Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(545,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("672.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.k (of order \(2\), degree \(1\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.6 | ||
Root | \(1.17915 + 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.545 |
Dual form | 672.2.k.d.545.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.848071 | + | 1.51022i | 0.489634 | + | 0.871928i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.69614 | 0.758537 | 0.379269 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379269 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155 | − | 0.662153i | 0.968176 | − | 0.250270i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.56155 | + | 2.56155i | −0.520518 | + | 0.853851i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.00000i | − | 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.34475i | 1.20502i | 0.798112 | + | 0.602509i | \(0.205832\pi\) | ||||
−0.798112 | + | 0.602509i | \(0.794168\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.43845 | + | 2.56155i | 0.371405 | + | 0.661390i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.04090 | 1.46513 | 0.732566 | − | 0.680696i | \(-0.238322\pi\) | ||||
0.732566 | + | 0.680696i | \(0.238322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.02045i | − | 0.692938i | −0.938061 | − | 0.346469i | \(-0.887381\pi\) | ||
0.938061 | − | 0.346469i | \(-0.112619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.17238 | + | 3.30697i | 0.692270 | + | 0.721639i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.12311i | − | 0.234184i | −0.993121 | − | 0.117092i | \(-0.962643\pi\) | ||
0.993121 | − | 0.117092i | \(-0.0373572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.12311 | −0.424621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19283 | − | 0.185917i | −0.999360 | − | 0.0357798i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.12311i | − | 0.208555i | −0.994548 | − | 0.104278i | \(-0.966747\pi\) | ||
0.994548 | − | 0.104278i | \(-0.0332531\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.71659i | 0.847124i | 0.905867 | + | 0.423562i | \(0.139220\pi\) | ||||
−0.905867 | + | 0.423562i | \(0.860780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.04090 | − | 3.39228i | 1.05158 | − | 0.590521i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.34475 | − | 1.12311i | 0.734398 | − | 0.189839i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.24621 | −1.35567 | −0.677834 | − | 0.735215i | \(-0.737081\pi\) | ||||
−0.677834 | + | 0.735215i | \(0.737081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.56155 | + | 3.68466i | −1.05069 | + | 0.590018i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.04090 | 0.943429 | 0.471715 | − | 0.881751i | \(-0.343635\pi\) | ||||
0.471715 | + | 0.881751i | \(0.343635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.64861 | + | 4.34475i | −0.394832 | + | 0.647678i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.39228 | −0.494815 | −0.247408 | − | 0.968911i | \(-0.579579\pi\) | ||||
−0.247408 | + | 0.968911i | \(0.579579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.12311 | − | 3.39228i | 0.874729 | − | 0.484612i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.12311 | + | 9.12311i | 0.717378 | + | 1.27749i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.12311i | 1.25315i | 0.779359 | + | 0.626577i | \(0.215545\pi\) | ||||
−0.779359 | + | 0.626577i | \(0.784455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.78456i | − | 0.914830i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.56155 | − | 2.56155i | 0.604192 | − | 0.339286i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3857 | 1.35210 | 0.676048 | − | 0.736857i | \(-0.263691\pi\) | ||||
0.676048 | + | 0.736857i | \(0.263691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1293i | 1.42496i | 0.701691 | + | 0.712482i | \(0.252429\pi\) | ||||
−0.701691 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.30386 | + | 7.59554i | −0.290259 | + | 0.956948i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.36932i | 0.914051i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.24621 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.69614 | − | 0.952473i | 0.204191 | − | 0.114664i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.2462i | − | 1.69071i | −0.534202 | − | 0.845357i | \(-0.679388\pi\) | ||
0.534202 | − | 0.845357i | \(-0.320612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.80054 | − | 3.20636i | −0.207909 | − | 0.370239i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.64861 | − | 10.2462i | −0.301838 | − | 1.16766i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.12311 | 0.576394 | 0.288197 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288197 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.12311 | − | 8.00000i | −0.458123 | − | 0.888889i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.1702 | −1.88468 | −0.942338 | − | 0.334663i | \(-0.891378\pi\) | ||||
−0.942338 | + | 0.334663i | \(0.891378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2462 | 1.11136 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.69614 | − | 0.952473i | 0.181845 | − | 0.102116i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.43318 | −0.999915 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.87689 | + | 11.1293i | 0.301580 | + | 1.16667i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.12311 | + | 4.00000i | −0.738632 | + | 0.414781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 5.12311i | − | 0.525620i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.4741i | − | 1.57115i | −0.618764 | − | 0.785577i | \(-0.712366\pi\) | ||
0.618764 | − | 0.785577i | \(-0.287634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.2462 | + | 6.24621i | 1.02978 | + | 0.627768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.08842 | −0.506317 | −0.253159 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253159 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0138i | 0.986691i | 0.869834 | + | 0.493345i | \(0.164226\pi\) | ||||
−0.869834 | + | 0.493345i | \(0.835774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.38080 | + | 5.60908i | 0.525112 | + | 0.547390i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 14.2462i | − | 1.37723i | −0.725126 | − | 0.688617i | \(-0.758218\pi\) | ||
0.725126 | − | 0.688617i | \(-0.241782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.246211 | 0.0235828 | 0.0117914 | − | 0.999930i | \(-0.496247\pi\) | ||||
0.0117914 | + | 0.999930i | \(0.496247\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.99337 | − | 12.4536i | −0.663781 | − | 1.18205i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.12311i | − | 0.481941i | −0.970532 | − | 0.240971i | \(-0.922534\pi\) | ||
