Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(109,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.l (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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 9x^{14} + 31x^{12} - 282x^{10} + 1695x^{8} - 3318x^{6} + 4606x^{4} - 4116x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Root | \(-0.817131 - 0.735533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.109 |
Dual form | 2268.2.l.n.541.3 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −1.03112 | −0.461130 | −0.230565 | − | 0.973057i | \(-0.574057\pi\) | ||||
−0.230565 | + | 0.973057i | \(0.574057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.07542 | − | 2.41733i | 0.406472 | − | 0.913663i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58576 | 0.478124 | 0.239062 | − | 0.971004i | \(-0.423160\pi\) | ||||
0.239062 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.52415 | + | 4.37196i | −0.700074 | + | 1.21256i | 0.268366 | + | 0.963317i | \(0.413516\pi\) |
−0.968440 | + | 0.249246i | \(0.919817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.58242 | − | 4.47288i | 0.626329 | − | 1.08483i | −0.361954 | − | 0.932196i | \(-0.617890\pi\) |
0.988282 | − | 0.152637i | \(-0.0487765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.392975 | − | 0.680652i | −0.0901546 | − | 0.156152i | 0.817421 | − | 0.576040i | \(-0.195403\pi\) |
−0.907576 | + | 0.419888i | \(0.862069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.86577 | 1.22310 | 0.611549 | − | 0.791207i | \(-0.290547\pi\) | ||||
0.611549 | + | 0.791207i | \(0.290547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.93679 | −0.787359 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.44511 | − | 7.69915i | −0.825435 | − | 1.42970i | −0.901586 | − | 0.432600i | \(-0.857596\pi\) |
0.0761506 | − | 0.997096i | \(-0.475737\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.575423 | + | 0.996661i | 0.103349 | + | 0.179006i | 0.913062 | − | 0.407820i | \(-0.133711\pi\) |
−0.809713 | + | 0.586825i | \(0.800377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.10889 | + | 2.49255i | −0.187436 | + | 0.421318i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.07991 | + | 7.06661i | 0.670732 | + | 1.16174i | 0.977697 | + | 0.210022i | \(0.0673535\pi\) |
−0.306964 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.87206 | − | 6.70660i | 0.604714 | − | 1.04739i | −0.387383 | − | 0.921919i | \(-0.626621\pi\) |
0.992097 | − | 0.125476i | \(-0.0400458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.26628 | + | 2.19326i | 0.193106 | + | 0.334470i | 0.946278 | − | 0.323354i | \(-0.104811\pi\) |
−0.753172 | + | 0.657824i | \(0.771477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.24595 | − | 7.35420i | 0.619335 | − | 1.07272i | −0.370272 | − | 0.928923i | \(-0.620736\pi\) |
0.989607 | − | 0.143796i | \(-0.0459310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.68693 | − | 5.19930i | −0.669562 | − | 0.742756i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.41270 | + | 4.17892i | −0.331410 | + | 0.574019i | −0.982789 | − | 0.184734i | \(-0.940858\pi\) |
0.651378 | + | 0.758753i | \(0.274191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.63510 | −0.220477 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.93622 | + | 3.35364i | 0.252075 | + | 0.436607i | 0.964097 | − | 0.265551i | \(-0.0855537\pi\) |
−0.712022 | + | 0.702157i | \(0.752220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.82204 | − | 8.35201i | 0.617398 | − | 1.06937i | −0.372560 | − | 0.928008i | \(-0.621520\pi\) |
0.989959 | − | 0.141357i | \(-0.0451467\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.60270 | − | 4.50801i | 0.322825 | − | 0.559150i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.837220 | + | 1.45011i | 0.102283 | + | 0.177159i | 0.912625 | − | 0.408798i | \(-0.134052\pi\) |
−0.810342 | + | 0.585957i | \(0.800719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2795 | −1.69467 | −0.847333 | − | 0.531062i | \(-0.821793\pi\) | ||||
−0.847333 | + | 0.531062i | \(0.821793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.04382 | − | 5.27205i | 0.356252 | − | 0.617047i | −0.631079 | − | 0.775718i | \(-0.717388\pi\) |
0.987331 | + | 0.158671i | \(0.0507211\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.70536 | − | 3.83329i | 0.194344 | − | 0.436844i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.15533 | − | 7.19724i | 0.467511 | − | 0.809753i | −0.531800 | − | 0.846870i | \(-0.678484\pi\) |
0.999311 | + | 0.0371172i | \(0.0118175\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.12095 | − | 12.3339i | −0.781626 | − | 1.35382i | −0.930994 | − | 0.365034i | \(-0.881057\pi\) |
0.149368 | − | 0.988782i | \(-0.452276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.66278 | + | 4.61207i | −0.288819 | + | 0.500249i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.69272 | − | 11.5921i | −0.709426 | − | 1.22876i | −0.965070 | − | 0.261992i | \(-0.915621\pi\) |
0.255644 | − | 0.966771i | \(-0.417713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85392 | + | 10.8034i | 0.823315 | + | 1.13250i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.405203 | + | 0.701833i | 0.0415730 | + | 0.0720065i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.67500 | − | 4.63323i | −0.271605 | − | 0.470433i | 0.697668 | − | 0.716421i | \(-0.254221\pi\) |
−0.969273 | + | 0.245988i | \(0.920888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.18076 | 0.316498 | 0.158249 | − | 0.987399i | \(-0.449415\pi\) | ||||
0.158249 | + | 0.987399i | \(0.449415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.4132 | −1.12458 | −0.562288 | − | 0.826941i | \(-0.690079\pi\) | ||||
−0.562288 | + | 0.826941i | \(0.690079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.311386 | + | 0.539337i | 0.0301028 | + | 0.0521396i | 0.880684 | − | 0.473704i | \(-0.157083\pi\) |
