Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1297,2268)]
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, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1297");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.k (of order \(3\), degree \(2\), 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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.3 | ||
Root | \(1.04556 - 0.339889i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.1297 |
Dual form | 2268.2.k.g.1621.3 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.515559 | + | 0.892975i | −0.230565 | + | 0.399350i | −0.957975 | − | 0.286853i | \(-0.907391\pi\) |
0.727409 | + | 0.686204i | \(0.240724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.55575 | − | 2.14001i | 0.588020 | − | 0.808846i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.792879 | + | 1.37331i | 0.239062 | + | 0.414067i | 0.960445 | − | 0.278468i | \(-0.0898268\pi\) |
−0.721383 | + | 0.692536i | \(0.756493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.04830 | 1.40015 | 0.700074 | − | 0.714071i | \(-0.253150\pi\) | ||||
0.700074 | + | 0.714071i | \(0.253150\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.58242 | − | 4.47288i | −0.626329 | − | 1.08483i | −0.988282 | − | 0.152637i | \(-0.951223\pi\) |
0.361954 | − | 0.932196i | \(-0.382110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.392975 | + | 0.680652i | −0.0901546 | + | 0.156152i | −0.907576 | − | 0.419888i | \(-0.862069\pi\) |
0.817421 | + | 0.576040i | \(0.195403\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.93289 | − | 5.07991i | 0.611549 | − | 1.05923i | −0.379431 | − | 0.925220i | \(-0.623880\pi\) |
0.990980 | − | 0.134014i | \(-0.0427866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96840 | + | 3.40936i | 0.393679 | + | 0.681873i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.89021 | −1.65087 | −0.825435 | − | 0.564496i | \(-0.809070\pi\) | ||||
−0.825435 | + | 0.564496i | \(0.809070\pi\) | |||||||
\(30\) | 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 | −0.306964 | − | 0.951721i | \(-0.599313\pi\) |
0.977697 | − | 0.210022i | \(-0.0673535\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.74411 | 1.20943 | 0.604714 | − | 0.796443i | \(-0.293288\pi\) | ||||
0.604714 | + | 0.796443i | \(0.293288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53256 | −0.386212 | −0.193106 | − | 0.981178i | \(-0.561856\pi\) | ||||
−0.193106 | + | 0.981178i | \(0.561856\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.24595 | + | 7.35420i | −0.619335 | + | 1.07272i | 0.370272 | + | 0.928923i | \(0.379264\pi\) |
−0.989607 | + | 0.143796i | \(0.954069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.15926 | − | 6.65865i | −0.308465 | − | 0.951236i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.41270 | + | 4.17892i | 0.331410 | + | 0.574019i | 0.982789 | − | 0.184734i | \(-0.0591423\pi\) |
−0.651378 | + | 0.758753i | \(0.725809\pi\) | |||||||
\(54\) | 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 | 0.712022 | − | 0.702157i | \(-0.247780\pi\) |
−0.964097 | + | 0.265551i | \(0.914446\pi\) | |||||||
\(60\) | 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 | \(-0.178207\pi\) | ||||
0.847333 | + | 0.531062i | \(0.178207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.04382 | + | 5.27205i | 0.356252 | + | 0.617047i | 0.987331 | − | 0.158671i | \(-0.0507211\pi\) |
−0.631079 | + | 0.775718i | \(0.717388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.17241 | + | 0.439762i | 0.475490 | + | 0.0501155i | ||||
\(78\) | 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 | ||||||||
\(83\) | −14.2419 | −1.56325 | −0.781626 | − | 0.623747i | \(-0.785609\pi\) | ||||
−0.781626 | + | 0.623747i | \(0.785609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.32556 | 0.577638 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.69272 | − | 11.5921i | 0.709426 | − | 1.22876i | −0.255644 | − | 0.966771i | \(-0.582287\pi\) |
0.965070 | − | 0.261992i | \(-0.0843793\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 5.34999 | 0.543210 | 0.271605 | − | 0.962409i | \(-0.412446\pi\) | ||||
0.271605 | + | 0.962409i | \(0.412446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.59038 | + | 2.75462i | 0.158249 | + | 0.274095i | 0.934237 | − | 0.356652i | \(-0.116082\pi\) |
−0.775988 | + | 0.630747i | \(0.782749\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.70660 | − | 9.88412i | 0.562288 | − | 0.973911i | −0.435008 | − | 0.900426i | \(-0.643255\pi\) |
