Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(793,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1369.5 | ||
Character | \(\chi\) | \(=\) | 1512.1369 |
Dual form | 1512.2.q.d.793.5 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.234085 | + | 0.405446i | −0.104686 | + | 0.181321i | −0.913610 | − | 0.406592i | \(-0.866717\pi\) |
0.808924 | + | 0.587913i | \(0.200050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.212345 | + | 2.63722i | 0.0802590 | + | 0.996774i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.674293 | − | 1.16791i | −0.203307 | − | 0.352138i | 0.746285 | − | 0.665626i | \(-0.231836\pi\) |
−0.949592 | + | 0.313489i | \(0.898502\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.16486 | − | 5.48171i | −0.877775 | − | 1.52035i | −0.853777 | − | 0.520640i | \(-0.825694\pi\) |
−0.0239988 | − | 0.999712i | \(-0.507640\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47120 | − | 4.28024i | 0.599353 | − | 1.03811i | −0.393563 | − | 0.919298i | \(-0.628758\pi\) |
0.992917 | − | 0.118813i | \(-0.0379089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38910 | + | 4.13804i | 0.548097 | + | 0.949332i | 0.998405 | + | 0.0564585i | \(0.0179809\pi\) |
−0.450308 | + | 0.892873i | \(0.648686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.81399 | − | 6.60603i | 0.795273 | − | 1.37745i | −0.127393 | − | 0.991852i | \(-0.540661\pi\) |
0.922666 | − | 0.385600i | \(-0.126006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.39041 | + | 4.14031i | 0.478082 | + | 0.828062i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.80565 | − | 3.12747i | 0.335300 | − | 0.580757i | −0.648242 | − | 0.761434i | \(-0.724496\pi\) |
0.983542 | + | 0.180677i | \(0.0578290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.49878 | 1.16721 | 0.583607 | − | 0.812036i | \(-0.301641\pi\) | ||||
0.583607 | + | 0.812036i | \(0.301641\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11896 | − | 0.531237i | −0.189138 | − | 0.0897954i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.24214 | + | 9.07966i | 0.861803 | + | 1.49269i | 0.870187 | + | 0.492722i | \(0.163998\pi\) |
−0.00838383 | + | 0.999965i | \(0.502669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0251630 | + | 0.0435837i | 0.00392981 | + | 0.00680662i | 0.867984 | − | 0.496593i | \(-0.165416\pi\) |
−0.864054 | + | 0.503399i | \(0.832082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.431869 | + | 0.748019i | −0.0658594 | + | 0.114072i | −0.897075 | − | 0.441879i | \(-0.854312\pi\) |
0.831215 | + | 0.555950i | \(0.187646\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9883 | 1.60282 | 0.801408 | − | 0.598118i | \(-0.204085\pi\) | ||||
0.801408 | + | 0.598118i | \(0.204085\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90982 | + | 1.12000i | −0.987117 | + | 0.160000i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.84976 | + | 10.1321i | −0.803526 | + | 1.39175i | 0.113756 | + | 0.993509i | \(0.463712\pi\) |
−0.917282 | + | 0.398239i | \(0.869622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.631366 | 0.0851334 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.87784 | 0.504852 | 0.252426 | − | 0.967616i | \(-0.418772\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.74462 | 0.479450 | 0.239725 | − | 0.970841i | \(-0.422943\pi\) | ||||
0.239725 | + | 0.970841i | \(0.422943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.96338 | 0.367562 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.64871 | −0.323592 | −0.161796 | − | 0.986824i | \(-0.551729\pi\) | ||||
−0.161796 | + | 0.986824i | \(0.551729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.04562 | 0.836161 | 0.418081 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418081 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30117 | + | 5.71779i | −0.386373 | + | 0.669217i | −0.991959 | − | 0.126563i | \(-0.959605\pi\) |
0.605586 | + | 0.795780i | \(0.292939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.93685 | − | 2.02626i | 0.334685 | − | 0.230913i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.17902 | 0.357667 | 0.178834 | − | 0.983879i | \(-0.442768\pi\) | ||||
0.178834 | + | 0.983879i | \(0.442768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.90272 | + | 8.49176i | −0.538143 | + | 0.932092i | 0.460861 | + | 0.887472i | \(0.347541\pi\) |
−0.999004 | + | 0.0446192i | \(0.985793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15694 | + | 2.00388i | 0.125488 | + | 0.217351i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.30709 | − | 9.19214i | −0.562550 | − | 0.974365i | −0.997273 | − | 0.0738011i | \(-0.976487\pi\) |
0.434723 | − | 0.900564i | \(-0.356846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7844 | − | 9.51045i | 1.44500 | − | 0.996966i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.23701 | −0.229512 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.97792 | − | 12.0861i | 0.708500 | − | 1.22716i | −0.256913 | − | 0.966434i | \(-0.582706\pi\) |
0.965413 | − | 0.260724i | \(-0.0839611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.12472 | + | 3.68013i | 0.211418 | + | 0.366187i | 0.952159 | − | 0.305604i | \(-0.0988585\pi\) |
−0.740741 | + | 0.671791i | \(0.765525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.47820 | − | 7.75647i | 0.441250 | − | 0.764268i | −0.556532 | − | 0.830826i | \(-0.687868\pi\) |
0.997783 | + | 0.0665580i | \(0.0212017\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.810731 | + | 1.40423i | 0.0783763 | + | 0.135752i | 0.902550 | − | 0.430586i | \(-0.141693\pi\) |
−0.824173 | + | 0.566338i | \(0.808360\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.97644 | − | 5.15534i | 0.285091 | − | 0.493792i | −0.687540 | − | 0.726146i | \(-0.741309\pi\) |
0.972631 | + | 0.232354i | \(0.0746428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.14346 | − | 7.17669i | −0.389784 | − | 0.675126i | 0.602636 | − | 0.798016i | \(-0.294117\pi\) |
