Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(809,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.3 | ||
Character | \(\chi\) | \(=\) | 1620.809 |
Dual form | 1620.3.b.b.809.4 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.80229 | − | 1.39212i | −0.960458 | − | 0.278424i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 12.3801i | − | 1.76858i | −0.466938 | − | 0.884290i | \(-0.654643\pi\) | ||
0.466938 | − | 0.884290i | \(-0.345357\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.62899i | 0.420817i | 0.977614 | + | 0.210408i | \(0.0674794\pi\) | ||||
−0.977614 | + | 0.210408i | \(0.932521\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.26353i | 0.0971944i | 0.998818 | + | 0.0485972i | \(0.0154751\pi\) | ||||
−0.998818 | + | 0.0485972i | \(0.984525\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.9122 | 1.34778 | 0.673889 | − | 0.738833i | \(-0.264623\pi\) | ||||
0.673889 | + | 0.738833i | \(0.264623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.8729 | 1.73015 | 0.865075 | − | 0.501642i | \(-0.167270\pi\) | ||||
0.865075 | + | 0.501642i | \(0.167270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.797117 | 0.0346573 | 0.0173286 | − | 0.999850i | \(-0.494484\pi\) | ||||
0.0173286 | + | 0.999850i | \(0.494484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.1240 | + | 13.3707i | 0.844961 | + | 0.534828i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.6411i | 1.36694i | 0.729980 | + | 0.683468i | \(0.239529\pi\) | ||||
−0.729980 | + | 0.683468i | \(0.760471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.46043 | 0.0471107 | 0.0235553 | − | 0.999723i | \(-0.492501\pi\) | ||||
0.0235553 | + | 0.999723i | \(0.492501\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.2345 | + | 59.4527i | −0.492414 | + | 1.69865i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 44.9884i | − | 1.21590i | −0.793974 | − | 0.607952i | \(-0.791991\pi\) | ||
0.793974 | − | 0.607952i | \(-0.208009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 39.1346i | − | 0.954502i | −0.878767 | − | 0.477251i | \(-0.841633\pi\) | ||
0.878767 | − | 0.477251i | \(-0.158367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 36.3817i | − | 0.846085i | −0.906110 | − | 0.423043i | \(-0.860962\pi\) | ||
0.906110 | − | 0.423043i | \(-0.139038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 61.0408 | 1.29874 | 0.649370 | − | 0.760473i | \(-0.275033\pi\) | ||||
0.649370 | + | 0.760473i | \(0.275033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −104.266 | −2.12788 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.9872 | −0.263909 | −0.131954 | − | 0.991256i | \(-0.542125\pi\) | ||||
−0.131954 | + | 0.991256i | \(0.542125\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.44409 | − | 22.2297i | 0.117165 | − | 0.404177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 58.0138i | − | 0.983285i | −0.870797 | − | 0.491643i | \(-0.836397\pi\) | ||
0.870797 | − | 0.491643i | \(-0.163603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −55.0506 | −0.902469 | −0.451234 | − | 0.892405i | \(-0.649016\pi\) | ||||
−0.451234 | + | 0.892405i | \(0.649016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75898 | − | 6.06783i | 0.0270612 | − | 0.0933512i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 66.9919i | − | 0.999880i | −0.866060 | − | 0.499940i | \(-0.833355\pi\) | ||
0.866060 | − | 0.499940i | \(-0.166645\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 70.6560i | − | 0.995156i | −0.867419 | − | 0.497578i | \(-0.834223\pi\) | ||
0.867419 | − | 0.497578i | \(-0.165777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 23.1498i | − | 0.317121i | −0.987349 | − | 0.158561i | \(-0.949315\pi\) | ||
0.987349 | − | 0.158561i | \(-0.0506853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 57.3071 | 0.744248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −29.1451 | −0.368925 | −0.184462 | − | 0.982840i | \(-0.559054\pi\) | ||||
−0.184462 | + | 0.982840i | \(0.559054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −130.433 | −1.57148 | −0.785741 | − | 0.618556i | \(-0.787718\pi\) | ||||
−0.785741 | + | 0.618556i | \(0.787718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −110.031 | − | 31.8965i | −1.29448 | − | 0.375253i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.0873i | 0.540307i | 0.962817 | + | 0.270153i | \(0.0870744\pi\) | ||||
−0.962817 | + | 0.270153i | \(0.912926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.6425 | 0.171896 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −157.865 | − | 45.7629i | −1.66174 | − | 0.481715i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.3761i | − | 0.199753i | −0.995000 | − | 0.0998766i | \(-0.968155\pi\) | ||
0.995000 | − | 0.0998766i | \(-0.0318448\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 129.502i | 1.28219i | 0.767460 | + | 0.641097i | \(0.221520\pi\) | ||||
−0.767460 | + | 0.641097i | \(0.778480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.40246i | − | 0.0815772i | −0.999168 | − | 0.0407886i | \(-0.987013\pi\) | ||
0.999168 | − | 0.0407886i | \(-0.0129870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 61.1389 | 0.571391 | 0.285696 | − | 0.958320i | \(-0.407775\pi\) | ||||
0.285696 | + | 0.958320i | \(0.407775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −161.771 | −1.48414 | −0.742068 | − | 0.670324i | \(-0.766155\pi\) | ||||
