Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (of order \(10\), degree \(4\), 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{60})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(-0.994522 + 0.104528i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1500.649 |
Dual form | 1500.2.o.a.349.1 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.747238i | 0.282430i | 0.989979 | + | 0.141215i | \(0.0451008\pi\) | ||||
−0.989979 | + | 0.141215i | \(0.954899\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0646021 | − | 0.198825i | 0.0194783 | − | 0.0599480i | −0.940845 | − | 0.338837i | \(-0.889966\pi\) |
0.960323 | + | 0.278889i | \(0.0899663\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.38108 | + | 0.773659i | −0.660392 | + | 0.214574i | −0.619991 | − | 0.784609i | \(-0.712864\pi\) |
−0.0404014 | + | 0.999184i | \(0.512864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00842 | + | 5.51712i | 0.972185 | + | 1.33810i | 0.940935 | + | 0.338586i | \(0.109949\pi\) |
0.0312497 | + | 0.999512i | \(0.490051\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00739 | − | 0.731913i | 0.231112 | − | 0.167912i | −0.466203 | − | 0.884678i | \(-0.654378\pi\) |
0.697314 | + | 0.716766i | \(0.254378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.604528 | − | 0.439216i | −0.131919 | − | 0.0958447i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.09174 | − | 1.00457i | −0.644673 | − | 0.209467i | −0.0316092 | − | 0.999500i | \(-0.510063\pi\) |
−0.613064 | + | 0.790033i | \(0.710063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.19332 | − | 3.04662i | −0.778680 | − | 0.565744i | 0.125903 | − | 0.992043i | \(-0.459817\pi\) |
−0.904582 | + | 0.426299i | \(0.859817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.02547 | + | 2.19813i | −0.543390 | + | 0.394796i | −0.825342 | − | 0.564633i | \(-0.809018\pi\) |
0.281953 | + | 0.959428i | \(0.409018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.122881 | + | 0.169131i | 0.0213908 | + | 0.0294419i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.86924 | + | 0.607352i | −0.307301 | + | 0.0998480i | −0.458608 | − | 0.888639i | \(-0.651652\pi\) |
0.151307 | + | 0.988487i | \(0.451652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.773659 | − | 2.38108i | 0.123885 | − | 0.381278i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.993096 | + | 3.05644i | 0.155096 | + | 0.477335i | 0.998171 | − | 0.0604609i | \(-0.0192570\pi\) |
−0.843075 | + | 0.537796i | \(0.819257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.7127i | 1.93866i | 0.245755 | + | 0.969332i | \(0.420964\pi\) | ||||
−0.245755 | + | 0.969332i | \(0.579036\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.81017 | + | 5.24425i | −0.555770 | + | 0.764952i | −0.990781 | − | 0.135473i | \(-0.956745\pi\) |
0.435011 | + | 0.900425i | \(0.356745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.44163 | 0.920234 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.81953 | −0.954926 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.43520 | + | 3.35177i | −0.334501 | + | 0.460401i | −0.942825 | − | 0.333288i | \(-0.891842\pi\) |
0.608325 | + | 0.793688i | \(0.291842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.24520i | 0.164931i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.61882 | − | 11.1376i | −0.471131 | − | 1.44999i | −0.851106 | − | 0.524995i | \(-0.824067\pi\) |
0.379975 | − | 0.924997i | \(-0.375933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85634 | + | 11.8686i | −0.493753 | + | 1.51962i | 0.325138 | + | 0.945667i | \(0.394589\pi\) |
−0.818891 | + | 0.573949i | \(0.805411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.710666 | − | 0.230909i | 0.0895355 | − | 0.0290918i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71460 | − | 2.35995i | −0.209472 | − | 0.288314i | 0.691334 | − | 0.722535i | \(-0.257023\pi\) |
−0.900806 | + | 0.434222i | \(0.857023\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.62999 | − | 1.91080i | 0.316614 | − | 0.230034i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.29912 | − | 3.85004i | −0.628890 | − | 0.456916i | 0.227125 | − | 0.973866i | \(-0.427067\pi\) |
−0.856016 | + | 0.516950i | \(0.827067\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.39603 | + | 0.778516i | 0.280434 | + | 0.0911184i | 0.445857 | − | 0.895104i | \(-0.352899\pi\) |
−0.165423 | + | 0.986223i | \(0.552899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.148570 | + | 0.0482732i | 0.0169311 | + | 0.00550124i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.28621 | − | 6.02028i | −0.932271 | − | 0.677335i | 0.0142765 | − | 0.999898i | \(-0.495455\pi\) |
−0.946548 | + | 0.322563i | \(0.895455\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.33658 | − | 4.59240i | −0.366237 | − | 0.504082i | 0.585636 | − | 0.810574i | \(-0.300845\pi\) |
−0.951873 | + | 0.306492i | \(0.900845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.92954 | − | 1.60171i | 0.528502 | − | 0.171721i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.284829 | − | 0.876615i | 0.0301919 | − | 0.0929210i | −0.934825 | − | 0.355109i | \(-0.884444\pi\) |
0.965017 | + | 0.262188i | \(0.0844439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.578108 | − | 1.77923i | −0.0606022 | − | 0.186514i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.73968i | − | 0.387787i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.13679 | + | 12.5757i | −0.927700 | + | 1.27687i | 0.0330496 | + | 0.999454i | \(0.489478\pi\) |
−0.960750 | + | 0.277416i | \(0.910522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.209057 | −0.0210110 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0405 | −1.09857 | −0.549285 | − | 0.835635i | \(-0.685100\pi\) | ||||
−0.549285 | + | 0.835635i | \(0.685100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.16097 | + | 11.2326i | −0.804124 | + | 1.10678i | 0.188079 | + | 0.982154i | \(0.439774\pi\) |
−0.992203 | + | 0.124628i | \(0.960226\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.02510i | 0.0991002i | 0.998772 | + | 0.0495501i | \(0.0157788\pi\) | ||||
−0.998772 | + | 0.0495501i | \(0.984221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.07199 | + | 6.37694i | 0.198461 | + | 0.610800i | 0.999919 | + | 0.0127488i | \(0.00405817\pi\) |
−0.801458 | + | 0.598051i | \(0.795942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.607352 | − | 1.86924i | 0.0576473 | − | 0.177420i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.91428 | − | 2.57151i | 0.744513 | − | 0.241907i | 0.0878944 | − | 0.996130i | \(-0.471986\pi\) |