0.997296 | − | 0.0734850i | \(-0.0234121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.311386 | + | 0.539337i | −0.0301028 | + | 0.0521396i | −0.880684 | − | 0.473704i | \(-0.842917\pi\) |
0.850582 | + | 0.525843i | \(0.176250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.971921 | + | 1.68342i | 0.0930932 | + | 0.161242i | 0.908811 | − | 0.417208i | \(-0.136991\pi\) |
−0.815718 | + | 0.578450i | \(0.803658\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.58833 | 0.337561 | 0.168781 | − | 0.985654i | \(-0.446017\pi\) | ||||
0.168781 | + | 0.985654i | \(0.446017\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.02415 | + | 5.23798i | 0.282004 | + | 0.488445i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.5896 | − | 1.43231i | −1.24576 | − | 0.131300i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.24269 | − | 7.34855i | 0.385699 | − | 0.668050i | ||||
\(122\) | 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 | ||||||||
\(131\) | 4.07898 | − | 7.06501i | 0.356382 | − | 0.617272i | −0.630971 | − | 0.775806i | \(-0.717343\pi\) |
0.987354 | + | 0.158534i | \(0.0506767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.845228 | + | 1.89990i | 0.0732906 | + | 0.164742i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.28181 | + | 12.6125i | 0.622127 | + | 1.07756i | 0.989089 | + | 0.147320i | \(0.0470647\pi\) |
−0.366962 | + | 0.930236i | \(0.619602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8343 | −1.00377 | −0.501884 | − | 0.864935i | \(-0.667360\pi\) | ||||
−0.501884 | + | 0.864935i | \(0.667360\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 7.02477 | − | 12.1673i | 0.575492 | − | 0.996781i | −0.420496 | − | 0.907294i | \(-0.638144\pi\) |
0.995988 | − | 0.0894868i | \(-0.0285227\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24269 | − | 2.15240i | −0.101128 | − | 0.175159i | 0.811021 | − | 0.585016i | \(-0.198912\pi\) |
−0.912150 | + | 0.409857i | \(0.865579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.18666 | −0.0953147 | ||||||||
\(156\) | 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 | 0.287063 | + | 0.957912i | \(0.407321\pi\) |
−0.973107 | + | 0.230352i | \(0.926012\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.5476 | 1.89955 | 0.949775 | − | 0.312935i | \(-0.101312\pi\) | ||||
0.949775 | + | 0.312935i | \(0.101312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4854 | 0.960413 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0344569 | − | 0.0596811i | 0.00261971 | − | 0.00453747i | −0.864713 | − | 0.502267i | \(-0.832499\pi\) |
0.867332 | + | 0.497730i | \(0.165833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3584 | + | 1.09175i | 0.783022 | + | 0.0825286i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.96086 | + | 6.86041i | 0.296049 | + | 0.512771i | 0.975228 | − | 0.221201i | \(-0.0709976\pi\) |
−0.679180 | + | 0.733972i | \(0.737664\pi\) | |||||||
\(180\) | 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 | \(0.363864\pi\) |
−0.995404 | + | 0.0957664i | \(0.969470\pi\) | |||||||
\(192\) | 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 | \(-0.759686\pi\) | ||||
−0.728293 | + | 0.685266i | \(0.759686\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50056 | − | 11.2593i | −0.460812 | − | 0.798150i | 0.538189 | − | 0.842824i | \(-0.319109\pi\) |
−0.999002 | + | 0.0446737i | \(0.985775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8310 | + | 19.0251i | −0.970745 | + | 1.33530i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.99255 | + | 6.91530i | −0.278852 | + | 0.482985i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.24633 | −0.0862101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.23849 | 0.291789 | 0.145895 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145895 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(212\) | 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 | ||||||||
\(223\) | −11.6666 | −0.781252 | −0.390626 | − | 0.920549i | \(-0.627742\pi\) | ||||
−0.390626 | + | 0.920549i | \(0.627742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.08989 | − | 3.61980i | −0.138711 | − | 0.240255i | 0.788298 | − | 0.615294i | \(-0.210963\pi\) |
−0.927009 | + | 0.375039i | \(0.877629\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.19086 | − | 7.25878i | 0.276940 | − | 0.479674i | −0.693683 | − | 0.720280i | \(-0.744013\pi\) |