−0.992420 | + | 0.122890i | \(0.960784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.78559 | + | 3.09274i | 0.166508 | + | 0.288399i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.8127 | + | 5.60819i | 1.08287 | + | 0.514102i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.59066 | − | 7.95125i | 0.417333 | − | 0.722841i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.57908 | −0.409565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.12368 | 0.720860 | 0.360430 | − | 0.932786i | \(-0.382630\pi\) | ||||
0.360430 | + | 0.932786i | \(0.382630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.74823 | − | 16.8844i | 0.851707 | − | 1.47520i | −0.0279597 | − | 0.999609i | \(-0.508901\pi\) |
0.879667 | − | 0.475591i | \(-0.157766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.4056 | + | 7.17927i | −0.902280 | + | 0.622521i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.55175 | − | 13.0800i | −0.645189 | − | 1.11750i | −0.984258 | − | 0.176739i | \(-0.943445\pi\) |
0.339069 | − | 0.940762i | \(-0.389888\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.18826 | − | 3.79017i | −0.185605 | − | 0.321478i | 0.758175 | − | 0.652051i | \(-0.226091\pi\) |
−0.943780 | + | 0.330573i | \(0.892758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.26809 | + | 7.39255i | −0.356916 | + | 0.618196i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.845348 | + | 1.46419i | 0.0702023 | + | 0.121594i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.87820 | + | 10.1813i | −0.481561 | + | 0.834087i | −0.999776 | − | 0.0211627i | \(-0.993263\pi\) |
0.518215 | + | 0.855250i | \(0.326597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.57153 | + | 4.45401i | 0.209268 | + | 0.362462i | 0.951484 | − | 0.307698i | \(-0.0995586\pi\) |
−0.742216 | + | 0.670160i | \(0.766225\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.52126 | + | 2.63490i | −0.122191 | + | 0.211641i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0889 | −0.964803 | −0.482401 | − | 0.875950i | \(-0.660235\pi\) | ||||
−0.482401 | + | 0.875950i | \(0.660235\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2314 | + | 8.65557i | 1.43684 | + | 0.682154i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74663 | − | 4.75730i | −0.215133 | − | 0.372621i | 0.738181 | − | 0.674603i | \(-0.235685\pi\) |
−0.953314 | + | 0.301982i | \(0.902352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.59378 | + | 6.22461i | 0.278095 | + | 0.481675i | 0.970911 | − | 0.239440i | \(-0.0769637\pi\) |
−0.692816 | + | 0.721114i | \(0.743630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.5327 | + | 23.4394i | −1.04098 | + | 1.80303i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.95902 | 0.605113 | 0.302557 | − | 0.953131i | \(-0.402160\pi\) | ||||
0.302557 | + | 0.953131i | \(0.402160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4113 | + | 7.18320i | −0.787020 | + | 0.542999i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.168821 | + | 0.292406i | −0.0126182 | + | 0.0218554i | −0.872266 | − | 0.489032i | \(-0.837350\pi\) |
0.859647 | + | 0.510888i | \(0.170683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.05801 | 0.524618 | 0.262309 | − | 0.964984i | \(-0.415516\pi\) | ||||
0.262309 | + | 0.964984i | \(0.415516\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90842 | −0.360874 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.66524 | −0.487411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7187 | −1.28208 | −0.641039 | − | 0.767508i | \(-0.721496\pi\) | ||||
−0.641039 | + | 0.767508i | \(0.721496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8024 | −1.20946 | −0.604732 | − | 0.796429i | \(-0.706720\pi\) | ||||
−0.604732 | + | 0.796429i | \(0.706720\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.97545 | −0.425733 | −0.212867 | − | 0.977081i | \(-0.568280\pi\) | ||||
−0.212867 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.26093 | − | 10.8443i | 0.443826 | − | 0.768729i | −0.554144 | − | 0.832421i | \(-0.686954\pi\) |
0.997970 | + | 0.0636923i | \(0.0202876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.63124 | + | 4.09778i | 0.605794 | + | 0.287607i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0235611 | −0.00164558 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.22190 | − | 5.58050i | 0.222864 | − | 0.386011i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.17688 | + | 2.03842i | 0.0810198 | + | 0.140330i | 0.903688 | − | 0.428191i | \(-0.140849\pi\) |
−0.822668 | + | 0.568521i | \(0.807516\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.202188 | − | 0.350199i | −0.0137891 | − | 0.0238834i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.37999 | + | 17.1387i | 0.0936795 | + | 1.16345i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.2840 | −2.10439 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.30709 | − | 9.19215i | 0.355389 | − | 0.615552i | −0.631795 | − | 0.775135i | \(-0.717682\pi\) |
0.987184 | + | 0.159583i | \(0.0510150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.637749 | + | 1.10461i | 0.0423289 | + | 0.0733158i | 0.886414 | − | 0.462894i | \(-0.153189\pi\) |
−0.844085 | + | 0.536210i | \(0.819856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.73313 | − | 11.6621i | 0.444938 | − | 0.770655i | −0.553110 | − | 0.833108i | \(-0.686559\pi\) |
0.998048 | + | 0.0624532i | \(0.0198924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.98509 | − | 17.2947i | −0.654145 | − | 1.13301i | −0.982107 | − | 0.188321i | \(-0.939695\pi\) |
0.327963 | − | 0.944691i | \(-0.393638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.57220 | + | 4.45519i | −0.167792 | + | 0.290624i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1092 | + | 24.4379i | 0.912650 | + | 1.58076i | 0.810305 | + | 0.586008i | \(0.199301\pi\) |
