Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(793,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.q (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.7 | ||
Character | \(\chi\) | \(=\) | 1512.793 |
Dual form | 1512.2.q.d.1369.7 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 0.263002 | + | 0.455533i | 0.117618 | + | 0.203721i | 0.918823 | − | 0.394669i | \(-0.129141\pi\) |
−0.801205 | + | 0.598390i | \(0.795807\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.333150 | + | 2.62469i | −0.125919 | + | 0.992041i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.30526 | − | 3.99283i | 0.695062 | − | 1.20388i | −0.275098 | − | 0.961416i | \(-0.588710\pi\) |
0.970160 | − | 0.242466i | \(-0.0779564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.244554 | − | 0.423580i | 0.0678270 | − | 0.117480i | −0.830118 | − | 0.557588i | \(-0.811727\pi\) |
0.897945 | + | 0.440109i | \(0.145060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.75579 | − | 4.77318i | −0.668378 | − | 1.15767i | −0.978357 | − | 0.206922i | \(-0.933655\pi\) |
0.309979 | − | 0.950743i | \(-0.399678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83782 | − | 3.18319i | 0.421624 | − | 0.730274i | −0.574475 | − | 0.818522i | \(-0.694794\pi\) |
0.996099 | + | 0.0882484i | \(0.0281269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0269769 | − | 0.0467253i | −0.00562506 | − | 0.00974289i | 0.863199 | − | 0.504864i | \(-0.168457\pi\) |
−0.868824 | + | 0.495121i | \(0.835124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.36166 | − | 4.09051i | 0.472332 | − | 0.818103i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.28471 | + | 5.68929i | 0.609956 | + | 1.05647i | 0.991247 | + | 0.132019i | \(0.0421461\pi\) |
−0.381292 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.07640 | 1.09135 | 0.545676 | − | 0.837996i | \(-0.316273\pi\) | ||||
0.545676 | + | 0.837996i | \(0.316273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.28325 | + | 0.538539i | −0.216909 | + | 0.0910297i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.223731 | − | 0.387513i | 0.0367811 | − | 0.0637068i | −0.847049 | − | 0.531515i | \(-0.821623\pi\) |
0.883830 | + | 0.467808i | \(0.154956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.52284 | + | 4.36968i | −0.394001 | + | 0.682430i | −0.992973 | − | 0.118340i | \(-0.962243\pi\) |
0.598972 | + | 0.800770i | \(0.295576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.84893 | + | 4.93449i | 0.434458 | + | 0.752503i | 0.997251 | − | 0.0740947i | \(-0.0236067\pi\) |
−0.562794 | + | 0.826598i | \(0.690273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.19621 | 1.34140 | 0.670702 | − | 0.741726i | \(-0.265993\pi\) | ||||
0.670702 | + | 0.741726i | \(0.265993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77802 | − | 1.74883i | −0.968289 | − | 0.249833i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37138 | + | 7.57145i | 0.600455 | + | 1.04002i | 0.992752 | + | 0.120180i | \(0.0383471\pi\) |
−0.392297 | + | 0.919839i | \(0.628320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.42515 | 0.327008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.63076 | 0.863252 | 0.431626 | − | 0.902053i | \(-0.357940\pi\) | ||||
0.431626 | + | 0.902053i | \(0.357940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.465625 | −0.0596171 | −0.0298086 | − | 0.999556i | \(-0.509490\pi\) | ||||
−0.0298086 | + | 0.999556i | \(0.509490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.257273 | 0.0319108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.19358 | 0.634496 | 0.317248 | − | 0.948343i | \(-0.397241\pi\) | ||||
0.317248 | + | 0.948343i | \(0.397241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.76328 | −0.209263 | −0.104632 | − | 0.994511i | \(-0.533366\pi\) | ||||
−0.104632 | + | 0.994511i | \(0.533366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.23776 | − | 9.07207i | −0.613034 | − | 1.06181i | −0.990726 | − | 0.135875i | \(-0.956616\pi\) |
0.377692 | − | 0.925931i | \(-0.376718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.71195 | + | 7.38081i | 1.10678 | + | 0.841121i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.3702 | 1.84179 | 0.920895 | − | 0.389812i | \(-0.127460\pi\) | ||||
0.920895 | + | 0.389812i | \(0.127460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.49251 | − | 7.78126i | −0.493117 | − | 0.854104i | 0.506851 | − | 0.862034i | \(-0.330809\pi\) |
−0.999969 | + | 0.00792925i | \(0.997476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44956 | − | 2.51071i | 0.157227 | − | 0.272325i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.05145 | − | 12.2135i | 0.747452 | − | 1.29463i | −0.201588 | − | 0.979470i | \(-0.564610\pi\) |
0.949040 | − | 0.315155i | \(-0.102056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.03029 | + | 0.782994i | 0.108004 | + | 0.0820801i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93340 | 0.198363 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.22413 | + | 9.04847i | 0.530430 | + | 0.918732i | 0.999370 | + | 0.0355020i | \(0.0113030\pi\) |
−0.468939 | + | 0.883230i | \(0.655364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.98254 | + | 8.63001i | −0.495781 | + | 0.858718i | −0.999988 | − | 0.00486475i | \(-0.998451\pi\) |
0.504207 | + | 0.863583i | \(0.331785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.82553 | − | 10.0901i | −0.574006 | − | 0.994208i | −0.996149 | − | 0.0876783i | \(-0.972055\pi\) |
0.422143 | − | 0.906529i | \(-0.361278\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.45556 | + | 4.25316i | −0.237388 | + | 0.411168i | −0.959964 | − | 0.280123i | \(-0.909625\pi\) |
0.722576 | + | 0.691292i | \(0.242958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.76353 | − | 16.9109i | −0.935177 | − | 1.61977i | −0.774319 | − | 0.632796i | \(-0.781907\pi\) |
