Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.6 | ||
Root | \(1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.i.895.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.874032i | 0.504623i | 0.967646 | + | 0.252311i | \(0.0811907\pi\) | ||||
−0.967646 | + | 0.252311i | \(0.918809\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.70246 | 1.65579 | 0.827895 | − | 0.560883i | \(-0.189538\pi\) | ||||
0.827895 | + | 0.560883i | \(0.189538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | − | 2.23607i | −0.534522 | − | 0.845154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.874032 | 0.242413 | 0.121206 | − | 0.992627i | \(-0.461324\pi\) | ||||
0.121206 | + | 0.992627i | \(0.461324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.23607i | 0.835549i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.57649i | − | 1.10996i | −0.831863 | − | 0.554981i | \(-0.812725\pi\) | ||
0.831863 | − | 0.554981i | \(-0.187275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.95440i | − | 0.448369i | −0.974547 | − | 0.224184i | \(-0.928028\pi\) | ||
0.974547 | − | 0.224184i | \(-0.0719718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.95440 | − | 1.23607i | 0.426484 | − | 0.269732i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.23607i | − | 0.257738i | −0.991662 | − | 0.128869i | \(-0.958865\pi\) | ||
0.991662 | − | 0.128869i | \(-0.0411347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.70820 | 1.74164 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57649i | 0.880746i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2333 | −1.83796 | −0.918982 | − | 0.394301i | \(-0.870987\pi\) | ||||
−0.918982 | + | 0.394301i | \(0.870987\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82843i | 0.492366i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.23607 | − | 8.27895i | −0.885057 | − | 1.39940i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.9443i | − | 1.79923i | −0.436687 | − | 0.899614i | \(-0.643848\pi\) | ||
0.436687 | − | 0.899614i | \(-0.356152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.763932i | 0.122327i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.90879i | 0.610450i | 0.952280 | + | 0.305225i | \(0.0987317\pi\) | ||||
−0.952280 | + | 0.305225i | \(0.901268\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.70820 | 0.260499 | 0.130249 | − | 0.991481i | \(-0.458422\pi\) | ||||
0.130249 | + | 0.991481i | \(0.458422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.27895 | 1.23415 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.07262 | 1.17751 | 0.588756 | − | 0.808311i | \(-0.299618\pi\) | ||||
0.588756 | + | 0.808311i | \(0.299618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 6.32456i | −0.428571 | + | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.472136i | − | 0.0648529i | −0.999474 | − | 0.0324264i | \(-0.989677\pi\) | ||
0.999474 | − | 0.0324264i | \(-0.0103235\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.9814 | 1.61557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70820 | 0.226257 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.1074i | − | 1.44606i | −0.690818 | − | 0.723029i | \(-0.742749\pi\) | ||
0.690818 | − | 0.723029i | \(-0.257251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.94665 | −1.14550 | −0.572751 | − | 0.819730i | \(-0.694124\pi\) | ||||
−0.572751 | + | 0.819730i | \(0.694124\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.16228 | − | 5.00000i | −0.398410 | − | 0.629941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.23607 | 0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.70820 | −1.18605 | −0.593023 | − | 0.805186i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805186i | \(0.702066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08036 | 0.130060 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.0000i | − | 1.18678i | −0.804914 | − | 0.593391i | \(-0.797789\pi\) | ||
0.804914 | − | 0.593391i | \(-0.202211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1421i | 1.65521i | 0.561310 | + | 0.827606i | \(0.310298\pi\) | ||||
−0.561310 | + | 0.827606i | \(0.689702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.61125i | 0.878871i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.57649 | − | 7.23607i | −0.521540 | − | 0.824626i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4721i | 1.40322i | 0.712559 | + | 0.701612i | \(0.247536\pi\) | ||||
−0.712559 | + | 0.701612i | \(0.752464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1877i | 1.33778i | 0.743362 | + | 0.668889i | \(0.233230\pi\) | ||||
−0.743362 | + | 0.668889i | \(0.766770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 16.9443i | − | 1.83786i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.74806 | −0.187412 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.82068i | 1.04099i | 0.853865 | + | 0.520495i | \(0.174253\pi\) | ||||
−0.853865 | + | 0.520495i | \(0.825747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | − | 1.95440i | −0.129575 | − | 0.204876i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.94427i | − | 0.927478i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.23607i | − | 0.742405i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.57649i | 0.464672i | 0.972636 | + | 0.232336i | \(0.0746369\pi\) | ||||
−0.972636 | + | 0.232336i | \(0.925363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.23607 | 0.727252 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.37016 | 0.434847 | 0.217424 | − | 0.976077i | \(-0.430235\pi\) | ||||
0.217424 | + | 0.976077i | \(0.430235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.24419 | −0.516726 | −0.258363 | − | 0.966048i | \(-0.583183\pi\) | ||||
−0.258363 | + | 0.966048i | \(0.583183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.23607 | − | 4.57649i | 0.706168 | − | 0.446620i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7082 | 1.32522 | 0.662611 | − | 0.748964i | \(-0.269448\pi\) | ||||
0.662611 | + | 0.748964i | \(0.269448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.4721i | − | 1.19461i | −0.802013 | − | 0.597307i | \(-0.796237\pi\) | ||
0.802013 | − | 0.597307i | \(-0.203763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.56564 | 0.907931 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.7082 | 1.47770 | 0.738852 | − | 0.673868i | \(-0.235368\pi\) | ||||
0.738852 | + | 0.673868i | \(0.235368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.57649i | − | 0.426760i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.95440 | 0.180684 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.2333 | + | 6.47214i | −0.938089 | + | 0.593300i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41641 | −0.308047 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.7295 | 1.22800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.23607i | 0.464626i | 0.972641 | + | 0.232313i | \(0.0746294\pi\) | ||||