−0.850582 | + | 0.525843i | \(0.823750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.971921 | − | 1.68342i | 0.0930932 | − | 0.161242i | −0.815718 | − | 0.578450i | \(-0.803658\pi\) |
0.908811 | + | 0.417208i | \(0.136991\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.79416 | − | 3.10758i | 0.168781 | − | 0.292337i | −0.769211 | − | 0.638995i | \(-0.779350\pi\) |
0.937991 | + | 0.346658i | \(0.112684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.04830 | −0.564007 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.03522 | − | 11.0528i | −0.736587 | − | 1.01321i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.48537 | −0.771398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21489 | 0.824205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6202 | 1.03113 | 0.515563 | − | 0.856852i | \(-0.327583\pi\) | ||||
0.515563 | + | 0.856852i | \(0.327583\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.15797 | 0.712765 | 0.356382 | − | 0.934340i | \(-0.384010\pi\) | ||||
0.356382 | + | 0.934340i | \(0.384010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.06797 | + | 0.217959i | −0.179316 | + | 0.0188995i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5636 | 1.24425 | 0.622127 | − | 0.782916i | \(-0.286269\pi\) | ||||
0.622127 | + | 0.782916i | \(0.286269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.91713 | − | 10.2488i | 0.501884 | − | 0.869289i | −0.498113 | − | 0.867112i | \(-0.665974\pi\) |
0.999998 | − | 0.00217698i | \(-0.000692954\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00269 | + | 6.93287i | −0.334722 | + | 0.579756i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58343 | + | 7.93873i | 0.380633 | + | 0.659276i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0495 | 1.15098 | 0.575492 | − | 0.817808i | \(-0.304811\pi\) | ||||
0.575492 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.48537 | 0.202257 | 0.101128 | − | 0.994873i | \(-0.467755\pi\) | ||||
0.101128 | + | 0.994873i | \(0.467755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.593329 | − | 1.02768i | −0.0476573 | − | 0.0825449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.51967 | + | 2.63214i | 0.121283 | + | 0.210068i | 0.920274 | − | 0.391275i | \(-0.127966\pi\) |
−0.798991 | + | 0.601343i | \(0.794633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.30818 | − | 14.1795i | 0.497154 | − | 1.11750i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.75883 | − | 15.1707i | −0.686045 | − | 1.18826i | −0.973107 | − | 0.230352i | \(-0.926012\pi\) |
0.287063 | − | 0.957912i | \(-0.407321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2738 | − | 21.2588i | 0.949775 | − | 1.64506i | 0.203877 | − | 0.978996i | \(-0.434646\pi\) |
0.745897 | − | 0.666061i | \(-0.232021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24269 | − | 10.8126i | −0.480207 | − | 0.831742i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.0344569 | + | 0.0596811i | −0.00261971 | + | 0.00453747i | −0.867332 | − | 0.497730i | \(-0.834167\pi\) |
0.864713 | + | 0.502267i | \(0.167501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.23372 | + | 9.51652i | −0.320039 | + | 0.719381i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.96086 | + | 6.86041i | −0.296049 | + | 0.512771i | −0.975228 | − | 0.221201i | \(-0.929002\pi\) |
0.679180 | + | 0.733972i | \(0.262336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.59688 | 0.267354 | 0.133677 | − | 0.991025i | \(-0.457322\pi\) | ||||
0.133677 | + | 0.991025i | \(0.457322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.20687 | − | 7.28651i | −0.309295 | − | 0.535715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.09509 | − | 7.09291i | 0.299463 | − | 0.518685i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.02458 | − | 13.8990i | 0.580638 | − | 1.00569i | −0.414766 | − | 0.909928i | \(-0.636136\pi\) |
0.995404 | − | 0.0957664i | \(-0.0305302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7865 | + | 18.6828i | 0.776430 | + | 1.34482i | 0.933987 | + | 0.357306i | \(0.116305\pi\) |
−0.157558 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4441 | 1.45659 | 0.728293 | − | 0.685266i | \(-0.240314\pi\) | ||||
0.728293 | + | 0.685266i | \(0.240314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50056 | + | 11.2593i | −0.460812 | + | 0.798150i | −0.999002 | − | 0.0446737i | \(-0.985775\pi\) |
0.538189 | + | 0.842824i | \(0.319109\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.3917 | + | 2.46543i | −1.64178 | + | 0.173039i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99255 | + | 6.91530i | −0.278852 | + | 0.482985i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.623163 | − | 1.07935i | −0.0431051 | − | 0.0746602i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.11924 | + | 3.67064i | −0.145895 | + | 0.252697i | −0.929706 | − | 0.368302i | \(-0.879939\pi\) |
0.783812 | + | 0.620999i | \(0.213273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.30569 | − | 2.26151i | −0.0890470 | − | 0.154234i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.02808 | − | 0.319152i | 0.205559 | − | 0.0216655i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.0368 | + | 22.5805i | 0.876953 | + | 1.51893i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.83329 | + | 10.1036i | 0.390626 | + | 0.676584i | 0.992532 | − | 0.121982i | \(-0.0389252\pi\) |
−0.601906 | + | 0.798567i | \(0.705592\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.17979 | −0.277422 | −0.138711 | − | 0.990333i | \(-0.544296\pi\) | ||||
−0.138711 | + | 0.990333i | \(0.544296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.38172 | −0.553879 | −0.276940 | − | 0.960887i | \(-0.589320\pi\) | ||||
−0.276940 | + | 0.960887i | \(0.589320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.499512 | − | 0.865180i | −0.0327241 | − | 0.0566798i | 0.849200 | − | 0.528072i | \(-0.177085\pi\) |
