Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(1295,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.1295");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 648) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1295.5 | ||
Character | \(\chi\) | \(=\) | 2592.1295 |
Dual form | 2592.2.f.c.1295.6 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.78731 | −0.799309 | −0.399655 | − | 0.916666i | \(-0.630870\pi\) | ||||
−0.399655 | + | 0.916666i | \(0.630870\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.35928i | − 1.26969i | −0.772640 | − | 0.634845i | \(-0.781064\pi\) | ||||
0.772640 | − | 0.634845i | \(-0.218936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.62525i | − 1.09305i | −0.837442 | − | 0.546526i | \(-0.815950\pi\) | ||||
0.837442 | − | 0.546526i | \(-0.184050\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.71824i | − 0.476555i | −0.971197 | − | 0.238277i | \(-0.923417\pi\) | ||||
0.971197 | − | 0.238277i | \(-0.0765828\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.25325i | − 1.51664i | −0.651885 | − | 0.758318i | \(-0.726022\pi\) | ||||
0.651885 | − | 0.758318i | \(-0.273978\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57204 | 1.04890 | 0.524449 | − | 0.851442i | \(-0.324271\pi\) | ||||
0.524449 | + | 0.851442i | \(0.324271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.617331 | −0.128722 | −0.0643612 | − | 0.997927i | \(-0.520501\pi\) | ||||
−0.0643612 | + | 0.997927i | \(0.520501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.80552 | −0.361105 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.67561 | −1.05394 | −0.526968 | − | 0.849885i | \(-0.676671\pi\) | ||||
−0.526968 | + | 0.849885i | \(0.676671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.09500i | 1.45391i | 0.686687 | + | 0.726953i | \(0.259064\pi\) | ||||
−0.686687 | + | 0.726953i | \(0.740936\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00408i | 1.01487i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.06318i | 1.16118i | 0.814196 | + | 0.580590i | \(0.197178\pi\) | ||||
−0.814196 | + | 0.580590i | \(0.802822\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92652i | 1.08174i | 0.841106 | + | 0.540870i | \(0.181905\pi\) | ||||
−0.841106 | + | 0.540870i | \(0.818095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.66621 | 1.01659 | 0.508294 | − | 0.861184i | \(-0.330277\pi\) | ||||
0.508294 | + | 0.861184i | \(0.330277\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.01238 | −0.147670 | −0.0738352 | − | 0.997270i | \(-0.523524\pi\) | ||||
−0.0738352 | + | 0.997270i | \(0.523524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.28477 | −0.612111 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5493 | −1.44906 | −0.724529 | − | 0.689244i | \(-0.757943\pi\) | ||||
−0.724529 | + | 0.689244i | \(0.757943\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.47944i | 0.873687i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 5.00538i | − 0.651644i | −0.945431 | − | 0.325822i | \(-0.894359\pi\) | ||||
0.945431 | − | 0.325822i | \(-0.105641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 14.2966i | − 1.83050i | −0.402888 | − | 0.915249i | \(-0.631994\pi\) | ||||
0.402888 | − | 0.915249i | \(-0.368006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.07103i | 0.380915i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.38311 | 1.14633 | 0.573165 | − | 0.819440i | \(-0.305716\pi\) | ||||
0.573165 | + | 0.819440i | \(0.305716\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.70917 | −1.15227 | −0.576133 | − | 0.817356i | \(-0.695439\pi\) | ||||
−0.576133 | + | 0.817356i | \(0.695439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2438 | −1.78415 | −0.892075 | − | 0.451886i | \(-0.850751\pi\) | ||||
−0.892075 | + | 0.451886i | \(0.850751\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.1782 | −1.38784 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 15.4256i | − 1.73552i | −0.496988 | − | 0.867758i | \(-0.665561\pi\) | ||||
0.496988 | − | 0.867758i | \(-0.334439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.46882i | 0.710046i | 0.934858 | + | 0.355023i | \(0.115527\pi\) | ||||
−0.934858 | + | 0.355023i | \(0.884473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1765i | 1.21226i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.45494i | − 0.154223i | −0.997022 | − | 0.0771115i | \(-0.975430\pi\) | ||||
0.997022 | − | 0.0771115i | \(-0.0245697\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.77206 | −0.605077 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.17165 | −0.838394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.85931 | −0.594923 | −0.297461 | − | 0.954734i | \(-0.596140\pi\) | ||||
−0.297461 | + | 0.954734i | \(0.596140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.86358 | −0.284937 | −0.142468 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142468 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 4.84323i | − 0.477218i | −0.971116 | − | 0.238609i | \(-0.923309\pi\) | ||||
0.971116 | − | 0.238609i | \(-0.0766914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.8641i | 1.05027i | 0.851018 | + | 0.525137i | \(0.175986\pi\) | ||||