0.656618 | + | 0.754223i | \(0.271986\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.47159 | + | 2.02547i | 0.136048 | + | 0.187254i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.12260 | + | 2.99525i | −0.377918 | + | 0.274574i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.86383 | + | 6.43995i | 0.805803 | + | 0.585450i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.05644 | − | 0.993096i | −0.275590 | − | 0.0895445i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8248 | − | 4.49195i | −1.22675 | − | 0.398597i | −0.377217 | − | 0.926125i | \(-0.623119\pi\) |
−0.849537 | + | 0.527529i | \(0.823119\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.2848 | − | 7.47232i | −0.905523 | − | 0.657901i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00611 | + | 4.36370i | −0.524757 | + | 0.381258i | −0.818393 | − | 0.574659i | \(-0.805135\pi\) |
0.293636 | + | 0.955917i | \(0.405135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.546913 | + | 0.752762i | 0.0474234 | + | 0.0652727i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.97636 | − | 2.26676i | 0.596030 | − | 0.193662i | 0.00456114 | − | 0.999990i | \(-0.498548\pi\) |
0.591469 | + | 0.806328i | \(0.298548\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.10219 | + | 18.7806i | −0.517581 | + | 1.59295i | 0.260954 | + | 0.965351i | \(0.415963\pi\) |
−0.778536 | + | 0.627600i | \(0.784037\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00313 | − | 6.16499i | −0.168694 | − | 0.519185i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.523398i | 0.0437687i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.78630 | + | 5.21139i | −0.312289 | + | 0.429828i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.7551 | 1.78224 | 0.891122 | − | 0.453763i | \(-0.149919\pi\) | ||||
0.891122 | + | 0.453763i | \(0.149919\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1308 | 0.824432 | 0.412216 | − | 0.911086i | \(-0.364755\pi\) | ||||
0.412216 | + | 0.911086i | \(0.364755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00842 | − | 5.51712i | 0.324062 | − | 0.446033i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.99520i | − | 0.797704i | −0.917015 | − | 0.398852i | \(-0.869409\pi\) | ||
0.917015 | − | 0.398852i | \(-0.130591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.28026 | − | 3.94024i | −0.101531 | − | 0.312481i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.750652 | − | 2.31027i | 0.0591597 | − | 0.182075i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.43763 | + | 0.792035i | −0.190930 | + | 0.0620369i | −0.402921 | − | 0.915235i | \(-0.632005\pi\) |
0.211991 | + | 0.977272i | \(0.432005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.2560 | + | 16.8690i | 0.948401 | + | 1.30536i | 0.952234 | + | 0.305369i | \(0.0987797\pi\) |
−0.00383355 | + | 0.999993i | \(0.501220\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.44624 | + | 3.95692i | −0.418941 | + | 0.304379i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00739 | − | 0.731913i | −0.0770372 | − | 0.0559708i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.95438 | − | 0.635016i | −0.148589 | − | 0.0482794i | 0.233778 | − | 0.972290i | \(-0.424891\pi\) |
−0.382367 | + | 0.924011i | \(0.624891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1376 | + | 3.61882i | 0.837153 | + | 0.272007i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8247 | − | 11.4973i | −1.18279 | − | 0.859349i | −0.190309 | − | 0.981724i | \(-0.560949\pi\) |
−0.992484 | + | 0.122375i | \(0.960949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.96251 | − | 4.33202i | 0.443190 | − | 0.321996i | −0.343711 | − | 0.939075i | \(-0.611684\pi\) |
0.786901 | + | 0.617079i | \(0.211684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.33519 | − | 10.0960i | −0.542233 | − | 0.746319i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.35589 | − | 0.440557i | 0.0991528 | − | 0.0322167i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.230909 | + | 0.710666i | −0.0167962 | + | 0.0516933i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.693806 | − | 2.13532i | −0.0502021 | − | 0.154506i | 0.922813 | − | 0.385249i | \(-0.125884\pi\) |
−0.973015 | + | 0.230743i | \(0.925884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.10589i | − | 0.0796035i | −0.999208 | − | 0.0398018i | \(-0.987327\pi\) | ||
0.999208 | − | 0.0398018i | \(-0.0126726\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1299 | − | 16.6953i | 0.864217 | − | 1.18949i | −0.116331 | − | 0.993211i | \(-0.537113\pi\) |
0.980547 | − | 0.196282i | \(-0.0628868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3822 | 0.877749 | 0.438874 | − | 0.898548i | \(-0.355377\pi\) | ||||
0.438874 | + | 0.898548i | \(0.355377\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.91706 | 0.205753 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.27655 | − | 3.13341i | 0.159783 | − | 0.219922i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.25085i | 0.225950i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0804429 | − | 0.247578i | −0.00556435 | − | 0.0171253i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.37422 | − | 19.6178i | 0.438820 | − | 1.35055i | −0.450302 | − | 0.892876i | \(-0.648684\pi\) |
0.889121 | − | 0.457671i | \(-0.151316\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.22949 | − | 2.02409i | 0.426838 | − | 0.138688i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.64253 | − | 2.26074i | −0.111502 | − | 0.153469i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.03818 | + | 1.48083i | −0.137728 | + | 0.100065i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8127 | − | 10.0355i | −0.929145 | − | 0.675063i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.95129 | + | 1.28385i | 0.264598 | + | 0.0859732i | 0.438312 | − | 0.898823i | \(-0.355577\pi\) |
−0.173713 | + | 0.984796i | \(0.555577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.4725 | − | 7.30175i | −1.49155 | − | 0.484634i | −0.554010 | − | 0.832510i | \(-0.686903\pi\) |
−0.937541 | + | 0.347876i | \(0.886903\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7565 | + | 10.7212i | 0.975139 | + | 0.708480i | 0.956617 | − | 0.291348i | \(-0.0941039\pi\) |
0.0185221 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.126381 | + | 0.0918211i | −0.00831525 | + | 0.00604138i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.33276 | + | 1.83438i | 0.0873117 | + | 0.120174i | 0.850438 | − | 0.526075i | \(-0.176337\pi\) |
−0.763127 | + | 0.646249i | \(0.776337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.74102 | − | 3.16505i | 0.632747 | − | 0.205592i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.28631 | + | 16.2696i | −0.341943 | + | 1.05239i | 0.621257 | + | 0.783607i | \(0.286622\pi\) |
−0.963200 | + | 0.268786i | \(0.913378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.71435 | + | 26.8200i | 0.561341 | + | 1.72763i | 0.678581 | + | 0.734526i | \(0.262595\pi\) |
