Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.2 | ||
Character | \(\chi\) | \(=\) | 3024.1873 |
Dual form | 3024.2.t.l.289.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −2.66802 | −1.19317 | −0.596587 | − | 0.802548i | \(-0.703477\pi\) | ||||
−0.596587 | + | 0.802548i | \(0.703477\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.94471 | − | 1.79391i | −0.735032 | − | 0.678033i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36451 | 0.411416 | 0.205708 | − | 0.978613i | \(-0.434050\pi\) | ||||
0.205708 | + | 0.978613i | \(0.434050\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.75597 | + | 4.77348i | −0.764368 | + | 1.32392i | 0.176212 | + | 0.984352i | \(0.443616\pi\) |
−0.940580 | + | 0.339572i | \(0.889718\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.23930 | − | 2.14654i | 0.300575 | − | 0.520611i | −0.675691 | − | 0.737185i | \(-0.736155\pi\) |
0.976266 | + | 0.216573i | \(0.0694880\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19600 | + | 3.80358i | 0.503797 | + | 0.872601i | 0.999990 | + | 0.00438950i | \(0.00139723\pi\) |
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.69002 | −0.977936 | −0.488968 | − | 0.872302i | \(-0.662627\pi\) | ||||
−0.488968 | + | 0.872302i | \(0.662627\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.11832 | 0.423664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.94810 | − | 5.10625i | −0.547448 | − | 0.948207i | −0.998448 | − | 0.0556837i | \(-0.982266\pi\) |
0.451001 | − | 0.892524i | \(-0.351067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.55839 | + | 2.69921i | 0.279895 | + | 0.484792i | 0.971358 | − | 0.237619i | \(-0.0763671\pi\) |
−0.691464 | + | 0.722411i | \(0.743034\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.18852 | + | 4.78617i | 0.877021 | + | 0.809011i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.15627 | − | 5.46681i | −0.518887 | − | 0.898739i | −0.999759 | − | 0.0219479i | \(-0.993013\pi\) |
0.480872 | − | 0.876791i | \(-0.340320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.38693 | + | 2.40224i | −0.216603 | + | 0.375167i | −0.953767 | − | 0.300546i | \(-0.902831\pi\) |
0.737164 | + | 0.675713i | \(0.236164\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87889 | + | 8.45048i | 0.744023 | + | 1.28869i | 0.950650 | + | 0.310267i | \(0.100418\pi\) |
−0.206626 | + | 0.978420i | \(0.566248\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.02505 | − | 8.70364i | 0.732979 | − | 1.26956i | −0.222626 | − | 0.974904i | \(-0.571463\pi\) |
0.955605 | − | 0.294652i | \(-0.0952039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.563800 | + | 6.97726i | 0.0805429 | + | 0.996751i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47823 | − | 2.56037i | 0.203050 | − | 0.351694i | −0.746459 | − | 0.665431i | \(-0.768248\pi\) |
0.949510 | + | 0.313737i | \(0.101581\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.64055 | −0.490891 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.77809 | − | 3.07974i | −0.231487 | − | 0.400948i | 0.726759 | − | 0.686893i | \(-0.241026\pi\) |
−0.958246 | + | 0.285945i | \(0.907692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.663043 | + | 1.14842i | −0.0848940 | + | 0.147041i | −0.905346 | − | 0.424675i | \(-0.860388\pi\) |
0.820452 | + | 0.571715i | \(0.193722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.35297 | − | 12.7357i | 0.912024 | − | 1.57967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.14937 | + | 7.18692i | 0.506926 | + | 0.878021i | 0.999968 | + | 0.00801592i | \(0.00255158\pi\) |
−0.493042 | + | 0.870006i | \(0.664115\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3069 | 1.46056 | 0.730279 | − | 0.683149i | \(-0.239390\pi\) | ||||
0.730279 | + | 0.683149i | \(0.239390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.11577 | + | 1.93257i | −0.130591 | + | 0.226190i | −0.923905 | − | 0.382623i | \(-0.875021\pi\) |
0.793314 | + | 0.608813i | \(0.208354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.65358 | − | 2.44781i | −0.302404 | − | 0.278954i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.41535 | − | 11.1117i | 0.721783 | − | 1.25017i | −0.238501 | − | 0.971142i | \(-0.576656\pi\) |
0.960284 | − | 0.279023i | \(-0.0900106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.15934 | + | 8.93625i | 0.566312 | + | 0.980881i | 0.996926 | + | 0.0783447i | \(0.0249635\pi\) |
−0.430615 | + | 0.902536i | \(0.641703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.30648 | + | 5.72700i | −0.358638 | + | 0.621180i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.73159 | − | 13.3915i | −0.819547 | − | 1.41950i | −0.906017 | − | 0.423242i | \(-0.860892\pi\) |
0.0864698 | − | 0.996254i | \(-0.472441\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9227 | − | 4.33908i | 1.45950 | − | 0.454860i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.85896 | − | 10.1480i | −0.601117 | − | 1.04117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.55369 | − | 4.42311i | −0.259288 | − | 0.449099i | 0.706764 | − | 0.707450i | \(-0.250154\pi\) |
−0.966051 | + | 0.258351i | \(0.916821\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.69496 | 0.268159 | 0.134079 | − | 0.990971i | \(-0.457192\pi\) | ||||
0.134079 | + | 0.990971i | \(0.457192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0214 | 1.28304 | 0.641519 | − | 0.767107i | \(-0.278304\pi\) | ||||
0.641519 | + | 0.767107i | \(0.278304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.49753 | − | 2.59379i | −0.144771 | − | 0.250751i | 0.784516 | − | 0.620108i | \(-0.212911\pi\) |
−0.929288 | + | 0.369357i | \(0.879578\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0132 | − | 17.3434i | 0.959093 | − | 1.66120i | 0.234383 | − | 0.972144i | \(-0.424693\pi\) |