0.970532 | − | 0.240971i | \(-0.0774657\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.90495i | − | 0.177637i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.1293 | − | 6.78456i | −1.02891 | − | 0.627233i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.4741 | − | 4.00000i | 1.41851 | − | 0.366679i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.12311 | + | 9.12311i | 0.461935 | + | 0.822603i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0818 | −1.08063 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.78456 | − | 12.0818i | −0.597348 | − | 1.06374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.08842 | 0.444578 | 0.222289 | − | 0.974981i | \(-0.428647\pi\) | ||||
0.222289 | + | 0.974981i | \(0.428647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 7.73704i | −0.173422 | − | 0.670886i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.80776 | − | 0.315342i | −0.758052 | − | 0.0271403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.24621i | − | 0.191907i | −0.995386 | − | 0.0959534i | \(-0.969410\pi\) | ||
0.995386 | − | 0.0959534i | \(-0.0305900\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.15640i | − | 0.606998i | −0.952832 | − | 0.303499i | \(-0.901845\pi\) | ||
0.952832 | − | 0.303499i | \(-0.0981549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.87689 | − | 5.12311i | −0.242278 | − | 0.431443i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3790 | 1.45331 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.90495i | − | 0.158197i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.3159 | + | 6.37037i | 0.850844 | + | 0.525419i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.1231i | − | 1.40278i | −0.712778 | − | 0.701390i | \(-0.752563\pi\) | ||
0.712778 | − | 0.701390i | \(-0.247437\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4924 | 1.01662 | 0.508309 | − | 0.861174i | \(-0.330271\pi\) | ||||
0.508309 | + | 0.861174i | \(0.330271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.43318 | + | 15.4741i | −0.762627 | + | 1.25100i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000i | 0.642575i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.43981i | 0.194718i | 0.995249 | + | 0.0973590i | \(0.0310395\pi\) | ||||
−0.995249 | + | 0.0973590i | \(0.968961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.7779 | + | 7.73704i | −1.09266 | + | 0.613587i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.743668 | − | 2.87689i | −0.0586093 | − | 0.226731i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.2462 | −1.42915 | −0.714577 | − | 0.699557i | \(-0.753381\pi\) | ||||
−0.714577 | + | 0.699557i | \(0.753381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.2462 | − | 5.75379i | 0.797666 | − | 0.447932i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.7713 | −1.60733 | −0.803666 | − | 0.595081i | \(-0.797120\pi\) | ||||
−0.803666 | + | 0.595081i | \(0.797120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.87689 | −0.452069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.73704 | + | 4.71659i | 0.591666 | + | 0.360687i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.69614 | 0.128955 | 0.0644776 | − | 0.997919i | \(-0.479462\pi\) | ||||
0.0644776 | + | 0.997919i | \(0.479462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.43845 | + | 1.40582i | −0.411108 | + | 0.106270i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.80776 | + | 15.6847i | 0.662032 | + | 1.17893i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.49242i | − | 0.634753i | −0.948300 | − | 0.317377i | \(-0.897198\pi\) | ||
0.948300 | − | 0.317377i | \(-0.102802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.1293i | − | 0.827236i | −0.910451 | − | 0.413618i | \(-0.864265\pi\) | ||
0.910451 | − | 0.413618i | \(-0.135735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.8078 | + | 9.43845i | −1.24247 | + | 0.697710i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.9867 | −1.02833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 24.1636i | − | 1.76702i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.4248 | + | 2.96221i | −0.976511 | + | 0.215469i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.24621i | 0.451960i | 0.974132 | + | 0.225980i | \(0.0725584\pi\) | ||||
−0.974132 | + | 0.225980i | \(0.927442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.876894 | 0.0631202 | 0.0315601 | − | 0.999502i | \(-0.489952\pi\) | ||||
0.0315601 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.1293 | + | 6.24970i | −0.796987 | + | 0.447550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3693i | 0.810030i | 0.914310 | + | 0.405015i | \(0.132734\pi\) | ||||
−0.914310 | + | 0.405015i | \(0.867266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1498i | 1.00305i | 0.865143 | + | 0.501525i | \(0.167228\pi\) | ||||
−0.865143 | + | 0.501525i | \(0.832772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.90495 | − | 3.39228i | −0.134364 | − | 0.239273i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.743668 | − | 2.87689i | −0.0521953 | − | 0.201918i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2462 | 0.715626 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87689 | + | 1.75379i | 0.199958 | + | 0.121897i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0818 | −0.835715 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.24621 | −0.154636 | −0.0773178 | − | 0.997006i | \(-0.524636\pi\) | ||||
−0.0773178 | + | 0.997006i | \(0.524636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.5150 | − | 12.0818i | 1.47418 | − | 0.827831i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.5691 | −0.925407 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.12311 | + | 12.0818i | 0.212010 | + | 0.820165i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.2462i | 1.76551i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.9752i | − | 1.80639i | −0.429225 | − | 0.903197i | \(-0.641213\pi\) | ||
0.429225 | − | 0.903197i | \(-0.358787\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.31534 | − | 5.43845i | 0.221023 | − | 0.362563i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.48071 | 0.562884 | 0.281442 | − | 0.959578i | \(-0.409187\pi\) | ||||
0.281442 | + | 0.959578i | \(0.409187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.8188i | − | 1.30967i | −0.755774 | − | 0.654833i | \(-0.772739\pi\) | ||
0.755774 | − | 0.654833i | \(-0.227261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.2279 | − | 12.6895i | 0.870329 | − | 0.834908i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.4924i | − | 1.34250i | −0.741230 | − | 0.671252i | \(-0.765757\pi\) | ||
0.741230 | − | 0.671252i | \(-0.234243\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.75379 | −0.375336 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.34475 | + | 7.73704i | 0.282222 | + | 0.502575i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.12311i | 0.590125i | 0.955478 | + | 0.295062i | \(0.0953404\pi\) | ||||
−0.955478 | + | 0.295062i | \(0.904660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.68951i | 0.559741i | 0.960038 | + | 0.279870i | \(0.0902915\pi\) | ||||
