Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(161,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.h (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 13x^{10} + 129x^{8} - 512x^{6} + 1548x^{4} - 160x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(1.88569 + 1.08870i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.161 |
Dual form | 1728.3.h.j.161.4 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −3.32298 | −0.664596 | −0.332298 | − | 0.943174i | \(-0.607824\pi\) | ||||
−0.332298 | + | 0.943174i | \(0.607824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.21979 | 0.602827 | 0.301414 | − | 0.953494i | \(-0.402542\pi\) | ||||
0.301414 | + | 0.953494i | \(0.402542\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.0645 | 1.46041 | 0.730203 | − | 0.683231i | \(-0.239426\pi\) | ||||
0.730203 | + | 0.683231i | \(0.239426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 17.6528i | − 1.35791i | −0.734180 | − | 0.678955i | \(-0.762433\pi\) | ||||
0.734180 | − | 0.678955i | \(-0.237567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.44668i | 0.261569i | 0.991411 | + | 0.130785i | \(0.0417496\pi\) | ||||
−0.991411 | + | 0.130785i | \(0.958250\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.5756i | 1.39872i | 0.714772 | + | 0.699358i | \(0.246531\pi\) | ||||
−0.714772 | + | 0.699358i | \(0.753469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.59004i | 0.243045i | 0.992589 | + | 0.121523i | \(0.0387777\pi\) | ||||
−0.992589 | + | 0.121523i | \(0.961222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.9578 | −0.558313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 50.0589 | 1.72617 | 0.863084 | − | 0.505060i | \(-0.168530\pi\) | ||||
0.863084 | + | 0.505060i | \(0.168530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.4803 | −0.370333 | −0.185166 | − | 0.982707i | \(-0.559282\pi\) | ||||
−0.185166 | + | 0.982707i | \(0.559282\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.0223 | −0.400636 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.5810i | 0.664352i | 0.943217 | + | 0.332176i | \(0.107783\pi\) | ||||
−0.943217 | + | 0.332176i | \(0.892217\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 18.5756i | − 0.453063i | −0.974004 | − | 0.226532i | \(-0.927261\pi\) | ||||
0.974004 | − | 0.226532i | \(-0.0727387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 37.2356i | − 0.865943i | −0.901408 | − | 0.432972i | \(-0.857465\pi\) | ||||
0.901408 | − | 0.432972i | \(-0.142535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 73.5339i | − 1.56455i | −0.622932 | − | 0.782276i | \(-0.714059\pi\) | ||||
0.622932 | − | 0.782276i | \(-0.285941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −31.1934 | −0.636599 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.32602 | 0.0438872 | 0.0219436 | − | 0.999759i | \(-0.493015\pi\) | ||||
0.0219436 | + | 0.999759i | \(0.493015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −53.3819 | −0.970579 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 26.8934 | 0.455820 | 0.227910 | − | 0.973682i | \(-0.426811\pi\) | ||||
0.227910 | + | 0.973682i | \(0.426811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3091i | 0.201788i | 0.994897 | + | 0.100894i | \(0.0321703\pi\) | ||||
−0.994897 | + | 0.100894i | \(0.967830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.6600i | 0.902461i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45.2356i | 0.675158i | 0.941297 | + | 0.337579i | \(0.109608\pi\) | ||||
−0.941297 | + | 0.337579i | \(0.890392\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 83.3476i | − 1.17391i | −0.809620 | − | 0.586955i | \(-0.800327\pi\) | ||||
0.809620 | − | 0.586955i | \(-0.199673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.04219 | −0.0416738 | −0.0208369 | − | 0.999783i | \(-0.506633\pi\) | ||||
−0.0208369 | + | 0.999783i | \(0.506633\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 67.7886 | 0.880372 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.2115 | 0.217867 | 0.108933 | − | 0.994049i | \(-0.465256\pi\) | ||||
0.108933 | + | 0.994049i | \(0.465256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 92.8734 | 1.11896 | 0.559479 | − | 0.828845i | \(-0.311001\pi\) | ||||
0.559479 | + | 0.828845i | \(0.311001\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 14.7762i | − 0.173838i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 160.431i | 1.80260i | 0.433197 | + | 0.901299i | \(0.357386\pi\) | ||||
−0.433197 | + | 0.901299i | \(0.642614\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 74.4912i | − 0.818585i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 88.3101i | − 0.929580i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 122.538 | 1.26328 | 0.631639 | − | 0.775263i | \(-0.282383\pi\) | ||||
0.631639 | + | 0.775263i | \(0.282383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 104.556 | 1.03520 | 0.517602 | − | 0.855622i | \(-0.326825\pi\) | ||||
0.517602 | + | 0.855622i | \(0.326825\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 172.509 | 1.67484 | 0.837420 | − | 0.546560i | \(-0.184063\pi\) | ||||
