Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1009,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2091141441.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2017.2 | ||
Root | \(0.335492 + 1.69925i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2017 |
Dual form | 3024.2.r.m.1009.2 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.164508 | + | 0.284936i | 0.0735702 | + | 0.127427i | 0.900464 | − | 0.434931i | \(-0.143227\pi\) |
−0.826893 | + | 0.562359i | \(0.809894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.664508 | − | 1.15096i | 0.200357 | − | 0.347028i | −0.748287 | − | 0.663375i | \(-0.769123\pi\) |
0.948643 | + | 0.316348i | \(0.102457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.53937 | − | 2.66626i | −0.426944 | − | 0.739489i | 0.569656 | − | 0.821883i | \(-0.307076\pi\) |
−0.996600 | + | 0.0823948i | \(0.973743\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.35741 | −1.78443 | −0.892217 | − | 0.451606i | \(-0.850851\pi\) | ||||
−0.892217 | + | 0.451606i | \(0.850851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.93671 | 0.673727 | 0.336864 | − | 0.941553i | \(-0.390634\pi\) | ||||
0.336864 | + | 0.941553i | \(0.390634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34321 | + | 5.79062i | 0.697108 | + | 1.20743i | 0.969465 | + | 0.245231i | \(0.0788637\pi\) |
−0.272356 | + | 0.962196i | \(0.587803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44587 | − | 4.23638i | 0.489175 | − | 0.847276i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.88258 | + | 6.72483i | −0.720977 | + | 1.24877i | 0.239631 | + | 0.970864i | \(0.422974\pi\) |
−0.960608 | + | 0.277906i | \(0.910360\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63555 | − | 2.83286i | −0.293754 | − | 0.508796i | 0.680940 | − | 0.732339i | \(-0.261571\pi\) |
−0.974694 | + | 0.223542i | \(0.928238\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.329016 | −0.0556138 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.329016 | 0.0540899 | 0.0270449 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270449 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.135552 | + | 0.234783i | 0.0211696 | + | 0.0366669i | 0.876416 | − | 0.481555i | \(-0.159928\pi\) |
−0.855247 | + | 0.518221i | \(0.826594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.48255 | + | 9.49606i | −0.836081 | + | 1.44814i | 0.0570654 | + | 0.998370i | \(0.481826\pi\) |
−0.893147 | + | 0.449765i | \(0.851508\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.571014 | + | 0.989025i | −0.0832910 | + | 0.144264i | −0.904662 | − | 0.426131i | \(-0.859876\pi\) |
0.821371 | + | 0.570395i | \(0.193210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.42828 | −0.882992 | −0.441496 | − | 0.897263i | \(-0.645552\pi\) | ||||
−0.441496 | + | 0.897263i | \(0.645552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.437267 | 0.0589611 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.372170 | − | 0.644618i | −0.0484525 | − | 0.0839221i | 0.840782 | − | 0.541374i | \(-0.182096\pi\) |
−0.889234 | + | 0.457452i | \(0.848762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.42195 | + | 7.65904i | −0.566173 | + | 0.980640i | 0.430767 | + | 0.902463i | \(0.358243\pi\) |
−0.996940 | + | 0.0781767i | \(0.975090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.506476 | − | 0.877243i | 0.0628207 | − | 0.108809i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.28640 | + | 7.42426i | 0.523667 | + | 0.907018i | 0.999620 | + | 0.0275474i | \(0.00876971\pi\) |
−0.475954 | + | 0.879470i | \(0.657897\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60769 | 0.190798 | 0.0953990 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0953990 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.4941 | −1.57936 | −0.789680 | − | 0.613519i | \(-0.789754\pi\) | ||||
−0.789680 | + | 0.613519i | \(0.789754\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.664508 | + | 1.15096i | 0.0757277 | + | 0.131164i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.628926 | + | 1.08933i | −0.0707597 | + | 0.122559i | −0.899234 | − | 0.437467i | \(-0.855876\pi\) |
0.828475 | + | 0.560026i | \(0.189209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0316459 | − | 0.0548124i | 0.00347359 | − | 0.00601644i | −0.864283 | − | 0.503005i | \(-0.832228\pi\) |
0.867757 | + | 0.496989i | \(0.165561\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21035 | − | 2.09639i | −0.131281 | − | 0.227386i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.3071 | −1.19855 | −0.599274 | − | 0.800544i | \(-0.704544\pi\) | ||||
−0.599274 | + | 0.800544i | \(0.704544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.07874 | 0.322739 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.483112 | + | 0.836774i | 0.0495662 | + | 0.0858512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.51420 | − | 9.55087i | 0.559882 | − | 0.969744i | −0.437624 | − | 0.899158i | \(-0.644180\pi\) |
0.997506 | − | 0.0705859i | \(-0.0224869\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.12079 | − | 12.3336i | 0.708546 | − | 1.22724i | −0.256851 | − | 0.966451i | \(-0.582685\pi\) |
0.965397 | − | 0.260786i | \(-0.0839816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.29288 | + | 9.16753i | 0.521522 | + | 0.903303i | 0.999687 | + | 0.0250330i | \(0.00796907\pi\) |
−0.478164 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5574 | −1.50399 | −0.751993 | − | 0.659171i | \(-0.770907\pi\) | ||||
−0.751993 | + | 0.659171i | \(0.770907\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3574 | −1.37519 | −0.687595 | − | 0.726094i | \(-0.741334\pi\) | ||||
−0.687595 | + | 0.726094i | \(0.741334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.94966 | − | 3.37691i | −0.183409 | − | 0.317673i | 0.759630 | − | 0.650355i | \(-0.225380\pi\) |
