Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.12 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.a.2591.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.43403 | + | 1.98264i | 1.53575 | + | 0.886663i | 0.999081 | + | 0.0428680i | \(0.0136495\pi\) |
0.536665 | + | 0.843795i | \(0.319684\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01359i | 0.761066i | 0.924767 | + | 0.380533i | \(0.124259\pi\) | ||||
−0.924767 | + | 0.380533i | \(0.875741\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.45028 | 1.04030 | 0.520150 | − | 0.854075i | \(-0.325876\pi\) | ||||
0.520150 | + | 0.854075i | \(0.325876\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.581638 | + | 1.00743i | 0.161317 | + | 0.279410i | 0.935341 | − | 0.353746i | \(-0.115092\pi\) |
−0.774024 | + | 0.633156i | \(0.781759\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.94137 | − | 1.12085i | −0.470850 | − | 0.271846i | 0.245745 | − | 0.969334i | \(-0.420967\pi\) |
−0.716596 | + | 0.697489i | \(0.754301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27660 | + | 0.843027i | −0.981119 | + | 0.193404i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.36603 | + | 2.36603i | 0.284836 | + | 0.493351i | 0.972570 | − | 0.232612i | \(-0.0747274\pi\) |
−0.687733 | + | 0.725964i | \(0.741394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.36172 | + | 9.28677i | 1.07234 | + | 1.85735i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0525704 | + | 0.0303515i | −0.00976207 | + | 0.00563614i | −0.504873 | − | 0.863194i | \(-0.668461\pi\) |
0.495111 | + | 0.868830i | \(0.335127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.92460i | 0.525274i | 0.964895 | + | 0.262637i | \(0.0845921\pi\) | ||||
−0.964895 | + | 0.262637i | \(0.915408\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.99223 | + | 6.91474i | −0.674809 | + | 1.16880i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5602 | 1.73608 | 0.868040 | − | 0.496494i | \(-0.165380\pi\) | ||||
0.868040 | + | 0.496494i | \(0.165380\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.71482 | + | 5.60885i | 1.51720 | + | 0.875956i | 0.999796 | + | 0.0202151i | \(0.00643509\pi\) |
0.517405 | + | 0.855741i | \(0.326898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.21445 | − | 3.58792i | −0.947695 | − | 0.547152i | −0.0553311 | − | 0.998468i | \(-0.517621\pi\) |
−0.892364 | + | 0.451316i | \(0.850955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.99139 | − | 10.3774i | −0.873934 | − | 1.51370i | −0.857894 | − | 0.513827i | \(-0.828227\pi\) |
−0.0160399 | − | 0.999871i | \(-0.505106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.94545 | 0.420778 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.31473 | + | 1.33641i | −0.317952 | + | 0.183570i | −0.650479 | − | 0.759524i | \(-0.725432\pi\) |
0.332527 | + | 0.943094i | \(0.392099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.8484 | + | 6.84067i | 1.59764 | + | 0.922396i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.08260 | + | 10.5354i | −0.791887 | + | 1.37159i | 0.132910 | + | 0.991128i | \(0.457568\pi\) |
−0.924797 | + | 0.380461i | \(0.875765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.76443 | − | 6.52019i | −0.481986 | − | 0.834825i | 0.517800 | − | 0.855502i | \(-0.326751\pi\) |
−0.999786 | + | 0.0206771i | \(0.993418\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.61271i | 0.572137i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.77551 | − | 1.60244i | 0.339082 | − | 0.195769i | −0.320784 | − | 0.947152i | \(-0.603946\pi\) |
0.659866 | + | 0.751383i | \(0.270613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.20934 | − | 7.29079i | 0.499557 | − | 0.865258i | −0.500443 | − | 0.865770i | \(-0.666829\pi\) |
1.00000 | 0.000511518i | \(0.000162821\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.71876 | − | 2.97697i | 0.201165 | − | 0.348428i | −0.747739 | − | 0.663993i | \(-0.768860\pi\) |
0.948904 | + | 0.315564i | \(0.102194\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.94746i | 0.791737i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.16778 | − | 2.98362i | −0.581421 | − | 0.335683i | 0.180277 | − | 0.983616i | \(-0.442301\pi\) |
−0.761698 | + | 0.647932i | \(0.775634\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1548 | −1.33416 | −0.667079 | − | 0.744987i | \(-0.732455\pi\) | ||||
−0.667079 | + | 0.744987i | \(0.732455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.44448 | − | 7.69806i | −0.482071 | − | 0.834972i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2015 | + | 7.04454i | −1.29336 | + | 0.746720i | −0.979248 | − | 0.202667i | \(-0.935039\pi\) |
−0.314109 | + | 0.949387i | \(0.601706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02855 | + | 1.17118i | −0.212649 | + | 0.122773i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.3574 | − | 5.58397i | −1.67823 | − | 0.572903i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.03755 | − | 8.72530i | 0.511486 | − | 0.885920i | −0.488425 | − | 0.872606i | \(-0.662429\pi\) |
0.999911 | − | 0.0133139i | \(-0.00423808\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.305411 | + | 0.176329i | −0.0303895 | + | 0.0175454i | −0.515118 | − | 0.857119i | \(-0.672252\pi\) |
0.484728 | + | 0.874665i | \(0.338918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.1116i | 1.39046i | 0.718789 | + | 0.695229i | \(0.244697\pi\) | ||||
−0.718789 | + | 0.695229i | \(0.755303\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.568348 | 0.0549443 | 0.0274721 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274721 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.79592 | + | 6.57472i | −0.363583 | + | 0.629744i | −0.988548 | − | 0.150909i | \(-0.951780\pi\) |