−0.160858 | − | 0.986978i | \(-0.551426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.48658 | + | 9.50304i | −0.516134 | + | 0.893971i | 0.483690 | + | 0.875239i | \(0.339296\pi\) |
−0.999825 | + | 0.0187317i | \(0.994037\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0141899 | − | 0.0245777i | 0.00132322 | − | 0.00229188i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.4462 | − | 5.64293i | 1.23261 | − | 0.517287i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.12844 | − | 8.88272i | −0.466222 | − | 0.807520i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.11451 | 0.457456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6107 | −1.47396 | −0.736979 | − | 0.675915i | \(-0.763748\pi\) | ||||
−0.736979 | + | 0.675915i | \(0.763748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.90848 | + | 5.03763i | 0.254115 | + | 0.440140i | 0.964655 | − | 0.263517i | \(-0.0848825\pi\) |
−0.710540 | + | 0.703657i | \(0.751549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.74263 | + | 5.88418i | 0.671371 | + | 0.510223i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.61313 | + | 7.99017i | −0.394126 | + | 0.682647i | −0.992989 | − | 0.118205i | \(-0.962286\pi\) |
0.598863 | + | 0.800852i | \(0.295619\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.88477 | − | 11.9248i | 0.583959 | − | 1.01145i | −0.411046 | − | 0.911615i | \(-0.634836\pi\) |
0.995004 | − | 0.0998314i | \(-0.0318303\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.12752 | − | 1.95292i | −0.0942880 | − | 0.163312i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72777 | + | 2.99259i | −0.143484 | + | 0.248521i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.15043 | − | 7.18875i | −0.340016 | − | 0.588926i | 0.644419 | − | 0.764673i | \(-0.277099\pi\) |
−0.984435 | + | 0.175747i | \(0.943766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.24894 | − | 12.5555i | 0.589911 | − | 1.02176i | −0.404333 | − | 0.914612i | \(-0.632496\pi\) |
0.994244 | − | 0.107143i | \(-0.0341704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.59811 | + | 2.76800i | 0.128363 | + | 0.222331i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4887 | −0.996705 | −0.498352 | − | 0.866975i | \(-0.666061\pi\) | ||||
−0.498352 | + | 0.866975i | \(0.666061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.131627 | − | 0.0552394i | 0.0103736 | − | 0.00435348i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.48448 | + | 4.30325i | −0.194600 | + | 0.337057i | −0.946769 | − | 0.321913i | \(-0.895674\pi\) |
0.752169 | + | 0.658970i | \(0.229007\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0088 | − | 17.3357i | 0.774504 | − | 1.34148i | −0.160569 | − | 0.987025i | \(-0.551333\pi\) |
0.935073 | − | 0.354456i | \(-0.115334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38039 | + | 11.0512i | 0.490799 | + | 0.850089i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.05485 | −0.688427 | −0.344214 | − | 0.938891i | \(-0.611854\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.94956 | + | 7.56138i | 0.752116 | + | 0.571587i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.69175 | + | 13.3225i | 0.574908 | + | 0.995770i | 0.996052 | + | 0.0887763i | \(0.0282956\pi\) |
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.54973 | −0.709826 | −0.354913 | − | 0.934899i | \(-0.615489\pi\) | ||||
−0.354913 | + | 0.934899i | \(0.615489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.235367 | 0.0173045 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.4113 | −1.85826 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0433 | 0.799063 | 0.399531 | − | 0.916720i | \(-0.369173\pi\) | ||||
0.399531 | + | 0.916720i | \(0.369173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.6991 | 1.92185 | 0.960923 | − | 0.276817i | \(-0.0892796\pi\) | ||||
0.960923 | + | 0.276817i | \(0.0892796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8386 | −0.914715 | −0.457357 | − | 0.889283i | \(-0.651204\pi\) | ||||
−0.457357 | + | 0.889283i | \(0.651204\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1408 | + | 17.5644i | 0.718864 | + | 1.24511i | 0.961450 | + | 0.274979i | \(0.0886710\pi\) |
−0.242586 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0269 | + | 6.72597i | −1.12487 | + | 0.472071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.65405 | −0.185367 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.47329 | − | 14.6762i | −0.586109 | − | 1.01517i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.77903 | − | 8.27752i | 0.329002 | − | 0.569848i | −0.653312 | − | 0.757088i | \(-0.726621\pi\) |
0.982314 | + | 0.187241i | \(0.0599545\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.49855 | + | 2.59556i | −0.102200 | + | 0.177016i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.02435 | + | 15.9487i | −0.137422 | + | 1.08267i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.69576 | −0.181337 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9155 | + | 20.6383i | 0.797921 | + | 1.38204i | 0.920968 | + | 0.389639i | \(0.127400\pi\) |
−0.123046 | + | 0.992401i | \(0.539266\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.33567 | + | 2.31345i | −0.0886514 | + | 0.153549i | −0.906941 | − | 0.421257i | \(-0.861589\pi\) |
0.818290 | + | 0.574806i | \(0.194922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.16258 | − | 5.47775i | −0.208989 | − | 0.361980i | 0.742407 | − | 0.669949i | \(-0.233684\pi\) |
−0.951396 | + | 0.307969i | \(0.900351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.63381 | + | 8.02600i | −0.303571 | + | 0.525801i | −0.976942 | − | 0.213504i | \(-0.931512\pi\) |
0.673371 | + | 0.739305i | \(0.264846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.41862 | + | 4.18918i | 0.157774 | + | 0.273272i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.69219 | + | 2.93096i | −0.109459 | + | 0.189588i | −0.915551 | − | 0.402202i | \(-0.868245\pi\) |