−0.943039 | + | 0.332682i | \(0.892046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.09997 | + | 1.90520i | −0.102573 | + | 0.177661i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.67871 | − | 6.37171i | 0.337226 | − | 0.584093i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.61686 | + | 7.99663i | 0.419714 | + | 0.726967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.25454 | 0.291095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00787 | 0.621848 | 0.310924 | − | 0.950435i | \(-0.399362\pi\) | ||||
0.310924 | + | 0.950435i | \(0.399362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.33280 | − | 5.77258i | −0.291188 | − | 0.504353i | 0.682903 | − | 0.730509i | \(-0.260717\pi\) |
−0.974091 | + | 0.226156i | \(0.927384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.46835 | + | 2.54326i | −0.127322 | + | 0.220529i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.41926 | + | 14.5826i | −0.719306 | + | 1.24587i | 0.241969 | + | 0.970284i | \(0.422207\pi\) |
−0.961275 | + | 0.275591i | \(0.911127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.81032 | − | 13.5279i | −0.662463 | − | 1.14742i | −0.979967 | − | 0.199162i | \(-0.936178\pi\) |
0.317504 | − | 0.948257i | \(-0.397155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.09169 | −0.342164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.55486 | −0.212170 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.53233 | − | 13.0464i | −0.617073 | − | 1.06880i | −0.990017 | − | 0.140948i | \(-0.954985\pi\) |
0.372944 | − | 0.927854i | \(-0.378348\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.86714 | + | 6.69808i | −0.314703 | + | 0.545082i | −0.979374 | − | 0.202054i | \(-0.935238\pi\) |
0.664671 | + | 0.747136i | \(0.268572\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.538122 | − | 0.932055i | 0.0432230 | − | 0.0748645i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.35812 | + | 7.54849i | 0.347816 | + | 0.602435i | 0.985861 | − | 0.167564i | \(-0.0535901\pi\) |
−0.638045 | + | 0.769999i | \(0.720257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.68643 | −0.526964 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4513 | −1.05359 | −0.526793 | − | 0.849993i | \(-0.676606\pi\) | ||||
−0.526793 | + | 0.849993i | \(0.676606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.81804 | + | 10.0771i | 0.450214 | + | 0.779793i | 0.998399 | − | 0.0565638i | \(-0.0180144\pi\) |
−0.548185 | + | 0.836357i | \(0.684681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.76069 | − | 3.04961i | 0.135438 | − | 0.234585i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.885831 | − | 1.53430i | 0.0673485 | − | 0.116651i | −0.830385 | − | 0.557190i | \(-0.811879\pi\) |
0.897733 | + | 0.440539i | \(0.145213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.44587 | + | 4.23638i | 0.184891 | + | 0.320240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.73139 | −0.503128 | −0.251564 | − | 0.967841i | \(-0.580945\pi\) | ||||
−0.251564 | + | 0.967841i | \(0.580945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2711 | −0.986433 | −0.493217 | − | 0.869906i | \(-0.664179\pi\) | ||||
−0.493217 | + | 0.869906i | \(0.664179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0541257 | + | 0.0937484i | 0.00397940 | + | 0.00689252i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.88906 | + | 8.46810i | −0.357523 | + | 0.619249i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4083 | + | 18.0277i | −0.753117 | + | 1.30444i | 0.193187 | + | 0.981162i | \(0.438117\pi\) |
−0.946305 | + | 0.323276i | \(0.895216\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2585 | + | 17.7683i | 0.738426 | + | 1.27899i | 0.953204 | + | 0.302328i | \(0.0977638\pi\) |
−0.214778 | + | 0.976663i | \(0.568903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.20781 | −0.513535 | −0.256768 | − | 0.966473i | \(-0.582658\pi\) | ||||
−0.256768 | + | 0.966473i | \(0.582658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3276 | 1.01566 | 0.507828 | − | 0.861458i | \(-0.330448\pi\) | ||||
0.507828 | + | 0.861458i | \(0.330448\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.88258 | − | 6.72483i | −0.272504 | − | 0.471991i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0445987 | + | 0.0772471i | −0.00311491 | + | 0.00539517i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.95147 | − | 3.38004i | 0.134986 | − | 0.233802i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.68897 | − | 6.38948i | −0.253959 | − | 0.439870i | 0.710653 | − | 0.703543i | \(-0.248400\pi\) |
−0.964612 | + | 0.263672i | \(0.915066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.60769 | −0.246043 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.27110 | 0.222057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3258 | + | 19.6168i | 0.761854 | + | 1.31957i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3549 | + | 23.1313i | −0.894308 | + | 1.54899i | −0.0596502 | + | 0.998219i | \(0.518999\pi\) |
−0.834658 | + | 0.550768i | \(0.814335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.46386 | − | 14.6598i | 0.561766 | − | 0.973007i | −0.435576 | − | 0.900152i | \(-0.643455\pi\) |
0.997342 | − | 0.0728556i | \(-0.0232112\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.22580 | + | 14.2475i | 0.543576 | + | 0.941501i | 0.998695 | + | 0.0510706i | \(0.0162633\pi\) |
−0.455119 | + | 0.890431i | \(0.650403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.10855 | −0.269160 | −0.134580 | − | 0.990903i | \(-0.542969\pi\) | ||||
−0.134580 | + | 0.990903i | \(0.542969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.375745 | −0.0245109 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4182 | − | 18.0448i | −0.673895 | − | 1.16722i | −0.976791 | − | 0.214197i | \(-0.931287\pi\) |
