Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(737,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 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("4140.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.5 | ||
Character | \(\chi\) | \(=\) | 4140.737 |
Dual form | 4140.2.s.b.2393.5 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.79146 | + | 1.33815i | −0.801167 | + | 0.598441i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07691 | − | 2.07691i | −0.784997 | − | 0.784997i | 0.195672 | − | 0.980669i | \(-0.437311\pi\) |
−0.980669 | + | 0.195672i | \(0.937311\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.22627i | 0.972758i | 0.873748 | + | 0.486379i | \(0.161683\pi\) | ||||
−0.873748 | + | 0.486379i | \(0.838317\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.92009 | − | 4.92009i | 1.36459 | − | 1.36459i | 0.496620 | − | 0.867968i | \(-0.334574\pi\) |
0.867968 | − | 0.496620i | \(-0.165426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.44072 | + | 3.44072i | −0.834498 | + | 0.834498i | −0.988128 | − | 0.153631i | \(-0.950903\pi\) |
0.153631 | + | 0.988128i | \(0.450903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.09153i | 0.250415i | 0.992131 | + | 0.125207i | \(0.0399596\pi\) | ||||
−0.992131 | + | 0.125207i | \(0.960040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41868 | − | 4.79451i | 0.283737 | − | 0.958902i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.42174 | −1.19249 | −0.596244 | − | 0.802803i | \(-0.703341\pi\) | ||||
−0.596244 | + | 0.802803i | \(0.703341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.08128 | −0.912626 | −0.456313 | − | 0.889819i | \(-0.650830\pi\) | ||||
−0.456313 | + | 0.889819i | \(0.650830\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.49993 | + | 0.941481i | 1.09869 | + | 0.159139i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.18217 | + | 3.18217i | 0.523145 | + | 0.523145i | 0.918520 | − | 0.395375i | \(-0.129385\pi\) |
−0.395375 | + | 0.918520i | \(0.629385\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.93089i | 0.613901i | 0.951725 | + | 0.306951i | \(0.0993087\pi\) | ||||
−0.951725 | + | 0.306951i | \(0.900691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.659981 | + | 0.659981i | −0.100646 | + | 0.100646i | −0.755637 | − | 0.654991i | \(-0.772673\pi\) |
0.654991 | + | 0.755637i | \(0.272673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.43041 | − | 9.43041i | 1.37557 | − | 1.37557i | 0.523608 | − | 0.851960i | \(-0.324586\pi\) |
0.851960 | − | 0.523608i | \(-0.175414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.62709i | 0.232441i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.54110 | − | 5.54110i | −0.761128 | − | 0.761128i | 0.215398 | − | 0.976526i | \(-0.430895\pi\) |
−0.976526 | + | 0.215398i | \(0.930895\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.31725 | − | 5.77975i | −0.582138 | − | 0.779342i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.11321 | 0.275117 | 0.137559 | − | 0.990494i | \(-0.456074\pi\) | ||||
0.137559 | + | 0.990494i | \(0.456074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.31239 | −0.168035 | −0.0840174 | − | 0.996464i | \(-0.526775\pi\) | ||||
−0.0840174 | + | 0.996464i | \(0.526775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.23032 | + | 15.3980i | −0.276637 | + | 1.90989i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.76215 | + | 7.76215i | 0.948298 | + | 0.948298i | 0.998728 | − | 0.0504298i | \(-0.0160591\pi\) |
−0.0504298 | + | 0.998728i | \(0.516059\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.31910i | − | 0.512583i | −0.966600 | − | 0.256291i | \(-0.917499\pi\) | ||
0.966600 | − | 0.256291i | \(-0.0825007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.21024 | + | 7.21024i | −0.843895 | + | 0.843895i | −0.989363 | − | 0.145468i | \(-0.953531\pi\) |
0.145468 | + | 0.989363i | \(0.453531\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.70067 | − | 6.70067i | 0.763612 | − | 0.763612i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.2687i | − | 1.15532i | −0.816277 | − | 0.577661i | \(-0.803965\pi\) | ||
0.816277 | − | 0.577661i | \(-0.196035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.143504 | + | 0.143504i | 0.0157516 | + | 0.0157516i | 0.714939 | − | 0.699187i | \(-0.246455\pi\) |
−0.699187 | + | 0.714939i | \(0.746455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.55971 | − | 10.7681i | 0.169174 | − | 1.16797i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9640 | 1.58618 | 0.793090 | − | 0.609105i | \(-0.208471\pi\) | ||||
0.793090 | + | 0.609105i | \(0.208471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.4371 | −2.14240 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.46064 | − | 1.95544i | −0.149859 | − | 0.200624i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.05998 | + | 5.05998i | 0.513763 | + | 0.513763i | 0.915677 | − | 0.401914i | \(-0.131655\pi\) |
−0.401914 | + | 0.915677i | \(0.631655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.34542i | 0.432386i | 0.976351 | + | 0.216193i | \(0.0693640\pi\) | ||||
−0.976351 | + | 0.216193i | \(0.930636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5424 | − | 13.5424i | 1.33437 | − | 1.33437i | 0.432955 | − | 0.901416i | \(-0.357471\pi\) |
0.901416 | − | 0.432955i | \(-0.142529\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.26237 | + | 4.26237i | −0.412059 | + | 0.412059i | −0.882455 | − | 0.470396i | \(-0.844111\pi\) |
0.470396 | + | 0.882455i | \(0.344111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.29238i | − | 0.506918i | −0.967346 | − | 0.253459i | \(-0.918432\pi\) | ||