−0.972641 | + | 0.232313i | \(0.925371\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.49302i | 0.131454i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0270i | 0.876064i | 0.898959 | + | 0.438032i | \(0.144324\pi\) | ||||
−0.898959 | + | 0.438032i | \(0.855676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.37016 | + | 2.76393i | −0.378941 | + | 0.239663i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.9443i | 1.45833i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5123i | 1.57019i | 0.619374 | + | 0.785096i | \(0.287387\pi\) | ||||
−0.619374 | + | 0.785096i | \(0.712613\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.05573i | 0.594199i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.82843 | 0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.40492i | 0.614945i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.52786 | − | 2.62210i | −0.455931 | − | 0.216267i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4164i | 1.09911i | 0.835456 | + | 0.549557i | \(0.185204\pi\) | ||||
−0.835456 | + | 0.549557i | \(0.814796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.76393i | 0.550441i | 0.961381 | + | 0.275220i | \(0.0887509\pi\) | ||||
−0.961381 | + | 0.275220i | \(0.911249\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 10.2333i | − | 0.827317i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −37.8885 | −3.04328 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.37016 | 0.348777 | 0.174388 | − | 0.984677i | \(-0.444205\pi\) | ||||
0.174388 | + | 0.984677i | \(0.444205\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.412662 | 0.0327262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.76393 | + | 1.74806i | −0.217828 | + | 0.137767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7639 | 0.999748 | 0.499874 | − | 0.866098i | \(-0.333380\pi\) | ||||
0.499874 | + | 0.866098i | \(0.333380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.4721i | 0.815255i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9010 | 0.843548 | 0.421774 | − | 0.906701i | \(-0.361408\pi\) | ||||
0.421774 | + | 0.906701i | \(0.361408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2361 | −0.941236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.37016i | − | 0.334195i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.69161 | 0.660811 | 0.330406 | − | 0.943839i | \(-0.392814\pi\) | ||||
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.3153 | − | 19.4721i | −0.930946 | − | 1.47196i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.70820 | 0.729713 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6525 | 0.796203 | 0.398102 | − | 0.917341i | \(-0.369669\pi\) | ||||
0.398102 | + | 0.917341i | \(0.369669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.70246 | 0.275202 | 0.137601 | − | 0.990488i | \(-0.456061\pi\) | ||||
0.137601 | + | 0.990488i | \(0.456061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.81966i | − | 0.578046i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 40.5207i | − | 2.97914i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.8098i | − | 1.08300i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.2333 | − | 6.47214i | 0.744366 | − | 0.470779i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.05573i | 0.365820i | 0.983130 | + | 0.182910i | \(0.0585516\pi\) | ||||
−0.983130 | + | 0.182910i | \(0.941448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.76393 | −0.486878 | −0.243439 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243439 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.82843i | 0.202548i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.05573i | − | 0.0752175i | −0.999293 | − | 0.0376088i | \(-0.988026\pi\) | ||
0.999293 | − | 0.0376088i | \(-0.0119741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0618 | −0.925925 | −0.462962 | − | 0.886378i | \(-0.653213\pi\) | ||||
−0.462962 | + | 0.886378i | \(0.653213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.48528i | − | 0.598506i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.47214 | − | 2.82843i | 0.313882 | − | 0.198517i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4721i | 1.01078i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.76393i | − | 0.192107i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.32456i | − | 0.437479i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.23607 | 0.222780 | 0.111390 | − | 0.993777i | \(-0.464470\pi\) | ||||
0.111390 | + | 0.993777i | \(0.464470\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.74032 | 0.598877 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.32456 | 0.431331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.4721 | + | 22.8825i | 0.982433 | + | 1.55336i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.3607 | −0.835257 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.00000i | − | 0.269069i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8021 | 1.45998 | 0.729988 | − | 0.683460i | \(-0.239526\pi\) | ||||
0.729988 | + | 0.683460i | \(0.239526\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.4721 | 1.29814 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 20.2604i | − | 1.34473i | −0.740221 | − | 0.672364i | \(-0.765279\pi\) | ||
0.740221 | − | 0.672364i | \(-0.234721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.27895 | −0.547088 | −0.273544 | − | 0.961859i | \(-0.588196\pi\) | ||||
−0.273544 | + | 0.961859i | \(0.588196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.32456 | − | 4.00000i | 0.416125 | − | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4164 | −0.878938 | −0.439469 | − | 0.898258i | \(-0.644833\pi\) | ||||
−0.439469 | + | 0.898258i | \(0.644833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.8885 | 1.94971 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9010 | −0.708099 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.6525i | − | 0.818421i | −0.912440 | − | 0.409210i | \(-0.865804\pi\) | ||
0.912440 | − | 0.409210i | \(-0.134196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.57649i | − | 0.294798i | −0.989077 | − | 0.147399i | \(-0.952910\pi\) | ||
0.989077 | − | 0.147399i | \(-0.0470901\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0965i | 1.03259i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.1074 | + | 23.4164i | −0.709624 | + | 1.49602i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.70820i | − | 0.108690i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6525 | −0.675073 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.0965i | − | 1.01600i | −0.861356 | − | 0.508002i | \(-0.830384\pi\) | ||
