Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 46x^{12} + 126x^{10} + 315x^{8} + 1134x^{6} + 3726x^{4} + 7290x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(1.56478 - 0.742611i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.449 |
Dual form | 2736.2.dc.d.1889.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.99029 | + | 1.72644i | −1.33730 | + | 0.772089i | −0.986406 | − | 0.164328i | \(-0.947455\pi\) |
−0.350891 | + | 0.936416i | \(0.614121\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.128302 | −0.0484936 | −0.0242468 | − | 0.999706i | \(-0.507719\pi\) | ||||
−0.0242468 | + | 0.999706i | \(0.507719\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.15544i | 1.85594i | 0.372660 | + | 0.927968i | \(0.378446\pi\) | ||||
−0.372660 | + | 0.927968i | \(0.621554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.67404 | + | 1.54386i | 0.741646 | + | 0.428190i | 0.822668 | − | 0.568523i | \(-0.192485\pi\) |
−0.0810213 | + | 0.996712i | \(0.525818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.91297 | + | 2.83650i | −1.19157 | + | 0.687953i | −0.958662 | − | 0.284546i | \(-0.908157\pi\) |
−0.232907 | + | 0.972499i | \(0.574824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.96121 | + | 1.81902i | 0.908764 | + | 0.417311i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.18882 | + | 1.26372i | 0.456401 | + | 0.263503i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.254129 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.46121 | − | 5.99499i | 0.692242 | − | 1.19900i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.40809 | − | 5.90299i | 0.632867 | − | 1.09616i | −0.354096 | − | 0.935209i | \(-0.615211\pi\) |
0.986963 | − | 0.160948i | \(-0.0514553\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0357i | 1.80247i | 0.433336 | + | 0.901233i | \(0.357336\pi\) | ||||
−0.433336 | + | 0.901233i | \(0.642664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.383660 | − | 0.221506i | 0.0648503 | − | 0.0374413i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.1899i | − | 1.67520i | −0.546282 | − | 0.837601i | \(-0.683957\pi\) | ||
0.546282 | − | 0.837601i | \(-0.316043\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.34048 | − | 4.05384i | −0.365522 | − | 0.633103i | 0.623338 | − | 0.781953i | \(-0.285776\pi\) |
−0.988860 | + | 0.148850i | \(0.952443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.02536 | − | 5.24008i | −0.461363 | − | 0.799104i | 0.537666 | − | 0.843158i | \(-0.319306\pi\) |
−0.999029 | + | 0.0440537i | \(0.985973\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.266142 | + | 0.153657i | 0.0388208 | + | 0.0224132i | 0.519285 | − | 0.854601i | \(-0.326198\pi\) |
−0.480464 | + | 0.877014i | \(0.659532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98354 | −0.997648 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.05789 | + | 7.02848i | −0.557395 | + | 0.965436i | 0.440318 | + | 0.897842i | \(0.354866\pi\) |
−0.997713 | + | 0.0675941i | \(0.978468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6270 | − | 18.4065i | −1.43295 | − | 2.48194i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.05789 | + | 7.02848i | 0.528293 | + | 0.915030i | 0.999456 | + | 0.0329839i | \(0.0105010\pi\) |
−0.471163 | + | 0.882046i | \(0.656166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.20460 | + | 3.81849i | −0.282271 | + | 0.488907i | −0.971944 | − | 0.235214i | \(-0.924421\pi\) |
0.689673 | + | 0.724121i | \(0.257754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.6615 | −1.32240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.51713 | + | 2.60797i | 0.551855 | + | 0.318614i | 0.749870 | − | 0.661585i | \(-0.230116\pi\) |
−0.198015 | + | 0.980199i | \(0.563449\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.67423 | − | 6.36396i | −0.436051 | − | 0.755263i | 0.561329 | − | 0.827592i | \(-0.310290\pi\) |
−0.997381 | + | 0.0723293i | \(0.976957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.15886 | + | 5.47131i | 0.369717 | + | 0.640368i | 0.989521 | − | 0.144388i | \(-0.0461213\pi\) |
−0.619804 | + | 0.784756i | \(0.712788\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.789755i | − | 0.0900010i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.95818 | + | 1.70791i | −0.332821 | + | 0.192154i | −0.657093 | − | 0.753810i | \(-0.728214\pi\) |
0.324272 | + | 0.945964i | \(0.394881\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.267885i | 0.0294042i | 0.999892 | + | 0.0147021i | \(0.00468000\pi\) | ||||
−0.999892 | + | 0.0147021i | \(0.995320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.79411 | − | 16.9639i | 1.06232 | − | 1.83999i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.52931 | + | 7.84499i | −0.480105 | + | 0.831567i | −0.999740 | − | 0.0228219i | \(-0.992735\pi\) |
0.519634 | + | 0.854389i | \(0.326068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.343085 | − | 0.198080i | −0.0359651 | − | 0.0207644i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.9856 | + | 1.39941i | −1.53749 | + | 0.143577i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2083 | + | 9.35787i | −1.64570 | + | 0.950147i | −0.666951 | + | 0.745101i | \(0.732401\pi\) |
−0.978752 | + | 0.205046i | \(0.934266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.78204 | + | 3.91561i | 0.674838 | + | 0.389618i | 0.797907 | − | 0.602780i | \(-0.205940\pi\) |
−0.123069 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.23558i | − | 0.811476i | −0.913989 | − | 0.405738i | \(-0.867015\pi\) | ||
0.913989 | − | 0.405738i | \(-0.132985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.1744 | −1.66031 | −0.830156 | − | 0.557531i | \(-0.811749\pi\) | ||||
−0.830156 | + | 0.557531i | \(0.811749\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.49872 | − | 1.44264i | 0.239334 | − | 0.138180i | −0.375537 | − | 0.926808i | \(-0.622542\pi\) |
