Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(721,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.t (of order \(4\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 721.13 | ||
Character | \(\chi\) | \(=\) | 2880.721 |
Dual form | 2880.2.t.e.2161.13 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.69880i | 0.642086i | 0.947065 | + | 0.321043i | \(0.104033\pi\) | ||||
−0.947065 | + | 0.321043i | \(0.895967\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72808 | + | 1.72808i | −0.521036 | + | 0.521036i | −0.917884 | − | 0.396849i | \(-0.870104\pi\) |
0.396849 | + | 0.917884i | \(0.370104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.217214 | + | 0.217214i | 0.0602443 | + | 0.0602443i | 0.736587 | − | 0.676343i | \(-0.236436\pi\) |
−0.676343 | + | 0.736587i | \(0.736436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.27804 | −0.795042 | −0.397521 | − | 0.917593i | \(-0.630129\pi\) | ||||
−0.397521 | + | 0.917593i | \(0.630129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73107 | − | 1.73107i | −0.397135 | − | 0.397135i | 0.480086 | − | 0.877221i | \(-0.340605\pi\) |
−0.877221 | + | 0.480086i | \(0.840605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.93129i | − | 0.611216i | −0.952157 | − | 0.305608i | \(-0.901140\pi\) | ||
0.952157 | − | 0.305608i | \(-0.0988597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.42961 | − | 6.42961i | −1.19395 | − | 1.19395i | −0.975949 | − | 0.218000i | \(-0.930047\pi\) |
−0.218000 | − | 0.975949i | \(-0.569953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.75081 | −1.39209 | −0.696043 | − | 0.718000i | \(-0.745058\pi\) | ||||
−0.696043 | + | 0.718000i | \(0.745058\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.20123 | + | 1.20123i | 0.203046 | + | 0.203046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.70155 | − | 4.70155i | 0.772930 | − | 0.772930i | −0.205688 | − | 0.978618i | \(-0.565943\pi\) |
0.978618 | + | 0.205688i | \(0.0659431\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.36530i | − | 0.681745i | −0.940109 | − | 0.340873i | \(-0.889277\pi\) | ||
0.940109 | − | 0.340873i | \(-0.110723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.30731 | − | 4.30731i | 0.656858 | − | 0.656858i | −0.297777 | − | 0.954635i | \(-0.596245\pi\) |
0.954635 | + | 0.297777i | \(0.0962452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.568734 | 0.0829584 | 0.0414792 | − | 0.999139i | \(-0.486793\pi\) | ||||
0.0414792 | + | 0.999139i | \(0.486793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.11408 | 0.587725 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.749102 | − | 0.749102i | 0.102897 | − | 0.102897i | −0.653784 | − | 0.756681i | \(-0.726820\pi\) |
0.756681 | + | 0.653784i | \(0.226820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44387i | 0.329532i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.21126 | − | 2.21126i | 0.287882 | − | 0.287882i | −0.548360 | − | 0.836242i | \(-0.684748\pi\) |
0.836242 | + | 0.548360i | \(0.184748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.39554 | + | 7.39554i | 0.946902 | + | 0.946902i | 0.998660 | − | 0.0517574i | \(-0.0164822\pi\) |
−0.0517574 | + | 0.998660i | \(0.516482\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.307187 | 0.0381019 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00587 | − | 9.00587i | −1.10024 | − | 1.10024i | −0.994381 | − | 0.105862i | \(-0.966240\pi\) |
−0.105862 | − | 0.994381i | \(-0.533760\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.32389i | − | 0.275795i | −0.990447 | − | 0.137897i | \(-0.955966\pi\) | ||
0.990447 | − | 0.137897i | \(-0.0440344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.285439i | 0.0334081i | 0.999860 | + | 0.0167040i | \(0.00531731\pi\) | ||||
−0.999860 | + | 0.0167040i | \(0.994683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.93566 | − | 2.93566i | −0.334550 | − | 0.334550i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.59608 | 0.292082 | 0.146041 | − | 0.989279i | \(-0.453347\pi\) | ||||
0.146041 | + | 0.989279i | \(0.453347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7338 | − | 10.7338i | −1.17819 | − | 1.17819i | −0.980204 | − | 0.197988i | \(-0.936559\pi\) |
−0.197988 | − | 0.980204i | \(-0.563441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.31792 | + | 2.31792i | −0.251414 | + | 0.251414i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.1057i | − | 1.07121i | −0.844470 | − | 0.535604i | \(-0.820084\pi\) | ||
0.844470 | − | 0.535604i | \(-0.179916\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.369003 | + | 0.369003i | −0.0386821 | + | 0.0386821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44811 | −0.251170 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0062 | −1.01598 | −0.507990 | − | 0.861363i | \(-0.669611\pi\) | ||||
−0.507990 | + | 0.861363i | \(0.669611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.37039 | − | 8.37039i | 0.832885 | − | 0.832885i | −0.155025 | − | 0.987911i | \(-0.549546\pi\) |
0.987911 | + | 0.155025i | \(0.0495458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.53186i | 0.643604i | 0.946807 | + | 0.321802i | \(0.104288\pi\) | ||||
−0.946807 | + | 0.321802i | \(0.895712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.25677 | − | 5.25677i | 0.508191 | − | 0.508191i | −0.405780 | − | 0.913971i | \(-0.633000\pi\) |
0.913971 | + | 0.405780i | \(0.133000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6006 | + | 11.6006i | 1.11114 | + | 1.11114i | 0.992997 | + | 0.118143i | \(0.0376941\pi\) |