0.861356 | − | 0.508002i | \(-0.169616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.00000i | − | 0.251478i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.8098 | 0.927428 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.9706i | − | 1.05859i | −0.848436 | − | 0.529297i | \(-0.822456\pi\) | ||
0.848436 | − | 0.529297i | \(-0.177544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.4721 | + | 15.4775i | −1.52062 | + | 0.961727i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47214i | 0.276818i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.8885i | 1.96633i | 0.182715 | + | 0.983166i | \(0.441511\pi\) | ||||
−0.182715 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.74806i | − | 0.107383i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.58359 | −0.525307 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0965 | −0.981423 | −0.490711 | − | 0.871322i | \(-0.663263\pi\) | ||||
−0.490711 | + | 0.871322i | \(0.663263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.4744 | −0.818514 | −0.409257 | − | 0.912419i | \(-0.634212\pi\) | ||||
−0.409257 | + | 0.912419i | \(0.634212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.70820 | − | 1.08036i | 0.103385 | − | 0.0653865i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.1803 | 1.69934 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05573i | 0.0634326i | 0.999497 | + | 0.0317163i | \(0.0100973\pi\) | ||||
−0.999497 | + | 0.0317163i | \(0.989903\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.8825 | −1.36994 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.8885 | −1.90231 | −0.951156 | − | 0.308712i | \(-0.900102\pi\) | ||||
−0.951156 | + | 0.308712i | \(0.900102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.86629i | 0.467602i | 0.972284 | + | 0.233801i | \(0.0751165\pi\) | ||||
−0.972284 | + | 0.233801i | \(0.924884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.32456 | 0.374634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.74032 | − | 5.52786i | 0.515925 | − | 0.326299i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.94427 | −0.232016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | −0.234484 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.6004 | −0.736123 | −0.368062 | − | 0.929801i | \(-0.619978\pi\) | ||||
−0.368062 | + | 0.929801i | \(0.619978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 41.1246i | − | 2.39437i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.8098i | 0.859354i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.08036i | − | 0.0624790i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.41577 | − | 3.81966i | −0.139242 | − | 0.220162i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.81966i | 0.219434i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.1246 | −1.89671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.4397i | − | 0.595824i | −0.954593 | − | 0.297912i | \(-0.903710\pi\) | ||
0.954593 | − | 0.297912i | \(-0.0962902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.58359i | − | 0.260751i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1421 | −0.801927 | −0.400963 | − | 0.916094i | \(-0.631325\pi\) | ||||
−0.400963 | + | 0.916094i | \(0.631325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8716i | 1.57540i | 0.616061 | + | 0.787698i | \(0.288727\pi\) | ||||
−0.616061 | + | 0.787698i | \(0.711273\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.7082 | − | 18.5123i | −0.659683 | − | 1.04305i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.8885i | 0.892390i | 0.894936 | + | 0.446195i | \(0.147221\pi\) | ||||
−0.894936 | + | 0.446195i | \(0.852779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.47214i | 0.362370i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.9814i | 0.668737i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.94427 | −0.497673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.61125 | 0.422196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.9010 | 0.602829 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4164 | − | 18.0509i | −0.629407 | − | 0.995180i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.1246 | 1.38097 | 0.690487 | − | 0.723345i | \(-0.257396\pi\) | ||||
0.690487 | + | 0.723345i | \(0.257396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 24.4721i | − | 1.34106i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −35.9442 | −1.96384 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1246 | −0.823890 | −0.411945 | − | 0.911209i | \(-0.635150\pi\) | ||||
−0.411945 | + | 0.911209i | \(0.635150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7295i | 0.745683i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.1158 | −1.79332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3848 | − | 2.23607i | 0.992685 | − | 0.120736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.76393 | 0.255741 | 0.127871 | − | 0.991791i | \(-0.459186\pi\) | ||||
0.127871 | + | 0.991791i | \(0.459186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.4211 | −1.20017 | −0.600087 | − | 0.799935i | \(-0.704867\pi\) | ||||
−0.600087 | + | 0.799935i | \(0.704867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000i | 0.213504i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.8021i | 1.16041i | 0.814471 | + | 0.580204i | \(0.197027\pi\) | ||||
−0.814471 | + | 0.580204i | \(0.802973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 37.0246i | − | 1.96506i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.65685 | − | 8.94427i | −0.299392 | − | 0.473381i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.7639i | 1.20143i | 0.799462 | + | 0.600717i | \(0.205118\pi\) | ||||
−0.799462 | + | 0.600717i | \(0.794882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.1803 | 0.798965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.461370i | − | 0.0242156i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.3607i | 2.74068i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.65685 | −0.295285 | −0.147643 | − | 0.989041i | \(-0.547169\pi\) | ||||
−0.147643 | + | 0.989041i | \(0.547169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.74032i | 0.455003i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.05573 | + | 0.667701i | −0.0548107 | + | 0.0346653i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.9443i | − | 1.18801i | −0.804462 | − | 0.594005i | \(-0.797546\pi\) | ||
0.804462 | − | 0.594005i | \(-0.202454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000i | 0.619677i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.74806i | 0.0900299i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.7082 | −1.11508 | −0.557538 | − | 0.830152i | \(-0.688254\pi\) | ||||