−0.742068 | + | 0.670324i | \(0.766155\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.2475 | 0.303075 | 0.151538 | − | 0.988451i | \(-0.451578\pi\) | ||||
0.151538 | + | 0.988451i | \(0.451578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.82799 | − | 1.10968i | −0.0332869 | − | 0.00964940i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 283.655i | − | 2.38365i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 99.5725 | 0.822913 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −82.8301 | − | 93.6172i | −0.662641 | − | 0.748937i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 104.320i | − | 0.821421i | −0.911766 | − | 0.410710i | \(-0.865281\pi\) | ||
0.911766 | − | 0.410710i | \(-0.134719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 219.634i | 1.67660i | 0.545211 | + | 0.838299i | \(0.316449\pi\) | ||||
−0.545211 | + | 0.838299i | \(0.683551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 406.968i | − | 3.05991i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 189.475 | 1.38303 | 0.691514 | − | 0.722363i | \(-0.256944\pi\) | ||||
0.691514 | + | 0.722363i | \(0.256944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 220.040 | 1.58302 | 0.791511 | − | 0.611155i | \(-0.209295\pi\) | ||||
0.791511 | + | 0.611155i | \(0.209295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.84885 | −0.0409010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55.1851 | − | 190.368i | 0.380587 | − | 1.31289i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.3969i | − | 0.0697782i | −0.999391 | − | 0.0348891i | \(-0.988892\pi\) | ||
0.999391 | − | 0.0348891i | \(-0.0111078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −81.7621 | −0.541471 | −0.270736 | − | 0.962654i | \(-0.587267\pi\) | ||||
−0.270736 | + | 0.962654i | \(0.587267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.01341 | − | 2.03309i | −0.0452478 | − | 0.0131167i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 132.312i | − | 0.842749i | −0.906887 | − | 0.421375i | \(-0.861548\pi\) | ||
0.906887 | − | 0.421375i | \(-0.138452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.86836i | − | 0.0612942i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 81.7721i | 0.501669i | 0.968030 | + | 0.250835i | \(0.0807051\pi\) | ||||
−0.968030 | + | 0.250835i | \(0.919295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 27.7023 | 0.165882 | 0.0829411 | − | 0.996554i | \(-0.473569\pi\) | ||||
0.0829411 | + | 0.996554i | \(0.473569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.403 | 0.990553 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −278.615 | −1.61049 | −0.805246 | − | 0.592940i | \(-0.797967\pi\) | ||||
−0.805246 | + | 0.592940i | \(0.797967\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 165.530 | − | 261.517i | 0.945887 | − | 1.49438i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 175.928i | − | 0.982839i | −0.870923 | − | 0.491419i | \(-0.836478\pi\) | ||
0.870923 | − | 0.491419i | \(-0.163522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −180.887 | −0.999377 | −0.499689 | − | 0.866205i | \(-0.666552\pi\) | ||||
−0.499689 | + | 0.866205i | \(0.666552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −62.6292 | + | 216.048i | −0.338536 | + | 1.16782i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 106.060i | 0.567167i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 138.769i | − | 0.726540i | −0.931684 | − | 0.363270i | \(-0.881660\pi\) | ||
0.931684 | − | 0.363270i | \(-0.118340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 178.975i | − | 0.927332i | −0.886010 | − | 0.463666i | \(-0.846534\pi\) | ||
0.886010 | − | 0.463666i | \(-0.153466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 136.877 | 0.694809 | 0.347405 | − | 0.937715i | \(-0.387063\pi\) | ||||
0.347405 | + | 0.937715i | \(0.387063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4634 | 0.0576050 | 0.0288025 | − | 0.999585i | \(-0.490831\pi\) | ||||
0.0288025 | + | 0.999585i | \(0.490831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 490.760 | 2.41754 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54.4799 | + | 187.936i | −0.265756 | + | 0.916760i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 152.168i | 0.728077i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −77.4456 | −0.367041 | −0.183520 | − | 0.983016i | \(-0.558749\pi\) | ||||
−0.183520 | + | 0.983016i | \(0.558749\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −50.6476 | + | 174.715i | −0.235570 | + | 0.812630i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 18.0802i | − | 0.0833190i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.9502i | 0.130996i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 144.235i | − | 0.646794i | −0.946263 | − | 0.323397i | \(-0.895175\pi\) | ||
0.946263 | − | 0.323397i | \(-0.104825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −49.1034 | −0.216314 | −0.108157 | − | 0.994134i | \(-0.534495\pi\) | ||||
−0.108157 | + | 0.994134i | \(0.534495\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −100.980 | −0.440962 | −0.220481 | − | 0.975391i | \(-0.570763\pi\) | ||||
−0.220481 | + | 0.975391i | \(0.570763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −120.466 | −0.517021 | −0.258510 | − | 0.966009i | \(-0.583232\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −293.136 | − | 84.9759i | −1.24739 | − | 0.361600i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 181.396i | 0.758978i | 0.925196 | + | 0.379489i | \(0.123900\pi\) | ||||
