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 | 2591.15 | ||
Root | \(-0.826679 + 0.826679i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.h.2591.1 |
$q$-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 | \(0.142183\pi\) | ||||
−0.901886 | + | 0.431975i | \(0.857817\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13572 | −0.342433 | −0.171216 | − | 0.985233i | \(-0.554770\pi\) | ||||
−0.171216 | + | 0.985233i | \(0.554770\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.19404 | −0.885868 | −0.442934 | − | 0.896554i | \(-0.646062\pi\) | ||||
−0.442934 | + | 0.896554i | \(0.646062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.93127i | − 1.43855i | −0.694728 | − | 0.719273i | \(-0.744475\pi\) | ||||
0.694728 | − | 0.719273i | \(-0.255525\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.33820i | 0.307005i | 0.988148 | + | 0.153502i | \(0.0490553\pi\) | ||||
−0.988148 | + | 0.153502i | \(0.950945\pi\) | |||||||
\(20\) | 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 | ||||||||
\(29\) | − 1.65336i | − 0.307021i | −0.988147 | − | 0.153510i | \(-0.950942\pi\) | ||||
0.988147 | − | 0.153510i | \(-0.0490579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.3902i | − 1.86613i | −0.359702 | − | 0.933067i | \(-0.617122\pi\) | ||||
0.359702 | − | 0.933067i | \(-0.382878\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.93185 | −0.326543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.538007 | 0.0884479 | 0.0442239 | − | 0.999022i | \(-0.485918\pi\) | ||||
0.0442239 | + | 0.999022i | \(0.485918\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.51648i | 1.48623i | 0.669166 | + | 0.743113i | \(0.266651\pi\) | ||||
−0.669166 | + | 0.743113i | \(0.733349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.65815i | 1.01536i | 0.861546 | + | 0.507679i | \(0.169496\pi\) | ||||
−0.861546 | + | 0.507679i | \(0.830504\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1739 | 1.62988 | 0.814942 | − | 0.579543i | \(-0.196769\pi\) | ||||
0.814942 | + | 0.579543i | \(0.196769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.68863i | 0.231952i | 0.993252 | + | 0.115976i | \(0.0369995\pi\) | ||||
−0.993252 | + | 0.115976i | \(0.963001\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.19404i | − 0.295845i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.82842 | −0.238041 | −0.119020 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119020 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1904 | 1.81689 | 0.908447 | − | 0.418001i | \(-0.137269\pi\) | ||||
0.908447 | + | 0.418001i | \(0.137269\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 6.17042i | − 0.765346i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 9.53225i | − 1.16455i | −0.812992 | − | 0.582275i | \(-0.802163\pi\) | ||||
0.812992 | − | 0.582275i | \(-0.197837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9690 | 1.30178 | 0.650888 | − | 0.759174i | \(-0.274397\pi\) | ||||
0.650888 | + | 0.759174i | \(0.274397\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.319943 | 0.0374465 | 0.0187232 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187232 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.13572i | − 0.129427i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 12.9465i | − 1.45659i | −0.685263 | − | 0.728295i | \(-0.740313\pi\) | ||||
0.685263 | − | 0.728295i | \(-0.259687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.24562 | 0.356253 | 0.178127 | − | 0.984008i | \(-0.442996\pi\) | ||||
0.178127 | + | 0.984008i | \(0.442996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4583 | 1.24283 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.7621i | 1.45878i | 0.684098 | + | 0.729390i | \(0.260196\pi\) | ||||
−0.684098 | + | 0.729390i | \(0.739804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.19404i | − 0.334827i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.58521 | −0.265237 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.33820 | 0.237408 | 0.118704 | − | 0.992930i | \(-0.462126\pi\) | ||||
0.118704 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2075i | 1.61271i | 0.591433 | + | 0.806354i | \(0.298563\pi\) | ||||
−0.591433 | + | 0.806354i | \(0.701437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.80019i | 0.177378i | 0.996059 | + | 0.0886892i | \(0.0282678\pi\) | ||||
−0.996059 | + | 0.0886892i | \(0.971732\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0993527 | 0.00960479 | 0.00480239 | − | 0.999988i | \(-0.498471\pi\) | ||||
0.00480239 | + | 0.999988i | \(0.498471\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.40635 | −0.326269 | −0.163134 | − | 0.986604i | \(-0.552160\pi\) | ||||
−0.163134 | + | 0.986604i | \(0.552160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2092i | 1.05447i | 0.849719 | + | 0.527236i | \(0.176772\pi\) | ||||