0.614871 | + | 0.788628i | \(0.289208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.45803 | 0.795665 | 0.397832 | − | 0.917458i | \(-0.369763\pi\) | ||||
0.397832 | + | 0.917458i | \(0.369763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.72693 | −0.813791 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.630343 | − | 0.363929i | 0.0577834 | − | 0.0333613i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.8895 | −2.44450 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.63789i | 0.593710i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.02341 | + | 0.590867i | 0.0908131 | + | 0.0524310i | 0.544719 | − | 0.838619i | \(-0.316636\pi\) |
−0.453906 | + | 0.891050i | \(0.649970\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.266142 | + | 0.153657i | −0.0232529 | + | 0.0134251i | −0.511581 | − | 0.859235i | \(-0.670940\pi\) |
0.488328 | + | 0.872660i | \(0.337607\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.508231 | − | 0.233384i | −0.0440692 | − | 0.0202369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4904 | − | 6.05665i | −0.896257 | − | 0.517454i | −0.0202731 | − | 0.999794i | \(-0.506454\pi\) |
−0.875984 | + | 0.482340i | \(0.839787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.55592 | − | 6.15903i | 0.301609 | − | 0.522402i | −0.674891 | − | 0.737917i | \(-0.735810\pi\) |
0.976501 | + | 0.215515i | \(0.0691429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.50314 | + | 16.4599i | −0.794693 | + | 1.37645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.5355i | 1.95452i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.69193 | − | 3.28624i | 0.466301 | − | 0.269219i | −0.248389 | − | 0.968660i | \(-0.579901\pi\) |
0.714690 | + | 0.699441i | \(0.246568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4775i | 0.934022i | 0.884251 | + | 0.467011i | \(0.154669\pi\) | ||||
−0.884251 | + | 0.467011i | \(0.845331\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.3261 | − | 30.0096i | −1.39166 | − | 2.41043i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.42242 | − | 16.3201i | −0.751991 | − | 1.30249i | −0.946857 | − | 0.321656i | \(-0.895760\pi\) |
0.194866 | − | 0.980830i | \(-0.437573\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.280830 | − | 0.162137i | −0.0221325 | − | 0.0127782i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.23625 | 0.0968303 | 0.0484152 | − | 0.998827i | \(-0.484583\pi\) | ||||
0.0484152 | + | 0.998827i | \(0.484583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.35818 | − | 7.54859i | 0.337246 | − | 0.584128i | −0.646667 | − | 0.762772i | \(-0.723838\pi\) |
0.983914 | + | 0.178644i | \(0.0571711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.73299 | − | 3.00163i | −0.133307 | − | 0.230895i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.98057 | − | 10.3587i | −0.454695 | − | 0.787554i | 0.543976 | − | 0.839101i | \(-0.316918\pi\) |
−0.998671 | + | 0.0515467i | \(0.983585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.444080 | + | 0.769169i | −0.0335693 | + | 0.0581437i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2645 | −0.916690 | −0.458345 | − | 0.888774i | \(-0.651558\pi\) | ||||
−0.458345 | + | 0.888774i | \(0.651558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.82596 | + | 2.78627i | 0.358711 | + | 0.207102i | 0.668515 | − | 0.743699i | \(-0.266930\pi\) |
−0.309804 | + | 0.950800i | \(0.600264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.5922 | + | 30.4706i | 1.29340 | + | 2.24024i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.4599 | − | 30.2415i | −1.27680 | − | 2.21148i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.552731i | 0.0399942i | 0.999800 | + | 0.0199971i | \(0.00636570\pi\) | ||||
−0.999800 | + | 0.0199971i | \(0.993634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.05895 | − | 1.76609i | 0.220188 | − | 0.127126i | −0.385849 | − | 0.922562i | \(-0.626092\pi\) |
0.606037 | + | 0.795436i | \(0.292758\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.8123i | − | 1.26907i | −0.772893 | − | 0.634536i | \(-0.781191\pi\) | ||
0.772893 | − | 0.634536i | \(-0.218809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.03231 | − | 12.1803i | 0.498507 | − | 0.863440i | −0.501491 | − | 0.865163i | \(-0.667215\pi\) |
0.999999 | + | 0.00172286i | \(0.000548403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.437265 | + | 0.757365i | −0.0306900 | + | 0.0531566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9974 | + | 8.08143i | 0.977624 | + | 0.564431i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1969 | + | 24.3830i | −0.774503 | + | 1.68661i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.38991 | + | 3.11187i | −0.371057 | + | 0.214230i | −0.673920 | − | 0.738804i | \(-0.735391\pi\) |
0.302863 | + | 0.953034i | \(0.402057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0934 | + | 10.4462i | 1.23396 | + | 0.712426i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.28760i | − | 0.0874080i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.5166 | −1.17830 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7146 | − | 12.5369i | 1.45412 | − | 0.839534i | 0.455405 | − | 0.890285i | \(-0.349495\pi\) |
0.998711 | + | 0.0507502i | \(0.0161612\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.767319 | −0.0509288 | −0.0254644 | − | 0.999676i | \(-0.508106\pi\) | ||||
−0.0254644 | + | 0.999676i | \(0.508106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8613 | 1.18031 | 0.590154 | − | 0.807291i | \(-0.299067\pi\) | ||||
0.590154 | + | 0.807291i | \(0.299067\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.84166 | − | 1.64063i | 0.186163 | − | 0.107482i | −0.404022 | − | 0.914749i | \(-0.632388\pi\) |