0.624965 | + | 0.780653i | \(0.285113\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.53420i | 0.708758i | 0.935102 | + | 0.354379i | \(0.115308\pi\) | ||||
−0.935102 | + | 0.354379i | \(0.884692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8334i | 1.01022i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.25693 | − | 3.90912i | 0.206892 | − | 0.358348i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.904464 | 0.0822240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.6950i | 2.02990i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9834 | − | 10.9601i | 1.68451 | − | 0.972550i | 0.725906 | − | 0.687794i | \(-0.241421\pi\) |
0.958600 | − | 0.284755i | \(-0.0919124\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.400659 | + | 0.693962i | −0.0350057 | + | 0.0606317i | −0.882997 | − | 0.469378i | \(-0.844478\pi\) |
0.847992 | + | 0.530009i | \(0.177812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.69751 | − | 8.61133i | −0.147193 | − | 0.746697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.2281 | + | 7.05989i | −1.04472 | + | 0.603167i | −0.921165 | − | 0.389171i | \(-0.872761\pi\) |
−0.123550 | + | 0.992338i | \(0.539428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3243 | − | 8.84752i | 1.29979 | − | 0.750436i | 0.319426 | − | 0.947611i | \(-0.396510\pi\) |
0.980368 | + | 0.197175i | \(0.0631767\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00682 | + | 3.47591i | 0.167818 | + | 0.290670i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.240704 | −0.0199894 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.11433 | + | 2.95276i | 0.418982 | + | 0.241900i | 0.694642 | − | 0.719356i | \(-0.255563\pi\) |
−0.275660 | + | 0.961255i | \(0.588896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.22190i | 0.343573i | 0.985134 | + | 0.171787i | \(0.0549540\pi\) | ||||
−0.985134 | + | 0.171787i | \(0.945046\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.79843 | + | 10.0432i | −0.465741 | + | 0.806687i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.17447 | − | 7.23039i | 0.333159 | − | 0.577048i | −0.649970 | − | 0.759959i | \(-0.725219\pi\) |
0.983129 | + | 0.182911i | \(0.0585521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.76422 | + | 2.75062i | −0.375473 | + | 0.216779i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.38206i | 0.343229i | 0.985164 | + | 0.171615i | \(0.0548984\pi\) | ||||
−0.985164 | + | 0.171615i | \(0.945102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0993411 | − | 0.172064i | −0.00768724 | − | 0.0133147i | 0.862156 | − | 0.506643i | \(-0.169114\pi\) |
−0.869843 | + | 0.493328i | \(0.835780\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.82339 | − | 10.0864i | 0.447953 | − | 0.775878i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.74407 | − | 1.00694i | −0.132599 | − | 0.0765562i | 0.432233 | − | 0.901762i | \(-0.357726\pi\) |
−0.564832 | + | 0.825206i | \(0.691059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.6998 | + | 10.7963i | −1.41357 | + | 0.816124i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2320 | 0.914265 | 0.457133 | − | 0.889399i | \(-0.348876\pi\) | ||||
0.457133 | + | 0.889399i | \(0.348876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.42980 | − | 4.20854i | −0.180606 | − | 0.312818i | 0.761481 | − | 0.648187i | \(-0.224472\pi\) |
−0.942087 | + | 0.335369i | \(0.891139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 36.2639 | + | 20.9370i | 2.66618 | + | 1.53932i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.69827 | − | 3.86725i | −0.489826 | − | 0.282801i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2782 | −0.816063 | −0.408032 | − | 0.912968i | \(-0.633785\pi\) | ||||
−0.408032 | + | 0.912968i | \(0.633785\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.46037 | − | 5.99353i | 0.249083 | − | 0.431424i | −0.714189 | − | 0.699953i | \(-0.753204\pi\) |
0.963272 | + | 0.268529i | \(0.0865376\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 12.5858i | − | 0.896702i | −0.893858 | − | 0.448351i | \(-0.852011\pi\) | ||
0.893858 | − | 0.448351i | \(-0.147989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.34790 | + | 4.24231i | −0.520879 | + | 0.300730i | −0.737294 | − | 0.675572i | \(-0.763897\pi\) |
0.216415 | + | 0.976301i | \(0.430564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0611156 | − | 0.105855i | −0.00428947 | − | 0.00742958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.2407 | + | 38.5220i | 1.55336 | + | 2.69049i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.7555 | + | 2.90868i | −1.02066 | + | 0.201198i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.69295 | − | 5.01887i | −0.598447 | − | 0.345514i | 0.169983 | − | 0.985447i | \(-0.445629\pi\) |
−0.768430 | + | 0.639933i | \(0.778962\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.2271 | − | 24.6420i | −0.970279 | − | 1.68057i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.88895 | −0.399768 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.60771i | − | 0.175414i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.3326 | + | 12.3164i | 1.42854 | + | 0.824767i | 0.997006 | − | 0.0773302i | \(-0.0246396\pi\) |
0.431533 | + | 0.902097i | \(0.357973\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.6879 | 1.24036 | 0.620180 | − | 0.784459i | \(-0.287059\pi\) | ||||
0.620180 | + | 0.784459i | \(0.287059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1273 | 1.39613 | 0.698065 | − | 0.716034i | \(-0.254045\pi\) | ||||
0.698065 | + | 0.716034i | \(0.254045\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.7091 | − | 6.76023i | −0.767086 | − | 0.442877i | 0.0647482 | − | 0.997902i | \(-0.479376\pi\) |