−0.117240 | + | 0.993104i | \(0.537405\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.83243 | + | 2.52212i | −0.116595 | + | 0.160479i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.67652 | 0.359735 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9575 | 1.51219 | 0.756093 | − | 0.654464i | \(-0.227106\pi\) | ||||
0.756093 | + | 0.654464i | \(0.227106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.399467 | + | 0.549819i | −0.0251142 | + | 0.0345668i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.5421i | − | 1.78041i | −0.455561 | − | 0.890204i | \(-0.650561\pi\) | ||
0.455561 | − | 0.890204i | \(-0.349439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.453837 | − | 1.39677i | −0.0282000 | − | 0.0867908i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.60171 | + | 4.92954i | −0.0991431 | + | 0.305131i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.38270 | + | 1.09911i | −0.208586 | + | 0.0677738i | −0.411447 | − | 0.911434i | \(-0.634976\pi\) |
0.202860 | + | 0.979208i | \(0.434976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.541778 | + | 0.745693i | 0.0331563 | + | 0.0456357i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.6733 | − | 17.1997i | 1.44339 | − | 1.04868i | 0.456066 | − | 0.889946i | \(-0.349258\pi\) |
0.987321 | − | 0.158736i | \(-0.0507419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0784 | + | 14.5878i | 1.21968 | + | 0.886147i | 0.996073 | − | 0.0885338i | \(-0.0282181\pi\) |
0.223603 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.77923 | + | 0.578108i | 0.107684 | + | 0.0349887i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5745 | − | 5.38539i | −0.995867 | − | 0.323577i | −0.234654 | − | 0.972079i | \(-0.575396\pi\) |
−0.761213 | + | 0.648502i | \(0.775396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.02547 | + | 2.19813i | 0.181130 | + | 0.131599i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.03664 | + | 2.20625i | −0.181151 | + | 0.131614i | −0.674665 | − | 0.738124i | \(-0.735712\pi\) |
0.493515 | + | 0.869738i | \(0.335712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.62409 | + | 13.2464i | 0.572093 | + | 0.787418i | 0.992801 | − | 0.119778i | \(-0.0382183\pi\) |
−0.420708 | + | 0.907196i | \(0.638218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.28389 | + | 0.742080i | −0.134814 | + | 0.0438036i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.11787 | + | 28.0619i | −0.536345 | + | 1.65070i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.80349 | − | 14.7836i | −0.281586 | − | 0.866632i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.70991i | − | 0.508838i | −0.967094 | − | 0.254419i | \(-0.918116\pi\) | ||
0.967094 | − | 0.254419i | \(-0.0818843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.122881 | − | 0.169131i | 0.00713025 | − | 0.00981395i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.13888 | 0.470683 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.49939 | −0.547536 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.48944 | − | 8.93194i | 0.372808 | − | 0.513127i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.7123i | − | 1.01090i | −0.862857 | − | 0.505448i | \(-0.831327\pi\) | ||
0.862857 | − | 0.505448i | \(-0.168673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.29048 | − | 13.2047i | −0.244077 | − | 0.751191i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.26921 | − | 19.2946i | 0.355494 | − | 1.09410i | −0.600228 | − | 0.799829i | \(-0.704924\pi\) |
0.955722 | − | 0.294270i | \(-0.0950763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7535 | − | 6.41831i | 1.11654 | − | 0.362785i | 0.308091 | − | 0.951357i | \(-0.400310\pi\) |
0.808445 | + | 0.588572i | \(0.200310\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.85429 | + | 13.5633i | 0.553472 | + | 0.761789i | 0.990478 | − | 0.137670i | \(-0.0439613\pi\) |
−0.437006 | + | 0.899458i | \(0.643961\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.876642 | + | 0.636918i | −0.0490825 | + | 0.0356606i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.829324 | − | 0.602539i | −0.0462884 | − | 0.0336305i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.07610 | + | 2.62408i | 0.449366 | + | 0.146008i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.37694 | − | 2.07199i | −0.352646 | − | 0.114582i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.91870 | − | 2.84711i | −0.216045 | − | 0.156966i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.2090 | − | 15.4092i | 1.16575 | − | 0.846968i | 0.175257 | − | 0.984523i | \(-0.443924\pi\) |
0.990494 | + | 0.137555i | \(0.0439243\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.15525 | + | 1.59007i | 0.0633074 | + | 0.0871352i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7298 | − | 8.03519i | 1.34712 | − | 0.437705i | 0.455395 | − | 0.890289i | \(-0.349498\pi\) |
0.891722 | + | 0.452584i | \(0.149498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.57151 | + | 7.91428i | −0.139665 | + | 0.429845i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.241591 | + | 0.743542i | 0.0130829 | + | 0.0402651i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0441i | 0.542331i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.70460 | − | 3.72256i | 0.145191 | − | 0.199838i | −0.730228 | − | 0.683204i | \(-0.760586\pi\) |
0.875418 | + | 0.483366i | \(0.160586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2108 | 1.56362 | 0.781810 | − | 0.623516i | \(-0.214297\pi\) | ||||
0.781810 | + | 0.623516i | \(0.214297\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50361 | −0.133633 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.5292 | − | 22.7505i | 0.879759 | − | 1.21088i | −0.0967283 | − | 0.995311i | \(-0.530838\pi\) |
0.976488 | − | 0.215574i | \(-0.0691622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.09582i | − | 0.269699i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.90570 | + | 8.94282i | 0.153357 | + | 0.471984i | 0.997991 | − | 0.0633604i | \(-0.0201817\pi\) |
−0.844634 | + | 0.535345i | \(0.820182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39218 | + | 16.5954i | −0.283799 | + | 0.873444i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.4201 | + | 3.38568i | −0.546911 | + | 0.177702i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.9349 | − | 17.8033i | −0.675195 | − | 0.929326i | 0.324669 | − | 0.945828i | \(-0.394747\pi\) |
−0.999864 | + | 0.0165016i | \(0.994747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.59996 | − | 1.88898i | 0.135349 | − | 0.0983365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.50457 | − | 1.81968i | −0.130031 | − | 0.0944728i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.7085 | − | 5.75384i | −0.916911 | − | 0.297923i | −0.187712 | − | 0.982224i | \(-0.560107\pi\) |
