Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(2735,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2736.2735");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2735.15 | ||
Character | \(\chi\) | \(=\) | 2736.2735 |
Dual form | 2736.3.b.e.2735.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.60057i | − | 1.12011i | −0.828454 | − | 0.560057i | \(-0.810779\pi\) | ||
0.828454 | − | 0.560057i | \(-0.189221\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.03549i | − | 0.290784i | −0.989374 | − | 0.145392i | \(-0.953556\pi\) | ||
0.989374 | − | 0.145392i | \(-0.0464444\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.92287 | −0.174807 | −0.0874033 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874033 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.11778i | 0.393675i | 0.980436 | + | 0.196838i | \(0.0630672\pi\) | ||||
−0.980436 | + | 0.196838i | \(0.936933\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.3173i | 1.01867i | 0.860569 | + | 0.509333i | \(0.170108\pi\) | ||||
−0.860569 | + | 0.509333i | \(0.829892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.8026 | − | 2.73143i | −0.989613 | − | 0.143760i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.7178 | 1.24860 | 0.624301 | − | 0.781184i | \(-0.285384\pi\) | ||||
0.624301 | + | 0.781184i | \(0.285384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.36637 | −0.254655 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.2559 | −0.767446 | −0.383723 | − | 0.923448i | \(-0.625358\pi\) | ||||
−0.383723 | + | 0.923448i | \(0.625358\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.4633 | 0.595592 | 0.297796 | − | 0.954630i | \(-0.403748\pi\) | ||||
0.297796 | + | 0.954630i | \(0.403748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.3999 | −0.325711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 63.4541i | − | 1.71498i | −0.514504 | − | 0.857488i | \(-0.672024\pi\) | ||
0.514504 | − | 0.857488i | \(-0.327976\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −46.0569 | −1.12334 | −0.561669 | − | 0.827362i | \(-0.689841\pi\) | ||||
−0.561669 | + | 0.827362i | \(0.689841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.5390i | 0.384629i | 0.981333 | + | 0.192314i | \(0.0615993\pi\) | ||||
−0.981333 | + | 0.192314i | \(0.938401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −57.8149 | −1.23010 | −0.615052 | − | 0.788486i | \(-0.710865\pi\) | ||||
−0.615052 | + | 0.788486i | \(0.710865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.8568 | 0.915445 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −84.0450 | −1.58576 | −0.792878 | − | 0.609381i | \(-0.791418\pi\) | ||||
−0.792878 | + | 0.609381i | \(0.791418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7692i | 0.195803i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 117.362i | 1.98918i | 0.103880 | + | 0.994590i | \(0.466874\pi\) | ||||
−0.103880 | + | 0.994590i | \(0.533126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.7069 | −1.56896 | −0.784482 | − | 0.620151i | \(-0.787071\pi\) | ||||
−0.784482 | + | 0.620151i | \(0.787071\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28.6625 | 0.440961 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −84.1311 | −1.25569 | −0.627844 | − | 0.778339i | \(-0.716062\pi\) | ||||
−0.627844 | + | 0.778339i | \(0.716062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 50.6045i | − | 0.712740i | −0.934345 | − | 0.356370i | \(-0.884014\pi\) | ||
0.934345 | − | 0.356370i | \(-0.115986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29031 | 0.0450727 | 0.0225364 | − | 0.999746i | \(-0.492826\pi\) | ||||
0.0225364 | + | 0.999746i | \(0.492826\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.91399i | 0.0508310i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −25.0961 | −0.317672 | −0.158836 | − | 0.987305i | \(-0.550774\pi\) | ||||
−0.158836 | + | 0.987305i | \(0.550774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 119.982 | 1.44557 | 0.722785 | − | 0.691073i | \(-0.242862\pi\) | ||||
0.722785 | + | 0.691073i | \(0.242862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.9869 | 1.14102 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −53.2945 | −0.598815 | −0.299407 | − | 0.954125i | \(-0.596789\pi\) | ||||
−0.299407 | + | 0.954125i | \(0.596789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4172 | 0.114475 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.2976 | + | 105.305i | −0.161027 | + | 1.10848i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.9959i | 0.948412i | 0.880414 | + | 0.474206i | \(0.157265\pi\) | ||||
−0.880414 | + | 0.474206i | \(0.842735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.8113i | 0.176349i | 0.996105 | + | 0.0881746i | \(0.0281033\pi\) | ||||
−0.996105 | + | 0.0881746i | \(0.971897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 165.918 | 1.61086 | 0.805428 | − | 0.592694i | \(-0.201936\pi\) | ||||
0.805428 | + | 0.592694i | \(0.201936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4956i | 0.126127i | 0.998010 | + | 0.0630636i | \(0.0200871\pi\) | ||||