0.967346 | − | 0.253459i | \(-0.0815682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0012 | + | 10.0012i | 0.940830 | + | 0.940830i | 0.998345 | − | 0.0575143i | \(-0.0183175\pi\) |
−0.0575143 | + | 0.998345i | \(0.518317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.21297 | − | 0.320538i | −0.206361 | − | 0.0298903i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.2921 | 1.31016 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.591160 | 0.0537418 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.87428 | + | 10.4876i | 0.346526 | + | 0.938040i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.950873 | − | 0.950873i | −0.0843763 | − | 0.0843763i | 0.663659 | − | 0.748035i | \(-0.269003\pi\) |
−0.748035 | + | 0.663659i | \(0.769003\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.03565i | − | 0.789449i | −0.918800 | − | 0.394724i | \(-0.870840\pi\) | ||
0.918800 | − | 0.394724i | \(-0.129160\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.26701 | − | 2.26701i | 0.196575 | − | 0.196575i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5209 | − | 14.5209i | 1.24060 | − | 1.24060i | 0.280848 | − | 0.959752i | \(-0.409384\pi\) |
0.959752 | − | 0.280848i | \(-0.0906156\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.41041i | 0.289267i | 0.989485 | + | 0.144633i | \(0.0462003\pi\) | ||||
−0.989485 | + | 0.144633i | \(0.953800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8736 | + | 15.8736i | 1.32741 | + | 1.32741i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.5043 | − | 8.59328i | 0.955382 | − | 0.713633i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.97015 | 0.161401 | 0.0807003 | − | 0.996738i | \(-0.474284\pi\) | ||||
0.0807003 | + | 0.996738i | \(0.474284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6629 | 1.43739 | 0.718693 | − | 0.695327i | \(-0.244741\pi\) | ||||
0.718693 | + | 0.695327i | \(0.244741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.10294 | − | 6.79954i | 0.731165 | − | 0.546152i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2551 | + | 10.2551i | 0.818444 | + | 0.818444i | 0.985882 | − | 0.167439i | \(-0.0535497\pi\) |
−0.167439 | + | 0.985882i | \(0.553550\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2.93719i | − | 0.231483i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74811 | + | 2.74811i | −0.215249 | + | 0.215249i | −0.806493 | − | 0.591244i | \(-0.798637\pi\) |
0.591244 | + | 0.806493i | \(0.298637\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.98842 | − | 4.98842i | 0.386016 | − | 0.386016i | −0.487248 | − | 0.873264i | \(-0.661999\pi\) |
0.873264 | + | 0.487248i | \(0.161999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 35.4146i | − | 2.72420i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2447 | + | 14.2447i | 1.08300 | + | 1.08300i | 0.996228 | + | 0.0867761i | \(0.0276565\pi\) |
0.0867761 | + | 0.996228i | \(0.472344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9042 | + | 7.01128i | −0.975468 | + | 0.530003i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5103 | −0.785573 | −0.392787 | − | 0.919630i | \(-0.628489\pi\) | ||||
−0.392787 | + | 0.919630i | \(0.628489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0040 | 1.18957 | 0.594785 | − | 0.803885i | \(-0.297237\pi\) | ||||
0.594785 | + | 0.803885i | \(0.297237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.95897 | − | 1.44251i | −0.732198 | − | 0.106055i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.1007 | − | 11.1007i | −0.811764 | − | 0.811764i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.10514i | 0.152323i | 0.997096 | + | 0.0761613i | \(0.0242664\pi\) | ||||
−0.997096 | + | 0.0761613i | \(0.975734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3295 | − | 13.3295i | 0.959482 | − | 0.959482i | −0.0397288 | − | 0.999210i | \(-0.512649\pi\) |
0.999210 | + | 0.0397288i | \(0.0126494\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5873 | − | 14.5873i | 1.03930 | − | 1.03930i | 0.0401091 | − | 0.999195i | \(-0.487229\pi\) |
0.999195 | − | 0.0401091i | \(-0.0127705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.9827i | − | 0.778545i | −0.921123 | − | 0.389273i | \(-0.872726\pi\) | ||
0.921123 | − | 0.389273i | \(-0.127274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.3374 | + | 13.3374i | 0.936099 | + | 0.936099i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.26014 | − | 7.04204i | −0.367384 | − | 0.491838i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.52159 | −0.243593 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0673 | 1.45033 | 0.725166 | − | 0.688574i | \(-0.241763\pi\) | ||||
0.725166 | + | 0.688574i | \(0.241763\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.299175 | − | 2.06549i | 0.0204036 | − | 0.140865i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5534 | + | 10.5534i | 0.716408 | + | 0.716408i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.8573i | 2.27749i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0582 | + | 15.0582i | −1.00837 | + | 1.00837i | −0.00840967 | + | 0.999965i | \(0.502677\pi\) |
−0.999965 | + | 0.00840967i | \(0.997323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.52586 | + | 5.52586i | −0.366764 | + | 0.366764i | −0.866296 | − | 0.499531i | \(-0.833506\pi\) |
0.499531 | + | 0.866296i | \(0.333506\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2128i | 1.40178i | 0.713269 | + | 0.700891i | \(0.247214\pi\) | ||||
−0.713269 | + | 0.700891i | \(0.752786\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.93354 | + | 6.93354i | 0.454231 | + | 0.454231i | 0.896756 | − | 0.442525i | \(-0.145917\pi\) |