−0.881924 | + | 0.471392i | \(0.843752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.37807 | + | 7.58305i | −0.285594 | + | 0.494663i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.15412 | + | 10.6593i | −0.398077 | + | 0.689490i | −0.993489 | − | 0.113931i | \(-0.963656\pi\) |
0.595411 | + | 0.803421i | \(0.296989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.47832 | 0.417306 | 0.208653 | − | 0.977990i | \(-0.433092\pi\) | ||||
0.208653 | + | 0.977990i | \(0.433092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.83278 | + | 5.36109i | 0.308755 | + | 0.342507i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.96771 | 0.252459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.2236 | −0.771544 | −0.385772 | − | 0.922594i | \(-0.626065\pi\) | ||||
−0.385772 | + | 0.922594i | \(0.626065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.30169 | 0.584792 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9271 | −0.993506 | −0.496753 | − | 0.867892i | \(-0.665474\pi\) | ||||
−0.496753 | + | 0.867892i | \(0.665474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.4699 | − | 2.26288i | 1.33408 | − | 0.140608i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.0610 | −1.42200 | −0.711002 | − | 0.703190i | \(-0.751758\pi\) | ||||
−0.711002 | + | 0.703190i | \(0.751758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.48778 | − | 4.30897i | 0.152823 | − | 0.264698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.51107 | + | 9.54546i | −0.336016 | + | 0.581997i | −0.983679 | − | 0.179930i | \(-0.942413\pi\) |
0.647663 | + | 0.761927i | \(0.275746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74213 | + | 4.74951i | 0.166572 | + | 0.288512i | 0.937213 | − | 0.348759i | \(-0.113397\pi\) |
−0.770640 | + | 0.637271i | \(0.780063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.24280 | −0.376455 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.0662 | −1.80651 | −0.903253 | − | 0.429109i | \(-0.858828\pi\) | ||||
−0.903253 | + | 0.429109i | \(0.858828\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.90908 | + | 10.2348i | 0.352506 | + | 0.610559i | 0.986688 | − | 0.162625i | \(-0.0519961\pi\) |
−0.634182 | + | 0.773184i | \(0.718663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5605 | − | 18.2914i | −0.627758 | − | 1.08731i | −0.988001 | − | 0.154450i | \(-0.950639\pi\) |
0.360243 | − | 0.932859i | \(-0.382694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0479 | − | 16.5725i | −0.711167 | − | 0.978241i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.83778 | − | 8.37928i | −0.284575 | − | 0.492899i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.15098 | − | 10.6538i | 0.359344 | − | 0.622402i | −0.628507 | − | 0.777804i | \(-0.716334\pi\) |
0.987851 | + | 0.155401i | \(0.0496671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.99648 | − | 3.45800i | −0.116239 | − | 0.201332i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.8061 | + | 25.6449i | −0.856259 | + | 1.48308i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.66362 | − | 0.702329i | 0.384085 | − | 0.0404816i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.97209 | + | 8.61191i | −0.284701 | + | 0.493117i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.5033 | −1.91213 | −0.956067 | − | 0.293147i | \(-0.905297\pi\) | ||||
−0.956067 | + | 0.293147i | \(0.905297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8057 | + | 25.6442i | 0.839555 | + | 1.45415i | 0.890268 | + | 0.455438i | \(0.150517\pi\) |
−0.0507130 | + | 0.998713i | \(0.516149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.85745 | − | 10.1454i | 0.331082 | − | 0.573452i | −0.651642 | − | 0.758527i | \(-0.725920\pi\) |
0.982724 | + | 0.185075i | \(0.0592529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.08084 | − | 1.87207i | 0.0607061 | − | 0.105146i | −0.834075 | − | 0.551651i | \(-0.813998\pi\) |
0.894781 | + | 0.446505i | \(0.147331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.04886 | − | 12.2090i | −0.394660 | − | 0.683572i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.05930 | −0.225866 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.93707 | − | 17.2115i | 0.551209 | − | 0.954723i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.2113 | − | 18.1727i | −0.728363 | − | 1.00189i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6001 | + | 27.0202i | −0.857461 | + | 1.48517i | 0.0168824 | + | 0.999857i | \(0.494626\pi\) |
−0.874343 | + | 0.485308i | \(0.838707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.863273 | − | 1.49523i | −0.0471656 | − | 0.0816933i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.94425 | + | 3.36753i | −0.105910 | + | 0.183441i | −0.914110 | − | 0.405467i | \(-0.867109\pi\) |
0.808200 | + | 0.588908i | \(0.200442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.912481 | + | 1.58046i | 0.0494136 | + | 0.0855869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6088 | + | 5.73840i | −0.950787 | + | 0.309845i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.37831 | + | 14.5117i | 0.449771 | + | 0.779027i | 0.998371 | − | 0.0570585i | \(-0.0181722\pi\) |
−0.548600 | + | 0.836085i | \(0.684839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.9097 | + | 27.5564i | 0.851625 | + | 1.47506i | 0.879741 | + | 0.475454i | \(0.157716\pi\) |
−0.0281152 | + | 0.999605i | \(0.508951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.33733 | −0.390527 | −0.195263 | − | 0.980751i | \(-0.562556\pi\) | ||||
−0.195263 | + | 0.980751i | \(0.562556\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.7239 | 0.781461 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.16644 | + | 12.4126i | 0.378230 | + | 0.655114i | 0.990805 | − | 0.135299i | \(-0.0431994\pi\) |