0.837420 | + | 0.546560i | \(0.184063\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82654 | 0.0264163 | 0.0132081 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132081 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 59.6686i | − 0.547419i | −0.961812 | − | 0.273709i | \(-0.911749\pi\) | ||||
0.961812 | − | 0.273709i | \(-0.0882506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 153.682i | 1.36002i | 0.733203 | + | 0.680010i | \(0.238025\pi\) | ||||
−0.733203 | + | 0.680010i | \(0.761975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 18.5756i | − 0.161527i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.7640i | 0.157681i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 137.067 | 1.13278 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 129.456 | 1.03565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 52.3530 | 0.412228 | 0.206114 | − | 0.978528i | \(-0.433918\pi\) | ||||
0.206114 | + | 0.978528i | \(0.433918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118.364 | 0.903546 | 0.451773 | − | 0.892133i | \(-0.350792\pi\) | ||||
0.451773 | + | 0.892133i | \(0.350792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 112.143i | 0.843184i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 188.689i | − 1.37729i | −0.725097 | − | 0.688646i | \(-0.758205\pi\) | ||||
0.725097 | − | 0.688646i | \(-0.241795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 104.000i | 0.748201i | 0.927388 | + | 0.374101i | \(0.122049\pi\) | ||||
−0.927388 | + | 0.374101i | \(0.877951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 283.583i | − 1.98310i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −166.345 | −1.14720 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 289.387 | 1.94220 | 0.971098 | − | 0.238679i | \(-0.0767145\pi\) | ||||
0.971098 | + | 0.238679i | \(0.0767145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −151.374 | −1.00247 | −0.501237 | − | 0.865310i | \(-0.667122\pi\) | ||||
−0.501237 | + | 0.865310i | \(0.667122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38.1488 | 0.246121 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 176.964i | − 1.12716i | −0.826061 | − | 0.563581i | \(-0.809423\pi\) | ||||
0.826061 | − | 0.563581i | \(-0.190577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.5888i | 0.146514i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 196.962i | − 1.20836i | −0.796849 | − | 0.604179i | \(-0.793501\pi\) | ||||
0.796849 | − | 0.604179i | \(-0.206499\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 319.981i | − 1.91605i | −0.286682 | − | 0.958026i | \(-0.592552\pi\) | ||||
0.286682 | − | 0.958026i | \(-0.407448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −142.622 | −0.843919 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3852 | −0.0831512 | −0.0415756 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415756 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −58.8990 | −0.336566 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 131.342 | 0.733755 | 0.366878 | − | 0.930269i | \(-0.380427\pi\) | ||||
0.366878 | + | 0.930269i | \(0.380427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 339.492i | 1.87565i | 0.347110 | + | 0.937824i | \(0.387163\pi\) | ||||
−0.347110 | + | 0.937824i | \(0.612837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 81.6822i | − 0.441526i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 71.4335i | 0.381997i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 34.4036i | − 0.180124i | −0.995936 | − | 0.0900618i | \(-0.971294\pi\) | ||||
0.995936 | − | 0.0900618i | \(-0.0287065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 179.513 | 0.930121 | 0.465060 | − | 0.885279i | \(-0.346033\pi\) | ||||
0.465060 | + | 0.885279i | \(0.346033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 261.378 | 1.32679 | 0.663396 | − | 0.748268i | \(-0.269114\pi\) | ||||
0.663396 | + | 0.748268i | \(0.269114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −208.861 | −1.04955 | −0.524776 | − | 0.851240i | \(-0.675851\pi\) | ||||
−0.524776 | + | 0.851240i | \(0.675851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 211.238 | 1.04058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 61.7263i | 0.301104i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 426.923i | 2.04269i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 71.5178i | − 0.338947i | −0.985535 | − | 0.169474i | \(-0.945793\pi\) | ||||
0.985535 | − | 0.169474i | \(-0.0542067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.733i | 0.575502i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −48.4445 | −0.223247 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 78.4964 | 0.355187 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −33.5721 | −0.150548 | −0.0752739 | − | 0.997163i | \(-0.523983\pi\) | ||||
−0.0752739 | + | 0.997163i | \(0.523983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −56.3024 | −0.248028 | −0.124014 | − | 0.992280i | \(-0.539577\pi\) | ||||
−0.124014 | + | 0.992280i | \(0.539577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 382.162i | − 1.66883i | −0.551136 | − | 0.834416i | \(-0.685805\pi\) | ||||