0.590185 | + | 0.807268i | \(0.299055\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.06112 | −0.0692199 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.14557i | − | 0.203470i | −0.994812 | − | 0.101735i | \(-0.967561\pi\) | ||
0.994812 | − | 0.101735i | \(-0.0324394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2096 | − | 7.04921i | −0.786488 | − | 0.454079i | 0.0522365 | − | 0.998635i | \(-0.483365\pi\) |
−0.838725 | + | 0.544556i | \(0.816698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.8828 | − | 12.0567i | 1.33415 | − | 0.770273i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.78414 | + | 10.9797i | 0.495293 | + | 0.698621i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4984 | + | 8.94801i | 0.978251 | + | 0.564793i | 0.901742 | − | 0.432276i | \(-0.142289\pi\) |
0.0765091 | + | 0.997069i | \(0.475623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.77874 | + | 13.4732i | −0.489045 | + | 0.847051i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.96287 | + | 6.86390i | −0.247197 | + | 0.428158i | −0.962747 | − | 0.270403i | \(-0.912843\pi\) |
0.715550 | + | 0.698562i | \(0.246176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.30738i | 0.0812365i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.5199 | + | 13.0018i | −1.38863 | + | 0.801728i | −0.993161 | − | 0.116750i | \(-0.962752\pi\) |
−0.395473 | + | 0.918478i | \(0.629419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.0229i | − | 1.72143i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.18882 | − | 3.79115i | −0.133455 | − | 0.231150i | 0.791551 | − | 0.611103i | \(-0.209274\pi\) |
−0.925006 | + | 0.379952i | \(0.875940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00000 | + | 1.73205i | 0.0607457 | + | 0.105215i | 0.894799 | − | 0.446469i | \(-0.147319\pi\) |
−0.834053 | + | 0.551684i | \(0.813985\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 36.9018 | + | 21.3053i | 2.22526 | + | 1.28476i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.86130 | 0.171919 | 0.0859593 | − | 0.996299i | \(-0.472605\pi\) | ||||
0.0859593 | + | 0.996299i | \(0.472605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1841 | + | 24.5676i | −0.846153 | + | 1.46558i | 0.0384627 | + | 0.999260i | \(0.487754\pi\) |
−0.884616 | + | 0.466320i | \(0.845579\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.3316 | + | 23.0911i | 0.792483 | + | 1.37262i | 0.924425 | + | 0.381363i | \(0.124545\pi\) |
−0.131942 | + | 0.991257i | \(0.542121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.300289 | + | 0.520115i | 0.0177255 | + | 0.0307014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.59148 | − | 13.1488i | 0.446558 | − | 0.773461i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.4011 | 1.42553 | 0.712764 | − | 0.701404i | \(-0.247443\pi\) | ||||
0.712764 | + | 0.701404i | \(0.247443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.2685 | − | 14.0114i | −1.41297 | − | 0.815778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.90200 | + | 6.75847i | 0.225659 | + | 0.390852i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.388159 | + | 0.672312i | 0.0223731 | + | 0.0387514i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 15.2245i | − | 0.871752i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.8811 | + | 13.2104i | −1.30589 | + | 0.753957i | −0.981408 | − | 0.191935i | \(-0.938524\pi\) |
−0.324484 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.45845i | − | 0.309520i | −0.987952 | − | 0.154760i | \(-0.950540\pi\) | ||
0.987952 | − | 0.154760i | \(-0.0494605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.57630 | − | 16.5866i | 0.541285 | − | 0.937532i | −0.457546 | − | 0.889186i | \(-0.651271\pi\) |
0.998831 | − | 0.0483465i | \(-0.0153952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.60365 | − | 11.4379i | 0.370898 | − | 0.642414i | −0.618806 | − | 0.785544i | \(-0.712383\pi\) |
0.989704 | + | 0.143130i | \(0.0457167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.3355 | + | 20.9783i | 2.03440 | + | 1.17456i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.6209 | + | 2.29920i | −1.36995 | + | 0.127931i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5108 | − | 10.6872i | 1.02680 | − | 0.592822i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0341466 | − | 0.0197145i | −0.00188256 | − | 0.00108690i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.76881i | 0.427013i | 0.976942 | + | 0.213506i | \(0.0684884\pi\) | ||||
−0.976942 | + | 0.213506i | \(0.931512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.0100 | −0.983992 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.26573 | + | 4.19487i | −0.395789 | + | 0.228509i | −0.684666 | − | 0.728857i | \(-0.740052\pi\) |
0.288876 | + | 0.957366i | \(0.406718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −61.7742 | −3.34526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.79411 | 0.0968731 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.5491 | − | 14.7508i | 1.37155 | − | 0.791862i | 0.380423 | − | 0.924813i | \(-0.375778\pi\) |
0.991123 | + | 0.132950i | \(0.0424451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.753350 | 0.0403259 | 0.0201630 | − | 0.999797i | \(-0.493581\pi\) | ||||
0.0201630 | + | 0.999797i | \(0.493581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 13.9472i | − | 0.742337i | −0.928566 | − | 0.371168i | \(-0.878957\pi\) | ||
0.928566 | − | 0.371168i | \(-0.121043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.9740 | + | 12.6867i | 1.16626 | + | 0.673341i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.73687 | − | 1.00278i | 0.0916684 | − | 0.0529248i | −0.453465 | − | 0.891274i | \(-0.649812\pi\) |