−0.729199 | + | 0.684302i | \(0.760107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.3417 | + | 4.01005i | 0.635628 | + | 0.206528i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.6515 | − | 9.91838i | −0.701230 | − | 0.509473i | 0.179103 | − | 0.983830i | \(-0.442680\pi\) |
−0.880332 | + | 0.474357i | \(0.842680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7601 | − | 8.54421i | 0.602488 | − | 0.437733i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.32445 | − | 7.32847i | −0.272066 | − | 0.374467i | 0.651020 | − | 0.759061i | \(-0.274342\pi\) |
−0.923086 | + | 0.384594i | \(0.874342\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.0905 | − | 3.92843i | 0.614593 | − | 0.199693i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.2225 | + | 31.4616i | −0.518301 | + | 1.59517i | 0.258893 | + | 0.965906i | \(0.416642\pi\) |
−0.777194 | + | 0.629261i | \(0.783358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.85069 | − | 21.0843i | −0.346454 | − | 1.06628i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 7.42396i | − | 0.374489i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7706 | + | 17.5773i | −0.640939 | + | 0.882177i | −0.998665 | − | 0.0516494i | \(-0.983552\pi\) |
0.357726 | + | 0.933827i | \(0.383552\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.930465 | −0.0465815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.1663 | 1.00706 | 0.503529 | − | 0.863978i | \(-0.332035\pi\) | ||||
0.503529 | + | 0.863978i | \(0.332035\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.50327 | − | 7.57460i | 0.274137 | − | 0.377318i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.410887i | 0.0203669i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.34139 | + | 13.3614i | 0.214668 | + | 0.660679i | 0.999177 | + | 0.0405623i | \(0.0129149\pi\) |
−0.784509 | + | 0.620117i | \(0.787085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.26676 | + | 6.97636i | −0.111811 | + | 0.344118i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.32244 | − | 2.70412i | 0.409520 | − | 0.133061i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.6071 | − | 15.9757i | −0.568400 | − | 0.782336i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3919 | + | 11.9094i | −0.800794 | + | 0.581811i | −0.911147 | − | 0.412081i | \(-0.864802\pi\) |
0.110353 | + | 0.993892i | \(0.464802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54258 | − | 2.57384i | −0.172655 | − | 0.125441i | 0.498102 | − | 0.867119i | \(-0.334031\pi\) |
−0.670757 | + | 0.741677i | \(0.734031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.16499 | + | 2.00313i | 0.299752 | + | 0.0973953i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.86866 | − | 2.88160i | −0.429184 | − | 0.139450i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.423438 | − | 0.307645i | −0.0204438 | − | 0.0148533i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.944967 | + | 0.686559i | −0.0455175 | + | 0.0330704i | −0.610311 | − | 0.792162i | \(-0.708956\pi\) |
0.564794 | + | 0.825232i | \(0.308956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.32187 | + | 1.81940i | 0.0635250 | + | 0.0874347i | 0.839597 | − | 0.543209i | \(-0.182791\pi\) |
−0.776072 | + | 0.630644i | \(0.782791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.84985 | + | 1.25089i | −0.184163 | + | 0.0598383i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.83477 | + | 21.0353i | −0.326206 | + | 1.00396i | 0.644688 | + | 0.764446i | \(0.276987\pi\) |
−0.970893 | + | 0.239512i | \(0.923013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.99057 | − | 6.12636i | −0.0947893 | − | 0.291731i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 28.1534i | − | 1.33761i | −0.743439 | − | 0.668804i | \(-0.766807\pi\) | ||
0.743439 | − | 0.668804i | \(-0.233193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7873 | + | 17.6002i | −0.604819 | + | 0.832462i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.5924 | −0.783044 | −0.391522 | − | 0.920169i | \(-0.628051\pi\) | ||||
−0.391522 | + | 0.920169i | \(0.628051\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.671852 | 0.0316363 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.95473 | + | 8.19598i | −0.279777 | + | 0.385081i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 11.1599i | − | 0.522039i | −0.965334 | − | 0.261019i | \(-0.915941\pi\) | ||
0.965334 | − | 0.261019i | \(-0.0840586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.10735 | + | 6.48576i | 0.0983628 | + | 0.302729i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.93631 | − | 5.95935i | 0.0901830 | − | 0.277555i | −0.895785 | − | 0.444487i | \(-0.853386\pi\) |
0.985968 | + | 0.166932i | \(0.0533861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1961 | + | 5.26243i | −0.752696 | + | 0.244566i | −0.660141 | − | 0.751142i | \(-0.729503\pi\) |
−0.0925550 | + | 0.995708i | \(0.529503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.9823 | + | 15.1159i | 0.508202 | + | 0.699481i | 0.983615 | − | 0.180282i | \(-0.0577012\pi\) |
−0.475413 | + | 0.879763i | \(0.657701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.76344 | − | 1.28122i | 0.0814283 | − | 0.0591611i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.08629 | + | 5.87503i | 0.372597 | + | 0.270707i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.52760 | + | 0.821266i | 0.116219 | + | 0.0377618i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.94024 | + | 1.28026i | 0.180411 | + | 0.0586191i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.38111 | + | 1.72998i | 0.108796 | + | 0.0790448i | 0.640853 | − | 0.767664i | \(-0.278581\pi\) |
−0.532057 | + | 0.846708i | \(0.678581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.98092 | − | 2.89230i | 0.181514 | − | 0.131878i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.42782 | + | 1.96523i | 0.0649683 | + | 0.0894212i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3297 | − | 4.33109i | 0.604028 | − | 0.196261i | 0.00899199 | − | 0.999960i | \(-0.497138\pi\) |
0.595036 | + | 0.803699i | \(0.297138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.792035 | − | 2.43763i | 0.0358170 | − | 0.110234i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.76416 | + | 8.50720i | 0.124745 | + | 0.383925i | 0.993854 | − | 0.110695i | \(-0.0353075\pi\) |
−0.869110 | + | 0.494619i | \(0.835308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 35.3472i | − | 1.59196i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.87690 | − | 3.95971i | 0.129046 | − | 0.177617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.39366 | 0.107155 | 0.0535774 | − | 0.998564i | \(-0.482938\pi\) | ||||