−0.960038 | + | 0.279870i | \(0.909709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.58511 | − | 13.0114i | 0.550735 | − | 0.834680i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3857 | − | 5.75379i | 0.663515 | − | 0.367596i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.1231 | 0.835003 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.5616 | − | 25.9309i | −0.922801 | − | 1.64330i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1702 | −1.08377 | −0.541887 | − | 0.840451i | \(-0.682290\pi\) | ||||
−0.541887 | + | 0.840451i | \(0.682290\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.49242 | −0.282436 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.68951 | + | 15.4741i | 0.544158 | + | 0.969024i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7304 | 0.918857 | 0.459429 | − | 0.888215i | \(-0.348054\pi\) | ||||
0.459429 | + | 0.888215i | \(0.348054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.1231 | + | 5.46026i | −1.31253 | + | 0.339284i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.87689 | + | 1.75379i | 0.178075 | + | 0.108557i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2462i | 1.37176i | 0.727715 | + | 0.685880i | \(0.240583\pi\) | ||||
−0.727715 | + | 0.685880i | \(0.759417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4741i | 0.950565i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | − | 14.2462i | −0.489592 | − | 0.871854i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.08842 | −0.310247 | −0.155123 | − | 0.987895i | \(-0.549577\pi\) | ||||
−0.155123 | + | 0.987895i | \(0.549577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4061i | 0.814362i | 0.913347 | + | 0.407181i | \(0.133488\pi\) | ||||
−0.913347 | + | 0.407181i | \(0.866512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.3680 | + | 13.7832i | −0.869588 | + | 0.834197i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.49242i | 0.512112i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0818 | − | 7.36520i | −0.723318 | − | 0.440943i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0000i | 0.954480i | 0.878773 | + | 0.477240i | \(0.158363\pi\) | ||||
−0.878773 | + | 0.477240i | \(0.841637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8459i | 0.941941i | 0.882149 | + | 0.470971i | \(0.156096\pi\) | ||||
−0.882149 | + | 0.470971i | \(0.843904\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.73704 | − | 4.34475i | 0.458303 | − | 0.257361i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.4741 | − | 4.00000i | 0.913406 | − | 0.236113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.4924 | 1.14661 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.3693 | − | 13.1231i | 1.36993 | − | 0.769290i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.7647 | 1.62203 | 0.811015 | − | 0.585026i | \(-0.198916\pi\) | ||||
0.811015 | + | 0.585026i | \(0.198916\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.6155 | 1.02562 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.743668 | + | 20.7713i | −0.0431520 | + | 1.20527i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.87962 | 0.282196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.4924 | + | 5.29723i | −1.18116 | + | 0.305327i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.31534 | − | 7.68466i | −0.247910 | − | 0.441472i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.8769i | 1.08089i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3586i | 0.819487i | 0.912201 | + | 0.409743i | \(0.134382\pi\) | ||||
−0.912201 | + | 0.409743i | \(0.865618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.1231 | + | 8.49242i | −0.860323 | + | 0.483117i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.78456 | 0.384717 | 0.192359 | − | 0.981325i | \(-0.438386\pi\) | ||||
0.192359 | + | 0.981325i | \(0.438386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.8531i | 1.85697i | 0.371374 | + | 0.928483i | \(0.378887\pi\) | ||||
−0.371374 | + | 0.928483i | \(0.621113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.90767 | + | 12.8831i | −0.220172 | + | 0.725881i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.12311i | − | 0.512405i | −0.966623 | − | 0.256202i | \(-0.917529\pi\) | ||
0.966623 | − | 0.256202i | \(-0.0824713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.49242 | −0.251527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.5150 | − | 12.0818i | 1.20085 | − | 0.674340i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.2462i | − | 1.01525i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 9.22437i | − | 0.511676i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.208805 | + | 0.371834i | 0.0115469 | + | 0.0205625i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.68951 | + | 2.24621i | −0.479068 | + | 0.123838i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7538 | 0.755977 | 0.377988 | − | 0.925810i | \(-0.376616\pi\) | ||||
0.377988 | + | 0.925810i | \(0.376616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8769 | − | 21.1231i | 0.705649 | − | 1.15754i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.80989 | −0.208157 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.6155 | −1.72221 | −0.861104 | − | 0.508429i | \(-0.830226\pi\) | ||||
−0.861104 | + | 0.508429i | \(0.830226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.73704 | − | 4.34475i | 0.420218 | − | 0.235975i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.8664 | 1.02167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4384 | − | 12.7439i | 0.725608 | − | 0.688108i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.87689 | − | 1.61553i | 0.154887 | − | 0.0869771i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.7386i | 1.43541i | 0.696350 | + | 0.717703i | \(0.254806\pi\) | ||||
−0.696350 | + | 0.717703i | \(0.745194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.34475i | − | 0.232569i | −0.993216 | − | 0.116285i | \(-0.962902\pi\) | ||
0.993216 | − | 0.116285i | \(-0.0370985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.807764 | − | 22.5616i | 0.0431153 | − | 1.20425i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.2995 | 1.50623 | 0.753116 | − | 0.657888i | \(-0.228550\pi\) | ||||
0.753116 | + | 0.657888i | \(0.228550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 24.1636i | − | 1.28247i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.1640 | + | 19.9770i | 1.01427 | + | 1.05730i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.3693i | − | 0.600050i | −0.953931 | − | 0.300025i | \(-0.903005\pi\) | ||
0.953931 | − | 0.300025i | \(-0.0969950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.87689 | 0.519837 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.24035 | − | 7.55112i | −0.222561 | − | 0.396331i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7575i | 0.561536i | 0.959776 | + | 0.280768i | \(0.0905892\pi\) | ||||
−0.959776 | + | 0.280768i | \(0.909411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.43318 | + | 15.4741i | −0.491072 | + | 0.805548i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.04090 | + | 23.3693i | 0.313628 | + | 1.21327i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2462 | − | 18.2462i | −0.529112 | − | 0.942230i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.87962 | 0.251313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.78456 | + | 12.0818i | 0.347584 | + | 0.618969i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.5559 | −1.40804 | −0.704019 | − | 0.710181i | \(-0.748613\pi\) | ||||