−0.557538 | + | 0.830152i | \(0.688254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.57649 | −0.234461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.0649 | −0.769779 | −0.384890 | − | 0.922963i | \(-0.625760\pi\) | ||||
−0.384890 | + | 0.922963i | \(0.625760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.9443 | − | 26.7912i | −0.863560 | − | 1.36541i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.81966 | 0.194164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.8328i | 1.25907i | 0.776971 | + | 0.629537i | \(0.216755\pi\) | ||||
−0.776971 | + | 0.629537i | \(0.783245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65685 | −0.286079 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.76393 | −0.442082 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.1776i | 2.32345i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4288 | −0.774351 | −0.387175 | − | 0.922006i | \(-0.626549\pi\) | ||||
−0.387175 | + | 0.922006i | \(0.626549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.41577 | − | 3.81966i | −0.120940 | − | 0.191222i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6525 | −0.831585 | −0.415792 | − | 0.909460i | \(-0.636496\pi\) | ||||
−0.415792 | + | 0.909460i | \(0.636496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.94427 | −0.445546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0270 | 0.498246 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 35.4164i | − | 1.75553i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.7109i | − | 1.27132i | −0.771969 | − | 0.635661i | \(-0.780728\pi\) | ||
0.771969 | − | 0.635661i | \(-0.219272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.08347i | 0.152096i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.8369 | + | 15.7082i | −1.22214 | + | 0.772950i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.1246i | 2.21508i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.1803 | −0.792355 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.94355i | − | 0.339215i | −0.985512 | − | 0.169607i | \(-0.945750\pi\) | ||
0.985512 | − | 0.169607i | \(-0.0542499\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.41641i | − | 0.458928i | −0.973317 | − | 0.229464i | \(-0.926303\pi\) | ||
0.973317 | − | 0.229464i | \(-0.0736973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.0509 | 0.877666 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 39.8530i | − | 1.93316i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6525 | + | 20.0053i | 0.612296 | + | 0.968125i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.47214i | 0.119356i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.7082i | − | 0.756638i | −0.925675 | − | 0.378319i | \(-0.876502\pi\) | ||
0.925675 | − | 0.378319i | \(-0.123498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 17.2256i | − | 0.827810i | −0.910320 | − | 0.413905i | \(-0.864165\pi\) | ||
0.910320 | − | 0.413905i | \(-0.135835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.47214 | −0.310315 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.41577 | −0.115562 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.49302 | −0.0712582 | −0.0356291 | − | 0.999365i | \(-0.511343\pi\) | ||||
−0.0356291 | + | 0.999365i | \(0.511343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.70820 | + | 14.1421i | −0.319438 | + | 0.673435i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.2918 | 0.869069 | 0.434535 | − | 0.900655i | \(-0.356913\pi\) | ||||
0.434535 | + | 0.900655i | \(0.356913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.3607i | 1.72366i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7264 | −0.554638 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3607 | −0.677722 | −0.338861 | − | 0.940836i | \(-0.610042\pi\) | ||||
−0.338861 | + | 0.940836i | \(0.610042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.6491i | 0.595623i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.91189 | −0.277765 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.57649 | − | 7.23607i | −0.214549 | − | 0.339232i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.652476 | 0.0305215 | 0.0152608 | − | 0.999884i | \(-0.495142\pi\) | ||||
0.0152608 | + | 0.999884i | \(0.495142\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.9443 | 0.977595 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.6947 | 0.498103 | 0.249051 | − | 0.968490i | \(-0.419881\pi\) | ||||
0.249051 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.88854i | 0.180716i | 0.995909 | + | 0.0903580i | \(0.0288011\pi\) | ||||
−0.995909 | + | 0.0903580i | \(0.971199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 33.1158i | − | 1.53571i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.70246i | 0.171329i | 0.996324 | + | 0.0856647i | \(0.0273014\pi\) | ||||
−0.996324 | + | 0.0856647i | \(0.972699\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7295 | + | 21.7082i | 0.633968 | + | 1.00239i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.81966i | 0.176001i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.52786 | 0.254171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 17.0193i | − | 0.780898i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.05573i | − | 0.0483385i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.89794 | 0.406557 | 0.203279 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203279 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.56564i | − | 0.436156i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.52786 | − | 2.41577i | −0.0695202 | − | 0.109921i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.9443i | 0.769400i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.0689i | − | 1.09067i | −0.838220 | − | 0.545333i | \(-0.816403\pi\) | ||
0.838220 | − | 0.545333i | \(-0.183597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.1561i | 0.504496i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2918 | −0.644980 | −0.322490 | − | 0.946573i | \(-0.604520\pi\) | ||||
−0.322490 | + | 0.946573i | \(0.604520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.15298 | 0.412230 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.7912 | 1.20418 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.3607 | + | 14.1421i | −1.00301 | + | 0.634361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.7639 | 0.929521 | 0.464761 | − | 0.885436i | \(-0.346140\pi\) | ||||
0.464761 | + | 0.885436i | \(0.346140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.52786i | 0.425674i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4698 | −1.00188 | −0.500939 | − | 0.865482i | \(-0.667012\pi\) | ||||