0.724710 | − | 0.689054i | \(-0.241974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.23211 | − | 10.7943i | 0.586267 | − | 1.01544i | −0.408449 | − | 0.912781i | \(-0.633930\pi\) |
0.994716 | − | 0.102664i | \(-0.0327365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.5130 | 1.16685 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.26077 | + | 1.95120i | −0.573924 | + | 0.178866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.13810 | −0.830737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.68837 | 0.687669 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0734 | −1.33754 | −0.668772 | − | 0.743467i | \(-0.733180\pi\) | ||||
−0.668772 | + | 0.743467i | \(0.733180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8406 | 1.29663 | 0.648316 | − | 0.761371i | \(-0.275473\pi\) | ||||
0.648316 | + | 0.761371i | \(0.275473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.55269 | − | 11.3363i | 0.221346 | − | 0.982980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.1559 | 1.72203 | 0.861017 | − | 0.508577i | \(-0.169828\pi\) | ||||
0.861017 | + | 0.508577i | \(0.169828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91552 | − | 17.1742i | 0.841023 | − | 1.45669i | −0.0480074 | − | 0.998847i | \(-0.515287\pi\) |
0.889031 | − | 0.457848i | \(-0.151380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.76056 | + | 6.51347i | −0.314473 | + | 0.544684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.86557 | + | 13.6236i | 0.653200 | + | 1.13138i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3033 | −1.41754 | −0.708772 | − | 0.705438i | \(-0.750750\pi\) | ||||
−0.708772 | + | 0.705438i | \(0.750750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.98976 | 0.324682 | 0.162341 | − | 0.986735i | \(-0.448096\pi\) | ||||
0.162341 | + | 0.986735i | \(0.448096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.15781 | − | 7.20153i | −0.333963 | − | 0.578441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0994 | + | 20.9568i | 0.965637 | + | 1.67253i | 0.707895 | + | 0.706318i | \(0.249645\pi\) |
0.257742 | + | 0.966214i | \(0.417022\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.12073 | + | 8.41345i | 0.718814 | + | 0.663073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34498 | − | 4.06162i | −0.183673 | − | 0.318131i | 0.759456 | − | 0.650559i | \(-0.225465\pi\) |
−0.943129 | + | 0.332428i | \(0.892132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.12627 | + | 10.6110i | −0.474065 | + | 0.821104i | −0.999559 | − | 0.0296928i | \(-0.990547\pi\) |
0.525494 | + | 0.850797i | \(0.323880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.69072 | − | 15.0528i | −0.668517 | − | 1.15791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.05503 | + | 7.02352i | −0.308298 | + | 0.533988i | −0.977990 | − | 0.208651i | \(-0.933093\pi\) |
0.669692 | + | 0.742639i | \(0.266426\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.11952 | − | 3.80007i | −0.311406 | − | 0.287258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.91636 | − | 8.51538i | 0.367466 | − | 0.636469i | −0.621703 | − | 0.783253i | \(-0.713559\pi\) |
0.989169 | + | 0.146784i | \(0.0468922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8876 | 1.18092 | 0.590458 | − | 0.807068i | \(-0.298947\pi\) | ||||
0.590458 | + | 0.807068i | \(0.298947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.42097 | + | 14.5856i | 0.619122 | + | 1.07235i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.69105 | − | 2.92898i | 0.123661 | − | 0.214188i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.10949 | − | 1.92170i | 0.0802800 | − | 0.139049i | −0.823090 | − | 0.567911i | \(-0.807752\pi\) |
0.903370 | + | 0.428862i | \(0.141085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.92084 | − | 5.05904i | −0.210247 | − | 0.364158i | 0.741545 | − | 0.670903i | \(-0.234093\pi\) |
−0.951792 | + | 0.306745i | \(0.900760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.93695 | −0.138002 | −0.0690010 | − | 0.997617i | \(-0.521981\pi\) | ||||
−0.0690010 | + | 0.997617i | \(0.521981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84540 | + | 3.19633i | −0.130817 | + | 0.226582i | −0.923992 | − | 0.382412i | \(-0.875093\pi\) |
0.793175 | + | 0.608994i | \(0.208427\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.42694 | + | 15.2188i | −0.240524 | + | 1.06815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.70037 | − | 6.40922i | 0.258445 | − | 0.447639i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.99647 | + | 5.19004i | 0.207270 | + | 0.359002i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.67097 | − | 9.82241i | 0.390406 | − | 0.676202i | −0.602097 | − | 0.798423i | \(-0.705668\pi\) |
0.992503 | + | 0.122220i | \(0.0390014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.0170 | − | 22.5460i | −0.887749 | − | 1.53763i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.81151 | − | 8.04478i | 0.122973 | − | 0.546115i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.83096 | + | 11.8316i | 0.459500 | + | 0.795878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.965547 | + | 1.67238i | 0.0646578 | + | 0.111991i | 0.896542 | − | 0.442958i | \(-0.146071\pi\) |
−0.831884 | + | 0.554949i | \(0.812738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.7283 | 1.30941 | 0.654705 | − | 0.755884i | \(-0.272793\pi\) | ||||
0.654705 | + | 0.755884i | \(0.272793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.4197 | 1.74586 | 0.872931 | − | 0.487844i | \(-0.162216\pi\) | ||||
0.872931 | + | 0.487844i | \(0.162216\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.24071 | + | 7.34513i | 0.277818 | + | 0.481196i | 0.970842 | − | 0.239719i | \(-0.0770553\pi\) |
−0.693024 | + | 0.720915i | \(0.743722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.4069 | + | 23.2215i | −0.874571 | + | 1.51480i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.08023 | + | 13.9954i | −0.522667 | + | 0.905286i | 0.476985 | + | 0.878911i | \(0.341730\pi\) |