0.806092 | + | 0.591790i | \(0.201578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.57982 | + | 11.3966i | −0.423844 | + | 0.734119i | −0.996312 | − | 0.0858082i | \(-0.972653\pi\) |
0.572468 | + | 0.819927i | \(0.305986\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.985984 | − | 3.54756i | −0.0629922 | − | 0.226645i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.898890 | − | 1.55692i | −0.0571950 | − | 0.0990647i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.30235 | 0.145323 | 0.0726614 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726614 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.248755 | −0.0156391 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.5661 | − | 25.2293i | −0.908610 | − | 1.57376i | −0.815997 | − | 0.578056i | \(-0.803811\pi\) |
−0.0926132 | − | 0.995702i | \(-0.529522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.942567 | + | 0.716324i | 0.0585683 | + | 0.0445102i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35919 | + | 2.35418i | −0.0838110 | + | 0.145165i | −0.904884 | − | 0.425658i | \(-0.860043\pi\) |
0.821073 | + | 0.570823i | \(0.193376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.29936 | + | 3.98261i | −0.141249 | + | 0.244650i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.80840 | − | 4.86428i | −0.171231 | − | 0.296581i | 0.767620 | − | 0.640906i | \(-0.221441\pi\) |
−0.938850 | + | 0.344325i | \(0.888108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.25164 | + | 12.5602i | −0.440506 | + | 0.762978i | −0.997727 | − | 0.0673860i | \(-0.978534\pi\) |
0.557221 | + | 0.830364i | \(0.311867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8885 | − | 18.8594i | −0.656600 | − | 1.13726i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.873953 | − | 1.51373i | 0.0525108 | − | 0.0909513i | −0.838575 | − | 0.544786i | \(-0.816611\pi\) |
0.891086 | + | 0.453835i | \(0.149944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.35657 | − | 9.27786i | −0.319546 | − | 0.553471i | 0.660847 | − | 0.750521i | \(-0.270197\pi\) |
−0.980393 | + | 0.197050i | \(0.936864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5967 | −0.748793 | −0.374397 | − | 0.927269i | \(-0.622150\pi\) | ||||
−0.374397 | + | 0.927269i | \(0.622150\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6286 | − | 8.07743i | −0.627386 | − | 0.476796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.68881 | + | 11.5854i | −0.393459 | + | 0.681491i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.57575 | − | 2.72928i | 0.0920562 | − | 0.159446i | −0.816320 | − | 0.577600i | \(-0.803989\pi\) |
0.908376 | + | 0.418154i | \(0.137323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.74391 | + | 3.02053i | 0.101534 | + | 0.175862i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0263892 | −0.00152613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9006 | + | 5.83364i | −0.801220 | + | 0.336245i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.122460 | − | 0.212107i | −0.00701206 | − | 0.0121452i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.3884 | −1.16363 | −0.581813 | − | 0.813322i | \(-0.697657\pi\) | ||||
−0.581813 | + | 0.813322i | \(0.697657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7014 | −1.28728 | −0.643640 | − | 0.765328i | \(-0.722577\pi\) | ||||
−0.643640 | + | 0.765328i | \(0.722577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7078 | −0.944380 | −0.472190 | − | 0.881497i | \(-0.656536\pi\) | ||||
−0.472190 | + | 0.881497i | \(0.656536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3280 | −0.580080 | −0.290040 | − | 0.957015i | \(-0.593669\pi\) | ||||
−0.290040 | + | 0.957015i | \(0.593669\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.2884 | 1.69583 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.2586 | −1.12722 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15511 | − | 2.00070i | −0.0640738 | − | 0.110979i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.06371 | + | 24.1372i | −0.168908 | + | 1.33073i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.6315 | −1.24394 | −0.621970 | − | 0.783041i | \(-0.713668\pi\) | ||||
−0.621970 | + | 0.783041i | \(0.713668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.36592 | + | 2.36585i | 0.0746283 | + | 0.129260i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.78253 | − | 11.7477i | 0.369468 | − | 0.639938i | −0.620014 | − | 0.784590i | \(-0.712873\pi\) |
0.989482 | + | 0.144653i | \(0.0462066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.0077 | − | 24.2620i | 0.758558 | − | 1.31386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.84824 | − | 17.2076i | 0.369770 | − | 0.929123i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.0262 | 1.77294 | 0.886470 | − | 0.462786i | \(-0.153150\pi\) | ||||
0.886470 | + | 0.462786i | \(0.153150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1773 | − | 17.6276i | −0.544778 | − | 0.943584i | −0.998621 | − | 0.0525019i | \(-0.983280\pi\) |
0.453842 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.75381 | + | 4.76975i | −0.146571 | + | 0.253868i | −0.929958 | − | 0.367666i | \(-0.880157\pi\) |
0.783387 | + | 0.621534i | \(0.213490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.463748 | − | 0.803234i | −0.0246132 | − | 0.0426312i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4656 | − | 18.1270i | 0.552354 | − | 0.956704i | −0.445751 | − | 0.895157i | \(-0.647063\pi\) |
0.998104 | − | 0.0615472i | \(-0.0196035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.74486 | + | 4.75424i | 0.144467 | + | 0.250223i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.75509 | − | 4.77195i | 0.144208 | − | 0.249775i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.14319 | + | 3.71211i | −0.111873 | + | 0.193770i | −0.916526 | − | 0.399976i | \(-0.869018\pi\) |