−0.998010 | + | 0.0630636i | \(0.979913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 165.686i | 1.52005i | 0.649893 | + | 0.760026i | \(0.274814\pi\) | ||||
−0.649893 | + | 0.760026i | \(0.725186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −121.607 | −1.07617 | −0.538086 | − | 0.842890i | \(-0.680852\pi\) | ||||
−0.538086 | + | 0.842890i | \(0.680852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 160.836i | − | 1.39858i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.2493 | 0.296212 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.303 | −0.969443 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 104.359i | − | 0.834871i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.455 | 0.806732 | 0.403366 | − | 0.915039i | \(-0.367840\pi\) | ||||
0.403366 | + | 0.915039i | \(0.367840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −72.6073 | −0.554254 | −0.277127 | − | 0.960833i | \(-0.589382\pi\) | ||||
−0.277127 | + | 0.960833i | \(0.589382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.55980 | + | 38.2726i | −0.0418030 | + | 0.287764i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 76.2677i | 0.556698i | 0.960480 | + | 0.278349i | \(0.0897872\pi\) | ||||
−0.960480 | + | 0.278349i | \(0.910213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 124.076i | 0.892635i | 0.894875 | + | 0.446318i | \(0.147265\pi\) | ||||
−0.894875 | + | 0.446318i | \(0.852735\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 9.84085i | − | 0.0688171i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 124.646i | 0.859627i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 129.953i | 0.872169i | 0.899906 | + | 0.436085i | \(0.143635\pi\) | ||||
−0.899906 | + | 0.436085i | \(0.856365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 249.910 | 1.65503 | 0.827515 | − | 0.561443i | \(-0.189754\pi\) | ||||
0.827515 | + | 0.561443i | \(0.189754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 103.405i | − | 0.667131i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 190.291 | 1.21204 | 0.606021 | − | 0.795449i | \(-0.292765\pi\) | ||||
0.606021 | + | 0.795449i | \(0.292765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 58.4548i | − | 0.363074i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82.9371i | 0.508816i | 0.967097 | + | 0.254408i | \(0.0818807\pi\) | ||||
−0.967097 | + | 0.254408i | \(0.918119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 168.465i | 1.00877i | 0.863478 | + | 0.504386i | \(0.168281\pi\) | ||||
−0.863478 | + | 0.504386i | \(0.831719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.808 | 0.845020 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −49.1469 | −0.284086 | −0.142043 | − | 0.989860i | \(-0.545367\pi\) | ||||
−0.142043 | + | 0.989860i | \(0.545367\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.9587i | 0.0740496i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 180.041i | 1.00582i | 0.864339 | + | 0.502909i | \(0.167737\pi\) | ||||
−0.864339 | + | 0.502909i | \(0.832263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 175.436i | 0.969262i | 0.874719 | + | 0.484631i | \(0.161046\pi\) | ||||
−0.874719 | + | 0.484631i | \(0.838954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −355.379 | −1.92097 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 33.2990i | − | 0.178070i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −107.606 | −0.563382 | −0.281691 | − | 0.959505i | \(-0.590895\pi\) | ||||
−0.281691 | + | 0.959505i | \(0.590895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 142.932i | 0.740581i | 0.928916 | + | 0.370290i | \(0.120742\pi\) | ||||
−0.928916 | + | 0.370290i | \(0.879258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 250.495i | 1.27155i | 0.771875 | + | 0.635775i | \(0.219319\pi\) | ||||
−0.771875 | + | 0.635775i | \(0.780681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 297.036i | − | 1.49264i | −0.665586 | − | 0.746321i | \(-0.731818\pi\) | ||
0.665586 | − | 0.746321i | \(-0.268182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 45.3017i | 0.223161i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 257.945i | 1.25827i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36.1551 | + | 5.25220i | 0.172991 | + | 0.0251301i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 138.786 | 0.657755 | 0.328877 | − | 0.944373i | \(-0.393330\pi\) | ||||
0.328877 | + | 0.944373i | \(0.393330\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 92.6280 | 0.430828 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 37.5820i | − | 0.173189i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −88.6263 | −0.401024 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6702 | −0.0568169 | −0.0284084 | − | 0.999596i | \(-0.509044\pi\) | ||||
−0.0284084 | + | 0.999596i | \(0.509044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 94.4859i | 0.416237i | 0.978104 | + | 0.208119i | \(0.0667340\pi\) | ||||
−0.978104 | + | 0.208119i | \(0.933266\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −278.839 | −1.21764 | −0.608820 | − | 0.793309i | \(-0.708357\pi\) | ||||
−0.608820 | + | 0.793309i | \(0.708357\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 228.437i | − | 0.980416i | −0.871605 | − | 0.490208i | \(-0.836921\pi\) | ||
