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 | 2591.2 | ||
Root | \(1.53379 + 1.53379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.h.2591.16 |
$q$-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 | ||||||||
\(5\) | − 1.93185i | − 0.863950i | −0.901886 | − | 0.431975i | \(-0.857817\pi\) | ||||
0.901886 | − | 0.431975i | \(-0.142183\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.58521 | 1.08098 | 0.540491 | − | 0.841350i | \(-0.318239\pi\) | ||||
0.540491 | + | 0.841350i | \(0.318239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.92609 | 1.64360 | 0.821801 | − | 0.569774i | \(-0.192969\pi\) | ||||
0.821801 | + | 0.569774i | \(0.192969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.96655i | − 1.68964i | −0.535053 | − | 0.844818i | \(-0.679709\pi\) | ||||
0.535053 | − | 0.844818i | \(-0.320291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.33820i | 1.22467i | 0.790599 | + | 0.612334i | \(0.209769\pi\) | ||||
−0.790599 | + | 0.612334i | \(0.790231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.96713 | 0.618689 | 0.309344 | − | 0.950950i | \(-0.399890\pi\) | ||||
0.309344 | + | 0.950950i | \(0.399890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.26795 | 0.253590 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.06757i | − 0.569634i | −0.958582 | − | 0.284817i | \(-0.908067\pi\) | ||||
0.958582 | − | 0.284817i | \(-0.0919328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.27006i | 0.228109i | 0.993474 | + | 0.114055i | \(0.0363839\pi\) | ||||
−0.993474 | + | 0.114055i | \(0.963616\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.93185 | −0.326543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.65815 | 1.58779 | 0.793895 | − | 0.608055i | \(-0.208050\pi\) | ||||
0.793895 | + | 0.608055i | \(0.208050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.10227i | 1.26536i | 0.774413 | + | 0.632681i | \(0.218046\pi\) | ||||
−0.774413 | + | 0.632681i | \(0.781954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.46199i | 0.375450i | 0.982222 | + | 0.187725i | \(0.0601114\pi\) | ||||
−0.982222 | + | 0.187725i | \(0.939889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.45299 | 0.941265 | 0.470632 | − | 0.882329i | \(-0.344026\pi\) | ||||
0.470632 | + | 0.882329i | \(0.344026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2092i | 1.53970i | 0.638224 | + | 0.769850i | \(0.279669\pi\) | ||||
−0.638224 | + | 0.769850i | \(0.720331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 6.92609i | − 0.933914i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.34847 | 0.826500 | 0.413250 | − | 0.910618i | \(-0.364394\pi\) | ||||
0.413250 | + | 0.910618i | \(0.364394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7263 | −1.37336 | −0.686680 | − | 0.726960i | \(-0.740933\pi\) | ||||
−0.686680 | + | 0.726960i | \(0.740933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 11.4483i | − 1.41999i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.26430i | − 0.765306i | −0.923892 | − | 0.382653i | \(-0.875011\pi\) | ||||
0.923892 | − | 0.382653i | \(-0.124989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.92887 | −0.228915 | −0.114457 | − | 0.993428i | \(-0.536513\pi\) | ||||
−0.114457 | + | 0.993428i | \(0.536513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.12379 | −0.248571 | −0.124285 | − | 0.992247i | \(-0.539664\pi\) | ||||
−0.124285 | + | 0.992247i | \(0.539664\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.58521i | − 0.408573i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.71379i | 0.980378i | 0.871616 | + | 0.490189i | \(0.163072\pi\) | ||||
−0.871616 | + | 0.490189i | \(0.836928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.96655 | 0.874443 | 0.437221 | − | 0.899354i | \(-0.355963\pi\) | ||||
0.437221 | + | 0.899354i | \(0.355963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.4583 | −1.45976 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 9.04118i | − 0.958363i | −0.877716 | − | 0.479181i | \(-0.840934\pi\) | ||||
0.877716 | − | 0.479181i | \(-0.159066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.92609i | − 0.621223i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3126 | 1.05805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.33820 | −0.440478 | −0.220239 | − | 0.975446i | \(-0.570684\pi\) | ||||
−0.220239 | + | 0.975446i | \(0.570684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.13216i | 0.610173i | 0.952325 | + | 0.305086i | \(0.0986854\pi\) | ||||
−0.952325 | + | 0.305086i | \(0.901315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.9963i | 1.37910i | 0.724238 | + | 0.689551i | \(0.242192\pi\) | ||||
−0.724238 | + | 0.689551i | \(0.757808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.34251 | −0.903174 | −0.451587 | − | 0.892227i | \(-0.649142\pi\) | ||||
−0.451587 | + | 0.892227i | \(0.649142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.0666 | 1.82625 | 0.913125 | − | 0.407681i | \(-0.133662\pi\) | ||||