0.804652 | + | 0.593746i | \(0.202352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.3290 | + | 8.95110i | −1.10735 | + | 0.464718i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64461 | + | 9.77675i | 0.292267 | + | 0.506221i | 0.974345 | − | 0.225058i | \(-0.0722571\pi\) |
−0.682079 | + | 0.731279i | \(0.738924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.21316 | 0.165486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5828 | −1.05727 | −0.528634 | − | 0.848850i | \(-0.677295\pi\) | ||||
−0.528634 | + | 0.848850i | \(0.677295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8108 | − | 18.7248i | −0.552405 | − | 0.956793i | −0.998100 | − | 0.0616083i | \(-0.980377\pi\) |
0.445696 | − | 0.895184i | \(-0.352956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.807939 | + | 6.36528i | −0.0411764 | + | 0.324405i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.34241 | + | 12.7174i | −0.372275 | + | 0.644799i | −0.989915 | − | 0.141662i | \(-0.954755\pi\) |
0.617640 | + | 0.786461i | \(0.288089\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.148685 | + | 0.257531i | −0.00751934 | + | 0.0130239i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.30539 | + | 7.45716i | 0.216628 | + | 0.375210i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.13424 | + | 5.42866i | −0.157303 | + | 0.272457i | −0.933895 | − | 0.357547i | \(-0.883613\pi\) |
0.776592 | + | 0.630003i | \(0.216947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.6951 | + | 25.4526i | 0.733836 | + | 1.27104i | 0.955232 | + | 0.295857i | \(0.0956052\pi\) |
−0.221396 | + | 0.975184i | \(0.571061\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.48601 | − | 2.57384i | 0.0740232 | − | 0.128212i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.03152 | − | 1.78664i | −0.0511303 | − | 0.0885603i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.63285 | −0.0807392 | −0.0403696 | − | 0.999185i | \(-0.512854\pi\) | ||||
−0.0403696 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20904 | + | 17.4037i | −0.108700 | + | 0.856381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.36308 | − | 4.09298i | 0.115999 | − | 0.200916i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.01823 | − | 15.6200i | 0.440569 | − | 0.763088i | −0.557162 | − | 0.830404i | \(-0.688110\pi\) |
0.997732 | + | 0.0673151i | \(0.0214433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8278 | + | 29.1465i | 0.820135 | + | 1.42052i | 0.905581 | + | 0.424172i | \(0.139435\pi\) |
−0.0854466 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.0330 | −1.26279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.155123 | − | 1.22212i | 0.00750691 | − | 0.0591426i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1545 | + | 19.3202i | 0.537295 | + | 0.930622i | 0.999048 | + | 0.0436135i | \(0.0138870\pi\) |
−0.461754 | + | 0.887008i | \(0.652780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.32414 | 0.351976 | 0.175988 | − | 0.984392i | \(-0.443688\pi\) | ||||
0.175988 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.198314 | −0.00948664 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6728 | −1.17757 | −0.588785 | − | 0.808289i | \(-0.700394\pi\) | ||||
−0.588785 | + | 0.808289i | \(0.700394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.5363 | −1.45082 | −0.725412 | − | 0.688315i | \(-0.758351\pi\) | ||||
−0.725412 | + | 0.688315i | \(0.758351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41819 | 0.351656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.4782 | 1.95748 | 0.978738 | − | 0.205116i | \(-0.0657572\pi\) | ||||
0.978738 | + | 0.205116i | \(0.0657572\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6316 | + | 20.1465i | 0.547710 | + | 0.948662i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0857103 | + | 0.675262i | −0.00401816 | + | 0.0316568i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6289 | −0.543978 | −0.271989 | − | 0.962300i | \(-0.587681\pi\) | ||||
−0.271989 | + | 0.962300i | \(0.587681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.60886 | + | 9.71483i | 0.261231 | + | 0.452465i | 0.966569 | − | 0.256406i | \(-0.0825383\pi\) |
−0.705339 | + | 0.708871i | \(0.749205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.9362 | + | 34.5305i | −0.926514 | + | 1.60477i | −0.137405 | + | 0.990515i | \(0.543876\pi\) |
−0.789108 | + | 0.614254i | \(0.789457\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7818 | + | 20.4067i | −0.545198 | + | 0.944311i | 0.453397 | + | 0.891309i | \(0.350212\pi\) |
−0.998594 | + | 0.0530016i | \(0.983121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73024 | + | 13.6315i | −0.0798950 | + | 0.629446i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.2701 | 1.20790 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.68059 | − | 15.0352i | −0.398293 | − | 0.689864i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.11485 | − | 12.3233i | 0.325086 | − | 0.563065i | −0.656444 | − | 0.754375i | \(-0.727940\pi\) |
0.981530 | + | 0.191310i | \(0.0612735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.109428 | − | 0.189536i | −0.00498951 | − | 0.00864208i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.74792 | + | 4.75953i | −0.124776 | + | 0.216119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9818 | − | 24.2171i | −0.633574 | − | 1.09738i | −0.986815 | − | 0.161850i | \(-0.948254\pi\) |
0.353242 | − | 0.935532i | \(-0.385079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.2543 | + | 29.8853i | −0.778676 | + | 1.34871i | 0.154030 | + | 0.988066i | \(0.450775\pi\) |
−0.932705 | + | 0.360639i | \(0.882558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1040 | − | 31.3570i | 0.815362 | − | 1.41225i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.587437 | − | 4.62808i | 0.0263502 | − | 0.207598i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1436 | − | 22.7654i | −0.588390 | − | 1.01912i | −0.994443 | − | 0.105272i | \(-0.966429\pi\) |