0.871605 | − | 0.490208i | \(-0.163079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 323.796i | 1.37786i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 373.960 | 1.56469 | 0.782344 | − | 0.622847i | \(-0.214024\pi\) | ||||
0.782344 | + | 0.622847i | \(0.214024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 176.349i | 0.731737i | 0.930667 | + | 0.365869i | \(0.119228\pi\) | ||||
−0.930667 | + | 0.365869i | \(0.880772\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 251.224i | − | 1.02540i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.9789 | − | 96.2278i | 0.0565946 | − | 0.389586i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −135.240 | −0.538804 | −0.269402 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269402 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −55.2207 | −0.218264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −309.723 | −1.20515 | −0.602574 | − | 0.798063i | \(-0.705858\pi\) | ||||
−0.602574 | + | 0.798063i | \(0.705858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −129.160 | −0.498688 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −141.881 | −0.539472 | −0.269736 | − | 0.962934i | \(-0.586936\pi\) | ||||
−0.269736 | + | 0.962934i | \(0.586936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 470.700i | 1.77623i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −105.620 | −0.392640 | −0.196320 | − | 0.980540i | \(-0.562899\pi\) | ||||
−0.196320 | + | 0.980540i | \(0.562899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 302.476i | 1.11615i | 0.829792 | + | 0.558074i | \(0.188459\pi\) | ||||
−0.829792 | + | 0.558074i | \(0.811541\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2417 | 0.0445154 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 282.695 | 1.02056 | 0.510281 | − | 0.860008i | \(-0.329542\pi\) | ||||
0.510281 | + | 0.860008i | \(0.329542\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 40.2186 | 0.143127 | 0.0715634 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715634 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 500.954i | − | 1.77016i | −0.465443 | − | 0.885078i | \(-0.654105\pi\) | ||
0.465443 | − | 0.885078i | \(-0.345895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 93.7483i | 0.326649i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8901 | −0.0376819 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −434.359 | −1.48245 | −0.741226 | − | 0.671255i | \(-0.765755\pi\) | ||||
−0.741226 | + | 0.671255i | \(0.765755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 657.292 | 2.22811 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 146.972i | 0.491544i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.6650 | 0.111844 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 536.013i | 1.75742i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.42383 | 0.0241819 | 0.0120909 | − | 0.999927i | \(-0.496151\pi\) | ||||
0.0120909 | + | 0.999927i | \(0.496151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −113.742 | −0.365730 | −0.182865 | − | 0.983138i | \(-0.558537\pi\) | ||||
−0.182865 | + | 0.983138i | \(0.558537\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −109.444 | −0.349662 | −0.174831 | − | 0.984598i | \(-0.555938\pi\) | ||||
−0.174831 | + | 0.984598i | \(0.555938\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −527.650 | −1.66451 | −0.832255 | − | 0.554392i | \(-0.812951\pi\) | ||||
−0.832255 | + | 0.554392i | \(0.812951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.7954 | 0.134155 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 47.3011 | − | 325.612i | 0.146443 | − | 1.00809i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 32.5817i | − | 0.100251i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 117.682i | 0.357695i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −159.854 | −0.482942 | −0.241471 | − | 0.970408i | \(-0.577630\pi\) | ||||
−0.241471 | + | 0.970408i | \(0.577630\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 471.182i | 1.40651i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 314.698i | − | 0.933823i | −0.884304 | − | 0.466911i | \(-0.845367\pi\) | ||
0.884304 | − | 0.466911i | \(-0.154633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.5027 | −0.104113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 191.045i | − | 0.556981i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 92.4423 | 0.266404 | 0.133202 | − | 0.991089i | \(-0.457474\pi\) | ||||
0.133202 | + | 0.991089i | \(0.457474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 100.178 | 0.287043 | 0.143522 | − | 0.989647i | \(-0.454157\pi\) | ||||
0.143522 | + | 0.989647i | \(0.454157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 30.9310i | − | 0.0876232i | −0.999040 | − | 0.0438116i | \(-0.986050\pi\) | ||
0.999040 | − | 0.0438116i | \(-0.0139501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −283.414 | −0.798350 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 105.868 | 0.294897 | 0.147448 | − | 0.989070i | \(-0.452894\pi\) | ||||
