Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(881,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.881");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.h (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Character | \(\chi\) | \(=\) | 1568.881 |
Dual form | 1568.3.h.a.881.4 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −3.89635 | −1.29878 | −0.649392 | − | 0.760454i | \(-0.724976\pi\) | ||||
−0.649392 | + | 0.760454i | \(0.724976\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.85969 | 1.77194 | 0.885969 | − | 0.463744i | \(-0.153494\pi\) | ||||
0.885969 | + | 0.463744i | \(0.153494\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.18155 | 0.686839 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.64596i | − 0.331451i | −0.986172 | − | 0.165725i | \(-0.947004\pi\) | ||||
0.986172 | − | 0.165725i | \(-0.0529965\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.79378 | −0.599522 | −0.299761 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299761 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.5205 | −2.30136 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.4749i | 0.616170i | 0.951359 | + | 0.308085i | \(0.0996881\pi\) | ||||
−0.951359 | + | 0.308085i | \(0.900312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.7853 | 0.567646 | 0.283823 | − | 0.958877i | \(-0.408397\pi\) | ||||
0.283823 | + | 0.958877i | \(0.408397\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.9111 | 0.561351 | 0.280675 | − | 0.959803i | \(-0.409442\pi\) | ||||
0.280675 | + | 0.959803i | \(0.409442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 53.4941 | 2.13977 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.9817 | 0.406728 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.2327i | 0.594231i | 0.954842 | + | 0.297115i | \(0.0960246\pi\) | ||||
−0.954842 | + | 0.297115i | \(0.903975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 30.2297i | − 0.975151i | −0.873081 | − | 0.487575i | \(-0.837881\pi\) | ||||
0.873081 | − | 0.487575i | \(-0.162119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.2059i | 0.430483i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.5843i | 1.06985i | 0.844900 | + | 0.534924i | \(0.179660\pi\) | ||||
−0.844900 | + | 0.534924i | \(0.820340\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.3673 | 0.778649 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 73.6801i | − 1.79707i | −0.438897 | − | 0.898537i | \(-0.644631\pi\) | ||||
0.438897 | − | 0.898537i | \(-0.355369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.8501i | 0.950002i | 0.879985 | + | 0.475001i | \(0.157552\pi\) | ||||
−0.879985 | + | 0.475001i | \(0.842448\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 54.7667 | 1.21704 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 41.8030i | 0.889426i | 0.895673 | + | 0.444713i | \(0.146694\pi\) | ||||
−0.895673 | + | 0.444713i | \(0.853306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 40.8138i | − 0.800271i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.41173i | 0.120976i | 0.998169 | + | 0.0604880i | \(0.0192657\pi\) | ||||
−0.998169 | + | 0.0604880i | \(0.980734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 32.3020i | − 0.587310i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −42.0232 | −0.737249 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.9148 | −0.269743 | −0.134871 | − | 0.990863i | \(-0.543062\pi\) | ||||
−0.134871 | + | 0.990863i | \(0.543062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1570 | 0.199294 | 0.0996472 | − | 0.995023i | \(-0.468229\pi\) | ||||
0.0996472 | + | 0.995023i | \(0.468229\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −69.0505 | −1.06232 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.79739i | 0.116379i | 0.998306 | + | 0.0581895i | \(0.0185328\pi\) | ||||
−0.998306 | + | 0.0581895i | \(0.981467\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −50.3060 | −0.729073 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41.3627 | 0.582574 | 0.291287 | − | 0.956636i | \(-0.405917\pi\) | ||||
0.291287 | + | 0.956636i | \(0.405917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 89.6091i | − 1.22752i | −0.789492 | − | 0.613761i | \(-0.789656\pi\) | ||||
0.789492 | − | 0.613761i | \(-0.210344\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −208.432 | −2.77909 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −70.7950 | −0.896140 | −0.448070 | − | 0.893999i | \(-0.647888\pi\) | ||||
−0.448070 | + | 0.893999i | \(0.647888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −98.4224 | −1.21509 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 60.8673 | 0.733341 | 0.366671 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366671 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92.8043i | 1.09182i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 67.1446i | − 0.771777i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 27.0204i | − 0.303600i | −0.988411 | − | 0.151800i | \(-0.951493\pi\) | ||||
0.988411 | − | 0.151800i | \(-0.0485070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 117.785i | 1.26651i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 95.5542 | 1.00583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.26608i | 0.0336710i | 0.999858 | + | 0.0168355i | \(0.00535916\pi\) | ||||
−0.999858 | + | 0.0168355i | \(0.994641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 22.5377i | − 0.227653i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 137.714 | 1.36351 | 0.681754 | − | 0.731582i | \(-0.261218\pi\) | ||||
0.681754 | + | 0.731582i | \(0.261218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 99.6787i | − 0.967754i | −0.875136 | − | 0.483877i | \(-0.839228\pi\) | ||||
0.875136 | − | 0.483877i | \(-0.160772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 94.0107i | 0.878605i | 0.898339 | + | 0.439302i | \(0.144774\pi\) | ||||
−0.898339 | + | 0.439302i | \(0.855226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 195.949i | 1.79770i | 0.438258 | + | 0.898849i | \(0.355595\pi\) | ||||