0.102345 | + | 0.994749i | \(0.467365\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.67622 | + | 15.0277i | 0.558884 | + | 0.968016i | 0.997590 | + | 0.0693852i | \(0.0221038\pi\) |
−0.438706 | + | 0.898631i | \(0.644563\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.16338 | − | 3.06374i | 0.0743257 | − | 0.195735i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.1223 | − | 26.1927i | 0.962212 | − | 1.66660i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.29051 | −0.397054 | −0.198527 | − | 0.980095i | \(-0.563616\pi\) | ||||
−0.198527 | + | 0.980095i | \(0.563616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2870 | −0.646738 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.06819 | + | 5.31426i | −0.191388 | + | 0.331494i | −0.945711 | − | 0.325010i | \(-0.894632\pi\) |
0.754322 | + | 0.656504i | \(0.227966\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8319 | + | 15.7527i | −1.41870 | + | 0.978825i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.93957 | + | 5.09148i | 0.181262 | + | 0.313954i | 0.942310 | − | 0.334740i | \(-0.108649\pi\) |
−0.761049 | + | 0.648695i | \(0.775315\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.73868 | − | 4.74352i | −0.168235 | − | 0.291392i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4633 | − | 26.7832i | 0.942812 | − | 1.63300i | 0.182738 | − | 0.983162i | \(-0.441504\pi\) |
0.760074 | − | 0.649837i | \(-0.225163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.44528 | + | 9.43150i | 0.330777 | + | 0.572923i | 0.982664 | − | 0.185393i | \(-0.0593558\pi\) |
−0.651887 | + | 0.758316i | \(0.726022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.22367 | − | 5.58356i | 0.194395 | − | 0.336701i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.79498 | − | 16.9654i | −0.588524 | − | 1.01935i | −0.994426 | − | 0.105436i | \(-0.966376\pi\) |
0.405903 | − | 0.913916i | \(-0.366957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.142477 | − | 0.246777i | 0.00849944 | − | 0.0147215i | −0.861744 | − | 0.507343i | \(-0.830628\pi\) |
0.870244 | + | 0.492621i | \(0.163961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.84269 | 0.168981 | 0.0844903 | − | 0.996424i | \(-0.473074\pi\) | ||||
0.0844903 | + | 0.996424i | \(0.473074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.109596 | + | 0.0756152i | −0.00646926 | + | 0.00446342i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.71364 | − | 6.43221i | −0.218449 | − | 0.378365i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.45979 | + | 2.52842i | 0.0852816 | + | 0.147712i | 0.905511 | − | 0.424322i | \(-0.139488\pi\) |
−0.820230 | + | 0.572034i | \(0.806154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.907743 | + | 1.57226i | −0.0528509 | + | 0.0915404i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −48.2831 | −2.79228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.06439 | − | 0.980094i | −0.118990 | − | 0.0564917i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.876558 | + | 1.51824i | −0.0501916 | + | 0.0869344i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.12553 | −0.235457 | −0.117728 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117728 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3917 | −0.872781 | −0.436390 | − | 0.899757i | \(-0.643743\pi\) | ||||
−0.436390 | + | 0.899757i | \(0.643743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7240 | −1.17139 | −0.585694 | − | 0.810533i | \(-0.699178\pi\) | ||||
−0.585694 | + | 0.810533i | \(0.699178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.488292 | 0.0274252 | 0.0137126 | − | 0.999906i | \(-0.495635\pi\) | ||||
0.0137126 | + | 0.999906i | \(0.495635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.87014 | −0.272675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.6157 | 1.31402 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.1306 | − | 26.2070i | 0.839297 | − | 1.45370i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.33333 | + | 28.9787i | 0.128640 | + | 1.59764i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9573 | −1.04199 | −0.520993 | − | 0.853561i | \(-0.674438\pi\) | ||||
−0.520993 | + | 0.853561i | \(0.674438\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.620023 | − | 1.07391i | 0.0338755 | − | 0.0586740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6202 | + | 20.1268i | 0.632993 | + | 1.09638i | 0.986937 | + | 0.161109i | \(0.0515071\pi\) |
−0.353944 | + | 0.935267i | \(0.615160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.38208 | − | 7.58998i | −0.237303 | − | 0.411020i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.42096 | − | 17.9849i | −0.238709 | − | 0.971091i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1888 | −0.976425 | −0.488212 | − | 0.872725i | \(-0.662351\pi\) | ||||
−0.488212 | + | 0.872725i | \(0.662351\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.40155 | + | 16.2840i | −0.503253 | + | 0.871661i | 0.496740 | + | 0.867900i | \(0.334530\pi\) |
−0.999993 | + | 0.00376081i | \(0.998803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.95997 | − | 10.3230i | −0.317217 | − | 0.549436i | 0.662689 | − | 0.748895i | \(-0.269415\pi\) |
−0.979906 | + | 0.199458i | \(0.936082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.64927 | + | 2.85662i | −0.0875342 | + | 0.151614i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.3849 | + | 30.1115i | 0.917540 | + | 1.58923i | 0.803140 | + | 0.595791i | \(0.203161\pi\) |
0.114400 | + | 0.993435i | \(0.463505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91559 | + | 3.31790i | −0.100821 | + | 0.174626i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.54551 | − | 2.67689i | −0.0808954 | − | 0.140115i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4431 | + | 25.0161i | 0.753922 | + | 1.30583i | 0.945909 | + | 0.324433i | \(0.105174\pi\) |