−0.849719 | + | 0.527236i | \(0.823228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.73205i | 0.534516i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.93127 | 0.543719 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.71014 | −0.882740 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1087i | 1.08304i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.1180i | 1.07530i | 0.843168 | + | 0.537651i | \(0.180688\pi\) | ||||
−0.843168 | + | 0.537651i | \(0.819312\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.54884 | 0.135323 | 0.0676614 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676614 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.33820 | −0.116037 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.895484i | 0.0765063i | 0.999268 | + | 0.0382532i | \(0.0121793\pi\) | ||||
−0.999268 | + | 0.0382532i | \(0.987821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9021i | 1.17916i | 0.807711 | + | 0.589579i | \(0.200706\pi\) | ||||
−0.807711 | + | 0.589579i | \(0.799294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.62754 | 0.303350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.19404 | 0.265251 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.72391i | 0.386998i | 0.981100 | + | 0.193499i | \(0.0619836\pi\) | ||||
−0.981100 | + | 0.193499i | \(0.938016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 3.51399i | − 0.285964i | −0.989725 | − | 0.142982i | \(-0.954331\pi\) | ||||
0.989725 | − | 0.142982i | \(-0.0456691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.0723 | 1.61225 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.8747 | −1.74579 | −0.872894 | − | 0.487910i | \(-0.837760\pi\) | ||||
−0.872894 | + | 0.487910i | \(0.837760\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.96713i | 0.233842i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5863i | 0.907513i | 0.891126 | + | 0.453756i | \(0.149916\pi\) | ||||
−0.891126 | + | 0.453756i | \(0.850084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.74973 | −0.212781 | −0.106390 | − | 0.994324i | \(-0.533929\pi\) | ||||
−0.106390 | + | 0.994324i | \(0.533929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.79809 | −0.215237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.893593i | − 0.0679386i | −0.999423 | − | 0.0339693i | \(-0.989185\pi\) | ||||
0.999423 | − | 0.0339693i | \(-0.0108148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.26795i | 0.0958479i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.7645 | 1.10355 | 0.551775 | − | 0.833993i | \(-0.313951\pi\) | ||||
0.551775 | + | 0.833993i | \(0.313951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1904 | 1.20342 | 0.601711 | − | 0.798714i | \(-0.294486\pi\) | ||||
0.601711 | + | 0.798714i | \(0.294486\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.03935i | 0.0764146i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.73627i | 0.492605i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.20679 | 0.666180 | 0.333090 | − | 0.942895i | \(-0.391909\pi\) | ||||
0.333090 | + | 0.942895i | \(0.391909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.04988 | 0.579443 | 0.289722 | − | 0.957111i | \(-0.406437\pi\) | ||||
0.289722 | + | 0.957111i | \(0.406437\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.9319i | − 1.70508i | −0.522662 | − | 0.852540i | \(-0.675061\pi\) | ||||
0.522662 | − | 0.852540i | \(-0.324939\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.6581i | − 0.826424i | −0.910635 | − | 0.413212i | \(-0.864407\pi\) | ||||
0.910635 | − | 0.413212i | \(-0.135593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.65336 | 0.116043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.3844 | −1.28402 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.51982i | − 0.105128i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.97387i | − 0.480101i | −0.970760 | − | 0.240051i | \(-0.922836\pi\) | ||||
0.970760 | − | 0.240051i | \(-0.0771640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.8625 | −0.877219 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3902 | 0.705332 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9447i | 1.27436i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.74455i | 0.652543i | 0.945276 | + | 0.326272i | \(0.105792\pi\) | ||||
−0.945276 | + | 0.326272i | \(0.894208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.7309 | 0.844980 | 0.422490 | − | 0.906368i | \(-0.361156\pi\) | ||||
0.422490 | + | 0.906368i | \(0.361156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.1259 | −0.999548 | −0.499774 | − | 0.866156i | \(-0.666584\pi\) | ||||
−0.499774 | + | 0.866156i | \(0.666584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.1211i | 1.44920i | 0.689168 | + | 0.724601i | \(0.257976\pi\) | ||||
−0.689168 | + | 0.724601i | \(0.742024\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.5863i | 1.40814i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1077 | 0.718494 | 0.359247 | − | 0.933242i | \(-0.383033\pi\) | ||||