−0.925196 | + | 0.379489i | \(0.876100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 162.308 | 0.673475 | 0.336738 | − | 0.941599i | \(-0.390676\pi\) | ||||
0.336738 | + | 0.941599i | \(0.390676\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 500.716 | + | 145.150i | 2.04374 | + | 0.592451i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.5358i | 0.168161i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 445.457i | 1.77473i | 0.461069 | + | 0.887364i | \(0.347466\pi\) | ||||
−0.461069 | + | 0.887364i | \(0.652534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.68984i | 0.0145844i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −247.417 | −0.962713 | −0.481357 | − | 0.876525i | \(-0.659856\pi\) | ||||
−0.481357 | + | 0.876525i | \(0.659856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −556.960 | −2.15042 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −86.0242 | −0.327088 | −0.163544 | − | 0.986536i | \(-0.552293\pi\) | ||||
−0.163544 | + | 0.986536i | \(0.552293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 67.1704 | + | 19.4718i | 0.253473 | + | 0.0734784i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 368.618i | − | 1.37033i | −0.728389 | − | 0.685164i | \(-0.759731\pi\) | ||
0.728389 | − | 0.685164i | \(-0.240269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −130.740 | −0.482434 | −0.241217 | − | 0.970471i | \(-0.577546\pi\) | ||||
−0.241217 | + | 0.970471i | \(0.577546\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −61.8928 | + | 97.7828i | −0.225065 | + | 0.355574i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 217.270i | − | 0.784370i | −0.919886 | − | 0.392185i | \(-0.871719\pi\) | ||
0.919886 | − | 0.392185i | \(-0.128281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 172.327i | − | 0.613264i | −0.951828 | − | 0.306632i | \(-0.900798\pi\) | ||
0.951828 | − | 0.306632i | \(-0.0992021\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 436.158i | 1.54119i | 0.637324 | + | 0.770596i | \(0.280041\pi\) | ||||
−0.637324 | + | 0.770596i | \(0.719959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −484.489 | −1.68811 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 235.970 | 0.816504 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.0406 | −0.0991148 | −0.0495574 | − | 0.998771i | \(-0.515781\pi\) | ||||
−0.0495574 | + | 0.998771i | \(0.515781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −80.7621 | + | 278.599i | −0.273770 | + | 0.944405i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.00718i | 0.00336849i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −450.407 | −1.49637 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 264.369 | + | 76.6369i | 0.866784 | + | 0.251269i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 306.163i | − | 0.997273i | −0.866811 | − | 0.498637i | \(-0.833834\pi\) | ||
0.866811 | − | 0.498637i | \(-0.166166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 397.221i | − | 1.27724i | −0.769524 | − | 0.638618i | \(-0.779506\pi\) | ||
0.769524 | − | 0.638618i | \(-0.220494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 391.762i | − | 1.25164i | −0.779969 | − | 0.625818i | \(-0.784765\pi\) | ||
0.779969 | − | 0.625818i | \(-0.215235\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −161.788 | −0.510372 | −0.255186 | − | 0.966892i | \(-0.582137\pi\) | ||||
−0.255186 | + | 0.966892i | \(0.582137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −183.498 | −0.575230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 753.190 | 2.33186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.8943 | + | 26.6908i | −0.0519823 | + | 0.0821255i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 755.689i | − | 2.29693i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 237.189 | 0.716582 | 0.358291 | − | 0.933610i | \(-0.383360\pi\) | ||||
0.358291 | + | 0.933610i | \(0.383360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −93.2607 | + | 321.715i | −0.278390 | + | 0.960343i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 422.049i | − | 1.25237i | −0.779674 | − | 0.626185i | \(-0.784615\pi\) | ||
0.779674 | − | 0.626185i | \(-0.215385\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.76031i | 0.0198250i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 684.196i | 1.99474i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −552.495 | −1.59220 | −0.796102 | − | 0.605163i | \(-0.793108\pi\) | ||||
−0.796102 | + | 0.605163i | \(0.793108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 397.177 | 1.13804 | 0.569022 | − | 0.822322i | \(-0.307322\pi\) | ||||
0.569022 | + | 0.822322i | \(0.307322\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −308.675 | −0.874433 | −0.437216 | − | 0.899356i | \(-0.644036\pi\) | ||||
−0.437216 | + | 0.899356i | \(0.644036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −98.3615 | + | 339.311i | −0.277075 | + | 0.955806i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 278.225i | − | 0.775000i | −0.921870 | − | 0.387500i | \(-0.873339\pi\) | ||
0.921870 | − | 0.387500i | \(-0.126661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 719.626 | 1.99342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.2273 | + | 111.172i | −0.0882940 | + | 0.304582i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 608.243i | 1.65734i | 0.559738 | + | 0.828669i | \(0.310902\pi\) | ||||