0.551136 | − | 0.834416i | \(-0.314195\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 43.9645i | 0.188689i | 0.995540 | + | 0.0943445i | \(0.0300755\pi\) | ||||
−0.995540 | + | 0.0943445i | \(0.969924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 244.352i | 1.03979i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 172.049i | 0.719872i | 0.932977 | + | 0.359936i | \(0.117202\pi\) | ||||
−0.932977 | + | 0.359936i | \(0.882798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −383.547 | −1.59148 | −0.795741 | − | 0.605638i | \(-0.792918\pi\) | ||||
−0.795741 | + | 0.605638i | \(0.792918\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 103.655 | 0.423081 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 469.134 | 1.89933 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 184.391 | 0.734627 | 0.367314 | − | 0.930097i | \(-0.380278\pi\) | ||||
0.367314 | + | 0.930097i | \(0.380278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 89.8010i | 0.354945i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 302.918i | 1.17867i | 0.807889 | + | 0.589334i | \(0.200610\pi\) | ||||
−0.807889 | + | 0.589334i | \(0.799390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 103.727i | 0.400490i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 397.614i | − 1.51184i | −0.654664 | − | 0.755920i | \(-0.727190\pi\) | ||||
0.654664 | − | 0.755920i | \(-0.272810\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.72932 | −0.0291672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −73.1579 | −0.271962 | −0.135981 | − | 0.990711i | \(-0.543419\pi\) | ||||
−0.135981 | + | 0.990711i | \(0.543419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −325.980 | −1.20288 | −0.601439 | − | 0.798919i | \(-0.705406\pi\) | ||||
−0.601439 | + | 0.798919i | \(0.705406\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −224.225 | −0.815363 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 341.933i | − 1.23441i | −0.786800 | − | 0.617207i | \(-0.788264\pi\) | ||||
0.786800 | − | 0.617207i | \(-0.211736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 137.251i | − 0.488438i | −0.969720 | − | 0.244219i | \(-0.921468\pi\) | ||||
0.969720 | − | 0.244219i | \(-0.0785315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 351.727i | 1.24285i | 0.783473 | + | 0.621425i | \(0.213446\pi\) | ||||
−0.783473 | + | 0.621425i | \(0.786554\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 78.3851i | − 0.273119i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.227 | 0.931582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −417.493 | −1.42489 | −0.712445 | − | 0.701728i | \(-0.752412\pi\) | ||||
−0.712445 | + | 0.701728i | \(0.752412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −89.3660 | −0.302936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 98.6801 | 0.330034 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 157.126i | − 0.522014i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 40.9028i | − 0.134107i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 93.7177i | − 0.305269i | −0.988283 | − | 0.152635i | \(-0.951224\pi\) | ||||
0.988283 | − | 0.152635i | \(-0.0487758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 183.230i | − 0.589162i | −0.955626 | − | 0.294581i | \(-0.904820\pi\) | ||||
0.955626 | − | 0.294581i | \(-0.0951802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 126.882 | 0.405375 | 0.202688 | − | 0.979243i | \(-0.435032\pi\) | ||||
0.202688 | + | 0.979243i | \(0.435032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 371.872 | 1.17310 | 0.586548 | − | 0.809914i | \(-0.300486\pi\) | ||||
0.586548 | + | 0.809914i | \(0.300486\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 804.169 | 2.52090 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −118.173 | −0.365861 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 246.395i | 0.758138i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 310.298i | − 0.943154i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 548.352i | − 1.65665i | −0.560247 | − | 0.828326i | \(-0.689294\pi\) | ||||
0.560247 | − | 0.828326i | \(-0.310706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 150.317i | − 0.448707i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 329.663 | 0.978227 | 0.489114 | − | 0.872220i | \(-0.337320\pi\) | ||||
0.489114 | + | 0.872220i | \(0.337320\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −184.425 | −0.540836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −338.399 | −0.986587 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −567.567 | −1.63564 | −0.817820 | − | 0.575474i | \(-0.804818\pi\) | ||||
−0.817820 | + | 0.575474i | \(0.804818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 425.470i | 1.21911i | 0.792743 | + | 0.609556i | \(0.208652\pi\) | ||||
−0.792743 | + | 0.609556i | \(0.791348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 299.260i | 0.847762i | 0.905718 | + | 0.423881i | \(0.139333\pi\) | ||||
−0.905718 | + | 0.423881i | \(0.860667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 276.962i | 0.780176i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 279.248i | 0.777850i | 0.921269 | + | 0.388925i | \(0.127153\pi\) | ||||
