25673 | + | 1.25673i | −0.304083 | + | 0.952646i | \(0.598350\pi\) |
−0.952646 | + | 0.304083i | \(0.901650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.58679 | 0.116740 | 0.0583700 | − | 0.998295i | \(-0.481410\pi\) | ||||
0.0583700 | + | 0.998295i | \(0.481410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.85213 | − | 8.85213i | 0.398680 | − | 0.398680i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.0473 | − | 13.0473i | −0.585252 | − | 0.585252i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.5951 | 1.14579 | 0.572897 | − | 0.819627i | \(-0.305819\pi\) | ||||
0.572897 | + | 0.819627i | \(0.305819\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.39909 | + | 9.39909i | −0.419085 | + | 0.419085i | −0.884888 | − | 0.465804i | \(-0.845765\pi\) |
0.465804 | + | 0.884888i | \(0.345765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5877 | − | 16.4121i | 0.604643 | − | 0.730328i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.5075i | 0.510059i | 0.966933 | + | 0.255030i | \(0.0820852\pi\) | ||||
−0.966933 | + | 0.255030i | \(0.917915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.8263 | −1.09825 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.511449 | − | 0.0481519i | 0.0225371 | − | 0.00212183i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.64938 | − | 8.64938i | −0.380399 | − | 0.380399i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.12668i | 0.356036i | 0.984027 | + | 0.178018i | \(0.0569686\pi\) | ||||
−0.984027 | + | 0.178018i | \(0.943031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2646 | + | 23.2646i | −1.01729 | + | 1.01729i | −0.0174440 | + | 0.999848i | \(0.505553\pi\) |
−0.999848 | + | 0.0174440i | \(0.994447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0902278 | − | 0.0902278i | −0.00393038 | − | 0.00393038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.4335i | − | 0.931892i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.87638 | − | 6.87638i | −0.297849 | − | 0.297849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.49633 | − | 37.1365i | −0.151160 | − | 1.60555i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 14.6834i | − | 0.632458i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6496i | 0.930787i | 0.885104 | + | 0.465393i | \(0.154087\pi\) | ||||
−0.885104 | + | 0.465393i | \(0.845913\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4862 | − | 18.7053i | 0.663357 | − | 0.801246i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.4574 | + | 15.4574i | 0.660912 | + | 0.660912i | 0.955595 | − | 0.294683i | \(-0.0952141\pi\) |
−0.294683 | + | 0.955595i | \(0.595214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.13794i | 0.0910795i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.1566 | + | 30.1566i | 1.28239 | + | 1.28239i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.9318 | − | 10.9318i | 0.463194 | − | 0.463194i | −0.436507 | − | 0.899701i | \(-0.643785\pi\) |
0.899701 | + | 0.436507i | \(0.143785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.8451i | − | 1.22002i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.9005 | + | 13.9005i | 0.585835 | + | 0.585835i | 0.936501 | − | 0.350666i | \(-0.114045\pi\) |
−0.350666 | + | 0.936501i | \(0.614045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.59205 | + | 27.5316i | 0.109048 | + | 1.15826i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.03632 | 0.127289 | 0.0636446 | − | 0.997973i | \(-0.479728\pi\) | ||||
0.0636446 | + | 0.997973i | \(0.479728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.26119i | 0.0527792i | 0.999652 | + | 0.0263896i | \(0.00840105\pi\) | ||||
−0.999652 | + | 0.0263896i | \(0.991599\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.5519 | + | 18.7546i | 1.14899 | + | 0.782119i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.10444 | + | 5.10444i | −0.212501 | + | 0.212501i | −0.805329 | − | 0.592828i | \(-0.798011\pi\) |
0.592828 | + | 0.805329i | \(0.298011\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.65081 | −0.151461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.75469 | + | 6.75469i | 0.279751 | + | 0.279751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.16591 | − | 2.16591i | 0.0893966 | − | 0.0893966i | −0.660994 | − | 0.750391i | \(-0.729865\pi\) |
0.750391 | + | 0.660994i | \(0.229865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0217916 | 0.000897908 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.8495 | + | 14.8495i | −0.609795 | + | 0.609795i | −0.942892 | − | 0.333097i | \(-0.891906\pi\) |
0.333097 | + | 0.942892i | \(0.391906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.8785 | − | 14.3476i | 0.486971 | − | 0.588196i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.1979 | 0.825262 | 0.412631 | − | 0.910898i | \(-0.364610\pi\) | ||||