−0.559738 | + | 0.828669i | \(0.689098\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 173.162i | 0.466744i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 358.878i | 0.962140i | 0.876682 | + | 0.481070i | \(0.159752\pi\) | ||||
−0.876682 | + | 0.481070i | \(0.840248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −50.0877 | −0.132859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 353.208 | 0.931948 | 0.465974 | − | 0.884798i | \(-0.345704\pi\) | ||||
0.465974 | + | 0.884798i | \(0.345704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 271.388 | 0.708586 | 0.354293 | − | 0.935135i | \(-0.384722\pi\) | ||||
0.354293 | + | 0.935135i | \(0.384722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −275.206 | − | 79.7783i | −0.714820 | − | 0.207216i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 262.697i | − | 0.675314i | −0.941269 | − | 0.337657i | \(-0.890366\pi\) | ||
0.941269 | − | 0.337657i | \(-0.109634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.2637 | 0.0467103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 139.963 | + | 40.5733i | 0.354337 | + | 0.102717i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 53.4516i | 0.134639i | 0.997731 | + | 0.0673194i | \(0.0214447\pi\) | ||||
−0.997731 | + | 0.0673194i | \(0.978555\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 184.917i | − | 0.461139i | −0.973056 | − | 0.230570i | \(-0.925941\pi\) | ||
0.973056 | − | 0.230570i | \(-0.0740590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.84529i | 0.00457889i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 208.251 | 0.511673 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 232.105 | 0.567493 | 0.283746 | − | 0.958899i | \(-0.408423\pi\) | ||||
0.283746 | + | 0.958899i | \(0.408423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −718.215 | −1.73902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 626.377 | + | 181.578i | 1.50934 | + | 0.437537i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 388.092i | − | 0.926235i | −0.886297 | − | 0.463117i | \(-0.846731\pi\) | ||
0.886297 | − | 0.463117i | \(-0.153269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 154.003 | 0.365803 | 0.182902 | − | 0.983131i | \(-0.441451\pi\) | ||||
0.182902 | + | 0.983131i | \(0.441451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 483.998 | + | 306.353i | 1.13882 | + | 0.720830i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 681.530i | 1.59609i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 238.147i | 0.552544i | 0.961079 | + | 0.276272i | \(0.0890991\pi\) | ||||
−0.961079 | + | 0.276272i | \(0.910901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 523.956i | − | 1.21006i | −0.796203 | − | 0.605030i | \(-0.793161\pi\) | ||
0.796203 | − | 0.605030i | \(-0.206839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.2035 | 0.0599623 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 456.345 | 1.03951 | 0.519755 | − | 0.854316i | \(-0.326023\pi\) | ||||
0.519755 | + | 0.854316i | \(0.326023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 271.780 | 0.613499 | 0.306749 | − | 0.951790i | \(-0.400759\pi\) | ||||
0.306749 | + | 0.951790i | \(0.400759\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 66.9432 | − | 230.929i | 0.150434 | − | 0.518942i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 386.192i | 0.860116i | 0.902801 | + | 0.430058i | \(0.141507\pi\) | ||||
−0.902801 | + | 0.430058i | \(0.858493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 181.153 | 0.401671 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −75.1201 | − | 21.7763i | −0.165099 | − | 0.0478599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.48832i | 0.00982126i | 0.999988 | + | 0.00491063i | \(0.00156311\pi\) | ||||
−0.999988 | + | 0.00491063i | \(0.998437\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 327.360i | 0.710108i | 0.934846 | + | 0.355054i | \(0.115538\pi\) | ||||
−0.934846 | + | 0.355054i | \(0.884462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 212.141i | − | 0.458188i | −0.973404 | − | 0.229094i | \(-0.926424\pi\) | ||
0.973404 | − | 0.229094i | \(-0.0735763\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −471.246 | −1.00909 | −0.504546 | − | 0.863385i | \(-0.668340\pi\) | ||||
−0.504546 | + | 0.863385i | \(0.668340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −829.364 | −1.76837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 168.410 | 0.356047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 694.407 | + | 439.534i | 1.46191 | + | 0.925334i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 880.071i | − | 1.83731i | −0.395062 | − | 0.918654i | \(-0.629277\pi\) | ||
0.395062 | − | 0.918654i | \(-0.370723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.8441 | 0.118179 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.9737 | + | 93.0495i | −0.0556160 | + | 0.191855i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 606.421i | 1.24522i | 0.782533 | + | 0.622609i | \(0.213927\pi\) | ||||
−0.782533 | + | 0.622609i | \(0.786073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 563.512i | 1.14768i | 0.818967 | + | 0.573841i | \(0.194547\pi\) | ||||
−0.818967 | + | 0.573841i | \(0.805453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 908.266i | 1.84233i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −874.726 | −1.76001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 71.8813 | 0.144051 | 0.0720254 | − | 0.997403i | \(-0.477054\pi\) | ||||
