Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 242x^{12} + 13297x^{8} + 201600x^{4} + 331776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.11 | ||
Root | \(-2.55743 + 2.55743i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.h.2591.5 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.517638i | 0.231495i | 0.993279 | + | 0.115747i | \(0.0369263\pi\) | ||||
−0.993279 | + | 0.115747i | \(0.963074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.18300 | −0.959710 | −0.479855 | − | 0.877348i | \(-0.659311\pi\) | ||||
−0.479855 | + | 0.877348i | \(0.659311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64764 | −0.734324 | −0.367162 | − | 0.930157i | \(-0.619670\pi\) | ||||
−0.367162 | + | 0.930157i | \(0.619670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.15854i | 1.25113i | 0.780172 | + | 0.625565i | \(0.215132\pi\) | ||||
−0.780172 | + | 0.625565i | \(0.784868\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 8.23349i | − 1.88889i | −0.328666 | − | 0.944446i | \(-0.606599\pi\) | ||||
0.328666 | − | 0.944446i | \(-0.393401\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.38134 | 0.913573 | 0.456786 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456786 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73205 | 0.946410 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.11485i | − 0.949804i | −0.880039 | − | 0.474902i | \(-0.842484\pi\) | ||||
0.880039 | − | 0.474902i | \(-0.157516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.548511i | 0.0985155i | 0.998786 | + | 0.0492577i | \(0.0156856\pi\) | ||||
−0.998786 | + | 0.0492577i | \(0.984314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.517638 | −0.0874968 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.37969 | −0.391219 | −0.195609 | − | 0.980682i | \(-0.562669\pi\) | ||||
−0.195609 | + | 0.980682i | \(0.562669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.473945i | 0.0740177i | 0.999315 | + | 0.0370089i | \(0.0117830\pi\) | ||||
−0.999315 | + | 0.0370089i | \(0.988217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.816460i | − 0.124509i | −0.998060 | − | 0.0622545i | \(-0.980171\pi\) | ||||
0.998060 | − | 0.0622545i | \(-0.0198290\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.493272 | 0.0719512 | 0.0359756 | − | 0.999353i | \(-0.488546\pi\) | ||||
0.0359756 | + | 0.999353i | \(0.488546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 0.915903i | − 0.125809i | −0.998020 | − | 0.0629045i | \(-0.979964\pi\) | ||||
0.998020 | − | 0.0629045i | \(-0.0200363\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.64764i | − 0.222168i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.7229 | 1.65638 | 0.828189 | − | 0.560449i | \(-0.189371\pi\) | ||||
0.828189 | + | 0.560449i | \(0.189371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.40231 | −0.435621 | −0.217811 | − | 0.975991i | \(-0.569891\pi\) | ||||
−0.217811 | + | 0.975991i | \(0.569891\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.37052i | − 0.169992i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.585849i | 0.0715729i | 0.999359 | + | 0.0357864i | \(0.0113936\pi\) | ||||
−0.999359 | + | 0.0357864i | \(0.988606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.95020 | 0.824837 | 0.412419 | − | 0.910994i | \(-0.364684\pi\) | ||||
0.412419 | + | 0.910994i | \(0.364684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.41703 | 0.282892 | 0.141446 | − | 0.989946i | \(-0.454825\pi\) | ||||
0.141446 | + | 0.989946i | \(0.454825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.18300i | − 0.362736i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5787i | 1.41522i | 0.706605 | + | 0.707609i | \(0.250226\pi\) | ||||
−0.706605 | + | 0.707609i | \(0.749774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.215871 | −0.0236949 | −0.0118475 | − | 0.999930i | \(-0.503771\pi\) | ||||
−0.0118475 | + | 0.999930i | \(0.503771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.67026 | −0.289630 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1525i | 1.07617i | 0.842892 | + | 0.538083i | \(0.180851\pi\) | ||||
−0.842892 | + | 0.538083i | \(0.819149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.64764i | − 0.277548i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.26197 | 0.437269 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.23349 | −0.734450 | −0.367225 | − | 0.930132i | \(-0.619692\pi\) | ||||
−0.367225 | + | 0.930132i | \(0.619692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6975i | 1.76097i | 0.474073 | + | 0.880486i | \(0.342783\pi\) | ||||
−0.474073 | + | 0.880486i | \(0.657217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 4.85380i | − 0.478259i | −0.970988 | − | 0.239129i | \(-0.923138\pi\) | ||||
0.970988 | − | 0.239129i | \(-0.0768620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3360 | 1.77261 | 0.886306 | − | 0.463100i | \(-0.153263\pi\) | ||||