−0.442525 | + | 0.896756i | \(0.645917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.27489 | + | 29.5136i | −0.278863 | + | 1.92525i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2837 | −1.05331 | −0.526653 | − | 0.850081i | \(-0.676553\pi\) | ||||
−0.526653 | + | 0.850081i | \(0.676553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.40648 | −0.219430 | −0.109715 | − | 0.993963i | \(-0.534994\pi\) | ||||
−0.109715 | + | 0.993963i | \(0.534994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17729 | − | 2.91487i | −0.139102 | − | 0.186224i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.37044 | + | 5.37044i | 0.341713 | + | 0.341713i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 28.7535i | − | 1.81490i | −0.420158 | − | 0.907451i | \(-0.638025\pi\) | ||
0.420158 | − | 0.907451i | \(-0.361975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28132 | + | 2.28132i | −0.143425 | + | 0.143425i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.06985 | − | 2.06985i | 0.129114 | − | 0.129114i | −0.639597 | − | 0.768711i | \(-0.720899\pi\) |
0.768711 | + | 0.639597i | \(0.220899\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.2181i | − | 0.821335i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.35079 | + | 3.35079i | 0.206619 | + | 0.206619i | 0.802829 | − | 0.596210i | \(-0.203327\pi\) |
−0.596210 | + | 0.802829i | \(0.703327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.3415 | + | 2.51183i | 1.06528 | + | 0.154300i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.03191 | 0.428743 | 0.214372 | − | 0.976752i | \(-0.431230\pi\) | ||||
0.214372 | + | 0.976752i | \(0.431230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7733 | −0.654432 | −0.327216 | − | 0.944950i | \(-0.606110\pi\) | ||||
−0.327216 | + | 0.944950i | \(0.606110\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4684 | + | 4.57706i | 0.932780 | + | 0.276007i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.25480 | + | 4.25480i | 0.255646 | + | 0.255646i | 0.823281 | − | 0.567634i | \(-0.192141\pi\) |
−0.567634 | + | 0.823281i | \(0.692141\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7221i | 1.29583i | 0.761711 | + | 0.647917i | \(0.224360\pi\) | ||||
−0.761711 | + | 0.647917i | \(0.775640\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.94900 | − | 7.94900i | 0.472519 | − | 0.472519i | −0.430210 | − | 0.902729i | \(-0.641560\pi\) |
0.902729 | + | 0.430210i | \(0.141560\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.16409 | − | 8.16409i | 0.481911 | − | 0.481911i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.67714i | − | 0.392773i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.0812 | − | 13.0812i | −0.764213 | − | 0.764213i | 0.212868 | − | 0.977081i | \(-0.431720\pi\) |
−0.977081 | + | 0.212868i | \(0.931720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.78575 | + | 2.82781i | −0.220415 | + | 0.164641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.95806 | 0.402395 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.74144 | 0.158014 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.35111 | − | 1.75619i | 0.134624 | − | 0.100559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9966 | − | 15.9966i | −0.912973 | − | 0.912973i | 0.0835323 | − | 0.996505i | \(-0.473380\pi\) |
−0.996505 | + | 0.0835323i | \(0.973380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14.9516i | − | 0.847825i | −0.905703 | − | 0.423913i | \(-0.860656\pi\) | ||
0.905703 | − | 0.423913i | \(-0.139344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7743 | + | 12.7743i | −0.722047 | + | 0.722047i | −0.969022 | − | 0.246975i | \(-0.920563\pi\) |
0.246975 | + | 0.969022i | \(0.420563\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8104 | − | 15.8104i | 0.888000 | − | 0.888000i | −0.106331 | − | 0.994331i | \(-0.533910\pi\) |
0.994331 | + | 0.106331i | \(0.0339103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 20.7183i | − | 1.16000i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.75566 | − | 3.75566i | −0.208971 | − | 0.208971i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.6094 | − | 30.5695i | −0.921323 | − | 1.69569i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.1722 | −2.15963 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.7571 | 1.03098 | 0.515491 | − | 0.856895i | \(-0.327609\pi\) | ||||
0.515491 | + | 0.856895i | \(0.327609\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.2926 | − | 3.51865i | −1.32725 | − | 0.192245i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.63677 | − | 8.63677i | −0.470475 | − | 0.470475i | 0.431593 | − | 0.902068i | \(-0.357952\pi\) |
−0.902068 | + | 0.431593i | \(0.857952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.3936i | − | 0.887764i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1590 | + | 11.1590i | −0.602532 | + | 0.602532i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.6113 | + | 17.6113i | −0.945424 | + | 0.945424i | −0.998586 | − | 0.0531621i | \(-0.983070\pi\) |
0.0531621 | + | 0.998586i | \(0.483070\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.3085i | 1.51532i | 0.652650 | + | 0.757659i | \(0.273657\pi\) | ||||
−0.652650 | + | 0.757659i | \(0.726343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.72532 | + | 8.72532i | 0.464402 | + | 0.464402i | 0.900095 | − | 0.435693i | \(-0.143497\pi\) |
−0.435693 | + | 0.900095i | \(0.643497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.77962 | + | 7.73751i | 0.306751 | + | 0.410664i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.2104 | 0.961107 | 0.480553 | − | 0.876965i | \(-0.340436\pi\) | ||||