0.0720254 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 124.538 | 0.247591 | 0.123795 | − | 0.992308i | \(-0.460493\pi\) | ||||
0.123795 | + | 0.992308i | \(0.460493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 180.281 | − | 621.904i | 0.356993 | − | 1.23149i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 538.157i | − | 1.05728i | −0.848845 | − | 0.528642i | \(-0.822702\pi\) | ||
0.848845 | − | 0.528642i | \(-0.177298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −286.596 | −0.560854 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.6972 | + | 40.3510i | −0.0227130 | + | 0.0783515i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 282.557i | 0.546532i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 147.767i | − | 0.283622i | −0.989894 | − | 0.141811i | \(-0.954707\pi\) | ||
0.989894 | − | 0.141811i | \(-0.0452925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 701.166i | 1.34066i | 0.742063 | + | 0.670331i | \(0.233848\pi\) | ||||
−0.742063 | + | 0.670331i | \(0.766152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.4617 | 0.0634947 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −528.365 | −0.998799 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.4476 | 0.0927723 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −293.607 | − | 85.1125i | −0.548798 | − | 0.159089i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 482.646i | − | 0.895446i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −573.411 | −1.05991 | −0.529955 | − | 0.848026i | \(-0.677791\pi\) | ||||
−0.529955 | + | 0.848026i | \(0.677791\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 776.871 | + | 225.204i | 1.42545 | + | 0.413218i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 305.020i | 0.557624i | 0.960346 | + | 0.278812i | \(0.0899406\pi\) | ||||
−0.960346 | + | 0.278812i | \(0.910059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1303.12i | 2.36501i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 360.818i | 0.652473i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 686.875 | 1.23317 | 0.616585 | − | 0.787288i | \(-0.288516\pi\) | ||||
0.616585 | + | 0.787288i | \(0.288516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.9692 | 0.0822348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −465.062 | −0.826043 | −0.413021 | − | 0.910721i | \(-0.635527\pi\) | ||||
−0.413021 | + | 0.910721i | \(0.635527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −164.467 | − | 47.6765i | −0.291091 | − | 0.0843833i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1101.68i | − | 1.93618i | −0.250611 | − | 0.968088i | \(-0.580631\pi\) | ||
0.250611 | − | 0.968088i | \(-0.419369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 762.054 | 1.33460 | 0.667298 | − | 0.744791i | \(-0.267451\pi\) | ||||
0.667298 | + | 0.744791i | \(0.267451\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8383 | + | 10.6580i | 0.0292840 | + | 0.0185357i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 673.918i | 1.16797i | 0.811765 | + | 0.583985i | \(0.198507\pi\) | ||||
−0.811765 | + | 0.583985i | \(0.801493\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1614.77i | 2.77929i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 64.7464i | − | 0.111057i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 389.360 | 0.663305 | 0.331653 | − | 0.943402i | \(-0.392394\pi\) | ||||
0.331653 | + | 0.943402i | \(0.392394\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.0085 | 0.0815085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 640.797 | 1.08060 | 0.540301 | − | 0.841472i | \(-0.318310\pi\) | ||||
0.540301 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −394.881 | + | 1362.19i | −0.663665 | + | 2.28940i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 466.425i | 0.778673i | 0.921096 | + | 0.389336i | \(0.127296\pi\) | ||||
−0.921096 | + | 0.389336i | \(0.872704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −986.430 | −1.64131 | −0.820657 | − | 0.571421i | \(-0.806392\pi\) | ||||
−0.820657 | + | 0.571421i | \(0.806392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −478.176 | − | 138.617i | −0.790374 | − | 0.229118i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 869.964i | 1.43322i | 0.697474 | + | 0.716610i | \(0.254307\pi\) | ||||
−0.697474 | + | 0.716610i | \(0.745693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 77.1267i | 0.126230i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 376.400i | 0.614029i | 0.951705 | + | 0.307014i | \(0.0993300\pi\) | ||||
−0.951705 | + | 0.307014i | \(0.900670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −116.125 | −0.188208 | −0.0941041 | − | 0.995562i | \(-0.529999\pi\) | ||||
−0.0941041 | + | 0.995562i | \(0.529999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 239.530 | 0.386963 | 0.193482 | − | 0.981104i | \(-0.438022\pi\) | ||||
0.193482 | + | 0.981104i | \(0.438022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 595.324 | 0.955576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 267.448 | + | 564.886i | 0.427917 | + | 0.903818i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1030.78i | − | 1.63877i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −590.863 | −0.936392 | −0.468196 | − | 0.883625i | \(-0.655096\pi\) | ||||
−0.468196 | + | 0.883625i | \(0.655096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −145.226 | + | 500.977i | −0.228703 | + | 0.788941i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 131.743i | − | 0.206818i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 766.027i | − | 1.19505i | −0.801850 | − | 0.597525i | \(-0.796151\pi\) | ||