0.406054 | − | 0.913849i | \(-0.366905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.09068 | −0.271570 | −0.135785 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135785 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.24167 | −0.233251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.08615 | − | 7.07742i | −0.181116 | − | 0.313701i | 0.761145 | − | 0.648582i | \(-0.224637\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.5564 | − | 10.7252i | 1.13055 | − | 0.474453i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.06425 | − | 5.30744i | 0.135027 | − | 0.233874i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1996 | − | 36.7189i | 0.932360 | − | 1.61489i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0485 | − | 22.6007i | −0.571666 | − | 0.990155i | −0.996395 | − | 0.0848346i | \(-0.972964\pi\) |
0.424729 | − | 0.905321i | \(-0.360370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.6655 | − | 23.6694i | 0.597553 | − | 1.03499i | −0.395628 | − | 0.918411i | \(-0.629473\pi\) |
0.993181 | − | 0.116581i | \(-0.0371935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.7453 | − | 29.0037i | −0.729437 | − | 1.26342i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4985 | − | 19.9161i | 0.499937 | − | 0.865916i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.23394 | + | 2.13725i | 0.0534478 | + | 0.0925744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.58327 | −0.111685 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.6079 | + | 23.0320i | −0.973790 | + | 0.992057i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.79086 | + | 10.0301i | −0.248969 | + | 0.431226i | −0.963240 | − | 0.268643i | \(-0.913425\pi\) |
0.714271 | + | 0.699869i | \(0.246758\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.13566 | − | 8.89522i | 0.219987 | − | 0.381029i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.3651 | + | 35.2734i | 0.870750 | + | 1.50818i | 0.861222 | + | 0.508228i | \(0.169699\pi\) |
0.00952755 | + | 0.999955i | \(0.496967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.1468 | 1.02869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.45372 | + | 42.9667i | −0.231916 | + | 1.82713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0085 | − | 17.3353i | −0.424075 | − | 0.734520i | 0.572258 | − | 0.820074i | \(-0.306068\pi\) |
−0.996334 | + | 0.0855533i | \(0.972734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.78687 | 0.117872 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.9328 | −1.05079 | −0.525396 | − | 0.850858i | \(-0.676083\pi\) | ||||
−0.525396 | + | 0.850858i | \(0.676083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.77193 | −0.242827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.80025 | 0.410848 | 0.205424 | − | 0.978673i | \(-0.434143\pi\) | ||||
0.205424 | + | 0.978673i | \(0.434143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7895 | −1.70699 | −0.853494 | − | 0.521103i | \(-0.825521\pi\) | ||||
−0.853494 | + | 0.521103i | \(0.825521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.254841 | −0.0106276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2505 | − | 17.7544i | −0.426734 | − | 0.739125i | 0.569846 | − | 0.821751i | \(-0.307003\pi\) |
−0.996581 | + | 0.0826259i | \(0.973669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.9201 | − | 9.19914i | 0.909399 | − | 0.381645i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.3086 | 1.66941 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.2916 | + | 33.4141i | 0.796251 | + | 1.37915i | 0.922042 | + | 0.387090i | \(0.126520\pi\) |
−0.125791 | + | 0.992057i | \(0.540147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1673 | − | 19.3423i | 0.460141 | − | 0.796987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.26539 | − | 2.19172i | 0.0519634 | − | 0.0900032i | −0.838874 | − | 0.544326i | \(-0.816785\pi\) |
0.890837 | + | 0.454323i | \(0.150119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.10693 | + | 4.64109i | 0.250360 | + | 0.190266i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0218 | 0.654634 | 0.327317 | − | 0.944915i | \(-0.393855\pi\) | ||||
0.327317 | + | 0.944915i | \(0.393855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1601 | − | 38.3824i | −0.903929 | − | 1.56565i | −0.822349 | − | 0.568983i | \(-0.807337\pi\) |
−0.0815796 | − | 0.996667i | \(-0.525996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.69758 | − | 4.67235i | 0.109672 | − | 0.189958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.79607 | + | 8.30704i | 0.194666 | + | 0.337172i | 0.946791 | − | 0.321849i | \(-0.104304\pi\) |
−0.752125 | + | 0.659021i | \(0.770971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.24897 | − | 3.89533i | 0.0909835 | − | 0.157588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2371 | + | 19.4632i | 0.453861 | + | 0.786110i | 0.998622 | − | 0.0524815i | \(-0.0167131\pi\) |
−0.544761 | + | 0.838591i | \(0.683380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.7056 | + | 20.2746i | −0.471248 | + | 0.816226i | −0.999459 | − | 0.0328875i | \(-0.989530\pi\) |
0.528211 | + | 0.849113i | \(0.322863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.98843 | + | 13.8364i | −0.321082 | + | 0.556131i | −0.980712 | − | 0.195460i | \(-0.937380\pi\) |
0.659629 | + | 0.751591i | \(0.270713\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.7074 | + | 22.5768i | 1.19020 | + | 0.904521i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4632 | − | 18.1227i | −0.418527 | − | 0.724910i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.46622 | −0.0983348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.882517 | −0.0351324 | −0.0175662 | − | 0.999846i | \(-0.505592\pi\) | ||||