0.886306 | + | 0.463100i | \(0.153263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.35524 | 0.896069 | 0.448035 | − | 0.894016i | \(-0.352124\pi\) | ||||
0.448035 | + | 0.894016i | \(0.352124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5.53748i | − 0.520922i | −0.965484 | − | 0.260461i | \(-0.916125\pi\) | ||||
0.965484 | − | 0.260461i | \(-0.0838746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.26795i | 0.211487i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.15854 | −0.472883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.868519 | −0.0789563 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.03768i | 0.450584i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4070i | 1.54462i | 0.635244 | + | 0.772312i | \(0.280900\pi\) | ||||
−0.635244 | + | 0.772312i | \(0.719100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8911 | 0.951558 | 0.475779 | − | 0.879565i | \(-0.342166\pi\) | ||||
0.475779 | + | 0.879565i | \(0.342166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.23349 | 0.713934 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6707i | 1.33884i | 0.742886 | + | 0.669418i | \(0.233457\pi\) | ||||
−0.742886 | + | 0.669418i | \(0.766543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3600i | 1.21800i | 0.793172 | + | 0.608998i | \(0.208428\pi\) | ||||
−0.793172 | + | 0.608998i | \(0.791572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.42744 | 0.704738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.64764 | 0.219875 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.7367i | 1.86266i | 0.364171 | + | 0.931332i | \(0.381352\pi\) | ||||
−0.364171 | + | 0.931332i | \(0.618648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 5.06467i | − 0.412157i | −0.978535 | − | 0.206079i | \(-0.933930\pi\) | ||||
0.978535 | − | 0.206079i | \(-0.0660703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.283930 | −0.0228058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5069 | 1.39720 | 0.698602 | − | 0.715510i | \(-0.253806\pi\) | ||||
0.698602 | + | 0.715510i | \(0.253806\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.38134i | 0.345298i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.74466i | − 0.763261i | −0.924315 | − | 0.381630i | \(-0.875363\pi\) | ||||
0.924315 | − | 0.381630i | \(-0.124637\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.4241 | −1.50308 | −0.751542 | − | 0.659685i | \(-0.770690\pi\) | ||||
−0.751542 | + | 0.659685i | \(0.770690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.99000 | −0.460769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.2673i | 1.31281i | 0.754410 | + | 0.656404i | \(0.227923\pi\) | ||||
−0.754410 | + | 0.656404i | \(0.772077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.73205i | 0.357709i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.2858 | −0.843540 | −0.421770 | − | 0.906703i | \(-0.638591\pi\) | ||||
−0.421770 | + | 0.906703i | \(0.638591\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.40231 | −0.104233 | −0.0521164 | − | 0.998641i | \(-0.516597\pi\) | ||||
−0.0521164 | + | 0.998641i | \(0.516597\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.23182i | − 0.0905652i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.4196i | − 1.20072i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00639 | 0.434607 | 0.217303 | − | 0.976104i | \(-0.430274\pi\) | ||||
0.217303 | + | 0.976104i | \(0.430274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5288 | 1.18977 | 0.594884 | − | 0.803812i | \(-0.297198\pi\) | ||||
0.594884 | + | 0.803812i | \(0.297198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.84687i | − 0.416572i | −0.978068 | − | 0.208286i | \(-0.933211\pi\) | ||||
0.978068 | − | 0.208286i | \(-0.0667885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 4.18354i | − 0.296563i | −0.988945 | − | 0.148282i | \(-0.952626\pi\) | ||||
0.988945 | − | 0.148282i | \(-0.0473742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.11485 | 0.358992 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.245332 | −0.0171347 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.2072i | 1.81279i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 21.2882i | − 1.46554i | −0.680478 | − | 0.732769i | \(-0.738228\pi\) | ||||
0.680478 | − | 0.732769i | \(-0.261772\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.422631 | 0.0288232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.548511 | −0.0372354 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 13.6580i | − 0.918735i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 12.5887i | − 0.843004i | −0.906828 | − | 0.421502i | \(-0.861503\pi\) | ||||
0.906828 | − | 0.421502i | \(-0.138497\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.19330 | 0.0792024 | 0.0396012 | − | 0.999216i | \(-0.487391\pi\) | ||||
0.0396012 | + | 0.999216i | \(0.487391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.7694 | −1.17423 | −0.587117 | − | 0.809502i | \(-0.699737\pi\) | ||||