0.0535774 | + | 0.998564i | \(0.482938\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8512 | −0.931564 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.95152 | + | 6.81519i | −0.220777 | + | 0.303874i | −0.905010 | − | 0.425389i | \(-0.860137\pi\) |
0.684233 | + | 0.729264i | \(0.260137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.73192i | − | 0.298975i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.98528 | − | 30.7315i | −0.442590 | − | 1.36215i | −0.885106 | − | 0.465390i | \(-0.845914\pi\) |
0.442516 | − | 0.896761i | \(-0.354086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.581737 | + | 1.79040i | −0.0257345 | + | 0.0792027i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.18426 | − | 0.384789i | 0.0522864 | − | 0.0169889i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.796543 | + | 1.09635i | 0.0350319 | + | 0.0482173i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.66249 | − | 1.20787i | 0.0729754 | − | 0.0530197i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.88427 | − | 2.09554i | −0.126362 | − | 0.0918074i | 0.522809 | − | 0.852450i | \(-0.324884\pi\) |
−0.649171 | + | 0.760642i | \(0.724884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8511 | + | 10.0241i | 1.34903 | + | 0.438325i | 0.892365 | − | 0.451315i | \(-0.149045\pi\) |
0.456662 | + | 0.889640i | \(0.349045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.2547 | − | 7.88082i | −1.05655 | − | 0.343294i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0577 | − | 7.30732i | −0.437290 | − | 0.317710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.47420 | + | 6.88341i | −0.411145 | + | 0.298715i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.72928 | − | 6.50929i | −0.204848 | − | 0.281949i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.6030 | − | 6.04449i | 0.802781 | − | 0.260839i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.416143 | − | 1.28076i | 0.0179246 | − | 0.0551661i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.40378 | − | 10.4757i | −0.146340 | − | 0.450388i | 0.850841 | − | 0.525423i | \(-0.176093\pi\) |
−0.997181 | + | 0.0750356i | \(0.976093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.37007i | 0.316280i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.13718 | + | 4.31795i | −0.134136 | + | 0.184622i | −0.870801 | − | 0.491635i | \(-0.836399\pi\) |
0.736665 | + | 0.676258i | \(0.236399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4794 | 0.532606 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.45418 | −0.274957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.49859 | − | 6.19177i | 0.191299 | − | 0.263301i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.0652731i | − | 0.00276571i | −0.999999 | − | 0.00138286i | \(-0.999560\pi\) | ||
0.999999 | − | 0.00138286i | \(-0.000440177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.83527 | − | 30.2699i | −0.415988 | − | 1.28028i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.440557 | + | 1.35589i | −0.0186003 | + | 0.0572459i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.3359 | + | 8.88197i | −1.15207 | + | 0.374330i | −0.821923 | − | 0.569599i | \(-0.807098\pi\) |
−0.330147 | + | 0.943929i | \(0.607098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.439216 | − | 0.604528i | −0.0184453 | − | 0.0253878i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.68501 | + | 4.85694i | −0.280250 | + | 0.203614i | −0.719026 | − | 0.694983i | \(-0.755412\pi\) |
0.438776 | + | 0.898596i | \(0.355412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.49451 | − | 6.89817i | −0.397333 | − | 0.288679i | 0.371121 | − | 0.928585i | \(-0.378974\pi\) |
−0.768454 | + | 0.639905i | \(0.778974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.13532 | + | 0.693806i | 0.0892041 | + | 0.0289842i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3418 | + | 6.60944i | 0.846838 | + | 0.275154i | 0.700121 | − | 0.714024i | \(-0.253129\pi\) |
0.146717 | + | 0.989178i | \(0.453129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.894682 | + | 0.650024i | 0.0371817 | + | 0.0270141i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43162 | − | 2.49322i | 0.142368 | − | 0.103436i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.509096 | + | 0.700710i | 0.0210846 | + | 0.0290204i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.2133 | + | 12.7412i | −1.61851 | + | 0.525885i | −0.971589 | − | 0.236674i | \(-0.923943\pi\) |
−0.646918 | + | 0.762559i | \(0.723943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.43899 | + | 4.42876i | −0.0592925 | + | 0.182484i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.37705 | + | 19.6265i | 0.262317 | + | 0.807328i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2238i | 0.953685i | 0.878989 | + | 0.476843i | \(0.158219\pi\) | ||||
−0.878989 | + | 0.476843i | \(0.841781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.27806 | + | 10.0174i | −0.297871 | + | 0.409984i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6226 | 0.924335 | 0.462168 | − | 0.886793i | \(-0.347072\pi\) | ||||
0.462168 | + | 0.886793i | \(0.347072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9540 | −0.528405 | −0.264203 | − | 0.964467i | \(-0.585109\pi\) | ||||
−0.264203 | + | 0.964467i | \(0.585109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.71460 | + | 2.35995i | −0.0698240 | + | 0.0961045i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.54036i | 0.184288i | 0.995746 | + | 0.0921439i | \(0.0293720\pi\) | ||||
−0.995746 | + | 0.0921439i | \(0.970628\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.19686 | + | 3.68354i | 0.0484990 | + | 0.149265i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.01505 | − | 15.4347i | 0.202887 | − | 0.624423i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.1128 | + | 7.83471i | −0.973905 | + | 0.316441i | −0.752391 | − | 0.658716i | \(-0.771100\pi\) |
−0.221514 | + | 0.975157i | \(0.571100\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5790 | + | 36.5829i | 1.07003 | + | 1.47277i | 0.870045 | + | 0.492972i | \(0.164090\pi\) |
0.199986 | + | 0.979799i | \(0.435910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.3666 | − | 18.4299i | 1.01957 | − | 0.740762i | 0.0533766 | − | 0.998574i | \(-0.483002\pi\) |
0.966195 | + | 0.257812i | \(0.0830016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.62999 | − | 1.91080i | −0.105538 | − | 0.0766779i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.655040 | + | 0.212835i | 0.0262436 | + | 0.00852707i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.247578 | + | 0.0804429i | 0.00988730 | + | 0.00321258i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8435 | − | 7.87828i | −0.432360 | − | 0.314128i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.8455 | + | 18.7779i | −1.02889 | + | 0.747535i | −0.968087 | − | 0.250614i | \(-0.919367\pi\) |