0.970623 | + | 0.240607i | \(0.0773464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.499512 | − | 0.865180i | 0.0327241 | − | 0.0566798i | −0.849200 | − | 0.528072i | \(-0.822915\pi\) |
0.881924 | + | 0.471392i | \(0.156248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.37807 | − | 7.58305i | −0.285594 | − | 0.494663i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.3082 | −0.796154 | −0.398077 | − | 0.917352i | \(-0.630322\pi\) | ||||
−0.398077 | + | 0.917352i | \(0.630322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.23916 | − | 5.61039i | −0.208653 | − | 0.361397i | 0.742638 | − | 0.669694i | \(-0.233575\pi\) |
−0.951290 | + | 0.308296i | \(0.900241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.05923 | + | 1.50477i | 0.450998 | + | 0.0961360i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.98386 | + | 3.43614i | −0.126230 | + | 0.218636i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2236 | 0.771544 | 0.385772 | − | 0.922594i | \(-0.373935\pi\) | ||||
0.385772 | + | 0.922594i | \(0.373935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.30169 | 0.584792 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.96355 | + | 13.7933i | −0.496753 | + | 0.860401i | −0.999993 | − | 0.00374541i | \(-0.998808\pi\) |
0.503240 | + | 0.864147i | \(0.332141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.77525 | − | 19.7249i | −0.545267 | − | 1.22565i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.5305 | − | 19.9714i | −0.711002 | − | 1.23149i | −0.964481 | − | 0.264150i | \(-0.914908\pi\) |
0.253480 | − | 0.967341i | \(-0.418425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.97556 | −0.305647 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.51107 | + | 9.54546i | 0.336016 | + | 0.581997i | 0.983679 | − | 0.179930i | \(-0.0575871\pi\) |
−0.647663 | + | 0.761927i | \(0.724254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.74213 | − | 4.74951i | 0.166572 | − | 0.288512i | −0.770640 | − | 0.637271i | \(-0.780063\pi\) |
0.937213 | + | 0.348759i | \(0.113397\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.12140 | + | 5.40643i | −0.188228 | + | 0.326020i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0331 | + | 26.0381i | 0.903253 | + | 1.56448i | 0.823246 | + | 0.567685i | \(0.192161\pi\) |
0.0800068 | + | 0.996794i | \(0.474506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8182 | 0.705013 | 0.352506 | − | 0.935809i | \(-0.385329\pi\) | ||||
0.352506 | + | 0.935809i | \(0.385329\pi\) | |||||||
\(282\) | 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 | ||||||||
\(293\) | 12.3020 | 0.718688 | 0.359344 | − | 0.933205i | \(-0.383000\pi\) | ||||
0.359344 | + | 0.933205i | \(0.383000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.99295 | 0.232479 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8061 | − | 25.6449i | 0.856259 | − | 1.48308i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.94005 | + | 5.41970i | −0.227100 | + | 0.312386i | ||||
\(302\) | 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 | \(-0.849483\pi\) |
0.0507130 | − | 0.998713i | \(-0.483851\pi\) | |||||||
\(312\) | 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 | −0.894781 | − | 0.446505i | \(-0.852669\pi\) |
0.834075 | + | 0.551651i | \(0.186002\pi\) | |||||||
\(318\) | 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 | ||||||||
\(329\) | 9.13238 | + | 20.5277i | 0.503484 | + | 1.13173i | ||||
\(330\) | 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 | ||||||||
\(335\) | −1.72655 | −0.0943313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.88849 | 0.211820 | 0.105910 | − | 0.994376i | \(-0.466225\pi\) | ||||
0.105910 | + | 0.994376i | \(0.466225\pi\) | |||||||
\(338\) | 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 | 0.548600 | − | 0.836085i | \(-0.315161\pi\) |
−0.998371 | + | 0.0570585i | \(0.981828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.8194 | −1.70325 | −0.851625 | − | 0.524151i | \(-0.824383\pi\) | ||||
−0.851625 | + | 0.524151i | \(0.824383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.66867 | − | 6.35431i | −0.195263 | − | 0.338206i | 0.751723 | − | 0.659478i | \(-0.229223\pi\) |
−0.946987 | + | 0.321272i | \(0.895889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.36193 | + | 12.7512i | −0.390731 | + | 0.676765i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.16644 | + | 12.4126i | −0.378230 | + | 0.655114i | −0.990805 | − | 0.135299i | \(-0.956801\pi\) |