−0.831834 | + | 0.555024i | \(0.812709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 47.5151i | − | 3.09954i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.03083 | −0.584156 | −0.292078 | − | 0.956395i | \(-0.594347\pi\) | ||||
−0.292078 | + | 0.956395i | \(0.594347\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.41260 | + | 11.1069i | 0.413072 | + | 0.715461i | 0.995224 | − | 0.0976185i | \(-0.0311225\pi\) |
−0.582152 | + | 0.813080i | \(0.697789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.1148 | + | 5.83976i | 0.646209 | + | 0.373089i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.33672 | − | 3.81802i | −0.212310 | − | 0.242935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.31032 | + | 5.73363i | 0.208945 | + | 0.361904i | 0.951383 | − | 0.308012i | \(-0.0996636\pi\) |
−0.742437 | + | 0.669916i | \(0.766330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.71318 | + | 8.16347i | 0.296315 | + | 0.513233i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.26650 | − | 4.77267i | 0.515650 | − | 0.297711i | −0.219503 | − | 0.975612i | \(-0.570444\pi\) |
0.735153 | + | 0.677901i | \(0.237110\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.2639i | 1.32127i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.80613 | − | 10.0565i | 0.358022 | − | 0.620112i | −0.629609 | − | 0.776912i | \(-0.716785\pi\) |
0.987630 | + | 0.156801i | \(0.0501181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5985 | −0.651058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4154 | − | 7.16804i | −0.756981 | − | 0.437043i | 0.0712296 | − | 0.997460i | \(-0.477308\pi\) |
−0.828211 | + | 0.560417i | \(0.810641\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4945 | − | 10.1004i | −1.06271 | − | 0.613558i | −0.136532 | − | 0.990636i | \(-0.543595\pi\) |
−0.926181 | + | 0.377078i | \(0.876929\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.4995 | + | 32.0420i | 1.11556 | + | 1.93220i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.68936 | 0.221672 | 0.110836 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110836 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.04933 | − | 5.22464i | 0.539838 | − | 0.311676i | −0.205175 | − | 0.978725i | \(-0.565776\pi\) |
0.745013 | + | 0.667050i | \(0.232443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.881832 | + | 0.509126i | 0.0524195 | + | 0.0302644i | 0.525981 | − | 0.850497i | \(-0.323698\pi\) |
−0.473561 | + | 0.880761i | \(0.657032\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.2939 | + | 19.5617i | −0.666660 | + | 1.15469i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.98740 | − | 10.3705i | −0.352200 | − | 0.610028i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1692i | 0.944613i | 0.881434 | + | 0.472307i | \(0.156578\pi\) | ||||
−0.881434 | + | 0.472307i | \(0.843422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.7757 | + | 24.1192i | −2.43228 | + | 1.40427i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.58907 | + | 2.75234i | −0.0918981 | + | 0.159172i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.22460 | − | 12.5134i | 0.416419 | − | 0.721259i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 29.8541i | − | 1.70944i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.2016 | + | 13.9728i | 1.38126 | + | 0.797469i | 0.992308 | − | 0.123791i | \(-0.0395052\pi\) |
0.388948 | + | 0.921260i | \(0.372839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.4234 | −0.987992 | −0.493996 | − | 0.869464i | \(-0.664464\pi\) | ||||
−0.493996 | + | 0.869464i | \(0.664464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4149 | + | 23.2353i | 0.758256 | + | 1.31334i | 0.943739 | + | 0.330690i | \(0.107282\pi\) |
−0.185483 | + | 0.982647i | \(0.559385\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.5318 | − | 15.8955i | 1.54634 | − | 0.892778i | 0.547920 | − | 0.836531i | \(-0.315420\pi\) |
0.998417 | − | 0.0562477i | \(-0.0179136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.181383 | + | 0.104721i | −0.0101555 | + | 0.00586327i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.24735 | + | 3.15679i | 0.514536 | + | 0.175649i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23716 | + | 10.8031i | −0.345975 | + | 0.599247i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.8958 | − | 12.0642i | 1.15202 | − | 0.665122i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4861i | 0.686299i | 0.939281 | + | 0.343150i | \(0.111494\pi\) | ||||
−0.939281 | + | 0.343150i | \(0.888506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7082 | 0.694326 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6772 | + | 20.2255i | −0.636096 | + | 1.10175i | 0.350185 | + | 0.936680i | \(0.386119\pi\) |
−0.986282 | + | 0.165071i | \(0.947215\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0907i | 0.546442i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0261i | 1.08131i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.78797 | + | 10.0251i | −0.310715 | + | 0.538174i | −0.978517 | − | 0.206165i | \(-0.933902\pi\) |
0.667803 | + | 0.744338i | \(0.267235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.34938 | −0.179288 | −0.0896441 | − | 0.995974i | \(-0.528573\pi\) | ||||
−0.0896441 | + | 0.995974i | \(0.528573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.21760i | 0.118031i | 0.998257 | + | 0.0590156i | \(0.0187962\pi\) | ||||
−0.998257 | + | 0.0590156i | \(0.981204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.9100 | − | 16.6912i | 1.53439 | − | 0.885878i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.9153 | − | 24.1020i | 0.734422 | − | 1.27206i | −0.220554 | − | 0.975375i | \(-0.570786\pi\) |
0.954976 | − | 0.296682i | \(-0.0958802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5786 | − | 7.21058i | 0.925190 | − | 0.379504i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.8045 | − | 6.81535i | 0.617878 | − | 0.356732i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3348 | − | 8.85356i | 0.800471 | − | 0.462152i | −0.0431651 | − | 0.999068i | \(-0.513744\pi\) |