0.545133 | + | 0.838349i | \(0.316479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3823 | + | 14.4110i | 0.651702 | + | 0.758475i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.8918 | − | 10.9072i | −0.988842 | − | 0.570908i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.98159 | + | 5.16427i | −0.155638 | + | 0.269573i | −0.933291 | − | 0.359121i | \(-0.883077\pi\) |
0.777653 | + | 0.628693i | \(0.216410\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.520636 | − | 0.901767i | 0.0270301 | − | 0.0468174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.2317i | 0.944003i | 0.881598 | + | 0.472001i | \(0.156468\pi\) | ||||
−0.881598 | + | 0.472001i | \(0.843532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.2268 | − | 10.5232i | 0.938727 | − | 0.541974i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2245i | − | 1.24433i | −0.782887 | − | 0.622164i | \(-0.786254\pi\) | ||
0.782887 | − | 0.622164i | \(-0.213746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.43857 | + | 14.6160i | 0.431191 | + | 0.746845i | 0.996976 | − | 0.0777079i | \(-0.0247602\pi\) |
−0.565785 | + | 0.824553i | \(0.691427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.36347 | + | 2.36159i | 0.0694887 | + | 0.120358i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0649 | − | 12.7392i | −1.11873 | − | 0.645901i | −0.177656 | − | 0.984093i | \(-0.556851\pi\) |
−0.941077 | + | 0.338192i | \(0.890185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.3381 | −0.725111 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.89720 | − | 10.2143i | 0.296720 | − | 0.513935i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4070 | + | 28.4178i | 0.823446 | + | 1.42625i | 0.903101 | + | 0.429427i | \(0.141285\pi\) |
−0.0796559 | + | 0.996822i | \(0.525382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.43184 | + | 12.8723i | 0.371128 | + | 0.642813i | 0.989739 | − | 0.142884i | \(-0.0456376\pi\) |
−0.618611 | + | 0.785697i | \(0.712304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.4937 | + | 26.8359i | −0.771797 | + | 1.33679i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 62.7231 | 3.10907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8468 | + | 11.4586i | 0.981361 | + | 0.566589i | 0.902681 | − | 0.430311i | \(-0.141596\pi\) |
0.0786806 | + | 0.996900i | \(0.474929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.520636 | − | 0.901767i | −0.0256188 | − | 0.0443731i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.462489 | − | 0.801054i | −0.0227027 | − | 0.0393222i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.0255i | 1.90652i | 0.302152 | + | 0.953260i | \(0.402295\pi\) | ||||
−0.302152 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.5330 | + | 13.5868i | −1.14693 | + | 0.662179i | −0.948137 | − | 0.317863i | \(-0.897035\pi\) |
−0.198791 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 39.2709i | 1.90492i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.282855 | − | 0.489919i | 0.0136883 | − | 0.0237089i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2273 | − | 21.1783i | 0.588968 | − | 1.02012i | −0.405400 | − | 0.914139i | \(-0.632868\pi\) |
0.994368 | − | 0.105983i | \(-0.0337988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0455 | − | 6.95450i | −0.578872 | − | 0.334212i | 0.181813 | − | 0.983333i | \(-0.441803\pi\) |
−0.760685 | + | 0.649121i | \(0.775137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.37165 | + | 8.98735i | 0.304797 | + | 0.429923i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.3212 | + | 18.6607i | −1.54261 | + | 0.890624i | −0.543933 | + | 0.839128i | \(0.683066\pi\) |
−0.998673 | + | 0.0514959i | \(0.983601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.7798 | − | 9.11046i | −0.749720 | − | 0.432851i | 0.0758729 | − | 0.997118i | \(-0.475826\pi\) |
−0.825593 | + | 0.564267i | \(0.809159\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 31.2783i | − | 1.48274i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.75528 | 0.413187 | 0.206594 | − | 0.978427i | \(-0.433762\pi\) | ||||
0.206594 | + | 0.978427i | \(0.433762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9532 | − | 14.4067i | 1.17500 | − | 0.678386i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.36790 | 0.0641280 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9974 | −0.561217 | −0.280608 | − | 0.959822i | \(-0.590536\pi\) | ||||
−0.280608 | + | 0.959822i | \(0.590536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.25947 | − | 1.88185i | 0.151809 | − | 0.0876467i | −0.422172 | − | 0.906516i | \(-0.638732\pi\) |
0.573980 | + | 0.818869i | \(0.305399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.9277 | −1.90207 | −0.951036 | − | 0.309081i | \(-0.899979\pi\) | ||||
−0.951036 | + | 0.309081i | \(0.899979\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.9556i | − | 1.10853i | −0.832339 | − | 0.554267i | \(-0.812998\pi\) | ||
0.832339 | − | 0.554267i | \(-0.187002\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.579556 | − | 0.334607i | −0.0267614 | − | 0.0154507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.2550 | − | 18.6224i | 1.48309 | − | 0.856260i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.6156 | − | 17.4514i | 1.12944 | − | 0.800725i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.82400 | − | 3.93984i | −0.311796 | − | 0.180016i | 0.335934 | − | 0.941886i | \(-0.390948\pi\) |
−0.647730 | + | 0.761870i | \(0.724282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7317 | − | 27.2481i | 0.717304 | − | 1.24241i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.3116 | − | 55.9654i | 1.46720 | − | 2.54126i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.9933i | 1.44976i | 0.688878 | + | 0.724878i | \(0.258104\pi\) | ||||
−0.688878 | + | 0.724878i | \(0.741896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.45502 | − | 3.72681i | 0.291311 | − | 0.168189i | −0.347222 | − | 0.937783i | \(-0.612875\pi\) |