0.612574 | + | 0.790413i | \(0.290134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.19114 | + | 15.9195i | 0.483744 | + | 0.837870i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.27708 | −0.328557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7865 | − | 22.1469i | −0.667450 | − | 1.15606i | −0.978615 | − | 0.205702i | \(-0.934052\pi\) |
0.311165 | − | 0.950356i | \(-0.399281\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6965 | + | 1.33818i | 0.659169 | + | 0.0694748i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5734 | + | 26.9739i | −0.806361 | + | 1.39666i | 0.109008 | + | 0.994041i | \(0.465233\pi\) |
−0.915368 | + | 0.402617i | \(0.868101\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −18.7673 | + | 32.5060i | −0.958967 | + | 1.66098i | −0.233949 | + | 0.972249i | \(0.575165\pi\) |
−0.725018 | + | 0.688730i | \(0.758168\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.54382 | + | 3.49913i | −0.129645 | + | 0.178332i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.3213 | + | 26.5372i | 0.776819 | + | 1.34549i | 0.933766 | + | 0.357883i | \(0.116501\pi\) |
−0.156947 | + | 0.987607i | \(0.550165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.2958 | −1.53212 | ||||||||
\(392\) | 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 | −0.925002 | − | 0.379962i | \(-0.875937\pi\) |
0.791558 | + | 0.611094i | \(0.209270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.328399 | + | 0.568803i | −0.0163994 | + | 0.0284047i | −0.874109 | − | 0.485730i | \(-0.838554\pi\) |
0.857709 | + | 0.514135i | \(0.171887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.90491 | + | 5.03145i | 0.144704 | + | 0.250634i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9395 | 0.641387 | ||||||||
\(408\) | 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 | ||||||||
\(419\) | 20.8848 | 1.02029 | 0.510146 | − | 0.860088i | \(-0.329592\pi\) | ||||
0.510146 | + | 0.860088i | \(0.329592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5958 | 0.662617 | 0.331309 | − | 0.943522i | \(-0.392510\pi\) | ||||
0.331309 | + | 0.943522i | \(0.392510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.1665 | − | 17.6088i | 0.493145 | − | 0.854153i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3715 | − | 23.3129i | −0.501910 | − | 1.12819i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.9416 | + | 24.1475i | 0.671541 | + | 1.16314i | 0.977467 | + | 0.211088i | \(0.0677006\pi\) |
−0.305926 | + | 0.952055i | \(0.598966\pi\) | |||||||
\(432\) | 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 | \(-0.519127\pi\) |
0.894488 | − | 0.447091i | \(-0.147540\pi\) | |||||||
\(444\) | 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 | \(-0.500726\pi\) | ||||
−0.00228067 | + | 0.999997i | \(0.500726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.14014 | + | 10.6350i | 0.289128 | + | 0.500785i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.59800 | + | 12.5831i | 0.262438 | + | 0.589907i | ||||
\(456\) | 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 | ||||||||
\(461\) | 16.1763 | 0.753407 | 0.376704 | − | 0.926334i | \(-0.377058\pi\) | ||||
0.376704 | + | 0.926334i | \(0.377058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4859 | −0.580271 | −0.290135 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290135 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.72717 | − | 11.6518i | 0.311296 | − | 0.539181i | −0.667347 | − | 0.744747i | \(-0.732570\pi\) |
0.978643 | + | 0.205566i | \(0.0659035\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | −3.09412 | −0.141968 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.98107 | + | 12.0916i | 0.318973 | + | 0.552478i | 0.980274 | − | 0.197643i | \(-0.0633287\pi\) |
−0.661301 | + | 0.750121i | \(0.729995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5966 | − | 35.6744i | 0.939124 | − | 1.62661i | ||||
\(482\) | 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 | 0.981538 | + | 0.191270i | \(0.0612605\pi\) |
−0.325124 | + | 0.945671i | \(0.605406\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.7550 | −1.88438 | −0.942189 | − | 0.335081i | \(-0.891236\pi\) | ||||
−0.942189 | + | 0.335081i | \(0.891236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.9583 | + | 39.7649i | 1.03399 | + | 1.79092i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.2154 | − | 30.5582i | 0.996497 | − | 1.37072i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7230 | + | 18.5728i | −0.480028 | + | 0.831433i | −0.999738 | − | 0.0229099i | \(-0.992707\pi\) |