0.118143 | + | 0.992997i | \(0.462306\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.80988 | −0.358404 | −0.179202 | − | 0.983812i | \(-0.557352\pi\) | ||||
−0.179202 | + | 0.983812i | \(0.557352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.07273 | − | 2.07273i | −0.193283 | − | 0.193283i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.56874i | − | 0.510485i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.02748i | 0.457044i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4060 | −1.45579 | −0.727897 | − | 0.685687i | \(-0.759502\pi\) | ||||
−0.727897 | + | 0.685687i | \(0.759502\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7965 | − | 10.7965i | −0.943291 | − | 0.943291i | 0.0551849 | − | 0.998476i | \(-0.482425\pi\) |
−0.998476 | + | 0.0551849i | \(0.982425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.94075 | − | 2.94075i | 0.254995 | − | 0.254995i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.96450i | 0.424146i | 0.977254 | + | 0.212073i | \(0.0680214\pi\) | ||||
−0.977254 | + | 0.212073i | \(0.931979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.85795 | − | 5.85795i | 0.496865 | − | 0.496865i | −0.413596 | − | 0.910461i | \(-0.635727\pi\) |
0.910461 | + | 0.413596i | \(0.135727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.750726 | −0.0627789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.09284 | −0.755119 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.8051 | + | 11.8051i | −0.967108 | + | 0.967108i | −0.999476 | − | 0.0323682i | \(-0.989695\pi\) |
0.0323682 | + | 0.999476i | \(0.489695\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7013i | 0.870862i | 0.900222 | + | 0.435431i | \(0.143404\pi\) | ||||
−0.900222 | + | 0.435431i | \(0.856596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.48065 | + | 5.48065i | −0.440216 | + | 0.440216i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.87849 | + | 4.87849i | 0.389346 | + | 0.389346i | 0.874454 | − | 0.485108i | \(-0.161220\pi\) |
−0.485108 | + | 0.874454i | \(0.661220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.97967 | 0.392453 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3627 | + | 10.3627i | 0.811665 | + | 0.811665i | 0.984883 | − | 0.173218i | \(-0.0554165\pi\) |
−0.173218 | + | 0.984883i | \(0.555417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 22.8744i | − | 1.77007i | −0.465520 | − | 0.885037i | \(-0.654133\pi\) | ||
0.465520 | − | 0.885037i | \(-0.345867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9056i | − | 0.992741i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.15292 | − | 3.15292i | −0.239712 | − | 0.239712i | 0.577019 | − | 0.816731i | \(-0.304216\pi\) |
−0.816731 | + | 0.577019i | \(0.804216\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.69880 | 0.128417 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.950602 | − | 0.950602i | −0.0710513 | − | 0.0710513i | 0.670688 | − | 0.741739i | \(-0.265999\pi\) |
−0.741739 | + | 0.670688i | \(0.765999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0786 | − | 11.0786i | 0.823465 | − | 0.823465i | −0.163139 | − | 0.986603i | \(-0.552162\pi\) |
0.986603 | + | 0.163139i | \(0.0521618\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.64899i | − | 0.488844i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.66472 | − | 5.66472i | 0.414245 | − | 0.414245i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.3378 | −1.76102 | −0.880509 | − | 0.474029i | \(-0.842799\pi\) | ||||
−0.880509 | + | 0.474029i | \(0.842799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.6566 | −1.77482 | −0.887409 | − | 0.460982i | \(-0.847497\pi\) | ||||
−0.887409 | + | 0.460982i | \(0.847497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.20031 | + | 1.20031i | −0.0855185 | + | 0.0855185i | −0.748572 | − | 0.663054i | \(-0.769260\pi\) |
0.663054 | + | 0.748572i | \(0.269260\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1355i | 1.28559i | 0.766037 | + | 0.642797i | \(0.222226\pi\) | ||||
−0.766037 | + | 0.642797i | \(0.777774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.9226 | − | 10.9226i | 0.766618 | − | 0.766618i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.08673 | − | 3.08673i | −0.215587 | − | 0.215587i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.98286 | 0.413843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3307 | − | 10.3307i | −0.711197 | − | 0.711197i | 0.255588 | − | 0.966786i | \(-0.417731\pi\) |
−0.966786 | + | 0.255588i | \(0.917731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.09145i | − | 0.415434i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 13.1671i | − | 0.893839i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.712036 | − | 0.712036i | −0.0478968 | − | 0.0478968i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6110 | 0.710567 | 0.355283 | − | 0.934759i | \(-0.384384\pi\) | ||||
0.355283 | + | 0.934759i | \(0.384384\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.89383 | + | 2.89383i | 0.192071 | + | 0.192071i | 0.796590 | − | 0.604520i | \(-0.206635\pi\) |
−0.604520 | + | 0.796590i | \(0.706635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.02023 | − | 7.02023i | 0.463910 | − | 0.463910i | −0.436025 | − | 0.899935i | \(-0.643614\pi\) |
0.899935 | + | 0.436025i | \(0.143614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.30153i | − | 0.0852663i | −0.999091 | − | 0.0426332i | \(-0.986425\pi\) | ||
