Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.2 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.g.3025.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.66698i | − 1.63993i | −0.572417 | − | 0.819963i | \(-0.693994\pi\) | ||||
0.572417 | − | 0.819963i | \(-0.306006\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.45794i | 1.34412i | 0.740498 | + | 0.672059i | \(0.234590\pi\) | ||||
−0.740498 | + | 0.672059i | \(0.765410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.51546i | 0.420314i | 0.977668 | + | 0.210157i | \(0.0673975\pi\) | ||||
−0.977668 | + | 0.210157i | \(0.932602\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.45516 | −0.838000 | −0.419000 | − | 0.907986i | \(-0.637619\pi\) | ||||
−0.419000 | + | 0.907986i | \(0.637619\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.29933i | − 0.527503i | −0.964591 | − | 0.263752i | \(-0.915040\pi\) | ||||
0.964591 | − | 0.263752i | \(-0.0849600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.76326 | 1.82727 | 0.913633 | − | 0.406539i | \(-0.133265\pi\) | ||||
0.913633 | + | 0.406539i | \(0.133265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.44677 | −1.68935 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.62037i | 0.300895i | 0.988618 | + | 0.150448i | \(0.0480715\pi\) | ||||
−0.988618 | + | 0.150448i | \(0.951928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.26498 | 1.66404 | 0.832020 | − | 0.554746i | \(-0.187184\pi\) | ||||
0.832020 | + | 0.554746i | \(0.187184\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.66698i | 0.619833i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.69381i | − 0.936056i | −0.883714 | − | 0.468028i | \(-0.844965\pi\) | ||||
0.883714 | − | 0.468028i | \(-0.155035\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.86926 | −1.07280 | −0.536399 | − | 0.843965i | \(-0.680216\pi\) | ||||
−0.536399 | + | 0.843965i | \(0.680216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.880042i | − 0.134205i | −0.997746 | − | 0.0671026i | \(-0.978625\pi\) | ||||
0.997746 | − | 0.0671026i | \(-0.0213755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5955 | −1.54551 | −0.772753 | − | 0.634707i | \(-0.781121\pi\) | ||||
−0.772753 | + | 0.634707i | \(0.781121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.5036i | − 1.58014i | −0.613014 | − | 0.790072i | \(-0.710043\pi\) | ||||
0.613014 | − | 0.790072i | \(-0.289957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.3472 | 2.20425 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.99426i | − 0.389819i | −0.980821 | − | 0.194909i | \(-0.937559\pi\) | ||||
0.980821 | − | 0.194909i | \(-0.0624413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 8.51202i | − 1.08985i | −0.838484 | − | 0.544926i | \(-0.816558\pi\) | ||||
0.838484 | − | 0.544926i | \(-0.183442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.55718 | 0.689284 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.6629i | − 1.30268i | −0.758786 | − | 0.651341i | \(-0.774207\pi\) | ||||
0.758786 | − | 0.651341i | \(-0.225793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6172 | −1.26003 | −0.630015 | − | 0.776583i | \(-0.716951\pi\) | ||||
−0.630015 | + | 0.776583i | \(0.716951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.85523 | 0.919385 | 0.459692 | − | 0.888078i | \(-0.347960\pi\) | ||||
0.459692 | + | 0.888078i | \(0.347960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.45794i | − 0.508029i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.57730 | −0.514986 | −0.257493 | − | 0.966280i | \(-0.582896\pi\) | ||||
−0.257493 | + | 0.966280i | \(0.582896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.60500i | 0.285936i | 0.989727 | + | 0.142968i | \(0.0456645\pi\) | ||||
−0.989727 | + | 0.142968i | \(0.954335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6700i | 1.37426i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.14381 | −0.227244 | −0.113622 | − | 0.993524i | \(-0.536245\pi\) | ||||
−0.113622 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.51546i | − 0.158864i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.43162 | −0.865066 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8317 | −1.40440 | −0.702199 | − | 0.711981i | \(-0.747798\pi\) | ||||
−0.702199 | + | 0.711981i | \(0.747798\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.2333i | − 1.01826i | −0.860691 | − | 0.509128i | \(-0.829968\pi\) | ||||
0.860691 | − | 0.509128i | \(-0.170032\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7223 | 1.25357 | 0.626784 | − | 0.779193i | \(-0.284371\pi\) | ||||
0.626784 | + | 0.779193i | \(0.284371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.40575i | 0.619268i | 0.950856 | + | 0.309634i | \(0.100206\pi\) | ||||
−0.950856 | + | 0.309634i | \(0.899794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.38839i | − 0.324549i | −0.986746 | − | 0.162274i | \(-0.948117\pi\) | ||||