−0.704019 | + | 0.710181i | \(0.748613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.49242 | − | 17.3790i | −0.228955 | − | 0.885717i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4924 | − | 20.4924i | 0.635026 | − | 1.04169i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.87689i | 0.348672i | 0.984686 | + | 0.174336i | \(0.0557779\pi\) | ||||
−0.984686 | + | 0.174336i | \(0.944222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.78456i | − | 0.343110i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.31534 | + | 7.68466i | 0.217680 | + | 0.387640i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.68951 | 0.437217 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0343i | 0.654171i | 0.944995 | + | 0.327085i | \(0.106067\pi\) | ||||
−0.944995 | + | 0.327085i | \(0.893933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.98852 | − | 9.58200i | 0.500051 | − | 0.479700i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 13.1231i | − | 0.655337i | −0.944793 | − | 0.327668i | \(-0.893737\pi\) | ||
0.944793 | − | 0.327668i | \(-0.106263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.4924 | −1.02080 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.99337 | − | 13.5691i | −0.347503 | − | 0.674255i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.9848i | 1.63500i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.87962i | 0.241282i | 0.992696 | + | 0.120641i | \(0.0384949\pi\) | ||||
−0.992696 | + | 0.120641i | \(0.961505\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.39228 | − | 1.90495i | 0.167329 | − | 0.0939640i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.6034 | − | 6.87689i | 1.30907 | − | 0.338390i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.1231 | −1.42960 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.8078 | − | 6.06913i | 0.529258 | − | 0.297207i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.9548 | −1.17027 | −0.585134 | − | 0.810937i | \(-0.698958\pi\) | ||||
−0.585134 | + | 0.810937i | \(0.698958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.29723 | − | 8.68951i | 0.257560 | − | 0.422498i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.8255 | −0.622126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.36932 | + | 28.5083i | 0.356626 | + | 1.37962i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.7386 | + | 26.2462i | 0.711588 | + | 1.26718i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.1231i | − | 1.59548i | −0.602999 | − | 0.797742i | \(-0.706028\pi\) | ||
0.602999 | − | 0.797742i | \(-0.293972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.8531i | 1.57882i | 0.613867 | + | 0.789409i | \(0.289613\pi\) | ||||
−0.613867 | + | 0.789409i | \(0.710387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.87689 | − | 1.61553i | 0.137937 | − | 0.0774586i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.39228 | −0.162275 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.2183i | 1.91951i | 0.280831 | + | 0.959757i | \(0.409390\pi\) | ||||
−0.280831 | + | 0.959757i | \(0.590610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.872043 | + | 20.9819i | −0.0415259 | + | 0.999137i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.2462i | 1.81713i | 0.417741 | + | 0.908566i | \(0.362822\pi\) | ||||
−0.417741 | + | 0.908566i | \(0.637178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | −0.758473 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.8597 | − | 14.5216i | 1.22312 | − | 0.686848i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.24621i | 0.106005i | 0.998594 | + | 0.0530026i | \(0.0168792\pi\) | ||||
−0.998594 | + | 0.0530026i | \(0.983121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 24.1636i | − | 1.13782i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5945 | + | 18.8664i | 0.497771 | + | 0.886419i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.87962 | + | 18.8769i | 0.228760 | + | 0.884962i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.3693 | −0.625390 | −0.312695 | − | 0.949854i | \(-0.601232\pi\) | ||||
−0.312695 | + | 0.949854i | \(0.601232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.3693 | − | 1.12311i | −1.46419 | − | 0.0524221i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.208805 | −0.00972500 | −0.00486250 | − | 0.999988i | \(-0.501548\pi\) | ||||
−0.00486250 | + | 0.999988i | \(0.501548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.3693 | −1.45786 | −0.728928 | − | 0.684590i | \(-0.759981\pi\) | ||||
−0.728928 | + | 0.684590i | \(0.759981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.0818 | + | 6.78456i | −0.560280 | + | 0.314627i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.48071 | 0.392440 | 0.196220 | − | 0.980560i | \(-0.437133\pi\) | ||||
0.196220 | + | 0.980560i | \(0.437133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.75379 | + | 1.48734i | −0.265685 | + | 0.0686788i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.68466 | + | 2.06913i | −0.169780 | + | 0.0953405i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.0000i | 1.47136i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.41273i | 0.294236i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.3693 | − | 14.2462i | −1.07001 | − | 0.652289i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.5559 | −1.25906 | −0.629530 | − | 0.776976i | \(-0.716752\pi\) | ||||
−0.629530 | + | 0.776976i | \(0.716752\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 35.8278i | − | 1.63361i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.71407 | − | 3.56291i | 0.168996 | − | 0.162118i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 26.2462i | − | 1.19178i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.4741 | − | 27.5559i | −0.699762 | − | 1.24612i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4924i | 0.744293i | 0.928174 | + | 0.372146i | \(0.121378\pi\) | ||||
−0.928174 | + | 0.372146i | \(0.878622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.78456i | − | 0.305561i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.3790 | + | 10.5945i | 0.781129 | + | 0.476185i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.43318 | − | 36.4924i | −0.423136 | − | 1.63691i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4924 | 0.559238 | 0.279619 | − | 0.960111i | \(-0.409792\pi\) | ||||
0.279619 | + | 0.960111i | \(0.409792\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.6155 | − | 31.3693i | −0.787004 | − | 1.40148i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.3790 | 0.774892 | 0.387446 | − | 0.921892i | \(-0.373357\pi\) | ||||
0.387446 | + | 0.921892i | \(0.373357\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.63068 | −0.384060 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.98402 | − | 8.87543i | −0.221348 | − | 0.394172i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.2520 | −1.29657 | −0.648286 | − | 0.761397i | \(-0.724514\pi\) | ||||