0.913125 | + | 0.407681i | \(0.133662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.68863i | 0.158853i | 0.996841 | + | 0.0794266i | \(0.0253089\pi\) | ||||
−0.996841 | + | 0.0794266i | \(0.974691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.73205i | − 0.534516i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.96655 | −0.638623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.85373 | 0.168521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 12.1087i | − 1.08304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2424i | 1.35254i | 0.736653 | + | 0.676271i | \(0.236405\pi\) | ||||
−0.736653 | + | 0.676271i | \(0.763595\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0699 | −1.40403 | −0.702017 | − | 0.712160i | \(-0.747717\pi\) | ||||
−0.702017 | + | 0.712160i | \(0.747717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.33820 | 0.462881 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.82545i | 0.326830i | 0.986557 | + | 0.163415i | \(0.0522509\pi\) | ||||
−0.986557 | + | 0.163415i | \(0.947749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9021i | 1.34880i | 0.738368 | + | 0.674398i | \(0.235597\pi\) | ||||
−0.738368 | + | 0.674398i | \(0.764403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.2463 | 1.77670 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.92609 | −0.492135 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.17987i | − 0.670121i | −0.942197 | − | 0.335061i | \(-0.891243\pi\) | ||||
0.942197 | − | 0.335061i | \(-0.108757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 8.04988i | − 0.655090i | −0.944836 | − | 0.327545i | \(-0.893779\pi\) | ||||
0.944836 | − | 0.327545i | \(-0.106221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.45356 | 0.197075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6420 | −1.40798 | −0.703992 | − | 0.710208i | \(-0.748601\pi\) | ||||
−0.703992 | + | 0.710208i | \(0.748601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.96713i | − 0.233842i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2.46621i | − 0.193169i | −0.995325 | − | 0.0965843i | \(-0.969208\pi\) | ||||
0.995325 | − | 0.0965843i | \(-0.0307917\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.1340 | 1.24849 | 0.624243 | − | 0.781230i | \(-0.285408\pi\) | ||||
0.624243 | + | 0.781230i | \(0.285408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.1186 | 1.70143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 12.0042i | − 0.912665i | −0.889809 | − | 0.456332i | \(-0.849163\pi\) | ||||
0.889809 | − | 0.456332i | \(-0.150837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.26795i | − 0.0958479i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.4871 | −1.08282 | −0.541408 | − | 0.840760i | \(-0.682109\pi\) | ||||
−0.541408 | + | 0.840760i | \(0.682109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.72629 | −0.648620 | −0.324310 | − | 0.945951i | \(-0.605132\pi\) | ||||
−0.324310 | + | 0.945951i | \(0.605132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 18.6581i | − 1.37177i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 24.9765i | − 1.82647i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6628 | 0.916245 | 0.458122 | − | 0.888889i | \(-0.348522\pi\) | ||||
0.458122 | + | 0.888889i | \(0.348522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.51399 | −0.252942 | −0.126471 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126471 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.3056i | − 0.805488i | −0.915313 | − | 0.402744i | \(-0.868057\pi\) | ||||
0.915313 | − | 0.402744i | \(-0.131943\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.53801i | 0.179915i | 0.995946 | + | 0.0899573i | \(0.0286731\pi\) | ||||
−0.995946 | + | 0.0899573i | \(0.971327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.06757 | −0.215301 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.6524 | 1.09321 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.1386i | 1.32384i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 22.8303i | − 1.57170i | −0.618416 | − | 0.785851i | \(-0.712225\pi\) | ||||
0.618416 | − | 0.785851i | \(-0.287775\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.75620 | 0.324370 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.27006 | 0.0862172 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 41.2844i | − 2.77709i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4048i | 1.29944i | 0.760173 | + | 0.649721i | \(0.225114\pi\) | ||||
−0.760173 | + | 0.649721i | \(0.774886\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.6287 | 1.70104 | 0.850519 | − | 0.525944i | \(-0.176288\pi\) | ||||
0.850519 | + | 0.525944i | \(0.176288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.8023 | −1.44074 | −0.720368 | − | 0.693592i | \(-0.756027\pi\) | ||||