0.986746 | − | 0.162274i | \(-0.0518829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.40668 | −0.132329 | −0.0661644 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661644 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 32.1347i | − 2.99658i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.45516 | 0.316734 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.87319 | −0.806653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.6393i | 1.13049i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4597 | −0.928152 | −0.464076 | − | 0.885795i | \(-0.653614\pi\) | ||||
−0.464076 | + | 0.885795i | \(0.653614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.6638i | − 1.10644i | −0.833034 | − | 0.553221i | \(-0.813398\pi\) | ||||
0.833034 | − | 0.553221i | \(-0.186602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29933i | 0.199378i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.87026 | −0.586966 | −0.293483 | − | 0.955964i | \(-0.594814\pi\) | ||||
−0.293483 | + | 0.955964i | \(0.594814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4362i | 1.13964i | 0.821768 | + | 0.569822i | \(0.192988\pi\) | ||||
−0.821768 | + | 0.569822i | \(0.807012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.75584 | −0.564952 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.94188 | 0.493446 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.35294i | − 0.520453i | −0.965548 | − | 0.260227i | \(-0.916203\pi\) | ||||
0.965548 | − | 0.260227i | \(-0.0837973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5918 | −1.59436 | −0.797179 | − | 0.603743i | \(-0.793675\pi\) | ||||
−0.797179 | + | 0.603743i | \(0.793675\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 33.9745i | − 2.72890i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 22.6978i | − 1.81148i | −0.423834 | − | 0.905740i | \(-0.639316\pi\) | ||||
0.423834 | − | 0.905740i | \(-0.360684\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.76326 | −0.690642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.60107i | 0.282058i | 0.990005 | + | 0.141029i | \(0.0450410\pi\) | ||||
−0.990005 | + | 0.141029i | \(0.954959\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.46351 | 0.422779 | 0.211390 | − | 0.977402i | \(-0.432201\pi\) | ||||
0.211390 | + | 0.977402i | \(0.432201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7034 | 0.823336 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.71944i | − 0.130727i | −0.997862 | − | 0.0653634i | \(-0.979179\pi\) | ||||
0.997862 | − | 0.0653634i | \(-0.0208207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.44677 | 0.638516 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9956i | 0.821846i | 0.911670 | + | 0.410923i | \(0.134794\pi\) | ||||
−0.911670 | + | 0.410923i | \(0.865206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.6227i | 1.97885i | 0.145040 | + | 0.989426i | \(0.453669\pi\) | ||||
−0.145040 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.8791 | −1.53506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.4029i | − 1.12637i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1581 | −1.60330 | −0.801652 | − | 0.597791i | \(-0.796045\pi\) | ||||
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5599 | 0.832098 | 0.416049 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416049 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.1740i | 0.938611i | 0.883036 | + | 0.469305i | \(0.155496\pi\) | ||||
−0.883036 | + | 0.469305i | \(0.844504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.1012 | 0.857828 | 0.428914 | − | 0.903345i | \(-0.358896\pi\) | ||||
0.428914 | + | 0.903345i | \(0.358896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.62037i | − 0.113728i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.1895i | 1.75931i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.2503 | 0.709027 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7501i | 1.49734i | 0.662944 | + | 0.748669i | \(0.269307\pi\) | ||||
−0.662944 | + | 0.748669i | \(0.730693\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.22710 | −0.220086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.26498 | −0.628948 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 5.23617i | − 0.352223i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.00739 | 0.201390 | 0.100695 | − | 0.994917i | \(-0.467893\pi\) | ||||
0.100695 | + | 0.994917i | \(0.467893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.1508i | 0.740102i | 0.929011 | + | 0.370051i | \(0.120660\pi\) | ||||
−0.929011 | + | 0.370051i | \(0.879340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.46317i | 0.162771i | 0.996683 | + | 0.0813853i | \(0.0259344\pi\) | ||||
−0.996683 | + | 0.0813853i | \(0.974066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.1143 | −1.71080 | −0.855401 | − | 0.517966i | \(-0.826689\pi\) | ||||
−0.855401 | + | 0.517966i | \(0.826689\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.8534i | 2.53451i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.4496 | −1.58151 | −0.790757 | − | 0.612130i | \(-0.790313\pi\) | ||||