0.843636 | + | 0.536916i | \(0.180411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.69098 | − | 4.66092i | −0.139709 | − | 0.241983i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5551 | −0.753632 | −0.376816 | − | 0.926288i | \(-0.622981\pi\) | ||||
−0.376816 | + | 0.926288i | \(0.622981\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0611538 | − | 0.0353072i | −0.00314958 | − | 0.00181841i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.2376i | 1.50184i | 0.660396 | + | 0.750918i | \(0.270389\pi\) | ||||
−0.660396 | + | 0.750918i | \(0.729611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0506 | + | 26.0684i | −0.769049 | + | 1.33203i | 0.169030 | + | 0.985611i | \(0.445936\pi\) |
−0.938079 | + | 0.346421i | \(0.887397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.7743 | + | 23.8578i | −0.702004 | + | 1.21591i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0759 | + | 17.9417i | −1.57561 | + | 0.909678i | −0.580148 | + | 0.814511i | \(0.697005\pi\) |
−0.995461 | + | 0.0951670i | \(0.969661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.12444i | − | 0.309726i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.8309 | − | 20.4917i | −0.595276 | − | 1.03105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.45262 | + | 2.51602i | −0.0729051 | + | 0.126275i | −0.900173 | − | 0.435532i | \(-0.856560\pi\) |
0.827268 | + | 0.561807i | \(0.189894\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.60454 | − | 5.54519i | −0.479628 | − | 0.276913i | 0.240633 | − | 0.970616i | \(-0.422645\pi\) |
−0.720261 | + | 0.693703i | \(0.755978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.94632 | + | 1.70106i | −0.146767 | + | 0.0847357i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.4356 | 1.80604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7055 | − | 34.1309i | −0.974375 | − | 1.68767i | −0.681984 | − | 0.731368i | \(-0.738882\pi\) |
−0.292391 | − | 0.956299i | \(-0.594451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.2139 | − | 12.2479i | −1.04387 | − | 0.602679i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.7398 | − | 24.0985i | −2.04893 | − | 1.18295i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.6128 | 1.25127 | 0.625634 | − | 0.780117i | \(-0.284840\pi\) | ||||
0.625634 | + | 0.780117i | \(0.284840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.77587 | − | 3.07590i | 0.0865507 | − | 0.149910i | −0.819500 | − | 0.573079i | \(-0.805749\pi\) |
0.906051 | + | 0.423169i | \(0.139082\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 24.0387i | − | 1.16605i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1290 | − | 7.58003i | 0.635357 | − | 0.366823i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2267 | − | 26.3734i | −0.733444 | − | 1.27036i | −0.955403 | − | 0.295307i | \(-0.904578\pi\) |
0.221958 | − | 0.975056i | \(-0.428755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.8335 | − | 34.3527i | −0.953140 | − | 1.65089i | −0.738569 | − | 0.674178i | \(-0.764498\pi\) |
−0.214570 | − | 0.976709i | \(-0.568835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.83658 | − | 8.96696i | −0.374875 | − | 0.428948i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.3319 | − | 15.7801i | −1.30448 | − | 0.753142i | −0.323311 | − | 0.946293i | \(-0.604796\pi\) |
−0.981169 | + | 0.193151i | \(0.938129\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5707 | − | 25.2371i | −0.692273 | − | 1.19905i | −0.971091 | − | 0.238709i | \(-0.923276\pi\) |
0.278818 | − | 0.960344i | \(-0.410057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −55.8671 | −2.64836 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.03245i | − | 0.0487241i | −0.999703 | − | 0.0243620i | \(-0.992245\pi\) | ||
0.999703 | − | 0.0243620i | \(-0.00775545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.5189 | + | 19.3521i | 1.57834 | + | 0.911257i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.28812 | −0.435434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.59378 | −0.261666 | −0.130833 | − | 0.991404i | \(-0.541765\pi\) | ||||
−0.130833 | + | 0.991404i | \(0.541765\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.5916 | − | 19.9715i | −1.61109 | − | 0.930165i | −0.989117 | − | 0.147128i | \(-0.952997\pi\) |
−0.621975 | − | 0.783037i | \(-0.713670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.1366i | − | 1.40057i | −0.713865 | − | 0.700283i | \(-0.753057\pi\) | ||
0.713865 | − | 0.700283i | \(-0.246943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.8956 | 1.01321 | 0.506603 | − | 0.862179i | \(-0.330901\pi\) | ||||
0.506603 | + | 0.862179i | \(0.330901\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.22666 | + | 5.58874i | 0.148993 | + | 0.258064i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4416 | − | 12.3793i | −0.985887 | − | 0.569202i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.7589 | − | 35.1957i | −1.41132 | − | 1.61489i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.01871 | + | 8.69266i | 0.229311 | + | 0.397178i | 0.957604 | − | 0.288088i | \(-0.0930195\pi\) |
−0.728293 | + | 0.685266i | \(0.759686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.14219 | + | 10.6386i | 0.280060 | + | 0.485078i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.5982 | − | 19.9753i | 1.57102 | − | 0.907032i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.09614i | − | 0.185614i | −0.995684 | − | 0.0928070i | \(-0.970416\pi\) | ||
0.995684 | − | 0.0928070i | \(-0.0295840\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8753 | − | 29.2288i | 0.761570 | − | 1.31908i | −0.180472 | − | 0.983580i | \(-0.557762\pi\) |