0.147448 | + | 0.989070i | \(0.452894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 346.079 | + | 102.716i | 0.958666 | + | 0.284532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 18.4276i | − | 0.0504866i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 395.018i | 1.07634i | 0.842835 | + | 0.538172i | \(0.180885\pi\) | ||||
−0.842835 | + | 0.538172i | \(0.819115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 171.073i | 0.461113i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 286.369i | − | 0.767745i | −0.923386 | − | 0.383873i | \(-0.874590\pi\) | ||
0.923386 | − | 0.383873i | \(-0.125410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 113.901i | − | 0.302125i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −480.082 | −1.26671 | −0.633354 | − | 0.773862i | \(-0.718322\pi\) | ||||
−0.633354 | + | 0.773862i | \(0.718322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 557.892i | 1.45664i | 0.685239 | + | 0.728318i | \(0.259698\pi\) | ||||
−0.685239 | + | 0.728318i | \(0.740302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.9206 | 0.0569365 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 114.774i | 0.295048i | 0.989058 | + | 0.147524i | \(0.0471304\pi\) | ||||
−0.989058 | + | 0.147524i | \(0.952870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 497.316i | 1.27191i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 140.552i | 0.355829i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −397.320 | −1.00081 | −0.500403 | − | 0.865793i | \(-0.666815\pi\) | ||||
−0.500403 | + | 0.865793i | \(0.666815\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −624.793 | −1.55809 | −0.779044 | − | 0.626969i | \(-0.784295\pi\) | ||||
−0.779044 | + | 0.626969i | \(0.784295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 94.4914i | 0.234470i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 122.014i | 0.299789i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 411.111i | − | 1.00516i | −0.864530 | − | 0.502581i | \(-0.832384\pi\) | ||
0.864530 | − | 0.502581i | \(-0.167616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 238.888 | 0.578422 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 671.969i | − | 1.61920i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −528.326 | −1.26092 | −0.630460 | − | 0.776221i | \(-0.717134\pi\) | ||||
−0.630460 | + | 0.776221i | \(0.717134\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 115.321i | 0.273922i | 0.990576 | + | 0.136961i | \(0.0437335\pi\) | ||||
−0.990576 | + | 0.136961i | \(0.956267\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 110.249i | − | 0.259408i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 194.810i | 0.456230i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.49770i | 0.0127557i | 0.999980 | + | 0.00637784i | \(0.00203014\pi\) | ||||
−0.999980 | + | 0.00637784i | \(0.997970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 243.056i | − | 0.561330i | −0.959806 | − | 0.280665i | \(-0.909445\pi\) | ||
0.959806 | − | 0.280665i | \(-0.0905550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −539.971 | − | 78.4408i | −1.23563 | − | 0.179498i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −76.2189 | −0.173619 | −0.0868097 | − | 0.996225i | \(-0.527667\pi\) | ||||
−0.0868097 | + | 0.996225i | \(0.527667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 464.886 | 1.04940 | 0.524702 | − | 0.851286i | \(-0.324177\pi\) | ||||
0.524702 | + | 0.851286i | \(0.324177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 298.480i | 0.670741i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −336.034 | −0.748406 | −0.374203 | − | 0.927347i | \(-0.622084\pi\) | ||||
−0.374203 | + | 0.927347i | \(0.622084\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 88.5615 | 0.196367 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 58.3422i | − | 0.128225i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −671.906 | −1.47025 | −0.735127 | − | 0.677929i | \(-0.762878\pi\) | ||||
−0.735127 | + | 0.677929i | \(0.762878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 444.022i | 0.963172i | 0.876399 | + | 0.481586i | \(0.159939\pi\) | ||||
−0.876399 | + | 0.481586i | \(0.840061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 697.591i | − | 1.50668i | −0.657634 | − | 0.753338i | \(-0.728443\pi\) | ||
0.657634 | − | 0.753338i | \(-0.271557\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 415.168 | 0.889010 | 0.444505 | − | 0.895776i | \(-0.353380\pi\) | ||||
0.444505 | + | 0.895776i | \(0.353380\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 171.248i | 0.365134i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 31.8025i | − | 0.0672356i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 119.705 | + | 17.3893i | 0.252010 | + | 0.0366091i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 151.389 | 0.316051 | 0.158026 | − | 0.987435i | \(-0.449487\pi\) | ||||
0.158026 | + | 0.987435i | \(0.449487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 324.744 | 0.675144 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 515.230 | 1.06233 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 675.755 | 1.38759 | 0.693794 | − | 0.720174i | \(-0.255938\pi\) | ||||