−0.500939 | + | 0.865482i | \(0.667012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1803 | 0.720016 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.6947i | − | 0.474969i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.77198 | −0.433135 | −0.216568 | − | 0.976268i | \(-0.569486\pi\) | ||||
−0.216568 | + | 0.976268i | \(0.569486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.6228 | − | 20.0000i | 1.39891 | − | 0.884748i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.94427 | 0.394899 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.4164 | −0.855589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.1235 | 1.14891 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.59675i | 0.333460i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.2070i | 1.27958i | 0.768549 | + | 0.639791i | \(0.220979\pi\) | ||||
−0.768549 | + | 0.639791i | \(0.779021\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.86319i | 0.256379i | 0.991750 | + | 0.128190i | \(0.0409166\pi\) | ||||
−0.991750 | + | 0.128190i | \(0.959083\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.0193 | − | 10.7639i | 0.742782 | − | 0.469777i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.8328i | 2.04007i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.4721 | 0.933571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 24.8369i | − | 1.07783i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.41641i | 0.147981i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 50.7541 | 2.19429 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.31061i | 0.401782i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.70820 | + | 20.4667i | −0.418162 | + | 0.881563i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 0.472136i | − | 0.0202987i | −0.999948 | − | 0.0101494i | \(-0.996769\pi\) | ||
0.999948 | − | 0.0101494i | \(-0.00323070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.23607i | 0.138873i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 46.1776i | − | 1.97803i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.1246 | −1.58733 | −0.793667 | − | 0.608353i | \(-0.791831\pi\) | ||||
−0.793667 | + | 0.608353i | \(0.791831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.0053 | −0.853806 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.90879 | 0.166520 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.8885 | − | 17.6383i | 1.18594 | − | 0.750055i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 35.4164 | 1.50334 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.36068i | 0.100025i | 0.998749 | + | 0.0500126i | \(0.0159262\pi\) | ||||
−0.998749 | + | 0.0500126i | \(0.984074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.49302 | 0.0631482 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9443 | 0.546508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.6808i | 0.576576i | 0.957544 | + | 0.288288i | \(0.0930860\pi\) | ||||
−0.957544 | + | 0.288288i | \(0.906914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.1590 | 2.44677 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.82998 | − | 6.05573i | −0.160844 | − | 0.254317i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0689 | −1.00902 | −0.504510 | − | 0.863406i | \(-0.668327\pi\) | ||||
−0.504510 | + | 0.863406i | \(0.668327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.18034 | −0.342337 | −0.171168 | − | 0.985242i | \(-0.554754\pi\) | ||||
−0.171168 | + | 0.985242i | \(0.554754\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.41887 | −0.184601 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.7639i | − | 0.448887i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.97831i | − | 0.415402i | −0.978192 | − | 0.207701i | \(-0.933402\pi\) | ||
0.978192 | − | 0.207701i | \(-0.0665982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 5.91189i | − | 0.245690i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.2526 | − | 17.2361i | 1.13063 | − | 0.715073i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.52786i | − | 0.0632777i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.23607 | 0.299175 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 38.5663i | − | 1.59180i | −0.605426 | − | 0.795901i | \(-0.706997\pi\) | ||
0.605426 | − | 0.795901i | \(-0.293003\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000i | 0.824086i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.922740 | 0.0379565 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.3137i | 0.464598i | 0.972644 | + | 0.232299i | \(0.0746248\pi\) | ||||
−0.972644 | + | 0.232299i | \(0.925375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.8885 | + | 23.9628i | −1.55328 | + | 0.982380i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 11.4164i | − | 0.467242i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.4721i | − | 0.509598i | −0.966994 | − | 0.254799i | \(-0.917991\pi\) | ||
0.966994 | − | 0.254799i | \(-0.0820093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.3168i | − | 0.543204i | −0.962410 | − | 0.271602i | \(-0.912447\pi\) | ||
0.962410 | − | 0.271602i | \(-0.0875534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.7082 | −0.884026 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.95440 | −0.0794575 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.1081 | −1.62794 | −0.813968 | − | 0.580910i | \(-0.802697\pi\) | ||||
−0.813968 | + | 0.580910i | \(0.802697\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.47214 | + | 3.90879i | 0.100176 | + | 0.158392i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.05573 | 0.285444 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 17.4164i | − | 0.703442i | −0.936105 | − | 0.351721i | \(-0.885597\pi\) | ||
0.936105 | − | 0.351721i | \(-0.114403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.6491 | −0.510061 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.76393 | −0.111272 | −0.0556359 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556359 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.4319i | − | 0.700649i | −0.936628 | − | 0.350324i | \(-0.886071\pi\) | ||
0.936628 | − | 0.350324i | \(-0.113929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65685 | 0.227002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.9597 | − | 13.8885i | 0.879797 | − | 0.556433i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.29180 | 0.291672 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.52786 | 0.220762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.0864 | −1.99707 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.47214i | 0.337270i | 0.985679 | + | 0.168635i | \(0.0539360\pi\) | ||||