−0.851018 | + | 0.525137i | \(0.824014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.887009i | 0.0849601i | 0.999097 | + | 0.0424800i | \(0.0135259\pi\) | ||||
−0.999097 | + | 0.0424800i | \(0.986474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.17946i | − 0.393170i | −0.980487 | − | 0.196585i | \(-0.937015\pi\) | ||||
0.980487 | − | 0.196585i | \(-0.0629852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.10336 | 0.102889 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.0064 | −1.92566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14241 | −0.194764 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1636 | 1.08794 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0834i | 0.983494i | 0.870738 | + | 0.491747i | \(0.163641\pi\) | ||||
−0.870738 | + | 0.491747i | \(0.836359\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 9.60825i | − 0.839476i | −0.907645 | − | 0.419738i | \(-0.862122\pi\) | ||||
0.907645 | − | 0.419738i | \(-0.137878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 15.3588i | − 1.33177i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.47943i | 0.724447i | 0.932091 | + | 0.362223i | \(0.117982\pi\) | ||||
−0.932091 | + | 0.362223i | \(0.882018\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.67540 | −0.820657 | −0.410328 | − | 0.911938i | \(-0.634586\pi\) | ||||
−0.410328 | + | 0.911938i | \(0.634586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.22905 | −0.520900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.1441 | 0.842420 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1389 | 0.912530 | 0.456265 | − | 0.889844i | \(-0.349187\pi\) | ||||
0.456265 | + | 0.889844i | \(0.349187\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 4.99549i | − 0.406527i | −0.979124 | − | 0.203264i | \(-0.934845\pi\) | ||||
0.979124 | − | 0.203264i | \(-0.0651548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 14.4683i | − 1.16212i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.61192i | 0.687306i | 0.939097 | + | 0.343653i | \(0.111664\pi\) | ||||
−0.939097 | + | 0.343653i | \(0.888336\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07379i | 0.163437i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.04820 | 0.160427 | 0.0802137 | − | 0.996778i | \(-0.474440\pi\) | ||||
0.0802137 | + | 0.996778i | \(0.474440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.0064 | −1.62553 | −0.812763 | − | 0.582595i | \(-0.802037\pi\) | ||||
−0.812763 | + | 0.582595i | \(0.802037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0476 | 0.772895 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.81939 | −0.518469 | −0.259234 | − | 0.965814i | \(-0.583470\pi\) | ||||
−0.259234 | + | 0.965814i | \(0.583470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.06526i | 0.458491i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 22.5099i | − 1.68247i | −0.540671 | − | 0.841234i | \(-0.681830\pi\) | ||||
0.540671 | − | 0.841234i | \(-0.318170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.43198i | 0.626744i | 0.949630 | + | 0.313372i | \(0.101459\pi\) | ||||
−0.949630 | + | 0.313372i | \(0.898541\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 12.6241i | − 0.928142i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.6696 | −1.65776 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.08057 | 0.439975 | 0.219987 | − | 0.975503i | \(-0.429398\pi\) | ||||
0.219987 | + | 0.975503i | \(0.429398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4901 | −1.60235 | −0.801176 | − | 0.598429i | \(-0.795792\pi\) | ||||
−0.801176 | + | 0.598429i | \(0.795792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.83872i | 0.697448i | 0.937225 | + | 0.348724i | \(0.113385\pi\) | ||||
−0.937225 | + | 0.348724i | \(0.886615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.0660i | 1.33817i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 12.3798i | − 0.864645i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 16.5748i | − 1.14650i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2291 | −0.841883 | −0.420941 | − | 0.907088i | \(-0.638300\pi\) | ||||
−0.420941 | + | 0.907088i | \(0.638300\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9146 | −0.812567 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.1934 | 1.84601 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.7446 | −0.722760 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.45880i | − 0.432513i | −0.976337 | − | 0.216256i | \(-0.930615\pi\) | ||||
0.976337 | − | 0.216256i | \(-0.0693847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4781i | 0.828198i | 0.910232 | + | 0.414099i | \(0.135903\pi\) | ||||
−0.910232 | + | 0.414099i | \(0.864097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.63538i | 0.570642i | 0.958432 | + | 0.285321i | \(0.0921002\pi\) | ||||
−0.958432 | + | 0.285321i | \(0.907900\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.26702i | 0.410566i | 0.978703 | + | 0.205283i | \(0.0658115\pi\) | ||||
−0.978703 | + | 0.205283i | \(0.934189\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.80943 | 0.118034 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.0165 | 1.35944 | 0.679721 | − | 0.733471i | \(-0.262101\pi\) | ||||