0.519709 | + | 0.854343i | \(0.326040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.3098 | −1.26227 | −0.631135 | − | 0.775673i | \(-0.717411\pi\) | ||||
−0.631135 | + | 0.775673i | \(0.717411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.27974 | −0.145947 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.8142 | + | 27.3910i | −0.700951 | + | 1.21408i | 0.267182 | + | 0.963646i | \(0.413908\pi\) |
−0.968133 | + | 0.250437i | \(0.919426\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0177 | + | 1.68822i | 0.708580 | + | 0.0746826i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.88418 | + | 10.1917i | 0.259288 | + | 0.449100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4661 | −0.592238 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0364 | − | 26.0439i | −0.658759 | − | 1.14100i | −0.980937 | − | 0.194325i | \(-0.937749\pi\) |
0.322179 | − | 0.946679i | \(-0.395585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.73793 | − | 13.4025i | 0.338356 | − | 0.586050i | −0.645768 | − | 0.763534i | \(-0.723463\pi\) |
0.984124 | + | 0.177484i | \(0.0567959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.97197 | − | 5.14760i | 0.129461 | − | 0.224233i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.70363 | − | 9.87898i | −0.247984 | − | 0.429521i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.0946 | 1.69338 | ||||||||
\(534\) | 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 | −0.986082 | − | 0.166259i | \(-0.946831\pi\) |
0.637026 | + | 0.770842i | \(0.280164\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00433 | −0.0858562 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.9081 | −1.66359 | −0.831795 | − | 0.555083i | \(-0.812687\pi\) | ||||
−0.831795 | + | 0.555083i | \(0.812687\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.49363 | − | 6.05114i | 0.148834 | − | 0.257787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.93747 | − | 20.0896i | −0.380060 | − | 0.854296i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.86210 | − | 4.95730i | −0.121271 | − | 0.210048i | 0.798998 | − | 0.601334i | \(-0.205364\pi\) |
−0.920269 | + | 0.391286i | \(0.872030\pi\) | |||||||
\(558\) | 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 | 0.913427 | − | 0.407003i | \(-0.133426\pi\) |
−0.809188 | + | 0.587549i | \(0.800093\pi\) | |||||||
\(564\) | 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 | −0.644451 | − | 0.764646i | \(-0.722914\pi\) |
0.984428 | + | 0.175788i | \(0.0562473\pi\) | |||||||
\(570\) | 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 | −0.942582 | − | 0.333975i | \(-0.891610\pi\) |
0.182060 | − | 0.983287i | \(-0.441723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.1569 | + | 30.4778i | −0.919223 | + | 1.26443i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.82596 | + | 6.62676i | −0.158455 | + | 0.274452i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.8474 | −0.984289 | −0.492144 | − | 0.870514i | \(-0.663787\pi\) | ||||
−0.492144 | + | 0.870514i | \(0.663787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.904506 | −0.0372695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.54751 | − | 11.3406i | 0.268874 | − | 0.465704i | −0.699697 | − | 0.714439i | \(-0.746682\pi\) |
0.968571 | + | 0.248736i | \(0.0800151\pi\) | |||||||
\(594\) | 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 | \(-0.892338\pi\) |
0.184310 | − | 0.982868i | \(-0.440995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.0627 | −0.696000 | −0.348000 | − | 0.937494i | \(-0.613139\pi\) | ||||
−0.348000 | + | 0.937494i | \(0.613139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.37471 | + | 7.57722i | 0.177857 | + | 0.308058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.5973 | + | 20.0871i | −0.470719 | + | 0.815310i | −0.999439 | − | 0.0334867i | \(-0.989339\pi\) |
0.528720 | + | 0.848796i | \(0.322672\pi\) | |||||||
\(608\) | 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 | 0.827257 | + | 0.561824i | \(0.189900\pi\) |
0.0729255 | + | 0.997337i | \(0.476766\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.25406 | −0.251779 | −0.125890 | − | 0.992044i | \(-0.540178\pi\) | ||||
−0.125890 | + | 0.992044i | \(0.540178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.770208 | + | 1.33404i | 0.0309573 | + | 0.0536196i | 0.881089 | − | 0.472951i | \(-0.156811\pi\) |