−0.790757 | + | 0.612130i | \(0.790313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.01348 | −0.580609 | −0.290305 | − | 0.956934i | \(-0.593757\pi\) | ||||
−0.290305 | + | 0.956934i | \(0.593757\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.66698i | − 0.234275i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.48456 | 0.221717 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 24.7649i | − 1.56315i | −0.623814 | − | 0.781573i | \(-0.714418\pi\) | ||||
0.623814 | − | 0.781573i | \(-0.285582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.0661i | 2.45606i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.1618 | 1.07052 | 0.535262 | − | 0.844686i | \(-0.320213\pi\) | ||||
0.535262 | + | 0.844686i | \(0.320213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.69381i | 0.353796i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.02861 | −0.248415 | −0.124207 | − | 0.992256i | \(-0.539639\pi\) | ||||
−0.124207 | + | 0.992256i | \(0.539639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.1836 | −2.59132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 24.4193i | − 1.48887i | −0.667693 | − | 0.744436i | \(-0.732718\pi\) | ||||
0.667693 | − | 0.744436i | \(-0.267282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.21510 | 0.0738120 | 0.0369060 | − | 0.999319i | \(-0.488250\pi\) | ||||
0.0369060 | + | 0.999319i | \(0.488250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 37.6552i | − 2.27069i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1239i | 0.668371i | 0.942507 | + | 0.334185i | \(0.108461\pi\) | ||||
−0.942507 | + | 0.334185i | \(0.891539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.4678 | −1.75790 | −0.878952 | − | 0.476910i | \(-0.841757\pi\) | ||||
−0.878952 | + | 0.476910i | \(0.841757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 13.0312i | − 0.774624i | −0.921949 | − | 0.387312i | \(-0.873404\pi\) | ||||
0.921949 | − | 0.387312i | \(-0.126596\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.86926 | 0.405479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.06186 | −0.297756 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.86503i | 0.284218i | 0.989851 | + | 0.142109i | \(0.0453883\pi\) | ||||
−0.989851 | + | 0.142109i | \(0.954612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9799 | −0.639274 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.2804i | 0.768026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.880042i | 0.0507248i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.2134 | −1.78728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.07611i | − 0.518001i | −0.965877 | − | 0.259000i | \(-0.916607\pi\) | ||||
0.965877 | − | 0.259000i | \(-0.0833931\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.21020 | −0.0686240 | −0.0343120 | − | 0.999411i | \(-0.510924\pi\) | ||||
−0.0343120 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.15697 | −0.178443 | −0.0892214 | − | 0.996012i | \(-0.528438\pi\) | ||||
−0.0892214 | + | 0.996012i | \(0.528438\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.08197i | 0.397763i | 0.980024 | + | 0.198882i | \(0.0637309\pi\) | ||||
−0.980024 | + | 0.198882i | \(0.936269\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.22351 | −0.404439 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.94457i | 0.442048i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 12.8008i | − 0.710060i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5955 | 0.584146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.34765i | 0.403863i | 0.979400 | + | 0.201932i | \(0.0647219\pi\) | ||||
−0.979400 | + | 0.201932i | \(0.935278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.1007 | −2.13630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9873 | −1.47009 | −0.735046 | − | 0.678017i | \(-0.762840\pi\) | ||||
−0.735046 | + | 0.678017i | \(0.762840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.3027i | 2.23667i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.06776i | 0.486783i | 0.969928 | + | 0.243391i | \(0.0782599\pi\) | ||||
−0.969928 | + | 0.243391i | \(0.921740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6784i | 0.732191i | 0.930577 | + | 0.366095i | \(0.119306\pi\) | ||||
−0.930577 | + | 0.366095i | \(0.880694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.949067 | −0.0505138 | −0.0252569 | − | 0.999681i | \(-0.508040\pi\) | ||||
−0.0252569 | + | 0.999681i | \(0.508040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.9331i | 2.06636i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0508 | 0.794351 | 0.397175 | − | 0.917743i | \(-0.369991\pi\) | ||||
0.397175 | + | 0.917743i | \(0.369991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7131 | 0.721740 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 28.8050i | − 1.50772i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.70674 | 0.193490 | 0.0967451 | − | 0.995309i | \(-0.469157\pi\) | ||||