−0.0175662 | + | 0.999846i | \(0.505592\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.36864 | − | 7.56671i | −0.173364 | − | 0.300276i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.39836 | + | 2.44335i | −0.0950265 | + | 0.0968090i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.2141 | − | 35.0118i | 0.798408 | − | 1.38288i | −0.122244 | − | 0.992500i | \(-0.539009\pi\) |
0.920652 | − | 0.390384i | \(-0.127658\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.99047 | − | 5.17964i | 0.117932 | − | 0.204265i | −0.801016 | − | 0.598643i | \(-0.795707\pi\) |
0.918948 | + | 0.394378i | \(0.129040\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.4743 | + | 28.5343i | 0.647672 | + | 1.12180i | 0.983677 | + | 0.179941i | \(0.0575906\pi\) |
−0.336005 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2856 | − | 26.4755i | 0.600014 | − | 1.03925i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.0166 | + | 22.5455i | 0.509380 | + | 0.882272i | 0.999941 | + | 0.0108653i | \(0.00345861\pi\) |
−0.490561 | + | 0.871407i | \(0.663208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.52987 | + | 2.64982i | −0.0597771 | + | 0.103537i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.91651 | − | 8.51565i | −0.191520 | − | 0.331722i | 0.754234 | − | 0.656606i | \(-0.228008\pi\) |
−0.945754 | + | 0.324883i | \(0.894675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.51520 | −0.214516 | −0.107258 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107258 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.644111 | + | 5.07458i | −0.0249776 | + | 0.196784i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.177222 | − | 0.306958i | 0.00686208 | − | 0.0118855i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.07339 | + | 1.85916i | −0.0414376 | + | 0.0717720i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6176 | + | 33.9788i | 0.756205 | + | 1.30978i | 0.944773 | + | 0.327725i | \(0.106282\pi\) |
−0.188569 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.1632 | 1.42830 | 0.714149 | − | 0.699994i | \(-0.246814\pi\) | ||||
0.714149 | + | 0.699994i | \(0.246814\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.4899 | + | 10.6973i | −0.978211 | + | 0.410523i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.10586 | + | 8.84360i | 0.195370 | + | 0.338391i | 0.947022 | − | 0.321169i | \(-0.104076\pi\) |
−0.751652 | + | 0.659560i | \(0.770743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85305 | −0.185426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.27615 | 0.162908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.0761 | −1.33436 | −0.667179 | − | 0.744897i | \(-0.732499\pi\) | ||||
−0.667179 | + | 0.744897i | \(0.732499\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.24284 | 0.274737 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.8097 | 1.05337 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2500 | −0.651522 | −0.325761 | − | 0.945452i | \(-0.605621\pi\) | ||||
−0.325761 | + | 0.945452i | \(0.605621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.822352 | − | 1.42436i | −0.0310156 | − | 0.0537206i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.9912 | − | 15.9527i | −0.789455 | − | 0.599964i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5147 | −0.545110 | −0.272555 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272555 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.163922 | − | 0.283921i | −0.00613893 | − | 0.0106329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.593081 | − | 1.02725i | 0.0221800 | − | 0.0384168i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.4295 | − | 38.8491i | 0.836480 | − | 1.44883i | −0.0563403 | − | 0.998412i | \(-0.517943\pi\) |
0.892820 | − | 0.450414i | \(-0.148723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.4242 | − | 11.9287i | 1.05857 | − | 0.444248i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.0295 | 1.15241 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.22039 | − | 3.84582i | −0.0823496 | − | 0.142634i | 0.821909 | − | 0.569619i | \(-0.192909\pi\) |
−0.904259 | + | 0.426985i | \(0.859576\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7021 | − | 27.1969i | 0.580764 | − | 1.00591i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1360 | + | 33.1445i | 0.706803 | + | 1.22422i | 0.966037 | + | 0.258405i | \(0.0831968\pi\) |
−0.259233 | + | 0.965815i | \(0.583470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9725 | − | 20.7370i | 0.441014 | − | 0.763859i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.59381 | − | 4.49261i | −0.0954148 | − | 0.165263i | 0.814367 | − | 0.580350i | \(-0.197084\pi\) |
−0.909782 | + | 0.415087i | \(0.863751\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3351 | + | 28.2932i | −0.599276 | + | 1.03798i | 0.393653 | + | 0.919259i | \(0.371211\pi\) |
−0.992928 | + | 0.118716i | \(0.962122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.18314 | − | 3.78132i | 0.0799842 | − | 0.138537i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3452 | − | 7.86203i | −0.378004 | − | 0.287272i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.06106 | + | 13.9622i | 0.294152 | + | 0.509487i | 0.974787 | − | 0.223136i | \(-0.0716294\pi\) |
−0.680635 | + | 0.732623i | \(0.738296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.62595 | 0.277537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.6421 | 1.65889 | 0.829444 | − | 0.558589i | \(-0.188657\pi\) | ||||
0.829444 | + | 0.558589i | \(0.188657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.11500 | + | 10.5915i | 0.221669 | + | 0.383942i | 0.955315 | − | 0.295590i | \(-0.0955163\pi\) |