−0.587117 | + | 0.809502i | \(0.699737\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.1284i | − 0.925580i | −0.886468 | − | 0.462790i | \(-0.846848\pi\) | ||||
0.886468 | − | 0.462790i | \(-0.153152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.255337i | 0.0166563i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1600 | 0.915932 | 0.457966 | − | 0.888970i | \(-0.348578\pi\) | ||||
0.457966 | + | 0.888970i | \(0.348578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1864 | −1.30032 | −0.650161 | − | 0.759797i | \(-0.725298\pi\) | ||||
−0.650161 | + | 0.759797i | \(0.725298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.517638i | − 0.0330707i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.7993i | 1.38706i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7352 | 0.993197 | 0.496598 | − | 0.867980i | \(-0.334582\pi\) | ||||
0.496598 | + | 0.867980i | \(0.334582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.9458 | −0.876765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.72117i | − 0.606390i | −0.952929 | − | 0.303195i | \(-0.901947\pi\) | ||||
0.952929 | − | 0.303195i | \(-0.0980534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.37969i | − 0.147867i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.5487 | 1.20542 | 0.602712 | − | 0.797959i | \(-0.294087\pi\) | ||||
0.602712 | + | 0.797959i | \(0.294087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.474106 | 0.0291241 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00699i | 0.549166i | 0.961563 | + | 0.274583i | \(0.0885398\pi\) | ||||
−0.961563 | + | 0.274583i | \(0.911460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0252i | 0.973463i | 0.873552 | + | 0.486732i | \(0.161811\pi\) | ||||
−0.873552 | + | 0.486732i | \(0.838189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.0621 | −0.908279 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.31790 | −0.259437 | −0.129719 | − | 0.991551i | \(-0.541407\pi\) | ||||
−0.129719 | + | 0.991551i | \(0.541407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.06265i | 0.480977i | 0.970652 | + | 0.240489i | \(0.0773077\pi\) | ||||
−0.970652 | + | 0.240489i | \(0.922692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 27.4570i | − 1.63215i | −0.577948 | − | 0.816074i | \(-0.696146\pi\) | ||||
0.577948 | − | 0.816074i | \(-0.303854\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.473945 | −0.0279761 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.61057 | −0.565328 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1282i | 0.591694i | 0.955235 | + | 0.295847i | \(0.0956018\pi\) | ||||
−0.955235 | + | 0.295847i | \(0.904398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.58585i | 0.383443i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.6002 | −0.670858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.816460 | 0.0470600 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1.76117i | − 0.100844i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8441i | 0.618904i | 0.950915 | + | 0.309452i | \(0.100146\pi\) | ||||
−0.950915 | + | 0.309452i | \(0.899854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.7209 | 1.28839 | 0.644193 | − | 0.764863i | \(-0.277193\pi\) | ||||
0.644193 | + | 0.764863i | \(0.277193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.8222 | 0.724755 | 0.362377 | − | 0.932031i | \(-0.381965\pi\) | ||||
0.362377 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4593i | 0.587455i | 0.955889 | + | 0.293727i | \(0.0948958\pi\) | ||||
−0.955889 | + | 0.293727i | \(0.905104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.2806i | 0.911536i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.4728 | 2.36325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.5288 | −0.694971 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.493272i | 0.0271950i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.70760i | 0.203788i | 0.994795 | + | 0.101894i | \(0.0324902\pi\) | ||||
−0.994795 | + | 0.101894i | \(0.967510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.303258 | −0.0165688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9900 | 1.08892 | 0.544462 | − | 0.838785i | \(-0.316734\pi\) | ||||
0.544462 | + | 0.838785i | \(0.316734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.74591i | − 0.0945463i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.1226 | 1.18760 | 0.593801 | − | 0.804612i | \(-0.297627\pi\) | ||||
0.593801 | + | 0.804612i | \(0.297627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.997120 | 0.0533746 | 0.0266873 | − | 0.999644i | \(-0.491504\pi\) | ||||
0.0266873 | + | 0.999644i | \(0.491504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 20.5403i | − 1.09325i | −0.837378 | − | 0.546624i | \(-0.815913\pi\) | ||||
0.837378 | − | 0.546624i | \(-0.184087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.59769i | 0.190946i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.28121 | −0.331509 | −0.165755 | − | 0.986167i | \(-0.553006\pi\) | ||||