−0.612574 | + | 0.790413i | \(0.709866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.19114 | − | 15.9195i | 0.483744 | − | 0.837870i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.13854 | + | 5.43611i | −0.164279 | + | 0.284539i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5730 | 1.33490 | 0.667450 | − | 0.744654i | \(-0.267386\pi\) | ||||
0.667450 | + | 0.744654i | \(0.267386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.50715 | + | 10.3264i | 0.389752 | + | 0.536120i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.1468 | 1.61272 | 0.806361 | − | 0.591424i | \(-0.201434\pi\) | ||||
0.806361 | + | 0.591424i | \(0.201434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.8805 | 2.31146 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.72979 | −0.345686 | −0.172843 | − | 0.984949i | \(-0.555295\pi\) | ||||
−0.172843 | + | 0.984949i | \(0.555295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.5347 | −1.91793 | −0.958967 | − | 0.283519i | \(-0.908498\pi\) | ||||
−0.958967 | + | 0.283519i | \(0.908498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.75843 | + | 3.95258i | −0.0896178 | + | 0.201442i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.6425 | 1.55364 | 0.776819 | − | 0.629724i | \(-0.216832\pi\) | ||||
0.776819 | + | 0.629724i | \(0.216832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1479 | − | 26.2369i | 0.766061 | − | 1.32686i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.28464 | + | 7.42121i | −0.215583 | + | 0.373401i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.65885 | − | 4.60527i | −0.133444 | − | 0.231132i | 0.791558 | − | 0.611094i | \(-0.209270\pi\) |
−0.925002 | + | 0.379962i | \(0.875937\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.656797 | −0.0327989 | −0.0163994 | − | 0.999866i | \(-0.505220\pi\) | ||||
−0.0163994 | + | 0.999866i | \(0.505220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.80982 | −0.289408 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.46974 | + | 11.2059i | 0.320693 | + | 0.555457i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.7994 | + | 27.3654i | 0.781230 | + | 1.35313i | 0.931226 | + | 0.364443i | \(0.118741\pi\) |
−0.149995 | + | 0.988687i | \(0.547926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.1891 | − | 1.07391i | 0.501373 | − | 0.0528435i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.34254 | + | 12.7177i | 0.360431 | + | 0.624285i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4424 | − | 18.0868i | 0.510146 | − | 0.883598i | −0.489785 | − | 0.871843i | \(-0.662925\pi\) |
0.999931 | − | 0.0117550i | \(-0.00374180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.79788 | − | 11.7743i | −0.331309 | − | 0.573843i | 0.651460 | − | 0.758683i | \(-0.274157\pi\) |
−0.982769 | + | 0.184840i | \(0.940823\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1665 | + | 17.6088i | −0.493145 | + | 0.854153i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0038 | − | 20.6384i | −0.726085 | − | 0.998761i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.9416 | + | 24.1475i | −0.671541 | + | 1.16314i | 0.305926 | + | 0.952055i | \(0.401034\pi\) |
−0.977467 | + | 0.211088i | \(0.932299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7059 | −1.09118 | −0.545589 | − | 0.838053i | \(-0.683694\pi\) | ||||
−0.545589 | + | 0.838053i | \(0.683694\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.30510 | − | 3.99255i | −0.110268 | − | 0.190990i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9508 | + | 27.6276i | −0.761290 | + | 1.31859i | 0.180895 | + | 0.983502i | \(0.442100\pi\) |
−0.942186 | + | 0.335091i | \(0.891233\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5629 | + | 30.4198i | −0.834436 | + | 1.44529i | 0.0600520 | + | 0.998195i | \(0.480873\pi\) |
−0.894488 | + | 0.447091i | \(0.852460\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.90098 | + | 11.9529i | 0.327138 | + | 0.566620i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.0966532 | 0.00456135 | 0.00228067 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228067 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.14014 | − | 10.6350i | 0.289128 | − | 0.500785i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.09832 | − | 11.1396i | −0.379655 | − | 0.522232i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50925 | − | 14.7385i | 0.398046 | − | 0.689436i | −0.595439 | − | 0.803401i | \(-0.703022\pi\) |
0.993485 | + | 0.113965i | \(0.0363551\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.08817 | + | 14.0091i | 0.376704 | + | 0.652470i | 0.990580 | − | 0.136932i | \(-0.0437242\pi\) |
−0.613877 | + | 0.789402i | \(0.710391\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.24297 | − | 10.8131i | 0.290135 | − | 0.502529i | −0.683706 | − | 0.729757i | \(-0.739633\pi\) |
0.973842 | + | 0.227228i | \(0.0729663\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.72717 | − | 11.6518i | −0.311296 | − | 0.539181i | 0.667347 | − | 0.744747i | \(-0.267430\pi\) |
−0.978643 | + | 0.205566i | \(0.934097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.40575 | − | 0.464355i | 0.203439 | − | 0.0214419i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00802 | + | 3.47798i | 0.0923286 | + | 0.159918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.54706 | + | 2.67959i | 0.0709840 | + | 0.122948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.9621 | 0.637946 | 0.318973 | − | 0.947764i | \(-0.396662\pi\) | ||||
0.318973 | + | 0.947764i | \(0.396662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.1932 | −1.87825 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.75824 | + | 4.77741i | 0.125245 | + | 0.216931i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4858 | − | 25.0901i | 0.656413 | − | 1.13694i | −0.325124 | − | 0.945671i | \(-0.605406\pi\) |