0.801850 | − | 0.597525i | \(-0.203849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 76.0526i | 0.118278i | 0.998250 | + | 0.0591389i | \(0.0188355\pi\) | ||||
−0.998250 | + | 0.0591389i | \(0.981165\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 287.130 | 0.443786 | 0.221893 | − | 0.975071i | \(-0.428776\pi\) | ||||
0.221893 | + | 0.975071i | \(0.428776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 268.545 | 0.413783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −224.432 | −0.343694 | −0.171847 | − | 0.985124i | \(-0.554973\pi\) | ||||
−0.171847 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 305.757 | − | 1054.75i | 0.466804 | − | 1.61030i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1088.80i | 1.65220i | 0.563520 | + | 0.826102i | \(0.309447\pi\) | ||||
−0.563520 | + | 0.826102i | \(0.690553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 878.752 | 1.32943 | 0.664714 | − | 0.747098i | \(-0.268553\pi\) | ||||
0.664714 | + | 0.747098i | \(0.268553\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −566.548 | + | 1954.38i | −0.851951 | + | 2.93892i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.5986i | 0.0473743i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 254.828i | − | 0.379774i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 556.285i | 0.826575i | 0.910601 | + | 0.413287i | \(0.135619\pi\) | ||||
−0.910601 | + | 0.413287i | \(0.864381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 562.016 | 0.830157 | 0.415078 | − | 0.909786i | \(-0.363754\pi\) | ||||
0.415078 | + | 0.909786i | \(0.363754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −239.877 | −0.353280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −500.931 | −0.733427 | −0.366714 | − | 0.930334i | \(-0.619517\pi\) | ||||
−0.366714 | + | 0.930334i | \(0.619517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −909.913 | − | 263.771i | −1.32834 | − | 0.385067i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 17.6732i | − | 0.0256504i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 722.500 | 1.04559 | 0.522793 | − | 0.852460i | \(-0.324890\pi\) | ||||
0.522793 | + | 0.852460i | \(0.324890\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1056.70 | − | 306.322i | −1.52043 | − | 0.440751i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 896.660i | − | 1.28646i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 788.759i | − | 1.12519i | −0.826732 | − | 0.562595i | \(-0.809803\pi\) | ||
0.826732 | − | 0.562595i | \(-0.190197\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1478.90i | − | 2.10370i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1603.24 | 2.26766 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −399.286 | −0.563168 | −0.281584 | − | 0.959537i | \(-0.590860\pi\) | ||||
−0.281584 | + | 0.959537i | \(0.590860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.16413 | 0.00163273 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.0879 | + | 8.14229i | 0.0392838 | + | 0.0113878i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 844.389i | − | 1.17439i | −0.809444 | − | 0.587197i | \(-0.800232\pi\) | ||
0.809444 | − | 0.587197i | \(-0.199768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −104.023 | −0.144276 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −530.030 | + | 837.380i | −0.731076 | + | 1.15501i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 405.715i | 0.558067i | 0.960281 | + | 0.279033i | \(0.0900141\pi\) | ||||
−0.960281 | + | 0.279033i | \(0.909986\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 833.585i | − | 1.14033i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1204.99i | − | 1.64392i | −0.569548 | − | 0.821958i | \(-0.692882\pi\) | ||
0.569548 | − | 0.821958i | \(-0.307118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 310.105 | 0.420766 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 539.145 | 0.729561 | 0.364780 | − | 0.931094i | \(-0.381144\pi\) | ||||
0.364780 | + | 0.931094i | \(0.381144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −311.004 | −0.418579 | −0.209289 | − | 0.977854i | \(-0.567115\pi\) | ||||
−0.209289 | + | 0.977854i | \(0.567115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4738 | + | 49.9292i | −0.0194279 | + | 0.0670190i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 756.903i | − | 1.01055i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 926.577 | 1.23379 | 0.616895 | − | 0.787045i | \(-0.288390\pi\) | ||||
0.616895 | + | 0.787045i | \(0.288390\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 392.646 | + | 113.822i | 0.520060 | + | 0.150758i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 450.364i | 0.594933i | 0.954732 | + | 0.297467i | \(0.0961417\pi\) | ||||
−0.954732 | + | 0.297467i | \(0.903858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 671.249i | − | 0.882062i | −0.897492 | − | 0.441031i | \(-0.854613\pi\) | ||
0.897492 | − | 0.441031i | \(-0.145387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2002.73i | 2.62481i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 73.3021 | 0.0955698 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −74.7039 | −0.0971443 | −0.0485721 | − | 0.998820i | \(-0.515467\pi\) | ||||
−0.0485721 | + | 0.998820i | \(0.515467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1226.34 | −1.58647 | −0.793234 | − | 0.608917i | \(-0.791604\pi\) | ||||