−0.165755 | + | 0.986167i | \(0.553006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −48.7904 | −2.56791 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.25115i | 0.0654880i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.439376i | 0.0229352i | 0.999934 | + | 0.0114676i | \(0.00365034\pi\) | ||||
−0.999934 | + | 0.0114676i | \(0.996350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.915903 | 0.0475513 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.2016 | −1.77089 | −0.885447 | − | 0.464741i | \(-0.846148\pi\) | ||||
−0.885447 | + | 0.464741i | \(0.846148\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5423i | 0.697463i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.9681i | − 0.820229i | −0.912034 | − | 0.410114i | \(-0.865489\pi\) | ||||
0.912034 | − | 0.410114i | \(-0.134511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.6537 | 1.61743 | 0.808715 | − | 0.588200i | \(-0.200163\pi\) | ||||
0.808715 | + | 0.588200i | \(0.200163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64764 | 0.0839716 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.3751i | 1.28657i | 0.765627 | + | 0.643285i | \(0.222429\pi\) | ||||
−0.765627 | + | 0.643285i | \(0.777571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.6013i | 1.14300i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.51123 | −0.327615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.4470 | 1.72884 | 0.864422 | − | 0.502767i | \(-0.167685\pi\) | ||||
0.864422 | + | 0.502767i | \(0.167685\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2881i | 1.81214i | 0.423126 | + | 0.906071i | \(0.360933\pi\) | ||||
−0.423126 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.45226i | − 0.0723423i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.57456 | 0.375457 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.84590 | 0.338508 | 0.169254 | − | 0.985572i | \(-0.445864\pi\) | ||||
0.169254 | + | 0.985572i | \(0.445864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.7229i | 0.626052i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 0.111743i | − 0.00548525i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.12396 | 0.250322 | 0.125161 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125161 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.3926 | 0.798925 | 0.399463 | − | 0.916749i | \(-0.369197\pi\) | ||||
0.399463 | + | 0.916749i | \(0.369197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.4105i | 1.18408i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.40231i | − 0.164649i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.0475 | 1.20650 | 0.603248 | − | 0.797554i | \(-0.293873\pi\) | ||||
0.603248 | + | 0.797554i | \(0.293873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.1427 | 1.92914 | 0.964568 | − | 0.263834i | \(-0.0849870\pi\) | ||||
0.964568 | + | 0.263834i | \(0.0849870\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 36.0737i | − 1.72564i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.6905i | 1.08296i | 0.840715 | + | 0.541478i | \(0.182135\pi\) | ||||
−0.840715 | + | 0.541478i | \(0.817865\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.8137 | −1.27396 | −0.636979 | − | 0.770881i | \(-0.719816\pi\) | ||||
−0.636979 | + | 0.770881i | \(0.719816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.25534 | −0.249127 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.12725i | 0.289163i | 0.989493 | + | 0.144581i | \(0.0461836\pi\) | ||||
−0.989493 | + | 0.144581i | \(0.953816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.50856i | − 0.0710355i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.37052 | 0.0642510 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.2629 | 0.667192 | 0.333596 | − | 0.942716i | \(-0.391738\pi\) | ||||
0.333596 | + | 0.942716i | \(0.391738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2106i | 0.615279i | 0.951503 | + | 0.307639i | \(0.0995390\pi\) | ||||
−0.951503 | + | 0.307639i | \(0.900461\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.56112i | 0.119026i | 0.998228 | + | 0.0595128i | \(0.0189547\pi\) | ||||
−0.998228 | + | 0.0595128i | \(0.981045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.8012 | −1.05511 | −0.527557 | − | 0.849519i | \(-0.676892\pi\) | ||||
−0.527557 | + | 0.849519i | \(0.676892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.585849 | −0.0270520 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.59879i | 0.119493i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 38.9613i | − 1.78767i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.9525 | −1.68840 | −0.844201 | − | 0.536027i | \(-0.819924\pi\) | ||||
−0.844201 | + | 0.536027i | \(0.819924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.30057 | 0.287281 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.74433i | − 0.170021i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.80934i | 0.308560i | 0.988027 | + | 0.154280i | \(0.0493059\pi\) | ||||