0.942041 | − | 0.335497i | \(-0.108904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.136078 | 0.00612863 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6807 | + | 8.47590i | 0.658519 | + | 0.380196i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9048 | + | 10.9147i | 0.846296 | + | 0.488609i | 0.859399 | − | 0.511305i | \(-0.170838\pi\) |
−0.0131035 | + | 0.999914i | \(0.504171\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.689494 | + | 1.19424i | 0.0307430 | + | 0.0532485i | 0.880988 | − | 0.473139i | \(-0.156879\pi\) |
−0.850245 | + | 0.526388i | \(0.823546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.39839 | −0.0622275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5531 | + | 7.24751i | −0.556404 | + | 0.321240i | −0.751701 | − | 0.659504i | \(-0.770766\pi\) |
0.195297 | + | 0.980744i | \(0.437433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.99441 | + | 3.46087i | 0.265177 | + | 0.153100i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −27.9782 | + | 48.4597i | −1.23287 | + | 2.13539i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.6720 | − | 35.8050i | −0.909153 | − | 1.57470i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9019i | 0.696673i | 0.937370 | + | 0.348336i | \(0.113253\pi\) | ||||
−0.937370 | + | 0.348336i | \(0.886747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0835 | − | 18.5234i | 1.40291 | − | 0.809971i | 0.408221 | − | 0.912883i | \(-0.366149\pi\) |
0.994690 | + | 0.102912i | \(0.0328160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.27803 | − | 5.67772i | 0.142793 | − | 0.247325i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.76794 | − | 13.4545i | 0.337736 | − | 0.584977i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.0493i | 0.565227i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.95172 | + | 1.12683i | 0.0843804 | + | 0.0487171i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1626 | 0.437736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1041 | − | 26.1611i | −0.649376 | − | 1.12475i | −0.983272 | − | 0.182143i | \(-0.941697\pi\) |
0.333896 | − | 0.942610i | \(-0.391637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.0706 | + | 15.0519i | −1.11674 | + | 0.644751i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0038 | − | 21.9415i | 1.62492 | − | 0.938151i | 0.639349 | − | 0.768917i | \(-0.279204\pi\) |
0.985576 | − | 0.169234i | \(-0.0541295\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.199235 | − | 0.174120i | 0.00848771 | − | 0.00741774i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00779 | − | 10.4058i | 0.255477 | − | 0.442500i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.14237 | + | 0.659549i | −0.0484039 | + | 0.0279460i | −0.524007 | − | 0.851714i | \(-0.675563\pi\) |
0.475603 | + | 0.879660i | \(0.342230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.34747i | − | 0.353060i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.8925 | 1.17553 | 0.587765 | − | 0.809032i | \(-0.300008\pi\) | ||||
0.587765 | + | 0.809032i | \(0.300008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.9376 | + | 25.8727i | −0.628429 | + | 1.08847i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.1984i | − | 0.762918i | −0.924386 | − | 0.381459i | \(-0.875422\pi\) | ||
0.924386 | − | 0.381459i | \(-0.124578\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.6385i | − | 0.696299i | −0.937439 | − | 0.348150i | \(-0.886810\pi\) | ||
0.937439 | − | 0.348150i | \(-0.113190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.6485 | + | 25.3720i | −0.610885 | + | 1.05808i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7146 | 0.903990 | 0.451995 | − | 0.892021i | \(-0.350713\pi\) | ||||
0.451995 | + | 0.892021i | \(0.350713\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 24.4747i | − | 1.01538i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.98647 | + | 4.61099i | −0.330766 | + | 0.190968i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.12021 | + | 5.40437i | −0.128785 | + | 0.223062i | −0.923206 | − | 0.384305i | \(-0.874441\pi\) |
0.794421 | + | 0.607367i | \(0.207774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.46552 | − | 12.5073i | −0.101590 | − | 0.515356i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.1517 | − | 8.17048i | 0.581140 | − | 0.335522i | −0.180446 | − | 0.983585i | \(-0.557754\pi\) |
0.761586 | + | 0.648063i | \(0.224421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.5007 | − | 8.94936i | 0.635469 | − | 0.366888i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8274 | − | 30.8780i | −0.728408 | − | 1.26164i | −0.957556 | − | 0.288248i | \(-0.906927\pi\) |
0.229148 | − | 0.973392i | \(-0.426406\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.6218 | −1.37146 | −0.685732 | − | 0.727855i | \(-0.740518\pi\) | ||||
−0.685732 | + | 0.727855i | \(0.740518\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.10596 | + | 1.79323i | 0.126275 | + | 0.0729050i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.30198i | − | 0.377556i | −0.982020 | − | 0.188778i | \(-0.939547\pi\) | ||
0.982020 | − | 0.188778i | \(-0.0604526\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.96964 | − | 12.0718i | 0.281961 | − | 0.488371i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6974 | − | 23.7245i | 0.553232 | − | 0.958225i | −0.444807 | − | 0.895626i | \(-0.646728\pi\) |
0.998039 | − | 0.0625989i | \(-0.0199389\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.43300 | − | 2.55939i | 0.178466 | − | 0.103037i | −0.408106 | − | 0.912935i | \(-0.633811\pi\) |
0.586572 | + | 0.809897i | \(0.300477\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.5902i | − | 1.43049i | −0.698874 | − | 0.715245i | \(-0.746315\pi\) | ||