−0.0608071 | + | 0.998150i | \(0.519367\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.1245 | + | 16.6879i | 0.481905 | + | 0.663286i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.3380 | + | 4.98363i | −0.607715 | + | 0.197459i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.02409 | + | 6.22949i | −0.0800716 | + | 0.246435i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.7727 | + | 39.3103i | 0.504491 | + | 1.55267i | 0.801624 | + | 0.597829i | \(0.203970\pi\) |
−0.297132 | + | 0.954836i | \(0.596030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.2313i | 1.31052i | 0.755406 | + | 0.655258i | \(0.227440\pi\) | ||||
−0.755406 | + | 0.655258i | \(0.772560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8034 | − | 27.2571i | 0.778553 | − | 1.07159i | −0.216887 | − | 0.976197i | \(-0.569590\pi\) |
0.995440 | − | 0.0953892i | \(-0.0304096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.44822 | −0.0961009 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.79443 | 0.109522 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.8419 | + | 17.6754i | −0.502544 | + | 0.691692i | −0.982640 | − | 0.185524i | \(-0.940602\pi\) |
0.480096 | + | 0.877216i | \(0.340602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.51933i | − | 0.0982885i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.48829 | + | 10.7359i | 0.135884 | + | 0.418209i | 0.995727 | − | 0.0923507i | \(-0.0294381\pi\) |
−0.859842 | + | 0.510560i | \(0.829438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.3014 | + | 34.7821i | −0.439573 | + | 1.35287i | 0.448754 | + | 0.893655i | \(0.351868\pi\) |
−0.888327 | + | 0.459211i | \(0.848132\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.2378 | − | 5.27599i | 0.630625 | − | 0.204903i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.90412 | + | 13.6319i | 0.383489 | + | 0.527828i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.36117 | + | 2.44203i | −0.129950 | + | 0.0944145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.11064 | + | 1.53347i | 0.0814804 | + | 0.0591990i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31143 | − | 2.37563i | −0.281835 | − | 0.0915737i | 0.164689 | − | 0.986346i | \(-0.447338\pi\) |
−0.446523 | + | 0.894772i | \(0.647338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.4711 | − | 11.5253i | −1.36327 | − | 0.442952i | −0.466133 | − | 0.884714i | \(-0.654353\pi\) |
−0.897132 | + | 0.441763i | \(0.854353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.39705 | − | 6.82736i | −0.360626 | − | 0.262010i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1162 | − | 13.8888i | 0.732535 | − | 0.532218i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.4421 | + | 29.5125i | 0.820458 | + | 1.12926i | 0.989625 | + | 0.143676i | \(0.0458925\pi\) |
−0.169166 | + | 0.985587i | \(0.554108\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.3473 | + | 5.63649i | −0.661842 | + | 0.215046i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.20528 | − | 9.86483i | 0.122111 | − | 0.375820i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.99734 | − | 30.7686i | −0.380317 | − | 1.17049i | −0.939821 | − | 0.341667i | \(-0.889008\pi\) |
0.559504 | − | 0.828827i | \(-0.310992\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.156215i | − | 0.00593413i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.8820 | + | 17.7305i | −0.487940 | + | 0.671591i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.26742 | −0.0857617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.27498 | 0.199233 | 0.0996166 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996166 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.43853 | + | 1.97996i | −0.0542550 | + | 0.0746756i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 8.24988i | − | 0.310268i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.03055 | − | 27.7932i | −0.339149 | − | 1.04379i | −0.964642 | − | 0.263564i | \(-0.915102\pi\) |
0.625493 | − | 0.780230i | \(-0.284898\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.16505 | + | 9.74102i | −0.118699 | + | 0.365317i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5621 | − | 3.75677i | 0.433005 | − | 0.140692i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0552 | − | 13.8397i | −0.375517 | − | 0.516855i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.5675 | − | 25.8413i | 1.32644 | − | 0.963718i | 0.326616 | − | 0.945157i | \(-0.394092\pi\) |
0.999828 | − | 0.0185605i | \(-0.00590834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.39344 | − | 6.09819i | −0.312588 | − | 0.227108i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.8200 | − | 8.71435i | −0.997447 | − | 0.324090i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4614 | + | 9.24768i | 1.05558 | + | 0.342977i | 0.784854 | − | 0.619680i | \(-0.212738\pi\) |
0.270721 | + | 0.962658i | \(0.412738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −70.1373 | + | 50.9577i | −2.59412 | + | 1.88474i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.71402 | − | 13.3702i | −0.358795 | − | 0.493840i | 0.591017 | − | 0.806659i | \(-0.298727\pi\) |
−0.949813 | + | 0.312819i | \(0.898727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.579984 | + | 0.188448i | −0.0213640 | + | 0.00694158i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7285 | − | 48.4073i | 0.578581 | − | 1.78069i | −0.0450666 | − | 0.998984i | \(-0.514350\pi\) |
0.623648 | − | 0.781706i | \(-0.285650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.963364 | − | 2.96493i | −0.0353901 | − | 0.108919i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.6937i | 1.05267i | 0.850277 | + | 0.526336i | \(0.176434\pi\) | ||||
−0.850277 | + | 0.526336i | \(0.823566\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.33658 | + | 4.59240i | −0.122079 | + | 0.168027i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.765995 | −0.0279888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.927935 | −0.0338608 | −0.0169304 | − | 0.999857i | \(-0.505389\pi\) | ||||
−0.0169304 | + | 0.999857i | \(0.505389\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.0819 | + | 19.3821i | −0.513173 | + | 0.706322i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4243i | 1.50559i | 0.658254 | + | 0.752796i | \(0.271295\pi\) | ||||
−0.658254 | + | 0.752796i | \(0.728705\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.210012 | − | 0.646350i | −0.00762295 | − | 0.0234610i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.17031 | − | 3.60185i | 0.0424237 | − | 0.130567i | −0.927601 | − | 0.373572i | \(-0.878133\pi\) |