0.999091 | − | 0.0426332i | \(-0.0135747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.402156 | − | 0.402156i | 0.0262337 | − | 0.0262337i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.18489 | 0.270698 | 0.135349 | − | 0.990798i | \(-0.456784\pi\) | ||||
0.135349 | + | 0.990798i | \(0.456784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.57746 | −0.552523 | −0.276262 | − | 0.961082i | \(-0.589096\pi\) | ||||
−0.276262 | + | 0.961082i | \(0.589096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.90909 | − | 2.90909i | 0.185855 | − | 0.185855i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.752027i | − | 0.0478503i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.03798 | + | 8.03798i | −0.507353 | + | 0.507353i | −0.913713 | − | 0.406360i | \(-0.866798\pi\) |
0.406360 | + | 0.913713i | \(0.366798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.06550 | + | 5.06550i | 0.318465 | + | 0.318465i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.2973 | −1.95227 | −0.976136 | − | 0.217158i | \(-0.930321\pi\) | ||||
−0.976136 | + | 0.217158i | \(0.930321\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98699 | + | 7.98699i | 0.496288 | + | 0.496288i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6640i | 1.21253i | 0.795262 | + | 0.606266i | \(0.207333\pi\) | ||||
−0.795262 | + | 0.606266i | \(0.792667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.05939i | − | 0.0650779i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50053 | + | 3.50053i | 0.213431 | + | 0.213431i | 0.805723 | − | 0.592292i | \(-0.201777\pi\) |
−0.592292 | + | 0.805723i | \(0.701777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.81899 | 0.231987 | 0.115994 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115994 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.72808 | + | 1.72808i | 0.104207 | + | 0.104207i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.2534 | + | 15.2534i | −0.916487 | + | 0.916487i | −0.996772 | − | 0.0802850i | \(-0.974417\pi\) |
0.0802850 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.1406i | − | 0.604940i | −0.953159 | − | 0.302470i | \(-0.902189\pi\) | ||
0.953159 | − | 0.302470i | \(-0.0978113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9364 | − | 18.9364i | 1.12565 | − | 1.12565i | 0.134777 | − | 0.990876i | \(-0.456968\pi\) |
0.990876 | − | 0.134777i | \(-0.0430318\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.41578 | 0.437739 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.25445 | −0.367909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.0806 | − | 11.0806i | 0.647334 | − | 0.647334i | −0.305014 | − | 0.952348i | \(-0.598661\pi\) |
0.952348 | + | 0.305014i | \(0.0986610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.12719i | − | 0.182072i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.636717 | − | 0.636717i | 0.0368223 | − | 0.0368223i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.31726 | + | 7.31726i | 0.421760 | + | 0.421760i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4589 | 0.598874 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.43194 | − | 7.43194i | −0.424163 | − | 0.424163i | 0.462471 | − | 0.886634i | \(-0.346963\pi\) |
−0.886634 | + | 0.462471i | \(0.846963\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.5084i | 1.61656i | 0.588795 | + | 0.808282i | \(0.299602\pi\) | ||||
−0.588795 | + | 0.808282i | \(0.700398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5.85037i | − | 0.330683i | −0.986236 | − | 0.165341i | \(-0.947127\pi\) | ||
0.986236 | − | 0.165341i | \(-0.0528726\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.0284388 | − | 0.0284388i | −0.00159728 | − | 0.00159728i | 0.706308 | − | 0.707905i | \(-0.250360\pi\) |
−0.707905 | + | 0.706308i | \(0.750360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.2218 | 1.24418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.67453 | + | 5.67453i | 0.315739 | + | 0.315739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.217214 | − | 0.217214i | 0.0120489 | − | 0.0120489i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.966165i | 0.0532664i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8266 | − | 14.8266i | 0.814945 | − | 0.814945i | −0.170426 | − | 0.985371i | \(-0.554514\pi\) |
0.985371 | + | 0.170426i | \(0.0545143\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7362 | −0.695854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.5373 | −1.93584 | −0.967920 | − | 0.251260i | \(-0.919155\pi\) | ||||
−0.967920 | + | 0.251260i | \(0.919155\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.3940 | − | 13.3940i | 0.725326 | − | 0.725326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8806i | 1.01946i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2007 | − | 10.2007i | 0.547600 | − | 0.547600i | −0.378146 | − | 0.925746i | \(-0.623438\pi\) |
0.925746 | + | 0.378146i | \(0.123438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.9923 | + | 12.9923i | 0.695460 | + | 0.695460i | 0.963428 | − | 0.267968i | \(-0.0863520\pi\) |
−0.267968 | + | 0.963428i | \(0.586352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.6457 | −1.36498 | −0.682490 | − | 0.730895i | \(-0.739103\pi\) | ||||
−0.682490 | + | 0.730895i | \(0.739103\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.64324 | − | 1.64324i | −0.0872139 | − | 0.0872139i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 30.5800i | − | 1.61395i | −0.590584 | − | 0.806976i | \(-0.701102\pi\) | ||