−0.999652 | + | 0.0263743i | \(0.991604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9735 | 0.706868 | 0.353434 | − | 0.935460i | \(-0.385014\pi\) | ||||
0.353434 | + | 0.935460i | \(0.385014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.50423 | − | 18.6154i | −0.0961017 | − | 1.18930i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.2084 | −1.54034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.85873 | 0.180442 | 0.0902208 | − | 0.995922i | \(-0.471243\pi\) | ||||
0.0902208 | + | 0.995922i | \(0.471243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.39959 | −0.402339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.5875 | −1.53373 | −0.766864 | − | 0.641810i | \(-0.778184\pi\) | ||||
−0.766864 | + | 0.641810i | \(0.778184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.66893 | + | 16.2934i | −0.227976 | + | 1.01242i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.957972 | 0.0590711 | 0.0295355 | − | 0.999564i | \(-0.490597\pi\) | ||||
0.0295355 | + | 0.999564i | \(0.490597\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.94394 | + | 6.83111i | −0.242274 | + | 0.419632i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.31005 | + | 14.3934i | −0.506673 | + | 0.877583i | 0.493297 | + | 0.869861i | \(0.335791\pi\) |
−0.999970 | + | 0.00772245i | \(0.997542\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.21801 | − | 12.5020i | −0.438463 | − | 0.759440i | 0.559108 | − | 0.829095i | \(-0.311144\pi\) |
−0.997571 | + | 0.0696545i | \(0.977810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.89048 | 0.174302 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.46642 | −0.268361 | −0.134181 | − | 0.990957i | \(-0.542840\pi\) | ||||
−0.134181 | + | 0.990957i | \(0.542840\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.62617 | − | 4.54867i | −0.156664 | − | 0.271351i | 0.776999 | − | 0.629501i | \(-0.216741\pi\) |
−0.933664 | + | 0.358151i | \(0.883407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.65751 | + | 9.79909i | 0.336304 | + | 0.582495i | 0.983734 | − | 0.179629i | \(-0.0574898\pi\) |
−0.647431 | + | 0.762124i | \(0.724156\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.00658 | − | 2.18363i | 0.413585 | − | 0.128896i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.42826 | + | 9.40201i | 0.319309 | + | 0.553060i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.38422 | − | 9.32574i | 0.314549 | − | 0.544815i | −0.664792 | − | 0.747028i | \(-0.731480\pi\) |
0.979342 | + | 0.202213i | \(0.0648133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.74397 | + | 8.21679i | 0.276204 | + | 0.478400i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9255 | − | 22.3877i | 0.747503 | − | 1.29471i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67135 | − | 25.1860i | 0.326891 | − | 1.45170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.76901 | − | 3.06402i | 0.101293 | − | 0.175445i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.42151 | −0.537714 | −0.268857 | − | 0.963180i | \(-0.586646\pi\) | ||||
−0.268857 | + | 0.963180i | \(0.586646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65754 | + | 9.79914i | 0.320809 | + | 0.555658i | 0.980655 | − | 0.195743i | \(-0.0627118\pi\) |
−0.659846 | + | 0.751401i | \(0.729378\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8431 | + | 18.7808i | −0.612889 | + | 1.06156i | 0.377862 | + | 0.925862i | \(0.376660\pi\) |
−0.990751 | + | 0.135693i | \(0.956674\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6087 | + | 21.8389i | −0.708174 | + | 1.22659i | 0.257360 | + | 0.966316i | \(0.417147\pi\) |
−0.965534 | + | 0.260278i | \(0.916186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.02272 | − | 6.96755i | −0.225229 | − | 0.390108i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8860 | 0.605715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.83802 | + | 10.1118i | −0.323835 | + | 0.560899i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.3858 | + | 7.91160i | −1.39956 | + | 0.436180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.51226 | + | 14.7437i | −0.467876 | + | 0.810386i | −0.999326 | − | 0.0367042i | \(-0.988314\pi\) |
0.531450 | + | 0.847090i | \(0.321647\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0706 | − | 19.1748i | −0.604851 | − | 1.04763i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.85166 | − | 11.8674i | 0.373233 | − | 0.646459i | −0.616827 | − | 0.787098i | \(-0.711582\pi\) |
0.990061 | + | 0.140639i | \(0.0449157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.12644 | + | 3.68310i | 0.115153 | + | 0.199451i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4201 | − | 14.5802i | 0.616628 | − | 0.787254i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2183 | − | 21.1627i | −0.655912 | − | 1.13607i | −0.981664 | − | 0.190618i | \(-0.938951\pi\) |
0.325752 | − | 0.945455i | \(-0.394382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4881 | + | 19.8979i | 0.614943 | + | 1.06511i | 0.990394 | + | 0.138271i | \(0.0441544\pi\) |
−0.375451 | + | 0.926842i | \(0.622512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.0305 | −1.27901 | −0.639507 | − | 0.768785i | \(-0.720861\pi\) | ||||
−0.639507 | + | 0.768785i | \(0.720861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.8350 | −1.74270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.84234 | − | 17.0474i | −0.519459 | − | 0.899729i | −0.999744 | − | 0.0226169i | \(-0.992800\pi\) |
0.480285 | − | 0.877112i | \(-0.340533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.144819 | + | 0.250833i | −0.00762204 | + | 0.0132018i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97690 | − | 5.15613i | 0.155818 | − | 0.269884i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2006 | 0.741263 | 0.370632 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.46779 | + | 2.32737i | −0.387708 | + | 0.120831i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.4669 | −1.47396 | −0.736980 | − | 0.675914i | \(-0.763749\pi\) | ||||