0.698874 | − | 0.715245i | \(-0.253685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.1848 | − | 24.5688i | −0.568303 | − | 0.984330i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.1875 | + | 31.5016i | −0.727498 | + | 1.26006i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.5011 | − | 11.8363i | −0.817434 | − | 0.471946i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2225 | + | 16.8716i | −1.16333 | + | 0.671648i | −0.952099 | − | 0.305789i | \(-0.901080\pi\) |
−0.211229 | + | 0.977437i | \(0.567747\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 86.9195 | 3.44930 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.71318 | + | 2.96732i | 0.0678788 | + | 0.117570i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.8223 | − | 8.55766i | −0.585446 | − | 0.338007i | 0.177849 | − | 0.984058i | \(-0.443086\pi\) |
−0.763295 | + | 0.646051i | \(0.776419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.7033 | − | 18.3039i | −1.25025 | − | 0.721835i | −0.279094 | − | 0.960264i | \(-0.590034\pi\) |
−0.971160 | + | 0.238429i | \(0.923368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.1390 | −0.791746 | −0.395873 | − | 0.918305i | \(-0.629558\pi\) | ||||
−0.395873 | + | 0.918305i | \(0.629558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.9867 | + | 36.3500i | −0.823800 | + | 1.42686i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.6576i | − | 0.808394i | −0.914672 | − | 0.404197i | \(-0.867551\pi\) | ||
0.914672 | − | 0.404197i | \(-0.132449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.75175 | + | 1.58872i | −0.107520 | + | 0.0620766i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9945 | + | 19.0431i | 0.428285 | + | 0.741812i | 0.996721 | − | 0.0809156i | \(-0.0257844\pi\) |
−0.568435 | + | 0.822728i | \(0.692451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.94593 | + | 6.83455i | 0.153479 | + | 0.265833i | 0.932504 | − | 0.361159i | \(-0.117619\pi\) |
−0.779025 | + | 0.626993i | \(0.784286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.2438 | − | 32.9371i | 0.436017 | − | 1.27725i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.143625 | − | 0.0829220i | −0.00556119 | − | 0.00321075i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9884 | − | 22.4965i | −0.501410 | − | 0.868468i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9434 | 1.15423 | 0.577117 | − | 0.816662i | \(-0.304178\pi\) | ||||
0.577117 | + | 0.816662i | \(0.304178\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 23.5765i | − | 0.906120i | −0.891480 | − | 0.453060i | \(-0.850332\pi\) | ||
0.891480 | − | 0.453060i | \(-0.149668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5692 | + | 10.1436i | 0.674243 | + | 0.389275i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.9586 | 1.26112 | 0.630562 | − | 0.776139i | \(-0.282824\pi\) | ||||
0.630562 | + | 0.776139i | \(0.282824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.9888 | −2.13922 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.69267 | − | 1.55461i | −0.102582 | − | 0.0592260i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.8385i | 1.36336i | 0.731651 | + | 0.681680i | \(0.238750\pi\) | ||||
−0.731651 | + | 0.681680i | \(0.761250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 70.1657 | 2.66154 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5733 | − | 21.7777i | −0.476250 | − | 0.824888i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.8861 | + | 13.2133i | 0.864395 | + | 0.499059i | 0.865482 | − | 0.500941i | \(-0.167012\pi\) |
−0.00108645 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.1616 | + | 8.90251i | −1.70330 | + | 0.335764i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.355055 | − | 0.614973i | −0.0133532 | − | 0.0231285i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8389 | + | 44.7543i | 0.970401 | + | 1.68078i | 0.694346 | + | 0.719641i | \(0.255694\pi\) |
0.276055 | + | 0.961142i | \(0.410973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.91969 | + | 3.99508i | −0.259144 | + | 0.149617i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.9152i | 0.595194i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6038 | + | 21.8305i | −0.470043 | + | 0.814139i | −0.999413 | − | 0.0342525i | \(-0.989095\pi\) |
0.529370 | + | 0.848391i | \(0.322428\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.4150 | −1.05823 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.563735 | − | 0.325473i | −0.0209366 | − | 0.0120877i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.35763 | − | 1.93853i | −0.124528 | − | 0.0718960i | 0.436442 | − | 0.899732i | \(-0.356238\pi\) |
−0.560970 | + | 0.827836i | \(0.689572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.04302 | + | 13.9309i | 0.297482 | + | 0.515254i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0229 | 0.998115 | 0.499057 | − | 0.866569i | \(-0.333680\pi\) | ||||
0.499057 | + | 0.866569i | \(0.333680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.57629 | − | 5.52887i | 0.352747 | − | 0.203659i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6140 | + | 6.70537i | 0.427229 | + | 0.246661i | 0.698166 | − | 0.715936i | \(-0.254000\pi\) |
−0.270936 | + | 0.962597i | \(0.587333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.30822 | − | 5.73000i | 0.121367 | − | 0.210213i | −0.798940 | − | 0.601411i | \(-0.794606\pi\) |
0.920307 | + | 0.391197i | \(0.127939\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7085 | + | 20.2797i | 0.428967 | + | 0.742992i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.14442i | 0.0418162i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.29369 | + | 1.90162i | −0.120189 | + | 0.0693909i | −0.558889 | − | 0.829242i | \(-0.688772\pi\) |