−0.793234 | + | 0.608917i | \(0.791604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.8502 | + | 19.5270i | 0.0398067 | + | 0.0251961i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1286.47i | − | 1.65143i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 327.066 | 0.418778 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −184.193 | + | 635.399i | −0.234641 | + | 0.809426i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 259.191i | 0.329341i | 0.986349 | + | 0.164670i | \(0.0526561\pi\) | ||||
−0.986349 | + | 0.164670i | \(0.947344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 423.986i | − | 0.536013i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 69.5579i | − | 0.0877149i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1485.11 | 1.86337 | 0.931686 | − | 0.363265i | \(-0.118338\pi\) | ||||
0.931686 | + | 0.363265i | \(0.118338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1398.58 | 1.75041 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 107.160 | 0.133450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7379 | + | 47.3908i | −0.0170657 | + | 0.0588705i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.2026i | − | 0.0126114i | −0.999980 | − | 0.00630569i | \(-0.997993\pi\) | ||
0.999980 | − | 0.00630569i | \(-0.00200718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1113.80 | 1.37337 | 0.686685 | − | 0.726955i | \(-0.259065\pi\) | ||||
0.686685 | + | 0.726955i | \(0.259065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 113.836 | − | 392.694i | 0.139677 | − | 0.481833i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1195.97i | − | 1.46386i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 307.485i | 0.374525i | 0.982310 | + | 0.187262i | \(0.0599614\pi\) | ||||
−0.982310 | + | 0.187262i | \(0.940039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 595.499i | 0.723570i | 0.932261 | + | 0.361785i | \(0.117833\pi\) | ||||
−0.932261 | + | 0.361785i | \(0.882167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1110.81 | −1.34318 | −0.671592 | − | 0.740921i | \(-0.734389\pi\) | ||||
−0.671592 | + | 0.740921i | \(0.734389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 390.454 | 0.470994 | 0.235497 | − | 0.971875i | \(-0.424328\pi\) | ||||
0.235497 | + | 0.971875i | \(0.424328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2388.96 | −2.86790 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −133.035 | − | 38.5649i | −0.159323 | − | 0.0461855i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1072.65i | − | 1.27849i | −0.769003 | − | 0.639246i | \(-0.779247\pi\) | ||
0.769003 | − | 0.639246i | \(-0.220753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −730.420 | −0.868514 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −803.920 | − | 233.045i | −0.951385 | − | 0.275793i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1232.71i | − | 1.45539i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 35.8611i | − | 0.0421399i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 909.447i | − | 1.06617i | −0.846060 | − | 0.533087i | \(-0.821032\pi\) | ||
0.846060 | − | 0.533087i | \(-0.178968\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −651.464 | −0.760169 | −0.380084 | − | 0.924952i | \(-0.624105\pi\) | ||||
−0.380084 | + | 0.924952i | \(0.624105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 460.478 | 0.536063 | 0.268032 | − | 0.963410i | \(-0.413627\pi\) | ||||
0.268032 | + | 0.963410i | \(0.413627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 359.492 | 0.416560 | 0.208280 | − | 0.978069i | \(-0.433213\pi\) | ||||
0.208280 | + | 0.978069i | \(0.433213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1337.99 | + | 387.865i | 1.54681 | + | 0.448399i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 134.912i | − | 0.155250i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 84.6462 | 0.0971827 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1158.99 | + | 1025.44i | −1.32456 | + | 1.17193i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1139.04i | − | 1.29879i | −0.760451 | − | 0.649395i | \(-0.775022\pi\) | ||
0.760451 | − | 0.649395i | \(-0.224978\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1612.41i | 1.83020i | 0.403227 | + | 0.915100i | \(0.367888\pi\) | ||||
−0.403227 | + | 0.915100i | \(0.632112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 688.542i | 0.779775i | 0.920862 | + | 0.389888i | \(0.127486\pi\) | ||||
−0.920862 | + | 0.389888i | \(0.872514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1125.59 | −1.26899 | −0.634494 | − | 0.772927i | \(-0.718792\pi\) | ||||
−0.634494 | + | 0.772927i | \(0.718792\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1291.49 | −1.45275 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2006.59 | 2.24702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −244.913 | + | 844.858i | −0.273645 | + | 0.943976i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 57.8931i | 0.0643972i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −320.477 | −0.355690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 868.674 | + | 251.816i | 0.959860 | + | 0.278250i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 623.987i | − | 0.687968i | −0.938976 | − | 0.343984i | \(-0.888223\pi\) | ||
0.938976 | − | 0.343984i | \(-0.111777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1525.40i | 1.67442i | 0.546879 | + | 0.837212i | \(0.315816\pi\) | ||||