−0.191987 | + | 0.981398i | \(0.561493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.9626 | − | 13.2756i | −1.45175 | − | 0.689233i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.15472 | + | 12.3923i | −0.370457 | + | 0.641651i | −0.989636 | − | 0.143599i | \(-0.954132\pi\) |
0.619179 | + | 0.785250i | \(0.287466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.8585 | −1.17727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.15511 | 0.0593340 | 0.0296670 | − | 0.999560i | \(-0.490555\pi\) | ||||
0.0296670 | + | 0.999560i | \(0.490555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9131 | − | 29.2944i | 0.864219 | − | 1.49687i | −0.00360069 | − | 0.999994i | \(-0.501146\pi\) |
0.867820 | − | 0.496878i | \(-0.165521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.134068 | + | 1.66505i | 0.00683272 | + | 0.0848587i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.66080 | + | 16.7330i | 0.489822 | + | 0.848397i | 0.999931 | − | 0.0117128i | \(-0.00372838\pi\) |
−0.510109 | + | 0.860110i | \(0.670395\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8503 | − | 32.6496i | −0.953299 | − | 1.65116i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.744159 | + | 1.28892i | −0.0374427 | + | 0.0648526i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.18190 | − | 10.7074i | −0.310261 | − | 0.537387i | 0.668158 | − | 0.744019i | \(-0.267083\pi\) |
−0.978419 | + | 0.206632i | \(0.933750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2568 | + | 26.4256i | −0.761889 | + | 1.31963i | 0.179987 | + | 0.983669i | \(0.442394\pi\) |
−0.941876 | + | 0.335961i | \(0.890939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.5677 | − | 35.6244i | −1.02455 | − | 1.77458i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.06948 | − | 12.2447i | 0.350421 | − | 0.606947i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.25446 | −0.259816 | −0.129908 | − | 0.991526i | \(-0.541468\pi\) | ||||
−0.129908 | + | 0.991526i | \(0.541468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.823443 | + | 10.2267i | 0.0405190 | + | 0.503224i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29530 | − | 3.97558i | −0.112672 | − | 0.195154i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2824 | − | 26.4699i | −0.746594 | − | 1.29314i | −0.949446 | − | 0.313930i | \(-0.898354\pi\) |
0.202852 | − | 0.979209i | \(-0.434979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.11608 | − | 5.39721i | 0.151869 | − | 0.263044i | −0.780046 | − | 0.625722i | \(-0.784804\pi\) |
0.931914 | + | 0.362678i | \(0.118138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.6287 | 1.14616 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.795154 | + | 9.87538i | 0.0384802 | + | 0.477903i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8142 | + | 25.6590i | −0.713576 | + | 1.23595i | 0.249930 | + | 0.968264i | \(0.419592\pi\) |
−0.963506 | + | 0.267686i | \(0.913741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.36815 | 0.354091 | 0.177045 | − | 0.984203i | \(-0.443346\pi\) | ||||
0.177045 | + | 0.984203i | \(0.443346\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.4480 | 1.74355 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4427 | 0.498403 | 0.249201 | − | 0.968452i | \(-0.419832\pi\) | ||||
0.249201 | + | 0.968452i | \(0.419832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.66664 | −0.269230 | −0.134615 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134615 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.96923 | 0.235564 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4794 | −0.541748 | −0.270874 | − | 0.962615i | \(-0.587313\pi\) | ||||
−0.270874 | + | 0.962615i | \(0.587313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0339345 | − | 0.0587763i | 0.00159791 | − | 0.00276767i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.629261 | + | 7.81508i | 0.0295002 | + | 0.366377i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5872 | 0.916251 | 0.458126 | − | 0.888887i | \(-0.348521\pi\) | ||||
0.458126 | + | 0.888887i | \(0.348521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.3028 | + | 29.9693i | −0.805871 | + | 1.39581i | 0.109830 | + | 0.993950i | \(0.464969\pi\) |
−0.915701 | + | 0.401859i | \(0.868364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.91882 | + | 11.9837i | 0.321545 | + | 0.556932i | 0.980807 | − | 0.194981i | \(-0.0624646\pi\) |
−0.659262 | + | 0.751913i | \(0.729131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.71088 | − | 6.42743i | −0.171719 | − | 0.297426i | 0.767302 | − | 0.641286i | \(-0.221599\pi\) |
−0.939021 | + | 0.343860i | \(0.888265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.562442 | − | 6.98523i | −0.0259712 | − | 0.322548i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.16482 | 0.0535587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.4218 | + | 19.7832i | −0.524070 | + | 0.907716i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.89577 | − | 6.74767i | −0.178002 | − | 0.308309i | 0.763194 | − | 0.646170i | \(-0.223630\pi\) |
−0.941196 | + | 0.337860i | \(0.890297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.1813 | − | 57.4718i | 1.51294 | − | 2.62049i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.26684 | + | 5.65834i | 0.148340 | + | 0.256932i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.04434 | + | 1.80886i | −0.0473238 | + | 0.0819672i | −0.888717 | − | 0.458456i | \(-0.848403\pi\) |
0.841393 | + | 0.540423i | \(0.181736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.8767 | + | 29.2312i | 0.761633 | + | 1.31919i | 0.942008 | + | 0.335590i | \(0.108936\pi\) |
−0.180375 | + | 0.983598i | \(0.557731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.92422 | − | 15.4572i | −0.401927 | − | 0.696157i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.49611 | + | 18.5808i | 0.0671095 | + | 0.833464i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.9098 | + | 36.2169i | −0.936052 | + | 1.62129i | −0.163304 | + | 0.986576i | \(0.552215\pi\) |