0.438700 | + | 0.898633i | \(0.355439\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.37050 | + | 14.4981i | −0.304634 | + | 0.527641i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.06155 | + | 1.83865i | −0.0385826 | + | 0.0668270i | −0.884672 | − | 0.466214i | \(-0.845618\pi\) |
0.846089 | + | 0.533041i | \(0.178951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.72565i | − | 0.171305i | −0.996325 | − | 0.0856523i | \(-0.972703\pi\) | ||
0.996325 | − | 0.0856523i | \(-0.0272974\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2388 | − | 7.64343i | −0.479277 | − | 0.276711i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.1515 | −0.510981 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.04662 | + | 5.27690i | 0.109864 | + | 0.190290i | 0.915715 | − | 0.401828i | \(-0.131625\pi\) |
−0.805851 | + | 0.592118i | \(0.798292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.7456 | − | 6.78132i | 0.422460 | − | 0.243907i | −0.273669 | − | 0.961824i | \(-0.588237\pi\) |
0.696129 | + | 0.717917i | \(0.254904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.1601 | + | 15.6809i | −0.975619 | + | 0.563274i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −46.2748 | − | 15.7970i | −1.65797 | − | 0.565985i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5234 | − | 25.1553i | 0.519689 | − | 0.900128i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.6705 | − | 16.5529i | 1.02330 | − | 0.590800i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6702i | 0.594228i | 0.954842 | + | 0.297114i | \(0.0960241\pi\) | ||||
−0.954842 | + | 0.297114i | \(0.903976\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.1708 | −0.539411 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.37907 | − | 7.58478i | 0.155505 | − | 0.269343i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 29.7438i | − | 1.05358i | −0.849996 | − | 0.526790i | \(-0.823396\pi\) | ||
0.849996 | − | 0.526790i | \(-0.176604\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.8617i | 0.950300i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.93020 | − | 10.2714i | 0.209272 | − | 0.362470i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.8140 | −0.768841 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54.3612i | 1.91124i | 0.294608 | + | 0.955618i | \(0.404811\pi\) | ||||
−0.294608 | + | 0.955618i | \(0.595189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4006 | − | 18.7065i | 1.13774 | − | 0.656874i | 0.191869 | − | 0.981421i | \(-0.438545\pi\) |
0.945870 | + | 0.324547i | \(0.105212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.68804 | + | 15.0481i | −0.304329 | + | 0.527113i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6014 | + | 10.1051i | 1.03562 | + | 0.353534i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.6396 | − | 13.0710i | 0.790128 | − | 0.456180i | −0.0498798 | − | 0.998755i | \(-0.515884\pi\) |
0.840007 | + | 0.542575i | \(0.182550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.1146 | − | 17.3867i | 1.04973 | − | 0.606062i | 0.127156 | − | 0.991883i | \(-0.459415\pi\) |
0.922574 | + | 0.385821i | \(0.126082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.10335 | + | 14.0354i | 0.281781 | + | 0.488059i | 0.971823 | − | 0.235710i | \(-0.0757415\pi\) |
−0.690042 | + | 0.723769i | \(0.742408\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.59194 | 0.0552905 | 0.0276453 | − | 0.999618i | \(-0.491199\pi\) | ||||
0.0276453 | + | 0.999618i | \(0.491199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.71819 | − | 3.30140i | −0.198124 | − | 0.114387i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.787830i | − | 0.0272640i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.40972 | − | 7.63785i | 0.152240 | − | 0.263688i | −0.779810 | − | 0.626016i | \(-0.784685\pi\) |
0.932051 | + | 0.362328i | \(0.118018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4982 | + | 25.1115i | −0.499936 | + | 0.865915i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.9955 | − | 23.0914i | 1.37589 | − | 0.794368i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.82122i | 0.0625779i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.4255 | + | 24.9856i | 0.494499 | + | 0.856497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.3911 | + | 30.1223i | −0.595460 | + | 1.03137i | 0.398022 | + | 0.917376i | \(0.369697\pi\) |
−0.993482 | + | 0.113991i | \(0.963637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.9864 | − | 24.8182i | −1.46839 | − | 0.847773i | −0.469014 | − | 0.883191i | \(-0.655391\pi\) |
−0.999373 | + | 0.0354174i | \(0.988724\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9914 | + | 10.9647i | −0.647978 | + | 0.374110i | −0.787681 | − | 0.616083i | \(-0.788718\pi\) |
0.139703 | + | 0.990193i | \(0.455385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4011 | 0.592340 | 0.296170 | − | 0.955135i | \(-0.404290\pi\) | ||||
0.296170 | + | 0.955135i | \(0.404290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.99279 | − | 6.91572i | −0.135759 | − | 0.235142i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.8303 | − | 10.2943i | −0.604852 | − | 0.349212i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.22868 | + | 1.86408i | 0.109400 | + | 0.0631619i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −45.6985 | −1.54489 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9056 | − | 20.6212i | 0.402025 | − | 0.696328i | −0.591945 | − | 0.805978i | \(-0.701640\pi\) |
0.993970 | + | 0.109651i | \(0.0349732\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 38.8172i | − | 1.30779i | −0.756587 | − | 0.653893i | \(-0.773135\pi\) | ||
0.756587 | − | 0.653893i | \(-0.226865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1788 | + | 10.4955i | −0.611765 | + | 0.353203i | −0.773656 | − | 0.633606i | \(-0.781574\pi\) |