0.359247 | + | 0.933242i | \(0.383033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4458 | −0.994954 | −0.497477 | − | 0.867477i | \(-0.665740\pi\) | ||||
−0.497477 | + | 0.867477i | \(0.665740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.93185i | − 0.123421i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.27428i | − 0.271966i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.6241 | −1.80674 | −0.903368 | − | 0.428867i | \(-0.858913\pi\) | ||||
−0.903368 | + | 0.428867i | \(0.858913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36983 | −0.211859 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.74617i | − 0.483193i | −0.970377 | − | 0.241596i | \(-0.922329\pi\) | ||||
0.970377 | − | 0.241596i | \(-0.0776710\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.538007i | 0.0334301i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4877 | 0.893349 | 0.446675 | − | 0.894696i | \(-0.352608\pi\) | ||||
0.446675 | + | 0.894696i | \(0.352608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.26219 | −0.200395 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7174i | 0.653450i | 0.945119 | + | 0.326725i | \(0.105945\pi\) | ||||
−0.945119 | + | 0.326725i | \(0.894055\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 19.7086i | − 1.19721i | −0.801044 | − | 0.598606i | \(-0.795722\pi\) | ||||
0.801044 | − | 0.598606i | \(-0.204278\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.44004 | −0.0868374 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.26430 | 0.556638 | 0.278319 | − | 0.960489i | \(-0.410223\pi\) | ||||
0.278319 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.37727i | 0.261126i | 0.991440 | + | 0.130563i | \(0.0416785\pi\) | ||||
−0.991440 | + | 0.130563i | \(0.958322\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5.12168i | − 0.304452i | −0.988346 | − | 0.152226i | \(-0.951356\pi\) | ||||
0.988346 | − | 0.152226i | \(-0.0486442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.51648 | −0.561740 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.1800 | −1.06941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.0042i | 1.34392i | 0.740588 | + | 0.671959i | \(0.234547\pi\) | ||||
−0.740588 | + | 0.671959i | \(0.765453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3.53225i | − 0.205655i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.47714 | −0.548077 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.65815 | −0.383769 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.4137i | 1.56971i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.84180i | 0.561701i | 0.959751 | + | 0.280851i | \(0.0906165\pi\) | ||||
−0.959751 | + | 0.280851i | \(0.909383\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7593 | 0.893630 | 0.446815 | − | 0.894626i | \(-0.352558\pi\) | ||||
0.446815 | + | 0.894626i | \(0.352558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0828 | −1.07862 | −0.539310 | − | 0.842107i | \(-0.681315\pi\) | ||||
−0.539310 | + | 0.842107i | \(0.681315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.04008i | 0.451576i | 0.974176 | + | 0.225788i | \(0.0724957\pi\) | ||||
−0.974176 | + | 0.225788i | \(0.927504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.87775i | 0.105134i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.93724 | 0.441640 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.04988 | −0.224647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1739i | 0.616038i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 9.60039i | − 0.527685i | −0.964566 | − | 0.263843i | \(-0.915010\pi\) | ||||
0.964566 | − | 0.263843i | \(-0.0849899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.4149 | 1.00611 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7981 | 0.915050 | 0.457525 | − | 0.889197i | \(-0.348736\pi\) | ||||
0.457525 | + | 0.889197i | \(0.348736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8004i | 0.639025i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5900 | 0.622185 | 0.311092 | − | 0.950380i | \(-0.399305\pi\) | ||||
0.311092 | + | 0.950380i | \(0.399305\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2123 | 0.707238 | 0.353619 | − | 0.935389i | \(-0.384951\pi\) | ||||
0.353619 | + | 0.935389i | \(0.384951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 25.9360i | − 1.38044i | −0.723602 | − | 0.690218i | \(-0.757515\pi\) | ||||
0.723602 | − | 0.690218i | \(-0.242485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.1904i | 1.12467i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.2368 | 0.909725 | 0.454863 | − | 0.890562i | \(-0.349688\pi\) | ||||
0.454863 | + | 0.890562i | \(0.349688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2092 | 0.905748 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.618082i | 0.0323519i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 25.1763i | − 1.31419i | −0.753806 | − | 0.657097i | \(-0.771784\pi\) | ||||