−0.438258 | + | 0.898849i | \(0.644405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 154.234i | − 1.38950i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 101.873 | 0.901527 | 0.450763 | − | 0.892643i | \(-0.351152\pi\) | ||||
0.450763 | + | 0.892643i | \(0.351152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 114.388 | 0.994679 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −48.1777 | −0.411775 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 107.707 | 0.890141 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 287.083i | 2.33401i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 252.449 | 2.01960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 139.079 | 1.09511 | 0.547554 | − | 0.836770i | \(-0.315559\pi\) | ||||
0.547554 | + | 0.836770i | \(0.315559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 159.166i | − 1.23385i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.7051 | 0.700039 | 0.350020 | − | 0.936742i | \(-0.386175\pi\) | ||||
0.350020 | + | 0.936742i | \(0.386175\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 97.2941 | 0.720697 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 199.581 | 1.45679 | 0.728397 | − | 0.685155i | \(-0.240266\pi\) | ||||
0.728397 | + | 0.685155i | \(0.240266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 39.4768 | 0.284006 | 0.142003 | − | 0.989866i | \(-0.454646\pi\) | ||||
0.142003 | + | 0.989866i | \(0.454646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 162.879i | − 1.15517i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 28.4158i | 0.198712i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152.676i | 1.05294i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.7831i | 0.636128i | 0.948069 | + | 0.318064i | \(0.103033\pi\) | ||||
−0.948069 | + | 0.318064i | \(0.896967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −66.5686 | −0.440852 | −0.220426 | − | 0.975404i | \(-0.570745\pi\) | ||||
−0.220426 | + | 0.975404i | \(0.570745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 64.7511i | 0.423210i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 267.826i | − 1.72791i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25.5194 | 0.162544 | 0.0812720 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812720 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 24.9823i | − 0.157122i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 192.101i | − 1.17853i | −0.807939 | − | 0.589267i | \(-0.799417\pi\) | ||||
0.807939 | − | 0.589267i | \(-0.200583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 125.860i | 0.762789i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 184.150i | 1.10269i | 0.834276 | + | 0.551346i | \(0.185886\pi\) | ||||
−0.834276 | + | 0.551346i | \(0.814114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −108.257 | −0.640574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 66.6697 | 0.389882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 69.9037 | 0.404068 | 0.202034 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202034 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 62.0098 | 0.350338 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 239.313i | − 1.33695i | −0.743736 | − | 0.668473i | \(-0.766948\pi\) | ||||
0.743736 | − | 0.668473i | \(-0.233052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 36.2834 | 0.200461 | 0.100230 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100230 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −47.3678 | −0.258840 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 350.705i | 1.89570i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 38.1910 | 0.204230 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 325.243 | 1.70284 | 0.851422 | − | 0.524481i | \(-0.175740\pi\) | ||||
0.851422 | + | 0.524481i | \(0.175740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 199.640 | 1.03440 | 0.517201 | − | 0.855864i | \(-0.326974\pi\) | ||||
0.517201 | + | 0.855864i | \(0.326974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 269.045 | 1.37972 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5053i | 0.0787071i | 0.999225 | + | 0.0393536i | \(0.0125299\pi\) | ||||
−0.999225 | + | 0.0393536i | \(0.987470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 56.1617i | − 0.282220i | −0.989994 | − | 0.141110i | \(-0.954933\pi\) | ||||
0.989994 | − | 0.141110i | \(-0.0450671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 30.3814i | − 0.151151i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 652.783i | − 3.18431i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 79.8104 | 0.385558 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 39.3226i | − 0.188147i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 370.470i | 1.75578i | 0.478859 | + | 0.877892i | \(0.341051\pi\) | ||||
−0.478859 | + | 0.877892i | \(0.658949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −161.164 | −0.756638 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 361.919i | 1.68335i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 349.149i | 1.59429i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 81.6390i | − 0.369407i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.78533i | 0.0304275i | 0.999884 | + | 0.0152137i | \(0.00484287\pi\) | ||||
−0.999884 | + | 0.0152137i | \(0.995157\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 330.677 | 1.46968 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 296.618 | 1.30669 | 0.653344 | − | 0.757061i | \(-0.273365\pi\) | ||||
0.653344 | + | 0.757061i | \(0.273365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −178.193 | −0.778135 | −0.389067 | − | 0.921209i | \(-0.627203\pi\) | ||||
−0.389067 | + | 0.921209i | \(0.627203\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 117.802 | 0.505589 | 0.252795 | − | 0.967520i | \(-0.418650\pi\) | ||||
0.252795 | + | 0.967520i | \(0.418650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 370.362i | 1.57601i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 275.842 | 1.16389 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −46.3543 | −0.193951 | −0.0969755 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969755 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 366.618i | − 1.52124i | −0.649199 | − | 0.760619i | \(-0.724896\pi\) | ||||