0.693794 | + | 0.720174i | \(0.255938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 66.7682 | 0.135984 | 0.0679921 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679921 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 385.414i | − | 0.781772i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −103.005 | −0.207254 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 665.660i | 1.33399i | 0.745063 | + | 0.666994i | \(0.232419\pi\) | ||||
−0.745063 | + | 0.666994i | \(0.767581\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −462.048 | −0.918585 | −0.459293 | − | 0.888285i | \(-0.651897\pi\) | ||||
−0.459293 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 99.7532 | 0.197531 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.4701 | 0.0205699 | 0.0102850 | − | 0.999947i | \(-0.496726\pi\) | ||||
0.0102850 | + | 0.999947i | \(0.496726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.69739i | − | 0.0131064i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 929.236i | − | 1.80434i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 111.171 | 0.215030 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 674.371 | 1.29438 | 0.647189 | − | 0.762330i | \(-0.275945\pi\) | ||||
0.647189 | + | 0.762330i | \(0.275945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −371.563 | −0.710445 | −0.355223 | − | 0.934782i | \(-0.615595\pi\) | ||||
−0.355223 | + | 0.934782i | \(0.615595\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 319.736i | 0.606710i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 295.714 | 0.559005 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 235.709i | − | 0.442231i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 75.5831 | 0.141277 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −86.2539 | −0.160026 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 279.907 | 0.517389 | 0.258694 | − | 0.965959i | \(-0.416708\pi\) | ||||
0.258694 | + | 0.965959i | \(0.416708\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 927.934 | 1.70263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 498.484 | 0.911305 | 0.455652 | − | 0.890158i | \(-0.349406\pi\) | ||||
0.455652 | + | 0.890158i | \(0.349406\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 418.470 | + | 60.7906i | 0.759474 | + | 0.110328i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.0828i | 0.0923740i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 946.606i | − | 1.69947i | −0.527208 | − | 0.849736i | \(-0.676761\pi\) | ||
0.527208 | − | 0.849736i | \(-0.323239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −84.6431 | −0.151419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 900.136i | − | 1.59882i | −0.600786 | − | 0.799410i | \(-0.705145\pi\) | ||
0.600786 | − | 0.799410i | \(-0.294855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 681.070i | 1.20543i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −187.541 | −0.329597 | −0.164799 | − | 0.986327i | \(-0.552697\pi\) | ||||
−0.164799 | + | 0.986327i | \(0.552697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 885.114i | − | 1.55011i | −0.631893 | − | 0.775056i | \(-0.717722\pi\) | ||
0.631893 | − | 0.775056i | \(-0.282278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −182.828 | −0.317962 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 56.1526 | 0.0973183 | 0.0486591 | − | 0.998815i | \(-0.484505\pi\) | ||||
0.0486591 | + | 0.998815i | \(0.484505\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 244.223i | − | 0.420349i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 161.608 | 0.277201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1093.11 | −1.86220 | −0.931098 | − | 0.364769i | \(-0.881148\pi\) | ||||
−0.931098 | + | 0.364769i | \(0.881148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −347.160 | − | 50.4314i | −0.589405 | − | 0.0856220i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 604.504i | − | 1.01940i | −0.860352 | − | 0.509700i | \(-0.829757\pi\) | ||
0.860352 | − | 0.509700i | \(-0.170243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 197.416i | − | 0.331791i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 922.740i | 1.54047i | 0.637761 | + | 0.770234i | \(0.279861\pi\) | ||||
−0.637761 | + | 0.770234i | \(0.720139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 780.834i | 1.29922i | 0.760266 | + | 0.649612i | \(0.225069\pi\) | ||||
−0.760266 | + | 0.649612i | \(0.774931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 656.961i | 1.08589i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −426.722 | −0.703002 | −0.351501 | − | 0.936187i | \(-0.614329\pi\) | ||||
−0.351501 | + | 0.936187i | \(0.614329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 295.884i | − | 0.484262i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −226.053 | −0.368765 | −0.184383 | − | 0.982855i | \(-0.559029\pi\) | ||||
−0.184383 | + | 0.982855i | \(0.559029\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 873.370i | 1.41551i | 0.706457 | + | 0.707755i | \(0.250292\pi\) | ||||
−0.706457 | + | 0.707755i | \(0.749708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 453.397i | 0.732468i | 0.930523 | + | 0.366234i | \(0.119353\pi\) | ||||