0.302896 | − | 0.953024i | \(-0.402047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3477 | + | 19.6548i | −0.730969 | + | 1.26608i | 0.225501 | + | 0.974243i | \(0.427598\pi\) |
−0.956470 | + | 0.291832i | \(0.905735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.164508 | − | 0.284936i | 0.0105100 | − | 0.0182039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.52067 | − | 7.83004i | −0.287644 | − | 0.498213i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.00030 | 0.252497 | 0.126248 | − | 0.991999i | \(-0.459706\pi\) | ||||
0.126248 | + | 0.991999i | \(0.459706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.88637 | 0.558681 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.254753 | + | 0.441245i | 0.0158911 | + | 0.0275241i | 0.873862 | − | 0.486175i | \(-0.161608\pi\) |
−0.857971 | + | 0.513699i | \(0.828275\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.164508 | + | 0.284936i | −0.0102220 | + | 0.0177051i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.56344 | − | 2.70796i | 0.0964059 | − | 0.166980i | −0.813789 | − | 0.581161i | \(-0.802599\pi\) |
0.910194 | + | 0.414181i | \(0.135932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.05750 | − | 1.83165i | −0.0649619 | − | 0.112517i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.16505 | 0.253947 | 0.126974 | − | 0.991906i | \(-0.459474\pi\) | ||||
0.126974 | + | 0.991906i | \(0.459474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.0230 | 0.791092 | 0.395546 | − | 0.918446i | \(-0.370555\pi\) | ||||
0.395546 | + | 0.918446i | \(0.370555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.25061 | − | 5.63021i | −0.196019 | − | 0.339515i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.347709 | − | 0.602250i | 0.0208918 | − | 0.0361857i | −0.855390 | − | 0.517984i | \(-0.826683\pi\) |
0.876282 | + | 0.481798i | \(0.160016\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1488 | − | 27.9706i | 0.963359 | − | 1.66859i | 0.249399 | − | 0.968401i | \(-0.419767\pi\) |
0.713960 | − | 0.700186i | \(-0.246900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.06383 | − | 12.2349i | −0.419901 | − | 0.727290i | 0.576028 | − | 0.817430i | \(-0.304602\pi\) |
−0.995929 | + | 0.0901399i | \(0.971269\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.271104 | −0.0160027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.1315 | 2.18421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.33818 | + | 14.4422i | 0.487122 | + | 0.843720i | 0.999890 | − | 0.0148072i | \(-0.00471344\pi\) |
−0.512769 | + | 0.858527i | \(0.671380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.122450 | − | 0.212090i | 0.00712931 | − | 0.0123483i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2929 | − | 17.8278i | 0.595252 | − | 1.03101i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.48255 | − | 9.49606i | −0.316009 | − | 0.547344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.90978 | −0.166614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0345 | −1.54294 | −0.771469 | − | 0.636267i | \(-0.780478\pi\) | ||||
−0.771469 | + | 0.636267i | \(0.780478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7377 | + | 20.3302i | 0.665581 | + | 1.15282i | 0.979127 | + | 0.203248i | \(0.0651496\pi\) |
−0.313546 | + | 0.949573i | \(0.601517\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.364597 | − | 0.631501i | 0.0206083 | − | 0.0356946i | −0.855537 | − | 0.517741i | \(-0.826773\pi\) |
0.876146 | + | 0.482047i | \(0.160106\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7398 | − | 28.9943i | 0.940203 | − | 1.62848i | 0.175122 | − | 0.984547i | \(-0.443968\pi\) |
0.765082 | − | 0.643933i | \(-0.222699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.16001 | + | 8.93741i | 0.288905 | + | 0.500399i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6066 | −1.20222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0604 | −0.835401 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.571014 | − | 0.989025i | −0.0314810 | − | 0.0545267i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.92051 | + | 8.52257i | −0.270456 | + | 0.468443i | −0.968979 | − | 0.247145i | \(-0.920508\pi\) |
0.698523 | + | 0.715588i | \(0.253841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41029 | + | 2.44270i | −0.0770525 | + | 0.133459i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.93490 | + | 6.81545i | 0.214348 | + | 0.371261i | 0.953071 | − | 0.302748i | \(-0.0979041\pi\) |
−0.738723 | + | 0.674009i | \(0.764571\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.34735 | −0.235422 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.14721 | + | 14.1114i | 0.437365 | + | 0.757539i | 0.997485 | − | 0.0708727i | \(-0.0225784\pi\) |
−0.560120 | + | 0.828411i | \(0.689245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.79219 | − | 3.10416i | 0.0959336 | − | 0.166162i | −0.814064 | − | 0.580775i | \(-0.802750\pi\) |
0.909998 | + | 0.414613i | \(0.136083\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.80329 | + | 16.9798i | −0.521776 | + | 0.903743i | 0.477903 | + | 0.878413i | \(0.341397\pi\) |
−0.999679 | + | 0.0253304i | \(0.991936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.264478 | + | 0.458089i | 0.0140370 | + | 0.0243129i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.8040 | −0.886882 | −0.443441 | − | 0.896303i | \(-0.646243\pi\) | ||||
−0.443441 | + | 0.896303i | \(0.646243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3757 | −0.546092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.21988 | − | 3.84494i | −0.116194 | − | 0.201254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8160 | − | 29.1262i | 0.877790 | − | 1.52038i | 0.0240298 | − | 0.999711i | \(-0.492350\pi\) |