0.649199 | − | 0.760619i | \(-0.275104\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 284.653 | 1.17141 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.0581 | −0.340316 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −237.160 | −0.952452 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −129.896 | −0.517513 | −0.258756 | − | 0.965943i | \(-0.583313\pi\) | ||||
−0.258756 | + | 0.965943i | \(0.583313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 47.0732i | − 0.186060i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 361.598i | − 1.41803i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 268.345i | 1.04415i | 0.852901 | + | 0.522073i | \(0.174841\pi\) | ||||
−0.852901 | + | 0.522073i | \(0.825159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 106.525i | 0.408141i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 235.383 | 0.894991 | 0.447495 | − | 0.894286i | \(-0.352316\pi\) | ||||
0.447495 | + | 0.894286i | \(0.352316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 56.8059i | 0.214362i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 105.281i | 0.394311i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 354.695 | 1.31857 | 0.659285 | − | 0.751893i | \(-0.270859\pi\) | ||||
0.659285 | + | 0.751893i | \(0.270859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 421.870i | 1.55672i | 0.627820 | + | 0.778358i | \(0.283947\pi\) | ||||
−0.627820 | + | 0.778358i | \(0.716053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 195.037i | − 0.709226i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 368.529i | − 1.33043i | −0.746653 | − | 0.665214i | \(-0.768340\pi\) | ||||
0.746653 | − | 0.665214i | \(-0.231660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 186.866i | − 0.669772i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −35.2868 | −0.125576 | −0.0627879 | − | 0.998027i | \(-0.519999\pi\) | ||||
−0.0627879 | + | 0.998027i | \(0.519999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 196.617 | 0.694761 | 0.347380 | − | 0.937724i | \(-0.387071\pi\) | ||||
0.347380 | + | 0.937724i | \(0.387071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −372.313 | −1.30636 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 179.277 | 0.620335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 12.7258i | − 0.0437313i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −317.573 | −1.08387 | −0.541933 | − | 0.840421i | \(-0.682307\pi\) | ||||
−0.541933 | + | 0.840421i | \(0.682307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −141.001 | −0.477968 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 40.0386i | − 0.134810i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −100.626 | −0.336542 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −536.583 | −1.77090 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 107.707 | 0.353137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −132.193 | −0.430596 | −0.215298 | − | 0.976548i | \(-0.569072\pi\) | ||||
−0.215298 | + | 0.976548i | \(0.569072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 388.383i | 1.25690i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 462.404i | 1.48683i | 0.668831 | + | 0.743414i | \(0.266795\pi\) | ||||
−0.668831 | + | 0.743414i | \(0.733205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 566.042i | − 1.80844i | −0.427067 | − | 0.904220i | \(-0.640453\pi\) | ||||
0.427067 | − | 0.904220i | \(-0.359547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 177.033i | 0.558463i | 0.960224 | + | 0.279231i | \(0.0900796\pi\) | ||||
−0.960224 | + | 0.279231i | \(0.909920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 62.8296 | 0.196958 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 366.299i | − 1.14112i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 112.975i | 0.349766i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −416.922 | −1.28284 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 763.486i | − 2.33482i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 496.160i | 1.49897i | 0.662019 | + | 0.749487i | \(0.269700\pi\) | ||||
−0.662019 | + | 0.749487i | \(0.730300\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 244.693i | 0.734813i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 69.0825i | 0.206216i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −206.191 | −0.611843 | −0.305922 | − | 0.952057i | \(-0.598965\pi\) | ||||
−0.305922 | + | 0.952057i | \(0.598965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −396.931 | −1.17089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −110.216 | −0.323214 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −445.696 | −1.29187 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 606.190i | − 1.74694i | −0.486874 | − | 0.873472i | \(-0.661863\pi\) | ||||
0.486874 | − | 0.873472i | \(-0.338137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −136.343 | −0.390669 | −0.195335 | − | 0.980737i | \(-0.562579\pi\) | ||||
−0.195335 | + | 0.980737i | \(0.562579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −85.5887 | −0.243842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0743i | 0.0285390i | 0.999898 | + | 0.0142695i | \(0.00454228\pi\) | ||||
−0.999898 | + | 0.0142695i | \(0.995458\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 366.461 | 1.03229 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −395.616 | −1.10199 | −0.550997 | − | 0.834507i | \(-0.685752\pi\) | ||||
−0.550997 | + | 0.834507i | \(0.685752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −244.678 | −0.677778 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −419.664 | −1.15610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 793.909i | − 2.17509i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 189.932i | 0.517526i | 0.965941 | + | 0.258763i | \(0.0833149\pi\) | ||||