0.679721 | + | 0.733471i | \(0.262101\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.33856 | 0.408302 | 0.204151 | − | 0.978939i | \(-0.434557\pi\) | ||||
0.204151 | + | 0.978939i | \(0.434557\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.65822 | 0.489266 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 7.85588i | − 0.499858i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 8.50717i | − 0.536968i | −0.963284 | − | 0.268484i | \(-0.913477\pi\) | ||||
0.963284 | − | 0.268484i | \(-0.0865226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23798i | 0.140700i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.84997i | 0.364911i | 0.983214 | + | 0.182456i | \(0.0584046\pi\) | ||||
−0.983214 | + | 0.182456i | \(0.941595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.7272 | 1.47434 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0750 | 0.682911 | 0.341456 | − | 0.939898i | \(-0.389080\pi\) | ||||
0.341456 | + | 0.939898i | \(0.389080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.8549 | 1.15825 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.18889 | −0.316372 | −0.158186 | − | 0.987409i | \(-0.550565\pi\) | ||||
−0.158186 | + | 0.987409i | \(0.550565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 18.3273i | − 1.11330i | −0.830747 | − | 0.556651i | \(-0.812086\pi\) | ||||
0.830747 | − | 0.556651i | \(-0.187914\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.54546i | 0.394706i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.0332i | 1.26376i | 0.775064 | + | 0.631882i | \(0.217717\pi\) | ||||
−0.775064 | + | 0.631882i | \(0.782283\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 17.2197i | − 1.02724i | −0.858018 | − | 0.513619i | \(-0.828304\pi\) | ||||
0.858018 | − | 0.513619i | \(-0.171696\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.04596 | 0.478283 | 0.239141 | − | 0.970985i | \(-0.423134\pi\) | ||||
0.239141 | + | 0.970985i | \(0.423134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.2681 | 1.37347 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.1031 | −1.30018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1754 | −0.769717 | −0.384859 | − | 0.922976i | \(-0.625750\pi\) | ||||
−0.384859 | + | 0.922976i | \(0.625750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.94616i | 0.520865i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06072i | 0.0613433i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 22.3937i | − 1.29075i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.5525i | 1.46313i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.45699 | −0.368520 | −0.184260 | − | 0.982878i | \(-0.558989\pi\) | ||||
−0.184260 | + | 0.982878i | \(0.558989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9944 | 0.623435 | 0.311717 | − | 0.950175i | \(-0.399096\pi\) | ||||
0.311717 | + | 0.950175i | \(0.399096\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.238809 | 0.0134983 | 0.00674913 | − | 0.999977i | \(-0.497852\pi\) | ||||
0.00674913 | + | 0.999977i | \(0.497852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.06987 | −0.340918 | −0.170459 | − | 0.985365i | \(-0.554525\pi\) | ||||
−0.170459 | + | 0.985365i | \(0.554525\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.5755i | 1.15201i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 28.5901i | − 1.59080i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.10233i | 0.172086i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.40086i | 0.187495i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.2602 | −1.16857 | −0.584284 | − | 0.811549i | \(-0.698625\pi\) | ||||
−0.584284 | + | 0.811549i | \(0.698625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.7705 | −0.916272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5712 | 0.793745 | 0.396873 | − | 0.917874i | \(-0.370095\pi\) | ||||
0.396873 | + | 0.917874i | \(0.370095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.3464 | 1.58920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 9.12121i | − 0.492499i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.8615i | 1.28095i | 0.767978 | + | 0.640477i | \(0.221263\pi\) | ||||
−0.767978 | + | 0.640477i | \(0.778737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9869i | 1.12340i | 0.827340 | + | 0.561702i | \(0.189853\pi\) | ||||
−0.827340 | + | 0.561702i | \(0.810147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.33461i | 0.177483i | 0.996055 | + | 0.0887416i | \(0.0282845\pi\) | ||||
−0.996055 | + | 0.0887416i | \(0.971715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.3533 | 0.921018 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4127 | 1.28845 | 0.644227 | − | 0.764834i | \(-0.277179\pi\) | ||||
0.644227 | + | 0.764834i | \(0.277179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.90356 | 0.100187 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.2454 | 1.42609 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.40618i | − 0.177801i | −0.996040 | − | 0.0889007i | \(-0.971665\pi\) | ||||
0.996040 | − | 0.0889007i | \(-0.0283354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.4381i | 1.83985i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 27.5877i | − 1.42844i | −0.699922 | − | 0.714219i | \(-0.746782\pi\) | ||||