0.638533 | + | 0.769594i | \(0.279542\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.6682i | 1.74153i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.471411 | + | 0.816508i | 0.0211457 | + | 0.0366254i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.7230 | + | 20.3049i | 0.524794 | + | 0.908970i | 0.999583 | + | 0.0288705i | \(0.00919104\pi\) |
−0.474789 | + | 0.880100i | \(0.657476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0950195 | + | 0.0548595i | 0.00423671 | + | 0.00244606i | 0.502117 | − | 0.864800i | \(-0.332555\pi\) |
−0.497880 | + | 0.867246i | \(0.665888\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0403 | −1.20328 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.55979 | − | 16.5580i | 0.423730 | − | 0.733922i | −0.572571 | − | 0.819855i | \(-0.694054\pi\) |
0.996301 | + | 0.0859332i | \(0.0273872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.405288 | − | 0.701980i | −0.0179289 | − | 0.0310538i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2183 | + | 24.6267i | 0.626531 | + | 1.08518i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.945829 | + | 1.63822i | −0.0415975 | + | 0.0720490i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4449 | 1.46525 | 0.732624 | − | 0.680634i | \(-0.238296\pi\) | ||||
0.732624 | + | 0.680634i | \(0.238296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4569 | − | 18.7390i | −1.41924 | − | 0.819399i | −0.423009 | − | 0.906126i | \(-0.639026\pi\) |
−0.996232 | + | 0.0867263i | \(0.972359\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −28.4663 | − | 49.3051i | −1.24001 | − | 2.14776i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.30604 | − | 14.3865i | −0.361132 | − | 0.625499i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14.4535i | − | 0.626052i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 51.3564 | − | 29.6506i | 2.22033 | − | 1.28191i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 42.9868i | − | 1.85157i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5343 | − | 32.1023i | 0.796850 | − | 1.38018i | −0.124808 | − | 0.992181i | \(-0.539831\pi\) |
0.921658 | − | 0.388004i | \(-0.126835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.98126 | + | 8.62779i | −0.213374 | + | 0.369574i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3773 | + | 19.2704i | 1.42711 | + | 0.823944i | 0.996892 | − | 0.0787805i | \(-0.0251026\pi\) |
0.430220 | + | 0.902724i | \(0.358436\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2378 | − | 17.1836i | 1.03257 | − | 0.732045i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.379540 | − | 0.219128i | 0.0161397 | − | 0.00931825i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.6367 | − | 17.1108i | −1.25575 | − | 0.725007i | −0.283503 | − | 0.958971i | \(-0.591497\pi\) |
−0.972245 | + | 0.233965i | \(0.924830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.6829i | − | 0.790203i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.0940 | −0.551847 | −0.275923 | − | 0.961180i | \(-0.588984\pi\) | ||||
−0.275923 | + | 0.961180i | \(0.588984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.2919 | + | 14.6023i | −1.06404 | + | 0.614324i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.2587 | −1.14274 | −0.571371 | − | 0.820692i | \(-0.693588\pi\) | ||||
−0.571371 | + | 0.820692i | \(0.693588\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6836 | 0.656339 | 0.328169 | − | 0.944619i | \(-0.393568\pi\) | ||||
0.328169 | + | 0.944619i | \(0.393568\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.1519 | − | 8.74797i | 0.631879 | − | 0.364816i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.95534 | −0.247924 | −0.123962 | − | 0.992287i | \(-0.539560\pi\) | ||||
−0.123962 | + | 0.992287i | \(0.539560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.0343702i | − | 0.00142592i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.2634 | − | 24.9781i | −1.79179 | − | 1.03449i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.1425 | + | 8.16520i | −0.583725 | + | 0.337014i | −0.762612 | − | 0.646856i | \(-0.776084\pi\) |
0.178887 | + | 0.983870i | \(0.442750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.2551 | + | 39.7535i | −0.752189 | + | 1.63801i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.5930 | + | 15.3535i | 1.09204 | + | 0.630491i | 0.934120 | − | 0.356960i | \(-0.116187\pi\) |
0.157923 | + | 0.987451i | \(0.449520\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.25660 | + | 2.17650i | −0.0515157 | + | 0.0892279i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5825 | + | 25.2576i | −0.595823 | + | 1.03200i | 0.397607 | + | 0.917556i | \(0.369841\pi\) |
−0.993430 | + | 0.114440i | \(0.963493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.18206i | 0.374544i | 0.982308 | + | 0.187272i | \(0.0599646\pi\) | ||||
−0.982308 | + | 0.187272i | \(0.940035\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 80.4073 | − | 46.4232i | 3.26902 | − | 1.88737i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1903i | 0.900678i | 0.892858 | + | 0.450339i | \(0.148697\pi\) | ||||
−0.892858 | + | 0.450339i | \(0.851303\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.474451 | + | 0.821772i | 0.0191942 | + | 0.0332454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9682 | + | 20.7295i | 0.483389 | + | 0.837255i | 0.999818 | − | 0.0190752i | \(-0.00607221\pi\) |
−0.516429 | + | 0.856330i | \(0.672739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.193621 | + | 0.111787i | 0.00779487 | + | 0.00450037i | 0.503892 | − | 0.863766i | \(-0.331901\pi\) |
−0.496098 | + | 0.868267i | \(0.665234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.5284 | −1.34762 | −0.673811 | − | 0.738904i | \(-0.735344\pi\) | ||||