−0.965941 | + | 0.258763i | \(0.916685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 455.457i | − 1.23430i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 360.104i | 0.965425i | 0.875779 | + | 0.482713i | \(0.160348\pi\) | ||||
−0.875779 | + | 0.482713i | \(0.839652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −983.631 | −2.62302 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 134.308i | − 0.356254i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.2929i | − 0.0297966i | −0.999889 | − | 0.0148983i | \(-0.995258\pi\) | ||||
0.999889 | − | 0.0148983i | \(-0.00474246\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −541.900 | −1.42231 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 434.253i | − 1.13382i | −0.823779 | − | 0.566910i | \(-0.808139\pi\) | ||||
0.823779 | − | 0.566910i | \(-0.191861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 252.517i | 0.652499i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 43.1631i | 0.110959i | 0.998460 | + | 0.0554796i | \(0.0176688\pi\) | ||||
−0.998460 | + | 0.0554796i | \(0.982331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 135.242i | 0.345887i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −357.315 | −0.909199 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −627.222 | −1.58790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 486.790 | 1.22617 | 0.613086 | − | 0.790016i | \(-0.289928\pi\) | ||||
0.613086 | + | 0.790016i | \(0.289928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −546.914 | −1.36388 | −0.681938 | − | 0.731410i | \(-0.738862\pi\) | ||||
−0.681938 | + | 0.731410i | \(0.738862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 235.603i | 0.584624i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −871.992 | −2.15307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 144.323 | 0.354601 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 66.7668i | − 0.163244i | −0.996663 | − | 0.0816220i | \(-0.973990\pi\) | ||||
0.996663 | − | 0.0816220i | \(-0.0260100\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −777.637 | −1.89206 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 539.266 | 1.29944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −153.815 | −0.368862 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −550.169 | −1.31305 | −0.656527 | − | 0.754303i | \(-0.727975\pi\) | ||||
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 579.599i | 1.37672i | 0.725369 | + | 0.688360i | \(0.241669\pi\) | ||||
−0.725369 | + | 0.688360i | \(0.758331\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 258.408i | 0.610893i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 560.345i | 1.31846i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 110.718i | − 0.258084i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 431.870 | 1.00202 | 0.501009 | − | 0.865442i | \(-0.332962\pi\) | ||||
0.501009 | + | 0.865442i | \(0.332962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 0.143463i | 0 0.000331322i | −1.00000 | 0.000165661i | \(-0.999947\pi\) | |||||
1.00000 | 0.000165661i | \(-5.27316e-5\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 594.881i | − 1.36754i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 139.249 | 0.318648 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 191.349i | 0.435874i | 0.975963 | + | 0.217937i | \(0.0699328\pi\) | ||||
−0.975963 | + | 0.217937i | \(0.930067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 393.501i | − 0.888265i | −0.895961 | − | 0.444133i | \(-0.853512\pi\) | ||||
0.895961 | − | 0.444133i | \(-0.146488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 239.393i | − 0.537961i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 369.308i | − 0.826193i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −725.831 | −1.61655 | −0.808275 | − | 0.588805i | \(-0.799598\pi\) | ||||
−0.808275 | + | 0.588805i | \(0.799598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −268.634 | −0.595641 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 259.375 | 0.572571 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −69.3427 | −0.151735 | −0.0758673 | − | 0.997118i | \(-0.524173\pi\) | ||||
−0.0758673 | + | 0.997118i | \(0.524173\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 115.032i | 0.250614i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 768.006 | 1.66596 | 0.832978 | − | 0.553306i | \(-0.186634\pi\) | ||||
0.832978 | + | 0.553306i | \(0.186634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −215.717 | −0.465911 | −0.232956 | − | 0.972487i | \(-0.574840\pi\) | ||||
−0.232956 | + | 0.972487i | \(0.574840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1043.54i | 2.24418i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9376 | 0.0619648 | 0.0309824 | − | 0.999520i | \(-0.490136\pi\) | ||||
0.0309824 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −99.4325 | −0.211109 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 148.938 | 0.314879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 576.949 | 1.21463 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 39.6344i | 0.0830911i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 802.952i | − 1.67631i | −0.545433 | − | 0.838154i | \(-0.683635\pi\) | ||||
0.545433 | − | 0.838154i | \(-0.316365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 308.512i | − 0.641396i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.9365i | 0.0596629i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9239 | −0.0409116 | −0.0204558 | − | 0.999791i | \(-0.506512\pi\) | ||||
−0.0204558 | + | 0.999791i | \(0.506512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 748.493i | 1.53066i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 76.2017i | − 0.155197i | −0.996985 | − | 0.0775985i | \(-0.975275\pi\) | ||||
0.996985 | − | 0.0775985i | \(-0.0247252\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −180.510 | −0.366147 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 199.677i | − 0.403387i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 522.871i | − 1.04784i | −0.851768 | − | 0.523919i | \(-0.824470\pi\) | ||||