−0.772747 | + | 0.634714i | \(0.781118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.54978 | −0.292040 | −0.146020 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146020 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98946 | −0.0885299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.30653 | + | 10.9232i | −0.279532 | + | 0.484164i | −0.971269 | − | 0.237986i | \(-0.923513\pi\) |
0.691736 | + | 0.722150i | \(0.256846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7800 | − | 7.49175i | −0.698068 | − | 0.331415i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.09656 | + | 3.63134i | 0.0923853 | + | 0.160016i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.40936 | − | 12.8334i | −0.325863 | − | 0.564412i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2688 | + | 17.7861i | −0.449883 | + | 0.779221i | −0.998378 | − | 0.0569331i | \(-0.981868\pi\) |
0.548495 | + | 0.836154i | \(0.315201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4579 | + | 25.0419i | 0.632202 | + | 1.09501i | 0.987101 | + | 0.160101i | \(0.0511820\pi\) |
−0.354899 | + | 0.934905i | \(0.615485\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0598 | − | 27.8163i | 0.699574 | − | 1.21170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5931 | − | 30.4721i | −0.764917 | − | 1.32488i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.159275 | − | 0.275873i | 0.00689897 | − | 0.0119494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.759119 | −0.0328196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.96730 | + | 7.31483i | 0.257030 | + | 0.315072i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.29262 | + | 5.70299i | 0.141561 | + | 0.245191i | 0.928085 | − | 0.372369i | \(-0.121455\pi\) |
−0.786524 | + | 0.617560i | \(0.788121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.39348 | + | 2.41357i | 0.0596900 | + | 0.103386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.46777 | − | 7.73840i | 0.191028 | − | 0.330870i | −0.754563 | − | 0.656227i | \(-0.772151\pi\) |
0.945591 | + | 0.325357i | \(0.105485\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.2555 | 0.735108 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.675050 | + | 8.38376i | 0.0287060 | + | 0.356514i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.93523 | − | 5.08396i | 0.124370 | − | 0.215414i | −0.797117 | − | 0.603825i | \(-0.793642\pi\) |
0.921486 | + | 0.388411i | \(0.126976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.46723 | 0.231239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.5972 | −1.16308 | −0.581541 | − | 0.813517i | \(-0.697550\pi\) | ||||
−0.581541 | + | 0.813517i | \(0.697550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.87968 | 0.163220 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9202 | 1.17048 | 0.585238 | − | 0.810862i | \(-0.301001\pi\) | ||||
0.585238 | + | 0.810862i | \(0.301001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7974 | −1.33068 | −0.665339 | − | 0.746541i | \(-0.731713\pi\) | ||||
−0.665339 | + | 0.746541i | \(0.731713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.4680 | 1.52082 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7476 | − | 23.8115i | 0.572320 | − | 0.991287i | −0.424007 | − | 0.905659i | \(-0.639377\pi\) |
0.996327 | − | 0.0856281i | \(-0.0272897\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.4357 | − | 11.1263i | −0.972276 | − | 0.461599i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7778 | 0.653449 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.12422 | − | 12.3395i | 0.294048 | − | 0.509306i | −0.680715 | − | 0.732548i | \(-0.738331\pi\) |
0.974763 | + | 0.223242i | \(0.0716641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.5262 | + | 26.8922i | 0.639747 | + | 1.10807i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4636 | − | 26.7838i | −0.635015 | − | 1.09988i | −0.986512 | − | 0.163689i | \(-0.947661\pi\) |
0.351498 | − | 0.936189i | \(-0.385673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.03898 | + | 3.47661i | −0.206578 | + | 0.142527i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.5315 | −1.49264 | −0.746318 | − | 0.665589i | \(-0.768180\pi\) | ||||
−0.746318 | + | 0.665589i | \(0.768180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.11575 | − | 12.3248i | 0.290257 | − | 0.502741i | −0.683613 | − | 0.729845i | \(-0.739592\pi\) |
0.973871 | + | 0.227104i | \(0.0729257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.14920 | + | 3.72253i | 0.0873776 | + | 0.151342i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6729 | − | 25.4141i | 0.595553 | − | 1.03153i | −0.397916 | − | 0.917422i | \(-0.630266\pi\) |
0.993469 | − | 0.114106i | \(-0.0364003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.7766 | − | 60.2349i | −1.40691 | − | 2.43684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.79264 | + | 6.56905i | −0.153183 | + | 0.265321i | −0.932396 | − | 0.361438i | \(-0.882286\pi\) |
0.779213 | + | 0.626760i | \(0.215619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4367 | + | 18.0769i | 0.420165 | + | 0.727748i | 0.995955 | − | 0.0898500i | \(-0.0286388\pi\) |
−0.575790 | + | 0.817598i | \(0.695305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6300 | + | 21.8758i | 0.507642 | + | 0.879262i | 0.999961 | + | 0.00884679i | \(0.00281606\pi\) |
−0.492319 | + | 0.870415i | \(0.663851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.1147 | − | 15.9478i | 0.926072 | − | 0.638937i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8802 | + | 18.8450i | −0.435206 | + | 0.753799i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.8175 | 2.06610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0114 | −1.35397 | −0.676986 | − | 0.735996i | \(-0.736714\pi\) | ||||