−0.720368 | + | 0.693592i | \(0.756027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 28.1070i | − 1.84135i | −0.390327 | − | 0.920676i | \(-0.627638\pi\) | ||||
0.390327 | − | 0.920676i | \(-0.372362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 12.4662i | − 0.813206i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.79017 | −0.115796 | −0.0578982 | − | 0.998322i | \(-0.518440\pi\) | ||||
−0.0578982 | + | 0.998322i | \(0.518440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6785 | −1.26760 | −0.633802 | − | 0.773495i | \(-0.718507\pi\) | ||||
−0.633802 | + | 0.773495i | \(0.718507\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.93185i | 0.123421i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.6347i | 2.01287i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.9672 | 1.44968 | 0.724839 | − | 0.688918i | \(-0.241914\pi\) | ||||
0.724839 | + | 0.688918i | \(0.241914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.6378 | 0.668791 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 28.7563i | − 1.79377i | −0.442265 | − | 0.896884i | \(-0.645825\pi\) | ||||
0.442265 | − | 0.896884i | \(-0.354175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.65815i | − 0.600128i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.8415 | 1.90177 | 0.950883 | − | 0.309549i | \(-0.100178\pi\) | ||||
0.950883 | + | 0.309549i | \(0.100178\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.6545 | 1.33022 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.16635i | 0.497911i | 0.968515 | + | 0.248956i | \(0.0800873\pi\) | ||||
−0.968515 | + | 0.248956i | \(0.919913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46832i | 0.0891941i | 0.999005 | + | 0.0445970i | \(0.0142004\pi\) | ||||
−0.999005 | + | 0.0445970i | \(0.985800\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.54586 | 0.274126 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.53225 | −0.392485 | −0.196242 | − | 0.980555i | \(-0.562874\pi\) | ||||
−0.196242 | + | 0.980555i | \(0.562874\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2415i | 0.789921i | 0.918698 | + | 0.394960i | \(0.129242\pi\) | ||||
−0.918698 | + | 0.394960i | \(0.870758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.44219i | − 0.382948i | −0.981498 | − | 0.191474i | \(-0.938673\pi\) | ||||
0.981498 | − | 0.191474i | \(-0.0613268\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.10227 | 0.478262 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.5328 | −1.85487 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.5623i | − 0.792319i | −0.918182 | − | 0.396159i | \(-0.870343\pi\) | ||||
0.918182 | − | 0.396159i | \(-0.129657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 12.2643i | − 0.714055i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5835 | 1.01688 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.46199 | 0.141907 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.7216i | 1.18652i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 29.8710i | − 1.70483i | −0.522867 | − | 0.852414i | \(-0.675138\pi\) | ||||
0.522867 | − | 0.852414i | \(-0.324862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.6551 | −1.56817 | −0.784087 | − | 0.620651i | \(-0.786869\pi\) | ||||
−0.784087 | + | 0.620651i | \(0.786869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7430 | 0.946371 | 0.473185 | − | 0.880963i | \(-0.343104\pi\) | ||||
0.473185 | + | 0.880963i | \(0.343104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.136810i | 0.00768401i | 0.999993 | + | 0.00384201i | \(0.00122295\pi\) | ||||
−0.999993 | + | 0.00384201i | \(0.998777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 10.9979i | − 0.615764i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.1888 | 2.06924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.51399 | 0.416801 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 6.45299i | − 0.355765i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 21.9927i | − 1.20883i | −0.796670 | − | 0.604414i | \(-0.793407\pi\) | ||||
0.796670 | − | 0.604414i | \(-0.206593\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1017 | −0.661186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.11859 | −0.442248 | −0.221124 | − | 0.975246i | \(-0.570973\pi\) | ||||
−0.221124 | + | 0.975246i | \(0.570973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.55343i | 0.246582i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.86909 | 0.368752 | 0.184376 | − | 0.982856i | \(-0.440974\pi\) | ||||
0.184376 | + | 0.982856i | \(0.440974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.140506 | −0.00752111 | −0.00376055 | − | 0.999993i | \(-0.501197\pi\) | ||||
−0.00376055 | + | 0.999993i | \(0.501197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6711i | 1.31311i | 0.754279 | + | 0.656554i | \(0.227987\pi\) | ||||
−0.754279 | + | 0.656554i | \(0.772013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.72629i | 0.197771i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.8985 | −1.63076 | −0.815380 | − | 0.578926i | \(-0.803472\pi\) | ||||