−0.648286 | + | 0.761397i | \(0.724514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.561553 | + | 15.6847i | −0.0247932 | + | 0.692495i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.9848i | 0.748442i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.5691i | 0.596770i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.43845 | + | 2.56155i | 0.0631408 | + | 0.112440i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6354 | 0.728808 | 0.364404 | − | 0.931241i | \(-0.381273\pi\) | ||||
0.364404 | + | 0.931241i | \(0.381273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.8459i | − | 0.692893i | −0.938070 | − | 0.346447i | \(-0.887388\pi\) | ||
0.938070 | − | 0.346447i | \(-0.112612\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.73529 | − | 7.02104i | −0.293952 | − | 0.306423i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.4924i | 1.24115i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7386 | 0.945158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.2177 | + | 26.6034i | −0.703790 | + | 1.15449i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.2462i | 1.13685i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 24.1636i | − | 1.04468i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.8255 | − | 7.20217i | 0.553459 | − | 0.310797i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5691 | − | 24.4924i | −0.584464 | − | 1.05496i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4924 | 0.623078 | 0.311539 | − | 0.950233i | \(-0.399156\pi\) | ||||
0.311539 | + | 0.950233i | \(0.399156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.8078 | − | 9.43845i | 0.721290 | − | 0.405043i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.417609 | 0.0178884 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.7386 | −1.65634 | −0.828172 | − | 0.560474i | \(-0.810619\pi\) | ||||
−0.828172 | + | 0.560474i | \(0.810619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.5083 | − | 17.3790i | −1.21671 | − | 0.741718i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39228 | −0.144516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1231 | − | 3.39228i | 0.558051 | − | 0.144255i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.8617 | − | 21.1231i | −0.503503 | − | 0.896626i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.38447i | 0.101033i | 0.998723 | + | 0.0505167i | \(0.0160868\pi\) | ||||
−0.998723 | + | 0.0505167i | \(0.983913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.7580i | − | 1.47011i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.4924 | − | 20.4924i | 1.54071 | − | 0.865191i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.8730 | 0.500387 | 0.250193 | − | 0.968196i | \(-0.419506\pi\) | ||||
0.250193 | + | 0.968196i | \(0.419506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.68951i | − | 0.365570i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.8588 | − | 17.7623i | −0.666006 | − | 0.745946i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.3693i | − | 1.65045i | −0.564806 | − | 0.825224i | \(-0.691049\pi\) | ||
0.564806 | − | 0.825224i | \(-0.308951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.7386 | 0.951582 | 0.475791 | − | 0.879558i | \(-0.342162\pi\) | ||||
0.475791 | + | 0.879558i | \(0.342162\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.43318 | + | 5.29723i | −0.394077 | + | 0.221295i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.38447i | 0.0994394i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.7327i | − | 1.57083i | −0.618967 | − | 0.785417i | \(-0.712449\pi\) | ||
0.618967 | − | 0.785417i | \(-0.287551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.743668 | + | 1.32431i | 0.0309058 | + | 0.0550363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.9824 | + | 11.3693i | −1.82470 | + | 0.471679i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.4924 | 1.51136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.8769 | − | 11.5076i | −0.780464 | − | 0.475780i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.18348 | 0.131396 | 0.0656981 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656981 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.2462 | 0.587005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.1702 | + | 9.64198i | −0.706288 | + | 0.396618i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2431 | −0.543828 | −0.271914 | − | 0.962322i | \(-0.587657\pi\) | ||||
−0.271914 | + | 0.962322i | \(0.587657\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.2462 | − | 6.78456i | 1.07599 | − | 0.278140i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.3693 | + | 12.0000i | −0.874588 | + | 0.491127i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.24621i | 0.255213i | 0.991825 | + | 0.127607i | \(0.0407295\pi\) | ||||
−0.991825 | + | 0.127607i | \(0.959270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.3790i | − | 0.708905i | −0.935074 | − | 0.354452i | \(-0.884667\pi\) | ||
0.935074 | − | 0.354452i | \(-0.115333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.50758 | − | 5.75379i | 0.142840 | − | 0.234312i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.48071 | −0.344790 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.163030i | 0.00661717i | 0.999995 | + | 0.00330858i | \(0.00105316\pi\) | ||||
−0.999995 | + | 0.00330858i | \(0.998947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.71407 | − | 3.56291i | 0.150502 | − | 0.144377i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14.7386i | − | 0.596261i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.4924 | −0.908460 | −0.454230 | − | 0.890884i | \(-0.650086\pi\) | ||||
−0.454230 | + | 0.890884i | \(0.650086\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.68951 | + | 15.4741i | 0.350395 | + | 0.623975i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.61553i | 0.387107i | 0.981090 | + | 0.193553i | \(0.0620012\pi\) | ||||
−0.981090 | + | 0.193553i | \(0.937999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.53311i | 0.0616209i | 0.999525 | + | 0.0308105i | \(0.00980883\pi\) | ||||
−0.999525 | + | 0.0308105i | \(0.990191\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.208805 | + | 5.83209i | −0.00837904 | + | 0.234034i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.1636 | + | 6.24621i | −0.968094 | + | 0.250249i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.2462 | − | 18.2462i | −0.409194 | − | 0.728683i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.8145 | −1.98623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.12311 | −0.203948 | −0.101974 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101974 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.90495 | − | 3.39228i | −0.0757148 | − | 0.134831i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.5691 | 0.538474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7386 | + | 26.6034i | 0.583966 | + | 1.05406i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.4924 | + | 22.2462i | 1.44362 | + | 0.880047i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.1080i | 1.50517i | 0.658493 | + | 0.752587i | \(0.271194\pi\) | ||||