−0.850132 | + | 0.526570i | \(0.823478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.3950 | − | 32.3570i | −0.576723 | − | 1.29635i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.09116 | + | 8.81816i | −0.203647 | + | 0.352726i | ||||
\(626\) | 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 | ||||||||
\(635\) | −5.99090 | + | 10.3765i | −0.237742 | + | 0.411781i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9006 | − | 33.6149i | −0.431897 | − | 1.33187i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.87520 | + | 3.24794i | 0.0740660 | + | 0.128286i | 0.900680 | − | 0.434484i | \(-0.143069\pi\) |
−0.826614 | + | 0.562770i | \(0.809736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.63678 | 0.0645485 | 0.0322742 | − | 0.999479i | \(-0.489725\pi\) | ||||
0.0322742 | + | 0.999479i | \(0.489725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0748 | + | 17.4501i | 0.396082 | + | 0.686034i | 0.993239 | − | 0.116091i | \(-0.0370363\pi\) |
−0.597157 | + | 0.802125i | \(0.703703\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.07038 | − | 5.31806i | 0.120523 | − | 0.208752i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4570 | − | 37.1646i | 0.839677 | − | 1.45436i | −0.0504888 | − | 0.998725i | \(-0.516078\pi\) |
0.890165 | − | 0.455638i | \(-0.150589\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.20591 | + | 7.28486i | 0.164339 | + | 0.284643i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.7052 | −0.845515 | −0.422758 | − | 0.906243i | \(-0.638938\pi\) | ||||
−0.422758 | + | 0.906243i | \(0.638938\pi\) | |||||||
\(660\) | 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 | ||||||||
\(671\) | 15.2932 | 0.590386 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.7735 | −0.608024 | −0.304012 | − | 0.952668i | \(-0.598326\pi\) | ||||
−0.304012 | + | 0.952668i | \(0.598326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.32531 | + | 9.22370i | −0.204668 | + | 0.354496i | −0.950027 | − | 0.312168i | \(-0.898945\pi\) |
0.745359 | + | 0.666664i | \(0.232278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.32328 | − | 11.4490i | 0.319418 | − | 0.439373i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3656 | + | 24.8819i | 0.549683 | + | 0.952078i | 0.998296 | + | 0.0583524i | \(0.0185847\pi\) |
−0.448613 | + | 0.893726i | \(0.648082\pi\) | |||||||
\(684\) | 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 | \(-0.276781\pi\) | ||||
0.645184 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.20660 | + | 5.55399i | 0.120939 | + | 0.209473i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.36915 | + | 0.882088i | 0.314754 | + | 0.0331743i | ||||
\(708\) | 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 | ||||||||
\(713\) | 6.75060 | 0.252812 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.25450 | −0.308701 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.87829 | − | 10.1815i | 0.219223 | − | 0.379705i | −0.735348 | − | 0.677690i | \(-0.762981\pi\) |
0.954571 | + | 0.297985i | \(0.0963144\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | −45.6322 | −1.69240 | −0.846202 | − | 0.532862i | \(-0.821117\pi\) | ||||
−0.846202 | + | 0.532862i | \(0.821117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.54014 | + | 11.3279i | 0.241896 | + | 0.418976i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.4901 | + | 33.7579i | −0.719885 | + | 1.24688i | 0.241160 | + | 0.970485i | \(0.422472\pi\) |
−0.961045 | + | 0.276392i | \(0.910861\pi\) | |||||||
\(734\) | 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 | 0.564097 | − | 0.825708i | \(-0.309224\pi\) |
−0.997133 | + | 0.0756686i | \(0.975891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.19224 | −0.300544 | −0.150272 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150272 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.24337 | + | 12.5459i | 0.265377 | + | 0.459646i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.669743 | + | 1.50544i | 0.0244719 | + | 0.0550077i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0936 | − | 24.4109i | 0.514284 | − | 0.890766i | −0.485578 | − | 0.874193i | \(-0.661391\pi\) |
0.999863 | − | 0.0165733i | \(-0.00527570\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | −15.3534 | + | 26.5928i | −0.556559 | + | 0.963988i | 0.441222 | + | 0.897398i | \(0.354545\pi\) |