0.0967451 | + | 0.995309i | \(0.469157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5036i | 0.597239i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 31.3688i | − 1.62421i | −0.583508 | − | 0.812107i | \(-0.698320\pi\) | ||||
0.583508 | − | 0.812107i | \(-0.301680\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.45562 | −0.126471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 17.6560i | − 0.906930i | −0.891274 | − | 0.453465i | \(-0.850188\pi\) | ||||
0.891274 | − | 0.453465i | \(-0.149812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7974 | 0.909402 | 0.454701 | − | 0.890644i | \(-0.349746\pi\) | ||||
0.454701 | + | 0.890644i | \(0.349746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3472 | −0.833129 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 25.1886i | − 1.27711i | −0.769574 | − | 0.638557i | \(-0.779532\pi\) | ||||
0.769574 | − | 0.638557i | \(-0.220468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.2785 | −1.53125 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.7849i | 0.844539i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 34.3710i | − 1.72503i | −0.506032 | − | 0.862515i | \(-0.668888\pi\) | ||||
0.506032 | − | 0.862515i | \(-0.331112\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.65560 | 0.482178 | 0.241089 | − | 0.970503i | \(-0.422495\pi\) | ||||
0.241089 | + | 0.970503i | \(0.422495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.0408i | 0.699420i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.3826 | 1.25817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4161 | 1.40509 | 0.702543 | − | 0.711642i | \(-0.252048\pi\) | ||||
0.702543 | + | 0.711642i | \(0.252048\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.99426i | 0.147338i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.55248 | 0.468913 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 11.5381i | − 0.563673i | −0.959462 | − | 0.281837i | \(-0.909056\pi\) | ||||
0.959462 | − | 0.281837i | \(-0.0909436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.84814i | − 0.333758i | −0.985977 | − | 0.166879i | \(-0.946631\pi\) | ||||
0.985977 | − | 0.166879i | \(-0.0533689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.1850 | 1.41568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.51202i | 0.411925i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4500 | −0.503357 | −0.251679 | − | 0.967811i | \(-0.580983\pi\) | ||||
−0.251679 | + | 0.967811i | \(0.580983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1818 | 0.873763 | 0.436882 | − | 0.899519i | \(-0.356083\pi\) | ||||
0.436882 | + | 0.899519i | \(0.356083\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 20.1497i | − 0.963889i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.91836 | −0.377923 | −0.188961 | − | 0.981985i | \(-0.560512\pi\) | ||||
−0.188961 | + | 0.981985i | \(0.560512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 18.2916i | − 0.869062i | −0.900657 | − | 0.434531i | \(-0.856914\pi\) | ||||
0.900657 | − | 0.434531i | \(-0.143086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.86132i | 0.372662i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.2172 | −0.718144 | −0.359072 | − | 0.933310i | \(-0.616907\pi\) | ||||
−0.359072 | + | 0.933310i | \(0.616907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 30.6227i | − 1.44197i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.55718 | −0.260525 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.6658 | 1.80871 | 0.904354 | − | 0.426783i | \(-0.140353\pi\) | ||||
0.904354 | + | 0.426783i | \(0.140353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.18888i | 0.241670i | 0.992673 | + | 0.120835i | \(0.0385572\pi\) | ||||
−0.992673 | + | 0.120835i | \(0.961443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.81583 | 0.177337 | 0.0886683 | − | 0.996061i | \(-0.471739\pi\) | ||||
0.0886683 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.29246i | − 0.337455i | −0.985663 | − | 0.168727i | \(-0.946034\pi\) | ||||
0.985663 | − | 0.168727i | \(-0.0539657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.6629i | 0.492367i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.92317 | 0.180388 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.4220i | 0.891140i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.2695 | −0.743371 | −0.371686 | − | 0.928359i | \(-0.621220\pi\) | ||||
−0.371686 | + | 0.928359i | \(0.621220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.62876 | 0.393438 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 50.7207i | 2.30311i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.16667 | −0.324753 | −0.162376 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162376 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 17.8247i | − 0.804418i | −0.915548 | − | 0.402209i | \(-0.868243\pi\) | ||||