0.412631 | + | 0.910898i | \(0.364610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9787 | −1.26365 | −0.631823 | − | 0.775113i | \(-0.717693\pi\) | ||||
−0.631823 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.7071 | + | 16.5563i | −0.557272 | + | 0.673110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.72619 | − | 7.72619i | 0.313596 | − | 0.313596i | −0.532705 | − | 0.846301i | \(-0.678824\pi\) |
0.846301 | + | 0.532705i | \(0.178824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.5886 | 1.27794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.56398 | − | 7.56398i | 0.305506 | − | 0.305506i | −0.537657 | − | 0.843164i | \(-0.680691\pi\) |
0.843164 | + | 0.537657i | \(0.180691\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.1379 | − | 20.1379i | −0.810722 | − | 0.810722i | 0.174020 | − | 0.984742i | \(-0.444324\pi\) |
−0.984742 | + | 0.174020i | \(0.944324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.5448 | −1.06692 | −0.533462 | − | 0.845824i | \(-0.679109\pi\) | ||||
−0.533462 | + | 0.845824i | \(0.679109\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73869 | + | 1.73869i | −0.0696591 | + | 0.0696591i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2582 | + | 9.16811i | −0.930330 | + | 0.366724i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.3182i | 0.810139i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.2805 | 1.52392 | 0.761961 | − | 0.647623i | \(-0.224237\pi\) | ||||
0.761961 | + | 0.647623i | \(0.224237\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.13749 | − | 12.0820i | −0.0451401 | − | 0.479458i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.8128 | + | 26.8128i | 1.06236 | + | 1.06236i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.4013i | 0.963792i | 0.876228 | + | 0.481896i | \(0.160052\pi\) | ||||
−0.876228 | + | 0.481896i | \(0.839948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.08062 | − | 1.08062i | 0.0426157 | − | 0.0426157i | −0.685478 | − | 0.728094i | \(-0.740407\pi\) |
0.728094 | + | 0.685478i | \(0.240407\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0445 | + | 22.0445i | 0.866659 | + | 0.866659i | 0.992101 | − | 0.125442i | \(-0.0400348\pi\) |
−0.125442 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2298i | 0.401556i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.9241 | + | 20.9241i | 0.818823 | + | 0.818823i | 0.985937 | − | 0.167115i | \(-0.0534450\pi\) |
−0.167115 | + | 0.985937i | \(0.553445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.64824 | + | 3.19872i | −0.103475 | + | 0.124984i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.22520i | 0.281454i | 0.990048 | + | 0.140727i | \(0.0449440\pi\) | ||||
−0.990048 | + | 0.140727i | \(0.955056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.3836i | − | 0.792830i | −0.918071 | − | 0.396415i | \(-0.870254\pi\) | ||
0.918071 | − | 0.396415i | \(-0.129746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.298171 | + | 3.16704i | 0.0115626 | + | 0.122813i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.2523 | − | 31.2523i | −1.21009 | − | 1.21009i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.7973i | 0.571244i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.4517 | − | 19.4517i | −0.749807 | − | 0.749807i | 0.224636 | − | 0.974443i | \(-0.427881\pi\) |
−0.974443 | + | 0.224636i | \(0.927881\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.8145 | − | 24.8145i | 0.953698 | − | 0.953698i | −0.0452768 | − | 0.998974i | \(-0.514417\pi\) |
0.998974 | + | 0.0452768i | \(0.0144170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 65.9957i | − | 2.53268i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.85886 | + | 7.85886i | 0.300711 | + | 0.300711i | 0.841292 | − | 0.540581i | \(-0.181796\pi\) |
−0.540581 | + | 0.841292i | \(0.681796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.95794 | + | 0.560928i | −0.227641 | + | 0.0214320i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.6690 | −0.939814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.6748i | 1.88972i | 0.327479 | + | 0.944858i | \(0.393801\pi\) | ||||
−0.327479 | + | 0.944858i | \(0.606199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.2906 | + | 31.7556i | −0.997260 | + | 1.20456i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.26802 | − | 4.26802i | 0.161663 | − | 0.161663i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5703 | −1.15462 | −0.577312 | − | 0.816524i | \(-0.695898\pi\) | ||||