−0.658493 | + | 0.752587i | \(0.728806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.7123i | 1.36892i | 0.729051 | + | 0.684459i | \(0.239962\pi\) | ||||
−0.729051 | + | 0.684459i | \(0.760038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.5076 | − | 20.4924i | −0.453110 | − | 0.806888i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.39228 | −0.133364 | −0.0666822 | − | 0.997774i | \(-0.521241\pi\) | ||||
−0.0666822 | + | 0.997774i | \(0.521241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 41.5426i | − | 1.63069i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.5976 | + | 14.9628i | −0.611318 | + | 0.586438i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.1080i | 1.02168i | 0.859675 | + | 0.510842i | \(0.170666\pi\) | ||||
−0.859675 | + | 0.510842i | \(0.829334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.63068 | 0.337229 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 9.75379i | − | 0.379954i | −0.981789 | − | 0.189977i | \(-0.939159\pi\) | ||
0.981789 | − | 0.189977i | \(-0.0608413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1725i | 1.56253i | 0.624200 | + | 0.781265i | \(0.285425\pi\) | ||||
−0.624200 | + | 0.781265i | \(0.714575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.6377 | + | 22.2586i | −1.53940 | + | 0.864454i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.39228 | − | 13.1231i | −0.131547 | − | 0.508892i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.26137 | −0.0488403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.7386 | − | 22.8769i | 1.57505 | − | 0.884472i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.5173 | 1.71857 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.75379 | −0.298887 | −0.149443 | − | 0.988770i | \(-0.547748\pi\) | ||||
−0.149443 | + | 0.988770i | \(0.547748\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.0249 | + | 0.394722i | 0.424349 | + | 0.0151928i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.208805 | −0.00802501 | −0.00401250 | − | 0.999992i | \(-0.501277\pi\) | ||||
−0.00401250 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2462 | − | 39.6377i | −0.393213 | − | 1.52115i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.19224 | + | 12.8078i | 0.275607 | + | 0.490795i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 28.9848i | − | 1.10907i | −0.832159 | − | 0.554537i | \(-0.812895\pi\) | ||
0.832159 | − | 0.554537i | \(-0.187105\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.80989i | − | 0.145568i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.9309 | − | 16.8078i | 1.14193 | − | 0.641256i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.6377 | −1.51007 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.11550i | 0.0424357i | 0.999775 | + | 0.0212179i | \(0.00675436\pi\) | ||||
−0.999775 | + | 0.0212179i | \(0.993246\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.3822 | + | 9.21544i | 1.15412 | + | 0.350065i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 12.1383i | − | 0.460430i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.4924 | 1.38225 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.9481 | − | 17.3790i | 1.17057 | − | 0.657335i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.3542i | − | 1.67523i | −0.546258 | − | 0.837617i | \(-0.683948\pi\) | ||
0.546258 | − | 0.837617i | \(-0.316052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9073i | 0.939395i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.87962 | − | 8.68951i | −0.183777 | − | 0.327266i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.0343 | + | 3.36932i | −0.490204 | + | 0.126716i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2462 | −1.06081 | −0.530404 | − | 0.847745i | \(-0.677960\pi\) | ||||
−0.530404 | + | 0.847745i | \(0.677960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | + | 13.1231i | −0.300023 | + | 0.492155i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.29723 | 0.198383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.4773 | 1.10239 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.7779 | + | 7.73704i | −0.514546 | + | 0.288945i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.3658 | 1.16975 | 0.584873 | − | 0.811125i | \(-0.301144\pi\) | ||||
0.584873 | + | 0.811125i | \(0.301144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.63068 | + | 25.6509i | 0.246940 | + | 0.955290i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.1231 | + | 7.36932i | −0.488054 | + | 0.274068i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.38447i | 0.0885571i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.7465i | 1.77082i | 0.464810 | + | 0.885410i | \(0.346123\pi\) | ||||
−0.464810 | + | 0.885410i | \(0.653877\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9309 | + | 1.93087i | 0.997440 | + | 0.0715137i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.3272 | −1.78744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.4830i | − | 1.16285i | −0.813599 | − | 0.581426i | \(-0.802495\pi\) | ||
0.813599 | − | 0.581426i | \(-0.197505\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.4973 | + | 10.8050i | 0.645397 | + | 0.398550i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.98485i | 0.330961i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0000 | 0.882854 | 0.441427 | − | 0.897297i | \(-0.354472\pi\) | ||||
0.441427 | + | 0.897297i | \(0.354472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1293 | + | 19.8188i | 0.408846 | + | 0.728063i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.1231i | − | 0.628186i | −0.949392 | − | 0.314093i | \(-0.898300\pi\) | ||
0.949392 | − | 0.314093i | \(-0.101700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 29.0432i | − | 1.06406i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.8122 | − | 43.9824i | 0.981007 | − | 1.60923i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.43318 | − | 36.4924i | −0.344681 | − | 1.33340i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.9848 | −1.20363 | −0.601817 | − | 0.798634i | \(-0.705556\pi\) | ||||
−0.601817 | + | 0.798634i | \(0.705556\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.5616 | − | 25.9309i | −0.530652 | − | 0.944973i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.1889 | 0.771143 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4924 | 1.25365 | 0.626824 | − | 0.779161i | \(-0.284354\pi\) | ||||
0.626824 | + | 0.779161i | \(0.284354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.80989 | − | 6.78456i | −0.138290 | − | 0.246264i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6354 | 0.603031 | 0.301516 | − | 0.953461i | \(-0.402507\pi\) | ||||
0.301516 | + | 0.953461i | \(0.402507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.630683 | − | 0.163030i | 0.0228323 | − | 0.00590207i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0000 | + | 26.2462i | −0.578481 | + | 0.948934i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.1231i | 1.62930i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 26.0685i | − | 0.940055i | −0.882652 | − | 0.470028i | \(-0.844244\pi\) | ||