0.480553 | + | 0.876965i | \(0.340436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8086 | 0.937292 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.26847 | − | 22.5653i | 0.171079 | − | 1.18112i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.0211932 | − | 0.0211932i | −0.00110627 | − | 0.00110627i | 0.706553 | − | 0.707660i | \(-0.250249\pi\) |
−0.707660 | + | 0.706553i | \(0.750249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.0167i | 1.19497i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.42722 | + | 7.42722i | −0.384567 | + | 0.384567i | −0.872744 | − | 0.488178i | \(-0.837662\pi\) |
0.488178 | + | 0.872744i | \(0.337662\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.5956 | + | 31.5956i | −1.62725 | + | 1.62725i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.8634i | − | 0.814849i | −0.913239 | − | 0.407425i | \(-0.866427\pi\) | ||
0.913239 | − | 0.407425i | \(-0.133573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.680180 | + | 0.680180i | 0.0347556 | + | 0.0347556i | 0.724271 | − | 0.689515i | \(-0.242176\pi\) |
−0.689515 | + | 0.724271i | \(0.742176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.03747 | + | 20.9705i | −0.154804 | + | 1.06876i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.9723 | 0.759127 | 0.379564 | − | 0.925166i | \(-0.376074\pi\) | ||||
0.379564 | + | 0.925166i | \(0.376074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.86592 | −0.246080 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7412 | + | 18.3961i | 0.691392 | + | 0.925606i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.5879 | − | 23.5879i | −1.18384 | − | 1.18384i | −0.978741 | − | 0.205100i | \(-0.934248\pi\) |
−0.205100 | − | 0.978741i | \(-0.565752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.70223i | − | 0.484506i | −0.970213 | − | 0.242253i | \(-0.922114\pi\) | ||
0.970213 | − | 0.242253i | \(-0.0778864\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.0004 | + | 25.0004i | −1.24536 | + | 1.24536i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2665 | + | 10.2665i | −0.508894 | + | 0.508894i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.5760i | − | 1.51189i | −0.654637 | − | 0.755944i | \(-0.727178\pi\) | ||
0.654637 | − | 0.755944i | \(-0.272822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.38895 | − | 4.38895i | −0.215966 | − | 0.215966i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.449111 | − | 0.0650515i | −0.0220460 | − | 0.00319325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.8248 | −0.577681 | −0.288840 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288840 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1695 | 1.42163 | 0.710816 | − | 0.703378i | \(-0.248326\pi\) | ||||
0.710816 | + | 0.703378i | \(0.248326\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6153 | + | 21.3779i | 0.563424 | + | 1.03698i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.72572 | + | 2.72572i | 0.131907 | + | 0.131907i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0979i | 0.871745i | 0.900009 | + | 0.435872i | \(0.143560\pi\) | ||||
−0.900009 | + | 0.435872i | \(0.856440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0949 | + | 13.0949i | −0.629302 | + | 0.629302i | −0.947892 | − | 0.318591i | \(-0.896790\pi\) |
0.318591 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.771831 | + | 0.771831i | −0.0369217 | + | 0.0369217i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.0592i | − | 1.91192i | −0.293494 | − | 0.955961i | \(-0.594818\pi\) | ||
0.293494 | − | 0.955961i | \(-0.405182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.50371 | + | 6.50371i | 0.309000 | + | 0.309000i | 0.844522 | − | 0.535521i | \(-0.179885\pi\) |
−0.535521 | + | 0.844522i | \(0.679885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.8074 | + | 20.0241i | −1.27079 | + | 0.949235i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.85394 | −0.465036 | −0.232518 | − | 0.972592i | \(-0.574696\pi\) | ||||
−0.232518 | + | 0.972592i | \(0.574696\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.6821 | −0.597178 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.6124 | − | 27.3481i | 1.71642 | − | 1.28210i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.3000 | + | 22.3000i | 1.04315 | + | 1.04315i | 0.999026 | + | 0.0441258i | \(0.0140502\pi\) |
0.0441258 | + | 0.999026i | \(0.485950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.7661i | 0.780876i | 0.920629 | + | 0.390438i | \(0.127676\pi\) | ||||
−0.920629 | + | 0.390438i | \(0.872324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.78426 | − | 4.78426i | 0.222343 | − | 0.222343i | −0.587141 | − | 0.809485i | \(-0.699747\pi\) |
0.809485 | + | 0.587141i | \(0.199747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.47320 | − | 1.47320i | 0.0681714 | − | 0.0681714i | −0.672199 | − | 0.740370i | \(-0.734650\pi\) |
0.740370 | + | 0.672199i | \(0.234650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 32.2425i | − | 1.48882i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.12928 | − | 2.12928i | −0.0979044 | − | 0.0979044i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.23337 | + | 1.54854i | 0.240123 | + | 0.0710519i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.87686 | −0.451285 | −0.225643 | − | 0.974210i | \(-0.572448\pi\) | ||||
−0.225643 | + | 0.974210i | \(0.572448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.3131 | 1.42775 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8358 | − | 2.29373i | −0.719067 | − | 0.104153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.2808 | − | 27.2808i | −1.23621 | − | 1.23621i | −0.961537 | − | 0.274675i | \(-0.911430\pi\) |