0.970025 | + | 0.243005i | \(0.0781330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.76509 | + | 1.54827i | −0.172508 | + | 0.0560513i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.2334 | + | 23.7197i | 0.622262 | + | 0.856470i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.06014 | + | 0.770234i | −0.0382295 | + | 0.0277753i | −0.606736 | − | 0.794903i | \(-0.707521\pi\) |
0.568506 | + | 0.822679i | \(0.307521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.0911 | + | 16.7766i | 0.831604 | + | 0.604196i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.7066 | − | 9.00241i | −0.996536 | − | 0.323794i | −0.235055 | − | 0.971982i | \(-0.575527\pi\) |
−0.761480 | + | 0.648188i | \(0.775527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.39677 | + | 0.453837i | 0.0501087 | + | 0.0162813i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.23748 | + | 2.35217i | 0.115995 | + | 0.0842752i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.10782 | + | 0.804877i | −0.0396409 | + | 0.0288008i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.04662 | − | 4.19332i | −0.108877 | − | 0.149857i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.3341 | − | 14.4050i | 1.58034 | − | 0.513484i | 0.618197 | − | 0.786023i | \(-0.287864\pi\) |
0.962145 | + | 0.272540i | \(0.0878635\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.09911 | − | 3.38270i | 0.0391292 | − | 0.120427i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.92153 | + | 5.91385i | 0.0683217 | + | 0.210272i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 31.2435i | − | 1.10949i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.08703 | + | 11.1308i | −0.286457 | + | 0.394275i | −0.927859 | − | 0.372930i | \(-0.878353\pi\) |
0.641402 | + | 0.767205i | \(0.278353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.2059 | −1.56389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.921727 | −0.0325676 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.309577 | − | 0.426096i | 0.0109247 | − | 0.0150366i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.2618i | 1.03006i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.08886 | − | 9.50654i | −0.108599 | − | 0.334232i | 0.881960 | − | 0.471325i | \(-0.156224\pi\) |
−0.990558 | + | 0.137093i | \(0.956224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.72277 | − | 17.6129i | 0.200954 | − | 0.618472i | −0.798902 | − | 0.601462i | \(-0.794585\pi\) |
0.999855 | − | 0.0170101i | \(-0.00541474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6036 | + | 7.66927i | −0.827814 | + | 0.268973i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.30457 | + | 12.8066i | 0.325526 | + | 0.448048i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.51351 | + | 1.09963i | −0.0528862 | + | 0.0384240i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.9081 | − | 16.6437i | −0.799498 | − | 0.580869i | 0.111269 | − | 0.993790i | \(-0.464509\pi\) |
−0.910767 | + | 0.412921i | \(0.864509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3987 | − | 3.70366i | −0.397333 | − | 0.129101i | 0.103533 | − | 0.994626i | \(-0.466985\pi\) |
−0.500866 | + | 0.865525i | \(0.666985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7167 | + | 4.13191i | 0.442204 | + | 0.143681i | 0.521652 | − | 0.853158i | \(-0.325316\pi\) |
−0.0794485 | + | 0.996839i | \(0.525316\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3909 | − | 9.72909i | −0.465087 | − | 0.337905i | 0.330437 | − | 0.943828i | \(-0.392804\pi\) |
−0.795523 | + | 0.605923i | \(0.792804\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0991 | − | 10.2436i | 0.489094 | − | 0.355347i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.8208 | + | 35.5393i | 0.894637 | + | 1.23136i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.55665 | + | 1.15563i | −0.122936 | + | 0.0399442i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.56589 | + | 23.2854i | −0.261204 | + | 0.803902i | 0.731340 | + | 0.682013i | \(0.238895\pi\) |
−0.992544 | + | 0.121889i | \(0.961105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.659493 | − | 2.02971i | −0.0227411 | − | 0.0699900i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 3.75349i | − | 0.129277i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.81218 | + | 6.62339i | −0.165348 | + | 0.227582i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.3735 | −0.561936 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.38933 | 0.219023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.2475 | + | 15.4809i | −0.385108 | + | 0.530055i | −0.956929 | − | 0.290323i | \(-0.906237\pi\) |
0.571821 | + | 0.820379i | \(0.306237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.43367i | − | 0.253929i | −0.991907 | − | 0.126965i | \(-0.959477\pi\) | ||
0.991907 | − | 0.126965i | \(-0.0405235\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7368 | − | 39.1999i | −0.434575 | − | 1.33748i | −0.893522 | − | 0.449020i | \(-0.851773\pi\) |
0.458947 | − | 0.888464i | \(-0.348227\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.742080 | − | 2.28389i | 0.0252900 | − | 0.0778346i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.2532 | + | 11.7794i | −1.23407 | + | 0.400975i | −0.852189 | − | 0.523234i | \(-0.824725\pi\) |
−0.381886 | + | 0.924210i | \(0.624725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.3432 | − | 23.8709i | −0.589007 | − | 0.810698i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.73229 | + | 1.25858i | −0.0587639 | + | 0.0426945i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.90840 | + | 4.29270i | 0.200198 | + | 0.145453i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.7836 | + | 4.80349i | 0.500350 | + | 0.162574i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6047 | + | 8.96931i | 0.932145 | + | 0.302872i | 0.735439 | − | 0.677591i | \(-0.236976\pi\) |
0.196705 | + | 0.980463i | \(0.436976\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.04647 | + | 5.11956i | 0.237671 | + | 0.172678i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.8503 | − | 20.2344i | 0.938300 | − | 0.681715i | −0.00971098 | − | 0.999953i | \(-0.503091\pi\) |
0.948011 | + | 0.318238i | \(0.103091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.8077 | − | 31.3921i | −0.767539 | − | 1.05643i | −0.996549 | − | 0.0830028i | \(-0.973549\pi\) |
0.229010 | − | 0.973424i | \(-0.426451\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.48715 | + | 1.78288i | −0.184241 | + | 0.0598634i | −0.399684 | − | 0.916653i | \(-0.630880\pi\) |