0.853760 | − | 0.520666i | \(-0.174316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.21414 | − | 5.56705i | 0.166870 | − | 0.289027i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.2159 | + | 29.8189i | 0.891407 | + | 1.54396i | 0.838190 | + | 0.545379i | \(0.183614\pi\) |
0.0532169 | + | 0.998583i | \(0.483053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.9069 | 1.23127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.0913 | −0.929287 | −0.464644 | − | 0.885498i | \(-0.653818\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.03792 | + | 8.72594i | 0.257426 | + | 0.445875i | 0.965552 | − | 0.260212i | \(-0.0837923\pi\) |
−0.708126 | + | 0.706086i | \(0.750459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.218634 | + | 0.378684i | −0.0111426 | + | 0.0192995i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.715236 | + | 1.23882i | −0.0362639 | + | 0.0628109i | −0.883588 | − | 0.468266i | \(-0.844879\pi\) |
0.847324 | + | 0.531077i | \(0.178212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.5974 | − | 42.6040i | −1.24394 | − | 2.15457i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.413853 | −0.0208232 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5433 | −0.529152 | −0.264576 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264576 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.804044 | + | 1.39265i | 0.0401521 | + | 0.0695454i | 0.885403 | − | 0.464824i | \(-0.153882\pi\) |
−0.845251 | + | 0.534369i | \(0.820549\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.03543 | + | 8.72162i | −0.250833 | + | 0.434455i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.218634 | − | 0.378684i | 0.0108373 | − | 0.0187707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0174 | − | 22.5468i | −0.643670 | − | 1.11487i | −0.984607 | − | 0.174783i | \(-0.944077\pi\) |
0.340937 | − | 0.940086i | \(-0.389256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.744341 | 0.0366266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0208240 | 0.00102221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.00882 | − | 3.47938i | −0.0981372 | − | 0.169979i | 0.812776 | − | 0.582576i | \(-0.197955\pi\) |
−0.910914 | + | 0.412597i | \(0.864622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.63431 | + | 4.56275i | −0.128388 | + | 0.222375i | −0.923052 | − | 0.384675i | \(-0.874314\pi\) |
0.794664 | + | 0.607049i | \(0.207647\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.9953 | + | 31.1688i | −0.872901 | + | 1.51191i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.42195 | − | 7.65904i | −0.213993 | − | 0.370647i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7343 | −0.854230 | −0.427115 | − | 0.904197i | \(-0.640470\pi\) | ||||
−0.427115 | + | 0.904197i | \(0.640470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.76835 | −0.229152 | −0.114576 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114576 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.81804 | + | 17.0054i | 0.469661 | + | 0.813476i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1134 | − | 31.3733i | 0.864506 | − | 1.49737i | −0.00303091 | − | 0.999995i | \(-0.500965\pi\) |
0.867537 | − | 0.497373i | \(-0.165702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.81211 | + | 13.5310i | −0.371164 | + | 0.642876i | −0.989745 | − | 0.142846i | \(-0.954375\pi\) |
0.618581 | + | 0.785721i | \(0.287708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.86010 | − | 3.22179i | −0.0881773 | − | 0.152728i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4142 | 0.727441 | 0.363721 | − | 0.931508i | \(-0.381506\pi\) | ||||
0.363721 | + | 0.931508i | \(0.381506\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.360301 | 0.0169659 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.506476 | + | 0.877243i | 0.0237440 | + | 0.0411258i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.71214 | − | 8.16166i | 0.220424 | − | 0.381786i | −0.734512 | − | 0.678595i | \(-0.762589\pi\) |
0.954937 | + | 0.296809i | \(0.0959224\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0406 | − | 34.7113i | 0.933383 | − | 1.61667i | 0.155892 | − | 0.987774i | \(-0.450175\pi\) |
0.777491 | − | 0.628893i | \(-0.216492\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9717 | + | 19.0036i | 0.509900 | + | 0.883172i | 0.999934 | + | 0.0114690i | \(0.00365078\pi\) |
−0.490035 | + | 0.871703i | \(0.663016\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9808 | −0.970878 | −0.485439 | − | 0.874271i | \(-0.661340\pi\) | ||||
−0.485439 | + | 0.874271i | \(0.661340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.57280 | −0.395855 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.28640 | + | 12.6204i | 0.335029 | + | 0.580287i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.18282 | − | 12.4410i | 0.329570 | − | 0.570833i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.65194 | − | 11.5215i | 0.303935 | − | 0.526431i | −0.673089 | − | 0.739562i | \(-0.735033\pi\) |
0.977024 | + | 0.213131i | \(0.0683661\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.506476 | − | 0.877243i | −0.0230933 | − | 0.0399988i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.62852 | 0.164762 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.5519 | 1.74695 | 0.873477 | − | 0.486865i | \(-0.161860\pi\) | ||||
0.873477 | + | 0.486865i | \(0.161860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.25959 | + | 5.64578i | 0.147103 | + | 0.254791i | 0.930156 | − | 0.367165i | \(-0.119672\pi\) |