0.882652 | − | 0.470028i | \(-0.155756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.4924 | + | 22.2462i | 0.449904 | + | 0.801178i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0498 | 0.793077 | 0.396539 | − | 0.918018i | \(-0.370211\pi\) | ||||
0.396539 | + | 0.918018i | \(0.370211\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.0138i | − | 0.359707i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −26.1601 | − | 27.2699i | −0.938488 | − | 0.978304i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 18.2462i | − | 0.653738i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.9848 | −2.03908 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.208805 | + | 5.83209i | −0.00746206 | + | 0.208422i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.13826i | 0.147701i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.3332i | − | 0.617863i | −0.951084 | − | 0.308932i | \(-0.900029\pi\) | ||
0.951084 | − | 0.308932i | \(-0.0999715\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.5968 | + | 18.8664i | −1.19608 | + | 0.671660i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.39228 | − | 13.1231i | −0.120616 | − | 0.466604i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.3542 | −1.71711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.3693 | + | 13.1231i | −0.828824 | + | 0.465429i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.9548 | 0.848522 | 0.424261 | − | 0.905540i | \(-0.360534\pi\) | ||||
0.424261 | + | 0.905540i | \(0.360534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.4924 | −0.724970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.7304 | − | 24.1636i | 0.520473 | − | 0.853778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26137 | − | 4.87962i | −0.0444573 | − | 0.171984i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.31534 | − | 7.68466i | −0.151907 | − | 0.270513i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.6155i | 1.18186i | 0.806723 | + | 0.590930i | \(0.201239\pi\) | ||||
−0.806723 | + | 0.590930i | \(0.798761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.41273i | 0.225181i | 0.993641 | + | 0.112591i | \(0.0359149\pi\) | ||||
−0.993641 | + | 0.112591i | \(0.964085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.2462 | + | 11.3693i | −0.710066 | + | 0.398739i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.9481 | −1.08407 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.1636i | 0.845377i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −33.0008 | − | 10.0097i | −1.15314 | − | 0.349767i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.12311i | − | 0.0391967i | −0.999808 | − | 0.0195983i | \(-0.993761\pi\) | ||
0.999808 | − | 0.0195983i | \(-0.00623874\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.8769 | −0.379145 | −0.189572 | − | 0.981867i | \(-0.560710\pi\) | ||||
−0.189572 | + | 0.981867i | \(0.560710\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.8255 | + | 7.20217i | −0.446525 | + | 0.250747i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.7386i | − | 0.651606i | −0.945438 | − | 0.325803i | \(-0.894365\pi\) | ||
0.945438 | − | 0.325803i | \(-0.105635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.43981i | − | 0.0847381i | −0.999102 | − | 0.0423690i | \(-0.986509\pi\) | ||
0.999102 | − | 0.0423690i | \(-0.0134905\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.69614 | + | 3.02045i | 0.0588385 | + | 0.104778i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.9890 | − | 20.4924i | 1.28159 | − | 0.710020i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.2311 | −1.21922 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.876894 | − | 24.4924i | 0.0303099 | − | 0.846582i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.20217 | 0.248647 | 0.124323 | − | 0.992242i | \(-0.460324\pi\) | ||||
0.124323 | + | 0.992242i | \(0.460324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.7386 | 0.956505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.1636 | + | 13.5691i | −0.832238 | + | 0.467346i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.96804 | −0.342911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8078 | + | 3.31077i | −0.440080 | + | 0.113759i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.9309 | + | 13.4384i | −0.821305 | + | 0.461206i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.26137i | 0.317476i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9392i | 0.511509i | 0.966742 | + | 0.255754i | \(0.0823238\pi\) | ||||
−0.966742 | + | 0.255754i | \(0.917676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.1231 | + | 8.00000i | 0.448801 | + | 0.273594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.743668 | −0.0254032 | −0.0127016 | − | 0.999919i | \(-0.504043\pi\) | ||||
−0.0127016 | + | 0.999919i | \(0.504043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9663i | 0.374165i | 0.982344 | + | 0.187082i | \(0.0599032\pi\) | ||||
−0.982344 | + | 0.187082i | \(0.940097\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.1640 | + | 19.9770i | 0.653107 | + | 0.680816i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 55.2311i | − | 1.88009i | −0.341055 | − | 0.940044i | \(-0.610784\pi\) | ||
0.341055 | − | 0.940044i | \(-0.389216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.87689 | 0.0978173 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.5309 | + | 29.4379i | 0.561420 | + | 0.999764i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 20.4924i | − | 0.695158i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.75924i | − | 0.330679i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.6377 | + | 24.1636i | 1.34153 | + | 0.817813i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.9481 | + | 8.00000i | −1.04624 | + | 0.270449i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7538 | 0.396897 | 0.198449 | − | 0.980111i | \(-0.436410\pi\) | ||||
0.198449 | + | 0.980111i | \(0.436410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.5464 | + | 41.9309i | 0.794200 | + | 1.41429i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7051 | 0.596499 | 0.298250 | − | 0.954488i | \(-0.403597\pi\) | ||||
0.298250 | + | 0.954488i | \(0.403597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.7386 | 0.765216 | 0.382608 | − | 0.923911i | \(-0.375026\pi\) | ||||
0.382608 | + | 0.923911i | \(0.375026\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.9392 | + | 26.6034i | 0.502176 | + | 0.894263i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1768 | −0.341705 | −0.170853 | − | 0.985297i | \(-0.554652\pi\) | ||||