0.851768 | − | 0.523919i | \(-0.175530\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 717.512i | − 1.43216i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 132.060i | 0.262545i | 0.991346 | + | 0.131273i | \(0.0419064\pi\) | ||||
−0.991346 | + | 0.131273i | \(0.958094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1220.11 | 2.41605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 421.807 | 0.831967 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 310.157 | 0.609346 | 0.304673 | − | 0.952457i | \(-0.401453\pi\) | ||||
0.304673 | + | 0.952457i | \(0.401453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 118.440 | 0.230878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 883.122i | − 1.71480i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 152.412 | 0.294801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −272.369 | −0.524797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 61.0976i | − 0.117270i | −0.998279 | − | 0.0586349i | \(-0.981325\pi\) | ||||
0.998279 | − | 0.0586349i | \(-0.0186748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 513.846 | 0.982497 | 0.491249 | − | 0.871019i | \(-0.336541\pi\) | ||||
0.491249 | + | 0.871019i | \(0.336541\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 316.652 | 0.600858 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −362.304 | −0.684886 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −98.3784 | −0.185270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 574.246i | 1.07739i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 832.906i | 1.55683i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 932.449i | 1.73640i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 107.078i | − 0.197926i | −0.995091 | − | 0.0989630i | \(-0.968447\pi\) | ||||
0.995091 | − | 0.0989630i | \(-0.0315525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −141.373 | −0.260355 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1736.05i | 3.18541i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.3240i | 0.0792030i | 0.999216 | + | 0.0396015i | \(0.0126088\pi\) | ||||
−0.999216 | + | 0.0396015i | \(0.987391\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 75.1489 | 0.136883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 185.859i | 0.337313i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1366.47i | − 2.46211i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 72.5011i | 0.130164i | 0.997880 | + | 0.0650818i | \(0.0207308\pi\) | ||||
−0.997880 | + | 0.0650818i | \(0.979269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 318.377i | − 0.569547i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −148.805 | −0.265250 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −584.943 | −1.03897 | −0.519487 | − | 0.854478i | \(-0.673877\pi\) | ||||
−0.519487 | + | 0.854478i | \(0.673877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 902.559 | 1.59745 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 743.529 | 1.30673 | 0.653365 | − | 0.757043i | \(-0.273357\pi\) | ||||
0.653365 | + | 0.757043i | \(0.273357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1032.06i | − 1.80747i | −0.428097 | − | 0.903733i | \(-0.640816\pi\) | ||||
0.428097 | − | 0.903733i | \(-0.359184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1267.26 | −2.21163 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 690.666 | 1.20116 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 953.094i | 1.65181i | 0.563810 | + | 0.825905i | \(0.309335\pi\) | ||||
−0.563810 | + | 0.825905i | \(0.690665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −777.866 | −1.34346 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.3769 | 0.0400976 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −426.839 | −0.729640 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −96.2876 | −0.164033 | −0.0820167 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820167 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 326.035i | − 0.553540i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 60.4141i | − 0.102224i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 51.0193i | 0.0860358i | 0.999074 | + | 0.0430179i | \(0.0136973\pi\) | ||||
−0.999074 | + | 0.0430179i | \(0.986303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 218.826i | 0.366542i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −902.236 | −1.50624 | −0.753119 | − | 0.657885i | \(-0.771451\pi\) | ||||
−0.753119 | + | 0.657885i | \(0.771451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 903.595i | − 1.50349i | −0.659456 | − | 0.751743i | \(-0.729213\pi\) | ||||
0.659456 | − | 0.751743i | \(-0.270787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 48.2000i | 0.0799337i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 954.251 | 1.57727 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 354.410i | 0.583872i | 0.956438 | + | 0.291936i | \(0.0942994\pi\) | ||||
−0.956438 | + | 0.291936i | \(0.905701\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 325.804i | − 0.533230i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 335.999i | − 0.548123i | −0.961712 | − | 0.274061i | \(-0.911633\pi\) | ||||
0.961712 | − | 0.274061i | \(-0.0883671\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2543.47i | 4.13573i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 223.359 | 0.362008 | 0.181004 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181004 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −726.053 | −1.17294 | −0.586472 | − | 0.809969i | \(-0.699484\pi\) | ||||
−0.586472 | + | 0.809969i | \(0.699484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 141.785 | 0.228317 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 899.270 | 1.43883 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 153.215i | 0.244362i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −414.642 | −0.659208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 326.157 | 0.516888 | 0.258444 | − | 0.966026i | \(-0.416790\pi\) | ||||