−0.783052 | + | 0.621956i | \(0.786338\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.5658 | − | 49.4774i | 1.28654 | − | 2.22835i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.803846 | + | 1.39230i | −0.0360574 | + | 0.0624533i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3259 | + | 24.8132i | 0.641316 | + | 1.11079i | 0.985139 | + | 0.171758i | \(0.0549446\pi\) |
−0.343823 | + | 0.939034i | \(0.611722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2801 | 0.725892 | 0.362946 | − | 0.931810i | \(-0.381771\pi\) | ||||
0.362946 | + | 0.931810i | \(0.381771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.68571 | 0.208511 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.2296 | + | 22.9143i | 0.586391 | + | 1.01566i | 0.994700 | + | 0.102815i | \(0.0327851\pi\) |
−0.408309 | + | 0.912844i | \(0.633882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.74703 | − | 11.6862i | 0.298471 | − | 0.516967i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.74144 | + | 3.01626i | −0.0767370 | + | 0.132912i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.758887 | + | 1.31443i | 0.0333758 | + | 0.0578086i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.72559 | 0.338464 | 0.169232 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169232 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9546 | 0.741375 | 0.370687 | − | 0.928758i | \(-0.379122\pi\) | ||||
0.370687 | + | 0.928758i | \(0.379122\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0334 | + | 20.8425i | 0.524184 | + | 0.907914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8542 | + | 18.8000i | −0.471920 | + | 0.817390i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.417328 | − | 0.722833i | 0.0180765 | − | 0.0313094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.55931 | − | 4.43285i | −0.110648 | − | 0.191649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.32902 | −0.0572448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9353 | 0.943072 | 0.471536 | − | 0.881847i | \(-0.343700\pi\) | ||||
0.471536 | + | 0.881847i | \(0.343700\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.36191 | − | 4.09094i | −0.101173 | − | 0.175237i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4034 | − | 37.0718i | 0.915144 | − | 1.58508i | 0.108453 | − | 0.994102i | \(-0.465410\pi\) |
0.806691 | − | 0.590974i | \(-0.201256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.4020 | + | 19.7489i | −0.485742 | + | 0.841330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.628926 | − | 1.08933i | −0.0267447 | − | 0.0463231i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.5498 | −1.54866 | −0.774332 | − | 0.632780i | \(-0.781914\pi\) | ||||
−0.774332 | + | 0.632780i | \(0.781914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.7587 | 1.42784 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8582 | − | 34.3955i | −0.836925 | − | 1.44960i | −0.892453 | − | 0.451140i | \(-0.851017\pi\) |
0.0555277 | − | 0.998457i | \(-0.482316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.641469 | − | 1.11106i | 0.0269868 | − | 0.0467425i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4173 | − | 26.7035i | 0.646325 | − | 1.11947i | −0.337669 | − | 0.941265i | \(-0.609638\pi\) |
0.983994 | − | 0.178203i | \(-0.0570283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4009 | − | 33.6033i | −0.811901 | − | 1.40625i | −0.911532 | − | 0.411229i | \(-0.865100\pi\) |
0.0996310 | − | 0.995024i | \(-0.468234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.7083 | 1.36403 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.10713 | −0.0877211 | −0.0438606 | − | 0.999038i | \(-0.513966\pi\) | ||||
−0.0438606 | + | 0.999038i | \(0.513966\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0316459 | + | 0.0548124i | 0.00131289 | + | 0.00227400i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.27164 | + | 7.39870i | −0.176913 | + | 0.306423i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.46457 | + | 6.00081i | −0.142998 | + | 0.247680i | −0.928624 | − | 0.371022i | \(-0.879008\pi\) |
0.785626 | + | 0.618701i | \(0.212341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.80314 | − | 8.31928i | −0.197910 | − | 0.342790i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.0323 | 0.411977 | 0.205989 | − | 0.978554i | \(-0.433959\pi\) | ||||
0.205989 | + | 0.978554i | \(0.433959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.42070 | 0.0992392 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.6645 | + | 37.5240i | 0.885187 | + | 1.53319i | 0.845499 | + | 0.533977i | \(0.179303\pi\) |
0.0396877 | + | 0.999212i | \(0.487364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.2578 | − | 40.2837i | 0.948707 | − | 1.64321i | 0.200553 | − | 0.979683i | \(-0.435726\pi\) |
0.748154 | − | 0.663525i | \(-0.230941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.51902 | + | 2.63102i | −0.0617569 | + | 0.106966i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.9227 | + | 32.7751i | 0.768048 | + | 1.33030i | 0.938620 | + | 0.344953i | \(0.112105\pi\) |
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.51600 | 0.142242 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2811 | 1.22304 | 0.611522 | − | 0.791228i | \(-0.290558\pi\) | ||||
0.611522 | + | 0.791228i | \(0.290558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.08770 | − | 14.0083i | −0.325599 | − | 0.563954i | 0.656035 | − | 0.754731i | \(-0.272233\pi\) |
−0.981633 | + | 0.190777i | \(0.938899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.9377 | + | 22.4088i | −0.520012 | + | 0.900687i | 0.479718 | + | 0.877423i | \(0.340739\pi\) |
−0.999729 | + | 0.0232638i | \(0.992594\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65354 | − | 9.79221i | 0.226504 | − | 0.392317i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.6940 | − | 20.2546i | −0.467759 | − | 0.810182i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.42070 | −0.0965198 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2969 | −1.16629 | −0.583146 | − | 0.812368i | \(-0.698178\pi\) | ||||