0.590584 | − | 0.806976i | \(-0.298898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.0068i | − | 0.684567i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.201836 | + | 0.201836i | 0.0105646 | + | 0.0105646i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.2750 | −1.21494 | −0.607472 | − | 0.794341i | \(-0.707816\pi\) | ||||
−0.607472 | + | 0.794341i | \(0.707816\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.27258 | + | 1.27258i | 0.0660688 | + | 0.0660688i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.84829 | − | 4.84829i | 0.251035 | − | 0.251035i | −0.570360 | − | 0.821395i | \(-0.693196\pi\) |
0.821395 | + | 0.570360i | \(0.193196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.79320i | − | 0.143857i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3646 | − | 22.3646i | 1.14879 | − | 1.14879i | 0.162001 | − | 0.986791i | \(-0.448205\pi\) |
0.986791 | − | 0.162001i | \(-0.0517947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9345 | 1.12080 | 0.560400 | − | 0.828222i | \(-0.310647\pi\) | ||||
0.560400 | + | 0.828222i | \(0.310647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.15165 | −0.211588 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.7795 | + | 22.7795i | −1.15497 | + | 1.15497i | −0.169423 | + | 0.985543i | \(0.554191\pi\) |
−0.985543 | + | 0.169423i | \(0.945809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.60888i | 0.485942i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.83571 | − | 1.83571i | 0.0923645 | − | 0.0923645i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2806 | − | 26.2806i | −1.31899 | − | 1.31899i | −0.914578 | − | 0.404409i | \(-0.867477\pi\) |
−0.404409 | − | 0.914578i | \(-0.632523\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4543 | 0.821689 | 0.410845 | − | 0.911705i | \(-0.365234\pi\) | ||||
0.410845 | + | 0.911705i | \(0.365234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68358 | − | 1.68358i | −0.0838653 | − | 0.0838653i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.2493i | 0.805448i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.2439i | 1.64380i | 0.569629 | + | 0.821902i | \(0.307087\pi\) | ||||
−0.569629 | + | 0.821902i | \(0.692913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.75649 | + | 3.75649i | 0.184845 | + | 0.184845i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1800 | −0.745155 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3438 | + | 26.3438i | 1.28698 | + | 1.28698i | 0.936613 | + | 0.350366i | \(0.113943\pi\) |
0.350366 | + | 0.936613i | \(0.386057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.84601 | + | 8.84601i | −0.431128 | + | 0.431128i | −0.889012 | − | 0.457884i | \(-0.848608\pi\) |
0.457884 | + | 0.889012i | \(0.348608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.27804i | 0.159008i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.5636 | + | 12.5636i | −0.607993 | + | 0.607993i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.1304 | 1.35500 | 0.677498 | − | 0.735525i | \(-0.263064\pi\) | ||||
0.677498 | + | 0.735525i | \(0.263064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.3640 | 0.690288 | 0.345144 | − | 0.938550i | \(-0.387830\pi\) | ||||
0.345144 | + | 0.938550i | \(0.387830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.07427 | + | 5.07427i | −0.242735 | + | 0.242735i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0265i | 0.812628i | 0.913733 | + | 0.406314i | \(0.133186\pi\) | ||||
−0.913733 | + | 0.406314i | \(0.866814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6944 | + | 13.6944i | −0.650643 | + | 0.650643i | −0.953148 | − | 0.302505i | \(-0.902177\pi\) |
0.302505 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.14584 | − | 7.14584i | −0.338745 | − | 0.338745i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.9793 | 1.93393 | 0.966967 | − | 0.254900i | \(-0.0820426\pi\) | ||||
0.966967 | + | 0.254900i | \(0.0820426\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.54359 | + | 7.54359i | 0.355214 | + | 0.355214i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.521850i | 0.0244647i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.79658i | − | 0.224375i | −0.993687 | − | 0.112187i | \(-0.964214\pi\) | ||
0.993687 | − | 0.112187i | \(-0.0357856\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.15223 | + | 9.15223i | 0.426262 | + | 0.426262i | 0.887353 | − | 0.461091i | \(-0.152542\pi\) |
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4617 | 0.625620 | 0.312810 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312810 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.22075 | + | 1.22075i | 0.0564894 | + | 0.0564894i | 0.734787 | − | 0.678298i | \(-0.237282\pi\) |
−0.678298 | + | 0.734787i | \(0.737282\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2992 | − | 15.2992i | 0.706451 | − | 0.706451i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.8867i | 0.684493i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.73107 | + | 1.73107i | −0.0794271 | + | 0.0794271i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.1159 | −1.05619 | −0.528097 | − | 0.849184i | \(-0.677094\pi\) | ||||
−0.528097 | + | 0.849184i | \(0.677094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.04248 | 0.0931293 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.07549 | + | 7.07549i | −0.321281 | + | 0.321281i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.8892i | 0.991895i | 0.868353 | + | 0.495947i | \(0.165179\pi\) | ||||
−0.868353 | + | 0.495947i | \(0.834821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.64551 | + | 5.64551i | −0.254778 | + | 0.254778i | −0.822926 | − | 0.568148i | \(-0.807660\pi\) |