−0.921269 | + | 0.388925i | \(0.872847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −345.262 | −0.956405 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1091 | 0.0276962 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −402.044 | −1.09549 | −0.547744 | − | 0.836646i | \(-0.684513\pi\) | ||||
−0.547744 | + | 0.836646i | \(0.684513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.81532 | 0.0264564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 342.832i | − 0.919120i | −0.888147 | − | 0.459560i | \(-0.848007\pi\) | ||||
0.888147 | − | 0.459560i | \(-0.151993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 883.681i | − 2.34398i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 640.832i | − 1.69085i | −0.534095 | − | 0.845425i | \(-0.679347\pi\) | ||||
0.534095 | − | 0.845425i | \(-0.320653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 563.570i | 1.47146i | 0.677274 | + | 0.735731i | \(0.263161\pi\) | ||||
−0.677274 | + | 0.735731i | \(0.736839\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −225.260 | −0.585091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −342.245 | −0.879806 | −0.439903 | − | 0.898045i | \(-0.644987\pi\) | ||||
−0.439903 | + | 0.898045i | \(0.644987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.8571 | −0.0635732 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −57.1934 | −0.144793 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 403.500i | 1.01637i | 0.861247 | + | 0.508187i | \(0.169684\pi\) | ||||
−0.861247 | + | 0.508187i | \(0.830316\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 169.827i | 0.423508i | 0.977323 | + | 0.211754i | \(0.0679176\pi\) | ||||
−0.977323 | + | 0.211754i | \(0.932082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 202.660i | 0.502878i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 394.881i | 0.970223i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 356.191 | 0.870884 | 0.435442 | − | 0.900217i | \(-0.356592\pi\) | ||||
0.435442 | + | 0.900217i | \(0.356592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 113.484 | 0.274780 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −308.616 | −0.743654 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 417.045 | 0.995334 | 0.497667 | − | 0.867368i | \(-0.334190\pi\) | ||||
0.497667 | + | 0.867368i | \(0.334190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 660.848i | 1.56971i | 0.619679 | + | 0.784855i | \(0.287263\pi\) | ||||
−0.619679 | + | 0.784855i | \(0.712737\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 62.0659i | − 0.146037i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.9417i | 0.121643i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 639.445i | 1.48363i | 0.670604 | + | 0.741816i | \(0.266035\pi\) | ||||
−0.670604 | + | 0.741816i | \(0.733965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −464.454 | −1.07264 | −0.536321 | − | 0.844014i | \(-0.680186\pi\) | ||||
−0.536321 | + | 0.844014i | \(0.680186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −148.559 | −0.339951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 79.8478 | 0.181886 | 0.0909428 | − | 0.995856i | \(-0.471012\pi\) | ||||
0.0909428 | + | 0.995856i | \(0.471012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −389.622 | −0.879509 | −0.439754 | − | 0.898118i | \(-0.644934\pi\) | ||||
−0.439754 | + | 0.898118i | \(0.644934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 533.110i | − 1.19800i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 654.843i | 1.45845i | 0.684275 | + | 0.729224i | \(0.260119\pi\) | ||||
−0.684275 | + | 0.729224i | \(0.739881\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 298.407i | − 0.661656i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 247.533i | 0.544028i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 470.596 | 1.02975 | 0.514876 | − | 0.857265i | \(-0.327838\pi\) | ||||
0.514876 | + | 0.857265i | \(0.327838\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −805.808 | −1.74796 | −0.873979 | − | 0.485965i | \(-0.838468\pi\) | ||||
−0.873979 | + | 0.485965i | \(0.838468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 487.786 | 1.05353 | 0.526767 | − | 0.850010i | \(-0.323404\pi\) | ||||
0.526767 | + | 0.850010i | \(0.323404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 449.958 | 0.963508 | 0.481754 | − | 0.876306i | \(-0.340000\pi\) | ||||
0.481754 | + | 0.876306i | \(0.340000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 190.885i | 0.407003i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 598.169i | − 1.26463i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 370.937i | − 0.780920i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 152.266i | 0.317883i | 0.987288 | + | 0.158942i | \(0.0508082\pi\) | ||||
−0.987288 | + | 0.158942i | \(0.949192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 433.925 | 0.902130 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −407.191 | −0.839569 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 527.351 | 1.08286 | 0.541429 | − | 0.840747i | \(-0.317884\pi\) | ||||