0.753806 | − | 0.657097i | \(-0.228216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68863 | −0.0876694 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.46467 | 0.490062 | 0.245031 | − | 0.969515i | \(-0.421202\pi\) | ||||
0.245031 | + | 0.969515i | \(0.421202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.28090i | 0.271980i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.1265i | 0.931094i | 0.885023 | + | 0.465547i | \(0.154142\pi\) | ||||
−0.885023 | + | 0.465547i | \(0.845858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.2526 | −0.523884 | −0.261942 | − | 0.965084i | \(-0.584363\pi\) | ||||
−0.261942 | + | 0.965084i | \(0.584363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.19404 | 0.111819 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 27.6933i | − 1.40411i | −0.712124 | − | 0.702053i | \(-0.752267\pi\) | ||||
0.712124 | − | 0.702053i | \(-0.247733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 17.5988i | − 0.890012i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.0106 | 1.25842 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.91977 | 0.447670 | 0.223835 | − | 0.974627i | \(-0.428142\pi\) | ||||
0.223835 | + | 0.974627i | \(0.428142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.3761i | 0.817784i | 0.912583 | + | 0.408892i | \(0.134085\pi\) | ||||
−0.912583 | + | 0.408892i | \(0.865915\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.1867i | 1.65315i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.611026 | −0.0302874 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.3625 | 1.50133 | 0.750665 | − | 0.660683i | \(-0.229733\pi\) | ||||
0.750665 | + | 0.660683i | \(0.229733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.82842i | − 0.0899709i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.27006i | 0.307785i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.02467 | 0.392031 | 0.196015 | − | 0.980601i | \(-0.437200\pi\) | ||||
0.196015 | + | 0.980601i | \(0.437200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.45160 | 0.216958 | 0.108479 | − | 0.994099i | \(-0.465402\pi\) | ||||
0.108479 | + | 0.994099i | \(0.465402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 7.52055i | − 0.364800i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.1904i | 0.686721i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0363656 | −0.00175167 | −0.000875835 | − | 1.00000i | \(-0.500279\pi\) | ||||
−0.000875835 | 1.00000i | \(0.500279\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4033 | −1.26886 | −0.634430 | − | 0.772980i | \(-0.718765\pi\) | ||||
−0.634430 | + | 0.772980i | \(0.718765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.97062i | 0.189940i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 9.21652i | − 0.439881i | −0.975513 | − | 0.219940i | \(-0.929414\pi\) | ||||
0.975513 | − | 0.219940i | \(-0.0705862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.3496 | 1.82204 | 0.911022 | − | 0.412358i | \(-0.135295\pi\) | ||||
0.911022 | + | 0.412358i | \(0.135295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.5863 | −1.26031 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 8.83323i | − 0.416866i | −0.978037 | − | 0.208433i | \(-0.933164\pi\) | ||||
0.978037 | − | 0.208433i | \(-0.0668363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 10.8081i | − 0.508932i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.17042 | 0.289274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.6825 | 1.66916 | 0.834578 | − | 0.550890i | \(-0.185712\pi\) | ||||
0.834578 | + | 0.550890i | \(0.185712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6670i | 0.729687i | 0.931069 | + | 0.364843i | \(0.118878\pi\) | ||||
−0.931069 | + | 0.364843i | \(0.881122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 26.2445i | − 1.21969i | −0.792523 | − | 0.609843i | \(-0.791233\pi\) | ||||
0.792523 | − | 0.609843i | \(-0.208767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.7956 | 1.14741 | 0.573703 | − | 0.819064i | \(-0.305506\pi\) | ||||
0.573703 | + | 0.819064i | \(0.305506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.53225 | 0.440158 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.56179i | − 0.347692i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.69677i | 0.0778533i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.5665 | 1.48800 | 0.744000 | − | 0.668180i | \(-0.232926\pi\) | ||||
0.744000 | + | 0.668180i | \(0.232926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.71842 | −0.0783531 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.51706i | 0.205109i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.0724i | − 0.728308i | −0.931339 | − | 0.364154i | \(-0.881358\pi\) | ||||
0.931339 | − | 0.364154i | \(-0.118642\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.39378 | 0.288547 | 0.144274 | − | 0.989538i | \(-0.453915\pi\) | ||||