−0.676986 | + | 0.735996i | \(0.736714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.90163 | + | 3.29372i | −0.0754638 | + | 0.130707i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0082 | + | 34.3329i | 1.10972 | + | 1.36032i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.64947 | + | 4.58902i | 0.104648 | + | 0.181255i | 0.913594 | − | 0.406627i | \(-0.133295\pi\) |
−0.808946 | + | 0.587882i | \(0.799962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.4304 | + | 33.6544i | 0.766260 | + | 1.32720i | 0.939578 | + | 0.342335i | \(0.111218\pi\) |
−0.173318 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.11420 | + | 7.12601i | −0.161746 | + | 0.280152i | −0.935495 | − | 0.353340i | \(-0.885046\pi\) |
0.773749 | + | 0.633492i | \(0.218379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.61480 | − | 4.52897i | −0.102640 | − | 0.177778i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0164 | − | 36.4015i | 0.822436 | − | 1.42450i | −0.0814277 | − | 0.996679i | \(-0.525948\pi\) |
0.903863 | − | 0.427821i | \(-0.140719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.56382 | + | 7.90477i | 0.178323 | + | 0.308865i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.33484 | + | 12.7043i | −0.285725 | + | 0.494890i | −0.972785 | − | 0.231711i | \(-0.925568\pi\) |
0.687060 | + | 0.726601i | \(0.258901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.86605 | 0.228163 | 0.114081 | − | 0.993471i | \(-0.463608\pi\) | ||||
0.114081 | + | 0.993471i | \(0.463608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.475018 | − | 5.89947i | −0.0184204 | − | 0.228771i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7734 | − | 23.8563i | −0.533310 | − | 0.923720i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.52497 | − | 4.37338i | −0.0974754 | − | 0.168832i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.42591 | − | 16.3261i | 0.363342 | − | 0.629327i | −0.625167 | − | 0.780491i | \(-0.714969\pi\) |
0.988509 | + | 0.151165i | \(0.0483023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.9144 | −1.14970 | −0.574852 | − | 0.818257i | \(-0.694941\pi\) | ||||
−0.574852 | + | 0.818257i | \(0.694941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.3554 | + | 15.8358i | 1.28006 | + | 0.607724i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.8525 | + | 22.2612i | −0.491788 | + | 0.851802i | −0.999955 | − | 0.00945677i | \(-0.996990\pi\) |
0.508167 | + | 0.861258i | \(0.330323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.07099 | 0.270169 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 74.0547 | 2.82126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.4020 | 1.46088 | 0.730440 | − | 0.682976i | \(-0.239315\pi\) | ||||
0.730440 | + | 0.682976i | \(0.239315\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.04895 | 0.0777210 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.248731 | 0.00942137 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.5694 | −0.436972 | −0.218486 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218486 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0480 | + | 43.3844i | −0.944703 | + | 1.63627i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.25413 | + | 6.38482i | −0.348037 | + | 0.240126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.0550 | 1.95497 | 0.977483 | − | 0.211013i | \(-0.0676763\pi\) | ||||
0.977483 | + | 0.211013i | \(0.0676763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.7863 | − | 42.9311i | 0.928254 | − | 1.60778i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.99819 | − | 3.46096i | −0.0747280 | − | 0.129433i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.416175 | − | 0.720836i | −0.0155207 | − | 0.0268827i | 0.858161 | − | 0.513381i | \(-0.171607\pi\) |
−0.873681 | + | 0.486498i | \(0.838274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.4064 | + | 10.1629i | 0.797217 | + | 0.378488i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.2649 | 0.641203 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7029 | − | 18.5379i | 0.396948 | − | 0.687534i | −0.596400 | − | 0.802687i | \(-0.703403\pi\) |
0.993348 | + | 0.115154i | \(0.0367361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.13447 | + | 3.69701i | 0.0789461 | + | 0.136739i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.72620 | − | 6.45396i | 0.137630 | − | 0.238383i | −0.788969 | − | 0.614433i | \(-0.789385\pi\) |
0.926599 | + | 0.376051i | \(0.122718\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.78601 | + | 3.09346i | 0.0657885 | + | 0.113949i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9473 | + | 31.0857i | −0.660203 | + | 1.14351i | 0.320358 | + | 0.947296i | \(0.396197\pi\) |
−0.980562 | + | 0.196210i | \(0.937137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.8379 | − | 29.1641i | −0.617723 | − | 1.06993i | −0.989900 | − | 0.141766i | \(-0.954722\pi\) |
0.372177 | − | 0.928162i | \(-0.378611\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.75199 | − | 4.76659i | −0.100825 | − | 0.174634i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.53110 | + | 2.43625i | −0.129023 | + | 0.0890188i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.51689 | + | 13.0196i | −0.274295 | + | 0.475093i | −0.969957 | − | 0.243276i | \(-0.921778\pi\) |
0.695662 | + | 0.718369i | \(0.255111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.40782 | −0.0876295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.2548 | −1.24501 | −0.622507 | − | 0.782615i | \(-0.713886\pi\) | ||||
−0.622507 | + | 0.782615i | \(0.713886\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1043 | − | 36.5538i | 0.765031 | − | 1.32507i | −0.175199 | − | 0.984533i | \(-0.556057\pi\) |