0.699922 | − | 0.714219i | \(-0.253218\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.75209i | 0.502258i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.2051 | −1.55153 | −0.775766 | − | 0.631021i | \(-0.782636\pi\) | ||||
−0.775766 | + | 0.631021i | \(0.782636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.8403 | −0.809402 | −0.404701 | − | 0.914449i | \(-0.632624\pi\) | ||||
−0.404701 | + | 0.914449i | \(0.632624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.7663 | 1.10931 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.52797 | −0.330981 | −0.165491 | − | 0.986211i | \(-0.552921\pi\) | ||||
−0.165491 | + | 0.986211i | \(0.552921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.86032i | 0.195225i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.5703i | 1.38721i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 16.9116i | − 0.848767i | −0.905483 | − | 0.424383i | \(-0.860491\pi\) | ||||
0.905483 | − | 0.424383i | \(-0.139509\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.19139i | − 0.109433i | −0.998502 | − | 0.0547163i | \(-0.982575\pi\) | ||||
0.998502 | − | 0.0547163i | \(-0.0174255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.9092 | 0.692866 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.6058 | 1.26923 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.8532 | −0.635548 | −0.317774 | − | 0.948166i | \(-0.602935\pi\) | ||||
−0.317774 | + | 0.948166i | \(0.602935\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8145 | −0.827386 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 11.5618i | − 0.567546i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 21.0896i | − 1.03030i | −0.857101 | − | 0.515148i | \(-0.827737\pi\) | ||||
0.857101 | − | 0.515148i | \(-0.172263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.75783i | 0.378094i | 0.981968 | + | 0.189047i | \(0.0605398\pi\) | ||||
−0.981968 | + | 0.189047i | \(0.939460\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.2904i | 0.547664i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.0265 | −2.32416 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.8966 | −0.765712 | −0.382856 | − | 0.923808i | \(-0.625059\pi\) | ||||
−0.382856 | + | 0.923808i | \(0.625059\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.620460 | 0.0298174 | 0.0149087 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149087 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.82246 | −0.135017 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0905i | 0.624775i | 0.949955 | + | 0.312388i | \(0.101129\pi\) | ||||
−0.949955 | + | 0.312388i | \(0.898871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 35.2665i | − 1.67556i | −0.546006 | − | 0.837781i | \(-0.683853\pi\) | ||||
0.546006 | − | 0.837781i | \(-0.316147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.60042i | 0.123272i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 2.94608i | − 0.139034i | −0.997581 | − | 0.0695171i | \(-0.977854\pi\) | ||||
0.997581 | − | 0.0695171i | \(-0.0221459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.1103 | 1.18240 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.3165 | 0.483643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1675 | −1.17728 | −0.588642 | − | 0.808394i | \(-0.700337\pi\) | ||||
−0.588642 | + | 0.808394i | \(0.700337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.5377 | 1.65516 | 0.827579 | − | 0.561350i | \(-0.189718\pi\) | ||||
0.827579 | + | 0.561350i | \(0.189718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 30.1317i | − 1.40034i | −0.713978 | − | 0.700168i | \(-0.753108\pi\) | ||||
0.713978 | − | 0.700168i | \(-0.246892\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.04243i | 0.372159i | 0.982535 | + | 0.186080i | \(0.0595782\pi\) | ||||
−0.982535 | + | 0.186080i | \(0.940422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 31.5205i | − 1.45548i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 24.1666i | − 1.11118i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.25493 | −0.378762 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9108 | 1.73219 | 0.866094 | − | 0.499882i | \(-0.166623\pi\) | ||||
0.866094 | + | 0.499882i | \(0.166623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1363 | 0.553366 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4724 | 0.475527 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.286027i | 0.0129611i | 0.999979 | + | 0.00648057i | \(0.00206284\pi\) | ||||
−0.999979 | + | 0.00648057i | \(0.997937\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7.78671i | − 0.351410i | −0.984443 | − | 0.175705i | \(-0.943780\pi\) | ||||
0.984443 | − | 0.175705i | \(-0.0562204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.4910i | 1.59844i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.6158i | 1.46302i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.8136 | 1.06604 | 0.533022 | − | 0.846101i | \(-0.321056\pi\) | ||||
0.533022 | + | 0.846101i | \(0.321056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.8583 | 0.528735 | 0.264367 | − | 0.964422i | \(-0.414837\pi\) | ||||