−0.988027 | + | 0.154280i | \(0.950694\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1702 | 0.639492 | 0.319746 | − | 0.947503i | \(-0.396402\pi\) | ||||
0.319746 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.3852 | 1.18833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.95020i | 0.311759i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 34.6858i | − 1.55275i | −0.630273 | − | 0.776374i | \(-0.717057\pi\) | ||||
0.630273 | − | 0.776374i | \(-0.282943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.85580 | 0.439448 | 0.219724 | − | 0.975562i | \(-0.429484\pi\) | ||||
0.219724 | + | 0.975562i | \(0.429484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.16092 | −0.407656 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2874i | 0.721926i | 0.932580 | + | 0.360963i | \(0.117552\pi\) | ||||
−0.932580 | + | 0.360963i | \(0.882448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.41703i | 0.106923i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.51251 | 0.110714 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.57008 | −0.0690523 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 27.9338i | − 1.22380i | −0.790935 | − | 0.611900i | \(-0.790405\pi\) | ||||
0.790935 | − | 0.611900i | \(-0.209595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.13724i | 0.0934550i | 0.998908 | + | 0.0467275i | \(0.0148792\pi\) | ||||
−0.998908 | + | 0.0467275i | \(0.985121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.82952 | −0.123256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.80385 | −0.165385 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.25484i | − 0.0543529i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.49144i | 0.410351i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.18300 | 0.137101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.2037 | 0.868627 | 0.434313 | − | 0.900762i | \(-0.356991\pi\) | ||||
0.434313 | + | 0.900762i | \(0.356991\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84263i | 0.207435i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.7917i | 1.27380i | 0.770946 | + | 0.636901i | \(0.219784\pi\) | ||||
−0.770946 | + | 0.636901i | \(0.780216\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.1131 | −1.79408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5787 | −0.534902 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.18984i | − 0.177529i | −0.996053 | − | 0.0887645i | \(-0.971708\pi\) | ||||
0.996053 | − | 0.0887645i | \(-0.0282919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.16169i | 0.0914299i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.2275 | 1.52681 | 0.763405 | − | 0.645921i | \(-0.223526\pi\) | ||||
0.763405 | + | 0.645921i | \(0.223526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.86641 | 0.120591 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.93088i | 0.290557i | 0.989391 | + | 0.145279i | \(0.0464079\pi\) | ||||
−0.989391 | + | 0.145279i | \(0.953592\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 27.4822i | − 1.15009i | −0.818120 | − | 0.575047i | \(-0.804984\pi\) | ||||
0.818120 | − | 0.575047i | \(-0.195016\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7327 | 0.864615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9829 | −1.04005 | −0.520025 | − | 0.854151i | \(-0.674077\pi\) | ||||
−0.520025 | + | 0.854151i | \(0.674077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 0.215871i | − 0.00895583i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.91532i | 0.120740i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.7456 | −0.691164 | −0.345582 | − | 0.938389i | \(-0.612319\pi\) | ||||
−0.345582 | + | 0.938389i | \(0.612319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.51616 | 0.186085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.78732i | 0.114461i | 0.998361 | + | 0.0572307i | \(0.0182270\pi\) | ||||
−0.998361 | + | 0.0572307i | \(0.981773\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.67026i | − 0.109470i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.5145 | 1.08335 | 0.541677 | − | 0.840587i | \(-0.317790\pi\) | ||||
0.541677 | + | 0.840587i | \(0.317790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.5198 | −0.877811 | −0.438906 | − | 0.898533i | \(-0.644634\pi\) | ||||
−0.438906 | + | 0.898533i | \(0.644634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 0.449579i | − 0.0182780i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4052i | 0.503511i | 0.967791 | + | 0.251756i | \(0.0810079\pi\) | ||||
−0.967791 | + | 0.251756i | \(0.918992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.30601 | −0.0528354 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.8840 | 1.85324 | 0.926619 | − | 0.376002i | \(-0.122701\pi\) | ||||
0.926619 | + | 0.376002i | \(0.122701\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 37.1405i | − 1.49522i | −0.664139 | − | 0.747610i | \(-0.731202\pi\) | ||||