−0.736980 | + | 0.675914i | \(0.763749\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.4994 | 1.67381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.25098 | 0.218358 | 0.109179 | − | 0.994022i | \(-0.465178\pi\) | ||||
0.109179 | + | 0.994022i | \(0.465178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.8428 | −1.83148 | −0.915740 | − | 0.401772i | \(-0.868395\pi\) | ||||
−0.915740 | + | 0.401772i | \(0.868395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.07981 | + | 6.53080i | 0.360820 | + | 0.332840i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.7944 | 1.61204 | 0.806020 | − | 0.591888i | \(-0.201617\pi\) | ||||
0.806020 | + | 0.591888i | \(0.201617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.81235 | + | 10.0673i | −0.293943 | + | 0.509125i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.1163 | + | 29.6462i | −0.861213 | + | 1.49166i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.07669 | + | 5.32899i | 0.154415 | + | 0.267454i | 0.932846 | − | 0.360276i | \(-0.117317\pi\) |
−0.778431 | + | 0.627730i | \(0.783984\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.8229 | 0.740222 | 0.370111 | − | 0.928988i | \(-0.379320\pi\) | ||||
0.370111 | + | 0.928988i | \(0.379320\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1795 | −0.855770 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.30677 | − | 7.45954i | −0.213479 | − | 0.369756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7222 | − | 18.5713i | −0.530177 | − | 0.918293i | −0.999380 | − | 0.0352032i | \(-0.988792\pi\) |
0.469203 | − | 0.883090i | \(-0.344541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.06689 | + | 9.17892i | −0.101705 | + | 0.451665i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7652 | − | 23.8421i | −0.675708 | − | 1.17036i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2332 | − | 22.9205i | 0.646483 | − | 1.11974i | −0.337474 | − | 0.941335i | \(-0.609572\pi\) |
0.983957 | − | 0.178406i | \(-0.0570942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.54824 | − | 14.8060i | −0.416616 | − | 0.721600i | 0.578981 | − | 0.815341i | \(-0.303451\pi\) |
−0.995597 | + | 0.0937415i | \(0.970117\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.62524 | − | 4.54705i | 0.127343 | − | 0.220564i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.34959 | − | 1.04392i | 0.162098 | − | 0.0505186i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0292 | + | 20.8352i | −0.579425 | + | 1.00359i | 0.416120 | + | 0.909310i | \(0.363390\pi\) |
−0.995545 | + | 0.0942846i | \(0.969944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.58345 | −0.316380 | −0.158190 | − | 0.987409i | \(-0.550566\pi\) | ||||
−0.158190 | + | 0.987409i | \(0.550566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.2993 | − | 17.8389i | −0.492681 | − | 0.853348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6327 | − | 18.4164i | 0.507472 | − | 0.878967i | −0.492491 | − | 0.870318i | \(-0.663913\pi\) |
0.999963 | − | 0.00864927i | \(-0.00275318\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.471724 | − | 0.817050i | 0.0224123 | − | 0.0388192i | −0.854602 | − | 0.519284i | \(-0.826199\pi\) |
0.877014 | + | 0.480465i | \(0.159532\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.6280 | + | 35.7288i | 0.977862 | + | 1.69371i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.7959 | 0.839842 | 0.419921 | − | 0.907561i | \(-0.362058\pi\) | ||||
0.419921 | + | 0.907561i | \(0.362058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89249 | + | 3.27789i | −0.0891139 | + | 0.154350i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −37.1461 | + | 11.5768i | −1.74144 | + | 0.542727i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.88851 | − | 11.9313i | 0.322231 | − | 0.558120i | −0.658717 | − | 0.752391i | \(-0.728901\pi\) |
0.980948 | + | 0.194270i | \(0.0622339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.97576 | + | 5.15417i | 0.138595 | + | 0.240054i | 0.926965 | − | 0.375148i | \(-0.122408\pi\) |
−0.788370 | + | 0.615201i | \(0.789075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7618 | − | 30.7644i | 0.825463 | − | 1.42974i | −0.0761023 | − | 0.997100i | \(-0.524248\pi\) |
0.901565 | − | 0.432643i | \(-0.142419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2574 | + | 21.2305i | 0.567207 | + | 0.982431i | 0.996841 | + | 0.0794277i | \(0.0253093\pi\) |
−0.429634 | + | 0.903003i | \(0.641357\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82333 | − | 21.4200i | 0.222721 | − | 0.989086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.65731 | + | 11.5308i | 0.306103 | + | 0.530187i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.65183 | + | 8.05720i | 0.213440 | + | 0.369690i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.2352 | 0.878878 | 0.439439 | − | 0.898272i | \(-0.355177\pi\) | ||||
0.439439 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.7943 | 1.58648 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.81328 | + | 11.8009i | 0.309375 | + | 0.535853i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3089 | + | 21.3197i | −0.557770 | + | 0.966086i | 0.439912 | + | 0.898041i | \(0.355010\pi\) |
−0.997682 | + | 0.0680455i | \(0.978324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.73086 | − | 16.8543i | 0.439147 | − | 0.760626i | −0.558476 | − | 0.829520i | \(-0.688614\pi\) |
0.997624 | + | 0.0688947i | \(0.0219472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6143 | −0.658197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.9333 | − | 22.0774i | −1.07356 | − | 0.990306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.17781 | 0.321323 | 0.160661 | − | 0.987010i | \(-0.448637\pi\) | ||||