0.940230 | − | 0.340540i | \(-0.110610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2278 | + | 6.75480i | 0.515081 | + | 0.244540i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.2728 | − | 21.2572i | −0.443147 | − | 0.767553i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2741 | + | 38.5799i | 0.803226 | + | 1.39123i | 0.917482 | + | 0.397777i | \(0.130218\pi\) |
−0.114256 | + | 0.993451i | \(0.536448\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.61003 | − | 16.6451i | 0.345649 | − | 0.598681i | −0.639823 | − | 0.768523i | \(-0.720992\pi\) |
0.985471 | + | 0.169841i | \(0.0543256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.5347 | + | 26.9069i | 0.558024 | + | 0.966526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.120234 | + | 0.208251i | −0.00430783 | + | 0.00746138i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.75081 | − | 8.22864i | −0.169997 | − | 0.294444i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.82984 | − | 4.90142i | 0.101001 | − | 0.174939i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.3502 | −1.43833 | −0.719165 | − | 0.694839i | \(-0.755476\pi\) | ||||
−0.719165 | + | 0.694839i | \(0.755476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0466 | − | 12.4512i | 0.641665 | − | 0.442712i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.8512 | − | 20.5269i | −0.420849 | − | 0.728932i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.4965 | − | 38.9651i | −0.796867 | − | 1.38021i | −0.921647 | − | 0.388029i | \(-0.873156\pi\) |
0.124780 | − | 0.992184i | \(-0.460177\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1544 | − | 47.0328i | 0.960653 | − | 1.66390i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.90381 | 0.314209 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.77706 | + | 5.36573i | −0.274105 | + | 0.189117i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.8858 | + | 29.2470i | −0.593672 | + | 1.02827i | 0.400061 | + | 0.916489i | \(0.368989\pi\) |
−0.993733 | + | 0.111782i | \(0.964344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.7254 | −1.11403 | −0.557014 | − | 0.830503i | \(-0.688053\pi\) | ||||
−0.557014 | + | 0.830503i | \(0.688053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.57178 | 0.0900854 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.12711 | −0.144389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7504 | 0.410093 | 0.205046 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205046 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.50742 | −0.296550 | −0.148275 | − | 0.988946i | \(-0.547372\pi\) | ||||
−0.148275 | + | 0.988946i | \(0.547372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9662 | 0.485651 | 0.242825 | − | 0.970070i | \(-0.421926\pi\) | ||||
0.242825 | + | 0.970070i | \(0.421926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.5484 | + | 32.1267i | −0.644212 | + | 1.11581i | 0.340271 | + | 0.940327i | \(0.389481\pi\) |
−0.984483 | + | 0.175480i | \(0.943852\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.2817 | + | 32.3434i | −0.425534 | + | 1.12063i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.36499 | −0.116450 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.32105 | − | 2.28813i | 0.0456077 | − | 0.0789949i | −0.842320 | − | 0.538977i | \(-0.818811\pi\) |
0.887928 | + | 0.459982i | \(0.152144\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.97928 | + | 13.8205i | 0.275148 | + | 0.476570i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.33561 | − | 10.9736i | −0.217952 | − | 0.377503i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.9440 | + | 10.4181i | 0.754004 | + | 0.357972i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 79.9740 | 2.74147 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.3405 | − | 30.0346i | 0.593726 | − | 1.02836i | −0.399999 | − | 0.916516i | \(-0.630990\pi\) |
0.993725 | − | 0.111848i | \(-0.0356771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.8611 | + | 20.5441i | 0.405169 | + | 0.701773i | 0.994341 | − | 0.106234i | \(-0.0338793\pi\) |
−0.589172 | + | 0.808008i | \(0.700546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9075 | − | 18.8923i | 0.372158 | − | 0.644597i | −0.617739 | − | 0.786383i | \(-0.711951\pi\) |
0.989897 | + | 0.141786i | \(0.0452845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6899 | + | 25.4436i | 0.500049 | + | 0.866111i | 1.00000 | 5.68129e-5i | \(1.80841e-5\pi\) | |
−0.499951 | + | 0.866054i | \(0.666649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.86308 | + | 3.22696i | −0.0633467 | + | 0.109720i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.14359 | − | 3.71280i | −0.0727162 | − | 0.125948i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.38282 | + | 14.5195i | 0.284041 | + | 0.491973i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.972346 | − | 12.0760i | −0.0328713 | − | 0.408244i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.81065 | − | 4.86818i | 0.0949087 | − | 0.164387i | −0.814662 | − | 0.579936i | \(-0.803077\pi\) |
0.909571 | + | 0.415550i | \(0.136411\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.75442 | −0.0927987 | −0.0463994 | − | 0.998923i | \(-0.514775\pi\) | ||||
−0.0463994 | + | 0.998923i | \(0.514775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8917 | 1.14055 | 0.570274 | − | 0.821455i | \(-0.306837\pi\) | ||||
0.570274 | + | 0.821455i | \(0.306837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.8447 | + | 48.2284i | −0.934932 | + | 1.61935i | −0.160177 | + | 0.987088i | \(0.551206\pi\) |
−0.774755 | + | 0.632261i | \(0.782127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.72503 | + | 21.4239i | 0.0578555 | + | 0.718535i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.2523 | + | 45.4702i | 0.878498 | + | 1.52160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0790366 | − | 0.136895i | −0.00264190 | − | 0.00457591i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7345 | − | 20.3247i | 0.391367 | − | 0.677868i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.9118 | + | 50.0767i | 0.963192 | + | 1.66830i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.65217 | + | 2.86164i | −0.0549200 | + | 0.0951243i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7313 | − | 46.2999i | −0.887597 | − | 1.53736i | −0.842707 | − | 0.538372i | \(-0.819040\pi\) |