−0.930523 | + | 0.366234i | \(0.880647\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 108.480i | 0.174126i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −743.629 | −1.18981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1098.86 | 1.74699 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 482.242i | 0.764251i | 0.924110 | + | 0.382125i | \(0.124808\pi\) | ||||
−0.924110 | + | 0.382125i | \(0.875192\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 573.806i | − | 0.903631i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 229.567i | 0.360388i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 644.325 | 1.00519 | 0.502593 | − | 0.864523i | \(-0.332379\pi\) | ||||
0.502593 | + | 0.864523i | \(0.332379\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 712.415i | 1.10795i | 0.832532 | + | 0.553977i | \(0.186891\pi\) | ||||
−0.832532 | + | 0.553977i | \(0.813109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 395.657 | 0.611526 | 0.305763 | − | 0.952108i | \(-0.401088\pi\) | ||||
0.305763 | + | 0.952108i | \(0.401088\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 225.672i | − | 0.347722i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 84.4300i | 0.129296i | 0.997908 | + | 0.0646478i | \(0.0205924\pi\) | ||||
−0.997908 | + | 0.0646478i | \(0.979408\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 406.642i | 0.620828i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 999.513i | − | 1.51671i | −0.651841 | − | 0.758356i | \(-0.726003\pi\) | ||
0.651841 | − | 0.758356i | \(-0.273997\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 735.344i | − | 1.11247i | −0.831025 | − | 0.556236i | \(-0.812245\pi\) | ||
0.831025 | − | 0.556236i | \(-0.187755\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 214.348 | + | 31.1380i | 0.322328 | + | 0.0468241i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −639.142 | −0.958234 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 184.032 | 0.274266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 330.032i | 0.490389i | 0.969474 | + | 0.245194i | \(0.0788518\pi\) | ||||
−0.969474 | + | 0.245194i | \(0.921148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 527.650 | 0.779394 | 0.389697 | − | 0.920943i | \(-0.372580\pi\) | ||||
0.389697 | + | 0.920943i | \(0.372580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 187.257 | 0.275783 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 268.574i | − | 0.393227i | −0.980481 | − | 0.196614i | \(-0.937006\pi\) | ||
0.980481 | − | 0.196614i | \(-0.0629945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 427.142 | 0.623565 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 430.124i | − | 0.624273i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1084.24i | − | 1.56908i | −0.620076 | − | 0.784542i | \(-0.712898\pi\) | ||
0.620076 | − | 0.784542i | \(-0.287102\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 694.898 | 0.999853 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 797.582i | − | 1.14431i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 963.700i | 1.37475i | 0.726302 | + | 0.687375i | \(0.241237\pi\) | ||||
−0.726302 | + | 0.687375i | \(0.758763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −173.320 | + | 1193.10i | −0.246544 | + | 1.69716i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36.2546 | 0.0512795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1026.74 | 1.44815 | 0.724076 | − | 0.689720i | \(-0.242266\pi\) | ||||
0.724076 | + | 0.689720i | \(0.242266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 530.227 | 0.743657 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −55.1143 | −0.0770830 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −876.207 | −1.21865 | −0.609323 | − | 0.792922i | \(-0.708559\pi\) | ||||
−0.609323 | + | 0.792922i | \(0.708559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 337.725i | − | 0.468411i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 141.690 | 0.195434 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 477.628i | − | 0.656985i | −0.944507 | − | 0.328492i | \(-0.893459\pi\) | ||
0.944507 | − | 0.328492i | \(-0.106541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −286.412 | −0.391808 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 524.677 | 0.715793 | 0.357897 | − | 0.933761i | \(-0.383494\pi\) | ||||
0.357897 | + | 0.933761i | \(0.383494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 161.773 | 0.219503 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1277.94i | − | 1.72928i | −0.502388 | − | 0.864642i | \(-0.667545\pi\) | ||
0.502388 | − | 0.864642i | \(-0.332455\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 804.008i | 1.08211i | 0.840987 | + | 0.541055i | \(0.181975\pi\) | ||||
−0.840987 | + | 0.541055i | \(0.818025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 727.812 | 0.976929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.4702 | 0.0366758 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1147.57 | −1.52805 | −0.764027 | − | 0.645184i | \(-0.776781\pi\) | ||||
