Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.38 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.37 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 2.35025 | 1.05106 | 0.525531 | − | 0.850775i | \(-0.323867\pi\) | ||||
0.525531 | + | 0.850775i | \(0.323867\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.09095i | − 0.328934i | −0.986383 | − | 0.164467i | \(-0.947410\pi\) | ||||
0.986383 | − | 0.164467i | \(-0.0525904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.10613i | 1.13884i | 0.822048 | + | 0.569418i | \(0.192832\pi\) | ||||
−0.822048 | + | 0.569418i | \(0.807168\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.74991i | 1.15202i | 0.817442 | + | 0.576011i | \(0.195391\pi\) | ||||
−0.817442 | + | 0.576011i | \(0.804609\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.10196 | 1.62930 | 0.814650 | − | 0.579953i | \(-0.196929\pi\) | ||||
0.814650 | + | 0.579953i | \(0.196929\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.99240 | 0.832474 | 0.416237 | − | 0.909256i | \(-0.363349\pi\) | ||||
0.416237 | + | 0.909256i | \(0.363349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.523653 | 0.104731 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.09983 | 0.761319 | 0.380660 | − | 0.924715i | \(-0.375697\pi\) | ||||
0.380660 | + | 0.924715i | \(0.375697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.8933i | − 1.95649i | −0.207454 | − | 0.978245i | \(-0.566518\pi\) | ||||
0.207454 | − | 0.978245i | \(-0.433482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.35025i | 0.397264i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.27336i | − 0.373737i | −0.982385 | − | 0.186869i | \(-0.940166\pi\) | ||||
0.982385 | − | 0.186869i | \(-0.0598339\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.29246i | 0.201848i | 0.994894 | + | 0.100924i | \(0.0321799\pi\) | ||||
−0.994894 | + | 0.100924i | \(0.967820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.59200 | 1.31027 | 0.655134 | − | 0.755513i | \(-0.272612\pi\) | ||||
0.655134 | + | 0.755513i | \(0.272612\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.79438 | −0.991062 | −0.495531 | − | 0.868590i | \(-0.665026\pi\) | ||||
−0.495531 | + | 0.868590i | \(0.665026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.688525 | −0.0945762 | −0.0472881 | − | 0.998881i | \(-0.515058\pi\) | ||||
−0.0472881 | + | 0.998881i | \(0.515058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.56400i | − 0.345730i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 7.72675i | − 1.00594i | −0.864305 | − | 0.502968i | \(-0.832241\pi\) | ||||
0.864305 | − | 0.502968i | \(-0.167759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.70563i | 1.24268i | 0.783542 | + | 0.621339i | \(0.213411\pi\) | ||||
−0.783542 | + | 0.621339i | \(0.786589\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.65042i | 1.19699i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.23313 | −1.00584 | −0.502918 | − | 0.864334i | \(-0.667740\pi\) | ||||
−0.502918 | + | 0.864334i | \(0.667740\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.46122 | −0.766806 | −0.383403 | − | 0.923581i | \(-0.625248\pi\) | ||||
−0.383403 | + | 0.923581i | \(0.625248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.44644 | 0.988581 | 0.494290 | − | 0.869297i | \(-0.335428\pi\) | ||||
0.494290 | + | 0.869297i | \(0.335428\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.09095 | 0.124325 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.70061i | 0.641369i | 0.947186 | + | 0.320684i | \(0.103913\pi\) | ||||
−0.947186 | + | 0.320684i | \(0.896087\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0681i | 1.10512i | 0.833474 | + | 0.552558i | \(0.186348\pi\) | ||||
−0.833474 | + | 0.552558i | \(0.813652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1634i | 1.21085i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 2.54950i | − 0.270246i | −0.990829 | − | 0.135123i | \(-0.956857\pi\) | ||||
0.990829 | − | 0.135123i | \(-0.0431430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.10613 | −0.430440 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.6913 | 1.71250 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6447 | −1.58847 | −0.794237 | − | 0.607607i | \(-0.792129\pi\) | ||||
−0.794237 | + | 0.607607i | \(0.792129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3962 | 1.23347 | 0.616736 | − | 0.787170i | \(-0.288454\pi\) | ||||
0.616736 | + | 0.787170i | \(0.288454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2234i | 1.30294i | 0.758673 | + | 0.651472i | \(0.225848\pi\) | ||||
−0.758673 | + | 0.651472i | \(0.774152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 5.44530i | − 0.526417i | −0.964739 | − | 0.263209i | \(-0.915219\pi\) | ||||
0.964739 | − | 0.263209i | \(-0.0847808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 0.947776i | − 0.0907805i | −0.998969 | − | 0.0453902i | \(-0.985547\pi\) | ||||