0.981538 | − | 0.191270i | \(-0.0612605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8775 | + | 36.1609i | −0.942189 | + | 1.63192i | −0.180906 | + | 0.983500i | \(0.557903\pi\) |
−0.761283 | + | 0.648419i | \(0.775430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.9165 | −2.06798 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.3565 | + | 34.5182i | −0.688833 | + | 1.54835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4460 | 0.960056 | 0.480028 | − | 0.877253i | \(-0.340626\pi\) | ||||
0.480028 | + | 0.877253i | \(0.340626\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.3098 | 1.26227 | 0.631135 | − | 0.775673i | \(-0.282589\pi\) | ||||
0.631135 | + | 0.775673i | \(0.282589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.27974 | −0.145947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.6284 | −1.40190 | −0.700951 | − | 0.713209i | \(-0.747241\pi\) | ||||
−0.700951 | + | 0.713209i | \(0.747241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.47087 | − | 13.0276i | −0.418967 | − | 0.576307i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.7684 | 0.518576 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.73304 | − | 11.6620i | 0.296119 | − | 0.512893i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.0364 | − | 26.0439i | 0.658759 | − | 1.14100i | −0.322179 | − | 0.946679i | \(-0.604415\pi\) |
0.980937 | − | 0.194325i | \(-0.0622515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.73793 | + | 13.4025i | 0.338356 | + | 0.586050i | 0.984124 | − | 0.177484i | \(-0.0567959\pi\) |
−0.645768 | + | 0.763534i | \(0.723463\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.94393 | 0.258922 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4073 | 0.495968 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.5473 | + | 33.8570i | 0.846689 | + | 1.46651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.321076 | − | 0.556120i | −0.0138813 | − | 0.0240432i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.43234 | − | 8.24482i | −0.320133 | − | 0.355130i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.11884 | − | 14.0622i | −0.349056 | − | 0.604583i | 0.637026 | − | 0.770842i | \(-0.280164\pi\) |
−0.986082 | + | 0.166259i | \(0.946831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.00217 | + | 1.73580i | −0.0429281 | + | 0.0743536i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4541 | + | 33.6954i | 0.831795 | + | 1.44071i | 0.896613 | + | 0.442815i | \(0.146020\pi\) |
−0.0648180 | + | 0.997897i | \(0.520647\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.49363 | + | 6.05114i | −0.148834 | + | 0.257787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9293 | − | 17.7849i | −0.549812 | − | 0.756289i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.86210 | − | 4.95730i | 0.121271 | − | 0.210048i | −0.798998 | − | 0.601334i | \(-0.794636\pi\) |
0.920269 | + | 0.391286i | \(0.127970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.7851 | −0.540754 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.47334 | − | 4.28394i | −0.104239 | − | 0.180547i | 0.809188 | − | 0.587549i | \(-0.199907\pi\) |
−0.913427 | + | 0.407003i | \(0.866574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84999 | + | 3.20429i | −0.0778299 | + | 0.134805i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.10972 | + | 14.0465i | −0.339977 | + | 0.588858i | −0.984428 | − | 0.175788i | \(-0.943753\pi\) |
0.644451 | + | 0.764646i | \(0.277086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3029 | + | 31.7016i | 0.765954 | + | 1.32667i | 0.939741 | + | 0.341887i | \(0.111066\pi\) |
−0.173787 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.0923 | −0.963017 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.2684 | + | 31.6417i | −0.760522 | + | 1.31726i | 0.182060 | + | 0.983287i | \(0.441723\pi\) |
−0.942582 | + | 0.333975i | \(0.891610\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.4730 | + | 3.94956i | −1.55464 | + | 0.163855i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.82596 | + | 6.62676i | −0.158455 | + | 0.274452i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9237 | − | 20.6525i | −0.492144 | − | 0.852419i | 0.507815 | − | 0.861466i | \(-0.330453\pi\) |
−0.999959 | + | 0.00904721i | \(0.997120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.452253 | − | 0.783325i | 0.0186348 | − | 0.0322764i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.54751 | − | 11.3406i | −0.268874 | − | 0.465704i | 0.699697 | − | 0.714439i | \(-0.253318\pi\) |
−0.968571 | + | 0.248736i | \(0.919985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.28526 | + | 11.3967i | 0.339663 | + | 0.467220i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5770 | + | 32.1762i | 0.759034 | + | 1.31469i | 0.943344 | + | 0.331817i | \(0.107662\pi\) |
−0.184310 | + | 0.982868i | \(0.559005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.53133 | + | 14.7767i | 0.348000 | + | 0.602754i | 0.985894 | − | 0.167370i | \(-0.0535275\pi\) |
−0.637894 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.74942 | 0.355715 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1946 | 0.941438 | 0.470719 | − | 0.882283i | \(-0.343994\pi\) | ||||
0.470719 | + | 0.882283i | \(0.343994\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.4348 | + | 37.1262i | 0.867160 | + | 1.50197i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.2875 | − | 38.6030i | 0.900182 | − | 1.55916i | 0.0729255 | − | 0.997337i | \(-0.476766\pi\) |
0.827257 | − | 0.561824i | \(-0.189900\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.12703 | + | 5.41618i | −0.125890 | + | 0.218047i | −0.922080 | − | 0.386999i | \(-0.873512\pi\) |
0.796191 | + | 0.605046i | \(0.206845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.54042 | −0.0619145 | −0.0309573 | − | 0.999521i | \(-0.509856\pi\) | ||||