0.215444 | + | 0.976516i | \(0.430880\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.35656 | − | 10.3304i | 0.112575 | − | 0.346472i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0646021 | + | 0.198825i | 0.00216425 | + | 0.00666089i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.07173i | 0.270110i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.78391 | + | 6.58449i | −0.159730 | + | 0.219850i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.3836 | 0.646480 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.2534 | −0.941257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.58360 | − | 7.68517i | 0.185811 | − | 0.255746i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.7260i | 1.05345i | 0.850037 | + | 0.526723i | \(0.176579\pi\) | ||||
−0.850037 | + | 0.526723i | \(0.823421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.41170 | + | 10.5001i | 0.113159 | + | 0.348267i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.95450 | + | 15.2484i | −0.164150 | + | 0.505202i | −0.998973 | − | 0.0453174i | \(-0.985570\pi\) |
0.834823 | + | 0.550519i | \(0.185570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.12863 | + | 0.366716i | −0.0373523 | + | 0.0121365i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.26072 | − | 4.48800i | −0.107679 | − | 0.148207i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.82328 | + | 6.41049i | −0.291053 | + | 0.211462i | −0.723724 | − | 0.690089i | \(-0.757571\pi\) |
0.432671 | + | 0.901552i | \(0.357571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3296 | + | 10.4111i | 0.472176 | + | 0.343056i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.5962 | + | 5.06753i | 0.513357 | + | 0.166800i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.2047 | + | 4.29048i | 0.433700 | + | 0.140918i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3021 | + | 13.2973i | 0.600473 | + | 0.436269i | 0.846047 | − | 0.533108i | \(-0.178976\pi\) |
−0.245573 | + | 0.969378i | \(0.578976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.48925 | − | 4.71472i | 0.212677 | − | 0.154519i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.9247 | + | 16.4130i | 0.390398 | + | 0.537337i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90347 | − | 1.59323i | 0.160189 | − | 0.0520487i | −0.227824 | − | 0.973702i | \(-0.573161\pi\) |
0.388014 | + | 0.921654i | \(0.373161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.41831 | + | 19.7535i | −0.209454 | + | 0.644632i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.84942 | + | 11.8473i | 0.125488 | + | 0.386211i | 0.993990 | − | 0.109475i | \(-0.0349168\pi\) |
−0.868502 | + | 0.495686i | \(0.834917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.4474i | − | 0.340213i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.79345 | − | 13.4795i | 0.318244 | − | 0.438026i | −0.619686 | − | 0.784850i | \(-0.712740\pi\) |
0.937930 | + | 0.346824i | \(0.112740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.30743 | −0.204748 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.7651 | −0.543646 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.4812 | + | 41.9537i | −0.987382 | + | 1.35901i | −0.0546255 | + | 0.998507i | \(0.517396\pi\) |
−0.932756 | + | 0.360508i | \(0.882604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.08359i | − | 0.0350275i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.69381 | + | 5.21300i | 0.0546959 | + | 0.168337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.25786 | + | 16.1820i | −0.169608 | + | 0.522001i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.974929 | − | 0.316774i | 0.0314166 | − | 0.0102079i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.50713 | − | 10.3327i | −0.241413 | − | 0.332277i | 0.671068 | − | 0.741396i | \(-0.265836\pi\) |
−0.912481 | + | 0.409119i | \(0.865836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.86994 | + | 4.99131i | −0.220694 | + | 0.160344i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5679 | + | 9.13110i | 0.403323 | + | 0.293031i | 0.770893 | − | 0.636965i | \(-0.219810\pi\) |
−0.367570 | + | 0.929996i | \(0.619810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0336 | − | 4.55979i | −0.449896 | − | 0.146180i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.5811 | − | 10.2613i | −1.01037 | − | 0.328288i | −0.243367 | − | 0.969934i | \(-0.578252\pi\) |
−0.767001 | + | 0.641646i | \(0.778252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.155892 | − | 0.113262i | −0.00498234 | − | 0.00361988i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.42455 | − | 3.94117i | 0.173193 | − | 0.125832i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.8570 | − | 39.7183i | −0.920395 | − | 1.26682i | −0.963490 | − | 0.267745i | \(-0.913722\pi\) |
0.0430944 | − | 0.999071i | \(-0.486278\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.60671 | − | 1.49681i | 0.146633 | − | 0.0476440i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7707 | − | 39.3043i | 0.406086 | − | 1.24980i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.91583 | − | 24.3624i | −0.251455 | − | 0.773898i | −0.994508 | − | 0.104665i | \(-0.966623\pi\) |
0.743053 | − | 0.669233i | \(-0.233377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.2157i | 0.831932i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.36565 | + | 8.76157i | −0.201602 | + | 0.277482i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.696231 | + | 0.717818i | \(0.254859\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.96543 | −0.0621835 |
(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 | 1500.2.o.a.649.2 | 16 | ||
5.2 | odd | 4 | 1500.2.m.b.601.1 | 8 | |||
5.3 | odd | 4 | 300.2.m.a.121.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1500.2.o.a.649.3 | 16 | ||
15.8 | even | 4 | 900.2.n.a.721.1 | 8 | |||
25.6 | even | 5 | inner | 1500.2.o.a.349.4 | 16 | ||
25.8 | odd | 20 | 300.2.m.a.181.2 | yes | 8 | ||
25.9 | even | 10 | 7500.2.d.d.1249.5 | 8 | |||
25.12 | odd | 20 | 7500.2.a.d.1.1 | 4 | |||
25.13 | odd | 20 | 7500.2.a.g.1.4 | 4 | |||
25.16 | even | 5 | 7500.2.d.d.1249.4 | 8 | |||
25.17 | odd | 20 | 1500.2.m.b.901.1 | 8 | |||
25.19 | even | 10 | inner | 1500.2.o.a.349.1 | 16 | ||
75.8 | even | 20 | 900.2.n.a.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.a.121.2 | ✓ | 8 | 5.3 | odd | 4 | ||
300.2.m.a.181.2 | yes | 8 | 25.8 | odd | 20 | ||
900.2.n.a.181.1 | 8 | 75.8 | even | 20 | |||
900.2.n.a.721.1 | 8 | 15.8 | even | 4 | |||
1500.2.m.b.601.1 | 8 | 5.2 | odd | 4 | |||
1500.2.m.b.901.1 | 8 | 25.17 | odd | 20 | |||
1500.2.o.a.349.1 | 16 | 25.19 | even | 10 | inner | ||
1500.2.o.a.349.4 | 16 | 25.6 | even | 5 | inner | ||
1500.2.o.a.649.2 | 16 | 1.1 | even | 1 | trivial | ||
1500.2.o.a.649.3 | 16 | 5.4 | even | 2 | inner | ||
7500.2.a.d.1.1 | 4 | 25.12 | odd | 20 | |||
7500.2.a.g.1.4 | 4 | 25.13 | odd | 20 | |||
7500.2.d.d.1249.4 | 8 | 25.16 | even | 5 | |||
7500.2.d.d.1249.5 | 8 | 25.9 | even | 10 |