0.915548 | − | 0.402209i | \(-0.131757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.59864i | − 0.252150i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.6172 | 0.476247 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 37.6121i | − 1.68375i | −0.539673 | − | 0.841875i | \(-0.681452\pi\) | ||||
0.539673 | − | 0.841875i | \(-0.318548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.3707 | 0.908286 | 0.454143 | − | 0.890929i | \(-0.349945\pi\) | ||||
0.454143 | + | 0.890929i | \(0.349945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.5255 | −1.66986 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 26.6481i | − 1.18116i | −0.806980 | − | 0.590578i | \(-0.798900\pi\) | ||||
0.806980 | − | 0.590578i | \(-0.201100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.85523 | −0.347495 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 46.6526i | − 2.05576i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 47.2339i | − 2.07734i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2614 | −0.580992 | −0.290496 | − | 0.956876i | \(-0.593820\pi\) | ||||
−0.290496 | + | 0.956876i | \(0.593820\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 21.3786i | − 0.934821i | −0.884040 | − | 0.467411i | \(-0.845187\pi\) | ||||
0.884040 | − | 0.467411i | \(-0.154813\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.0120 | −1.39447 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.7948 | 2.33890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 10.4101i | − 0.450912i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.4898 | 1.01555 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.45794i | 0.192017i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 31.4969i | − 1.35416i | −0.735910 | − | 0.677080i | \(-0.763245\pi\) | ||||
0.735910 | − | 0.677080i | \(-0.236755\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.4252 | −0.532235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.38840i | − 0.0593637i | −0.999559 | − | 0.0296819i | \(-0.990551\pi\) | ||||
0.999559 | − | 0.0296819i | \(-0.00944942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72578 | 0.158723 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.57730 | 0.194647 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8246i | 0.458654i | 0.973349 | + | 0.229327i | \(0.0736525\pi\) | ||||
−0.973349 | + | 0.229327i | \(0.926347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.33367 | 0.0564083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.56473i | − 0.318816i | −0.987213 | − | 0.159408i | \(-0.949042\pi\) | ||||
0.987213 | − | 0.159408i | \(-0.0509585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.15826i | 0.217009i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.9063 | −0.918360 | −0.459180 | − | 0.888343i | \(-0.651857\pi\) | ||||
−0.459180 | + | 0.888343i | \(0.651857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.6061i | 1.82486i | 0.409235 | + | 0.912429i | \(0.365796\pi\) | ||||
−0.409235 | + | 0.912429i | \(0.634204\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −74.0213 | −3.08690 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6116 | 0.525028 | 0.262514 | − | 0.964928i | \(-0.415448\pi\) | ||||
0.262514 | + | 0.964928i | \(0.415448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.60500i | − 0.108073i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.2824 | 2.12390 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 10.5118i | − 0.433866i | −0.976186 | − | 0.216933i | \(-0.930395\pi\) | ||||
0.976186 | − | 0.216933i | \(-0.0696054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 21.3033i | − 0.877787i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.9765 | −0.984598 | −0.492299 | − | 0.870426i | \(-0.663843\pi\) | ||||
−0.492299 | + | 0.870426i | \(0.663843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 12.6700i | − 0.519420i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.2302 | 1.31689 | 0.658446 | − | 0.752628i | \(-0.271214\pi\) | ||||
0.658446 | + | 0.752628i | \(0.271214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3405 | 1.76790 | 0.883949 | − | 0.467584i | \(-0.154875\pi\) | ||||
0.883949 | + | 0.467584i | \(0.154875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.5378i | 1.32285i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.2372 | 0.537283 | 0.268642 | − | 0.963240i | \(-0.413425\pi\) | ||||
0.268642 | + | 0.963240i | \(0.413425\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 16.0570i | − 0.649598i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.23612i | − 0.251874i | −0.992038 | − | 0.125937i | \(-0.959806\pi\) | ||||
0.992038 | − | 0.125937i | \(-0.0401938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.66713 | 0.308667 | 0.154334 | − | 0.988019i | \(-0.450677\pi\) | ||||
0.154334 | + | 0.988019i | \(0.450677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 27.9974i | − 1.12531i | −0.826692 | − | 0.562655i | \(-0.809780\pi\) | ||||