−0.0309573 | + | 0.999521i | \(0.509856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.2194 | + | 3.71204i | −1.41104 | + | 0.148720i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.1823 | 0.407293 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.1441 | 1.68040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.5148 | −1.77210 | −0.886052 | − | 0.463585i | \(-0.846563\pi\) | ||||
−0.886052 | + | 0.463585i | \(0.846563\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.9818 | −0.475483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.5616 | − | 7.36726i | 1.36938 | − | 0.291902i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.75040 | 0.148132 | 0.0740660 | − | 0.997253i | \(-0.476402\pi\) | ||||
0.0740660 | + | 0.997253i | \(0.476402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.818392 | + | 1.41750i | −0.0322742 | + | 0.0559006i | −0.881711 | − | 0.471789i | \(-0.843608\pi\) |
0.849437 | + | 0.527690i | \(0.176942\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.0748 | + | 17.4501i | −0.396082 | + | 0.686034i | −0.993239 | − | 0.116091i | \(-0.962964\pi\) |
0.597157 | + | 0.802125i | \(0.296297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.07038 | + | 5.31806i | 0.120523 | + | 0.208752i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.9140 | 1.67935 | 0.839677 | − | 0.543087i | \(-0.182745\pi\) | ||||
0.839677 | + | 0.543087i | \(0.182745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.41183 | −0.328677 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8526 | − | 18.7973i | −0.422758 | − | 0.732238i | 0.573450 | − | 0.819240i | \(-0.305605\pi\) |
−0.996208 | + | 0.0870025i | \(0.972271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6907 | + | 21.9810i | 0.493613 | + | 0.854962i | 0.999973 | − | 0.00735996i | \(-0.00234277\pi\) |
−0.506360 | + | 0.862322i | \(0.669009\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.13232 | − | 0.224742i | 0.0826880 | − | 0.00871511i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.0740 | − | 45.1614i | −1.00959 | − | 1.74866i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.64658 | − | 13.2443i | 0.295193 | − | 0.511289i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.88676 | + | 13.6603i | 0.304012 | + | 0.526565i | 0.977041 | − | 0.213052i | \(-0.0683403\pi\) |
−0.673029 | + | 0.739616i | \(0.735007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.32531 | − | 9.22370i | 0.204668 | − | 0.354496i | −0.745359 | − | 0.666664i | \(-0.767722\pi\) |
0.950027 | + | 0.312168i | \(0.101055\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.0768 | + | 1.48366i | −0.540217 | + | 0.0569376i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3656 | + | 24.8819i | −0.549683 | + | 0.952078i | 0.448613 | + | 0.893726i | \(0.351918\pi\) |
−0.998296 | + | 0.0583524i | \(0.981415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0168 | −0.573763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.1801 | − | 21.0965i | −0.464023 | − | 0.803712i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.6136 | − | 33.9717i | 0.746136 | − | 1.29235i | −0.203526 | − | 0.979069i | \(-0.565240\pi\) |
0.949662 | − | 0.313276i | \(-0.101426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.10126 | + | 10.5677i | −0.231434 | + | 0.400855i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.9985 | − | 34.6385i | −0.757499 | − | 1.31203i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.1643 | −1.29037 | −0.645184 | − | 0.764028i | \(-0.723219\pi\) | ||||
−0.645184 | + | 0.764028i | \(0.723219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20660 | − | 5.55399i | 0.120939 | − | 0.209473i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.42066 | − | 7.68894i | 0.128647 | − | 0.289172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.85352 | + | 17.0668i | −0.370057 | + | 0.640957i | −0.989574 | − | 0.144026i | \(-0.953995\pi\) |
0.619517 | + | 0.784983i | \(0.287328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.37530 | + | 5.84619i | 0.126406 | + | 0.218941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.12725 | − | 7.14861i | 0.154350 | − | 0.267343i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.87829 | − | 10.1815i | −0.219223 | − | 0.379705i | 0.735348 | − | 0.677690i | \(-0.237019\pi\) |
−0.954571 | + | 0.297985i | \(0.903686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2740 | + | 27.5894i | −0.457108 | + | 1.02748i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4995 | + | 30.3100i | 0.649914 | + | 1.12568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8161 | + | 39.5186i | 0.846202 | + | 1.46567i | 0.884573 | + | 0.466402i | \(0.154450\pi\) |
−0.0383705 | + | 0.999264i | \(0.512217\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0803 | 0.483791 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.9803 | 1.43977 | 0.719885 | − | 0.694094i | \(-0.244195\pi\) | ||||
0.719885 | + | 0.694094i | \(0.244195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.32763 | + | 2.29952i | 0.0489038 | + | 0.0847039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.7719 | + | 20.3895i | −0.433036 | + | 0.750040i | −0.997133 | − | 0.0756686i | \(-0.975891\pi\) |
0.564097 | + | 0.825708i | \(0.309224\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.09612 | + | 7.09469i | −0.150272 | + | 0.260279i | −0.931327 | − | 0.364183i | \(-0.881348\pi\) |
0.781055 | + | 0.624462i | \(0.214682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4867 | −0.530753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.63862 | − | 0.172707i | 0.0598740 | − | 0.00631058i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.1873 | −1.02857 | −0.514284 | − | 0.857620i | \(-0.671942\pi\) | ||||
−0.514284 | + | 0.857620i | \(0.671942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.56271 | −0.0932667 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.42352 | 0.269812 | 0.134906 | − | 0.990858i | \(-0.456927\pi\) | ||||