0.144274 | + | 0.989538i | \(0.453915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.80652 | −0.441664 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9690i | 0.492025i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.52494i | 0.426395i | 0.977009 | + | 0.213197i | \(0.0683878\pi\) | ||||
−0.977009 | + | 0.213197i | \(0.931612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.31486 | −0.103215 | −0.0516073 | − | 0.998667i | \(-0.516434\pi\) | ||||
−0.0516073 | + | 0.998667i | \(0.516434\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.3105 | −1.39330 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.8925i | 1.54658i | 0.634050 | + | 0.773292i | \(0.281391\pi\) | ||||
−0.634050 | + | 0.773292i | \(0.718609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.319943i | 0.0141534i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.47771 | −0.153246 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.6904 | −0.558125 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9776i | 0.656181i | 0.944646 | + | 0.328091i | \(0.106405\pi\) | ||||
−0.944646 | + | 0.328091i | \(0.893595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.1347i | − 1.36143i | −0.732550 | − | 0.680714i | \(-0.761670\pi\) | ||||
0.732550 | − | 0.680714i | \(-0.238330\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −61.6271 | −2.68452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.1962 | −0.617224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 30.3961i | − 1.31660i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.191935i | 0.00829806i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.13572 | 0.0489189 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.89996 | 0.425633 | 0.212816 | − | 0.977092i | \(-0.431736\pi\) | ||||
0.212816 | + | 0.977092i | \(0.431736\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 6.58056i | − 0.281880i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.7324i | 1.82710i | 0.406723 | + | 0.913552i | \(0.366672\pi\) | ||||
−0.406723 | + | 0.913552i | \(0.633328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.21253 | 0.0942569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9465 | 0.550540 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.02932i | 0.128356i | 0.997938 | + | 0.0641781i | \(0.0204426\pi\) | ||||
−0.997938 | + | 0.0641781i | \(0.979557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 21.2664i | − 0.899473i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4593 | −1.24156 | −0.620782 | − | 0.783984i | \(-0.713185\pi\) | ||||
−0.620782 | + | 0.783984i | \(0.713185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.6545 | −0.911011 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.31152i | 0.390359i | 0.980768 | + | 0.195180i | \(0.0625290\pi\) | ||||
−0.980768 | + | 0.195180i | \(0.937471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.5869i | 1.28002i | 0.768366 | + | 0.640011i | \(0.221070\pi\) | ||||
−0.768366 | + | 0.640011i | \(0.778930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.76217 | 0.156893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.38387 | −0.265764 | −0.132882 | − | 0.991132i | \(-0.542423\pi\) | ||||
−0.132882 | + | 0.991132i | \(0.542423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.24562i | 0.134651i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.91781i | − 0.0794278i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.0962 | 0.829461 | 0.414730 | − | 0.909944i | \(-0.363876\pi\) | ||||
0.414730 | + | 0.909944i | \(0.363876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.9042 | 0.572912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.6194i | 1.87336i | 0.350183 | + | 0.936681i | \(0.386119\pi\) | ||||
−0.350183 | + | 0.936681i | \(0.613881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4583i | 0.469746i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.66390 | −0.108844 | −0.0544221 | − | 0.998518i | \(-0.517332\pi\) | ||||
−0.0544221 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.8851 | 1.09666 | 0.548332 | − | 0.836261i | \(-0.315263\pi\) | ||||
0.548332 | + | 0.836261i | \(0.315263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 18.7585i | − 0.762643i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 17.4027i | − 0.706354i | −0.935557 | − | 0.353177i | \(-0.885101\pi\) | ||||
0.935557 | − | 0.353177i | \(-0.114899\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.6900 | −1.44386 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6435 | 0.995343 | 0.497672 | − | 0.867366i | \(-0.334188\pi\) | ||||
0.497672 | + | 0.867366i | \(0.334188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 16.0367i | − 0.645615i | −0.946465 | − | 0.322807i | \(-0.895373\pi\) | ||||
0.946465 | − | 0.322807i | \(-0.104627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.90053i | 0.357742i | 0.983872 | + | 0.178871i | \(0.0572446\pi\) | ||||