−0.577312 | + | 0.816524i | \(0.695898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.45360 | − | 2.45360i | −0.0925393 | − | 0.0925393i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.7269 | + | 29.7269i | −1.11799 | + | 1.11799i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1384 | 0.418310 | 0.209155 | − | 0.977882i | \(-0.432929\pi\) | ||||
0.209155 | + | 0.977882i | \(0.432929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.318548 | + | 0.318548i | −0.0119297 | + | 0.0119297i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.751033 | + | 7.97714i | 0.0280870 | + | 0.298328i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.0316 | −1.53022 | −0.765111 | − | 0.643899i | \(-0.777316\pi\) | ||||
−0.765111 | + | 0.643899i | \(0.777316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.01359 | −0.0377482 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.5696 | − | 6.18758i | 1.20961 | − | 0.229801i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.35975 | − | 4.35975i | 0.161694 | − | 0.161694i | −0.621623 | − | 0.783317i | \(-0.713526\pi\) |
0.783317 | + | 0.621623i | \(0.213526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.9035 | 0.662185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.3786 | + | 28.3786i | −1.04819 | + | 1.04819i | −0.0494094 | + | 0.998779i | \(0.515734\pi\) |
−0.998779 | + | 0.0494094i | \(0.984266\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.21146 | + | 2.21146i | 0.0814603 | + | 0.0814603i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.53862 | −0.240527 | −0.120264 | − | 0.992742i | \(-0.538374\pi\) | ||||
−0.120264 | + | 0.992742i | \(0.538374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0409 | − | 20.0409i | 0.735230 | − | 0.735230i | −0.236421 | − | 0.971651i | \(-0.575974\pi\) |
0.971651 | + | 0.236421i | \(0.0759744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.14563 | + | 1.77638i | 0.0786098 | + | 0.0650816i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 73.5974i | 2.68919i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.89337 | −0.288033 | −0.144017 | − | 0.989575i | \(-0.546002\pi\) | ||||
−0.144017 | + | 0.989575i | \(0.546002\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.8974 | + | 28.8649i | −0.869717 | + | 1.05050i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.76852 | − | 5.76852i | −0.209660 | − | 0.209660i | 0.594463 | − | 0.804123i | \(-0.297365\pi\) |
−0.804123 | + | 0.594463i | \(0.797365\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7806i | 0.427045i | 0.976938 | + | 0.213522i | \(0.0684936\pi\) | ||||
−0.976938 | + | 0.213522i | \(0.931506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.8805 | + | 33.8805i | −1.22656 | + | 1.22656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.6803 | − | 18.6803i | −0.674506 | − | 0.674506i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7788i | 1.25416i | 0.778956 | + | 0.627078i | \(0.215749\pi\) | ||||
−0.778956 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.6201 | + | 27.6201i | 0.993426 | + | 0.993426i | 0.999979 | − | 0.00655287i | \(-0.00208586\pi\) |
−0.00655287 | + | 0.999979i | \(0.502086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0630687 | − | 0.331975i | −0.00226549 | − | 0.0119249i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.03080i | 0.0369323i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.92640i | 0.176280i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.7483 | + | 2.04756i | −0.776232 | + | 0.0730807i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.2310 | − | 18.2310i | −0.649864 | − | 0.649864i | 0.303096 | − | 0.952960i | \(-0.401980\pi\) |
−0.952960 | + | 0.303096i | \(0.901980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 54.5623i | − | 1.94001i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.0208 | − | 27.0208i | −0.959537 | − | 0.959537i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4983 | + | 11.4983i | −0.407290 | + | 0.407290i | −0.880793 | − | 0.473502i | \(-0.842990\pi\) |
0.473502 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.6064i | 0.693623i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.68695 | + | 4.68695i | 0.165399 | + | 0.165399i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.6542 | − | 41.9369i | −1.78533 | − | 1.47808i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.8481 | −0.627506 | −0.313753 | − | 0.949505i | \(-0.601586\pi\) | ||||
−0.313753 | + | 0.949505i | \(0.601586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.5242i | − | 1.45811i | −0.684454 | − | 0.729056i | \(-0.739959\pi\) | ||
0.684454 | − | 0.729056i | \(-0.260041\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.80165 | − | 19.1364i | −0.0631091 | − | 0.670317i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16201 | + | 2.16201i | −0.0756390 | + | 0.0756390i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.9849 | −1.01158 | −0.505790 | − | 0.862657i | \(-0.668799\pi\) | ||||