0.134906 | + | 0.990858i | \(0.456927\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7067 | −1.11312 | −0.556559 | − | 0.830808i | \(-0.687879\pi\) | ||||
−0.556559 | + | 0.830808i | \(0.687879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.02414 | − | 4.15984i | −0.109481 | − | 0.150596i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.5493 | −0.705884 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0973 | − | 34.8095i | 0.724727 | − | 1.25526i | −0.234360 | − | 0.972150i | \(-0.575299\pi\) |
0.959086 | − | 0.283113i | \(-0.0913673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.69611 | − | 2.93775i | 0.0610050 | − | 0.105664i | −0.833910 | − | 0.551901i | \(-0.813903\pi\) |
0.894915 | + | 0.446237i | \(0.147236\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.26532 | − | 3.92365i | −0.0813727 | − | 0.140942i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.08648 | −0.218071 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6438 | −0.810260 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.56696 | − | 2.71405i | −0.0559271 | − | 0.0968686i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.41657 | − | 9.38177i | −0.193080 | − | 0.334424i | 0.753190 | − | 0.657804i | \(-0.228514\pi\) |
−0.946269 | + | 0.323379i | \(0.895181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.58256 | − | 7.67904i | −0.198493 | − | 0.273035i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.3431 | + | 42.1635i | 0.864449 | + | 1.49727i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.4982 | − | 40.7001i | 0.832350 | − | 1.44167i | −0.0638193 | − | 0.997961i | \(-0.520328\pi\) |
0.896170 | − | 0.443712i | \(-0.146339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9296 | − | 37.9832i | −0.775814 | − | 1.34375i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.82676 | − | 8.36020i | 0.170333 | − | 0.295025i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.50448 | + | 14.6207i | −0.229253 | + | 0.515313i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5052 | − | 25.1238i | 0.509977 | − | 0.883306i | −0.489957 | − | 0.871747i | \(-0.662987\pi\) |
0.999933 | − | 0.0115587i | \(-0.00367932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6805 | 1.21780 | 0.608899 | − | 0.793248i | \(-0.291612\pi\) | ||||
0.608899 | + | 0.793248i | \(0.291612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.03139 | + | 15.6428i | 0.316356 | + | 0.547944i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.995233 | − | 1.72379i | 0.0348188 | − | 0.0603079i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6606 | − | 34.0532i | 0.686161 | − | 1.18847i | −0.286909 | − | 0.957958i | \(-0.592628\pi\) |
0.973070 | − | 0.230508i | \(-0.0740388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3432 | + | 36.9675i | 0.743978 | + | 1.28861i | 0.950671 | + | 0.310202i | \(0.100397\pi\) |
−0.206693 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5672 | −0.506551 | −0.253276 | − | 0.967394i | \(-0.581508\pi\) | ||||
−0.253276 | + | 0.967394i | \(0.581508\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6920 | − | 28.9113i | 0.579736 | − | 1.00413i | −0.415773 | − | 0.909468i | \(-0.636489\pi\) |
0.995509 | − | 0.0946641i | \(-0.0301777\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.3595 | + | 7.53733i | −1.22513 | + | 0.261153i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6557 | + | 21.9204i | −0.437970 | + | 0.758586i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.987290 | + | 1.71004i | 0.0340850 | + | 0.0590370i | 0.882565 | − | 0.470191i | \(-0.155815\pi\) |
−0.848480 | + | 0.529228i | \(0.822482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0179 | + | 43.3323i | −0.862687 | + | 1.49422i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.43695 | + | 11.1491i | 0.221438 | + | 0.383541i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.12536 | + | 20.5119i | −0.313551 | + | 0.704798i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.9318 | + | 41.4511i | 0.820371 | + | 1.42092i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.68637 | + | 11.5811i | 0.228937 | + | 0.396531i | 0.957493 | − | 0.288455i | \(-0.0931417\pi\) |
−0.728556 | + | 0.684986i | \(0.759808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.8648 | −0.917684 | −0.458842 | − | 0.888518i | \(-0.651736\pi\) | ||||
−0.458842 | + | 0.888518i | \(0.651736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.8424 | −1.56412 | −0.782062 | − | 0.623201i | \(-0.785832\pi\) | ||||
−0.782062 | + | 0.623201i | \(0.785832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.90612 | − | 10.2297i | −0.201047 | − | 0.348223i | 0.747819 | − | 0.663902i | \(-0.231101\pi\) |
−0.948866 | + | 0.315679i | \(0.897768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0355291 | − | 0.0615383i | 0.00120803 | − | 0.00209236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.58935 | − | 11.4131i | 0.223528 | − | 0.387162i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.45308 | −0.286422 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.90991 | − | 22.2754i | 0.335016 | − | 0.753046i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2092 | −0.851255 | −0.425628 | − | 0.904898i | \(-0.639947\pi\) | ||||
−0.425628 | + | 0.904898i | \(0.639947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.268589 | 0.00904898 | 0.00452449 | − | 0.999990i | \(-0.498560\pi\) | ||||
0.00452449 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8915 | 0.871319 | 0.435660 | − | 0.900112i | \(-0.356515\pi\) | ||||
0.435660 | + | 0.900112i | \(0.356515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.6793 | −1.46661 | −0.733303 | − | 0.679902i | \(-0.762023\pi\) | ||||