−0.983872 | + | 0.178871i | \(0.942755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.7621 | −0.551367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0526 | −0.682102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3.19107i | − 0.127236i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 2.32416i | − 0.0925234i | −0.998929 | − | 0.0462617i | \(-0.985269\pi\) | ||||
0.998929 | − | 0.0462617i | \(-0.0147308\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.4102 | −0.929007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19404 | 0.126553 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 46.6557i | − 1.84279i | −0.388627 | − | 0.921395i | \(-0.627050\pi\) | ||||
0.388627 | − | 0.921395i | \(-0.372950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.59617i | − 0.260128i | −0.991506 | − | 0.130064i | \(-0.958482\pi\) | ||||
0.991506 | − | 0.130064i | \(-0.0415182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.9672 | −0.942249 | −0.471124 | − | 0.882067i | \(-0.656152\pi\) | ||||
−0.471124 | + | 0.882067i | \(0.656152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.07658 | 0.0815129 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.280888i | 0.0109920i | 0.999985 | + | 0.00549600i | \(0.00174944\pi\) | ||||
−0.999985 | + | 0.00549600i | \(0.998251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.99213i | 0.116912i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.5965 | 1.85410 | 0.927049 | − | 0.374941i | \(-0.122337\pi\) | ||||
0.927049 | + | 0.374941i | \(0.122337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.56752 | −0.255447 | −0.127724 | − | 0.991810i | \(-0.540767\pi\) | ||||
−0.127724 | + | 0.991810i | \(0.540767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2.58521i | − 0.100250i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.90573i | − 0.189950i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.1163 | −0.622164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.50977 | 0.135292 | 0.0676458 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676458 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.30650i | − 0.0502129i | −0.999685 | − | 0.0251065i | \(-0.992008\pi\) | ||||
0.999685 | − | 0.0251065i | \(-0.00799247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.33820i | 0.0897320i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.8633 | 0.683519 | 0.341760 | − | 0.939787i | \(-0.388977\pi\) | ||||
0.341760 | + | 0.939787i | \(0.388977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.72994 | −0.0660977 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 5.39357i | − 0.205478i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 24.3267i | − 0.925430i | −0.886507 | − | 0.462715i | \(-0.846875\pi\) | ||||
0.886507 | − | 0.462715i | \(-0.153125\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.8567 | −1.01873 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.4449 | 2.13800 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.57815i | 0.0973754i | 0.998814 | + | 0.0486877i | \(0.0155039\pi\) | ||||
−0.998814 | + | 0.0486877i | \(0.984496\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.719962i | 0.0271539i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.2075 | −0.609547 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.7590 | 1.94385 | 0.971926 | − | 0.235287i | \(-0.0756031\pi\) | ||||
0.971926 | + | 0.235287i | \(0.0756031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 30.8290i | − 1.15456i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.00787i | 0.262079i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.17988 | −0.342352 | −0.171176 | − | 0.985240i | \(-0.554757\pi\) | ||||
−0.171176 | + | 0.985240i | \(0.554757\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.80019 | −0.0670428 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2.09637i | − 0.0778574i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 27.9032i | − 1.03487i | −0.855722 | − | 0.517436i | \(-0.826886\pi\) | ||||
0.855722 | − | 0.517436i | \(-0.173114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.4913 | 1.46064 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.7402 | −1.02461 | −0.512304 | − | 0.858804i | \(-0.671208\pi\) | ||||
−0.512304 | + | 0.858804i | \(0.671208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.8260i | 0.398780i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 24.0426i | − 0.884421i | −0.896911 | − | 0.442210i | \(-0.854194\pi\) | ||||
0.896911 | − | 0.442210i | \(-0.145806\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.7022 | 1.41985 | 0.709923 | − | 0.704279i | \(-0.248730\pi\) | ||||
0.709923 | + | 0.704279i | \(0.248730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.12590 | −0.334347 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0993527i | 0.00363027i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 17.9337i | − 0.654410i | −0.944953 | − | 0.327205i | \(-0.893893\pi\) | ||||