0.160661 | + | 0.987010i | \(0.448637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.1112 | 0.985889 | 0.492945 | − | 0.870061i | \(-0.335921\pi\) | ||||
0.492945 | + | 0.870061i | \(0.335921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.19021 | −0.319960 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.3575 | 1.38989 | 0.694947 | − | 0.719061i | \(-0.255428\pi\) | ||||
0.694947 | + | 0.719061i | \(0.255428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.63670 | − | 1.75670i | 0.249353 | − | 0.0777120i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −34.7414 | −1.53089 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.85675 | − | 11.8762i | 0.301559 | − | 0.522316i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.76588 | + | 3.05859i | −0.0773645 | + | 0.133999i | −0.902112 | − | 0.431502i | \(-0.857984\pi\) |
0.824748 | + | 0.565501i | \(0.191317\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03821 | + | 12.1905i | 0.307759 | + | 0.533055i | 0.977872 | − | 0.209205i | \(-0.0670875\pi\) |
−0.670113 | + | 0.742259i | \(0.733754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.72526 | 0.336518 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00374 | −0.0436409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.64469 | − | 13.2410i | −0.331128 | − | 0.573531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.99543 | + | 6.92029i | 0.172737 | + | 0.299190i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.769313 | + | 9.52056i | 0.0331367 | + | 0.410080i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5799 | + | 20.0569i | 0.497858 | + | 0.862315i | 0.999997 | − | 0.00247207i | \(-0.000786884\pi\) |
−0.502139 | + | 0.864787i | \(0.667454\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.7155 | + | 46.2725i | −1.14436 | + | 1.98210i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.76832 | + | 9.99102i | 0.246635 | + | 0.427185i | 0.962590 | − | 0.270962i | \(-0.0873417\pi\) |
−0.715955 | + | 0.698147i | \(0.754008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.9480 | − | 22.4266i | 0.551605 | − | 0.955407i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.4094 | + | 10.1005i | −1.37819 | + | 0.429518i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.04108 | − | 1.80321i | 0.0441122 | − | 0.0764045i | −0.843126 | − | 0.537716i | \(-0.819287\pi\) |
0.887238 | + | 0.461311i | \(0.152621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −53.7842 | −2.27483 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.35403 | + | 5.80936i | 0.141356 | + | 0.244835i | 0.928007 | − | 0.372562i | \(-0.121521\pi\) |
−0.786652 | + | 0.617397i | \(0.788187\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.6274 | + | 28.7995i | −0.699519 | + | 1.21160i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.01112 | + | 6.94746i | −0.168155 | + | 0.291253i | −0.937771 | − | 0.347254i | \(-0.887114\pi\) |
0.769616 | + | 0.638507i | \(0.220447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.34215 | + | 5.78877i | 0.139865 | + | 0.242253i | 0.927445 | − | 0.373959i | \(-0.122000\pi\) |
−0.787581 | + | 0.616212i | \(0.788667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.93496 | −0.414316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0088 | + | 24.2639i | −0.583193 | + | 1.01012i | 0.411906 | + | 0.911227i | \(0.364863\pi\) |
−0.995098 | + | 0.0988925i | \(0.968470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.99736 | − | 26.6338i | 0.248812 | − | 1.10496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.01706 | − | 3.49366i | 0.0835382 | − | 0.144692i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.35952 | − | 5.81886i | −0.138662 | − | 0.240170i | 0.788328 | − | 0.615255i | \(-0.210947\pi\) |
−0.926990 | + | 0.375085i | \(0.877614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.84443 | + | 11.8549i | −0.282020 | + | 0.488473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.19462 | + | 5.53325i | 0.131187 | + | 0.227223i | 0.924135 | − | 0.382067i | \(-0.124788\pi\) |
−0.792947 | + | 0.609290i | \(0.791454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.7038 | − | 5.20583i | 0.684791 | − | 0.213418i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.96098 | + | 5.12856i | 0.120982 | + | 0.209547i | 0.920155 | − | 0.391554i | \(-0.128062\pi\) |
−0.799173 | + | 0.601101i | \(0.794729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.97104 | − | 3.41393i | −0.0804002 | − | 0.139257i | 0.823022 | − | 0.568010i | \(-0.192287\pi\) |
−0.903422 | + | 0.428753i | \(0.858953\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.3806 | 0.991213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.09551 | 0.287998 | 0.143999 | − | 0.989578i | \(-0.454004\pi\) | ||||
0.143999 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.6978 | + | 47.9739i | 1.12053 | + | 1.94082i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.87000 | − | 11.8992i | 0.277477 | − | 0.480604i | −0.693280 | − | 0.720668i | \(-0.743835\pi\) |
0.970757 | + | 0.240064i | \(0.0771685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.3605 | − | 28.3372i | 0.658649 | − | 1.14081i | −0.322317 | − | 0.946632i | \(-0.604462\pi\) |
0.980966 | − | 0.194182i | \(-0.0622051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6180 | −0.909094 | −0.454547 | − | 0.890723i | \(-0.650199\pi\) | ||||
−0.454547 | + | 0.890723i | \(0.650199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.98740 | + | 39.9124i | −0.360073 | + | 1.59905i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1043 | −1.24417 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.6463 | −0.623858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.9355 | 1.74905 | 0.874523 | − | 0.484984i | \(-0.161175\pi\) | ||||