−0.583146 | + | 0.812368i | \(0.698178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.15285 | + | 1.99679i | 0.0457495 | + | 0.0792404i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.53937 | + | 2.66626i | −0.0609920 | + | 0.105641i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.82630 | + | 15.2876i | −0.348618 | + | 0.603824i | −0.986004 | − | 0.166720i | \(-0.946682\pi\) |
0.637386 | + | 0.770545i | \(0.280016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5426 | − | 25.1885i | −0.573504 | − | 0.993338i | −0.996202 | − | 0.0870676i | \(-0.972250\pi\) |
0.422698 | − | 0.906270i | \(-0.361083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.8747 | 1.56764 | 0.783819 | − | 0.620989i | \(-0.213269\pi\) | ||||
0.783819 | + | 0.620989i | \(0.213269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.989241 | −0.0388311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.08986 | + | 12.2800i | 0.277448 | + | 0.480553i | 0.970750 | − | 0.240094i | \(-0.0771782\pi\) |
−0.693302 | + | 0.720647i | \(0.743845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.09654 | − | 1.89927i | 0.0428455 | − | 0.0742106i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3592 | − | 19.6747i | 0.442491 | − | 0.766418i | −0.555382 | − | 0.831595i | \(-0.687428\pi\) |
0.997874 | + | 0.0651775i | \(0.0207614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0052 | − | 34.6500i | −0.778111 | − | 1.34773i | −0.933030 | − | 0.359800i | \(-0.882845\pi\) |
0.154919 | − | 0.987927i | \(-0.450488\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.966223 | −0.0374685 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.9212 | −2.01040 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.87684 | + | 10.1790i | 0.226873 | + | 0.392956i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.913881 | − | 1.58289i | 0.0352275 | − | 0.0610159i | −0.847874 | − | 0.530198i | \(-0.822118\pi\) |
0.883102 | + | 0.469182i | \(0.155451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2246 | + | 24.6376i | −0.546694 | + | 0.946902i | 0.451804 | + | 0.892117i | \(0.350781\pi\) |
−0.998498 | + | 0.0547845i | \(0.982553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.51420 | + | 9.55087i | 0.211616 | + | 0.366529i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.868335 | 0.0332259 | 0.0166130 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166130 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.54014 | −0.211678 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.89549 | + | 17.1395i | 0.376988 | + | 0.652962i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.71932 | + | 15.1023i | −0.331699 | + | 0.574519i | −0.982845 | − | 0.184433i | \(-0.940955\pi\) |
0.651146 | + | 0.758952i | \(0.274288\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.56972 | − | 4.45088i | 0.0974750 | − | 0.168832i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.997310 | − | 1.72739i | −0.0377758 | − | 0.0654296i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.23113 | −0.348655 | −0.174327 | − | 0.984688i | \(-0.555775\pi\) | ||||
−0.174327 | + | 0.984688i | \(0.555775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.966223 | 0.0364418 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.12079 | + | 12.3336i | 0.267805 | + | 0.463852i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.8231 | + | 18.7461i | −0.406469 | + | 0.704025i | −0.994491 | − | 0.104820i | \(-0.966573\pi\) |
0.588022 | + | 0.808845i | \(0.299907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9360 | − | 18.9417i | 0.409556 | − | 0.709373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.673115 | − | 1.16587i | −0.0251731 | − | 0.0436010i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.6526 | 1.81444 | 0.907218 | − | 0.420661i | \(-0.138202\pi\) | ||||
0.907218 | + | 0.420661i | \(0.138202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5858 | −0.394234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.9926 | + | 32.8962i | 0.705368 | + | 1.22173i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.11417 | − | 1.92980i | 0.0413222 | − | 0.0715722i | −0.844625 | − | 0.535359i | \(-0.820176\pi\) |
0.885947 | + | 0.463787i | \(0.153510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.3374 | − | 69.8664i | 1.49193 | − | 2.58410i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0129 | − | 32.9313i | −0.702258 | − | 1.21635i | −0.967672 | − | 0.252211i | \(-0.918842\pi\) |
0.265415 | − | 0.964134i | \(-0.414491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3934 | 0.419681 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.6048 | 1.78796 | 0.893978 | − | 0.448112i | \(-0.147903\pi\) | ||||
0.893978 | + | 0.448112i | \(0.147903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2700 | + | 36.8408i | 0.780322 | + | 1.35156i | 0.931754 | + | 0.363090i | \(0.118278\pi\) |
−0.151432 | + | 0.988468i | \(0.548388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47826 | − | 4.29247i | 0.0907963 | − | 0.157264i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.77868 | − | 13.4731i | 0.284227 | − | 0.492295i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.62893 | + | 8.01754i | 0.168912 | + | 0.292564i | 0.938038 | − | 0.346534i | \(-0.112641\pi\) |
−0.769126 | + | 0.639098i | \(0.779308\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.54470 | −0.0926111 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.0363 | 1.49149 | 0.745744 | − | 0.666232i | \(-0.232094\pi\) | ||||