−0.546879 | + | 0.837212i | \(0.684184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 603.772i | − | 0.661306i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2719.09 | 2.96520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −875.498 | −0.952663 | −0.476332 | − | 0.879266i | \(-0.658034\pi\) | ||||
−0.476332 | + | 0.879266i | \(0.658034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 89.2759 | 0.0967236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 601.527 | − | 950.337i | 0.650300 | − | 1.02739i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 394.172i | − | 0.424297i | −0.977237 | − | 0.212148i | \(-0.931954\pi\) | ||
0.977237 | − | 0.212148i | \(-0.0680460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3427.52 | −3.68155 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 147.648 | − | 509.333i | 0.157913 | − | 0.544741i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 600.533i | − | 0.640911i | −0.947264 | − | 0.320455i | \(-0.896164\pi\) | ||
0.947264 | − | 0.320455i | \(-0.103836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 660.729i | − | 0.702156i | −0.936346 | − | 0.351078i | \(-0.885815\pi\) | ||
0.936346 | − | 0.351078i | \(-0.114185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31.1949i | − | 0.0330804i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1265.59 | 1.33642 | 0.668210 | − | 0.743973i | \(-0.267061\pi\) | ||||
0.668210 | + | 0.743973i | \(0.267061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.2505 | 0.0308224 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 428.958 | 0.450113 | 0.225057 | − | 0.974346i | \(-0.427743\pi\) | ||||
0.225057 | + | 0.974346i | \(0.427743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −193.183 | + | 666.410i | −0.202286 | + | 0.697812i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2345.71i | − | 2.44599i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −958.867 | −0.997781 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −249.154 | + | 859.491i | −0.258191 | + | 0.890664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 443.284i | 0.458412i | 0.973378 | + | 0.229206i | \(0.0736129\pi\) | ||||
−0.973378 | + | 0.229206i | \(0.926387\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 444.042i | 0.457304i | 0.973508 | + | 0.228652i | \(0.0734317\pi\) | ||||
−0.973508 | + | 0.228652i | \(0.926568\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2724.11i | − | 2.79970i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −230.950 | −0.236387 | −0.118194 | − | 0.992991i | \(-0.537710\pi\) | ||||
−0.118194 | + | 0.992991i | \(0.537710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −222.595 | −0.227370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1121.24 | −1.14063 | −0.570316 | − | 0.821426i | \(-0.693179\pi\) | ||||
−0.570316 | + | 0.821426i | \(0.693179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −657.325 | − | 190.549i | −0.667335 | − | 0.193451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 29.0005i | − | 0.0293230i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 182.717 | 0.184377 | 0.0921884 | − | 0.995742i | \(-0.470614\pi\) | ||||
0.0921884 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −55.0506 | − | 15.9584i | −0.0553272 | − | 0.0160386i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1233.24i | − | 1.23695i | −0.785806 | − | 0.618473i | \(-0.787751\pi\) | ||
0.785806 | − | 0.618473i | \(-0.212249\pi\) | |||||||
\(998\) | 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 | 1620.3.b.b.809.3 | 24 | ||
3.2 | odd | 2 | inner | 1620.3.b.b.809.22 | 24 | ||
5.4 | even | 2 | inner | 1620.3.b.b.809.21 | 24 | ||
9.2 | odd | 6 | 180.3.t.a.149.7 | yes | 24 | ||
9.4 | even | 3 | 180.3.t.a.29.6 | ✓ | 24 | ||
9.5 | odd | 6 | 540.3.t.a.89.5 | 24 | |||
9.7 | even | 3 | 540.3.t.a.449.10 | 24 | |||
15.14 | odd | 2 | inner | 1620.3.b.b.809.4 | 24 | ||
45.2 | even | 12 | 900.3.p.f.401.1 | 24 | |||
45.4 | even | 6 | 180.3.t.a.29.7 | yes | 24 | ||
45.7 | odd | 12 | 2700.3.p.f.2501.1 | 24 | |||
45.13 | odd | 12 | 900.3.p.f.101.12 | 24 | |||
45.14 | odd | 6 | 540.3.t.a.89.10 | 24 | |||
45.22 | odd | 12 | 900.3.p.f.101.1 | 24 | |||
45.23 | even | 12 | 2700.3.p.f.1601.12 | 24 | |||
45.29 | odd | 6 | 180.3.t.a.149.6 | yes | 24 | ||
45.32 | even | 12 | 2700.3.p.f.1601.1 | 24 | |||
45.34 | even | 6 | 540.3.t.a.449.5 | 24 | |||
45.38 | even | 12 | 900.3.p.f.401.12 | 24 | |||
45.43 | odd | 12 | 2700.3.p.f.2501.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.6 | ✓ | 24 | 9.4 | even | 3 | ||
180.3.t.a.29.7 | yes | 24 | 45.4 | even | 6 | ||
180.3.t.a.149.6 | yes | 24 | 45.29 | odd | 6 | ||
180.3.t.a.149.7 | yes | 24 | 9.2 | odd | 6 | ||
540.3.t.a.89.5 | 24 | 9.5 | odd | 6 | |||
540.3.t.a.89.10 | 24 | 45.14 | odd | 6 | |||
540.3.t.a.449.5 | 24 | 45.34 | even | 6 | |||
540.3.t.a.449.10 | 24 | 9.7 | even | 3 | |||
900.3.p.f.101.1 | 24 | 45.22 | odd | 12 | |||
900.3.p.f.101.12 | 24 | 45.13 | odd | 12 | |||
900.3.p.f.401.1 | 24 | 45.2 | even | 12 | |||
900.3.p.f.401.12 | 24 | 45.38 | even | 12 | |||
1620.3.b.b.809.3 | 24 | 1.1 | even | 1 | trivial | ||
1620.3.b.b.809.4 | 24 | 15.14 | odd | 2 | inner | ||
1620.3.b.b.809.21 | 24 | 5.4 | even | 2 | inner | ||
1620.3.b.b.809.22 | 24 | 3.2 | odd | 2 | inner | ||
2700.3.p.f.1601.1 | 24 | 45.32 | even | 12 | |||
2700.3.p.f.1601.12 | 24 | 45.23 | even | 12 | |||
2700.3.p.f.2501.1 | 24 | 45.7 | odd | 12 | |||
2700.3.p.f.2501.12 | 24 | 45.43 | odd | 12 |