−0.673811 | + | 0.738904i | \(0.735344\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.581119 | − | 1.00653i | 0.0232820 | − | 0.0403257i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.84611 | + | 10.1258i | 0.233845 | + | 0.405031i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.9035 | + | 50.0624i | 1.15246 | + | 1.99612i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.6017 | + | 28.7549i | −0.660902 | + | 1.14472i | 0.319477 | + | 0.947594i | \(0.396493\pi\) |
−0.980379 | + | 0.197121i | \(0.936841\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.08039 | −0.161925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.6743 | − | 10.7816i | −0.739902 | − | 0.427183i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.5276 | + | 21.6984i | 0.494810 | + | 0.857035i | 0.999982 | − | 0.00598312i | \(-0.00190450\pi\) |
−0.505173 | + | 0.863018i | \(0.668571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.49677 | + | 6.05659i | 0.137899 | + | 0.238848i | 0.926701 | − | 0.375799i | \(-0.122632\pi\) |
−0.788802 | + | 0.614647i | \(0.789298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 33.0282i | − | 1.29847i | −0.760587 | − | 0.649236i | \(-0.775089\pi\) | ||
0.760587 | − | 0.649236i | \(-0.224911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.2634 | + | 24.9781i | −1.69824 | + | 0.980478i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.3504i | 1.03117i | 0.856838 | + | 0.515586i | \(0.172426\pi\) | ||||
−0.856838 | + | 0.515586i | \(0.827574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.530561 | − | 0.918958i | 0.0207307 | − | 0.0359067i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.27115 | − | 16.0581i | 0.361153 | − | 0.625535i | −0.626998 | − | 0.779021i | \(-0.715717\pi\) |
0.988151 | + | 0.153486i | \(0.0490500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.41916 | + | 5.43816i | 0.366363 | + | 0.211520i | 0.671868 | − | 0.740671i | \(-0.265492\pi\) |
−0.305505 | + | 0.952190i | \(0.598825\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.92268 | − | 0.179547i | 0.0745583 | − | 0.00696255i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.9194 | − | 8.61372i | 0.577682 | − | 0.333525i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.5045 | − | 13.5703i | −0.907381 | − | 0.523876i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1654i | 0.700225i | 0.936708 | + | 0.350113i | \(0.113857\pi\) | ||||
−0.936708 | + | 0.350113i | \(0.886143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7104 | 0.642233 | 0.321117 | − | 0.947040i | \(-0.395942\pi\) | ||||
0.321117 | + | 0.947040i | \(0.395942\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.07956 | − | 1.20063i | 0.0798060 | − | 0.0460760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.6896 | 0.944722 | 0.472361 | − | 0.881405i | \(-0.343402\pi\) | ||||
0.472361 | + | 0.881405i | \(0.343402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.8258 | 1.59808 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.7020 | + | 12.5296i | −0.826779 | + | 0.477341i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.76981 | −0.333619 | −0.166810 | − | 0.985989i | \(-0.553347\pi\) | ||||
−0.166810 | + | 0.985989i | \(0.553347\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.5564i | 0.931476i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.9974 | + | 13.2776i | 0.871090 | + | 0.502924i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.40318 | + | 2.54218i | −0.166306 | + | 0.0960167i | −0.580843 | − | 0.814016i | \(-0.697277\pi\) |
0.414537 | + | 0.910032i | \(0.363944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5355 | − | 40.3642i | 0.699081 | − | 1.52236i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.870149 | − | 0.502381i | −0.0327253 | − | 0.0188940i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.03554 | + | 5.25771i | −0.114002 | + | 0.197457i | −0.917380 | − | 0.398012i | \(-0.869700\pi\) |
0.803378 | + | 0.595469i | \(0.203034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.6823 | + | 21.9664i | −0.474955 | + | 0.822646i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 65.6265i | − | 2.45429i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.0422 | + | 6.37520i | −0.411803 | + | 0.237755i | −0.691564 | − | 0.722315i | \(-0.743078\pi\) |
0.279761 | + | 0.960070i | \(0.409745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.05664i | 0.0393514i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.5922 | − | 40.8630i | −0.876194 | − | 1.51761i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.69117 | + | 11.5895i | 0.248162 | + | 0.429829i | 0.963016 | − | 0.269445i | \(-0.0868402\pi\) |
−0.714854 | + | 0.699274i | \(0.753507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.7270 | + | 17.1629i | 1.09949 | + | 0.634792i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.7204 | 1.09775 | 0.548875 | − | 0.835905i | \(-0.315056\pi\) | ||||
0.548875 | + | 0.835905i | \(0.315056\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0532 | + | 27.8049i | −0.591327 | + | 1.02421i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0889 | + | 41.7232i | 0.886124 | + | 1.53481i | 0.844419 | + | 0.535683i | \(0.179946\pi\) |
0.0417050 | + | 0.999130i | \(0.486721\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6384 | + | 20.1582i | 0.426970 | + | 0.739534i | 0.996602 | − | 0.0823661i | \(-0.0262477\pi\) |
−0.569632 | + | 0.821900i | \(0.692914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.3470 | + | 19.6536i | −0.415722 | + | 0.720052i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.20351 | 0.0805145 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.2476 | + | 19.1955i | 1.21322 | + | 0.700453i | 0.963459 | − | 0.267854i | \(-0.0863145\pi\) |