0.258444 | + | 0.966026i | \(0.416790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1443.48i | − 2.28038i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1232.19 | 1.94046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 255.686 | 0.400135 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −598.375 | −0.933502 | −0.466751 | − | 0.884389i | \(-0.654576\pi\) | ||||
−0.466751 | + | 0.884389i | \(0.654576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1008.20 | 1.56796 | 0.783979 | − | 0.620787i | \(-0.213187\pi\) | ||||
0.783979 | + | 0.620787i | \(0.213187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1410.16i | − 2.18630i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 663.235i | 1.02509i | 0.858660 | + | 0.512546i | \(0.171298\pi\) | ||||
−0.858660 | + | 0.512546i | \(0.828702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.0248i | 0.0894064i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 990.608i | − 1.51701i | −0.651666 | − | 0.758506i | \(-0.725930\pi\) | ||||
0.651666 | − | 0.758506i | \(-0.274070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 812.479 | 1.24043 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 553.924i | − 0.843110i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 82.2318i | − 0.124783i | −0.998052 | − | 0.0623914i | \(-0.980127\pi\) | ||||
0.998052 | − | 0.0623914i | \(-0.0198727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −626.220 | −0.947382 | −0.473691 | − | 0.880691i | \(-0.657079\pi\) | ||||
−0.473691 | + | 0.880691i | \(0.657079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 318.094i | 0.479780i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 222.492i | 0.333572i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 26.4380i | − 0.0395187i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 44.3237i | − 0.0660562i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −150.211 | −0.223196 | −0.111598 | − | 0.993753i | \(-0.535597\pi\) | ||||
−0.111598 | + | 0.993753i | \(0.535597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 587.455 | 0.870303 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −556.414 | −0.821882 | −0.410941 | − | 0.911662i | \(-0.634800\pi\) | ||||
−0.410941 | + | 0.911662i | \(0.634800\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1155.73 | −1.69711 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 791.356i | 1.15865i | 0.815098 | + | 0.579323i | \(0.196683\pi\) | ||||
−0.815098 | + | 0.579323i | \(0.803317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1768.22 | 2.58135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 694.302 | 1.01063 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 49.9716i | − 0.0725277i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −976.534 | −1.41322 | −0.706609 | − | 0.707604i | \(-0.749776\pi\) | ||||
−0.706609 | + | 0.707604i | \(0.749776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 349.752 | 0.503241 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 771.790 | 1.10730 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −458.999 | −0.656651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 855.098i | 1.21983i | 0.792468 | + | 0.609913i | \(0.208796\pi\) | ||||
−0.792468 | + | 0.609913i | \(0.791204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 426.928i | 0.607294i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 1443.06i | − 2.04689i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 333.471i | 0.470340i | 0.971954 | + | 0.235170i | \(0.0755647\pi\) | ||||
−0.971954 | + | 0.235170i | \(0.924435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −437.623 | −0.615504 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 390.297i | − 0.547401i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 251.755i | 0.352105i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 180.613 | 0.251900 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.8230i | 0.0553866i | 0.999616 | + | 0.0276933i | \(0.00881618\pi\) | ||||
−0.999616 | + | 0.0276933i | \(0.991184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1428.47i | 1.97576i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 921.848i | 1.27151i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 489.402i | − 0.673180i | −0.941651 | − | 0.336590i | \(-0.890726\pi\) | ||||
0.941651 | − | 0.336590i | \(-0.109274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −223.307 | −0.306320 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −427.900 | −0.585363 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 178.318 | 0.243272 | 0.121636 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121636 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.4289 | 0.0385739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 882.401i | 1.19405i | 0.802224 | + | 0.597024i | \(0.203650\pi\) | ||||
−0.802224 | + | 0.597024i | \(0.796350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 327.520 | 0.441997 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1404.00 | −1.88964 | −0.944819 | − | 0.327591i | \(-0.893763\pi\) | ||||
−0.944819 | + | 0.327591i | \(0.893763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 839.749i | 1.12718i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 376.255 | 0.503687 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −205.680 | −0.273875 | −0.136938 | − | 0.990580i | \(-0.543726\pi\) | ||||
−0.136938 | + | 0.990580i | \(0.543726\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 506.119 | 0.672137 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −589.777 | −0.781162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0345i | 0.0198606i | 0.999951 | + | 0.00993032i | \(0.00316097\pi\) | ||||
−0.999951 | + | 0.00993032i | \(0.996839\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 183.414i | 0.241652i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 628.491i | − 0.825876i | −0.910759 | − | 0.412938i | \(-0.864503\pi\) | ||||
0.910759 | − | 0.412938i | \(-0.135497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 573.675i | 0.749901i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 124.037 | 0.161717 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 442.918i | − 0.575967i | −0.957635 | − | 0.287983i | \(-0.907015\pi\) | ||||