0.264367 | + | 0.964422i | \(0.414837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.11810 | 0.227753 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.3259 | 0.856607 | 0.428304 | − | 0.903635i | \(-0.359111\pi\) | ||||
0.428304 | + | 0.903635i | \(0.359111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.2082i | 2.26532i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.65635i | 0.381444i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.67012i | 0.161412i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 41.6156i | − 1.82321i | −0.411063 | − | 0.911607i | \(-0.634842\pi\) | ||||
0.411063 | − | 0.911607i | \(-0.365158\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.05911 | −0.264946 | −0.132473 | − | 0.991187i | \(-0.542292\pi\) | ||||
−0.132473 | + | 0.991187i | \(0.542292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 50.6201 | 2.20504 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6189 | −0.983431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.9014 | 0.515509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 19.4175i | − 0.839493i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5334i | 0.669069i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8716i | 0.768360i | 0.923258 | + | 0.384180i | \(0.125516\pi\) | ||||
−0.923258 | + | 0.384180i | \(0.874484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1.58536i | − 0.0679094i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.9412 | −1.32295 | −0.661476 | − | 0.749967i | \(-0.730069\pi\) | ||||
−0.661476 | + | 0.749967i | \(0.730069\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.9491 | −1.10547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.8189 | −2.20356 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.4742 | 1.07938 | 0.539689 | − | 0.841864i | \(-0.318542\pi\) | ||||
0.539689 | + | 0.841864i | \(0.318542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 11.4542i | − 0.484460i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 25.4376i | − 1.07207i | −0.844197 | − | 0.536034i | \(-0.819922\pi\) | ||||
0.844197 | − | 0.536034i | \(-0.180078\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.46999i | 0.314265i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 23.7604i | − 0.996089i | −0.867152 | − | 0.498044i | \(-0.834052\pi\) | ||||
0.867152 | − | 0.498044i | \(-0.165948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.27312 | 0.0532785 | 0.0266393 | − | 0.999645i | \(-0.491519\pi\) | ||||
0.0266393 | + | 0.999645i | \(0.491519\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.11461 | 0.0464823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.62218 | 0.317315 | 0.158658 | − | 0.987334i | \(-0.449283\pi\) | ||||
0.158658 | + | 0.987334i | \(0.449283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.7306 | 0.901537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.2438i | 1.58390i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 44.8459i | − 1.85099i | −0.378760 | − | 0.925495i | \(-0.623649\pi\) | ||||
0.378760 | − | 0.925495i | \(-0.376351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.0107i | 1.52500i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 21.3237i | − 0.875658i | −0.899058 | − | 0.437829i | \(-0.855748\pi\) | ||||
0.899058 | − | 0.437829i | \(-0.144252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.5450 | 1.53919 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.98423 | 0.0810736 | 0.0405368 | − | 0.999178i | \(-0.487093\pi\) | ||||
0.0405368 | + | 0.999178i | \(0.487093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.57621 | 0.390622 | 0.195311 | − | 0.980741i | \(-0.437428\pi\) | ||||
0.195311 | + | 0.980741i | \(0.437428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.82914 | 0.155677 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 30.7644i | − 1.24869i | −0.781149 | − | 0.624345i | \(-0.785366\pi\) | ||||
0.781149 | − | 0.624345i | \(-0.214634\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.73951i | 0.0703731i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.1482i | − 0.813777i | −0.913478 | − | 0.406889i | \(-0.866614\pi\) | ||||
0.913478 | − | 0.406889i | \(-0.133386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2103i | 1.13570i | 0.823131 | + | 0.567851i | \(0.192225\pi\) | ||||
−0.823131 | + | 0.567851i | \(0.807775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0393 | 0.966223 | 0.483111 | − | 0.875559i | \(-0.339507\pi\) | ||||
0.483111 | + | 0.875559i | \(0.339507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.88754 | −0.195815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.7125 | −0.508499 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.1678 | 1.76109 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 28.1191i | − 1.11940i | −0.828694 | − | 0.559701i | \(-0.810916\pi\) | ||||
0.828694 | − | 0.559701i | \(-0.189084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 19.8095i | − 0.786116i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.36228i | 0.291704i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.3724i | 0.409687i | 0.978795 | + | 0.204843i | \(0.0656685\pi\) | ||||