0.541429 | + | 0.840747i | \(0.317884\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 285.609 | 0.581689 | 0.290844 | − | 0.956770i | \(-0.406064\pi\) | ||||
0.290844 | + | 0.956770i | \(0.406064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 222.596i | 0.451512i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 351.709i | − 0.707665i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 420.062i | 0.841808i | 0.907105 | + | 0.420904i | \(0.138287\pi\) | ||||
−0.907105 | + | 0.420904i | \(0.861713\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 80.8820i | − 0.160799i | −0.996763 | − | 0.0803996i | \(-0.974380\pi\) | ||||
0.996763 | − | 0.0803996i | \(-0.0256197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −347.436 | −0.687992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −549.502 | −1.07957 | −0.539786 | − | 0.841802i | \(-0.681495\pi\) | ||||
−0.539786 | + | 0.841802i | \(0.681495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.8374 | −0.0251221 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −573.242 | −1.11309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1181.28i | − 2.28488i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 990.371i | − 1.90090i | −0.310870 | − | 0.950452i | \(-0.600620\pi\) | ||||
0.310870 | − | 0.950452i | \(-0.399380\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 103.016i | 0.196971i | 0.995139 | + | 0.0984853i | \(0.0313997\pi\) | ||||
−0.995139 | + | 0.0984853i | \(0.968600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 51.0492i | − 0.0968676i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 497.751 | 0.940929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −327.912 | −0.615219 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.39254 | −0.0175561 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −501.105 | −0.929693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 306.170i | 0.565934i | 0.959130 | + | 0.282967i | \(0.0913187\pi\) | ||||
−0.959130 | + | 0.282967i | \(0.908681\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 198.278i | 0.363812i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 421.171i | 0.769966i | 0.922924 | + | 0.384983i | \(0.125793\pi\) | ||||
−0.922924 | + | 0.384983i | \(0.874207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1330.34i | 2.41442i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 72.6288 | 0.131336 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −387.083 | −0.694942 | −0.347471 | − | 0.937691i | \(-0.612960\pi\) | ||||
−0.347471 | + | 0.937691i | \(0.612960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −657.313 | −1.17587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −915.887 | −1.62680 | −0.813399 | − | 0.581706i | \(-0.802385\pi\) | ||||
−0.813399 | + | 0.581706i | \(0.802385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 510.683i | − 0.903863i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 1080.19i | − 1.89840i | −0.314679 | − | 0.949198i | \(-0.601897\pi\) | ||||
0.314679 | − | 0.949198i | \(-0.398103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1025.40i | 1.79579i | 0.440206 | + | 0.897897i | \(0.354906\pi\) | ||||
−0.440206 | + | 0.897897i | \(0.645094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 78.0248i | − 0.135695i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −686.792 | −1.19028 | −0.595140 | − | 0.803622i | \(-0.702903\pi\) | ||||
−0.595140 | + | 0.803622i | \(0.702903\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 391.906 | 0.674538 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.3663 | 0.0640931 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −68.2446 | −0.116260 | −0.0581300 | − | 0.998309i | \(-0.518514\pi\) | ||||
−0.0581300 | + | 0.998309i | \(0.518514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 305.096i | − 0.517990i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1113.53i | 1.87779i | 0.344203 | + | 0.938895i | \(0.388149\pi\) | ||||
−0.344203 | + | 0.938895i | \(0.611851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 62.3525i | − 0.104794i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 127.721i | − 0.213223i | −0.994301 | − | 0.106612i | \(-0.966000\pi\) | ||||
0.994301 | − | 0.106612i | \(-0.0340002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −776.688 | −1.29233 | −0.646163 | − | 0.763200i | \(-0.723627\pi\) | ||||
−0.646163 | + | 0.763200i | \(0.723627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −455.470 | −0.752843 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 863.872 | 1.42318 | 0.711592 | − | 0.702593i | \(-0.247975\pi\) | ||||
0.711592 | + | 0.702593i | \(0.247975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1298.08 | −2.12452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 178.086i | − 0.290516i | −0.989394 | − | 0.145258i | \(-0.953599\pi\) | ||||
0.989394 | − | 0.145258i | \(-0.0464012\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 79.7883i | − 0.129317i | −0.997907 | − | 0.0646583i | \(-0.979404\pi\) | ||||