−0.815380 | + | 0.578926i | \(0.803472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49640 | −0.499811 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.10285i | 0.214753i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7326i | 1.18663i | 0.804969 | + | 0.593316i | \(0.202182\pi\) | ||||
−0.804969 | + | 0.593316i | \(0.797818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2092 | 0.581952 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9084 | 0.616594 | 0.308297 | − | 0.951290i | \(-0.400241\pi\) | ||||
0.308297 | + | 0.951290i | \(0.400241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 18.1787i | − 0.936252i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 27.2466i | − 1.39956i | −0.714356 | − | 0.699782i | \(-0.753280\pi\) | ||||
0.714356 | − | 0.699782i | \(-0.246720\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.2385 | −0.829749 | −0.414875 | − | 0.909879i | \(-0.636175\pi\) | ||||
−0.414875 | + | 0.909879i | \(0.636175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.92609 | −0.352986 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 11.0002i | − 0.557730i | −0.960330 | − | 0.278865i | \(-0.910042\pi\) | ||||
0.960330 | − | 0.278865i | \(-0.0899582\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 20.6706i | − 1.04536i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8338 | 0.846998 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.5608 | −1.38324 | −0.691618 | − | 0.722263i | \(-0.743102\pi\) | ||||
−0.691618 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 5.66929i | − 0.283111i | −0.989930 | − | 0.141555i | \(-0.954790\pi\) | ||||
0.989930 | − | 0.141555i | \(-0.0452103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.52648i | 0.374921i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.6265 | 1.71637 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.2382 | −0.753479 | −0.376739 | − | 0.926319i | \(-0.622955\pi\) | ||||
−0.376739 | + | 0.926319i | \(0.622955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6.34847i | − 0.312388i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 15.3902i | − 0.755475i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.7569 | −1.16060 | −0.580300 | − | 0.814403i | \(-0.697065\pi\) | ||||
−0.580300 | + | 0.814403i | \(0.697065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6010 | 1.63761 | 0.818805 | − | 0.574072i | \(-0.194637\pi\) | ||||
0.818805 | + | 0.574072i | \(0.194637\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 8.83323i | − 0.428475i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7263i | 0.519082i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.41960 | 0.164716 | 0.0823581 | − | 0.996603i | \(-0.473755\pi\) | ||||
0.0823581 | + | 0.996603i | \(0.473755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.42250 | 0.452816 | 0.226408 | − | 0.974033i | \(-0.427302\pi\) | ||||
0.226408 | + | 0.974033i | \(0.427302\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.8391i | 0.757688i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1040i | 0.673147i | 0.941657 | + | 0.336573i | \(0.109268\pi\) | ||||
−0.941657 | + | 0.336573i | \(0.890732\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.06481 | −0.240636 | −0.120318 | − | 0.992735i | \(-0.538391\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.4662 | −0.827978 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 7.52055i | − 0.354917i | −0.984128 | − | 0.177458i | \(-0.943212\pi\) | ||||
0.984128 | − | 0.177458i | \(-0.0567875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.0483i | 1.36783i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.4483 | −0.536706 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.3620 | −0.578268 | −0.289134 | − | 0.957289i | \(-0.593367\pi\) | ||||
−0.289134 | + | 0.957289i | \(0.593367\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.2111i | − 0.568727i | −0.958717 | − | 0.284363i | \(-0.908218\pi\) | ||||
0.958717 | − | 0.284363i | \(-0.0917822\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00422i | 0.371988i | 0.982551 | + | 0.185994i | \(0.0595504\pi\) | ||||
−0.982551 | + | 0.185994i | \(0.940450\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.9725 | −1.61834 | −0.809168 | − | 0.587577i | \(-0.800082\pi\) | ||||
−0.809168 | + | 0.587577i | \(0.800082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.26430 | −0.289258 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.82676i | 0.405855i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.76857i | 0.310563i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.141096 | −0.00644683 | −0.00322342 | − | 0.999995i | \(-0.501026\pi\) | ||||
−0.00322342 | + | 0.999995i | \(0.501026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.2351 | 2.60969 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.38076i | 0.380551i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5161i | 0.839044i | 0.907745 | + | 0.419522i | \(0.137802\pi\) | ||||