0.745744 | + | 0.666232i | \(0.232094\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1859 | − | 33.2309i | −0.695487 | − | 1.20462i | −0.970016 | − | 0.243040i | \(-0.921855\pi\) |
0.274529 | − | 0.961579i | \(-0.411478\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.17871 | − | 12.4339i | 0.259887 | − | 0.450137i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.14581 | + | 1.98461i | −0.0413730 | + | 0.0716601i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.149772 | + | 0.259412i | 0.00540090 | + | 0.00935463i | 0.868713 | − | 0.495315i | \(-0.164947\pi\) |
−0.863312 | + | 0.504670i | \(0.831614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.2941 | −1.44928 | −0.724639 | − | 0.689128i | \(-0.757994\pi\) | ||||
−0.724639 | + | 0.689128i | \(0.757994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0014 | −0.574788 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.398076 | + | 0.689488i | 0.0142626 | + | 0.0247035i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06832 | − | 1.85039i | 0.0382276 | − | 0.0662122i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.43389 | + | 2.48357i | −0.0511777 | + | 0.0886425i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2565 | + | 21.2289i | 0.436897 | + | 0.756728i | 0.997448 | − | 0.0713920i | \(-0.0227441\pi\) |
−0.560551 | + | 0.828120i | \(0.689411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.89932 | 0.138644 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.2280 | 0.966896 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.9140 | − | 46.6164i | −0.953343 | − | 1.65124i | −0.738115 | − | 0.674675i | \(-0.764284\pi\) |
−0.215228 | − | 0.976564i | \(-0.569049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.20119 | − | 7.27667i | 0.148627 | − | 0.257430i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.96691 | + | 15.5311i | −0.316435 | + | 0.548082i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09997 | − | 1.90520i | −0.0387689 | − | 0.0671496i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.44011 | −0.261580 | −0.130790 | − | 0.991410i | \(-0.541751\pi\) | ||||
−0.130790 | + | 0.991410i | \(0.541751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.94854 | −0.103537 | −0.0517687 | − | 0.998659i | \(-0.516486\pi\) | ||||
−0.0517687 | + | 0.998659i | \(0.516486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.21284 | − | 3.83276i | −0.0775125 | − | 0.134256i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.1007 | + | 27.8872i | −0.563291 | + | 0.975648i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.44331 | + | 14.6242i | −0.294674 | + | 0.510390i | −0.974909 | − | 0.222604i | \(-0.928544\pi\) |
0.680235 | + | 0.732994i | \(0.261878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3829 | + | 42.2325i | 0.849935 | + | 1.47213i | 0.881265 | + | 0.472622i | \(0.156692\pi\) |
−0.0313301 | + | 0.999509i | \(0.509974\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.4541 | −0.502618 | −0.251309 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251309 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.5659 | −1.13106 | −0.565530 | − | 0.824728i | \(-0.691328\pi\) | ||||
−0.565530 | + | 0.824728i | \(0.691328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.67871 | + | 6.37171i | 0.127460 | + | 0.220767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.91423 | + | 3.31554i | −0.0662446 | + | 0.114739i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.4412 | − | 42.3334i | 0.843803 | − | 1.46151i | −0.0428531 | − | 0.999081i | \(-0.513645\pi\) |
0.886656 | − | 0.462429i | \(-0.153022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6489 | − | 27.1047i | −0.539617 | − | 0.934644i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.15859 | 0.0398567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.23372 | −0.317274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.09997 | + | 1.90520i | 0.0377065 | + | 0.0653096i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5285 | − | 18.2360i | 0.360491 | − | 0.624388i | −0.627551 | − | 0.778575i | \(-0.715943\pi\) |
0.988042 | + | 0.154187i | \(0.0492760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.7290 | − | 32.4396i | 0.639771 | − | 1.10812i | −0.345711 | − | 0.938341i | \(-0.612362\pi\) |
0.985483 | − | 0.169776i | \(-0.0543043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2123 | + | 22.8844i | 0.450799 | + | 0.780807i | 0.998436 | − | 0.0559093i | \(-0.0178058\pi\) |
−0.547637 | + | 0.836716i | \(0.684472\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.1888 | −0.993597 | −0.496798 | − | 0.867866i | \(-0.665491\pi\) | ||||
−0.496798 | + | 0.867866i | \(0.665491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.582905 | 0.0198194 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.835853 | + | 1.44774i | 0.0283544 | + | 0.0491112i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1967 | − | 22.8573i | 0.447153 | − | 0.774491i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.62727 | + | 2.81852i | −0.0550118 | + | 0.0952832i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.70263 | − | 9.87725i | −0.192564 | − | 0.333531i | 0.753535 | − | 0.657408i | \(-0.228347\pi\) |
−0.946099 | + | 0.323877i | \(0.895014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7109 | 0.563005 | 0.281503 | − | 0.959560i | \(-0.409167\pi\) | ||||
0.281503 | + | 0.959560i | \(0.409167\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8347 | −0.398268 | −0.199134 | − | 0.979972i | \(-0.563813\pi\) | ||||
−0.199134 | + | 0.979972i | \(0.563813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8800 | − | 30.9691i | −0.600353 | − | 1.03984i | −0.992767 | − | 0.120053i | \(-0.961693\pi\) |