0.249761 | + | 0.968307i | \(0.419648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.8152 | − | 34.3209i | −0.721148 | − | 1.24906i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1942 | + | 34.9774i | 0.733971 | + | 1.27127i | 0.955173 | + | 0.296047i | \(0.0956684\pi\) |
−0.221203 | + | 0.975228i | \(0.570998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.5304i | − | 1.50548i | −0.658319 | − | 0.752739i | \(-0.728732\pi\) | ||
0.658319 | − | 0.752739i | \(-0.271268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.320591 | + | 0.185093i | −0.0116062 | + | 0.00670082i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0593i | 0.904838i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89531 | − | 8.47892i | 0.176529 | − | 0.305758i | −0.764160 | − | 0.645027i | \(-0.776846\pi\) |
0.940689 | + | 0.339269i | \(0.110180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.935403 | − | 1.62016i | 0.0336441 | − | 0.0582733i | −0.848713 | − | 0.528854i | \(-0.822622\pi\) |
0.882357 | + | 0.470580i | \(0.155955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 60.1639 | + | 34.7357i | 2.16115 | + | 1.24774i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.89714 | − | 20.3155i | −0.0679722 | − | 0.727878i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.1730 | − | 22.6165i | 1.40172 | − | 0.809284i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.3515 | + | 32.5345i | 2.01127 | + | 1.16121i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 15.6323i | − | 0.557232i | −0.960403 | − | 0.278616i | \(-0.910124\pi\) | ||
0.960403 | − | 0.278616i | \(-0.0898756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.08518 | −0.0385846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.7904 | + | 6.80720i | −0.418690 | + | 0.241731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.67372 | −0.342661 | −0.171330 | − | 0.985214i | \(-0.554807\pi\) | ||||
−0.171330 | + | 0.985214i | \(0.554807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.74340 | −0.0616769 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.6783 | + | 19.4442i | −1.18848 | + | 0.686171i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.11968 | 0.0394636 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9424i | 1.40430i | 0.712030 | + | 0.702149i | \(0.247776\pi\) | ||||
−0.712030 | + | 0.702149i | \(0.752224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.7438 | + | 20.0594i | 1.22002 | + | 0.704380i | 0.964922 | − | 0.262535i | \(-0.0845587\pi\) |
0.255099 | + | 0.966915i | \(0.417892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69673 | + | 2.13431i | −0.129491 | + | 0.0747616i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.45228 | − | 26.2602i | −0.0857946 | − | 0.918729i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.1307 | − | 11.6225i | −0.702566 | − | 0.405627i | 0.105736 | − | 0.994394i | \(-0.466280\pi\) |
−0.808302 | + | 0.588768i | \(0.799613\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.56092 | − | 14.8280i | 0.298415 | − | 0.516870i | −0.677359 | − | 0.735653i | \(-0.736875\pi\) |
0.975774 | + | 0.218783i | \(0.0702087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.8529 | + | 43.0465i | −0.864221 | + | 1.49687i | 0.00359800 | + | 0.999994i | \(0.498855\pi\) |
−0.867819 | + | 0.496881i | \(0.834479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 28.5577i | − | 0.991851i | −0.868365 | − | 0.495925i | \(-0.834829\pi\) | ||
0.868365 | − | 0.495925i | \(-0.165171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.3099 | − | 19.8088i | 1.18877 | − | 0.686335i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0966i | 1.04154i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.62736 | − | 8.01483i | −0.159754 | − | 0.276703i | 0.775026 | − | 0.631930i | \(-0.217737\pi\) |
−0.934780 | + | 0.355227i | \(0.884404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.73019 | − | 15.1211i | −0.301041 | − | 0.521418i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3643 | + | 5.98383i | 0.356543 | + | 0.205850i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.44997 | 0.118543 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8771 | − | 22.3038i | 0.441421 | − | 0.764563i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4398 | + | 28.4745i | 0.562887 | + | 0.974949i | 0.997243 | + | 0.0742075i | \(0.0236427\pi\) |
−0.434356 | + | 0.900741i | \(0.643024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.7060 | − | 28.9357i | −0.570667 | − | 0.988424i | −0.996498 | − | 0.0836213i | \(-0.973351\pi\) |
0.425831 | − | 0.904803i | \(-0.359982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0074 | + | 45.0462i | −0.887362 | + | 1.53696i | −0.0443790 | + | 0.999015i | \(0.514131\pi\) |
−0.842983 | + | 0.537941i | \(0.819202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.1258 | −0.889333 | −0.444666 | − | 0.895696i | \(-0.646678\pi\) | ||||
−0.444666 | + | 0.895696i | \(0.646678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.7673 | + | 20.6502i | 1.21612 | + | 0.702129i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.5129 | − | 18.2089i | −0.356626 | − | 0.617695i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.05267 | + | 13.9476i | 0.272854 | + | 0.472597i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 0.851653i | − | 0.0287911i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.7441 | − | 24.1010i | 1.40960 | − | 0.813832i | 0.414248 | − | 0.910164i | \(-0.364045\pi\) |
0.995349 | + | 0.0963324i | \(0.0307112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.73279i | − | 0.0583793i | −0.999574 | − | 0.0291897i | \(-0.990707\pi\) | ||
0.999574 | − | 0.0291897i | \(-0.00929268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.13330 | + | 3.69499i | −0.0717914 | + | 0.124346i | −0.899686 | − | 0.436537i | \(-0.856205\pi\) |