0.826692 | − | 0.562655i | \(-0.190220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.14381 | 0.0858900 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.11412 | 0.164565 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.6730i | 0.784415i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2806 | −0.727739 | −0.363869 | − | 0.931450i | \(-0.618545\pi\) | ||||
−0.363869 | + | 0.931450i | \(0.618545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.3557i | 1.52210i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.51546i | 0.0600449i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.99361 | 0.236733 | 0.118367 | − | 0.992970i | \(-0.462234\pi\) | ||||
0.118367 | + | 0.992970i | \(0.462234\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 29.0547i | − 1.14581i | −0.819623 | − | 0.572903i | \(-0.805817\pi\) | ||||
0.819623 | − | 0.572903i | \(-0.194183\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.7288 | −1.05082 | −0.525408 | − | 0.850850i | \(-0.676087\pi\) | ||||
−0.525408 | + | 0.850850i | \(0.676087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3482 | 0.523963 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.0011i | 1.60450i | 0.596991 | + | 0.802248i | \(0.296363\pi\) | ||||
−0.596991 | + | 0.802248i | \(0.703637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.4380 | −1.81448 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.91818i | 0.0747219i | 0.999302 | + | 0.0373609i | \(0.0118951\pi\) | ||||
−0.999302 | + | 0.0373609i | \(0.988105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9347i | 0.425312i | 0.977127 | + | 0.212656i | \(0.0682114\pi\) | ||||
−0.977127 | + | 0.212656i | \(0.931789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.43162 | 0.326964 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1997i | 0.549816i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.9460 | 1.46489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0071 | 0.385745 | 0.192872 | − | 0.981224i | \(-0.438220\pi\) | ||||
0.192872 | + | 0.981224i | \(0.438220\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 35.4441i | − 1.36223i | −0.732178 | − | 0.681113i | \(-0.761496\pi\) | ||||
0.732178 | − | 0.681113i | \(-0.238504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8317 | 0.530812 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.8397i | 1.33310i | 0.745459 | + | 0.666551i | \(0.232230\pi\) | ||||
−0.745459 | + | 0.666551i | \(0.767770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.1931i | 0.962580i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4333 | 0.664157 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 16.2381i | − 0.617727i | −0.951106 | − | 0.308864i | \(-0.900051\pi\) | ||||
0.951106 | − | 0.308864i | \(-0.0999486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 49.2704 | 1.86893 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7344 | 0.899004 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28.8081i | − 1.08807i | −0.839064 | − | 0.544033i | \(-0.816897\pi\) | ||||
0.839064 | − | 0.544033i | \(-0.183103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.0920 | −0.493773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.2333i | 0.384864i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 18.1039i | − 0.679906i | −0.940442 | − | 0.339953i | \(-0.889589\pi\) | ||||
0.940442 | − | 0.339953i | \(-0.110411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 81.1915 | 3.04064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.7736i | 0.926479i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.7731 | 0.476357 | 0.238179 | − | 0.971221i | \(-0.423450\pi\) | ||||
0.238179 | + | 0.971221i | \(0.423450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7223 | −0.473804 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 13.6869i | − 0.508319i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.1654 | 0.377012 | 0.188506 | − | 0.982072i | \(-0.439635\pi\) | ||||
0.188506 | + | 0.982072i | \(0.439635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.04069i | 0.112464i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 26.1041i | − 0.964178i | −0.876122 | − | 0.482089i | \(-0.839878\pi\) | ||||
0.876122 | − | 0.482089i | \(-0.160122\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.5345 | 1.75096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9.90517i | − 0.364368i | −0.983264 | − | 0.182184i | \(-0.941683\pi\) | ||||
0.983264 | − | 0.182184i | \(-0.0583166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.5353 | −1.23029 | −0.615146 | − | 0.788413i | \(-0.710903\pi\) | ||||
−0.615146 | + | 0.788413i | \(0.710903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2961 | −0.853504 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 6.40575i | − 0.234061i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.8436 | −1.96478 | −0.982391 | − | 0.186839i | \(-0.940176\pi\) | ||||
−0.982391 | + | 0.186839i | \(0.940176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 71.8428i | 2.61463i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.18921i | 0.0432225i | 0.999766 | + | 0.0216113i | \(0.00687962\pi\) | ||||