−0.733646 | + | 0.679532i | \(0.762183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47.6387 | − | 19.9924i | 1.72464 | − | 0.723773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.62158 | − | 2.80866i | 0.0585518 | − | 0.101415i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.17344 | − | 5.49656i | 0.114437 | − | 0.198211i | −0.803117 | − | 0.595821i | \(-0.796827\pi\) |
0.917555 | + | 0.397610i | \(0.130160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4515 | − | 42.3512i | −0.879459 | − | 1.52327i | −0.851936 | − | 0.523646i | \(-0.824572\pi\) |
−0.0275225 | − | 0.999621i | \(-0.508762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.3504 | − | 24.8556i | 0.515481 | − | 0.892839i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.27302 | + | 16.0613i | 0.332240 | + | 0.575457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.06483 | + | 7.04049i | −0.145451 | + | 0.251928i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.28455 | − | 5.68900i | −0.117231 | − | 0.203049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1498 | −0.825201 | −0.412600 | − | 0.910912i | \(-0.635379\pi\) | ||||
−0.412600 | + | 0.910912i | \(0.635379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.1147 | − | 17.5665i | −0.821864 | − | 0.624594i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.113870 | + | 0.197229i | −0.00404365 | + | 0.00700381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.2284 | + | 41.9648i | −0.858214 | + | 1.48647i | 0.0154170 | + | 0.999881i | \(0.495092\pi\) |
−0.873631 | + | 0.486589i | \(0.838241\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.3429 | − | 43.8951i | −0.896566 | − | 1.55290i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.2976 | −1.70439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0597815 | + | 0.0454323i | 0.00210702 | + | 0.00160128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.2647 | + | 17.7791i | 0.360889 | + | 0.625078i | 0.988107 | − | 0.153765i | \(-0.0491399\pi\) |
−0.627218 | + | 0.778844i | \(0.715807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7882 | 0.975776 | 0.487888 | − | 0.872906i | \(-0.337767\pi\) | ||||
0.487888 | + | 0.872906i | \(0.337767\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.61370 | −0.0915539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9432 | 0.732711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5586 | 0.577901 | 0.288950 | − | 0.957344i | \(-0.406694\pi\) | ||||
0.288950 | + | 0.957344i | \(0.406694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4704 | 0.887843 | 0.443922 | − | 0.896066i | \(-0.353587\pi\) | ||||
0.443922 | + | 0.896066i | \(0.353587\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0798 | −1.25462 | −0.627309 | − | 0.778771i | \(-0.715844\pi\) | ||||
−0.627309 | + | 0.778771i | \(0.715844\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3539 | + | 38.7180i | 0.776381 | + | 1.34473i | 0.934015 | + | 0.357234i | \(0.116280\pi\) |
−0.157633 | + | 0.987498i | \(0.550386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3314 | + | 37.1721i | 0.357960 | + | 1.28794i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5293 | 0.364383 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.86805 | + | 13.6279i | 0.271635 | + | 0.470486i | 0.969281 | − | 0.245957i | \(-0.0791022\pi\) |
−0.697645 | + | 0.716443i | \(0.745769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.07866 | + | 12.2606i | −0.244092 | + | 0.422779i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.35611 | + | 5.81296i | −0.115454 | + | 0.199972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0230 | − | 10.5013i | 0.859799 | − | 0.360829i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0241422 | −0.000827584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2010 | + | 24.5968i | 0.486231 | + | 0.842177i | 0.999875 | − | 0.0158264i | \(-0.00503792\pi\) |
−0.513643 | + | 0.858004i | \(0.671705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.48867 | + | 7.77461i | −0.153330 | + | 0.265575i | −0.932450 | − | 0.361300i | \(-0.882333\pi\) |
0.779120 | + | 0.626875i | \(0.215666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.471450 | + | 0.816575i | 0.0160857 | + | 0.0278612i | 0.873956 | − | 0.486005i | \(-0.161546\pi\) |
−0.857871 | + | 0.513866i | \(0.828213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0488 | − | 22.6011i | 0.444185 | − | 0.769351i | −0.553810 | − | 0.832643i | \(-0.686827\pi\) |
0.997995 | + | 0.0632920i | \(0.0201600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.38145 | − | 4.12478i | −0.0809716 | − | 0.140247i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.7375 | − | 65.3633i | 1.28016 | − | 2.21730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.27011 | − | 2.19989i | 0.0430360 | − | 0.0745405i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.70390 | + | 13.4240i | −0.0576022 | + | 0.453814i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1794 | + | 22.8275i | 0.445038 | + | 0.770829i | 0.998055 | − | 0.0623413i | \(-0.0198567\pi\) |
−0.553017 | + | 0.833170i | \(0.686523\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.6077 | 1.53656 | 0.768281 | − | 0.640113i | \(-0.221112\pi\) | ||||
0.768281 | + | 0.640113i | \(0.221112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.1575 | −0.880271 | −0.440136 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440136 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5963 | + | 32.2097i | 0.624401 | + | 1.08149i | 0.988656 | + | 0.150196i | \(0.0479904\pi\) |
−0.364255 | + | 0.931299i | \(0.618676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.53384 | − | 43.5979i | 0.185599 | − | 1.46223i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.9009 | − | 29.2733i | 0.565568 | − | 0.979593i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.04589 | + | 7.00769i | −0.135239 | + | 0.234241i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.9592 | + | 34.5704i | 0.665677 | + | 1.15299i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0932 | − | 41.7307i | 0.802662 | − | 1.39025i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.51160 | − | 4.35022i | −0.0834884 | − | 0.144606i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9231 | + | 22.3834i | −0.429103 | + | 0.743229i | −0.996794 | − | 0.0800134i | \(-0.974504\pi\) |