−0.274675 | − | 0.961537i | \(-0.588570\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.2576i | − | 0.733697i | −0.930281 | − | 0.366849i | \(-0.880437\pi\) | ||
0.930281 | − | 0.366849i | \(-0.119563\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0954 | − | 22.0954i | 0.995128 | − | 0.995128i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.97037 | + | 8.97037i | −0.402376 | + | 0.402376i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22.5006i | − | 1.00727i | −0.863918 | − | 0.503633i | \(-0.831997\pi\) | ||
0.863918 | − | 0.503633i | \(-0.168003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.90262 | − | 3.90262i | −0.174009 | − | 0.174009i | 0.614729 | − | 0.788738i | \(-0.289265\pi\) |
−0.788738 | + | 0.614729i | \(0.789265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.81485 | − | 7.78467i | −0.258757 | − | 0.346413i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.58821 | −0.0703961 | −0.0351980 | − | 0.999380i | \(-0.511206\pi\) | ||||
−0.0351980 | + | 0.999380i | \(0.511206\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.9500 | 1.32491 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.13888 | + | 42.3825i | −0.270512 | + | 1.86760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.4251 | + | 30.4251i | 1.33809 | + | 1.33809i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.3814i | − | 0.586249i | −0.956074 | − | 0.293125i | \(-0.905305\pi\) | ||
0.956074 | − | 0.293125i | \(-0.0946951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7895 | − | 17.7895i | 0.777881 | − | 0.777881i | −0.201589 | − | 0.979470i | \(-0.564611\pi\) |
0.979470 | + | 0.201589i | \(0.0646106\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.4833 | − | 17.4833i | 0.761584 | − | 0.761584i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3403 | + | 19.3403i | 0.837723 | + | 0.837723i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.93217 | − | 13.3396i | 0.0835350 | − | 0.576721i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.24942 | −0.226109 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.05304 | −0.303234 | −0.151617 | − | 0.988439i | \(-0.548448\pi\) | ||||
−0.151617 | + | 0.988439i | \(0.548448\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.08202 | + | 9.48110i | 0.303360 | + | 0.406126i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0260 | + | 28.0260i | 1.19830 | + | 1.19830i | 0.974674 | + | 0.223629i | \(0.0717903\pi\) |
0.223629 | + | 0.974674i | \(0.428210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.00955i | − | 0.298617i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.3272 | + | 21.3272i | −0.906925 | + | 0.906925i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.6010 | + | 21.6010i | −0.915263 | + | 0.915263i | −0.996680 | − | 0.0814174i | \(-0.974055\pi\) |
0.0814174 | + | 0.996680i | \(0.474055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.49433i | 0.274681i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.43394 | − | 8.43394i | −0.355448 | − | 0.355448i | 0.506684 | − | 0.862132i | \(-0.330871\pi\) |
−0.862132 | + | 0.506684i | \(0.830871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.2998 | − | 4.53362i | −1.31679 | − | 0.190731i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.5316 | 0.525352 | 0.262676 | − | 0.964884i | \(-0.415395\pi\) | ||||
0.262676 | + | 0.964884i | \(0.415395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.1831 | −1.22127 | −0.610637 | − | 0.791911i | \(-0.709086\pi\) | ||||
−0.610637 | + | 0.791911i | \(0.709086\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.39339 | − | 2.38707i | 0.183217 | − | 0.0995477i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5195 | + | 17.5195i | 0.729346 | + | 0.729346i | 0.970489 | − | 0.241143i | \(-0.0775224\pi\) |
−0.241143 | + | 0.970489i | \(0.577522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.596087i | − | 0.0247299i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.8771 | − | 17.8771i | 0.740394 | − | 0.740394i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.4525 | − | 27.4525i | 1.13309 | − | 1.13309i | 0.143426 | − | 0.989661i | \(-0.454188\pi\) |
0.989661 | − | 0.143426i | \(-0.0458118\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.54639i | − | 0.228535i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.8610 | − | 24.8610i | −1.02092 | − | 1.02092i | −0.999776 | − | 0.0211428i | \(-0.993270\pi\) |
−0.0211428 | − | 0.999776i | \(-0.506730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.6038 | + | 19.1251i | −1.04965 | + | 0.784051i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.7591 | 1.66537 | 0.832685 | − | 0.553747i | \(-0.186802\pi\) | ||||
0.832685 | + | 0.553747i | \(0.186802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0947750 | −0.00386595 | −0.00193298 | − | 0.999998i | \(-0.500615\pi\) | ||||
−0.00193298 | + | 0.999998i | \(0.500615\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.05904 | + | 0.791063i | −0.0430562 | + | 0.0321613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8813 | − | 11.8813i | −0.482246 | − | 0.482246i | 0.423602 | − | 0.905848i | \(-0.360766\pi\) |
−0.905848 | + | 0.423602i | \(0.860766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 92.7970i | − | 3.75416i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.27740 | + | 8.27740i | −0.334321 | + | 0.334321i | −0.854225 | − | 0.519904i | \(-0.825968\pi\) |
0.519904 | + | 0.854225i | \(0.325968\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.98713 | − | 2.98713i | 0.120257 | − | 0.120257i | −0.644417 | − | 0.764674i | \(-0.722900\pi\) |