0.998969 | − | 0.0453902i | \(-0.0144531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8819i | 1.58812i | 0.607840 | + | 0.794059i | \(0.292036\pi\) | ||||
−0.607840 | + | 0.794059i | \(0.707964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.38313 | 0.874981 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.74991 | −0.435423 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.80982 | 0.891802 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5205 | −0.940983 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2310i | 0.907852i | 0.891039 | + | 0.453926i | \(0.149977\pi\) | ||||
−0.891039 | + | 0.453926i | \(0.850023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.9013i | − 1.38930i | −0.719346 | − | 0.694651i | \(-0.755559\pi\) | ||||
0.719346 | − | 0.694651i | \(-0.244441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.10196i | 0.615818i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0619i | 0.859647i | 0.902913 | + | 0.429823i | \(0.141424\pi\) | ||||
−0.902913 | + | 0.429823i | \(0.858576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.44750 | 0.377232 | 0.188616 | − | 0.982051i | \(-0.439600\pi\) | ||||
0.188616 | + | 0.982051i | \(0.439600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.47959 | 0.374602 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.63561 | 0.800193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3264 | 1.00981 | 0.504907 | − | 0.863174i | \(-0.331527\pi\) | ||||
0.504907 | + | 0.863174i | \(0.331527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.25492i | 0.753154i | 0.926385 | + | 0.376577i | \(0.122899\pi\) | ||||
−0.926385 | + | 0.376577i | \(0.877101\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 25.6019i | − 2.05639i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.19774i | 0.335016i | 0.985871 | + | 0.167508i | \(0.0535720\pi\) | ||||
−0.985871 | + | 0.167508i | \(0.946428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.99240i | 0.314645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6952 | 1.85595 | 0.927977 | − | 0.372639i | \(-0.121547\pi\) | ||||
0.927977 | + | 0.372639i | \(0.121547\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.79250 | −0.370855 | −0.185427 | − | 0.982658i | \(-0.559367\pi\) | ||||
−0.185427 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.86033 | −0.296949 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2897 | −1.39054 | −0.695271 | − | 0.718747i | \(-0.744716\pi\) | ||||
−0.695271 | + | 0.718747i | \(0.744716\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.523653i | 0.0395844i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.64806i | 0.496899i | 0.968645 | + | 0.248450i | \(0.0799210\pi\) | ||||
−0.968645 | + | 0.248450i | \(0.920079\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.46631i | − 0.183320i | −0.995790 | − | 0.0916598i | \(-0.970783\pi\) | ||||
0.995790 | − | 0.0916598i | \(-0.0292172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 5.34294i | − 0.392821i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.18192 | 0.378939 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.9048 | 0.933760 | 0.466880 | − | 0.884321i | \(-0.345378\pi\) | ||||
0.466880 | + | 0.884321i | \(0.345378\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3689 | 1.32222 | 0.661112 | − | 0.750287i | \(-0.270085\pi\) | ||||
0.661112 | + | 0.750287i | \(0.270085\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0957 | −1.07552 | −0.537761 | − | 0.843098i | \(-0.680730\pi\) | ||||
−0.537761 | + | 0.843098i | \(0.680730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.51621i | 0.249258i | 0.992203 | + | 0.124629i | \(0.0397740\pi\) | ||||
−0.992203 | + | 0.124629i | \(0.960226\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.09983i | 0.287752i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.03759i | 0.212155i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 7.74789i | − 0.535933i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.2502 | 1.39408 | 0.697041 | − | 0.717031i | \(-0.254500\pi\) | ||||
0.697041 | + | 0.717031i | \(0.254500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.1933 | 1.37717 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8933 | 0.739484 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5038 | −1.31196 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9963i | 0.870295i | 0.900359 | + | 0.435148i | \(0.143304\pi\) | ||||
−0.900359 | + | 0.435148i | \(0.856696\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 28.8974i | − 1.91799i | −0.283430 | − | 0.958993i | \(-0.591473\pi\) | ||||
0.283430 | − | 0.958993i | \(-0.408527\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.65438i | − 0.241488i | −0.992684 | − | 0.120744i | \(-0.961472\pi\) | ||||
0.992684 | − | 0.120744i | \(-0.0385281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 13.7096i | − 0.898143i | −0.893496 | − | 0.449071i | \(-0.851755\pi\) | ||||