−0.0448901 | − | 0.998992i | \(-0.514294\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.77060 | + | 16.9232i | −0.323714 | + | 0.560690i | −0.981251 | − | 0.192732i | \(-0.938265\pi\) |
0.657537 | + | 0.753422i | \(0.271598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.2235 | 0.437633 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.5979 | + | 22.1229i | 1.53880 | + | 0.730561i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0878895 | + | 0.152229i | 0.00289921 | + | 0.00502157i | 0.867471 | − | 0.497487i | \(-0.165744\pi\) |
−0.864572 | + | 0.502509i | \(0.832410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.2984 | − | 38.6220i | −0.733962 | − | 1.27126i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.0617 | + | 43.4082i | −0.824025 | + | 1.42725i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.6016 | 0.807152 | 0.403576 | − | 0.914946i | \(-0.367767\pi\) | ||||
0.403576 | + | 0.914946i | \(0.367767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.1429 | − | 25.9173i | −0.692929 | − | 0.849406i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.56023 | − | 2.70240i | 0.0510250 | − | 0.0883779i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5655 | −0.933195 | −0.466598 | − | 0.884470i | \(-0.654520\pi\) | ||||
−0.466598 | + | 0.884470i | \(0.654520\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.5604 | −1.22443 | −0.612217 | − | 0.790689i | \(-0.709722\pi\) | ||||
−0.612217 | + | 0.790689i | \(0.709722\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.383887 | 0.0125011 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.66763 | −0.314156 | −0.157078 | − | 0.987586i | \(-0.550207\pi\) | ||||
−0.157078 | + | 0.987586i | \(0.550207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41.7910 | 1.35659 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.1964 | −1.88517 | −0.942583 | − | 0.333971i | \(-0.891611\pi\) | ||||
−0.942583 | + | 0.333971i | \(0.891611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.14767 | − | 7.18397i | 0.134215 | − | 0.232468i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.8912 | − | 22.6931i | 1.06211 | − | 0.732797i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2341 | 0.362390 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.93319 | − | 6.81248i | 0.126614 | − | 0.219301i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.97991 | + | 13.8216i | 0.256617 | + | 0.444473i | 0.965333 | − | 0.261020i | \(-0.0840589\pi\) |
−0.708717 | + | 0.705493i | \(0.750726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67394 | + | 2.89935i | 0.0537193 | + | 0.0930445i | 0.891635 | − | 0.452756i | \(-0.149559\pi\) |
−0.837915 | + | 0.545800i | \(0.816226\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.53083 | − | 6.57573i | 0.305544 | − | 0.210808i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.8803 | −0.763999 | −0.382000 | − | 0.924162i | \(-0.624764\pi\) | ||||
−0.382000 | + | 0.924162i | \(0.624764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.15706 | + | 12.3964i | −0.228741 | + | 0.396190i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8786 | + | 32.6988i | 0.602135 | + | 1.04293i | 0.992497 | + | 0.122267i | \(0.0390165\pi\) |
−0.390362 | + | 0.920661i | \(0.627650\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39876 | − | 2.42272i | 0.0445682 | − | 0.0771944i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.29429 | + | 5.70588i | 0.104752 | + | 0.181436i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.08487 | + | 1.87904i | −0.0344619 | + | 0.0596898i | −0.882742 | − | 0.469858i | \(-0.844305\pi\) |
0.848280 | + | 0.529548i | \(0.177638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.93117 | + | 5.07694i | 0.0929245 | + | 0.160950i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.34727 | + | 7.52969i | 0.137679 | + | 0.238468i | 0.926618 | − | 0.376005i | \(-0.122702\pi\) |
−0.788938 | + | 0.614472i | \(0.789369\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.q.d.1369.5 | 22 | ||
3.2 | odd | 2 | 504.2.q.c.25.1 | ✓ | 22 | ||
4.3 | odd | 2 | 3024.2.q.l.2881.5 | 22 | |||
7.2 | even | 3 | 1512.2.t.c.289.7 | 22 | |||
9.4 | even | 3 | 1512.2.t.c.361.7 | 22 | |||
9.5 | odd | 6 | 504.2.t.c.193.7 | yes | 22 | ||
12.11 | even | 2 | 1008.2.q.l.529.11 | 22 | |||
21.2 | odd | 6 | 504.2.t.c.457.7 | yes | 22 | ||
28.23 | odd | 6 | 3024.2.t.k.289.7 | 22 | |||
36.23 | even | 6 | 1008.2.t.l.193.5 | 22 | |||
36.31 | odd | 6 | 3024.2.t.k.1873.7 | 22 | |||
63.23 | odd | 6 | 504.2.q.c.121.1 | yes | 22 | ||
63.58 | even | 3 | inner | 1512.2.q.d.793.5 | 22 | ||
84.23 | even | 6 | 1008.2.t.l.961.5 | 22 | |||
252.23 | even | 6 | 1008.2.q.l.625.11 | 22 | |||
252.247 | odd | 6 | 3024.2.q.l.2305.5 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.1 | ✓ | 22 | 3.2 | odd | 2 | ||
504.2.q.c.121.1 | yes | 22 | 63.23 | odd | 6 | ||
504.2.t.c.193.7 | yes | 22 | 9.5 | odd | 6 | ||
504.2.t.c.457.7 | yes | 22 | 21.2 | odd | 6 | ||
1008.2.q.l.529.11 | 22 | 12.11 | even | 2 | |||
1008.2.q.l.625.11 | 22 | 252.23 | even | 6 | |||
1008.2.t.l.193.5 | 22 | 36.23 | even | 6 | |||
1008.2.t.l.961.5 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.793.5 | 22 | 63.58 | even | 3 | inner | ||
1512.2.q.d.1369.5 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.t.c.289.7 | 22 | 7.2 | even | 3 | |||
1512.2.t.c.361.7 | 22 | 9.4 | even | 3 | |||
3024.2.q.l.2305.5 | 22 | 252.247 | odd | 6 | |||
3024.2.q.l.2881.5 | 22 | 4.3 | odd | 2 | |||
3024.2.t.k.289.7 | 22 | 28.23 | odd | 6 | |||
3024.2.t.k.1873.7 | 22 | 36.31 | odd | 6 |