0.664139 | − | 0.747610i | \(-0.268798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 17.5338i | − 0.704743i | −0.935860 | − | 0.352371i | \(-0.885375\pi\) | ||||
0.935860 | − | 0.352371i | \(-0.114625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.1525 | −0.406753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0526 | 0.842102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 12.2757i | − 0.489466i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2706i | 0.607911i | 0.952686 | + | 0.303956i | \(0.0983075\pi\) | ||||
−0.952686 | + | 0.303956i | \(0.901693\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.01054 | −0.357572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.64764 | 0.104903 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.3657i | 0.488417i | 0.969723 | + | 0.244208i | \(0.0785281\pi\) | ||||
−0.969723 | + | 0.244208i | \(0.921472\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12.9800i | − 0.511881i | −0.966693 | − | 0.255940i | \(-0.917615\pi\) | ||||
0.966693 | − | 0.255940i | \(-0.0823851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.183885 | 0.00722926 | 0.00361463 | − | 0.999993i | \(-0.498849\pi\) | ||||
0.00361463 | + | 0.999993i | \(0.498849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.4969 | −1.58964 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 35.9300i | − 1.40605i | −0.711165 | − | 0.703025i | \(-0.751832\pi\) | ||||
0.711165 | − | 0.703025i | \(-0.248168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.63764i | 0.220281i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0211 | 0.779913 | 0.389956 | − | 0.920833i | \(-0.372490\pi\) | ||||
0.389956 | + | 0.920833i | \(0.372490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.6434 | −1.30858 | −0.654288 | − | 0.756245i | \(-0.727032\pi\) | ||||
−0.654288 | + | 0.756245i | \(0.727032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.26197i | 0.165272i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 22.4099i | − 0.867715i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8295 | 0.418070 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.7523 | 0.954129 | 0.477065 | − | 0.878868i | \(-0.341701\pi\) | ||||
0.477065 | + | 0.878868i | \(0.341701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.2599i | 0.624920i | 0.949931 | + | 0.312460i | \(0.101153\pi\) | ||||
−0.949931 | + | 0.312460i | \(0.898847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 7.23349i | − 0.277596i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.52039 | −0.326024 | −0.163012 | − | 0.986624i | \(-0.552121\pi\) | ||||
−0.163012 | + | 0.986624i | \(0.552121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.11174 | −0.309934 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.42498i | 0.0923845i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 0.354195i | − 0.0134742i | −0.999977 | − | 0.00673710i | \(-0.997855\pi\) | ||||
0.999977 | − | 0.00673710i | \(-0.00214450\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.43326 | −0.281960 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.44486 | −0.0926058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 13.0877i | − 0.494315i | −0.968975 | − | 0.247157i | \(-0.920504\pi\) | ||||
0.968975 | − | 0.247157i | \(-0.0794964\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.5932i | 0.738971i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.6975 | −0.665585 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2340 | −0.459457 | −0.229729 | − | 0.973255i | \(-0.573784\pi\) | ||||
−0.229729 | + | 0.973255i | \(0.573784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.40321i | 0.0900011i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.36236i | 0.163143i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.54681 | −0.318742 | −0.159371 | − | 0.987219i | \(-0.550947\pi\) | ||||
−0.159371 | + | 0.987219i | \(0.550947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.85380 | 0.180765 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 24.2037i | − 0.898904i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.1151i | 1.67323i | 0.547793 | + | 0.836614i | \(0.315468\pi\) | ||||
−0.547793 | + | 0.836614i | \(0.684532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.21175 | 0.155777 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1541 | −0.448921 | −0.224460 | − | 0.974483i | \(-0.572062\pi\) | ||||
−0.224460 | + | 0.974483i | \(0.572062\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.86476i | − 0.0686892i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57113i | 0.0577949i | 0.999582 | + | 0.0288974i | \(0.00919962\pi\) | ||||
−0.999582 | + | 0.0288974i | \(0.990800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7028 | 0.576080 | 0.288040 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288040 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7694 | −0.431197 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.3360i | 0.669984i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 38.5392i | − 1.40632i | −0.711033 | − | 0.703159i | \(-0.751772\pi\) | ||||