−0.985679 | + | 0.168635i | \(0.946064\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.82843i | 0.112420i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.3863i | 0.769323i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.62210 | + | 5.52786i | −0.103891 | + | 0.219022i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 22.3607i | − | 0.884575i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.18034 | 0.244109 | 0.122054 | − | 0.992523i | \(-0.461052\pi\) | ||||
0.122054 | + | 0.992523i | \(0.461052\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.0996i | − | 0.713780i | −0.934146 | − | 0.356890i | \(-0.883837\pi\) | ||
0.934146 | − | 0.356890i | \(-0.116163\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.52786i | 0.217659i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5579 | 0.650958 | 0.325479 | − | 0.945549i | \(-0.394474\pi\) | ||||
0.325479 | + | 0.945549i | \(0.394474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 35.9442i | − | 1.41093i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0000 | + | 12.6491i | −0.783862 | + | 0.495758i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13.4164i | − | 0.525025i | −0.964929 | − | 0.262512i | \(-0.915449\pi\) | ||
0.964929 | − | 0.262512i | \(-0.0845510\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.1246i | 1.45058i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.6228i | 1.23372i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.0132 | 1.36392 | 0.681959 | − | 0.731390i | \(-0.261128\pi\) | ||||
0.681959 | + | 0.731390i | \(0.261128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5772 | −1.30600 | −0.653000 | − | 0.757358i | \(-0.726490\pi\) | ||||
−0.653000 | + | 0.757358i | \(0.726490\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49613 | 0.135778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.1803 | + | 10.2333i | −0.627447 | + | 0.396832i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47214 | 0.0957215 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0557i | 0.736737i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.9520 | −1.11768 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.8328 | 0.494669 | 0.247334 | − | 0.968930i | \(-0.420445\pi\) | ||||
0.247334 | + | 0.968930i | \(0.420445\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 39.8530i | 1.53394i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.53399 | 0.327988 | 0.163994 | − | 0.986461i | \(-0.447562\pi\) | ||||
0.163994 | + | 0.986461i | \(0.447562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2333 | − | 6.47214i | 0.392720 | − | 0.248378i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.7082 | 0.678580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1803 | −0.466068 | −0.233034 | − | 0.972469i | \(-0.574865\pi\) | ||||
−0.233034 | + | 0.972469i | \(0.574865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.0618 | 0.499065 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.23607i | − | 0.276073i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.412662i | − | 0.0157212i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.7456i | − | 1.09354i | −0.837284 | − | 0.546768i | \(-0.815858\pi\) | ||
0.837284 | − | 0.546768i | \(-0.184142\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.2333 | − | 16.1803i | −0.388733 | − | 0.614640i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 68.5410i | 2.59991i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.8885 | 0.677577 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 11.7264i | − | 0.443532i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 40.4721i | − | 1.52861i | −0.644854 | − | 0.764306i | \(-0.723082\pi\) | ||
0.644854 | − | 0.764306i | \(-0.276918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.3894 | −0.806718 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.1235i | 0.983870i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.18034 | − | 9.77198i | −0.232436 | − | 0.367513i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.52786i | − | 0.132492i | −0.997803 | − | 0.0662459i | \(-0.978898\pi\) | ||
0.997803 | − | 0.0662459i | \(-0.0211022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.8885i | 1.04590i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.6491i | 0.473713i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4721 | 0.391636 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.0587 | 0.412994 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.8670 | 1.37491 | 0.687453 | − | 0.726229i | \(-0.258729\pi\) | ||||
0.687453 | + | 0.726229i | \(0.258729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.41641 | + | 11.7264i | 0.276201 | + | 0.436713i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000 | 0.148762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.4164i | 0.646829i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5579 | 0.614099 | 0.307049 | − | 0.951694i | \(-0.400658\pi\) | ||||
0.307049 | + | 0.951694i | \(0.400658\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.94427 | −0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.81758i | − | 0.289144i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.1320 | 1.77779 | 0.888897 | − | 0.458106i | \(-0.151472\pi\) | ||||
0.888897 | + | 0.458106i | \(0.151472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.4667 | − | 9.70820i | −0.754925 | − | 0.358092i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.4164 | −1.15724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.5967 | 1.89802 | 0.949009 | − | 0.315250i | \(-0.102089\pi\) | ||||
0.949009 | + | 0.315250i | \(0.102089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.49302 | 0.0548476 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.29180i | − | 0.157451i | −0.996896 | − | 0.0787254i | \(-0.974915\pi\) | ||
0.996896 | − | 0.0787254i | \(-0.0250850\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.6737i | 1.81990i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.2526i | 0.997121i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.3863 | − | 30.6525i | −0.708361 | − | 1.12002i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 14.5410i | − | 0.530609i | −0.964165 | − | 0.265305i | \(-0.914527\pi\) | ||
0.964165 | − | 0.265305i | \(-0.0854725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.0689 | 0.512699 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.0432i | 0.911415i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.3607i | − | 0.812713i | −0.913715 | − | 0.406356i | \(-0.866799\pi\) | ||
0.913715 | − | 0.406356i | \(-0.133201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.49613 | 0.126901 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.9010i | 0.395163i | 0.980287 | + | 0.197581i | \(0.0633086\pi\) | ||||