0.893496 | − | 0.449071i | \(-0.148245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.9685 | −1.04167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5360 | −1.32836 | −0.664181 | − | 0.747572i | \(-0.731220\pi\) | ||||
−0.664181 | + | 0.747572i | \(0.731220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1694 | 1.42806 | 0.714030 | − | 0.700116i | \(-0.246868\pi\) | ||||
0.714030 | + | 0.700116i | \(0.246868\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.35025 | −0.150152 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.1616i | 1.85551i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.82901i | − 0.178565i | −0.996006 | − | 0.0892827i | \(-0.971543\pi\) | ||||
0.996006 | − | 0.0892827i | \(-0.0284575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.35552i | − 0.273829i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 19.2158i | − 1.19865i | −0.800505 | − | 0.599325i | \(-0.795436\pi\) | ||||
0.800505 | − | 0.599325i | \(-0.204564\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.27336 | 0.141259 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.5713 | −1.63846 | −0.819230 | − | 0.573465i | \(-0.805599\pi\) | ||||
−0.819230 | + | 0.573465i | \(0.805599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.61820 | −0.0994054 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.88420 | 0.480708 | 0.240354 | − | 0.970685i | \(-0.422736\pi\) | ||||
0.240354 | + | 0.970685i | \(0.422736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 15.1206i | − 0.918513i | −0.888304 | − | 0.459256i | \(-0.848116\pi\) | ||||
0.888304 | − | 0.459256i | \(-0.151884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 0.571280i | − 0.0344495i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1215i | 0.608141i | 0.952650 | + | 0.304071i | \(0.0983459\pi\) | ||||
−0.952650 | + | 0.304071i | \(0.901654\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6645i | 1.41170i | 0.708359 | + | 0.705852i | \(0.249436\pi\) | ||||
−0.708359 | + | 0.705852i | \(0.750564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1838 | −1.08091 | −0.540457 | − | 0.841371i | \(-0.681749\pi\) | ||||
−0.540457 | + | 0.841371i | \(0.681749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.29246 | −0.0762914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.56163 | −0.327155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.8327 | 1.21706 | 0.608529 | − | 0.793532i | \(-0.291760\pi\) | ||||
0.608529 | + | 0.793532i | \(0.291760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 18.1597i | − 1.05730i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.3933i | 0.948052i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.59200i | 0.495235i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.8106i | 1.30613i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.57939 | 0.261360 | 0.130680 | − | 0.991425i | \(-0.458284\pi\) | ||||
0.130680 | + | 0.991425i | \(0.458284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.20035 | −0.351589 | −0.175795 | − | 0.984427i | \(-0.556249\pi\) | ||||
−0.175795 | + | 0.984427i | \(0.556249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0230 | −1.24481 | −0.622406 | − | 0.782695i | \(-0.713845\pi\) | ||||
−0.622406 | + | 0.782695i | \(0.713845\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.35768 | 0.132420 | 0.0662102 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662102 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.47272i | − 0.250424i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.7336i | 1.87699i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.15019i | 0.119271i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 6.79438i | − 0.374586i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.15331 | −0.118357 | −0.0591784 | − | 0.998247i | \(-0.518848\pi\) | ||||
−0.0591784 | + | 0.998247i | \(0.518848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.3499 | −1.05720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.2469 | 1.26634 | 0.633169 | − | 0.774014i | \(-0.281754\pi\) | ||||
0.633169 | + | 0.774014i | \(0.281754\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.8840 | −0.643556 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 26.1260i | − 1.40252i | −0.712906 | − | 0.701260i | \(-0.752621\pi\) | ||||
0.712906 | − | 0.701260i | \(-0.247379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.68463i | − 0.197234i | −0.995125 | − | 0.0986169i | \(-0.968558\pi\) | ||||
0.995125 | − | 0.0986169i | \(-0.0314418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.5433i | − 0.827285i | −0.910439 | − | 0.413642i | \(-0.864256\pi\) | ||||
0.910439 | − | 0.413642i | \(-0.135744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1855 | −0.805960 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.0367 | −1.21583 | −0.607914 | − | 0.794003i | \(-0.707994\pi\) | ||||
−0.607914 | + | 0.794003i | \(0.707994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.4378 | 1.65462 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.8512 | 1.03906 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1135i | 0.841116i | 0.907266 | + | 0.420558i | \(0.138166\pi\) | ||||