0.568148 | + | 0.822926i | \(0.307660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.0765 | + | 21.0765i | 0.949239 | + | 0.949239i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.94782 | 0.177084 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.76144 | + | 9.76144i | 0.436982 | + | 0.436982i | 0.890995 | − | 0.454013i | \(-0.150008\pi\) |
−0.454013 | + | 0.890995i | \(0.650008\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8483i | 1.15252i | 0.817267 | + | 0.576259i | \(0.195488\pi\) | ||||
−0.817267 | + | 0.576259i | \(0.804512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 11.8375i | − | 0.526763i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.7719 | − | 10.7719i | −0.477455 | − | 0.477455i | 0.426862 | − | 0.904317i | \(-0.359619\pi\) |
−0.904317 | + | 0.426862i | \(0.859619\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.484903 | −0.0214509 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.61872 | + | 4.61872i | 0.203525 | + | 0.203525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.982817 | + | 0.982817i | −0.0432243 | + | 0.0432243i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.73686i | 0.382769i | 0.981515 | + | 0.191384i | \(0.0612977\pi\) | ||||
−0.981515 | + | 0.191384i | \(0.938702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.99908 | + | 8.99908i | −0.393502 | + | 0.393502i | −0.875934 | − | 0.482431i | \(-0.839754\pi\) |
0.482431 | + | 0.875934i | \(0.339754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4075 | 1.10677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.4075 | 0.626415 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.948204 | − | 0.948204i | 0.0410713 | − | 0.0410713i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.43419i | − | 0.321408i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.10945 | + | 7.10945i | −0.306226 | + | 0.306226i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.06136 | − | 5.06136i | −0.217605 | − | 0.217605i | 0.589884 | − | 0.807488i | \(-0.299174\pi\) |
−0.807488 | + | 0.589884i | \(0.799174\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.4058 | 0.702746 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8840 | − | 17.8840i | −0.764663 | − | 0.764663i | 0.212498 | − | 0.977161i | \(-0.431840\pi\) |
−0.977161 | + | 0.212498i | \(0.931840\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.2603i | 0.948319i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.41023i | 0.187542i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.40581 | + | 4.40581i | 0.186680 | + | 0.186680i | 0.794259 | − | 0.607579i | \(-0.207859\pi\) |
−0.607579 | + | 0.794259i | \(0.707859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.87122 | 0.0791440 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.2174 | − | 25.2174i | −1.06279 | − | 1.06279i | −0.997892 | − | 0.0648946i | \(-0.979329\pi\) |
−0.0648946 | − | 0.997892i | \(-0.520671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.69399 | + | 2.69399i | −0.113337 | + | 0.113337i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.5000i | 0.985173i | 0.870264 | + | 0.492586i | \(0.163948\pi\) | ||||
−0.870264 | + | 0.492586i | \(0.836052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.63302 | − | 8.63302i | 0.361281 | − | 0.361281i | −0.503004 | − | 0.864284i | \(-0.667772\pi\) |
0.864284 | + | 0.503004i | \(0.167772\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.93129 | −0.122243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6023 | −0.732792 | −0.366396 | − | 0.930459i | \(-0.619408\pi\) | ||||
−0.366396 | + | 0.930459i | \(0.619408\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.2347 | − | 18.2347i | 0.756501 | − | 0.756501i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.58902i | 0.107226i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.32030 | + | 4.32030i | −0.178318 | + | 0.178318i | −0.790622 | − | 0.612304i | \(-0.790243\pi\) |
0.612304 | + | 0.790622i | \(0.290243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4172 | + | 13.4172i | 0.552847 | + | 0.552847i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.94251 | −0.326160 | −0.163080 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163080 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.93769 | − | 3.93769i | −0.161430 | − | 0.161430i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.80370i | − | 0.277992i | −0.990293 | − | 0.138996i | \(-0.955613\pi\) | ||
0.990293 | − | 0.138996i | \(-0.0443875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.6158i | − | 1.00410i | −0.864838 | − | 0.502050i | \(-0.832579\pi\) | ||
0.864838 | − | 0.502050i | \(-0.167421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.55497 | + | 3.55497i | 0.144530 | + | 0.144530i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.9281 | −0.605912 | −0.302956 | − | 0.953005i | \(-0.597974\pi\) | ||||
−0.302956 | + | 0.953005i | \(0.597974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.123537 | + | 0.123537i | 0.00499777 | + | 0.00499777i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.32040 | + | 1.32040i | −0.0533306 | + | 0.0533306i | −0.733269 | − | 0.679939i | \(-0.762006\pi\) |
0.679939 | + | 0.733269i | \(0.262006\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.7296i | 1.55920i | 0.626281 | + | 0.779598i | \(0.284576\pi\) | ||||
−0.626281 | + | 0.779598i | \(0.715424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.60439 | + | 6.60439i | −0.265453 | + | 0.265453i | −0.827265 | − | 0.561812i | \(-0.810104\pi\) |