0.874523 | + | 0.484984i | \(0.161175\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.2160 | 1.59592 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.8596 | − | 16.5378i | −1.38119 | − | 0.655252i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.8595 | −1.57436 | −0.787178 | − | 0.616726i | \(-0.788459\pi\) | ||||
−0.787178 | + | 0.616726i | \(0.788459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.24049 | + | 16.0050i | −0.364410 | + | 0.631176i | −0.988681 | − | 0.150032i | \(-0.952062\pi\) |
0.624272 | + | 0.781207i | \(0.285396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.76068 | − | 15.1739i | 0.344418 | − | 0.596549i | −0.640830 | − | 0.767683i | \(-0.721410\pi\) |
0.985248 | + | 0.171134i | \(0.0547430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.42622 | − | 4.20234i | −0.0952376 | − | 0.164956i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.4055 | −1.07246 | −0.536230 | − | 0.844072i | \(-0.680152\pi\) | ||||
−0.536230 | + | 0.844072i | \(0.680152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.5951 | −1.54711 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2580 | − | 28.1597i | −0.633322 | − | 1.09695i | −0.986868 | − | 0.161529i | \(-0.948358\pi\) |
0.353546 | − | 0.935417i | \(-0.384976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4336 | − | 33.6599i | −0.755878 | − | 1.30922i | −0.944937 | − | 0.327253i | \(-0.893877\pi\) |
0.189059 | − | 0.981966i | \(-0.439456\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.81061 | + | 30.2454i | −0.264104 | + | 1.17287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8266 | + | 23.9484i | 0.535369 | + | 0.927286i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.904731 | + | 1.56704i | −0.0349268 | + | 0.0604949i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.50978 | − | 7.81117i | −0.173839 | − | 0.301099i | 0.765920 | − | 0.642936i | \(-0.222284\pi\) |
−0.939759 | + | 0.341838i | \(0.888951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.41435 | − | 16.3061i | 0.361823 | − | 0.626695i | −0.626438 | − | 0.779471i | \(-0.715488\pi\) |
0.988261 | + | 0.152776i | \(0.0488212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.96847 | + | 13.1827i | −0.113919 | + | 0.505907i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.35476 | − | 9.27471i | 0.204894 | − | 0.354887i | −0.745205 | − | 0.666836i | \(-0.767648\pi\) |
0.950099 | + | 0.311949i | \(0.100982\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.7763 | −2.05468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.14791 | + | 14.1126i | 0.310411 | + | 0.537647i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.52277 | − | 4.36956i | 0.0959705 | − | 0.166226i | −0.814043 | − | 0.580805i | \(-0.802738\pi\) |
0.910013 | + | 0.414579i | \(0.136071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.4548 | + | 45.8210i | −1.00349 | + | 1.73809i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.43766 | + | 5.95421i | 0.130211 | + | 0.225532i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.9138 | −1.69637 | −0.848186 | − | 0.529698i | \(-0.822305\pi\) | ||||
−0.848186 | + | 0.529698i | \(0.822305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.8623 | − | 24.0102i | 0.522827 | − | 0.905563i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.24092 | − | 4.83451i | −0.197105 | − | 0.181820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.72658 | + | 6.45463i | −0.139955 | + | 0.242409i | −0.927479 | − | 0.373875i | \(-0.878029\pi\) |
0.787524 | + | 0.616283i | \(0.211362\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.30887 | − | 12.6593i | −0.273719 | − | 0.474096i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.0332 | − | 17.3781i | 0.375222 | − | 0.649903i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.5574 | + | 37.3385i | 0.803954 | + | 1.39249i | 0.916995 | + | 0.398899i | \(0.130608\pi\) |
−0.113040 | + | 0.993590i | \(0.536059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.3229 | − | 23.3592i | −0.943074 | − | 0.869943i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.24501 | − | 10.8167i | −0.231934 | − | 0.401721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.389926 | + | 0.675372i | 0.0144616 | + | 0.0250482i | 0.873166 | − | 0.487424i | \(-0.162063\pi\) |
−0.858704 | + | 0.512472i | \(0.828730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.1857 | 0.894540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6772 | −0.579050 | −0.289525 | − | 0.957170i | \(-0.593497\pi\) | ||||
−0.289525 | + | 0.957170i | \(0.593497\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.66187 | + | 9.80664i | 0.208558 | + | 0.361232i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.87450 | + | 15.3711i | −0.326454 | + | 0.565434i | −0.981805 | − | 0.189889i | \(-0.939187\pi\) |
0.655352 | + | 0.755324i | \(0.272520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.74308 | + | 6.48321i | −0.137320 | + | 0.237846i | −0.926481 | − | 0.376340i | \(-0.877182\pi\) |
0.789161 | + | 0.614186i | \(0.210516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.1656 | 1.69138 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.74076 | + | 7.73060i | −0.0636062 | + | 0.282470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.3599 | −0.852415 | −0.426208 | − | 0.904625i | \(-0.640151\pi\) | ||||
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.6447 | −0.387402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2350 | 1.13525 | 0.567627 | − | 0.823286i | \(-0.307862\pi\) | ||||
0.567627 | + | 0.823286i | \(0.307862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6147 | −0.602282 | −0.301141 | − | 0.953580i | \(-0.597367\pi\) | ||||
−0.301141 | + | 0.953580i | \(0.597367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.5853 | + | 15.7651i | −1.83131 | + | 0.570736i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.6014 | 0.707766 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3794 | − | 31.8340i | 0.662777 | − | 1.14796i | −0.317106 | − | 0.948390i | \(-0.602711\pi\) |