0.764674 | + | 0.644417i | \(0.222900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.7419i | 1.03466i | 0.855787 | + | 0.517328i | \(0.173073\pi\) | ||||
−0.855787 | + | 0.517328i | \(0.826927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.0788 | − | 31.0788i | −1.24515 | − | 1.24515i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.9747 | − | 13.6038i | −0.838987 | − | 0.544152i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.8979 | −0.873127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.3196 | −1.32643 | −0.663215 | − | 0.748429i | \(-0.730809\pi\) | ||||
−0.663215 | + | 0.748429i | \(0.730809\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.97587 | + | 0.431039i | 0.118094 | + | 0.0171053i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.00541 | + | 8.00541i | 0.317186 | + | 0.317186i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 17.5390i | − | 0.692749i | −0.938096 | − | 0.346375i | \(-0.887413\pi\) | ||
0.938096 | − | 0.346375i | \(-0.112587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.97642 | − | 8.97642i | 0.353996 | − | 0.353996i | −0.507598 | − | 0.861594i | \(-0.669467\pi\) |
0.861594 | + | 0.507598i | \(0.169467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.46482 | + | 8.46482i | −0.332786 | + | 0.332786i | −0.853644 | − | 0.520857i | \(-0.825612\pi\) |
0.520857 | + | 0.853644i | \(0.325612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.81781i | 0.267622i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.27605 | − | 5.27605i | −0.206468 | − | 0.206468i | 0.596296 | − | 0.802764i | \(-0.296638\pi\) |
−0.802764 | + | 0.596296i | \(0.796638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0911 | + | 16.1870i | 0.472438 | + | 0.632480i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.6579 | −1.50590 | −0.752949 | − | 0.658078i | \(-0.771369\pi\) | ||||
−0.752949 | + | 0.658078i | \(0.771369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4444 | 0.717406 | 0.358703 | − | 0.933452i | \(-0.383219\pi\) | ||||
0.358703 | + | 0.933452i | \(0.383219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.02766 | + | 7.09489i | −0.0398509 | + | 0.275128i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.54086 | − | 4.54086i | −0.175823 | − | 0.175823i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.23414i | − | 0.163457i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6806 | + | 18.6806i | −0.720085 | + | 0.720085i | −0.968622 | − | 0.248537i | \(-0.920050\pi\) |
0.248537 | + | 0.968622i | \(0.420050\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.2105 | − | 20.2105i | 0.776752 | − | 0.776752i | −0.202525 | − | 0.979277i | \(-0.564915\pi\) |
0.979277 | + | 0.202525i | \(0.0649146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 21.0182i | − | 0.806605i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.59310 | − | 1.59310i | −0.0609583 | − | 0.0609583i | 0.675970 | − | 0.736929i | \(-0.263725\pi\) |
−0.736929 | + | 0.675970i | \(0.763725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.58243 | + | 45.4447i | −0.251502 | + | 1.73635i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.5254 | −2.07725 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.4395 | 1.27210 | 0.636049 | − | 0.771649i | \(-0.280568\pi\) | ||||
0.636049 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.56365 | − | 6.10962i | −0.173109 | − | 0.231751i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.5251 | − | 13.5251i | −0.512299 | − | 0.512299i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.10675i | 0.117340i | 0.998277 | + | 0.0586702i | \(0.0186860\pi\) | ||||
−0.998277 | + | 0.0586702i | \(0.981314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.47344 | + | 3.47344i | −0.131003 | + | 0.131003i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.02504 | − | 9.02504i | 0.339422 | − | 0.339422i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.6094i | 1.93823i | 0.246606 | + | 0.969116i | \(0.420685\pi\) | ||||
−0.246606 | + | 0.969116i | \(0.579315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.59301 | − | 3.59301i | −0.134559 | − | 0.134559i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.6782 | − | 7.19563i | −1.85786 | − | 0.269101i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4648 | −0.800501 | −0.400251 | − | 0.916406i | \(-0.631077\pi\) | ||||
−0.400251 | + | 0.916406i | \(0.631077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.2525 | −2.09495 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.11043 | + | 30.7891i | −0.338353 | + | 1.14348i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.11843 | + | 2.11843i | 0.0785683 | + | 0.0785683i | 0.745299 | − | 0.666731i | \(-0.232307\pi\) |
−0.666731 | + | 0.745299i | \(0.732307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.54162i | − | 0.167978i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.2780 | − | 23.2780i | 0.859793 | − | 0.859793i | −0.131520 | − | 0.991313i | \(-0.541986\pi\) |
0.991313 | + | 0.131520i | \(0.0419858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.0428 | + | 25.0428i | −0.922464 | + | 0.922464i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 31.1982i | − | 1.14765i | −0.818979 | − | 0.573823i | \(-0.805460\pi\) | ||
0.818979 | − | 0.573823i | \(-0.194540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0202 | + | 31.0202i | 1.13802 | + | 1.13802i | 0.988805 | + | 0.149215i | \(0.0476747\pi\) |