−0.733303 | + | 0.679902i | \(0.762023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4966 | − | 28.0898i | 0.419124 | − | 0.942102i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.67420 | −0.223344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.08412 | − | 7.07390i | 0.136517 | − | 0.236454i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.11563 | − | 8.86053i | 0.170616 | − | 0.295515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4612 | + | 21.5835i | 0.415143 | + | 0.719050i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.70881 | −0.123285 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0292549 | −0.000971393 | −0.000485696 | − | 1.00000i | \(-0.500155\pi\) | ||||
−0.000485696 | 1.00000i | \(0.500155\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0048 | + | 24.2569i | 0.463998 | + | 0.803668i | 0.999156 | − | 0.0410839i | \(-0.0130811\pi\) |
−0.535158 | + | 0.844752i | \(0.679748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2921 | − | 19.5585i | −0.373714 | − | 0.647292i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.77326 | − | 19.7205i | 0.289719 | − | 0.651227i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.11476 | − | 10.5911i | −0.201707 | − | 0.349367i | 0.747371 | − | 0.664407i | \(-0.231316\pi\) |
−0.949079 | + | 0.315039i | \(0.897982\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0436 | − | 62.4294i | 1.18639 | − | 2.05489i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0618 | − | 27.8198i | −0.528107 | − | 0.914709i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.98202 | + | 6.89707i | −0.130646 | + | 0.226285i | −0.923926 | − | 0.382572i | \(-0.875038\pi\) |
0.793280 | + | 0.608857i | \(0.208372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.69707 | + | 5.23336i | −0.0556191 | + | 0.171516i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.22252 | + | 7.31363i | −0.138091 | + | 0.239181i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0407 | −0.491358 | −0.245679 | − | 0.969351i | \(-0.579011\pi\) | ||||
−0.245679 | + | 0.969351i | \(0.579011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.9559 | + | 50.1531i | 0.943936 | + | 1.63495i | 0.757867 | + | 0.652409i | \(0.226242\pi\) |
0.186069 | + | 0.982537i | \(0.440425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.7126 | − | 39.3394i | 0.739624 | − | 1.28107i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8442 | − | 20.5147i | 0.384883 | − | 0.666638i | −0.606870 | − | 0.794801i | \(-0.707575\pi\) |
0.991753 | + | 0.128164i | \(0.0409083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3661 | + | 26.6149i | 0.498806 | + | 0.863957i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.2226 | −0.460716 | −0.230358 | − | 0.973106i | \(-0.573990\pi\) | ||||
−0.230358 | + | 0.973106i | \(0.573990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.27429 | + | 14.3315i | −0.267750 | + | 0.463756i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.6621 | − | 35.2050i | 0.505754 | − | 1.13683i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8378 | − | 25.6998i | 0.478638 | − | 0.829025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.1222 | − | 19.2642i | −0.358035 | − | 0.620135i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3665 | − | 17.9554i | 0.333365 | − | 0.577405i | −0.649804 | − | 0.760102i | \(-0.725149\pi\) |
0.983169 | + | 0.182696i | \(0.0584825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.39847 | − | 14.5466i | −0.269520 | − | 0.466822i | 0.699218 | − | 0.714908i | \(-0.253532\pi\) |
−0.968738 | + | 0.248087i | \(0.920198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4112 | − | 25.3254i | −0.590236 | − | 0.811894i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.7163 | − | 32.4176i | −0.598788 | − | 1.03713i | −0.993000 | − | 0.118112i | \(-0.962316\pi\) |
0.394212 | − | 0.919020i | \(-0.371018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6130 | − | 18.3823i | −0.339194 | − | 0.587501i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.6778 | 1.64826 | 0.824132 | − | 0.566397i | \(-0.191663\pi\) | ||||
0.824132 | + | 0.566397i | \(0.191663\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.0803 | −0.671675 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.42771 | + | 12.8652i | 0.236188 | + | 0.409089i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5452 | − | 49.4418i | 0.906769 | − | 1.57057i | 0.0882435 | − | 0.996099i | \(-0.471875\pi\) |
0.818525 | − | 0.574471i | \(-0.194792\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.70284 | − | 11.6097i | 0.212494 | − | 0.368051i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.01490 | −0.0638126 | −0.0319063 | − | 0.999491i | \(-0.510158\pi\) | ||||
−0.0319063 | + | 0.999491i | \(0.510158\pi\) | |||||||
\(998\) | 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 | 2268.2.l.n.109.3 | 16 | ||
3.2 | odd | 2 | inner | 2268.2.l.n.109.6 | 16 | ||
7.2 | even | 3 | 2268.2.i.n.2053.6 | 16 | |||
9.2 | odd | 6 | 2268.2.i.n.865.3 | 16 | |||
9.4 | even | 3 | 2268.2.k.g.1621.6 | yes | 16 | ||
9.5 | odd | 6 | 2268.2.k.g.1621.3 | yes | 16 | ||
9.7 | even | 3 | 2268.2.i.n.865.6 | 16 | |||
21.2 | odd | 6 | 2268.2.i.n.2053.3 | 16 | |||
63.2 | odd | 6 | inner | 2268.2.l.n.541.6 | 16 | ||
63.16 | even | 3 | inner | 2268.2.l.n.541.3 | 16 | ||
63.23 | odd | 6 | 2268.2.k.g.1297.3 | ✓ | 16 | ||
63.58 | even | 3 | 2268.2.k.g.1297.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.3 | 16 | 9.2 | odd | 6 | |||
2268.2.i.n.865.6 | 16 | 9.7 | even | 3 | |||
2268.2.i.n.2053.3 | 16 | 21.2 | odd | 6 | |||
2268.2.i.n.2053.6 | 16 | 7.2 | even | 3 | |||
2268.2.k.g.1297.3 | ✓ | 16 | 63.23 | odd | 6 | ||
2268.2.k.g.1297.6 | yes | 16 | 63.58 | even | 3 | ||
2268.2.k.g.1621.3 | yes | 16 | 9.5 | odd | 6 | ||
2268.2.k.g.1621.6 | yes | 16 | 9.4 | even | 3 | ||
2268.2.l.n.109.3 | 16 | 1.1 | even | 1 | trivial | ||
2268.2.l.n.109.6 | 16 | 3.2 | odd | 2 | inner | ||
2268.2.l.n.541.3 | 16 | 63.16 | even | 3 | inner | ||
2268.2.l.n.541.6 | 16 | 63.2 | odd | 6 | inner |