−0.978795 | + | 0.204843i | \(0.934332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1042 | 0.753397 | 0.376698 | − | 0.926336i | \(-0.377059\pi\) | ||||
0.376698 | + | 0.926336i | \(0.377059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.61125 | −0.141973 | −0.0709864 | − | 0.997477i | \(-0.522615\pi\) | ||||
−0.0709864 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.1457 | −0.712282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.37996 | −0.0931351 | −0.0465675 | − | 0.998915i | \(-0.514828\pi\) | ||||
−0.0465675 | + | 0.998915i | \(0.514828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1729i | 0.671001i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.8158i | 1.66787i | 0.551864 | + | 0.833934i | \(0.313917\pi\) | ||||
−0.551864 | + | 0.833934i | \(0.686083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 35.5228i | − 1.38168i | −0.723009 | − | 0.690839i | \(-0.757241\pi\) | ||||
0.723009 | − | 0.690839i | \(-0.242759\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27.4509i | 1.06450i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.50373 | 0.135665 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −51.8289 | −2.00083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1137 | −0.659684 | −0.329842 | − | 0.944036i | \(-0.606995\pi\) | ||||
−0.329842 | + | 0.944036i | \(0.606995\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.19358 | 0.0843060 | 0.0421530 | − | 0.999111i | \(-0.486578\pi\) | ||||
0.0421530 | + | 0.999111i | \(0.486578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.6831i | 0.755367i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3775i | 0.397083i | 0.980092 | + | 0.198542i | \(0.0636205\pi\) | ||||
−0.980092 | + | 0.198542i | \(0.936380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 15.1554i | − 0.579057i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.1263i | 0.690556i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9195 | 1.48057 | 0.740284 | − | 0.672295i | \(-0.234691\pi\) | ||||
0.740284 | + | 0.672295i | \(0.234691\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.2929 | 0.655959 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.3132 | 1.64061 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.9799 | −1.01902 | −0.509509 | − | 0.860465i | \(-0.670173\pi\) | ||||
−0.509509 | + | 0.860465i | \(0.670173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.2932i | 1.21796i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.61957i | 0.361781i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 34.5022i | − 1.29576i | −0.761744 | − | 0.647878i | \(-0.775656\pi\) | ||||
0.761744 | − | 0.647878i | \(-0.224344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.99730i | − 0.187150i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1332 | 0.416360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.7134 | 1.29459 | 0.647296 | − | 0.762239i | \(-0.275900\pi\) | ||||
0.647296 | + | 0.762239i | \(0.275900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2698 | −0.605918 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.2475 | 0.380581 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 17.5891i | − 0.652344i | −0.945310 | − | 0.326172i | \(-0.894241\pi\) | ||||
0.945310 | − | 0.326172i | \(-0.105759\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 41.6854i | − 1.54179i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16.7192i | − 0.617538i | −0.951137 | − | 0.308769i | \(-0.900083\pi\) | ||||
0.951137 | − | 0.308769i | \(-0.0999170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 34.0161i | − 1.25300i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6373 | 0.759154 | 0.379577 | − | 0.925160i | \(-0.376070\pi\) | ||||
0.379577 | + | 0.925160i | \(0.376070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2777 | 0.780602 | 0.390301 | − | 0.920687i | \(-0.372371\pi\) | ||||
0.390301 | + | 0.920687i | \(0.372371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.9086 | −0.729394 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.4956 | 1.33352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 29.2150i | − 1.06607i | −0.846093 | − | 0.533035i | \(-0.821051\pi\) | ||||
0.846093 | − | 0.533035i | \(-0.178949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.92849i | 0.324941i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 48.0411i | − 1.74608i | −0.487644 | − | 0.873042i | \(-0.662144\pi\) | ||||
0.487644 | − | 0.873042i | \(-0.337856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.2715i | 1.31484i | 0.753524 | + | 0.657420i | \(0.228352\pi\) | ||||
−0.753524 | + | 0.657420i | \(0.771648\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.97971 | 0.107873 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.60045 | −0.310544 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.5241 | −1.17285 | −0.586424 | − | 0.810004i | \(-0.699465\pi\) | ||||
−0.586424 | + | 0.810004i | \(0.699465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.4139 | 1.05794 | 0.528972 | − | 0.848639i | \(-0.322578\pi\) | ||||