−0.505790 | + | 0.862657i | \(0.668799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.6586 | − | 20.6586i | −0.720112 | − | 0.720112i | 0.248516 | − | 0.968628i | \(-0.420057\pi\) |
−0.968628 | + | 0.248516i | \(0.920057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4075 | + | 25.4075i | −0.883504 | + | 0.883504i | −0.993889 | − | 0.110385i | \(-0.964792\pi\) |
0.110385 | + | 0.993889i | \(0.464792\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.7882 | −0.860931 | −0.430465 | − | 0.902607i | \(-0.641651\pi\) | ||||
−0.430465 | + | 0.902607i | \(0.641651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.6421 | + | 16.6421i | −0.576614 | + | 0.576614i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.88336 | − | 0.836351i | 0.307421 | − | 0.0289431i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.8553 | −1.82477 | −0.912383 | − | 0.409338i | \(-0.865760\pi\) | ||||
−0.912383 | + | 0.409338i | \(0.865760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9627 | −0.515954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.45279 | + | 5.34230i | 0.221983 | + | 0.183781i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.9881 | − | 29.9881i | 1.03040 | − | 1.03040i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 71.7331 | 2.45898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.39491 | + | 7.39491i | −0.253197 | + | 0.253197i | −0.822280 | − | 0.569083i | \(-0.807298\pi\) |
0.569083 | + | 0.822280i | \(0.307298\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.82308 | + | 6.82308i | 0.233072 | + | 0.233072i | 0.813974 | − | 0.580902i | \(-0.197300\pi\) |
−0.580902 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.6736 | −1.49012 | −0.745061 | − | 0.666996i | \(-0.767580\pi\) | ||||
−0.745061 | + | 0.666996i | \(0.767580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.1338 | + | 13.1338i | −0.447080 | + | 0.447080i | −0.894383 | − | 0.447303i | \(-0.852385\pi\) |
0.447303 | + | 0.894383i | \(0.352385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.9175 | − | 2.15764i | 0.779219 | − | 0.0733620i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 11.3865i | − | 0.386261i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.07654 | −0.273663 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 47.3840 | − | 13.7083i | 1.60187 | − | 0.463426i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.9437 | + | 28.9437i | 0.977360 | + | 0.977360i | 0.999749 | − | 0.0223891i | \(-0.00712727\pi\) |
−0.0223891 | + | 0.999749i | \(0.507127\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.23302i | − | 0.243687i | −0.992549 | − | 0.121843i | \(-0.961119\pi\) | ||
0.992549 | − | 0.121843i | \(-0.0388805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.01625 | − | 7.01625i | 0.236116 | − | 0.236116i | −0.579124 | − | 0.815239i | \(-0.696605\pi\) |
0.815239 | + | 0.579124i | \(0.196605\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.2597 | + | 15.2597i | 0.512371 | + | 0.512371i | 0.915252 | − | 0.402881i | \(-0.131991\pi\) |
−0.402881 | + | 0.915252i | \(0.631991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.9441i | 0.803061i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.36764 | − | 2.36764i | −0.0792301 | − | 0.0792301i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4764 | + | 13.6409i | 0.550745 | + | 0.455965i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.448102i | 0.0149450i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.3115i | − | 0.510100i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.66214 | − | 6.34353i | −0.254698 | − | 0.210866i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.0510 | + | 36.0510i | 1.19706 | + | 1.19706i | 0.975044 | + | 0.222011i | \(0.0712621\pi\) |
0.222011 | + | 0.975044i | \(0.428738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0944i | 0.798282i | 0.916890 | + | 0.399141i | \(0.130692\pi\) | ||||
−0.916890 | + | 0.399141i | \(0.869308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.689236 | + | 0.689236i | 0.0228104 | + | 0.0228104i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.79377 | − | 5.79377i | 0.191327 | − | 0.191327i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.1031i | 1.55379i | 0.629632 | + | 0.776893i | \(0.283206\pi\) | ||||
−0.629632 | + | 0.776893i | \(0.716794\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.99592 | − | 8.99592i | −0.296104 | − | 0.296104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.2772 | + | 44.4795i | −0.995508 | + | 1.46248i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.0301 | 1.11649 | 0.558246 | − | 0.829675i | \(-0.311474\pi\) | ||||