0.997907 | − | 0.0646583i | \(-0.0205957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 578.660i | − 0.934830i | −0.884038 | − | 0.467415i | \(-0.845185\pi\) | ||||
0.884038 | − | 0.467415i | \(-0.154815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 676.986i | 1.08666i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −81.2341 | −0.129975 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −109.304 | −0.173774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −999.072 | −1.58332 | −0.791658 | − | 0.610965i | \(-0.790782\pi\) | ||||
−0.791658 | + | 0.610965i | \(0.790782\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −173.968 | −0.273965 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 550.651i | 0.864445i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 66.9225i | − 0.104403i | −0.998637 | − | 0.0522016i | \(-0.983376\pi\) | ||||
0.998637 | − | 0.0522016i | \(-0.0166239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 521.676i | − 0.811315i | −0.914025 | − | 0.405658i | \(-0.867043\pi\) | ||||
0.914025 | − | 0.405658i | \(-0.132957\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 485.924i | 0.751041i | 0.926814 | + | 0.375521i | \(0.122536\pi\) | ||||
−0.926814 | + | 0.375521i | \(0.877464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 432.027 | 0.665681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −370.358 | −0.567165 | −0.283582 | − | 0.958948i | \(-0.591523\pi\) | ||||
−0.283582 | + | 0.958948i | \(0.591523\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −393.323 | −0.600493 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 291.218 | 0.441910 | 0.220955 | − | 0.975284i | \(-0.429083\pi\) | ||||
0.220955 | + | 0.975284i | \(0.429083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 441.331i | 0.667672i | 0.942631 | + | 0.333836i | \(0.108343\pi\) | ||||
−0.942631 | + | 0.333836i | \(0.891657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 372.650i | − 0.560376i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 279.831i | 0.419537i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 197.739i | 0.294692i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −432.036 | −0.641955 | −0.320977 | − | 0.947087i | \(-0.604011\pi\) | ||||
−0.320977 | + | 0.947087i | \(0.604011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −106.934 | −0.157953 | −0.0789764 | − | 0.996876i | \(-0.525165\pi\) | ||||
−0.0789764 | + | 0.996876i | \(0.525165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 517.084 | 0.761538 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 102.329 | 0.149823 | 0.0749113 | − | 0.997190i | \(-0.476133\pi\) | ||||
0.0749113 | + | 0.997190i | \(0.476133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 627.010i | 0.915343i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 41.0608i | − 0.0595948i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 387.134i | − 0.560252i | −0.959963 | − | 0.280126i | \(-0.909624\pi\) | ||||
0.959963 | − | 0.280126i | \(-0.0903763\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 345.590i | − 0.497251i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 82.5997 | 0.118507 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −942.899 | −1.34508 | −0.672538 | − | 0.740062i | \(-0.734796\pi\) | ||||
−0.672538 | + | 0.740062i | \(0.734796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −653.255 | −0.929240 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 441.203 | 0.624049 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 486.394i | 0.686028i | 0.939330 | + | 0.343014i | \(0.111448\pi\) | ||||
−0.939330 | + | 0.343014i | \(0.888552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 64.1754i | − 0.0900076i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 942.341i | 1.31796i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 370.683i | − 0.515553i | −0.966205 | − | 0.257777i | \(-0.917010\pi\) | ||||
0.966205 | − | 0.257777i | \(-0.0829899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 727.950 | 1.00964 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −698.712 | −0.963741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −799.119 | −1.09920 | −0.549600 | − | 0.835428i | \(-0.685220\pi\) | ||||
−0.549600 | + | 0.835428i | \(0.685220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 165.575 | 0.226504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 601.978i | − 0.821252i | −0.911804 | − | 0.410626i | \(-0.865310\pi\) | ||||
0.911804 | − | 0.410626i | \(-0.134690\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 726.685i | 0.986004i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 320.189i | − 0.433273i | −0.976252 | − | 0.216637i | \(-0.930491\pi\) | ||||
0.976252 | − | 0.216637i | \(-0.0695087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1138.71i | 1.53259i | 0.642491 | + | 0.766293i | \(0.277901\pi\) | ||||
−0.642491 | + | 0.766293i | \(0.722099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −961.628 | −1.29078 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9274 | 0.0159244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 258.212 | 0.343824 | 0.171912 | − | 0.985112i | \(-0.445006\pi\) | ||||