−0.999766 | + | 0.0216113i | \(0.993120\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.0810 | −1.38043 | −0.690217 | − | 0.723602i | \(-0.742485\pi\) | ||||
−0.690217 | + | 0.723602i | \(0.742485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.38839i | 0.122668i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.53769 | 0.163846 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.6053 | −1.39214 | −0.696071 | − | 0.717973i | \(-0.745070\pi\) | ||||
−0.696071 | + | 0.717973i | \(0.745070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 18.5902i | − 0.668642i | −0.942459 | − | 0.334321i | \(-0.891493\pi\) | ||||
0.942459 | − | 0.334321i | \(-0.108507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −78.2592 | −2.81115 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.7947i | 0.565905i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 47.3308i | − 1.69363i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −83.2324 | −2.97069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.3947i | 0.620056i | 0.950727 | + | 0.310028i | \(0.100338\pi\) | ||||
−0.950727 | + | 0.310028i | \(0.899662\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.40668 | 0.0500156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8997 | 0.458080 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 15.3683i | − 0.544374i | −0.962244 | − | 0.272187i | \(-0.912253\pi\) | ||||
0.962244 | − | 0.272187i | \(-0.0877470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.6090 | 1.29513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.0181i | 1.23576i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.1347i | 1.13260i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.7888 | 1.04732 | 0.523659 | − | 0.851928i | \(-0.324567\pi\) | ||||
0.523659 | + | 0.851928i | \(0.324567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 6.50515i | − 0.228427i | −0.993456 | − | 0.114213i | \(-0.963565\pi\) | ||||
0.993456 | − | 0.114213i | \(-0.0364347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.2051 | 0.462553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.02351 | −0.0707937 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.89581i | − 0.135965i | −0.997687 | − | 0.0679823i | \(-0.978344\pi\) | ||||
0.997687 | − | 0.0679823i | \(-0.0216562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.1577 | −1.64381 | −0.821907 | − | 0.569621i | \(-0.807090\pi\) | ||||
−0.821907 | + | 0.569621i | \(0.807090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.9915i | 1.07768i | 0.842408 | + | 0.538841i | \(0.181138\pi\) | ||||
−0.842408 | + | 0.538841i | \(0.818862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 34.2090i | − 1.18813i | −0.804417 | − | 0.594065i | \(-0.797522\pi\) | ||||
0.804417 | − | 0.594065i | \(-0.202478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.45516 | −0.119714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 20.0346i | − 0.693326i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.9980 | 1.41541 | 0.707704 | − | 0.706509i | \(-0.249731\pi\) | ||||
0.707704 | + | 0.706509i | \(0.249731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.3744 | 0.909462 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 39.2491i | − 1.35021i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.87319 | 0.304886 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 49.8963i | − 1.71042i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.3408i | 0.901891i | 0.892551 | + | 0.450946i | \(0.148913\pi\) | ||||
−0.892551 | + | 0.450946i | \(0.851087\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.4187 | −1.92723 | −0.963613 | − | 0.267300i | \(-0.913868\pi\) | ||||
−0.963613 | + | 0.267300i | \(0.913868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.5693i | 1.17949i | 0.807589 | + | 0.589745i | \(0.200772\pi\) | ||||
−0.807589 | + | 0.589745i | \(0.799228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.52709 | −0.0519826 | −0.0259913 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259913 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.30517 | −0.214382 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 20.4053i | − 0.692202i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1593 | 0.547535 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 12.6393i | − 0.427285i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 20.5638i | − 0.694389i | −0.937793 | − | 0.347195i | \(-0.887134\pi\) | ||||
0.937793 | − | 0.347195i | \(-0.112866\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.8073 | −0.566252 | −0.283126 | − | 0.959083i | \(-0.591371\pi\) | ||||
−0.283126 | + | 0.959083i | \(0.591371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 13.7849i | − 0.463900i | −0.972728 | − | 0.231950i | \(-0.925489\pi\) | ||||