−0.764027 | + | 0.645184i | \(0.776781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1399.64i | − | 1.85382i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −975.992 | −1.28929 | −0.644644 | − | 0.764483i | \(-0.722995\pi\) | ||||
−0.644644 | + | 0.764483i | \(0.722995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 685.045i | − | 0.900190i | −0.892981 | − | 0.450095i | \(-0.851390\pi\) | ||
0.892981 | − | 0.450095i | \(-0.148610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 337.251 | 0.442007 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −600.631 | −0.783091 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −557.401 | −0.724839 | −0.362420 | − | 0.932015i | \(-0.618049\pi\) | ||||
−0.362420 | + | 0.932015i | \(0.618049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −215.572 | −0.278877 | −0.139438 | − | 0.990231i | \(-0.544530\pi\) | ||||
−0.139438 | + | 0.990231i | \(0.544530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −117.545 | −0.151670 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 865.991 | + | 125.801i | 1.11167 | + | 0.161491i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 97.3061i | 0.124592i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1065.74i | − | 1.35762i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.9293 | 0.0647132 | 0.0323566 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323566 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 247.530i | 0.312934i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 489.807i | − | 0.617663i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 955.749 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1001.20i | − | 1.25307i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.32685 | −0.00787902 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −327.380 | −0.406684 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.2361i | − | 0.0175972i | −0.999961 | − | 0.00879860i | \(-0.997199\pi\) | ||
0.999961 | − | 0.00879860i | \(-0.00280072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −393.368 | −0.485041 | −0.242521 | − | 0.970146i | \(-0.577974\pi\) | ||||
−0.242521 | + | 0.970146i | \(0.577974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 464.495 | 0.569932 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.1752 | − | 310.977i | 0.0552940 | − | 0.380633i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 561.359i | − | 0.683751i | −0.939745 | − | 0.341875i | \(-0.888938\pi\) | ||
0.939745 | − | 0.341875i | \(-0.111062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 549.746i | 0.667978i | 0.942577 | + | 0.333989i | \(0.108395\pi\) | ||||
−0.942577 | + | 0.333989i | \(0.891605\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1419.13i | − | 1.71600i | −0.513653 | − | 0.857998i | \(-0.671708\pi\) | ||
0.513653 | − | 0.857998i | \(-0.328292\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1301.72i | − | 1.57023i | −0.619349 | − | 0.785116i | \(-0.712603\pi\) | ||
0.619349 | − | 0.785116i | \(-0.287397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 776.800i | 0.932533i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 943.500 | 1.12994 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1247.20i | − | 1.48653i | −0.668996 | − | 0.743266i | \(-0.733276\pi\) | ||
0.668996 | − | 0.743266i | \(-0.266724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −345.673 | −0.411026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 799.808i | − | 0.946518i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 238.768i | 0.281899i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1822.26i | − | 2.14132i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1275.12 | −1.49486 | −0.747430 | − | 0.664340i | \(-0.768713\pi\) | ||||
−0.747430 | + | 0.664340i | \(0.768713\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 546.505 | 0.637696 | 0.318848 | − | 0.947806i | \(-0.396704\pi\) | ||||
0.318848 | + | 0.947806i | \(0.396704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1577.83i | 1.83683i | 0.395621 | + | 0.918414i | \(0.370529\pi\) | ||||
−0.395621 | + | 0.918414i | \(0.629471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 737.992i | 0.855147i | 0.903981 | + | 0.427573i | \(0.140631\pi\) | ||||
−0.903981 | + | 0.427573i | \(0.859369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 275.250i | 0.318209i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.2566 | 0.0555312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 430.564i | − | 0.494333i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −212.421 | −0.242767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 975.085i | − | 1.11184i | −0.831235 | − | 0.555921i | \(-0.812366\pi\) | ||
0.831235 | − | 0.555921i | \(-0.187634\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 883.124i | 1.00241i | 0.865328 | + | 0.501206i | \(0.167110\pi\) | ||||
−0.865328 | + | 0.501206i | \(0.832890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 952.901i | 1.07916i | 0.841933 | + | 0.539581i | \(0.181417\pi\) | ||||
−0.841933 | + | 0.539581i | \(0.818583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1335.98i | 1.50618i | 0.657917 | + | 0.753090i | \(0.271438\pi\) | ||||