−0.907266 | + | 0.420558i | \(0.861834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 0.688525i | − 0.0357464i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.37018i | 0.433392i | 0.976239 | + | 0.216696i | \(0.0695280\pi\) | ||||
−0.976239 | + | 0.216696i | \(0.930472\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.8344i | 0.867018i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.66739 | 0.239748 | 0.119874 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119874 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.1113 | 0.567761 | 0.283880 | − | 0.958860i | \(-0.408378\pi\) | ||||
0.283880 | + | 0.958860i | \(0.408378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.56400 | 0.130674 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.8483 | −1.71618 | −0.858090 | − | 0.513500i | \(-0.828349\pi\) | ||||
−0.858090 | + | 0.513500i | \(0.828349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9636i | 0.959028i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3978i | 0.674118i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2554i | 1.51848i | 0.650813 | + | 0.759238i | \(0.274428\pi\) | ||||
−0.650813 | + | 0.759238i | \(0.725572\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 35.7603i | − 1.78578i | −0.450272 | − | 0.892891i | \(-0.648673\pi\) | ||||
0.450272 | − | 0.892891i | \(-0.351327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.7292 | 2.22812 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.48012 | −0.122935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9283 | 1.28207 | 0.641036 | − | 0.767511i | \(-0.278505\pi\) | ||||
0.641036 | + | 0.767511i | \(0.278505\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.72675 | 0.380208 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.6625i | 1.16155i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.32586i | − 0.309038i | −0.987990 | − | 0.154519i | \(-0.950617\pi\) | ||||
0.987990 | − | 0.154519i | \(-0.0493829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 27.3586i | − 1.33338i | −0.745336 | − | 0.666689i | \(-0.767711\pi\) | ||||
0.745336 | − | 0.666689i | \(-0.232289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.48730i | 0.120652i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.70563 | −0.469688 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.5526 | 1.32716 | 0.663582 | − | 0.748104i | \(-0.269035\pi\) | ||||
0.663582 | + | 0.748104i | \(0.269035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.0479 | 0.627040 | 0.313520 | − | 0.949582i | \(-0.398492\pi\) | ||||
0.313520 | + | 0.949582i | \(0.398492\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.3539 | 1.35635 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.42338i | 0.306571i | 0.988182 | + | 0.153286i | \(0.0489854\pi\) | ||||
−0.988182 | + | 0.153286i | \(0.951015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1824i | 1.05392i | 0.849891 | + | 0.526959i | \(0.176668\pi\) | ||||
−0.849891 | + | 0.526959i | \(0.823332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.99195i | − 0.284046i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.86593i | 0.0880586i | 0.999030 | + | 0.0440293i | \(0.0140195\pi\) | ||||
−0.999030 | + | 0.0440293i | \(0.985981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.41001 | 0.0663947 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.65042 | −0.452419 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.3835 | −1.32773 | −0.663863 | − | 0.747854i | \(-0.731084\pi\) | ||||
−0.663863 | + | 0.747854i | \(0.731084\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.2364 | 1.54797 | 0.773986 | − | 0.633202i | \(-0.218260\pi\) | ||||
0.773986 | + | 0.633202i | \(0.218260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.11779i | 0.0984219i | 0.998788 | + | 0.0492110i | \(0.0156707\pi\) | ||||
−0.998788 | + | 0.0492110i | \(0.984329\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.7416i | 0.635884i | 0.948110 | + | 0.317942i | \(0.102992\pi\) | ||||
−0.948110 | + | 0.317942i | \(0.897008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8.23313i | − 0.380171i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.37345i | − 0.430992i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.71896 | 0.170638 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.78287 | 0.401299 | 0.200650 | − | 0.979663i | \(-0.435695\pi\) | ||||
0.200650 | + | 0.979663i | \(0.435695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.33470 | 0.425626 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −36.7688 | −1.66959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4.42586i | − 0.200555i | −0.994960 | − | 0.100277i | \(-0.968027\pi\) | ||||
0.994960 | − | 0.100277i | \(-0.0319730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 18.5511i | − 0.837199i | −0.908171 | − | 0.418599i | \(-0.862521\pi\) | ||||