0.528972 | + | 0.848639i | \(0.322578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 14.6157i | − 0.525012i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.6683i | 1.13464i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.1981i | 1.25949i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 15.3922i | − 0.549370i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.2137 | 1.64734 | 0.823670 | − | 0.567069i | \(-0.191923\pi\) | ||||
0.823670 | + | 0.567069i | \(0.191923\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0400 | −0.499204 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.5651 | −0.872333 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5710 | 0.657818 | 0.328909 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328909 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.33065i | 0.223962i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 55.2625i | 1.95017i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.70650i | − 0.130637i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 22.3374i | − 0.785340i | −0.919679 | − | 0.392670i | \(-0.871551\pi\) | ||||
0.919679 | − | 0.392670i | \(-0.128449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.5840 | −1.56556 | −0.782778 | − | 0.622301i | \(-0.786198\pi\) | ||||
−0.782778 | + | 0.622301i | \(0.786198\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.66077 | −0.128231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.4782 | 1.06630 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3986 | −1.06092 | −0.530459 | − | 0.847710i | \(-0.677981\pi\) | ||||
−0.530459 | + | 0.847710i | \(0.677981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4691i | 0.504361i | 0.967680 | + | 0.252180i | \(0.0811476\pi\) | ||||
−0.967680 | + | 0.252180i | \(0.918852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.0725i | 1.81074i | 0.424627 | + | 0.905368i | \(0.360405\pi\) | ||||
−0.424627 | + | 0.905368i | \(0.639595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.34421i | 0.150881i | 0.997150 | + | 0.0754404i | \(0.0240363\pi\) | ||||
−0.997150 | + | 0.0754404i | \(0.975964\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.7937i | 0.928348i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.5450 | 1.29930 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.8480 | 1.58285 | 0.791424 | − | 0.611268i | \(-0.209340\pi\) | ||||
0.791424 | + | 0.611268i | \(0.209340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.21260 | 0.110779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.9582 | −0.617783 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.19695i | 0.247290i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 4.36032i | − 0.149470i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.0276i | 1.74715i | 0.486687 | + | 0.873577i | \(0.338205\pi\) | ||||
−0.486687 | + | 0.873577i | \(0.661795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.5834i | 1.79621i | 0.439778 | + | 0.898107i | \(0.355057\pi\) | ||||
−0.439778 | + | 0.898107i | \(0.644943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0195 | −0.546579 | −0.273289 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273289 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.3104 | −0.861575 | −0.430788 | − | 0.902453i | \(-0.641764\pi\) | ||||
−0.430788 | + | 0.902453i | \(0.641764\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.1884 | 0.414417 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55.9216 | −1.89701 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 16.1225i | − 0.546289i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 40.8609i | − 1.38135i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.15810i | − 0.106642i | −0.998577 | − | 0.0533208i | \(-0.983019\pi\) | ||||
0.998577 | − | 0.0533208i | \(-0.0169806\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.1113i | 0.576493i | 0.957556 | + | 0.288246i | \(0.0930722\pi\) | ||||
−0.957556 | + | 0.288246i | \(0.906928\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0162 | 0.639945 | 0.319972 | − | 0.947427i | \(-0.396326\pi\) | ||||
0.319972 | + | 0.947427i | \(0.396326\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.6696 | 1.29840 | 0.649199 | − | 0.760619i | \(-0.275104\pi\) | ||||
0.649199 | + | 0.760619i | \(0.275104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.2323 | 1.24873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.62863 | −0.154891 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.2322i | 1.34481i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 45.9441i | − 1.53232i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.9674i | 2.19769i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 15.0706i | − 0.500962i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.1652 | −1.46648 | −0.733241 | − | 0.679969i | \(-0.761993\pi\) | ||||
−0.733241 | + | 0.679969i | \(0.761993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.1399 | −0.998579 | −0.499290 | − | 0.866435i | \(-0.666406\pi\) | ||||
−0.499290 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.4511 | 0.776117 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.2768 | −1.06587 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 20.7713i | − 0.685183i | −0.939485 | − | 0.342591i | \(-0.888695\pi\) | ||||