0.711033 | − | 0.703159i | \(-0.248228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.62167 | 0.0954122 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.73416 | 0.0993747 | 0.0496873 | − | 0.998765i | \(-0.484178\pi\) | ||||
0.0496873 | + | 0.998765i | \(0.484178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 9.21155i | − 0.333919i | −0.985964 | − | 0.166959i | \(-0.946605\pi\) | ||||
0.985964 | − | 0.166959i | \(-0.0533949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.35524i | 0.338682i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.6856 | −1.21632 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.5687 | 1.57113 | 0.785564 | − | 0.618780i | \(-0.212373\pi\) | ||||
0.785564 | + | 0.618780i | \(0.212373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 38.5831i | − 1.38774i | −0.720101 | − | 0.693869i | \(-0.755905\pi\) | ||||
0.720101 | − | 0.693869i | \(-0.244095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.59558i | 0.0932361i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.90222 | 0.139811 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.1225 | −0.791605 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.06225i | 0.323446i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1846i | 0.398687i | 0.979930 | + | 0.199344i | \(0.0638810\pi\) | ||||
−0.979930 | + | 0.199344i | \(0.936119\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.53748 | 0.196890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00810 | 0.319887 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23.1800i | − 0.821079i | −0.911843 | − | 0.410539i | \(-0.865340\pi\) | ||||
0.911843 | − | 0.410539i | \(-0.134660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.54457i | 0.0900203i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.69340 | −0.271494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.26795 | −0.0799347 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 23.6450i | − 0.831313i | −0.909522 | − | 0.415657i | \(-0.863552\pi\) | ||||
0.909522 | − | 0.415657i | \(-0.136448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 24.5971i | − 0.863721i | −0.901940 | − | 0.431860i | \(-0.857857\pi\) | ||||
0.901940 | − | 0.431860i | \(-0.142143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.04421 | 0.176691 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.72232 | −0.235184 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.5879i | 1.80043i | 0.435446 | + | 0.900215i | \(0.356591\pi\) | ||||
−0.435446 | + | 0.900215i | \(0.643409\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0575i | 0.524873i | 0.964949 | + | 0.262437i | \(0.0845260\pi\) | ||||
−0.964949 | + | 0.262437i | \(0.915474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.65940 | 0.127250 | 0.0636249 | − | 0.997974i | \(-0.479734\pi\) | ||||
0.0636249 | + | 0.997974i | \(0.479734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9681 | 0.832448 | 0.416224 | − | 0.909262i | \(-0.363353\pi\) | ||||
0.416224 | + | 0.909262i | \(0.363353\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.15854i | − 0.178733i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 10.0547i | − 0.347956i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.5883 | −0.917931 | −0.458965 | − | 0.888454i | \(-0.651780\pi\) | ||||
−0.458965 | + | 0.888454i | \(0.651780\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.83831 | 0.0978726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.10065i | − 0.106666i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 0.868519i | − 0.0298427i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.4262 | −0.357407 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.0181 | −0.959321 | −0.479661 | − | 0.877454i | \(-0.659240\pi\) | ||||
−0.479661 | + | 0.877454i | \(0.659240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.9852i | 0.580205i | 0.956996 | + | 0.290102i | \(0.0936893\pi\) | ||||
−0.956996 | + | 0.290102i | \(0.906311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9576i | 0.680946i | 0.940254 | + | 0.340473i | \(0.110587\pi\) | ||||
−0.940254 | + | 0.340473i | \(0.889413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.3884 | −1.44292 | −0.721459 | − | 0.692457i | \(-0.756528\pi\) | ||||
−0.721459 | + | 0.692457i | \(0.756528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.93821 | −0.303908 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 40.0381i | − 1.35820i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.55112i | − 0.0525577i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.03768 | −0.170305 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.4993 | −0.827284 | −0.413642 | − | 0.910440i | \(-0.635743\pi\) | ||||
−0.413642 | + | 0.910440i | \(0.635743\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.5364i | 0.826652i | 0.910583 | + | 0.413326i | \(0.135633\pi\) | ||||