0.908171 | − | 0.418599i | \(-0.137479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.4738i | 0.877056i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6.46122i | − 0.289825i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.23350 | −0.234284 | −0.117142 | − | 0.993115i | \(-0.537373\pi\) | ||||
−0.117142 | + | 0.993115i | \(0.537373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2800 | −1.21635 | −0.608177 | − | 0.793802i | \(-0.708099\pi\) | ||||
−0.608177 | + | 0.793802i | \(0.708099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.1342 | 1.29646 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.0131 | 1.50761 | 0.753803 | − | 0.657101i | \(-0.228217\pi\) | ||||
0.753803 | + | 0.657101i | \(0.228217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.44644i | 0.373648i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.0783i | 1.36947i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.41234i | 0.325994i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 34.1052i | − 1.49417i | −0.664726 | − | 0.747087i | \(-0.731452\pi\) | ||||
0.664726 | − | 0.747087i | \(-0.268548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7371 | −1.08168 | −0.540840 | − | 0.841126i | \(-0.681894\pi\) | ||||
−0.540840 | + | 0.841126i | \(0.681894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.7420 | 2.25392 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.06071 | −0.306987 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.30700 | −0.229872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 12.7978i | − 0.553297i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.09095i | 0.0469906i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11043i | 0.0477412i | 0.999715 | + | 0.0238706i | \(0.00759897\pi\) | ||||
−0.999715 | + | 0.0238706i | \(0.992401\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 2.22751i | − 0.0954159i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6930 | 1.86818 | 0.934089 | − | 0.357040i | \(-0.116214\pi\) | ||||
0.934089 | + | 0.357040i | \(0.116214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.1168 | 1.24042 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.70061 | −0.242415 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.0536 | −1.40053 | −0.700263 | − | 0.713884i | \(-0.746934\pi\) | ||||
−0.700263 | + | 0.713884i | \(0.746934\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.2799i | 1.49218i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 17.6097i | − 0.742159i | −0.928601 | − | 0.371080i | \(-0.878988\pi\) | ||||
0.928601 | − | 0.371080i | \(-0.121012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.6767i | 1.66921i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0355i | 0.504555i | 0.967655 | + | 0.252277i | \(0.0811795\pi\) | ||||
−0.967655 | + | 0.252277i | \(0.918820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.04104 | 0.252810 | 0.126405 | − | 0.991979i | \(-0.459656\pi\) | ||||
0.126405 | + | 0.991979i | \(0.459656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.09063 | 0.0871854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.2605 | −1.30139 | −0.650696 | − | 0.759339i | \(-0.725523\pi\) | ||||
−0.650696 | + | 0.759339i | \(0.725523\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0681 | −0.417695 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.751147i | 0.0311093i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.7168i | 1.22654i | 0.789872 | + | 0.613272i | \(0.210147\pi\) | ||||
−0.789872 | + | 0.613272i | \(0.789853\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 77.3635i | − 3.18771i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.9618i | 0.819732i | 0.912146 | + | 0.409866i | \(0.134425\pi\) | ||||
−0.912146 | + | 0.409866i | \(0.865575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1634 | −0.457657 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.5569 | 1.08509 | 0.542543 | − | 0.840028i | \(-0.317461\pi\) | ||||
0.542543 | + | 0.840028i | \(0.317461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6439 | −0.801289 | −0.400645 | − | 0.916233i | \(-0.631214\pi\) | ||||
−0.400645 | + | 0.916233i | \(0.631214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.0555 | 0.937339 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0877i | 1.18063i | 0.807172 | + | 0.590316i | \(0.200997\pi\) | ||||
−0.807172 | + | 0.590316i | \(0.799003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 27.8986i | − 1.12866i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.44223i | 0.381368i | 0.981651 | + | 0.190684i | \(0.0610706\pi\) | ||||
−0.981651 | + | 0.190684i | \(0.938929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 29.4177i | − 1.18431i | −0.805823 | − | 0.592157i | \(-0.798277\pi\) | ||||