0.149215 | + | 0.988805i | \(0.452325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.52945 | + | 2.63636i | −0.129309 | + | 0.0965888i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.7051 | 0.646930 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.4332 | −1.22000 | −0.609998 | − | 0.792403i | \(-0.708830\pi\) | ||||
−0.609998 | + | 0.792403i | \(0.708830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.6425 | + | 23.6357i | −1.15159 | + | 0.860191i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.2431 | + | 17.2431i | 0.626711 | + | 0.626711i | 0.947239 | − | 0.320528i | \(-0.103860\pi\) |
−0.320528 | + | 0.947239i | \(0.603860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 9.73407i | − | 0.352860i | −0.984313 | − | 0.176430i | \(-0.943545\pi\) | ||
0.984313 | − | 0.176430i | \(-0.0564549\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9918 | + | 10.9918i | −0.397929 | + | 0.397929i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3972 | − | 10.3972i | 0.375421 | − | 0.375421i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.6710i | 0.565111i | 0.959251 | + | 0.282555i | \(0.0911821\pi\) | ||||
−0.959251 | + | 0.282555i | \(0.908818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.8704 | − | 16.8704i | −0.606785 | − | 0.606785i | 0.335320 | − | 0.942104i | \(-0.391156\pi\) |
−0.942104 | + | 0.335320i | \(0.891156\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.20874 | + | 24.3623i | −0.258946 | + | 0.875119i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.29069 | −0.153730 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.9346 | 0.498619 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.0945 | − | 4.64872i | −1.14550 | − | 0.165920i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.3273 | + | 30.3273i | 1.08105 | + | 1.08105i | 0.996411 | + | 0.0846416i | \(0.0269745\pi\) |
0.0846416 | + | 0.996411i | \(0.473025\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 41.5430i | − | 1.47710i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.45710 | + | 6.45710i | −0.229298 | + | 0.229298i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5433 | − | 11.5433i | 0.408884 | − | 0.408884i | −0.472465 | − | 0.881349i | \(-0.656636\pi\) |
0.881349 | + | 0.472465i | \(0.156636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.8949i | 2.29582i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.2622 | − | 23.2622i | −0.820905 | − | 0.820905i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.93041 | + | 5.26187i | 0.138529 | + | 0.185457i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6886 | −1.07895 | −0.539477 | − | 0.842000i | \(-0.681378\pi\) | ||||
−0.539477 | + | 0.842000i | \(0.681378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.2923 | 1.37974 | 0.689870 | − | 0.723933i | \(-0.257668\pi\) | ||||
0.689870 | + | 0.723933i | \(0.257668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.24574 | − | 8.60054i | 0.0436365 | − | 0.301264i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.720391 | − | 0.720391i | −0.0252033 | − | 0.0252033i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.4437i | 1.13229i | 0.824305 | + | 0.566147i | \(0.191566\pi\) | ||||
−0.824305 | + | 0.566147i | \(0.808434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.8530 | + | 12.8530i | −0.448027 | + | 0.448027i | −0.894698 | − | 0.446671i | \(-0.852609\pi\) |
0.446671 | + | 0.894698i | \(0.352609\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6467 | − | 25.6467i | 0.891825 | − | 0.891825i | −0.102870 | − | 0.994695i | \(-0.532803\pi\) |
0.994695 | + | 0.102870i | \(0.0328026\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.25217i | − | 0.147684i | −0.997270 | − | 0.0738420i | \(-0.976474\pi\) | ||
0.997270 | − | 0.0738420i | \(-0.0235260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.59835 | − | 5.59835i | −0.193971 | − | 0.193971i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.26130 | + | 15.6119i | −0.0782554 | + | 0.540270i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0668 | −0.416593 | −0.208296 | − | 0.978066i | \(-0.566792\pi\) | ||||
−0.208296 | + | 0.978066i | \(0.566792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2388 | 0.422027 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.3902 | + | 63.4440i | 1.63027 | + | 2.18254i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.22778 | − | 1.22778i | −0.0421872 | − | 0.0421872i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.50026i | 0.154267i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.5521 | + | 16.5521i | −0.566734 | + | 0.566734i | −0.931212 | − | 0.364478i | \(-0.881247\pi\) |
0.364478 | + | 0.931212i | \(0.381247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.4281 | + | 37.4281i | −1.27852 | + | 1.27852i | −0.337024 | + | 0.941496i | \(0.609420\pi\) |
−0.941496 | + | 0.337024i | \(0.890580\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.01433i | 0.273445i | 0.990609 | + | 0.136723i | \(0.0436569\pi\) | ||||
−0.990609 | + | 0.136723i | \(0.956343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.333122 | − | 0.333122i | −0.0113396 | − | 0.0113396i | 0.701414 | − | 0.712754i | \(-0.252552\pi\) |
−0.712754 | + | 0.701414i | \(0.752552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.5805 | − | 6.45725i | −1.51578 | − | 0.219553i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.1297 | 1.12385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.3810 | 2.58807 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.7353 | − | 29.8283i | 0.464337 | − | 1.00838i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0535 | + | 26.0535i | 0.879765 | + | 0.879765i | 0.993510 | − | 0.113745i | \(-0.0362846\pi\) |