0.944953 | − | 0.327205i | \(-0.106107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.78850 | 0.247059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.6326 | 1.18605 | 0.593026 | − | 0.805184i | \(-0.297933\pi\) | ||||
0.593026 | + | 0.805184i | \(0.297933\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.2699i | 1.89478i | 0.320078 | + | 0.947391i | \(0.396291\pi\) | ||||
−0.320078 | + | 0.947391i | \(0.603709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.40635i | − 0.123318i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.84007 | 0.210873 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.8516 | 0.535563 | 0.267782 | − | 0.963480i | \(-0.413709\pi\) | ||||
0.267782 | + | 0.963480i | \(0.413709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 22.6513i | − 0.814709i | −0.913270 | − | 0.407355i | \(-0.866451\pi\) | ||||
0.913270 | − | 0.407355i | \(-0.133549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 13.1742i | − 0.473233i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.7350 | −0.456278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4577 | −0.445770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 42.2586i | − 1.50827i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 18.0749i | − 0.644300i | −0.946689 | − | 0.322150i | \(-0.895594\pi\) | ||||
0.946689 | − | 0.322150i | \(-0.104406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2092 | −0.398553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.3247 | −1.60953 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.1587i | 1.67045i | 0.549911 | + | 0.835223i | \(0.314662\pi\) | ||||
−0.549911 | + | 0.835223i | \(0.685338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 66.2755i | − 2.34466i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.363366 | −0.0128229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.73205 | −0.202028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 48.6123i | − 1.70912i | −0.519354 | − | 0.854559i | \(-0.673828\pi\) | ||||
0.519354 | − | 0.854559i | \(-0.326172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2254i | 1.51785i | 0.651179 | + | 0.758924i | \(0.274275\pi\) | ||||
−0.651179 | + | 0.758924i | \(0.725725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3831 | −0.784046 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.90994 | −0.311719 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 35.5347i | − 1.24017i | −0.784535 | − | 0.620085i | \(-0.787098\pi\) | ||||
0.784535 | − | 0.620085i | \(-0.212902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.90023i | − 0.0662379i | −0.999451 | − | 0.0331189i | \(-0.989456\pi\) | ||||
0.999451 | − | 0.0331189i | \(-0.0105440\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.1105 | −1.42955 | −0.714775 | − | 0.699354i | \(-0.753471\pi\) | ||||
−0.714775 | + | 0.699354i | \(0.753471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1265 | −0.351707 | −0.175853 | − | 0.984416i | \(-0.556268\pi\) | ||||
−0.175853 | + | 0.984416i | \(0.556268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.93127i | 0.205506i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 5.31207i | − 0.183832i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.5726 | −1.60786 | −0.803932 | − | 0.594721i | \(-0.797263\pi\) | ||||
−0.803932 | + | 0.594721i | \(0.797263\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.2664 | 0.905738 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5.40549i | − 0.185954i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9.71014i | − 0.333644i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.59634 | 0.0547217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.1228 | 0.791710 | 0.395855 | − | 0.918313i | \(-0.370448\pi\) | ||||
0.395855 | + | 0.918313i | \(0.370448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 16.9208i | − 0.578004i | −0.957329 | − | 0.289002i | \(-0.906677\pi\) | ||||
0.957329 | − | 0.289002i | \(-0.0933234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.0925i | 1.26558i | 0.774324 | + | 0.632789i | \(0.218090\pi\) | ||||
−0.774324 | + | 0.632789i | \(0.781910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0782 | 0.819632 | 0.409816 | − | 0.912168i | \(-0.365593\pi\) | ||||
0.409816 | + | 0.912168i | \(0.365593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.72629 | 0.0586956 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.7036i | 0.498784i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.4464i | 1.03164i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1087 | −0.409350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.9708 | 0.505527 | 0.252764 | − | 0.967528i | \(-0.418660\pi\) | ||||
0.252764 | + | 0.967528i | \(0.418660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 36.4601i | − 1.22837i | −0.789162 | − | 0.614186i | \(-0.789485\pi\) | ||||