0.561812 | + | 0.827265i | \(0.310104\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.1677 | 0.687807 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4119 | + | 15.4119i | −0.614511 | + | 0.614511i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.8253i | − | 0.789233i | −0.918846 | − | 0.394617i | \(-0.870877\pi\) | ||
0.918846 | − | 0.394617i | \(-0.129123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6008 | + | 11.6008i | −0.460362 | + | 0.460362i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.893635 | + | 0.893635i | 0.0354071 | + | 0.0354071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.8775 | −0.745617 | −0.372808 | − | 0.927908i | \(-0.621605\pi\) | ||||
−0.372808 | + | 0.927908i | \(0.621605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9375 | − | 22.9375i | −0.904568 | − | 0.904568i | 0.0912588 | − | 0.995827i | \(-0.470911\pi\) |
−0.995827 | + | 0.0912588i | \(0.970911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.49513i | 0.255350i | 0.991816 | + | 0.127675i | \(0.0407514\pi\) | ||||
−0.991816 | + | 0.127675i | \(0.959249\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.64247i | 0.299993i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.1452 | + | 29.1452i | 1.14054 | + | 1.14054i | 0.988351 | + | 0.152190i | \(0.0486326\pi\) |
0.152190 | + | 0.988351i | \(0.451367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.2685 | −0.596590 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.7671 | + | 17.7671i | 0.692107 | + | 0.692107i | 0.962695 | − | 0.270589i | \(-0.0872183\pi\) |
−0.270589 | + | 0.962695i | \(0.587218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.75307 | − | 3.75307i | 0.145978 | − | 0.145978i | −0.630341 | − | 0.776319i | \(-0.717085\pi\) |
0.776319 | + | 0.630341i | \(0.217085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.15885i | − | 0.161273i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.8470 | + | 18.8470i | −0.729760 | + | 0.729760i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.5602 | −0.986740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.9037 | 1.88510 | 0.942550 | − | 0.334064i | \(-0.108420\pi\) | ||||
0.942550 | + | 0.334064i | \(0.108420\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0199 | + | 20.0199i | −0.769427 | + | 0.769427i | −0.978006 | − | 0.208579i | \(-0.933116\pi\) |
0.208579 | + | 0.978006i | \(0.433116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.9986i | − | 0.652347i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.3833 | − | 24.3833i | 0.932999 | − | 0.932999i | −0.0648930 | − | 0.997892i | \(-0.520671\pi\) |
0.997892 | + | 0.0648930i | \(0.0206706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.51043 | + | 3.51043i | 0.134127 | + | 0.134127i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.325431 | 0.0123979 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4576 | + | 14.4576i | 0.549994 | + | 0.549994i | 0.926439 | − | 0.376445i | \(-0.122854\pi\) |
−0.376445 | + | 0.926439i | \(0.622854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.28439i | − | 0.314245i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.3096i | 0.542016i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2194 | + | 13.2194i | 0.499291 | + | 0.499291i | 0.911217 | − | 0.411926i | \(-0.135144\pi\) |
−0.411926 | + | 0.911217i | \(0.635144\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.2775 | −0.613916 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.2196 | + | 14.2196i | 0.534784 | + | 0.534784i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.23663 | − | 5.23663i | 0.196666 | − | 0.196666i | −0.601903 | − | 0.798569i | \(-0.705591\pi\) |
0.798569 | + | 0.601903i | \(0.205591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.7198i | 0.850865i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.530844 | + | 0.530844i | −0.0198524 | + | 0.0198524i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.72657 | 0.176271 | 0.0881357 | − | 0.996108i | \(-0.471909\pi\) | ||||
0.0881357 | + | 0.996108i | \(0.471909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0963 | −0.413249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.42961 | + | 6.42961i | −0.238790 | + | 0.238790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.5233i | − | 1.68837i | −0.536056 | − | 0.844183i | \(-0.680086\pi\) | ||
0.536056 | − | 0.844183i | \(-0.319914\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.1195 | + | 14.1195i | −0.522230 | + | 0.522230i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.37965 | + | 6.37965i | 0.235638 | + | 0.235638i | 0.815041 | − | 0.579403i | \(-0.196714\pi\) |
−0.579403 | + | 0.815041i | \(0.696714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.1257 | 1.14653 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9104 | + | 25.9104i | 0.953129 | + | 0.953129i | 0.998950 | − | 0.0458203i | \(-0.0145902\pi\) |
−0.0458203 | + | 0.998950i | \(0.514590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.17917i | 0.153319i | 0.997057 | + | 0.0766595i | \(0.0244254\pi\) | ||||
−0.997057 | + | 0.0766595i | \(0.975575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.6949i | 0.611653i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.93020 | + | 8.93020i | 0.326302 | + | 0.326302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2420 | 0.884604 | 0.442302 | − | 0.896866i | \(-0.354162\pi\) | ||||