0.805823 | − | 0.592157i | \(-0.201723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.45956 | −0.179245 | −0.0896225 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896225 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.54950 | 0.102144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3441 | −1.09376 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.7982 | 0.430554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 23.6013i | − 0.939553i | −0.882786 | − | 0.469776i | \(-0.844335\pi\) | ||||
0.882786 | − | 0.469776i | \(-0.155665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.0453i | 0.954208i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.10613i | − 0.162691i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.81316i | 0.269104i | 0.990907 | + | 0.134552i | \(0.0429595\pi\) | ||||
−0.990907 | + | 0.134552i | \(0.957041\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.8069 | 0.623361 | 0.311681 | − | 0.950187i | \(-0.399108\pi\) | ||||
0.311681 | + | 0.950187i | \(0.399108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.5205 | −1.67165 | −0.835827 | − | 0.548992i | \(-0.815012\pi\) | ||||
−0.835827 | + | 0.548992i | \(0.815012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.42950 | −0.330887 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.40359 | 0.0940597 | 0.0470298 | − | 0.998893i | \(-0.485024\pi\) | ||||
0.0470298 | + | 0.998893i | \(0.485024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 37.3720i | − 1.46024i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.3292i | 1.02564i | 0.858497 | + | 0.512819i | \(0.171399\pi\) | ||||
−0.858497 | + | 0.512819i | \(0.828601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.09353i | − 0.314802i | −0.987535 | − | 0.157401i | \(-0.949689\pi\) | ||||
0.987535 | − | 0.157401i | \(-0.0503115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.6913i | 0.647262i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.3682 | 0.633778 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5884 | 0.408759 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.41009 | 0.131449 | 0.0657246 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657246 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.4265 | −0.477589 | −0.238794 | − | 0.971070i | \(-0.576752\pi\) | ||||
−0.238794 | + | 0.971070i | \(0.576752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 15.6447i | − 0.600387i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.4879i | 0.745682i | 0.927895 | + | 0.372841i | \(0.121616\pi\) | ||||
−0.927895 | + | 0.372841i | \(0.878384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.6480i | 0.903542i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 2.82717i | − 0.107707i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.44853 | −0.0931464 | −0.0465732 | − | 0.998915i | \(-0.514830\pi\) | ||||
−0.0465732 | + | 0.998915i | \(0.514830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.4527 | 0.396494 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.13906 | −0.232533 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.8472 | 0.825157 | 0.412578 | − | 0.910922i | \(-0.364628\pi\) | ||||
0.412578 | + | 0.910922i | \(0.364628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 16.1453i | − 0.608930i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.3962i | 0.466209i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 50.4998i | − 1.89656i | −0.317437 | − | 0.948279i | \(-0.602822\pi\) | ||||
0.317437 | − | 0.948279i | \(-0.397178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 43.4903i | − 1.62873i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5281 | 0.393730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.7799 | −0.513904 | −0.256952 | − | 0.966424i | \(-0.582718\pi\) | ||||
−0.256952 | + | 0.966424i | \(0.582718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.2234 | −0.492467 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.14689 | 0.0797334 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 12.5617i | − 0.465888i | −0.972490 | − | 0.232944i | \(-0.925164\pi\) | ||||
0.972490 | − | 0.232944i | \(-0.0748358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.8112i | 1.50946i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.04203i | 0.0384883i | 0.999815 | + | 0.0192442i | \(0.00612599\pi\) | ||||
−0.999815 | + | 0.0192442i | \(0.993874\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.98195i | 0.330854i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.73631 | −0.137442 | −0.0687212 | − | 0.997636i | \(-0.521892\pi\) | ||||
−0.0687212 | + | 0.997636i | \(0.521892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.44956 | 0.163239 | 0.0816193 | − | 0.996664i | \(-0.473991\pi\) | ||||
0.0816193 | + | 0.996664i | \(0.473991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.9700 | 1.06138 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.44530 | 0.198967 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 23.5520i | − 0.859426i | −0.902965 | − | 0.429713i | \(-0.858615\pi\) | ||||
0.902965 | − | 0.429713i | \(-0.141385\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7513i | 0.791612i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.5240i | 0.600576i | 0.953849 | + | 0.300288i | \(0.0970829\pi\) | ||||