−0.907745 | + | 0.419522i | \(0.862198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.4544 | 1.50978 | 0.754888 | − | 0.655854i | \(-0.227691\pi\) | ||||
0.754888 | + | 0.655854i | \(0.227691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.3704 | −0.962474 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.92887i | 0.0865216i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.8647i | 1.69506i | 0.530751 | + | 0.847528i | \(0.321910\pi\) | ||||
−0.530751 | + | 0.847528i | \(0.678090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.9336 | −0.888796 | −0.444398 | − | 0.895829i | \(-0.646582\pi\) | ||||
−0.444398 | + | 0.895829i | \(0.646582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8464 | 0.527159 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.33087i | 0.280611i | 0.990108 | + | 0.140305i | \(0.0448084\pi\) | ||||
−0.990108 | + | 0.140305i | \(0.955192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.12379i | 0.0939510i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.0389 | 1.19147 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.1353 | 1.01749 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 29.1404i | − 1.27666i | −0.769761 | − | 0.638332i | \(-0.779625\pi\) | ||||
0.769761 | − | 0.638332i | \(-0.220375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.13474i | − 0.311981i | −0.987759 | − | 0.155990i | \(-0.950143\pi\) | ||||
0.987759 | − | 0.155990i | \(-0.0498569\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.84792 | 0.385422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.1962 | −0.617224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.0148i | 2.07975i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0483i | 0.780298i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.58521 | −0.154426 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0243 | −1.24785 | −0.623926 | − | 0.781483i | \(-0.714464\pi\) | ||||
−0.623926 | + | 0.781483i | \(0.714464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 36.8338i | − 1.57779i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.8759i | 0.721563i | 0.932650 | + | 0.360782i | \(0.117490\pi\) | ||||
−0.932650 | + | 0.360782i | \(0.882510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.3753 | 0.697612 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71379 | 0.370548 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.41255i | 0.271708i | 0.990729 | + | 0.135854i | \(0.0433779\pi\) | ||||
−0.990729 | + | 0.135854i | \(0.956622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5900i | 0.617091i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.1803 | −1.44053 | −0.720263 | − | 0.693701i | \(-0.755979\pi\) | ||||
−0.720263 | + | 0.693701i | \(0.755979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.26219 | 0.137241 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4841i | 0.691050i | 0.938409 | + | 0.345525i | \(0.112299\pi\) | ||||
−0.938409 | + | 0.345525i | \(0.887701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 23.9105i | − 1.00062i | −0.865845 | − | 0.500312i | \(-0.833219\pi\) | ||||
0.865845 | − | 0.500312i | \(-0.166781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.76217 | 0.156893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.0967 | 1.25294 | 0.626471 | − | 0.779445i | \(-0.284499\pi\) | ||||
0.626471 | + | 0.779445i | \(0.284499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.96655i | − 0.330508i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.1873i | 1.66439i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.6853 | −0.482304 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.77983 | −0.279358 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6788i | 0.684914i | 0.939533 | + | 0.342457i | \(0.111259\pi\) | ||||
−0.939533 | + | 0.342457i | \(0.888741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.4583i | 0.551738i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.64980 | −0.353421 | −0.176711 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176711 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.6171 | −0.637035 | −0.318518 | − | 0.947917i | \(-0.603185\pi\) | ||||
−0.318518 | + | 0.947917i | \(0.603185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.58114i | − 0.145594i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20.8668i | − 0.846957i | −0.905906 | − | 0.423479i | \(-0.860809\pi\) | ||||
0.905906 | − | 0.423479i | \(-0.139191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.2410 | 1.54707 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5526 | 1.43596 | 0.717978 | − | 0.696066i | \(-0.245068\pi\) | ||||
0.717978 | + | 0.696066i | \(0.245068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 27.3777i | − 1.10218i | −0.834445 | − | 0.551091i | \(-0.814212\pi\) | ||||