0.979883 | − | 0.199573i | \(-0.0639556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.77690 | + | 8.27382i | −0.171813 | + | 0.297589i | −0.939054 | − | 0.343770i | \(-0.888296\pi\) |
0.767241 | + | 0.641359i | \(0.221629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.30116 | + | 5.71778i | 0.118581 | + | 0.205389i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.1828 | −0.436495 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7929 | 0.600897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.2814 | − | 55.9130i | −1.15217 | − | 1.99562i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.1339 | − | 17.5524i | −0.361233 | − | 0.625674i | 0.626931 | − | 0.779075i | \(-0.284311\pi\) |
−0.988164 | + | 0.153401i | \(0.950977\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.4837 | + | 9.81203i | −1.11943 | + | 0.348876i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.65465 | − | 6.33004i | −0.129780 | − | 0.224786i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.4236 | + | 37.1068i | −0.758863 | + | 1.31439i | 0.184567 | + | 0.982820i | \(0.440912\pi\) |
−0.943431 | + | 0.331570i | \(0.892422\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4551 | − | 21.5729i | −0.440630 | − | 0.763194i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.52248 | + | 2.63702i | −0.0537273 | + | 0.0930584i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.3343 | − | 22.4472i | −0.857670 | − | 0.791161i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4750 | − | 18.1432i | 0.368282 | − | 0.637883i | −0.621015 | − | 0.783798i | \(-0.713280\pi\) |
0.989297 | + | 0.145916i | \(0.0466129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0129 | 0.667633 | 0.333817 | − | 0.942638i | \(-0.391663\pi\) | ||||
0.333817 | + | 0.942638i | \(0.391663\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.25644 | + | 10.8365i | 0.219154 | + | 0.379585i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.4281 | + | 37.1145i | −0.749673 | + | 1.29847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6953 | + | 28.9171i | −0.582669 | + | 1.00921i | 0.412493 | + | 0.910961i | \(0.364658\pi\) |
−0.995162 | + | 0.0982515i | \(0.968675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.52040 | − | 7.82955i | −0.157571 | − | 0.272921i | 0.776421 | − | 0.630214i | \(-0.217033\pi\) |
−0.933992 | + | 0.357293i | \(0.883700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.4071 | 0.779172 | 0.389586 | − | 0.920990i | \(-0.372618\pi\) | ||||
0.389586 | + | 0.920990i | \(0.372618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4090 | + | 19.7610i | −0.396252 | + | 0.686328i | −0.993260 | − | 0.115907i | \(-0.963023\pi\) |
0.597008 | + | 0.802235i | \(0.296356\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.6757 | + | 7.43672i | 0.543129 | + | 0.257667i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.3450 | − | 28.3104i | 0.565642 | − | 0.979720i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.05060 | − | 13.9441i | −0.277938 | − | 0.481402i | 0.692934 | − | 0.721001i | \(-0.256318\pi\) |
−0.970872 | + | 0.239598i | \(0.922984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.88254 | + | 4.99271i | −0.0993980 | + | 0.172162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1870 | + | 40.1611i | 0.797657 | + | 1.38158i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7710 | + | 16.3929i | 0.610618 | + | 0.563267i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.8029 | + | 25.6394i | 0.507438 | + | 0.878909i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7818 | + | 22.1387i | 0.437639 | + | 0.758013i | 0.997507 | − | 0.0705689i | \(-0.0224815\pi\) |
−0.559868 | + | 0.828582i | \(0.689148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.6556 | 1.79868 | 0.899340 | − | 0.437250i | \(-0.144048\pi\) | ||||
0.899340 | + | 0.437250i | \(0.144048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.8862 | 1.05382 | 0.526912 | − | 0.849920i | \(-0.323350\pi\) | ||||
0.526912 | + | 0.849920i | \(0.323350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.929596 | − | 1.61011i | −0.0316438 | − | 0.0548087i | 0.849770 | − | 0.527154i | \(-0.176741\pi\) |
−0.881414 | + | 0.472345i | \(0.843408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8189 | − | 18.7389i | 0.367853 | − | 0.637141i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.75383 | − | 15.1621i | 0.296953 | − | 0.514338i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.7421 | −1.54991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.9517 | − | 13.7922i | −0.505459 | − | 0.466262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3037 | −0.449234 | −0.224617 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224617 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.2210 | −0.714954 | −0.357477 | − | 0.933922i | \(-0.616363\pi\) | ||||
−0.357477 | + | 0.933922i | \(0.616363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8289 | 1.67687 | 0.838437 | − | 0.544998i | \(-0.183470\pi\) | ||||
0.838437 | + | 0.544998i | \(0.183470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.77272 | −0.0595220 | −0.0297610 | − | 0.999557i | \(-0.509475\pi\) | ||||
−0.0297610 | + | 0.999557i | \(0.509475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3133 | + | 27.0402i | 0.983138 | + | 0.906899i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.1400 | 1.47709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1169 | + | 22.7192i | −0.438450 | + | 0.759419i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.18855 | − | 15.9150i | 0.306455 | − | 0.530796i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.66395 | − | 6.34615i | −0.122064 | − | 0.211421i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.3884 | −1.40904 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5750 | 0.351136 | 0.175568 | − | 0.984467i | \(-0.443824\pi\) | ||||