0.161891 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5521 | + | 32.1331i | 0.622918 | + | 1.07893i | 0.988940 | + | 0.148319i | \(0.0473862\pi\) |
−0.366022 | + | 0.930606i | \(0.619280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.0691 | + | 38.2249i | 0.740175 | + | 1.28202i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.3712 | + | 39.3290i | 1.15019 | + | 1.31610i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.0052 | + | 24.2517i | 1.40408 | + | 0.810645i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0887661 | − | 0.153747i | −0.00296051 | − | 0.00512776i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.99164 | 0.199611 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.2697i | − | 0.640546i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.8981 | − | 13.7976i | −0.793522 | − | 0.458140i | 0.0476787 | − | 0.998863i | \(-0.484818\pi\) |
−0.841201 | + | 0.540722i | \(0.818151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.3906 | 1.33820 | 0.669100 | − | 0.743173i | \(-0.266680\pi\) | ||||
0.669100 | + | 0.743173i | \(0.266680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.9373 | −1.38792 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.39736 | − | 0.806764i | −0.0461448 | − | 0.0266417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 37.5875i | − | 1.23990i | −0.784642 | − | 0.619949i | \(-0.787153\pi\) | ||
0.784642 | − | 0.619949i | \(-0.212847\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.79325 | 0.322349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 56.6206 | + | 98.0698i | 1.86167 | + | 3.22451i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1824 | + | 7.03353i | 0.399693 | + | 0.230763i | 0.686351 | − | 0.727270i | \(-0.259211\pi\) |
−0.286659 | + | 0.958033i | \(0.592545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.5965 | + | 2.48309i | −0.412834 | + | 0.0813801i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.3347 | − | 26.5605i | −0.501498 | − | 0.868621i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.6943 | − | 51.4321i | −0.970071 | − | 1.68021i | −0.695324 | − | 0.718696i | \(-0.744739\pi\) |
−0.274747 | − | 0.961517i | \(-0.588594\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3591 | + | 14.0637i | −0.794083 | + | 0.458464i | −0.841398 | − | 0.540416i | \(-0.818267\pi\) |
0.0473147 | + | 0.998880i | \(0.484934\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.6474i | 0.998017i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.2582 | + | 21.2319i | −0.398339 | + | 0.689944i | −0.993521 | − | 0.113647i | \(-0.963747\pi\) |
0.595182 | + | 0.803591i | \(0.297080\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.99878 | 0.129806 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7222 | − | 20.6242i | −1.15716 | − | 0.668085i | −0.206536 | − | 0.978439i | \(-0.566219\pi\) |
−0.950621 | + | 0.310354i | \(0.899552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.7298 | − | 22.3606i | −1.25327 | − | 0.723573i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.2157 | − | 24.6224i | −0.459050 | − | 0.795098i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.4467 | 0.724088 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.7660 | − | 13.7213i | 0.765055 | − | 0.441705i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.07230 | − | 1.77379i | −0.0987985 | − | 0.0570414i | 0.449787 | − | 0.893136i | \(-0.351500\pi\) |
−0.548585 | + | 0.836095i | \(0.684833\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.2213 | + | 31.5602i | −0.584749 | + | 1.01282i | 0.410158 | + | 0.912015i | \(0.365474\pi\) |
−0.994907 | + | 0.100800i | \(0.967860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.8153 | + | 30.8570i | 0.571132 | + | 0.989229i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14.7328i | − | 0.471345i | −0.971833 | − | 0.235672i | \(-0.924271\pi\) | ||
0.971833 | − | 0.235672i | \(-0.0757292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.0987 | + | 24.3057i | −1.34548 | + | 0.776813i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.5873 | − | 23.5340i | 0.433369 | − | 0.750617i | −0.563792 | − | 0.825917i | \(-0.690658\pi\) |
0.997161 | + | 0.0752996i | \(0.0239913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.9531 | − | 43.2201i | 0.795073 | − | 1.37711i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 19.6048i | − | 0.623395i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.8950 | + | 16.1052i | 0.886113 | + | 0.511598i | 0.872669 | − | 0.488312i | \(-0.162387\pi\) |
0.0134440 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.6439 | −1.06658 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.81673 | − | 13.5390i | −0.247558 | − | 0.428783i | 0.715290 | − | 0.698828i | \(-0.246295\pi\) |
−0.962848 | + | 0.270045i | \(0.912961\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.cg.a.1151.12 | yes | 24 | |
3.2 | odd | 2 | inner | 2736.2.cg.a.1151.1 | ✓ | 24 | |
4.3 | odd | 2 | 2736.2.cg.b.1151.12 | yes | 24 | ||
12.11 | even | 2 | 2736.2.cg.b.1151.1 | yes | 24 | ||
19.7 | even | 3 | 2736.2.cg.b.2591.1 | yes | 24 | ||
57.26 | odd | 6 | 2736.2.cg.b.2591.12 | yes | 24 | ||
76.7 | odd | 6 | inner | 2736.2.cg.a.2591.1 | yes | 24 | |
228.83 | even | 6 | inner | 2736.2.cg.a.2591.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.a.1151.1 | ✓ | 24 | 3.2 | odd | 2 | inner | |
2736.2.cg.a.1151.12 | yes | 24 | 1.1 | even | 1 | trivial | |
2736.2.cg.a.2591.1 | yes | 24 | 76.7 | odd | 6 | inner | |
2736.2.cg.a.2591.12 | yes | 24 | 228.83 | even | 6 | inner | |
2736.2.cg.b.1151.1 | yes | 24 | 12.11 | even | 2 | ||
2736.2.cg.b.1151.12 | yes | 24 | 4.3 | odd | 2 | ||
2736.2.cg.b.2591.1 | yes | 24 | 19.7 | even | 3 | ||
2736.2.cg.b.2591.12 | yes | 24 | 57.26 | odd | 6 |