0.834445 | − | 0.551091i | \(-0.185788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.5800i | 1.10853i | 0.832339 | + | 0.554267i | \(0.187001\pi\) | ||||
−0.832339 | + | 0.554267i | \(0.812999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.04118 | −0.362227 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0526 | −0.682102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 67.2839i | − 2.68279i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1207i | 0.721374i | 0.932687 | + | 0.360687i | \(0.117458\pi\) | ||||
−0.932687 | + | 0.360687i | \(0.882542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.4460 | 1.16853 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.92609 | −0.234800 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 10.9215i | − 0.431372i | −0.976463 | − | 0.215686i | \(-0.930801\pi\) | ||||
0.976463 | − | 0.215686i | \(-0.0691987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 43.2372i | − 1.70511i | −0.522639 | − | 0.852554i | \(-0.675052\pi\) | ||||
0.522639 | − | 0.852554i | \(-0.324948\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4472 | 0.764547 | 0.382274 | − | 0.924049i | \(-0.375141\pi\) | ||||
0.382274 | + | 0.924049i | \(0.375141\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7606 | 0.893431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7057i | 1.08421i | 0.840311 | + | 0.542105i | \(0.182372\pi\) | ||||
−0.840311 | + | 0.542105i | \(0.817628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.0447i | 1.21302i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.5359 | 0.799966 | 0.399983 | − | 0.916523i | \(-0.369016\pi\) | ||||
0.399983 | + | 0.916523i | \(0.369016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.763677 | 0.0297036 | 0.0148518 | − | 0.999890i | \(-0.495272\pi\) | ||||
0.0148518 | + | 0.999890i | \(0.495272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 10.3126i | − 0.399906i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 9.10188i | − 0.352426i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.4560 | −1.48458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2944 | −1.01357 | −0.506787 | − | 0.862071i | \(-0.669167\pi\) | ||||
−0.506787 | + | 0.862071i | \(0.669167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6603i | 0.678740i | 0.940653 | + | 0.339370i | \(0.110214\pi\) | ||||
−0.940653 | + | 0.339370i | \(0.889786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.33820i | 0.166485i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.9049 | −1.60345 | −0.801723 | − | 0.597695i | \(-0.796083\pi\) | ||||
−0.801723 | + | 0.597695i | \(0.796083\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.39020 | 0.282365 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 66.4267i | 2.53066i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 32.1831i | − 1.22430i | −0.790741 | − | 0.612151i | \(-0.790304\pi\) | ||||
0.790741 | − | 0.612151i | \(-0.209696\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.7204 | 1.16529 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.4449 | 2.13800 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8362i | 1.54236i | 0.636615 | + | 0.771182i | \(0.280334\pi\) | ||||
−0.636615 | + | 0.771182i | \(0.719666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.5571i | 1.94451i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.13216 | 0.230624 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.3986 | 0.916310 | 0.458155 | − | 0.888872i | \(-0.348510\pi\) | ||||
0.458155 | + | 0.888872i | \(0.348510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.76842i | 0.141129i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 41.0447i | − 1.53498i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.9008 | −0.518413 | −0.259206 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259206 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.9963 | 0.521251 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.88953i | − 0.144453i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.98652i | 0.110764i | 0.998465 | + | 0.0553820i | \(0.0176377\pi\) | ||||
−0.998465 | + | 0.0553820i | \(0.982362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.1516 | 0.634375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.16874 | −0.0801044 | −0.0400522 | − | 0.999198i | \(-0.512752\pi\) | ||||
−0.0400522 | + | 0.999198i | \(0.512752\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 22.4588i | − 0.827281i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 19.1144i | − 0.703134i | −0.936163 | − | 0.351567i | \(-0.885649\pi\) | ||||
0.936163 | − | 0.351567i | \(-0.114351\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.1582 | 1.54663 | 0.773317 | − | 0.634020i | \(-0.218596\pi\) | ||||
0.773317 | + | 0.634020i | \(0.218596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8023 | −0.578952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.34251i | 0.341368i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 19.2016i | − 0.700678i | −0.936623 | − | 0.350339i | \(-0.886066\pi\) | ||||