0.939485 | − | 0.342591i | \(-0.111305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.6827i | 0.549118i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 12.7527i | − 0.419307i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 28.5176i | − 0.935633i | −0.883826 | − | 0.467816i | \(-0.845041\pi\) | ||||
0.883826 | − | 0.467816i | \(-0.154959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.5902 | −0.642042 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.5175 | 1.32506 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.91394 | 0.291206 | 0.145603 | − | 0.989343i | \(-0.453488\pi\) | ||||
0.145603 | + | 0.989343i | \(0.453488\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.5450 | 0.408954 | 0.204477 | − | 0.978871i | \(-0.434451\pi\) | ||||
0.204477 | + | 0.978871i | \(0.434451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.27595i | − 0.139244i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 20.5765i | − 0.668648i | −0.942458 | − | 0.334324i | \(-0.891492\pi\) | ||||
0.942458 | − | 0.334324i | \(-0.108508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.1925i | 0.850246i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.3391i | 1.14475i | 0.819993 | + | 0.572374i | \(0.193977\pi\) | ||||
−0.819993 | + | 0.572374i | \(0.806023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.8679 | −0.351676 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.4848 | 0.919822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5291 | −1.11384 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.78731 | 0.0575355 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.1144i | 0.646836i | 0.946256 | + | 0.323418i | \(0.104832\pi\) | ||||
−0.946256 | + | 0.323418i | \(0.895168\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.49582i | 0.0800947i | 0.999198 | + | 0.0400474i | \(0.0127509\pi\) | ||||
−0.999198 | + | 0.0400474i | \(0.987249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.5024i | 1.04198i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 62.1836i | − 1.98943i | −0.102675 | − | 0.994715i | \(-0.532740\pi\) | ||||
0.102675 | − | 0.994715i | \(-0.467260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.27450 | −0.168574 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.8754 | −0.761507 | −0.380754 | − | 0.924677i | \(-0.624335\pi\) | ||||
−0.380754 | + | 0.924677i | \(0.624335\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 40.1967 | 1.28077 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.11526 | −0.130858 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.22210i | 0.0705873i | 0.999377 | + | 0.0352937i | \(0.0112367\pi\) | ||||
−0.999377 | + | 0.0352937i | \(0.988763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 17.5848i | − 0.557477i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 37.3871i | − 1.18406i | −0.805916 | − | 0.592030i | \(-0.798327\pi\) | ||||
0.805916 | − | 0.592030i | \(-0.201673\pi\) | |||||||
\(998\) | 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 | 2592.2.f.c.1295.5 | 24 | ||
3.2 | odd | 2 | inner | 2592.2.f.c.1295.19 | 24 | ||
4.3 | odd | 2 | 648.2.f.c.323.2 | yes | 24 | ||
8.3 | odd | 2 | inner | 2592.2.f.c.1295.20 | 24 | ||
8.5 | even | 2 | 648.2.f.c.323.24 | yes | 24 | ||
9.2 | odd | 6 | 2592.2.p.g.2159.6 | 48 | |||
9.4 | even | 3 | 2592.2.p.g.431.19 | 48 | |||
9.5 | odd | 6 | 2592.2.p.g.431.5 | 48 | |||
9.7 | even | 3 | 2592.2.p.g.2159.20 | 48 | |||
12.11 | even | 2 | 648.2.f.c.323.23 | yes | 24 | ||
24.5 | odd | 2 | 648.2.f.c.323.1 | ✓ | 24 | ||
24.11 | even | 2 | inner | 2592.2.f.c.1295.6 | 24 | ||
36.7 | odd | 6 | 648.2.l.g.539.17 | 48 | |||
36.11 | even | 6 | 648.2.l.g.539.8 | 48 | |||
36.23 | even | 6 | 648.2.l.g.107.10 | 48 | |||
36.31 | odd | 6 | 648.2.l.g.107.15 | 48 | |||
72.5 | odd | 6 | 648.2.l.g.107.17 | 48 | |||
72.11 | even | 6 | 2592.2.p.g.2159.19 | 48 | |||
72.13 | even | 6 | 648.2.l.g.107.8 | 48 | |||
72.29 | odd | 6 | 648.2.l.g.539.15 | 48 | |||
72.43 | odd | 6 | 2592.2.p.g.2159.5 | 48 | |||
72.59 | even | 6 | 2592.2.p.g.431.20 | 48 | |||
72.61 | even | 6 | 648.2.l.g.539.10 | 48 | |||
72.67 | odd | 6 | 2592.2.p.g.431.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.f.c.323.1 | ✓ | 24 | 24.5 | odd | 2 | ||
648.2.f.c.323.2 | yes | 24 | 4.3 | odd | 2 | ||
648.2.f.c.323.23 | yes | 24 | 12.11 | even | 2 | ||
648.2.f.c.323.24 | yes | 24 | 8.5 | even | 2 | ||
648.2.l.g.107.8 | 48 | 72.13 | even | 6 | |||
648.2.l.g.107.10 | 48 | 36.23 | even | 6 | |||
648.2.l.g.107.15 | 48 | 36.31 | odd | 6 | |||
648.2.l.g.107.17 | 48 | 72.5 | odd | 6 | |||
648.2.l.g.539.8 | 48 | 36.11 | even | 6 | |||
648.2.l.g.539.10 | 48 | 72.61 | even | 6 | |||
648.2.l.g.539.15 | 48 | 72.29 | odd | 6 | |||
648.2.l.g.539.17 | 48 | 36.7 | odd | 6 | |||
2592.2.f.c.1295.5 | 24 | 1.1 | even | 1 | trivial | ||
2592.2.f.c.1295.6 | 24 | 24.11 | even | 2 | inner | ||
2592.2.f.c.1295.19 | 24 | 3.2 | odd | 2 | inner | ||
2592.2.f.c.1295.20 | 24 | 8.3 | odd | 2 | inner | ||
2592.2.p.g.431.5 | 48 | 9.5 | odd | 6 | |||
2592.2.p.g.431.6 | 48 | 72.67 | odd | 6 | |||
2592.2.p.g.431.19 | 48 | 9.4 | even | 3 | |||
2592.2.p.g.431.20 | 48 | 72.59 | even | 6 | |||
2592.2.p.g.2159.5 | 48 | 72.43 | odd | 6 | |||
2592.2.p.g.2159.6 | 48 | 9.2 | odd | 6 | |||
2592.2.p.g.2159.19 | 48 | 72.11 | even | 6 | |||
2592.2.p.g.2159.20 | 48 | 9.7 | even | 3 |