−0.910583 | + | 0.413326i | \(0.864367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17.3082i | − 0.582466i | −0.956652 | − | 0.291233i | \(-0.905934\pi\) | ||||
0.956652 | − | 0.291233i | \(-0.0940655\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.8260 | −1.37080 | −0.685401 | − | 0.728166i | \(-0.740373\pi\) | ||||
−0.685401 | + | 0.728166i | \(0.740373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4070 | −0.583813 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.06135i | − 0.135908i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 5.84196i | − 0.195275i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.80555 | 0.0935704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.72473 | 0.157403 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 0.725889i | − 0.0241294i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 28.9282i | − 0.960545i | −0.877119 | − | 0.480273i | \(-0.840538\pi\) | ||||
0.877119 | − | 0.480273i | \(-0.159462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.90248 | −0.328084 | −0.164042 | − | 0.986453i | \(-0.552453\pi\) | ||||
−0.164042 | + | 0.986453i | \(0.552453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.687117 | 0.0227402 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.8911i | 0.359655i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 24.2910i | − 0.801287i | −0.916234 | − | 0.400644i | \(-0.868787\pi\) | ||||
0.916234 | − | 0.400644i | \(-0.131213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.4016 | −0.605698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.2608 | −0.370254 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.4046i | 0.997544i | 0.866733 | + | 0.498772i | \(0.166216\pi\) | ||||
−0.866733 | + | 0.498772i | \(0.833784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.23349i | 0.269842i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.49943 | 0.277961 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.54014 | −0.115651 | −0.0578257 | − | 0.998327i | \(-0.518417\pi\) | ||||
−0.0578257 | + | 0.998327i | \(0.518417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1731i | 0.853220i | 0.904436 | + | 0.426610i | \(0.140292\pi\) | ||||
−0.904436 | + | 0.426610i | \(0.859708\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.07651i | 0.0676206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3342 | −0.920739 | −0.460369 | − | 0.887727i | \(-0.652283\pi\) | ||||
−0.460369 | + | 0.887727i | \(0.652283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.39943 | −0.207734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 55.0723i | − 1.78397i | −0.452069 | − | 0.891983i | \(-0.649314\pi\) | ||||
0.452069 | − | 0.891983i | \(-0.350686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.10914i | 0.100609i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6707 | −0.506033 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6991 | 0.990295 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.55592i | 0.275425i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 25.0733i | − 0.806304i | −0.915133 | − | 0.403152i | \(-0.867915\pi\) | ||||
0.915133 | − | 0.403152i | \(-0.132085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.8089 | −1.56635 | −0.783176 | − | 0.621800i | \(-0.786402\pi\) | ||||
−0.783176 | + | 0.621800i | \(0.786402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3600 | −0.460359 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 61.2645i | − 1.96002i | −0.198940 | − | 0.980012i | \(-0.563750\pi\) | ||||
0.198940 | − | 0.980012i | \(-0.436250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 32.3155i | − 1.03281i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.74007 | 0.0873948 | 0.0436974 | − | 0.999045i | \(-0.486086\pi\) | ||||
0.0436974 | + | 0.999045i | \(0.486086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.02656 | 0.0964343 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.57719i | − 0.113748i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.02994i | 0.255079i | 0.991833 | + | 0.127540i | \(0.0407080\pi\) | ||||
−0.991833 | + | 0.127540i | \(0.959292\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.16556 | 0.0686529 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4217 | −0.520082 | −0.260041 | − | 0.965598i | \(-0.583736\pi\) | ||||
−0.260041 | + | 0.965598i | \(0.583736\pi\) | |||||||
\(998\) | 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 | 6048.2.h.h.2591.11 | yes | 16 | |
3.2 | odd | 2 | inner | 6048.2.h.h.2591.8 | yes | 16 | |
4.3 | odd | 2 | inner | 6048.2.h.h.2591.10 | yes | 16 | |
12.11 | even | 2 | inner | 6048.2.h.h.2591.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.h.2591.5 | ✓ | 16 | 12.11 | even | 2 | inner | |
6048.2.h.h.2591.8 | yes | 16 | 3.2 | odd | 2 | inner | |
6048.2.h.h.2591.10 | yes | 16 | 4.3 | odd | 2 | inner | |
6048.2.h.h.2591.11 | yes | 16 | 1.1 | even | 1 | trivial |