−0.980287 | + | 0.197581i | \(0.936691\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.8885 | + | 17.6383i | −1.00963 | + | 0.638548i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 37.8885i | − | 1.36986i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.70820i | − | 0.350543i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.8530i | 1.43714i | 0.695456 | + | 0.718568i | \(0.255202\pi\) | ||||
−0.695456 | + | 0.718568i | \(0.744798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8328 | 0.534191 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.9312 | −0.824777 | −0.412388 | − | 0.911008i | \(-0.635305\pi\) | ||||
−0.412388 | + | 0.911008i | \(0.635305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −89.1141 | −3.20107 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.5279 | − | 21.3894i | −0.485309 | − | 0.767342i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.63932 | 0.273707 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 32.3607i | − | 1.15796i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.15298 | −0.327101 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1803 | 0.577501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.61125i | − | 0.271312i | −0.990756 | − | 0.135656i | \(-0.956686\pi\) | ||
0.990756 | − | 0.135656i | \(-0.0433142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.8716 | −0.992256 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.2148 | − | 35.1246i | −0.789866 | − | 1.24889i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.81966 | −0.277684 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.52786 | 0.0541878 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.4397 | −0.369792 | −0.184896 | − | 0.982758i | \(-0.559195\pi\) | ||||
−0.184896 | + | 0.982758i | \(0.559195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.9443i | − | 1.30699i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.9597i | 0.775908i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 45.7649i | 1.61501i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2333 | + | 6.47214i | −0.360678 | + | 0.228113i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 14.0689i | − | 0.495248i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −56.0689 | −1.97128 | −0.985638 | − | 0.168869i | \(-0.945988\pi\) | ||||
−0.985638 | + | 0.168869i | \(0.945988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6684i | 1.04180i | 0.853618 | + | 0.520899i | \(0.174403\pi\) | ||||
−0.853618 | + | 0.520899i | \(0.825597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 11.7771i | − | 0.413040i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.2579 | 1.65537 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.33851i | − | 0.116800i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.76393 | − | 4.37016i | −0.0965796 | − | 0.152706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.8885i | 0.833716i | 0.908972 | + | 0.416858i | \(0.136869\pi\) | ||||
−0.908972 | + | 0.416858i | \(0.863131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.8328i | 1.28391i | 0.766742 | + | 0.641956i | \(0.221877\pi\) | ||||
−0.766742 | + | 0.641956i | \(0.778123\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.6305i | 0.857525i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.0689 | 1.18469 | 0.592346 | − | 0.805684i | \(-0.298202\pi\) | ||||
0.592346 | + | 0.805684i | \(0.298202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6808 | 0.475153 | 0.237576 | − | 0.971369i | \(-0.423647\pi\) | ||||
0.237576 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.922740 | −0.0320095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.9443 | + | 13.7295i | 1.00286 | + | 0.475698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.3607 | 1.39674 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 46.8328i | − | 1.61878i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.3910 | −0.358736 | −0.179368 | − | 0.983782i | \(-0.557405\pi\) | ||||
−0.179368 | + | 0.983782i | \(0.557405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 27.8716i | − | 0.959949i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.3035 | −1.55849 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.746512 | + | 1.18034i | 0.0256505 | + | 0.0405570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.87539 | −0.235963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.5279 | −0.463729 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.3035 | 1.55116 | 0.775582 | − | 0.631247i | \(-0.217457\pi\) | ||||
0.775582 | + | 0.631247i | \(0.217457\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 16.1803i | − | 0.553356i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.922740i | 0.0315202i | 0.999876 | + | 0.0157601i | \(0.00501680\pi\) | ||||
−0.999876 | + | 0.0157601i | \(0.994983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 54.0439i | − | 1.84395i | −0.387246 | − | 0.921976i | \(-0.626574\pi\) | ||
0.387246 | − | 0.921976i | \(-0.373426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.83153 | + | 7.63932i | 0.164658 | + | 0.260347i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.0000i | 0.340404i | 0.985409 | + | 0.170202i | \(0.0544420\pi\) | ||||
−0.985409 | + | 0.170202i | \(0.945558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.1803 | 1.09416 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.44742i | − | 0.117081i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.3607i | 1.36914i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.48528 | −0.287513 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.2333i | 0.346346i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.4164 | − | 30.7000i | −0.656394 | − | 1.03785i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.0000i | 1.01303i | 0.862232 | + | 0.506514i | \(0.169066\pi\) | ||||
−0.862232 | + | 0.506514i | \(0.830934\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 11.0132i | − | 0.371465i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.7082 | −1.53820 | −0.769102 | − | 0.639126i | \(-0.779296\pi\) | ||||
−0.769102 | + | 0.639126i | \(0.779296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 35.9442 | 1.20825 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.5579 | 0.555960 | 0.277980 | − | 0.960587i | \(-0.410335\pi\) | ||||
0.277980 | + | 0.960587i | \(0.410335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7082 | − | 7.40492i | 0.392681 | − | 0.248353i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.76393 | 0.293603 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 15.7771i | − | 0.527960i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.4404 | 1.31835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.944272 | 0.0315283 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 20.4667i | − | 0.682602i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.16073 | −0.0719842 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.33851 | − | 2.11146i | 0.111099 | − | 0.0702649i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.7082 | 0.455676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.7082 | −0.455173 | −0.227587 | − | 0.973758i | \(-0.573084\pi\) | ||||