0.175568 | + | 0.984467i | \(0.443824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2693 | + | 26.4473i | 0.505896 | + | 0.876237i | 0.999977 | + | 0.00682127i | \(0.00217130\pi\) |
−0.494081 | + | 0.869416i | \(0.664495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.03999 | + | 12.1936i | 0.232990 | + | 0.403550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.8608 | − | 26.6227i | −0.953066 | − | 0.879160i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.552490 | + | 0.956940i | 0.0182249 | + | 0.0315665i | 0.874994 | − | 0.484134i | \(-0.160865\pi\) |
−0.856769 | + | 0.515700i | \(0.827532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9174 | + | 58.7466i | −1.11640 | + | 1.93367i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.68598 | − | 11.5805i | −0.219834 | − | 0.380763i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.63729 | + | 4.56792i | −0.0865266 | + | 0.149869i | −0.906041 | − | 0.423191i | \(-0.860910\pi\) |
0.819514 | + | 0.573059i | \(0.194243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.3005 | + | 17.4665i | −0.829189 | + | 0.572442i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.51174 | + | 7.81456i | −0.147550 | + | 0.255564i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7481 | 0.579806 | 0.289903 | − | 0.957056i | \(-0.406377\pi\) | ||||
0.289903 | + | 0.957056i | \(0.406377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8684 | − | 24.0207i | −0.452096 | − | 0.783053i | 0.546420 | − | 0.837511i | \(-0.315990\pi\) |
−0.998516 | + | 0.0544582i | \(0.982657\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.50474 | − | 11.2665i | 0.211824 | − | 0.366889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.63828 | + | 13.2299i | −0.248211 | + | 0.429914i | −0.963029 | − | 0.269396i | \(-0.913176\pi\) |
0.714819 | + | 0.699310i | \(0.246509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.15006 | − | 10.6522i | −0.199639 | − | 0.345785i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.3569 | 0.821390 | 0.410695 | − | 0.911773i | \(-0.365286\pi\) | ||||
0.410695 | + | 0.911773i | \(0.365286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.96014 | + | 5.12712i | −0.0957880 | + | 0.165910i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.1974 | − | 36.1578i | −1.26575 | − | 1.16760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6429 | − | 18.4340i | 0.343318 | − | 0.594644i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.79286 | + | 13.4976i | 0.250861 | + | 0.434504i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5566 | − | 23.4808i | 0.435952 | − | 0.755090i | −0.561421 | − | 0.827530i | \(-0.689745\pi\) |
0.997373 | + | 0.0724398i | \(0.0230785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1555 | − | 36.6423i | −0.678911 | − | 1.17591i | −0.975309 | − | 0.220844i | \(-0.929119\pi\) |
0.296398 | − | 0.955064i | \(-0.404214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.0917 | + | 15.6113i | −1.60587 | + | 0.500475i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.18908 | + | 2.05955i | 0.0380421 | + | 0.0658908i | 0.884420 | − | 0.466693i | \(-0.154555\pi\) |
−0.846377 | + | 0.532583i | \(0.821221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5499 | − | 18.2729i | −0.337175 | − | 0.584004i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.29283 | 0.105025 | 0.0525124 | − | 0.998620i | \(-0.483277\pi\) | ||||
0.0525124 | + | 0.998620i | \(0.483277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.16782 | 0.164661 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.8821 | − | 39.6329i | −0.727607 | − | 1.26025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5482 | − | 51.1790i | 0.938630 | − | 1.62575i | 0.170600 | − | 0.985340i | \(-0.445429\pi\) |
0.768030 | − | 0.640414i | \(-0.221237\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.92356 | − | 8.52786i | 0.156087 | − | 0.270351i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9797 | −0.537754 | −0.268877 | − | 0.963175i | \(-0.586652\pi\) | ||||
−0.268877 | + | 0.963175i | \(0.586652\pi\) | |||||||
\(998\) | 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 | 3024.2.t.l.1873.2 | 22 | ||
3.2 | odd | 2 | 1008.2.t.k.193.3 | 22 | |||
4.3 | odd | 2 | 1512.2.t.d.361.2 | 22 | |||
7.2 | even | 3 | 3024.2.q.k.2305.10 | 22 | |||
9.2 | odd | 6 | 1008.2.q.k.529.6 | 22 | |||
9.7 | even | 3 | 3024.2.q.k.2881.10 | 22 | |||
12.11 | even | 2 | 504.2.t.d.193.9 | yes | 22 | ||
21.2 | odd | 6 | 1008.2.q.k.625.6 | 22 | |||
28.23 | odd | 6 | 1512.2.q.c.793.10 | 22 | |||
36.7 | odd | 6 | 1512.2.q.c.1369.10 | 22 | |||
36.11 | even | 6 | 504.2.q.d.25.6 | ✓ | 22 | ||
63.2 | odd | 6 | 1008.2.t.k.961.3 | 22 | |||
63.16 | even | 3 | inner | 3024.2.t.l.289.2 | 22 | ||
84.23 | even | 6 | 504.2.q.d.121.6 | yes | 22 | ||
252.79 | odd | 6 | 1512.2.t.d.289.2 | 22 | |||
252.191 | even | 6 | 504.2.t.d.457.9 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.6 | ✓ | 22 | 36.11 | even | 6 | ||
504.2.q.d.121.6 | yes | 22 | 84.23 | even | 6 | ||
504.2.t.d.193.9 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.d.457.9 | yes | 22 | 252.191 | even | 6 | ||
1008.2.q.k.529.6 | 22 | 9.2 | odd | 6 | |||
1008.2.q.k.625.6 | 22 | 21.2 | odd | 6 | |||
1008.2.t.k.193.3 | 22 | 3.2 | odd | 2 | |||
1008.2.t.k.961.3 | 22 | 63.2 | odd | 6 | |||
1512.2.q.c.793.10 | 22 | 28.23 | odd | 6 | |||
1512.2.q.c.1369.10 | 22 | 36.7 | odd | 6 | |||
1512.2.t.d.289.2 | 22 | 252.79 | odd | 6 | |||
1512.2.t.d.361.2 | 22 | 4.3 | odd | 2 | |||
3024.2.q.k.2305.10 | 22 | 7.2 | even | 3 | |||
3024.2.q.k.2881.10 | 22 | 9.7 | even | 3 | |||
3024.2.t.l.289.2 | 22 | 63.16 | even | 3 | inner | ||
3024.2.t.l.1873.2 | 22 | 1.1 | even | 1 | trivial |