−0.170853 | + | 0.985297i | \(0.554652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.4924 | − | 5.29723i | 0.687294 | − | 0.177663i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.0000 | + | 16.4924i | −1.07204 | + | 0.552517i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2462i | 0.342876i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 14.4043i | − | 0.481484i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.13826 | + | 7.36932i | 0.138173 | + | 0.246054i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.29723 | 0.176672 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.1117i | 1.83604i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.3790 | − | 26.4557i | −0.844561 | − | 0.880391i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.8769i | − | 0.627489i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.94584 | − | 13.0343i | 0.263547 | − | 0.432319i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.12311i | − | 0.0372101i | −0.999827 | − | 0.0186051i | \(-0.994077\pi\) | ||
0.999827 | − | 0.0186051i | \(-0.00592252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.6809i | 2.27300i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.5083 | + | 16.0089i | −0.942457 | + | 0.529239i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.0343 | − | 3.36932i | 0.430429 | − | 0.111265i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.6155 | −1.37277 | −0.686385 | − | 0.727239i | \(-0.740803\pi\) | ||||
−0.686385 | + | 0.727239i | \(0.740803\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.6847 | + | 12.1771i | −0.714534 | + | 0.401248i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.8963 | 2.03734 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.5076 | 0.575646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.6509 | − | 15.6371i | −0.842487 | − | 0.513590i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.8255 | 0.420790 | 0.210395 | − | 0.977616i | \(-0.432525\pi\) | ||||
0.210395 | + | 0.977616i | \(0.432525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.2462 | − | 18.4945i | −0.335806 | − | 0.606133i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.75379 | + | 10.2462i | 0.188371 | + | 0.335446i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 40.9848i | − | 1.34035i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.3537i | − | 0.664926i | −0.943116 | − | 0.332463i | \(-0.892120\pi\) | ||
0.943116 | − | 0.332463i | \(-0.107880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.6155 | + | 27.8617i | −1.61914 | + | 0.909234i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.9548 | 0.780903 | 0.390452 | − | 0.920623i | \(-0.372319\pi\) | ||||
0.390452 | + | 0.920623i | \(0.372319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.78456i | − | 0.220936i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.7704 | + | 5.02433i | −0.740720 | + | 0.163441i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.7386i | 0.868889i | 0.900699 | + | 0.434444i | \(0.143055\pi\) | ||||
−0.900699 | + | 0.434444i | \(0.856945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.7779 | − | 7.73704i | 0.446780 | − | 0.250891i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.24621i | − | 0.0727619i | −0.999338 | − | 0.0363810i | \(-0.988417\pi\) | ||
0.999338 | − | 0.0363810i | \(-0.0115830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.5945i | 0.342829i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.80989 | − | 6.78456i | −0.123156 | − | 0.219314i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.48734 | − | 5.75379i | −0.0480286 | − | 0.185800i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.75379 | 0.282380 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.4924 | + | 22.2462i | 1.17595 | + | 0.716874i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.48734 | 0.0478791 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.50758 | 0.112796 | 0.0563980 | − | 0.998408i | \(-0.482038\pi\) | ||||
0.0563980 | + | 0.998408i | \(0.482038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.5559 | − | 15.4741i | 0.885222 | − | 0.497099i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.0619 | 1.06101 | 0.530503 | − | 0.847683i | \(-0.322003\pi\) | ||||
0.530503 | + | 0.847683i | \(0.322003\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.73863 | − | 18.3315i | −0.151914 | − | 0.587681i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.9309 | − | 7.82292i | 0.446145 | − | 0.250534i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.7538i | 0.951908i | 0.879470 | + | 0.475954i | \(0.157897\pi\) | ||||
−0.879470 | + | 0.475954i | \(0.842103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.7327i | 1.20594i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.384472 | + | 0.630683i | −0.0122752 | + | 0.0201362i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.1250 | 1.31168 | 0.655842 | − | 0.754898i | \(-0.272314\pi\) | ||||
0.655842 | + | 0.754898i | \(0.272314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2840i | 0.614438i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.7616 | − | 11.2182i | −0.342545 | − | 0.357078i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.98485i | 0.285701i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1231 | −1.17925 | −0.589627 | − | 0.807676i | \(-0.700725\pi\) | ||||
−0.589627 | + | 0.807676i | \(0.700725\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.6642 | + | 20.7713i | 0.370152 | + | 0.659157i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000i | 0.760851i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 11.1293i | − | 0.352469i | −0.984348 | − | 0.176235i | \(-0.943608\pi\) | ||
0.984348 | − | 0.176235i | \(-0.0563917\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.8211 | + | 1.53311i | 1.35480 | + | 0.0485055i |
(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 | 672.2.k.d.545.6 | yes | 8 | |
3.2 | odd | 2 | inner | 672.2.k.d.545.4 | yes | 8 | |
4.3 | odd | 2 | 672.2.k.a.545.3 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 672.2.k.d.545.3 | yes | 8 | |
8.3 | odd | 2 | 1344.2.k.e.1217.6 | 8 | |||
8.5 | even | 2 | 1344.2.k.j.1217.3 | 8 | |||
12.11 | even | 2 | 672.2.k.a.545.5 | yes | 8 | ||
21.20 | even | 2 | inner | 672.2.k.d.545.5 | yes | 8 | |
24.5 | odd | 2 | 1344.2.k.j.1217.5 | 8 | |||
24.11 | even | 2 | 1344.2.k.e.1217.4 | 8 | |||
28.27 | even | 2 | 672.2.k.a.545.6 | yes | 8 | ||
56.13 | odd | 2 | 1344.2.k.j.1217.6 | 8 | |||
56.27 | even | 2 | 1344.2.k.e.1217.3 | 8 | |||
84.83 | odd | 2 | 672.2.k.a.545.4 | yes | 8 | ||
168.83 | odd | 2 | 1344.2.k.e.1217.5 | 8 | |||
168.125 | even | 2 | 1344.2.k.j.1217.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.k.a.545.3 | ✓ | 8 | 4.3 | odd | 2 | ||
672.2.k.a.545.4 | yes | 8 | 84.83 | odd | 2 | ||
672.2.k.a.545.5 | yes | 8 | 12.11 | even | 2 | ||
672.2.k.a.545.6 | yes | 8 | 28.27 | even | 2 | ||
672.2.k.d.545.3 | yes | 8 | 7.6 | odd | 2 | inner | |
672.2.k.d.545.4 | yes | 8 | 3.2 | odd | 2 | inner | |
672.2.k.d.545.5 | yes | 8 | 21.20 | even | 2 | inner | |
672.2.k.d.545.6 | yes | 8 | 1.1 | even | 1 | trivial | |
1344.2.k.e.1217.3 | 8 | 56.27 | even | 2 | |||
1344.2.k.e.1217.4 | 8 | 24.11 | even | 2 | |||
1344.2.k.e.1217.5 | 8 | 168.83 | odd | 2 | |||
1344.2.k.e.1217.6 | 8 | 8.3 | odd | 2 | |||
1344.2.k.j.1217.3 | 8 | 8.5 | even | 2 | |||
1344.2.k.j.1217.4 | 8 | 168.125 | even | 2 | |||
1344.2.k.j.1217.5 | 8 | 24.5 | odd | 2 | |||
1344.2.k.j.1217.6 | 8 | 56.13 | odd | 2 |