0.936623 | − | 0.350339i | \(-0.113934\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5512 | −0.565966 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.84797 | −0.139857 | −0.0699284 | − | 0.997552i | \(-0.522277\pi\) | ||||
−0.0699284 | + | 0.997552i | \(0.522277\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 45.3580i | − 1.64423i | −0.569325 | − | 0.822113i | \(-0.692795\pi\) | ||||
0.569325 | − | 0.822113i | \(-0.307205\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 19.0666i | − 0.690257i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.6216 | 1.35844 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.83239 | −0.210321 | −0.105161 | − | 0.994455i | \(-0.533536\pi\) | ||||
−0.105161 | + | 0.994455i | \(0.533536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 34.9259i | − 1.25620i | −0.778133 | − | 0.628099i | \(-0.783833\pi\) | ||||
0.778133 | − | 0.628099i | \(-0.216167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.61037i | 0.0578462i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.2516 | −1.54965 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.91540 | −0.247453 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.0817i | 1.21643i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 51.7877i | − 1.84603i | −0.384762 | − | 0.923016i | \(-0.625716\pi\) | ||||
0.384762 | − | 0.923016i | \(-0.374284\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.68863 | 0.0600409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −63.5650 | −2.25726 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 43.7027i | − 1.54803i | −0.633167 | − | 0.774015i | \(-0.718246\pi\) | ||||
0.633167 | − | 0.774015i | \(-0.281754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 44.9550i | − 1.59040i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.61424 | −0.268701 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.73205 | −0.202028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 19.6717i | − 0.691620i | −0.938304 | − | 0.345810i | \(-0.887604\pi\) | ||||
0.938304 | − | 0.345810i | \(-0.112396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.16694i | − 0.111206i | −0.998453 | − | 0.0556031i | \(-0.982292\pi\) | ||||
0.998453 | − | 0.0556031i | \(-0.0177082\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.76435 | −0.166888 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.1426 | −0.459802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.54805i | 0.263429i | 0.991288 | + | 0.131714i | \(0.0420482\pi\) | ||||
−0.991288 | + | 0.131714i | \(0.957952\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0280i | 0.872420i | 0.899845 | + | 0.436210i | \(0.143680\pi\) | ||||
−0.899845 | + | 0.436210i | \(0.856320\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.9477 | −0.937062 | −0.468531 | − | 0.883447i | \(-0.655217\pi\) | ||||
−0.468531 | + | 0.883447i | \(0.655217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.2466 | −0.668462 | −0.334231 | − | 0.942491i | \(-0.608477\pi\) | ||||
−0.334231 | + | 0.942491i | \(0.608477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.96655i | 0.241377i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 31.1685i | − 1.07863i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4979 | −0.880285 | −0.440142 | − | 0.897928i | \(-0.645072\pi\) | ||||
−0.440142 | + | 0.897928i | \(0.645072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.5900 | 0.675517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 42.7298i | − 1.46995i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.85373i | − 0.0636950i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.6570 | 0.982348 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4464 | 0.563114 | 0.281557 | − | 0.959544i | \(-0.409149\pi\) | ||||
0.281557 | + | 0.959544i | \(0.409149\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.0695i | 1.26627i | 0.774041 | + | 0.633135i | \(0.218232\pi\) | ||||
−0.774041 | + | 0.633135i | \(0.781768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6284i | 0.601472i | 0.953707 | + | 0.300736i | \(0.0972323\pi\) | ||||
−0.953707 | + | 0.300736i | \(0.902768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.5272 | −0.732794 | −0.366397 | − | 0.930459i | \(-0.619409\pi\) | ||||
−0.366397 | + | 0.930459i | \(0.619409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.1904 | −0.788497 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2408i | 1.05977i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 37.1228i | − 1.25786i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1087 | −0.409350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1862 | −0.951779 | −0.475890 | − | 0.879505i | \(-0.657874\pi\) | ||||
−0.475890 | + | 0.879505i | \(0.657874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3854i | 0.518346i | 0.965831 | + | 0.259173i | \(0.0834500\pi\) | ||||