−0.227587 | + | 0.973758i | \(0.573084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.77198 | 0.324116 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.1246i | 0.501101i | 0.968104 | + | 0.250550i | \(0.0806116\pi\) | ||||
−0.968104 | + | 0.250550i | \(0.919388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.4404i | 1.30529i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 28.9520i | − | 0.957123i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.4211 | − | 14.1803i | 0.740409 | − | 0.468276i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.9443i | 0.361018i | 0.983573 | + | 0.180509i | \(0.0577745\pi\) | ||||
−0.983573 | + | 0.180509i | \(0.942225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.12461 | 0.300666 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.74032i | − | 0.287691i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 95.3050i | − | 3.13361i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.7264 | −0.385145 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 36.8670i | − | 1.20957i | −0.796390 | − | 0.604783i | \(-0.793260\pi\) | ||
0.796390 | − | 0.604783i | \(-0.206740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3607 | + | 5.86319i | 0.405105 | + | 0.192158i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 12.3607i | − | 0.404670i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 54.8328i | − | 1.79322i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.49923i | − | 0.179652i | −0.995957 | − | 0.0898260i | \(-0.971369\pi\) | ||
0.995957 | − | 0.0898260i | \(-0.0286311\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.3607 | −0.794981 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.45363 | −0.242981 | −0.121491 | − | 0.992593i | \(-0.538767\pi\) | ||||
−0.121491 | + | 0.992593i | \(0.538767\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.83153 | 0.157336 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37.8885 | − | 23.9628i | 1.23251 | − | 0.779511i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.1246 | 0.816440 | 0.408220 | − | 0.912884i | \(-0.366150\pi\) | ||||
0.408220 | + | 0.912884i | \(0.366150\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.3607i | 0.401245i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.8871 | −0.450320 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.9443 | 0.613665 | 0.306833 | − | 0.951764i | \(-0.400731\pi\) | ||||
0.306833 | + | 0.951764i | \(0.400731\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.7186i | 0.605721i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.65685 | −0.182860 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.98915 | − | 7.88854i | −0.161108 | − | 0.254734i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.7214 | 2.37811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6525 | 0.987762 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.0432 | −0.806169 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6525i | 1.56456i | 0.622928 | + | 0.782279i | \(0.285943\pi\) | ||||
−0.622928 | + | 0.782279i | \(0.714057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 7.81758i | − | 0.251137i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 27.2526i | − | 0.874578i | −0.899321 | − | 0.437289i | \(-0.855939\pi\) | ||
0.899321 | − | 0.437289i | \(-0.144061\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.3948 | − | 26.1803i | 1.32705 | − | 0.839303i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.65248i | 0.213050i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.58359 | 0.210628 | 0.105314 | − | 0.994439i | \(-0.466415\pi\) | ||||
0.105314 | + | 0.994439i | \(0.466415\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.7804i | 1.01571i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 27.8885i | − | 0.890413i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.1776 | −1.47284 | −0.736418 | − | 0.676527i | \(-0.763484\pi\) | ||||
−0.736418 | + | 0.676527i | \(0.763484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.90879i | − | 0.124544i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.7771 | − | 9.97831i | 0.502190 | − | 0.317613i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.11146i | − | 0.0671404i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 10.3607i | − | 0.329118i | −0.986367 | − | 0.164559i | \(-0.947380\pi\) | ||
0.986367 | − | 0.164559i | \(-0.0526201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9597i | 0.696871i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.3607 | −1.53314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4906 | 0.902306 | 0.451153 | − | 0.892447i | \(-0.351013\pi\) | ||||
0.451153 | + | 0.892447i | \(0.351013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50.0864 | 1.58466 |
(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 | 1792.2.e.i.895.6 | 8 | ||
4.3 | odd | 2 | 1792.2.e.h.895.4 | 8 | |||
7.6 | odd | 2 | inner | 1792.2.e.i.895.3 | 8 | ||
8.3 | odd | 2 | inner | 1792.2.e.i.895.5 | 8 | ||
8.5 | even | 2 | 1792.2.e.h.895.3 | 8 | |||
16.3 | odd | 4 | 896.2.f.b.895.5 | yes | 8 | ||
16.5 | even | 4 | 896.2.f.a.895.6 | yes | 8 | ||
16.11 | odd | 4 | 896.2.f.a.895.4 | yes | 8 | ||
16.13 | even | 4 | 896.2.f.b.895.3 | yes | 8 | ||
28.27 | even | 2 | 1792.2.e.h.895.5 | 8 | |||
56.13 | odd | 2 | 1792.2.e.h.895.6 | 8 | |||
56.27 | even | 2 | inner | 1792.2.e.i.895.4 | 8 | ||
112.13 | odd | 4 | 896.2.f.b.895.6 | yes | 8 | ||
112.27 | even | 4 | 896.2.f.a.895.5 | yes | 8 | ||
112.69 | odd | 4 | 896.2.f.a.895.3 | ✓ | 8 | ||
112.83 | even | 4 | 896.2.f.b.895.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.f.a.895.3 | ✓ | 8 | 112.69 | odd | 4 | ||
896.2.f.a.895.4 | yes | 8 | 16.11 | odd | 4 | ||
896.2.f.a.895.5 | yes | 8 | 112.27 | even | 4 | ||
896.2.f.a.895.6 | yes | 8 | 16.5 | even | 4 | ||
896.2.f.b.895.3 | yes | 8 | 16.13 | even | 4 | ||
896.2.f.b.895.4 | yes | 8 | 112.83 | even | 4 | ||
896.2.f.b.895.5 | yes | 8 | 16.3 | odd | 4 | ||
896.2.f.b.895.6 | yes | 8 | 112.13 | odd | 4 | ||
1792.2.e.h.895.3 | 8 | 8.5 | even | 2 | |||
1792.2.e.h.895.4 | 8 | 4.3 | odd | 2 | |||
1792.2.e.h.895.5 | 8 | 28.27 | even | 2 | |||
1792.2.e.h.895.6 | 8 | 56.13 | odd | 2 | |||
1792.2.e.i.895.3 | 8 | 7.6 | odd | 2 | inner | ||
1792.2.e.i.895.4 | 8 | 56.27 | even | 2 | inner | ||
1792.2.e.i.895.5 | 8 | 8.3 | odd | 2 | inner | ||
1792.2.e.i.895.6 | 8 | 1.1 | even | 1 | trivial |