−0.953849 | + | 0.300288i | \(0.902917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 9.27488i | − 0.336214i | −0.985769 | − | 0.168107i | \(-0.946235\pi\) | ||||
0.985769 | − | 0.168107i | \(-0.0537655\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.947776 | 0.0343118 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.7270 | 1.14560 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.2106 | 0.656690 | 0.328345 | − | 0.944558i | \(-0.393509\pi\) | ||||
0.328345 | + | 0.944558i | \(0.393509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.51105 | −0.0543486 | −0.0271743 | − | 0.999631i | \(-0.508651\pi\) | ||||
−0.0271743 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.70429i | − 0.204904i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.17898i | 0.328871i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.04888i | 0.252229i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.86571i | 0.352122i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.25985 | 0.116201 | 0.0581005 | − | 0.998311i | \(-0.481496\pi\) | ||||
0.0581005 | + | 0.998311i | \(0.481496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.8819 | −0.600252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.8526 | −1.41521 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.5236 | −1.78964 | −0.894819 | − | 0.446428i | \(-0.852696\pi\) | ||||
−0.894819 | + | 0.446428i | \(0.852696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 32.2727i | − 1.14172i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 9.21465i | − 0.325178i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.38313i | 0.330712i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 17.9908i | − 0.632523i | −0.948672 | − | 0.316261i | \(-0.897572\pi\) | ||||
0.948672 | − | 0.316261i | \(-0.102428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.2314 | −0.780650 | −0.390325 | − | 0.920677i | \(-0.627637\pi\) | ||||
−0.390325 | + | 0.920677i | \(0.627637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55.6896 | 1.95072 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.0200 | 2.13482 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.7163 | −1.00221 | −0.501103 | − | 0.865388i | \(-0.667072\pi\) | ||||
−0.501103 | + | 0.865388i | \(0.667072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 46.1721i | − 1.60946i | −0.593641 | − | 0.804730i | \(-0.702310\pi\) | ||||
0.593641 | − | 0.804730i | \(-0.297690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 55.5900i | 1.93305i | 0.256568 | + | 0.966526i | \(0.417408\pi\) | ||||
−0.256568 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.13019i | 0.247642i | 0.992305 | + | 0.123821i | \(0.0395148\pi\) | ||||
−0.992305 | + | 0.123821i | \(0.960485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.74991i | − 0.164575i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2636 | −0.389791 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.3725 | −1.15215 | −0.576073 | − | 0.817399i | \(-0.695415\pi\) | ||||
−0.576073 | + | 0.817399i | \(0.695415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1914 | −0.420393 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.07273 | −0.312111 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.80982i | 0.337070i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.07615i | − 0.311127i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.4031i | 1.17794i | 0.808155 | + | 0.588969i | \(0.200466\pi\) | ||||
−0.808155 | + | 0.588969i | \(0.799534\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.5369i | 0.838164i | 0.907948 | + | 0.419082i | \(0.137648\pi\) | ||||
−0.907948 | + | 0.419082i | \(0.862352\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.8496 | −1.70085 | −0.850424 | − | 0.526098i | \(-0.823655\pi\) | ||||
−0.850424 | + | 0.526098i | \(0.823655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.18405 | −0.0403055 | −0.0201528 | − | 0.999797i | \(-0.506415\pi\) | ||||
−0.0201528 | + | 0.999797i | \(0.506415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42.9854 | −1.46155 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.21909 | 0.210968 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 33.8063i | − 1.14548i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 10.5205i | − 0.355658i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.6756i | 1.77873i | 0.457200 | + | 0.889364i | \(0.348853\pi\) | ||||
−0.457200 | + | 0.889364i | \(0.651147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.5193i | 1.63466i | 0.576172 | + | 0.817329i | \(0.304546\pi\) | ||||
−0.576172 | + | 0.817329i | \(0.695454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.3496 | −1.22326 | −0.611630 | − | 0.791144i | \(-0.709486\pi\) | ||||
−0.611630 | + | 0.791144i | \(0.709486\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.5979 | 0.490149 | 0.245075 | − | 0.969504i | \(-0.421188\pi\) | ||||