−0.997780 | + | 0.0665900i | \(0.978788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.11460 | + | 0.539066i | 0.185161 | + | 0.0195155i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.77465 | − | 16.9302i | −0.352942 | − | 0.611314i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.1946 | −1.44945 | −0.724727 | − | 0.689037i | \(-0.758034\pi\) | ||||
−0.724727 | + | 0.689037i | \(0.758034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.69611 | − | 2.93775i | −0.0610050 | − | 0.105664i | 0.833910 | − | 0.551901i | \(-0.186097\pi\) |
−0.894915 | + | 0.446237i | \(0.852764\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.26532 | + | 3.92365i | −0.0813727 | + | 0.140942i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.04324 | + | 5.27105i | −0.109035 | + | 0.188855i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3219 | + | 19.6101i | 0.405130 | + | 0.701706i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.13392 | −0.111854 | ||||||||
\(786\) | 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 | ||||||||
\(797\) | 46.9965 | 1.66470 | 0.832350 | − | 0.554250i | \(-0.186995\pi\) | ||||
0.832350 | + | 0.554250i | \(0.186995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.8593 | 1.55163 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.82676 | + | 8.36020i | −0.170333 | + | 0.295025i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.9142 | + | 1.67731i | 0.560900 | + | 0.0591175i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5052 | − | 25.1238i | −0.509977 | − | 0.883306i | −0.999933 | − | 0.0115587i | \(-0.996321\pi\) |
0.489957 | − | 0.871747i | \(-0.337013\pi\) | |||||||
\(810\) | 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 | \(0.407372\pi\) |
−0.973070 | + | 0.230508i | \(0.925961\pi\) | |||||||
\(822\) | 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 | \(-0.418492\pi\) | ||||
0.253276 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6920 | + | 28.9113i | 0.579736 | + | 1.00413i | 0.995509 | + | 0.0946641i | \(0.0301777\pi\) |
−0.415773 | + | 0.909468i | \(0.636489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.2072 | + | 26.8535i | −0.838731 | + | 0.930419i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6557 | + | 21.9204i | −0.437970 | + | 0.758586i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.97458 | 0.0681701 | 0.0340850 | − | 0.999419i | \(-0.489148\pi\) | ||||
0.0340850 | + | 0.999419i | \(0.489148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.0359 | 1.72537 | ||||||||
\(842\) | 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 | ||||||||
\(853\) | −13.3727 | −0.457874 | −0.228937 | − | 0.973441i | \(-0.573525\pi\) | ||||
−0.228937 | + | 0.973441i | \(0.573525\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4324 | − | 23.2656i | −0.458842 | − | 0.794738i | 0.540058 | − | 0.841628i | \(-0.318402\pi\) |
−0.998900 | + | 0.0468899i | \(0.985069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9212 | − | 39.7007i | 0.782062 | − | 1.35457i | −0.148677 | − | 0.988886i | \(-0.547502\pi\) |
0.930739 | − | 0.365685i | \(-0.119165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.90612 | − | 10.2297i | 0.201047 | − | 0.348223i | −0.747819 | − | 0.663902i | \(-0.768899\pi\) |
0.948866 | + | 0.315679i | \(0.102232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0355291 | + | 0.0615383i | 0.00120803 | + | 0.00209236i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.1787 | 0.447056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.22654 | + | 7.32059i | 0.143211 | + | 0.248049i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.3361 | + | 19.7199i | −0.484649 | + | 0.666655i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6046 | − | 21.8318i | 0.425628 | − | 0.737209i | −0.570851 | − | 0.821054i | \(-0.693387\pi\) |
0.996479 | + | 0.0838449i | \(0.0267200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.268589 | −0.00904898 | −0.00452449 | − | 0.999990i | \(-0.501440\pi\) | ||||
−0.00452449 | + | 0.999990i | \(0.501440\pi\) | |||||||
\(882\) | 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 | ||||||||
\(887\) | −21.8396 | + | 37.8274i | −0.733303 | + | 1.27012i | 0.222160 | + | 0.975010i | \(0.428689\pi\) |