−0.965831 | + | 0.259173i | \(0.916550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.4069i | 0.989621i | 0.869001 | + | 0.494811i | \(0.164763\pi\) | ||||
−0.869001 | + | 0.494811i | \(0.835237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.1982 | −0.946801 | −0.473401 | − | 0.880847i | \(-0.656974\pi\) | ||||
−0.473401 | + | 0.880847i | \(0.656974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.2424 | 0.511213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.4473i | 1.15274i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.9869i | 0.935500i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.89599 | 0.129939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 78.0894 | 2.60153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.8579i | 0.560375i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0718i | 0.500451i | 0.968188 | + | 0.250225i | \(0.0805047\pi\) | ||||
−0.968188 | + | 0.250225i | \(0.919495\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.49292 | 0.181989 | 0.0909943 | − | 0.995851i | \(-0.470996\pi\) | ||||
0.0909943 | + | 0.995851i | \(0.470996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.5618 | 0.945256 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0699i | 0.530675i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 18.6898i | − 0.616519i | −0.951302 | − | 0.308259i | \(-0.900254\pi\) | ||||
0.951302 | − | 0.308259i | \(-0.0997464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.4307 | −0.376245 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.2460 | 0.402647 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.6186i | 1.16861i | 0.811534 | + | 0.584305i | \(0.198633\pi\) | ||||
−0.811534 | + | 0.584305i | \(0.801367\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.33820i | − 0.174953i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48.2510 | −1.57798 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.3017 | −1.18592 | −0.592962 | − | 0.805230i | \(-0.702042\pi\) | ||||
−0.592962 | + | 0.805230i | \(0.702042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 31.7581i | − 1.03529i | −0.855597 | − | 0.517643i | \(-0.826810\pi\) | ||||
0.855597 | − | 0.517643i | \(-0.173190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0405i | 0.782865i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.0513 | −0.976536 | −0.488268 | − | 0.872694i | \(-0.662371\pi\) | ||||
−0.488268 | + | 0.872694i | \(0.662371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5858 | −0.408552 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.4957i | 1.70050i | 0.526376 | + | 0.850252i | \(0.323550\pi\) | ||||
−0.526376 | + | 0.850252i | \(0.676450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 24.4626i | − 0.791590i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.82545 | 0.123530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3870 | 0.947966 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.78850i | 0.218530i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4411i | 1.52560i | 0.646634 | + | 0.762801i | \(0.276176\pi\) | ||||
−0.646634 | + | 0.762801i | \(0.723824\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.9492 | −1.08948 | −0.544741 | − | 0.838605i | \(-0.683372\pi\) | ||||
−0.544741 | + | 0.838605i | \(0.683372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.9021 | 0.509797 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 12.2747i | − 0.392701i | −0.980534 | − | 0.196351i | \(-0.937091\pi\) | ||||
0.980534 | − | 0.196351i | \(-0.0629090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 32.4145i | − 1.03597i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.43320 | −0.173292 | −0.0866461 | − | 0.996239i | \(-0.527615\pi\) | ||||
−0.0866461 | + | 0.996239i | \(0.527615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8407 | −0.695901 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.30505i | 0.232287i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.4370i | 1.57042i | 0.619231 | + | 0.785209i | \(0.287444\pi\) | ||||
−0.619231 | + | 0.785209i | \(0.712556\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.90305 | 0.155437 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0925 | 0.889697 | 0.444849 | − | 0.895606i | \(-0.353257\pi\) | ||||
0.444849 | + | 0.895606i | \(0.353257\pi\) | |||||||
\(998\) | 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.2591.2 | ✓ | 16 | |
3.2 | odd | 2 | inner | 6048.2.h.h.2591.13 | yes | 16 | |
4.3 | odd | 2 | inner | 6048.2.h.h.2591.3 | yes | 16 | |
12.11 | even | 2 | inner | 6048.2.h.h.2591.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.h.2591.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6048.2.h.h.2591.3 | yes | 16 | 4.3 | odd | 2 | inner | |
6048.2.h.h.2591.13 | yes | 16 | 3.2 | odd | 2 | inner | |
6048.2.h.h.2591.16 | yes | 16 | 12.11 | even | 2 | inner |