0.567691 | + | 0.823242i | \(0.307837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.41211 | + | 4.17790i | 0.0799169 | + | 0.138420i | 0.903214 | − | 0.429191i | \(-0.141201\pi\) |
−0.823297 | + | 0.567611i | \(0.807868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.4256 | −1.37099 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.1912 | + | 5.95558i | −0.468635 | + | 0.196670i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.58183 | − | 16.5962i | 0.316075 | − | 0.547459i | −0.663590 | − | 0.748096i | \(-0.730968\pi\) |
0.979666 | + | 0.200638i | \(0.0643014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.431218 | + | 0.746891i | −0.0141937 | + | 0.0245842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05675 | − | 1.83035i | −0.0347458 | − | 0.0601815i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.0914 | −1.77468 | −0.887340 | − | 0.461115i | \(-0.847450\pi\) | ||||
−0.887340 | + | 0.461115i | \(0.847450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0236 | + | 18.3617i | −0.590700 | + | 0.601781i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.68322 | − | 11.5757i | −0.218565 | − | 0.378565i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.6345 | −0.543426 | −0.271713 | − | 0.962378i | \(-0.587590\pi\) | ||||
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.89912 | 0.0945085 | 0.0472543 | − | 0.998883i | \(-0.484953\pi\) | ||||
0.0472543 | + | 0.998883i | \(0.484953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.272233 | 0.00886512 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.7311 | 1.87601 | 0.938004 | − | 0.346625i | \(-0.112672\pi\) | ||||
0.938004 | + | 0.346625i | \(0.112672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.12366 | −0.166321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.4070 | −0.661046 | −0.330523 | − | 0.943798i | \(-0.607225\pi\) | ||||
−0.330523 | + | 0.943798i | \(0.607225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.90440 | + | 5.03057i | 0.0939843 | + | 0.162786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.4349 | − | 14.7700i | −0.627585 | − | 0.476947i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.92259 | 0.191051 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.02193 | + | 12.1623i | 0.226044 | + | 0.391519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.26365 | − | 7.38486i | 0.137110 | − | 0.237481i | −0.789292 | − | 0.614019i | \(-0.789552\pi\) |
0.926401 | + | 0.376537i | \(0.122885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.42651 | + | 16.3272i | −0.302511 | + | 0.523965i | −0.976704 | − | 0.214590i | \(-0.931158\pi\) |
0.674193 | + | 0.738555i | \(0.264492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0052 | + | 22.0431i | 0.929864 | + | 0.706671i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.611299 | −0.0195572 | −0.00977859 | − | 0.999952i | \(-0.503113\pi\) | ||||
−0.00977859 | + | 0.999952i | \(0.503113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.5108 | − | 56.3104i | −1.03905 | − | 1.79969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.62584 | + | 6.28013i | −0.115646 | + | 0.200305i | −0.918038 | − | 0.396493i | \(-0.870227\pi\) |
0.802392 | + | 0.596798i | \(0.203561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.37659 | − | 5.84842i | −0.107587 | − | 0.186346i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.153710 | − | 0.266234i | 0.00488770 | − | 0.00846575i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.49266 | − | 4.31741i | −0.0791819 | − | 0.137147i | 0.823715 | − | 0.567004i | \(-0.191897\pi\) |
−0.902897 | + | 0.429857i | \(0.858564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.33412 | + | 9.23896i | −0.169103 | + | 0.292895i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59172 | − | 2.75694i | 0.0504104 | − | 0.0873133i | −0.839719 | − | 0.543021i | \(-0.817280\pi\) |
0.890130 | + | 0.455708i | \(0.150614\pi\) | |||||||
\(998\) | 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 | 1512.2.q.d.793.7 | 22 | ||
3.2 | odd | 2 | 504.2.q.c.121.10 | yes | 22 | ||
4.3 | odd | 2 | 3024.2.q.l.2305.7 | 22 | |||
7.4 | even | 3 | 1512.2.t.c.361.5 | 22 | |||
9.2 | odd | 6 | 504.2.t.c.457.6 | yes | 22 | ||
9.7 | even | 3 | 1512.2.t.c.289.5 | 22 | |||
12.11 | even | 2 | 1008.2.q.l.625.2 | 22 | |||
21.11 | odd | 6 | 504.2.t.c.193.6 | yes | 22 | ||
28.11 | odd | 6 | 3024.2.t.k.1873.5 | 22 | |||
36.7 | odd | 6 | 3024.2.t.k.289.5 | 22 | |||
36.11 | even | 6 | 1008.2.t.l.961.6 | 22 | |||
63.11 | odd | 6 | 504.2.q.c.25.10 | ✓ | 22 | ||
63.25 | even | 3 | inner | 1512.2.q.d.1369.7 | 22 | ||
84.11 | even | 6 | 1008.2.t.l.193.6 | 22 | |||
252.11 | even | 6 | 1008.2.q.l.529.2 | 22 | |||
252.151 | odd | 6 | 3024.2.q.l.2881.7 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.10 | ✓ | 22 | 63.11 | odd | 6 | ||
504.2.q.c.121.10 | yes | 22 | 3.2 | odd | 2 | ||
504.2.t.c.193.6 | yes | 22 | 21.11 | odd | 6 | ||
504.2.t.c.457.6 | yes | 22 | 9.2 | odd | 6 | ||
1008.2.q.l.529.2 | 22 | 252.11 | even | 6 | |||
1008.2.q.l.625.2 | 22 | 12.11 | even | 2 | |||
1008.2.t.l.193.6 | 22 | 84.11 | even | 6 | |||
1008.2.t.l.961.6 | 22 | 36.11 | even | 6 | |||
1512.2.q.d.793.7 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.d.1369.7 | 22 | 63.25 | even | 3 | inner | ||
1512.2.t.c.289.5 | 22 | 9.7 | even | 3 | |||
1512.2.t.c.361.5 | 22 | 7.4 | even | 3 | |||
3024.2.q.l.2305.7 | 22 | 4.3 | odd | 2 | |||
3024.2.q.l.2881.7 | 22 | 252.151 | odd | 6 | |||
3024.2.t.k.289.5 | 22 | 36.7 | odd | 6 | |||
3024.2.t.k.1873.5 | 22 | 28.11 | odd | 6 |