0.957635 | − | 0.287983i | \(-0.0929848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1045.57i | − 1.35612i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −169.198 | −0.218885 | −0.109442 | − | 0.993993i | \(-0.534907\pi\) | ||||
−0.109442 | + | 0.993993i | \(0.534907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1617.11i | − 2.08659i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 794.660i | − 1.02010i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 150.807i | − 0.193094i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 189.244i | 0.241690i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 226.094 | 0.288018 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.4874 | 0.0590691 | 0.0295346 | − | 0.999564i | \(-0.490597\pi\) | ||||
0.0295346 | + | 0.999564i | \(0.490597\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −917.133 | −1.16240 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −94.7487 | −0.119481 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 221.336i | − 0.278410i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1351.86 | −1.69618 | −0.848092 | − | 0.529850i | \(-0.822248\pi\) | ||||
−0.848092 | + | 0.529850i | \(0.822248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −437.882 | −0.548038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 167.028i | − 0.208525i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −326.711 | −0.406863 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1382.02 | −1.71254 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1403.13 | −1.73440 | −0.867198 | − | 0.497963i | \(-0.834081\pi\) | ||||
−0.867198 | + | 0.497963i | \(0.834081\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 689.037 | 0.849614 | 0.424807 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424807 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1643.75i | − 2.02184i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1701.95i | − 2.08829i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 440.579i | 0.539265i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3423i | 0.0272135i | 0.999907 | + | 0.0136067i | \(0.00433129\pi\) | ||||
−0.999907 | + | 0.0136067i | \(0.995669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1024.22 | −1.24450 | −0.622249 | − | 0.782819i | \(-0.713781\pi\) | ||||
−0.622249 | + | 0.782819i | \(0.713781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 759.934i | 0.921132i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 466.377i | − 0.563938i | −0.959424 | − | 0.281969i | \(-0.909012\pi\) | ||||
0.959424 | − | 0.281969i | \(-0.0909875\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1500.70 | −1.81025 | −0.905126 | − | 0.425142i | \(-0.860224\pi\) | ||||
−0.905126 | + | 0.425142i | \(0.860224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1435.92i | 1.72794i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1631.51i | 1.95390i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 331.972i | − 0.396621i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1068.18i | − 1.27316i | −0.771212 | − | 0.636579i | \(-0.780349\pi\) | ||||
0.771212 | − | 0.636579i | \(-0.219651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 544.034 | 0.646890 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 137.490 | 0.163096 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −959.123 | −1.13506 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −766.090 | −0.902344 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 511.076i | 0.600559i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −918.640 | −1.07695 | −0.538476 | − | 0.842641i | \(-0.681000\pi\) | ||||
−0.538476 | + | 0.842641i | \(0.681000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 590.673 | 0.690846 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 505.952i | 0.590375i | 0.955439 | + | 0.295188i | \(0.0953822\pi\) | ||||
−0.955439 | + | 0.295188i | \(0.904618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1377.03 | 1.60306 | 0.801532 | − | 0.597952i | \(-0.204019\pi\) | ||||
0.801532 | + | 0.597952i | \(0.204019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −917.635 | −1.06331 | −0.531654 | − | 0.846962i | \(-0.678429\pi\) | ||||
−0.531654 | + | 0.846962i | \(0.678429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 619.325 | 0.715983 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −698.525 | −0.805681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 258.116i | 0.297026i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 60.7712i | − 0.0697717i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.1895i | 0.0231265i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 699.948i | 0.798116i | 0.916926 | + | 0.399058i | \(0.130663\pi\) | ||||
−0.916926 | + | 0.399058i | \(0.869337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1237.38 | 1.40771 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.37652i | 0.00723783i | 0.999993 | + | 0.00361891i | \(0.00115194\pi\) | ||||
−0.999993 | + | 0.00361891i | \(0.998848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1548.35i | 1.75351i | 0.480935 | + | 0.876756i | \(0.340297\pi\) | ||||
−0.480935 | + | 0.876756i | \(0.659703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 549.388 | 0.620777 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 732.369i | − 0.825670i | −0.910806 | − | 0.412835i | \(-0.864539\pi\) | ||||
0.910806 | − | 0.412835i | \(-0.135461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 358.844i | 0.402743i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 450.857i | 0.504879i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2120.24i | − 2.36899i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 392.074 | 0.437095 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 520.938 | 0.579464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −67.1621 | −0.0745418 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 321.459 | 0.355204 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 723.838i | − 0.798057i | −0.916939 | − | 0.399029i | \(-0.869347\pi\) | ||||