0.392414 | − | 0.919789i | \(-0.371640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.50394 | + | 6.06899i | −0.117518 | + | 0.203548i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.67690 | + | 2.90448i | −0.0561154 | + | 0.0971947i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.10737 | − | 1.91801i | −0.0370152 | − | 0.0641122i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.4007 | 0.847159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.2955 | 1.57564 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.18320 | − | 3.78142i | −0.0725721 | − | 0.125698i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.32308 | + | 14.4160i | −0.276363 | + | 0.478675i | −0.970478 | − | 0.241189i | \(-0.922463\pi\) |
0.694115 | + | 0.719864i | \(0.255796\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.88258 | + | 17.1171i | −0.327425 | + | 0.567116i | −0.982000 | − | 0.188881i | \(-0.939514\pi\) |
0.654575 | + | 0.755997i | \(0.272847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0420579 | − | 0.0728465i | −0.00139191 | − | 0.00241087i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.66560 | 0.220118 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2384 | 0.337734 | 0.168867 | − | 0.985639i | \(-0.445989\pi\) | ||||
0.168867 | + | 0.985639i | \(0.445989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.47483 | − | 4.28653i | −0.0814600 | − | 0.141093i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.804731 | − | 1.39384i | 0.0264594 | − | 0.0458290i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.5842 | + | 30.4567i | −0.576917 | + | 0.999250i | 0.418913 | + | 0.908026i | \(0.362411\pi\) |
−0.995830 | + | 0.0912240i | \(0.970922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.46835 | − | 2.54326i | −0.0481234 | − | 0.0833521i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.21715 | −0.105212 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.5829 | −1.03177 | −0.515884 | − | 0.856659i | \(-0.672536\pi\) | ||||
−0.515884 | + | 0.856659i | \(0.672536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.49641 | + | 11.2521i | 0.211777 | + | 0.366808i | 0.952271 | − | 0.305255i | \(-0.0987416\pi\) |
−0.740494 | + | 0.672063i | \(0.765408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.906357 | + | 1.56986i | −0.0295150 | + | 0.0511216i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7246 | − | 30.6998i | 0.575971 | − | 0.997610i | −0.419965 | − | 0.907540i | \(-0.637958\pi\) |
0.995935 | − | 0.0900699i | \(-0.0287090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7723 | + | 35.9787i | 0.674298 | + | 1.16792i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.0040 | 1.29586 | 0.647928 | − | 0.761702i | \(-0.275636\pi\) | ||||
0.647928 | + | 0.761702i | \(0.275636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.84898 | −0.221628 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.41926 | − | 14.5826i | −0.271872 | − | 0.470896i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1499 | − | 17.5802i | 0.327417 | − | 0.567104i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.37522 | + | 5.84605i | −0.108652 | + | 0.188191i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.03814 | + | 5.26222i | 0.0977001 | + | 0.169222i | 0.910732 | − | 0.412997i | \(-0.135518\pi\) |
−0.813032 | + | 0.582219i | \(0.802185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.1397 | 1.83370 | 0.916850 | − | 0.399232i | \(-0.130723\pi\) | ||||
0.916850 | + | 0.399232i | \(0.130723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6206 | 0.500775 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.91064 | − | 10.2375i | −0.189098 | − | 0.327528i | 0.755852 | − | 0.654743i | \(-0.227223\pi\) |
−0.944950 | + | 0.327215i | \(0.893890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.51364 | + | 13.0140i | −0.240137 | + | 0.415929i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.26336 | + | 16.0446i | −0.295455 | + | 0.511744i | −0.975091 | − | 0.221806i | \(-0.928805\pi\) |
0.679635 | + | 0.733550i | \(0.262138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18574 | − | 2.05377i | −0.0377809 | − | 0.0654384i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −73.3174 | −2.33136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5408 | −0.398371 | −0.199186 | − | 0.979962i | \(-0.563830\pi\) | ||||
−0.199186 | + | 0.979962i | \(0.563830\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.35700 | + | 4.08245i | 0.0747220 | + | 0.129422i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.94209 | + | 13.7561i | −0.251528 | + | 0.435660i | −0.963947 | − | 0.266095i | \(-0.914267\pi\) |
0.712418 | + | 0.701755i | \(0.247600\pi\) | |||||||
\(998\) | 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 | 3024.2.r.m.2017.2 | 8 | ||
3.2 | odd | 2 | 1008.2.r.l.673.4 | 8 | |||
4.3 | odd | 2 | 1512.2.r.e.505.2 | 8 | |||
9.2 | odd | 6 | 9072.2.a.cj.1.2 | 4 | |||
9.4 | even | 3 | inner | 3024.2.r.m.1009.2 | 8 | ||
9.5 | odd | 6 | 1008.2.r.l.337.4 | 8 | |||
9.7 | even | 3 | 9072.2.a.cg.1.3 | 4 | |||
12.11 | even | 2 | 504.2.r.e.169.1 | ✓ | 8 | ||
36.7 | odd | 6 | 4536.2.a.y.1.3 | 4 | |||
36.11 | even | 6 | 4536.2.a.z.1.2 | 4 | |||
36.23 | even | 6 | 504.2.r.e.337.1 | yes | 8 | ||
36.31 | odd | 6 | 1512.2.r.e.1009.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.e.169.1 | ✓ | 8 | 12.11 | even | 2 | ||
504.2.r.e.337.1 | yes | 8 | 36.23 | even | 6 | ||
1008.2.r.l.337.4 | 8 | 9.5 | odd | 6 | |||
1008.2.r.l.673.4 | 8 | 3.2 | odd | 2 | |||
1512.2.r.e.505.2 | 8 | 4.3 | odd | 2 | |||
1512.2.r.e.1009.2 | 8 | 36.31 | odd | 6 | |||
3024.2.r.m.1009.2 | 8 | 9.4 | even | 3 | inner | ||
3024.2.r.m.2017.2 | 8 | 1.1 | even | 1 | trivial | ||
4536.2.a.y.1.3 | 4 | 36.7 | odd | 6 | |||
4536.2.a.z.1.2 | 4 | 36.11 | even | 6 | |||
9072.2.a.cg.1.3 | 4 | 9.7 | even | 3 | |||
9072.2.a.cj.1.2 | 4 | 9.2 | odd | 6 |