−0.113745 | + | 0.993510i | \(0.536285\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.3712i | 0.618943i | 0.950909 | + | 0.309471i | \(0.100152\pi\) | ||||
−0.950909 | + | 0.309471i | \(0.899848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.69116 | + | 5.69116i | −0.191523 | + | 0.191523i | −0.796354 | − | 0.604831i | \(-0.793241\pi\) |
0.604831 | + | 0.796354i | \(0.293241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.36609 | − | 9.36609i | 0.314483 | − | 0.314483i | −0.532161 | − | 0.846643i | \(-0.678620\pi\) |
0.846643 | + | 0.532161i | \(0.178620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.94975i | 0.132470i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2936 | + | 10.2936i | 0.344463 | + | 0.344463i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.8287 | − | 14.0643i | 0.629375 | − | 0.470119i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.6307 | 1.08829 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.1308 | 1.27032 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.6706 | + | 21.4159i | −0.953044 | + | 0.711887i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.8287 | + | 15.8287i | 0.525584 | + | 0.525584i | 0.919252 | − | 0.393669i | \(-0.128794\pi\) |
−0.393669 | + | 0.919252i | \(0.628794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27.6363i | − | 0.915633i | −0.889047 | − | 0.457816i | \(-0.848632\pi\) | ||
0.889047 | − | 0.457816i | \(-0.151368\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.462982 | + | 0.462982i | −0.0153225 | + | 0.0153225i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.7662 | + | 18.7662i | −0.619715 | + | 0.619715i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.9429i | − | 1.11967i | −0.828603 | − | 0.559836i | \(-0.810864\pi\) | ||
0.828603 | − | 0.559836i | \(-0.189136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.2504 | − | 21.2504i | −0.699465 | − | 0.699465i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.7714 | − | 10.7424i | 0.650080 | − | 0.353209i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.7087 | −1.17156 | −0.585781 | − | 0.810469i | \(-0.699212\pi\) | ||||
−0.585781 | + | 0.810469i | \(0.699212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.77602 | −0.0582067 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.7410 | + | 5.03205i | 1.13615 | + | 0.164566i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1663 | + | 27.1663i | 0.887485 | + | 0.887485i | 0.994281 | − | 0.106796i | \(-0.0340592\pi\) |
−0.106796 | + | 0.994281i | \(0.534059\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.2931i | − | 0.563738i | −0.959453 | − | 0.281869i | \(-0.909046\pi\) | ||
0.959453 | − | 0.281869i | \(-0.0909544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.77956 | + | 2.77956i | −0.0905148 | + | 0.0905148i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6872 | − | 19.6872i | 0.639747 | − | 0.639747i | −0.310746 | − | 0.950493i | \(-0.600579\pi\) |
0.950493 | + | 0.310746i | \(0.100579\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 70.9501i | 2.30314i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.38568 | + | 7.38568i | 0.239246 | + | 0.239246i | 0.816538 | − | 0.577292i | \(-0.195891\pi\) |
−0.577292 | + | 0.816538i | \(0.695891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.81700 | − | 3.77128i | −0.0911561 | − | 0.122036i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −60.3169 | −1.94773 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.18055 | −0.167115 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.04240 | + | 41.7164i | −0.194512 | + | 1.34290i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2008 | + | 36.2008i | 1.16414 | + | 1.16414i | 0.983560 | + | 0.180580i | \(0.0577973\pi\) |
0.180580 | + | 0.983560i | \(0.442203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 7.32294i | − | 0.235004i | −0.993073 | − | 0.117502i | \(-0.962511\pi\) | ||
0.993073 | − | 0.117502i | \(-0.0374887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.08310 | − | 7.08310i | 0.227074 | − | 0.227074i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.4203 | + | 17.4203i | −0.557325 | + | 0.557325i | −0.928545 | − | 0.371220i | \(-0.878939\pi\) |
0.371220 | + | 0.928545i | \(0.378939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.2779i | 1.54297i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.3561 | − | 39.3561i | −1.25526 | − | 1.25526i | −0.953328 | − | 0.301936i | \(-0.902367\pi\) |
−0.301936 | − | 0.953328i | \(-0.597633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.61257 | + | 45.6528i | −0.210694 | + | 1.45462i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.933354 | −0.0296789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.3377 | −1.09077 | −0.545386 | − | 0.838185i | \(-0.683617\pi\) | ||||
−0.545386 | + | 0.838185i | \(0.683617\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.6966 | + | 19.6752i | 0.465913 | + | 0.623745i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.1018 | − | 14.1018i | −0.446609 | − | 0.446609i | 0.447616 | − | 0.894226i | \(-0.352273\pi\) |
−0.894226 | + | 0.447616i | \(0.852273\pi\) | |||||||
\(998\) | 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 | 4140.2.s.b.737.5 | ✓ | 44 | |
3.2 | odd | 2 | inner | 4140.2.s.b.737.18 | yes | 44 | |
5.3 | odd | 4 | inner | 4140.2.s.b.2393.18 | yes | 44 | |
15.8 | even | 4 | inner | 4140.2.s.b.2393.5 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.s.b.737.5 | ✓ | 44 | 1.1 | even | 1 | trivial | |
4140.2.s.b.737.18 | yes | 44 | 3.2 | odd | 2 | inner | |
4140.2.s.b.2393.5 | yes | 44 | 15.8 | even | 4 | inner | |
4140.2.s.b.2393.18 | yes | 44 | 5.3 | odd | 4 | inner |