0.827895 | + | 0.560883i | \(0.189538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.3211 | − | 24.8049i | 0.480855 | − | 0.832865i | −0.518904 | − | 0.854833i | \(-0.673660\pi\) |
0.999759 | + | 0.0219673i | \(0.00699297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.131306 | − | 0.0758094i | −0.00440385 | − | 0.00254256i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.774739 | + | 1.09279i | 0.0259257 | + | 0.0365687i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.6743 | − | 21.1739i | 1.22589 | − | 0.707766i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.2406 | + | 34.2026i | 1.97579 | + | 1.14072i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 46.0409i | − | 1.53384i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.2413 | −0.639603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1153 | + | 9.88155i | −0.568305 | + | 0.328111i | −0.756472 | − | 0.654026i | \(-0.773079\pi\) |
0.188167 | + | 0.982137i | \(0.439745\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0355 | −0.531278 | −0.265639 | − | 0.964073i | \(-0.585583\pi\) | ||||
−0.265639 | + | 0.964073i | \(0.585583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.64895 | −0.0545724 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0341466 | − | 0.0197145i | 0.00112762 | − | 0.000651031i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.5068 | −1.17126 | −0.585630 | − | 0.810579i | \(-0.699153\pi\) | ||||
−0.585630 | + | 0.810579i | \(0.699153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 22.6900i | − | 0.746851i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −61.0881 | − | 35.2692i | −2.00856 | − | 1.15964i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.5144 | − | 17.0402i | 0.968337 | − | 0.559070i | 0.0696082 | − | 0.997574i | \(-0.477825\pi\) |
0.898729 | + | 0.438505i | \(0.144492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.6633 | − | 12.7032i | −0.906626 | − | 0.416330i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 104.420 | + | 60.2871i | 3.41491 | + | 1.97160i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.05895 | − | 13.9585i | 0.263274 | − | 0.456005i | −0.703836 | − | 0.710363i | \(-0.748531\pi\) |
0.967110 | + | 0.254358i | \(0.0818642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8370 | + | 25.6984i | −0.483671 | + | 0.837743i | −0.999824 | − | 0.0187537i | \(-0.994030\pi\) |
0.516153 | + | 0.856496i | \(0.327363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.8308i | − | 0.385265i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4627 | − | 22.7838i | 1.28236 | − | 0.740373i | 0.305084 | − | 0.952325i | \(-0.401315\pi\) |
0.977280 | + | 0.211952i | \(0.0679822\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5074i | 0.633236i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.56950 | + | 11.3787i | 0.212807 | + | 0.368593i | 0.952592 | − | 0.304251i | \(-0.0984061\pi\) |
−0.739785 | + | 0.672843i | \(0.765073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.954258 | − | 1.65282i | −0.0308791 | − | 0.0534841i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.34594 | + | 0.777079i | 0.0434627 | + | 0.0250932i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −69.7153 | −2.24888 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.09809 | + | 10.5622i | −0.196304 | + | 0.340009i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.41811 | − | 11.1165i | −0.206392 | − | 0.357482i | 0.744183 | − | 0.667976i | \(-0.232839\pi\) |
−0.950575 | + | 0.310494i | \(0.899506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.87774 | + | 10.1805i | 0.188626 | + | 0.326709i | 0.944792 | − | 0.327670i | \(-0.106263\pi\) |
−0.756167 | + | 0.654379i | \(0.772930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.456231 | + | 0.790216i | −0.0146261 | + | 0.0253332i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.6204 | −1.07561 | −0.537806 | − | 0.843069i | \(-0.680747\pi\) | ||||
−0.537806 | + | 0.843069i | \(0.680747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.2894 | − | 27.8799i | −1.54334 | − | 0.891045i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.2420 | − | 21.2037i | −0.390458 | − | 0.676294i | 0.602052 | − | 0.798457i | \(-0.294350\pi\) |
−0.992510 | + | 0.122163i | \(0.961017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.7519 | + | 53.2638i | 0.979836 | + | 1.69713i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 15.2928i | − | 0.486282i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.56804 | + | 2.63736i | −0.145108 | + | 0.0837784i | −0.570796 | − | 0.821092i | \(-0.693365\pi\) |
0.425688 | + | 0.904870i | \(0.360032\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.5635i | 1.53957i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.422417 | + | 0.731648i | −0.0133781 | + | 0.0231715i | −0.872637 | − | 0.488369i | \(-0.837592\pi\) |
0.859259 | + | 0.511541i | \(0.170925\pi\) | |||||||
\(998\) | 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 | 2736.2.dc.d.449.1 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.d.449.8 | 16 | ||
4.3 | odd | 2 | 684.2.bk.a.449.1 | ✓ | 16 | ||
12.11 | even | 2 | 684.2.bk.a.449.8 | yes | 16 | ||
19.8 | odd | 6 | inner | 2736.2.dc.d.1889.8 | 16 | ||
57.8 | even | 6 | inner | 2736.2.dc.d.1889.1 | 16 | ||
76.27 | even | 6 | 684.2.bk.a.521.8 | yes | 16 | ||
228.179 | odd | 6 | 684.2.bk.a.521.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.bk.a.449.1 | ✓ | 16 | 4.3 | odd | 2 | ||
684.2.bk.a.449.8 | yes | 16 | 12.11 | even | 2 | ||
684.2.bk.a.521.1 | yes | 16 | 228.179 | odd | 6 | ||
684.2.bk.a.521.8 | yes | 16 | 76.27 | even | 6 | ||
2736.2.dc.d.449.1 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.d.449.8 | 16 | 3.2 | odd | 2 | inner | ||
2736.2.dc.d.1889.1 | 16 | 57.8 | even | 6 | inner | ||
2736.2.dc.d.1889.8 | 16 | 19.8 | odd | 6 | inner |