0.789162 | − | 0.614186i | \(-0.210515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9.37770i | − 0.315585i | −0.987472 | − | 0.157792i | \(-0.949562\pi\) | ||||
0.987472 | − | 0.157792i | \(-0.0504377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.8028 | −1.73937 | −0.869684 | − | 0.493609i | \(-0.835677\pi\) | ||||
−0.869684 | + | 0.493609i | \(0.835677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.1180 | −0.406426 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.9530i | 0.500382i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.5228i | 0.953413i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.1787 | −0.572942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0157 | 0.333673 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.2774i | 1.03970i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15.0718i | − 0.500451i | −0.968188 | − | 0.250225i | \(-0.919495\pi\) | ||||
0.968188 | − | 0.250225i | \(-0.0805047\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.0842 | 1.89128 | 0.945642 | − | 0.325209i | \(-0.105435\pi\) | ||||
0.945642 | + | 0.325209i | \(0.105435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.68612 | −0.121993 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.54884i | 0.0511472i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.23843i | 0.0738391i | 0.999318 | + | 0.0369195i | \(0.0117545\pi\) | ||||
−0.999318 | + | 0.0369195i | \(0.988245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.0353 | −1.15320 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.682166 | 0.0224295 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.4145i | 0.833824i | 0.908947 | + | 0.416912i | \(0.136888\pi\) | ||||
−0.908947 | + | 0.416912i | \(0.863112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.33820i | − 0.0438578i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.0135 | −0.425586 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.0906 | −1.24437 | −0.622183 | − | 0.782872i | \(-0.713754\pi\) | ||||
−0.622183 | + | 0.782872i | \(0.713754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 58.5266i | − 1.90791i | −0.299943 | − | 0.953957i | \(-0.596968\pi\) | ||||
0.299943 | − | 0.953957i | \(-0.403032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.2366i | 0.919511i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.7722 | −1.12995 | −0.564973 | − | 0.825109i | \(-0.691113\pi\) | ||||
−0.564973 | + | 0.825109i | \(0.691113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.02191 | −0.0331727 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.7143i | 0.541430i | 0.962660 | + | 0.270715i | \(0.0872601\pi\) | ||||
−0.962660 | + | 0.270715i | \(0.912740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.7862i | 0.575546i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.895484 | −0.0289167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −76.9562 | −2.48246 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.5512i | 0.500610i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.2257i | 1.67946i | 0.543001 | + | 0.839732i | \(0.317288\pi\) | ||||
−0.543001 | + | 0.839732i | \(0.682712\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.7723 | −0.827073 | −0.413536 | − | 0.910488i | \(-0.635707\pi\) | ||||
−0.413536 | + | 0.910488i | \(0.635707\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9021 | −0.445680 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.2747i | 0.392701i | 0.980534 | + | 0.196351i | \(0.0629090\pi\) | ||||
−0.980534 | + | 0.196351i | \(0.937091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 15.6299i | − 0.499534i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.5111 | 1.29210 | 0.646052 | − | 0.763293i | \(-0.276419\pi\) | ||||
0.646052 | + | 0.763293i | \(0.276419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.2330 | 1.47310 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7556i | 0.628191i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 15.4002i | − 0.489203i | −0.969624 | − | 0.244601i | \(-0.921343\pi\) | ||||
0.969624 | − | 0.244601i | \(-0.0786571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.5218 | 0.713989 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.6284 | −0.843329 | −0.421664 | − | 0.906752i | \(-0.638554\pi\) | ||||
−0.421664 | + | 0.906752i | \(0.638554\pi\) | |||||||
\(998\) | 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.2591.15 | yes | 16 | |
3.2 | odd | 2 | inner | 6048.2.h.h.2591.4 | yes | 16 | |
4.3 | odd | 2 | inner | 6048.2.h.h.2591.14 | yes | 16 | |
12.11 | even | 2 | inner | 6048.2.h.h.2591.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.h.2591.1 | ✓ | 16 | 12.11 | even | 2 | inner | |
6048.2.h.h.2591.4 | yes | 16 | 3.2 | odd | 2 | inner | |
6048.2.h.h.2591.14 | yes | 16 | 4.3 | odd | 2 | inner | |
6048.2.h.h.2591.15 | yes | 16 | 1.1 | even | 1 | trivial |