0.558246 | + | 0.829675i | \(0.311474\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.01936i | − | 0.131729i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.95123 | + | 0.466149i | −0.161923 | + | 0.0152447i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.9441 | − | 26.9441i | 0.880227 | − | 0.880227i | −0.113330 | − | 0.993557i | \(-0.536152\pi\) |
0.993557 | + | 0.113330i | \(0.0361519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1115 | −0.623018 | −0.311509 | − | 0.950243i | \(-0.600834\pi\) | ||||
−0.311509 | + | 0.950243i | \(0.600834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0682 | − | 15.0682i | −0.490687 | − | 0.490687i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.6896 | + | 26.6896i | −0.867294 | + | 0.867294i | −0.992172 | − | 0.124878i | \(-0.960146\pi\) |
0.124878 | + | 0.992172i | \(0.460146\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1173 | −0.555652 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0251 | + | 18.0251i | −0.583890 | + | 0.583890i | −0.935970 | − | 0.352080i | \(-0.885475\pi\) |
0.352080 | + | 0.935970i | \(0.385475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.45486 | − | 4.51611i | −0.176515 | − | 0.146138i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.8075 | 0.381284 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9954 | −0.999853 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.39159 | − | 0.319311i | 0.109179 | − | 0.0102790i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9523 | + | 20.9523i | −0.673779 | + | 0.673779i | −0.958585 | − | 0.284806i | \(-0.908071\pi\) |
0.284806 | + | 0.958585i | \(0.408071\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.93592 | 0.222584 | 0.111292 | − | 0.993788i | \(-0.464501\pi\) | ||||
0.111292 | + | 0.993788i | \(0.464501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.5182 | − | 57.5182i | 1.84395 | − | 1.84395i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.98111 | + | 6.98111i | 0.223346 | + | 0.223346i | 0.809906 | − | 0.586560i | \(-0.199518\pi\) |
−0.586560 | + | 0.809906i | \(0.699518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.656493 | 0.0209816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0079 | − | 21.0079i | 0.670047 | − | 0.670047i | −0.287680 | − | 0.957727i | \(-0.592884\pi\) |
0.957727 | + | 0.287680i | \(0.0928840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.65712 | + | 17.6013i | 0.0528004 | + | 0.560823i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 63.2081i | − | 2.00990i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.65846 | −0.211513 | −0.105756 | − | 0.994392i | \(-0.533726\pi\) | ||||
−0.105756 | + | 0.994392i | \(0.533726\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.1632 | − | 22.4886i | −0.861132 | − | 0.712936i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.19447 | − | 9.19447i | −0.291192 | − | 0.291192i | 0.546359 | − | 0.837551i | \(-0.316013\pi\) |
−0.837551 | + | 0.546359i | \(0.816013\pi\) | |||||||
\(998\) | 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 | 1440.2.bj.a.593.17 | 48 | ||
3.2 | odd | 2 | inner | 1440.2.bj.a.593.8 | 48 | ||
4.3 | odd | 2 | 360.2.x.a.53.2 | ✓ | 48 | ||
5.2 | odd | 4 | inner | 1440.2.bj.a.17.18 | 48 | ||
8.3 | odd | 2 | 360.2.x.a.53.11 | yes | 48 | ||
8.5 | even | 2 | inner | 1440.2.bj.a.593.7 | 48 | ||
12.11 | even | 2 | 360.2.x.a.53.23 | yes | 48 | ||
15.2 | even | 4 | inner | 1440.2.bj.a.17.7 | 48 | ||
20.7 | even | 4 | 360.2.x.a.197.14 | yes | 48 | ||
24.5 | odd | 2 | inner | 1440.2.bj.a.593.18 | 48 | ||
24.11 | even | 2 | 360.2.x.a.53.14 | yes | 48 | ||
40.27 | even | 4 | 360.2.x.a.197.23 | yes | 48 | ||
40.37 | odd | 4 | inner | 1440.2.bj.a.17.8 | 48 | ||
60.47 | odd | 4 | 360.2.x.a.197.11 | yes | 48 | ||
120.77 | even | 4 | inner | 1440.2.bj.a.17.17 | 48 | ||
120.107 | odd | 4 | 360.2.x.a.197.2 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.2 | ✓ | 48 | 4.3 | odd | 2 | ||
360.2.x.a.53.11 | yes | 48 | 8.3 | odd | 2 | ||
360.2.x.a.53.14 | yes | 48 | 24.11 | even | 2 | ||
360.2.x.a.53.23 | yes | 48 | 12.11 | even | 2 | ||
360.2.x.a.197.2 | yes | 48 | 120.107 | odd | 4 | ||
360.2.x.a.197.11 | yes | 48 | 60.47 | odd | 4 | ||
360.2.x.a.197.14 | yes | 48 | 20.7 | even | 4 | ||
360.2.x.a.197.23 | yes | 48 | 40.27 | even | 4 | ||
1440.2.bj.a.17.7 | 48 | 15.2 | even | 4 | inner | ||
1440.2.bj.a.17.8 | 48 | 40.37 | odd | 4 | inner | ||
1440.2.bj.a.17.17 | 48 | 120.77 | even | 4 | inner | ||
1440.2.bj.a.17.18 | 48 | 5.2 | odd | 4 | inner | ||
1440.2.bj.a.593.7 | 48 | 8.5 | even | 2 | inner | ||
1440.2.bj.a.593.8 | 48 | 3.2 | odd | 2 | inner | ||
1440.2.bj.a.593.17 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.bj.a.593.18 | 48 | 24.5 | odd | 2 | inner |