0.171912 | + | 0.985112i | \(0.445006\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 503.011 | 0.666240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 728.371i | 0.962181i | 0.876671 | + | 0.481090i | \(0.159759\pi\) | ||||
−0.876671 | + | 0.481090i | \(0.840241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 613.280i | − 0.805887i | −0.915225 | − | 0.402943i | \(-0.867987\pi\) | ||||
0.915225 | − | 0.402943i | \(-0.132013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 251.789i | − 0.329999i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 474.744i | − 0.618962i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −869.758 | −1.13103 | −0.565513 | − | 0.824740i | \(-0.691322\pi\) | ||||
−0.565513 | + | 0.824740i | \(0.691322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −255.034 | −0.329928 | −0.164964 | − | 0.986300i | \(-0.552751\pi\) | ||||
−0.164964 | + | 0.986300i | \(0.552751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 160.240 | 0.206761 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 493.657 | 0.633707 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1338.93i | − 1.71438i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 588.049i | 0.749107i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 984.076i | − 1.25041i | −0.780459 | − | 0.625207i | \(-0.785014\pi\) | ||||
0.780459 | − | 0.625207i | \(-0.214986\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 648.507i | 0.819857i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 217.290 | 0.274010 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 163.608 | 0.205280 | 0.102640 | − | 0.994719i | \(-0.467271\pi\) | ||||
0.102640 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 326.982 | 0.409239 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.8711 | −0.0608606 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 78.3851i | − 0.0973728i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1116.97i | − 1.38067i | −0.723488 | − | 0.690337i | \(-0.757462\pi\) | ||||
0.723488 | − | 0.690337i | \(-0.242538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 596.540i | 0.735562i | 0.929913 | + | 0.367781i | \(0.119882\pi\) | ||||
−0.929913 | + | 0.367781i | \(0.880118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 654.502i | 0.803070i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 989.557 | 1.21121 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 752.641 | 0.916737 | 0.458369 | − | 0.888762i | \(-0.348434\pi\) | ||||
0.458369 | + | 0.888762i | \(0.348434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 946.576 | 1.15015 | 0.575076 | − | 0.818100i | \(-0.304972\pi\) | ||||
0.575076 | + | 0.818100i | \(0.304972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −613.125 | −0.741385 | −0.370693 | − | 0.928756i | \(-0.620880\pi\) | ||||
−0.370693 | + | 0.928756i | \(0.620880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 346.852i | − 0.418398i | −0.977873 | − | 0.209199i | \(-0.932914\pi\) | ||||
0.977873 | − | 0.209199i | \(-0.0670857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 138.707i | − 0.166515i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1063.29i | 1.27340i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 717.830i | − 0.855578i | −0.903879 | − | 0.427789i | \(-0.859293\pi\) | ||||
0.903879 | − | 0.427789i | \(-0.140707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1664.89 | 1.97966 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 473.931 | 0.560865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 578.393 | 0.682873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −137.409 | −0.161468 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 510.640i | 0.598640i | 0.954153 | + | 0.299320i | \(0.0967598\pi\) | ||||
−0.954153 | + | 0.299320i | \(0.903240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 210.292i | 0.245381i | 0.992445 | + | 0.122691i | \(0.0391523\pi\) | ||||
−0.992445 | + | 0.122691i | \(0.960848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.80806i | 0.00210484i | 0.999999 | + | 0.00105242i | \(0.000334996\pi\) | ||||
−0.999999 | + | 0.00105242i | \(0.999665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 598.210i | − 0.693174i | −0.938018 | − | 0.346587i | \(-0.887340\pi\) | ||||
0.938018 | − | 0.346587i | \(-0.112660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.8016 | 0.0552619 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 276.493 | 0.318174 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 798.536 | 0.916803 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 546.277 | 0.624317 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 177.942i | − 0.202899i | −0.994841 | − | 0.101449i | \(-0.967652\pi\) | ||||
0.994841 | − | 0.101449i | \(-0.0323480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 291.465i | 0.330834i | 0.986224 | + | 0.165417i | \(0.0528970\pi\) | ||||
−0.986224 | + | 0.165417i | \(0.947103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1218.02i | − 1.37941i | −0.724091 | − | 0.689704i | \(-0.757741\pi\) | ||||