0.972728 | − | 0.231950i | \(-0.0745105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.0037 | 0.839541 | 0.419771 | − | 0.907630i | \(-0.362111\pi\) | ||||
0.419771 | + | 0.907630i | \(0.362111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4597 | 0.350808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3625i | 0.815260i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.3205 | 1.34777 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0127i | 0.500702i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.7469i | 1.32416i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 97.6251 | 3.24517 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.5827i | 0.783052i | 0.920167 | + | 0.391526i | \(0.128053\pi\) | ||||
−0.920167 | + | 0.391526i | \(0.871947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1770 | 0.966677 | 0.483338 | − | 0.875434i | \(-0.339424\pi\) | ||||
0.483338 | + | 0.875434i | \(0.339424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6129 | −0.384331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6638i | 0.418196i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.6854 | −1.70494 | −0.852472 | − | 0.522772i | \(-0.824898\pi\) | ||||
−0.852472 | + | 0.522772i | \(0.824898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 16.0900i | − 0.529609i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.0943i | 1.58133i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0819 | −0.658865 | −0.329432 | − | 0.944179i | \(-0.606857\pi\) | ||||
−0.329432 | + | 0.944179i | \(0.606857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.29933i | − 0.0753576i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.4821 | −1.84716 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1583 | −0.625875 | −0.312937 | − | 0.949774i | \(-0.601313\pi\) | ||||
−0.312937 | + | 0.949774i | \(0.601313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 54.2409i | − 1.76820i | −0.467296 | − | 0.884101i | \(-0.654772\pi\) | ||||
0.467296 | − | 0.884101i | \(-0.345228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −60.1971 | −1.96029 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.7355i | 1.55120i | 0.631228 | + | 0.775598i | \(0.282551\pi\) | ||||
−0.631228 | + | 0.775598i | \(0.717449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9043i | 0.386430i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2075 | 0.363046 | 0.181523 | − | 0.983387i | \(-0.441897\pi\) | ||||
0.181523 | + | 0.983387i | \(0.441897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.2534i | 2.62930i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.87026 | 0.221852 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.8399 | 1.76903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 42.3899i | − 1.36458i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5979 | 0.726701 | 0.363350 | − | 0.931653i | \(-0.381633\pi\) | ||||
0.363350 | + | 0.931653i | \(0.381633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.5586i | 1.49414i | 0.664747 | + | 0.747068i | \(0.268539\pi\) | ||||
−0.664747 | + | 0.747068i | \(0.731461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 13.4362i | − 0.430745i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.5968 | −1.39479 | −0.697393 | − | 0.716689i | \(-0.745657\pi\) | ||||
−0.697393 | + | 0.716689i | \(0.745657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 9.55697i | − 0.305442i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.5407 | −0.718937 | −0.359469 | − | 0.933157i | \(-0.617042\pi\) | ||||
−0.359469 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.3090 | 1.53925 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.71204i | − 0.245229i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2444 | −0.770148 | −0.385074 | − | 0.922886i | \(-0.625824\pi\) | ||||
−0.385074 | + | 0.922886i | \(0.625824\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 44.3747i | − 1.40677i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.3412i | 1.56265i | 0.624124 | + | 0.781325i | \(0.285456\pi\) | ||||
−0.624124 | + | 0.781325i | \(0.714544\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.g.3025.2 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.g.3025.24 | 24 | ||
4.3 | odd | 2 | 1512.2.c.f.757.16 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.f.757.15 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.g.3025.23 | 24 | ||
12.11 | even | 2 | 1512.2.c.f.757.9 | ✓ | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.g.3025.1 | 24 | ||
24.11 | even | 2 | 1512.2.c.f.757.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.9 | ✓ | 24 | 12.11 | even | 2 | ||
1512.2.c.f.757.10 | yes | 24 | 24.11 | even | 2 | ||
1512.2.c.f.757.15 | yes | 24 | 8.3 | odd | 2 | ||
1512.2.c.f.757.16 | yes | 24 | 4.3 | odd | 2 | ||
6048.2.c.g.3025.1 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.g.3025.2 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.g.3025.23 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.g.3025.24 | 24 | 3.2 | odd | 2 | inner |