−0.657917 | + | 0.753090i | \(0.728562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 208.546i | − | 0.234585i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1087.07 | + | 157.917i | 1.21733 | + | 0.176839i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1008.33 | 1.12663 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −410.919 | −0.457085 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1455.44i | − | 1.61536i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 982.544 | 1.08568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1446.42 | −1.59473 | −0.797365 | − | 0.603497i | \(-0.793773\pi\) | ||||
−0.797365 | + | 0.603497i | \(0.793773\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 550.253i | 0.604010i | 0.953306 | + | 0.302005i | \(0.0976559\pi\) | ||||
−0.953306 | + | 0.302005i | \(0.902344\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −230.711 | −0.252695 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 147.791i | 0.161168i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 670.051i | − | 0.729109i | −0.931182 | − | 0.364555i | \(-0.881221\pi\) | ||
0.931182 | − | 0.364555i | \(-0.118779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 258.983 | 0.280588 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 403.973i | 0.436727i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 354.307i | − | 0.381385i | −0.981650 | − | 0.190692i | \(-0.938927\pi\) | ||
0.981650 | − | 0.190692i | \(-0.0610733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −843.426 | − | 122.523i | −0.905935 | − | 0.131604i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −186.494 | −0.199458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 607.866 | 0.648737 | 0.324368 | − | 0.945931i | \(-0.394848\pi\) | ||||
0.324368 | + | 0.945931i | \(0.394848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −716.670 | −0.761604 | −0.380802 | − | 0.924657i | \(-0.624352\pi\) | ||||
−0.380802 | + | 0.924657i | \(0.624352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1322.65 | −1.40260 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −244.834 | −0.258536 | −0.129268 | − | 0.991610i | \(-0.541263\pi\) | ||||
−0.129268 | + | 0.991610i | \(0.541263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8391i | 0.0177440i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 655.921 | 0.688270 | 0.344135 | − | 0.938920i | \(-0.388172\pi\) | ||||
0.344135 | + | 0.938920i | \(0.388172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 602.655i | 0.631052i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 155.242 | 0.161879 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −620.105 | −0.645270 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 800.501 | 0.829535 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 992.013i | − | 1.02587i | −0.858428 | − | 0.512933i | \(-0.828559\pi\) | ||
0.858428 | − | 0.512933i | \(-0.171441\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 331.137i | 0.341027i | 0.985355 | + | 0.170514i | \(0.0545427\pi\) | ||||
−0.985355 | + | 0.170514i | \(0.945457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 252.556 | 0.259564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.0340 | −0.0225528 | −0.0112764 | − | 0.999936i | \(-0.503589\pi\) | ||||
−0.0112764 | + | 0.999936i | \(0.503589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 102.479 | 0.104677 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 534.361i | 0.543602i | 0.962354 | + | 0.271801i | \(0.0876192\pi\) | ||||
−0.962354 | + | 0.271801i | \(0.912381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1402.92 | 1.42428 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 474.965i | 0.480248i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −225.440 | −0.227488 | −0.113744 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113744 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1663.57 | −1.67193 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 694.382 | 0.696472 | 0.348236 | − | 0.937407i | \(-0.386781\pi\) | ||||
0.348236 | + | 0.937407i | \(0.386781\pi\) | |||||||
\(998\) | 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 | 2736.3.b.e.2735.15 | yes | 32 | |
3.2 | odd | 2 | inner | 2736.3.b.e.2735.20 | yes | 32 | |
4.3 | odd | 2 | inner | 2736.3.b.e.2735.17 | yes | 32 | |
12.11 | even | 2 | inner | 2736.3.b.e.2735.12 | yes | 32 | |
19.18 | odd | 2 | inner | 2736.3.b.e.2735.11 | ✓ | 32 | |
57.56 | even | 2 | inner | 2736.3.b.e.2735.18 | yes | 32 | |
76.75 | even | 2 | inner | 2736.3.b.e.2735.19 | yes | 32 | |
228.227 | odd | 2 | inner | 2736.3.b.e.2735.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.3.b.e.2735.11 | ✓ | 32 | 19.18 | odd | 2 | inner | |
2736.3.b.e.2735.12 | yes | 32 | 12.11 | even | 2 | inner | |
2736.3.b.e.2735.15 | yes | 32 | 1.1 | even | 1 | trivial | |
2736.3.b.e.2735.16 | yes | 32 | 228.227 | odd | 2 | inner | |
2736.3.b.e.2735.17 | yes | 32 | 4.3 | odd | 2 | inner | |
2736.3.b.e.2735.18 | yes | 32 | 57.56 | even | 2 | inner | |
2736.3.b.e.2735.19 | yes | 32 | 76.75 | even | 2 | inner | |
2736.3.b.e.2735.20 | yes | 32 | 3.2 | odd | 2 | inner |