0.442302 | + | 0.896866i | \(0.354162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.56699 | + | 7.56699i | 0.275391 | + | 0.275391i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.98821 | + | 2.98821i | −0.108608 | + | 0.108608i | −0.759323 | − | 0.650714i | \(-0.774470\pi\) |
0.650714 | + | 0.759323i | \(0.274470\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.9665i | 1.12254i | 0.827634 | + | 0.561268i | \(0.189686\pi\) | ||||
−0.827634 | + | 0.561268i | \(0.810314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.7072 | + | 19.7072i | −0.713448 | + | 0.713448i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.960634 | 0.0346865 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.1376 | 1.33921 | 0.669607 | − | 0.742715i | \(-0.266462\pi\) | ||||
0.669607 | + | 0.742715i | \(0.266462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.1287 | − | 36.1287i | 1.29946 | − | 1.29946i | 0.370712 | − | 0.928748i | \(-0.379114\pi\) |
0.928748 | − | 0.370712i | \(-0.120886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.75081i | 0.278417i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.55665 | + | 7.55665i | −0.270745 | + | 0.270745i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.01586 | + | 4.01586i | 0.143699 | + | 0.143699i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.89923 | 0.246244 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7811 | − | 17.7811i | −0.633828 | − | 0.633828i | 0.315198 | − | 0.949026i | \(-0.397929\pi\) |
−0.949026 | + | 0.315198i | \(0.897929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.47223i | − | 0.230126i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.21283i | 0.114091i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.4674 | + | 14.4674i | 0.512463 | + | 0.512463i | 0.915280 | − | 0.402817i | \(-0.131969\pi\) |
−0.402817 | + | 0.915280i | \(0.631969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.86433 | −0.0659554 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.493261 | − | 0.493261i | −0.0174068 | − | 0.0174068i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.52116 | − | 3.52116i | 0.124105 | − | 0.124105i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42.6805i | − | 1.50056i | −0.661117 | − | 0.750282i | \(-0.729917\pi\) | ||
0.661117 | − | 0.750282i | \(-0.270083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.8068 | + | 24.8068i | −0.871083 | + | 0.871083i | −0.992591 | − | 0.121507i | \(-0.961227\pi\) |
0.121507 | + | 0.992591i | \(0.461227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6550 | 0.513342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.9125 | −0.521723 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.88057 | + | 6.88057i | −0.240133 | + | 0.240133i | −0.816905 | − | 0.576772i | \(-0.804312\pi\) |
0.576772 | + | 0.816905i | \(0.304312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3873i | − | 0.919802i | −0.887970 | − | 0.459901i | \(-0.847885\pi\) | ||
0.887970 | − | 0.459901i | \(-0.152115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.319732 | − | 0.319732i | 0.0111182 | − | 0.0111182i | −0.701526 | − | 0.712644i | \(-0.747498\pi\) |
0.712644 | + | 0.701526i | \(0.247498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.47656 | + | 3.47656i | 0.120746 | + | 0.120746i | 0.764898 | − | 0.644152i | \(-0.222790\pi\) |
−0.644152 | + | 0.764898i | \(0.722790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.4861 | −0.467266 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.1746 | − | 16.1746i | −0.559747 | − | 0.559747i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 50.6941i | − | 1.75015i | −0.483983 | − | 0.875077i | \(-0.660810\pi\) | ||
0.483983 | − | 0.875077i | \(-0.339190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.6798i | 1.85103i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.12566 | − | 9.12566i | −0.313932 | − | 0.313932i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.54069 | −0.293462 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.7816 | − | 13.7816i | −0.472427 | − | 0.472427i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.15143 | − | 2.15143i | 0.0736635 | − | 0.0736635i | −0.669315 | − | 0.742979i | \(-0.733412\pi\) |
0.742979 | + | 0.669315i | \(0.233412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.79872i | − | 0.0614430i | −0.999528 | − | 0.0307215i | \(-0.990220\pi\) | ||
0.999528 | − | 0.0307215i | \(-0.00978050\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.27463 | + | 3.27463i | −0.111729 | + | 0.111729i | −0.760761 | − | 0.649032i | \(-0.775174\pi\) |
0.649032 | + | 0.760761i | \(0.275174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3753 | −0.659542 | −0.329771 | − | 0.944061i | \(-0.606972\pi\) | ||||
−0.329771 | + | 0.944061i | \(0.606972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.45891 | −0.151607 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.48624 | + | 4.48624i | −0.152185 | + | 0.152185i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.91240i | − | 0.132567i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.20123 | − | 1.20123i | 0.0406091 | − | 0.0406091i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4639 | − | 20.4639i | −0.691017 | − | 0.691017i | 0.271439 | − | 0.962456i | \(-0.412501\pi\) |
−0.962456 | + | 0.271439i | \(0.912501\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.8698 | −0.837883 | −0.418942 | − | 0.908013i | \(-0.637599\pi\) | ||||
−0.418942 | + | 0.908013i | \(0.637599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.70378 | + | 7.70378i | 0.259253 | + | 0.259253i | 0.824750 | − | 0.565497i | \(-0.191316\pi\) |