0.245075 | + | 0.969504i | \(0.421188\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2310 | −0.343136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.2534 | −1.61474 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.6246i | 0.522272i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 44.6606i | − 1.48951i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.27043i | − 0.108954i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 5.79644i | − 0.192680i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.77723 | −0.125421 | −0.0627104 | − | 0.998032i | \(-0.519974\pi\) | ||||
−0.0627104 | + | 0.998032i | \(0.519974\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5255 | −0.680040 | −0.340020 | − | 0.940418i | \(-0.610434\pi\) | ||||
−0.340020 | + | 0.940418i | \(0.610434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9838 | 0.363511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.9013 | 0.525107 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8082i | 0.653413i | 0.945126 | + | 0.326706i | \(0.105939\pi\) | ||||
−0.945126 | + | 0.326706i | \(0.894061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 26.5306i | − 0.873267i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.19045i | − 0.0391417i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.90178i | 0.0952044i | 0.998866 | + | 0.0476022i | \(0.0151580\pi\) | ||||
−0.998866 | + | 0.0476022i | \(0.984842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.10196 | −0.232757 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.1788 | 0.398289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.02197 | −0.294735 | −0.147368 | − | 0.989082i | \(-0.547080\pi\) | ||||
−0.147368 | + | 0.989082i | \(0.547080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0744 | 0.850000 | 0.425000 | − | 0.905193i | \(-0.360274\pi\) | ||||
0.425000 | + | 0.905193i | \(0.360274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.16001i | 0.168033i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.0960i | − 1.49792i | −0.662616 | − | 0.748960i | \(-0.730554\pi\) | ||||
0.662616 | − | 0.748960i | \(-0.269446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.6822i | 1.12583i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 43.0803i | − 1.39551i | −0.716338 | − | 0.697754i | \(-0.754183\pi\) | ||||
0.716338 | − | 0.697754i | \(-0.245817\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.3295 | 0.981439 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0619 | −0.324916 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −87.6634 | −2.82785 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.1715 | 1.38974 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.389484i | 0.0125249i | 0.999980 | + | 0.00626247i | \(0.00199342\pi\) | ||||
−0.999980 | + | 0.00626247i | \(0.998007\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 41.1601i | − 1.32089i | −0.750875 | − | 0.660445i | \(-0.770368\pi\) | ||||
0.750875 | − | 0.660445i | \(-0.229632\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.44750i | 0.142580i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 46.9292i | − 1.50140i | −0.660644 | − | 0.750699i | \(-0.729717\pi\) | ||||
0.660644 | − | 0.750699i | \(-0.270283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.78138 | −0.0888933 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.0802 | −1.24646 | −0.623232 | − | 0.782037i | \(-0.714181\pi\) | ||||
−0.623232 | + | 0.782037i | \(0.714181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.4785 | −1.13044 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.3027 | 1.09076 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.1043i | 0.733932i | 0.930234 | + | 0.366966i | \(0.119603\pi\) | ||||
−0.930234 | + | 0.366966i | \(0.880397\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.26396i | 0.261985i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 47.9056i | − 1.51719i | −0.651565 | − | 0.758593i | \(-0.725887\pi\) | ||||
0.651565 | − | 0.758593i | \(-0.274113\pi\) | |||||||
\(998\) | 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 | 6048.2.j.d.5615.38 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.11 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.12 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.12 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.38 | yes | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.37 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.11 | ✓ | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.37 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.11 | ✓ | 48 | 24.5 | odd | 2 | ||
1512.2.j.d.323.12 | yes | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.37 | yes | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.38 | yes | 48 | 8.5 | even | 2 | ||
6048.2.j.d.5615.11 | 48 | 3.2 | odd | 2 | inner | ||
6048.2.j.d.5615.12 | 48 | 8.3 | odd | 2 | inner | ||
6048.2.j.d.5615.37 | 48 | 24.11 | even | 2 | inner | ||
6048.2.j.d.5615.38 | 48 | 1.1 | even | 1 | trivial |