0.916939 | − | 0.399029i | \(-0.130653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 851.288 | 0.936511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1600.04 | −1.75636 | −0.878179 | − | 0.478332i | \(-0.841242\pi\) | ||||
−0.878179 | + | 0.478332i | \(0.841242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 221.920i | − 0.243066i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −419.664 | −0.458649 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 524.085 | 0.570277 | 0.285139 | − | 0.958486i | \(-0.407960\pi\) | ||||
0.285139 | + | 0.958486i | \(0.407960\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 515.070 | 0.559251 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −322.372 | −0.349266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2117.53i | 2.28922i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 616.169i | − 0.664691i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 637.154i | 0.685849i | 0.939363 | + | 0.342924i | \(0.111417\pi\) | ||||
−0.939363 | + | 0.342924i | \(0.888583\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1801.69i | − 1.93107i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 338.360 | 0.361883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 383.587i | 0.409378i | 0.978827 | + | 0.204689i | \(0.0656182\pi\) | ||||
−0.978827 | + | 0.204689i | \(0.934382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2205.50i | 2.34877i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −260.591 | −0.276930 | −0.138465 | − | 0.990367i | \(-0.544217\pi\) | ||||
−0.138465 | + | 0.990367i | \(0.544217\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 951.288i | − 1.00879i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 983.163i | 1.03819i | 0.854717 | + | 0.519093i | \(0.173730\pi\) | ||||
−0.854717 | + | 0.519093i | \(0.826270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 698.394i | 0.735926i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 689.781i | − 0.725322i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1137.60 | −1.19370 | −0.596851 | − | 0.802352i | \(-0.703582\pi\) | ||||
−0.596851 | + | 0.802352i | \(0.703582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2881.56 | 3.01734 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −244.806 | −0.255806 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.1670 | 0.0490812 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 581.132i | 0.603460i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1768.75 | 1.83290 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1296.35 | 1.34059 | 0.670297 | − | 0.742093i | \(-0.266167\pi\) | ||||
0.670297 | + | 0.742093i | \(0.266167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 440.188i | − 0.454271i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1330.47 | −1.37021 | −0.685105 | − | 0.728445i | \(-0.740244\pi\) | ||||
−0.685105 | + | 0.728445i | \(0.740244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1624.47 | 1.66613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1386.16 | 1.41879 | 0.709397 | − | 0.704809i | \(-0.248967\pi\) | ||||
0.709397 | + | 0.704809i | \(0.248967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98.5153 | −0.100629 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1211.27i | 1.23473i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 694.161i | − 0.706166i | −0.935592 | − | 0.353083i | \(-0.885133\pi\) | ||||
0.935592 | − | 0.353083i | \(-0.114867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 137.372i | 0.139464i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 527.418i | 0.533284i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 934.514 | 0.943001 | 0.471500 | − | 0.881866i | \(-0.343713\pi\) | ||||
0.471500 | + | 0.881866i | \(0.343713\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1933.22i | − 1.94684i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 497.576i | − 0.500076i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1538.21 | 1.54283 | 0.771417 | − | 0.636330i | \(-0.219548\pi\) | ||||
0.771417 | + | 0.636330i | \(0.219548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 434.702i | 0.435137i |
(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 | 1568.3.h.a.881.3 | 28 | ||
4.3 | odd | 2 | 392.3.h.a.293.18 | 28 | |||
7.2 | even | 3 | 224.3.n.a.17.13 | 28 | |||
7.3 | odd | 6 | 224.3.n.a.145.2 | 28 | |||
7.6 | odd | 2 | inner | 1568.3.h.a.881.25 | 28 | ||
8.3 | odd | 2 | 392.3.h.a.293.19 | 28 | |||
8.5 | even | 2 | inner | 1568.3.h.a.881.26 | 28 | ||
28.3 | even | 6 | 56.3.j.a.5.10 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.117.10 | 28 | |||
28.19 | even | 6 | 392.3.j.e.325.1 | 28 | |||
28.23 | odd | 6 | 56.3.j.a.45.1 | yes | 28 | ||
28.27 | even | 2 | 392.3.h.a.293.17 | 28 | |||
56.3 | even | 6 | 56.3.j.a.5.1 | ✓ | 28 | ||
56.11 | odd | 6 | 392.3.j.e.117.1 | 28 | |||
56.13 | odd | 2 | inner | 1568.3.h.a.881.4 | 28 | ||
56.19 | even | 6 | 392.3.j.e.325.10 | 28 | |||
56.27 | even | 2 | 392.3.h.a.293.20 | 28 | |||
56.37 | even | 6 | 224.3.n.a.17.2 | 28 | |||
56.45 | odd | 6 | 224.3.n.a.145.13 | 28 | |||
56.51 | odd | 6 | 56.3.j.a.45.10 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.1 | ✓ | 28 | 56.3 | even | 6 | ||
56.3.j.a.5.10 | yes | 28 | 28.3 | even | 6 | ||
56.3.j.a.45.1 | yes | 28 | 28.23 | odd | 6 | ||
56.3.j.a.45.10 | yes | 28 | 56.51 | odd | 6 | ||
224.3.n.a.17.2 | 28 | 56.37 | even | 6 | |||
224.3.n.a.17.13 | 28 | 7.2 | even | 3 | |||
224.3.n.a.145.2 | 28 | 7.3 | odd | 6 | |||
224.3.n.a.145.13 | 28 | 56.45 | odd | 6 | |||
392.3.h.a.293.17 | 28 | 28.27 | even | 2 | |||
392.3.h.a.293.18 | 28 | 4.3 | odd | 2 | |||
392.3.h.a.293.19 | 28 | 8.3 | odd | 2 | |||
392.3.h.a.293.20 | 28 | 56.27 | even | 2 | |||
392.3.j.e.117.1 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.117.10 | 28 | 28.11 | odd | 6 | |||
392.3.j.e.325.1 | 28 | 28.19 | even | 6 | |||
392.3.j.e.325.10 | 28 | 56.19 | even | 6 | |||
1568.3.h.a.881.3 | 28 | 1.1 | even | 1 | trivial | ||
1568.3.h.a.881.4 | 28 | 56.13 | odd | 2 | inner | ||
1568.3.h.a.881.25 | 28 | 7.6 | odd | 2 | inner | ||
1568.3.h.a.881.26 | 28 | 8.5 | even | 2 | inner |