−0.565497 | + | 0.824750i | \(0.691316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.9786i | 1.74527i | 0.488373 | + | 0.872635i | \(0.337591\pi\) | ||||
−0.488373 | + | 0.872635i | \(0.662409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 27.8705i | − | 0.934745i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.984520 | − | 0.984520i | −0.0329457 | − | 0.0329457i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.34435 | −0.0449368 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.8347 | + | 49.8347i | 1.66208 | + | 1.66208i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.45559 | + | 2.45559i | −0.0818075 | + | 0.0818075i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.6675i | − | 0.520805i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6946 | − | 21.6946i | 0.720357 | − | 0.720357i | −0.248321 | − | 0.968678i | \(-0.579879\pi\) |
0.968678 | + | 0.248321i | \(0.0798788\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.1996 | 0.768636 | 0.384318 | − | 0.923201i | \(-0.374437\pi\) | ||||
0.384318 | + | 0.923201i | \(0.374437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.0979 | 1.22776 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.3410 | − | 18.3410i | 0.605674 | − | 0.605674i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.3527i | − | 0.473451i | −0.971577 | − | 0.236726i | \(-0.923926\pi\) | ||
0.971577 | − | 0.236726i | \(-0.0760743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.504781 | − | 0.504781i | 0.0166151 | − | 0.0166151i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.70155 | − | 4.70155i | −0.154586 | − | 0.154586i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.7983 | 0.780798 | 0.390399 | − | 0.920646i | \(-0.372337\pi\) | ||||
0.390399 | + | 0.920646i | \(0.372337\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.12177 | − | 7.12177i | −0.233406 | − | 0.233406i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 8.01112i | − | 0.261992i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.2290i | − | 1.24889i | −0.781070 | − | 0.624444i | \(-0.785326\pi\) | ||
0.781070 | − | 0.624444i | \(-0.214674\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.41971 | + | 5.41971i | 0.176677 | + | 0.176677i | 0.789906 | − | 0.613228i | \(-0.210129\pi\) |
−0.613228 | + | 0.789906i | \(0.710129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7960 | −0.416694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.3115 | − | 40.3115i | −1.30995 | − | 1.30995i | −0.921450 | − | 0.388497i | \(-0.872994\pi\) |
−0.388497 | − | 0.921450i | \(-0.627006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0620013 | + | 0.0620013i | −0.00201265 | + | 0.00201265i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.2929i | 1.37000i | 0.728542 | + | 0.685001i | \(0.240198\pi\) | ||||
−0.728542 | + | 0.685001i | \(0.759802\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.2094 | + | 17.2094i | −0.556883 | + | 0.556883i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.43370 | −0.272338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.0750 | 0.937903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.4348 | + | 17.4348i | −0.561247 | + | 0.561247i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.3045i | − | 0.588632i | −0.955708 | − | 0.294316i | \(-0.904908\pi\) | ||
0.955708 | − | 0.294316i | \(-0.0950919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.3477 | − | 40.3477i | 1.29482 | − | 1.29482i | 0.363051 | − | 0.931769i | \(-0.381735\pi\) |
0.931769 | − | 0.363051i | \(-0.118265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.95149 | + | 9.95149i | 0.319030 | + | 0.319030i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8993 | 0.924569 | 0.462284 | − | 0.886732i | \(-0.347030\pi\) | ||||
0.462284 | + | 0.886732i | \(0.347030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4635 | + | 17.4635i | 0.558137 | + | 0.558137i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.4280i | 1.83167i | 0.401557 | + | 0.915834i | \(0.368469\pi\) | ||||
−0.401557 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.69749i | 0.0540866i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.6260 | − | 12.6260i | −0.401482 | − | 0.401482i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.9239 | 0.982332 | 0.491166 | − | 0.871066i | \(-0.336571\pi\) | ||||
0.491166 | + | 0.871066i | \(0.336571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8238 | + | 12.8238i | 0.406540 | + | 0.406540i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.2473 | + | 26.2473i | −0.831260 | + | 0.831260i | −0.987689 | − | 0.156429i | \(-0.950002\pi\) |
0.156429 | + | 0.987689i | \(0.450002\pi\) | |||||||
\(998\) | 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 | 2880.2.t.e.721.13 | 32 | ||
3.2 | odd | 2 | inner | 2880.2.t.e.721.5 | 32 | ||
4.3 | odd | 2 | 720.2.t.e.541.13 | yes | 32 | ||
12.11 | even | 2 | 720.2.t.e.541.4 | yes | 32 | ||
16.5 | even | 4 | inner | 2880.2.t.e.2161.13 | 32 | ||
16.11 | odd | 4 | 720.2.t.e.181.13 | yes | 32 | ||
48.5 | odd | 4 | inner | 2880.2.t.e.2161.5 | 32 | ||
48.11 | even | 4 | 720.2.t.e.181.4 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.t.e.181.4 | ✓ | 32 | 48.11 | even | 4 | ||
720.2.t.e.181.13 | yes | 32 | 16.11 | odd | 4 | ||
720.2.t.e.541.4 | yes | 32 | 12.11 | even | 2 | ||
720.2.t.e.541.13 | yes | 32 | 4.3 | odd | 2 | ||
2880.2.t.e.721.5 | 32 | 3.2 | odd | 2 | inner | ||
2880.2.t.e.721.13 | 32 | 1.1 | even | 1 | trivial | ||
2880.2.t.e.2161.5 | 32 | 48.5 | odd | 4 | inner | ||
2880.2.t.e.2161.13 | 32 | 16.5 | even | 4 | inner |