0.724091 | − | 0.689704i | \(-0.242259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 481.322i | − 0.542640i | −0.962489 | − | 0.271320i | \(-0.912540\pi\) | ||||
0.962489 | − | 0.271320i | \(-0.0874602\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 220.919 | 0.248502 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1954.21 | 2.18836 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −436.447 | −0.487651 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −574.691 | −0.639256 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.3431i | 0.0114795i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1128.13i | − 1.24655i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 808.482i | − 0.891381i | −0.895187 | − | 0.445690i | \(-0.852958\pi\) | ||||
0.895187 | − | 0.445690i | \(-0.147042\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.69529i | 0.00844708i | 0.999991 | + | 0.00422354i | \(0.00134440\pi\) | ||||
−0.999991 | + | 0.00422354i | \(0.998656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1491.96 | 1.63413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 499.473 | 0.544682 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 460.757 | 0.501368 | 0.250684 | − | 0.968069i | \(-0.419345\pi\) | ||||
0.250684 | + | 0.968069i | \(0.419345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1471.32 | −1.59406 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 343.097i | − 0.370916i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 353.817i | 0.380858i | 0.981701 | + | 0.190429i | \(0.0609880\pi\) | ||||
−0.981701 | + | 0.190429i | \(0.939012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 828.982i | − 0.890422i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 237.372i | − 0.253874i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −850.015 | −0.907166 | −0.453583 | − | 0.891214i | \(-0.649854\pi\) | ||||
−0.453583 | + | 0.891214i | \(0.649854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 826.634 | 0.878464 | 0.439232 | − | 0.898374i | \(-0.355251\pi\) | ||||
0.439232 | + | 0.898374i | \(0.355251\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 103.838 | 0.110115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1722.44 | 1.81884 | 0.909418 | − | 0.415884i | \(-0.136528\pi\) | ||||
0.909418 | + | 0.415884i | \(0.136528\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.7032i | 0.0565893i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 404.315i | 0.424255i | 0.977242 | + | 0.212128i | \(0.0680393\pi\) | ||||
−0.977242 | + | 0.212128i | \(0.931961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 114.322i | 0.119709i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 796.228i | − 0.830269i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −829.202 | −0.862854 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −596.519 | −0.618154 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1239.73 | −1.28203 | −0.641016 | − | 0.767527i | \(-0.721487\pi\) | ||||
−0.641016 | + | 0.767527i | \(0.721487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 905.483 | 0.932526 | 0.466263 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466263 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 438.858i | 0.451036i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1736.17i | 1.77704i | 0.458836 | + | 0.888521i | \(0.348267\pi\) | ||||
−0.458836 | + | 0.888521i | \(0.651733\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2577.24i | 2.63252i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1014.57i | − 1.03212i | −0.856552 | − | 0.516060i | \(-0.827398\pi\) | ||||
0.856552 | − | 0.516060i | \(-0.172602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −868.554 | −0.881781 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 208.148 | 0.210463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1470.74 | 1.48410 | 0.742048 | − | 0.670347i | \(-0.233855\pi\) | ||||
0.742048 | + | 0.670347i | \(0.233855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 694.041 | 0.697528 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 974.749i | 0.977683i | 0.872373 | + | 0.488841i | \(0.162580\pi\) | ||||
−0.872373 | + | 0.488841i | \(0.837420\pi\) | |||||||
\(998\) | 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 | 1728.3.h.j.161.3 | yes | 12 | |
3.2 | odd | 2 | 1728.3.h.i.161.9 | yes | 12 | ||
4.3 | odd | 2 | 1728.3.h.i.161.3 | ✓ | 12 | ||
8.3 | odd | 2 | inner | 1728.3.h.j.161.10 | yes | 12 | |
8.5 | even | 2 | 1728.3.h.i.161.10 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.3.h.j.161.9 | yes | 12 | |
24.5 | odd | 2 | inner | 1728.3.h.j.161.4 | yes | 12 | |
24.11 | even | 2 | 1728.3.h.i.161.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.3.h.i.161.3 | ✓ | 12 | 4.3 | odd | 2 | ||
1728.3.h.i.161.4 | yes | 12 | 24.11 | even | 2 | ||
1728.3.h.i.161.9 | yes | 12 | 3.2 | odd | 2 | ||
1728.3.h.i.161.10 | yes | 12 | 8.5 | even | 2 | ||
1728.3.h.j.161.3 | yes | 12 | 1.1 | even | 1 | trivial | |
1728.3.h.j.161.4 | yes | 12 | 24.5 | odd | 2 | inner | |
1728.3.h.j.161.9 | yes | 12 | 12.11 | even | 2 | inner | |
1728.3.h.j.161.10 | yes | 12 | 8.3 | odd | 2 | inner |