−0.955464 | + | 0.295109i | \(0.904644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0782 | − | 24.8673i | 0.606323 | − | 0.834023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.33710 | − | 5.78003i | −0.111672 | − | 0.193421i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.16823 | −0.273034 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | −1.85441 | + | 3.21192i | −0.0616425 | + | 0.106768i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0146274 | + | 0.0253355i | 0.000485696 | + | 0.000841251i | 0.866268 | − | 0.499579i | \(-0.166512\pi\) |
−0.865782 | + | 0.500421i | \(0.833179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.0095 | 0.927996 | 0.463998 | − | 0.885836i | \(-0.346414\pi\) | ||||
0.463998 | + | 0.885836i | \(0.346414\pi\) | |||||||
\(912\) | 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 | −0.949079 | − | 0.315039i | \(-0.897982\pi\) |
0.747371 | + | 0.664407i | \(0.231316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.0873 | 2.37278 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.1235 | 1.05621 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.98202 | − | 6.89707i | 0.130646 | − | 0.226285i | −0.793280 | − | 0.608857i | \(-0.791628\pi\) |
0.923926 | + | 0.382572i | \(0.124962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.38076 | + | 1.14698i | 0.176347 | + | 0.0375907i | ||||
\(932\) | 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 | \(-0.773758\pi\) |
−0.186069 | − | 0.982537i | \(-0.559575\pi\) | |||||||
\(942\) | 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 | −0.991753 | − | 0.128164i | \(-0.959092\pi\) |
0.606870 | + | 0.794801i | \(0.292425\pi\) | |||||||
\(948\) | 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 | \(-0.426010\pi\) | ||||
0.230358 | + | 0.973106i | \(0.426010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.27429 | − | 14.3315i | −0.267750 | − | 0.463756i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.3195 | + | 4.03878i | 1.23740 | + | 0.130419i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8378 | − | 25.6998i | 0.478638 | − | 0.829025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.2443 | −0.716070 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.7331 | −0.666730 | −0.333365 | − | 0.942798i | \(-0.608184\pi\) | ||||
−0.333365 | + | 0.942798i | \(0.608184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.39847 | − | 14.5466i | 0.269520 | − | 0.466822i | −0.699218 | − | 0.714908i | \(-0.746468\pi\) |
0.968738 | + | 0.248087i | \(0.0798018\pi\) | |||||||
\(972\) | 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 | \(0.0376843\pi\) |
−0.394212 | + | 0.919020i | \(0.628982\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.2261 | 0.678388 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8389 | + | 44.7543i | 0.824132 | + | 1.42744i | 0.902581 | + | 0.430521i | \(0.141670\pi\) |
−0.0784482 | + | 0.996918i | \(0.524997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5402 | − | 18.2561i | 0.335838 | − | 0.581688i | ||||
\(986\) | 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 | 0.818525 | + | 0.574471i | \(0.194792\pi\) |
0.0882435 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4057 | 0.424989 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00745 | + | 1.74496i | 0.0319063 | + | 0.0552633i | 0.881538 | − | 0.472114i | \(-0.156509\pi\) |
−0.849631 | + | 0.527377i | \(0.823176\pi\) | |||||||
\(998\) | 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.k.g.1297.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2268.2.k.g.1297.6 | yes | 16 | |
7.4 | even | 3 | inner | 2268.2.k.g.1621.3 | yes | 16 | |
9.2 | odd | 6 | 2268.2.i.n.2053.6 | 16 | |||
9.4 | even | 3 | 2268.2.l.n.541.6 | 16 | |||
9.5 | odd | 6 | 2268.2.l.n.541.3 | 16 | |||
9.7 | even | 3 | 2268.2.i.n.2053.3 | 16 | |||
21.11 | odd | 6 | inner | 2268.2.k.g.1621.6 | yes | 16 | |
63.4 | even | 3 | 2268.2.i.n.865.3 | 16 | |||
63.11 | odd | 6 | 2268.2.l.n.109.3 | 16 | |||
63.25 | even | 3 | 2268.2.l.n.109.6 | 16 | |||
63.32 | odd | 6 | 2268.2.i.n.865.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.i.n.865.3 | 16 | 63.4 | even | 3 | |||
2268.2.i.n.865.6 | 16 | 63.32 | odd | 6 | |||
2268.2.i.n.2053.3 | 16 | 9.7 | even | 3 | |||
2268.2.i.n.2053.6 | 16 | 9.2 | odd | 6 | |||
2268.2.k.g.1297.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2268.2.k.g.1297.6 | yes | 16 | 3.2 | odd | 2 | inner | |
2268.2.k.g.1621.3 | yes | 16 | 7.4 | even | 3 | inner | |
2268.2.k.g.1621.6 | yes | 16 | 21.11 | odd | 6 | inner | |
2268.2.l.n.109.3 | 16 | 63.11 | odd | 6 | |||
2268.2.l.n.109.6 | 16 | 63.25 | even | 3 | |||
2268.2.l.n.541.3 | 16 | 9.5 | odd | 6 | |||
2268.2.l.n.541.6 | 16 | 9.4 | even | 3 |