Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.5 | ||
Root | \(0.500000 - 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.i.1537.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.79793i | − 0.804060i | −0.915627 | − | 0.402030i | \(-0.868305\pi\) | ||||
0.915627 | − | 0.402030i | \(-0.131695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.158942 | −0.0600743 | −0.0300371 | − | 0.999549i | \(-0.509563\pi\) | ||||
−0.0300371 | + | 0.999549i | \(0.509563\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.37109i | 1.61944i | 0.586814 | + | 0.809722i | \(0.300382\pi\) | ||||
−0.586814 | + | 0.809722i | \(0.699618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.95687i | − 1.65214i | −0.563568 | − | 0.826070i | \(-0.690572\pi\) | ||||
0.563568 | − | 0.826070i | \(-0.309428\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79793 | 0.464224 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.05320 | −0.740511 | −0.370255 | − | 0.928930i | \(-0.620730\pi\) | ||||
−0.370255 | + | 0.928930i | \(0.620730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05320i | 0.700453i | 0.936665 | + | 0.350227i | \(0.113895\pi\) | ||||
−0.936665 | + | 0.350227i | \(0.886105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.158942i | − 0.0346839i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.76744 | 0.353488 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.96951i | − 0.551423i | −0.961240 | − | 0.275712i | \(-0.911087\pi\) | ||||
0.961240 | − | 0.275712i | \(-0.0889135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.15894 | −0.746968 | −0.373484 | − | 0.927637i | \(-0.621837\pi\) | ||||
−0.373484 | + | 0.927637i | \(0.621837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.37109 | −0.934986 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.285766i | 0.0483033i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.46742i | 1.39203i | 0.718025 | + | 0.696017i | \(0.245046\pi\) | ||||
−0.718025 | + | 0.696017i | \(0.754954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.95687 | 0.953863 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.60365 | −0.406622 | −0.203311 | − | 0.979114i | \(-0.565170\pi\) | ||||
−0.203311 | + | 0.979114i | \(0.565170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.13853i | − 1.24111i | −0.784162 | − | 0.620557i | \(-0.786907\pi\) | ||||
0.784162 | − | 0.620557i | \(-0.213093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.79793i | 0.268020i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97474 | −0.996391 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.05320i | − 0.427534i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.03049i | 0.690992i | 0.938420 | + | 0.345496i | \(0.112289\pi\) | ||||
−0.938420 | + | 0.345496i | \(0.887711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.65685 | 1.30213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.05320 | −0.404407 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.65685i | 0.736460i | 0.929735 | + | 0.368230i | \(0.120036\pi\) | ||||
−0.929735 | + | 0.368230i | \(0.879964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.18944i | − 0.664439i | −0.943202 | − | 0.332220i | \(-0.892202\pi\) | ||||
0.943202 | − | 0.332220i | \(-0.107798\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.158942 | 0.0200248 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7101 | −1.32842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.08532i | 0.132593i | 0.997800 | + | 0.0662966i | \(0.0211183\pi\) | ||||
−0.997800 | + | 0.0662966i | \(0.978882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.82843i | − 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.317883 | 0.0377258 | 0.0188629 | − | 0.999822i | \(-0.493995\pi\) | ||||
0.0188629 | + | 0.999822i | \(0.493995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.33897 | −0.156715 | −0.0783573 | − | 0.996925i | \(-0.524968\pi\) | ||||
−0.0783573 | + | 0.996925i | \(0.524968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.76744i | 0.204086i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.853690i | − 0.0972870i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.69382 | −1.09064 | −0.545320 | − | 0.838228i | \(-0.683592\pi\) | ||||
−0.545320 | + | 0.838228i | \(0.683592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.163788i | − 0.0179781i | −0.999960 | − | 0.00898906i | \(-0.997139\pi\) | ||||
0.999960 | − | 0.00898906i | \(-0.00286135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.48946i | 0.595415i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.96951 | 0.318364 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3990 | −1.52629 | −0.763147 | − | 0.646225i | \(-0.776347\pi\) | ||||
−0.763147 | + | 0.646225i | \(0.776347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.946795i | 0.0992511i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.15894i | − 0.431262i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.48946 | 0.563206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.571533 | −0.0580304 | −0.0290152 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290152 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 5.37109i | − 0.539815i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1158i | 1.00656i | 0.864123 | + | 0.503281i | \(0.167874\pi\) | ||||
−0.864123 | + | 0.503281i | \(0.832126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3507 | −1.11841 | −0.559207 | − | 0.829028i | \(-0.688894\pi\) | ||||
−0.559207 | + | 0.829028i | \(0.688894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.285766 | −0.0278879 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.02109i | 0.0987123i | 0.998781 | + | 0.0493561i | \(0.0157169\pi\) | ||||
−0.998781 | + | 0.0493561i | \(0.984283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.04313i | − 0.195696i | −0.995201 | − | 0.0978480i | \(-0.968804\pi\) | ||||
0.995201 | − | 0.0978480i | \(-0.0311959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.46742 | −0.803692 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.53488 | 0.332533 | 0.166267 | − | 0.986081i | \(-0.446829\pi\) | ||||
0.166267 | + | 0.986081i | \(0.446829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.08532i | 0.474209i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.95687i | 0.550713i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.485281 | 0.0444857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.8486 | −1.62260 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.60365i | − 0.234763i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 12.1674i | − 1.08829i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.49791 | 0.132918 | 0.0664591 | − | 0.997789i | \(-0.478830\pi\) | ||||
0.0664591 | + | 0.997789i | \(0.478830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.13853 | 0.716557 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.7422i | 1.28803i | 0.765013 | + | 0.644015i | \(0.222733\pi\) | ||||
−0.765013 | + | 0.644015i | \(0.777267\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.485281i | − 0.0420792i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.79793 | −0.154741 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.7954 | −1.17862 | −0.589309 | − | 0.807907i | \(-0.700600\pi\) | ||||
−0.589309 | + | 0.807907i | \(0.700600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.42847i | 0.290799i | 0.989373 | + | 0.145399i | \(0.0464467\pi\) | ||||
−0.989373 | + | 0.145399i | \(0.953553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.82843i | − 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.9949 | 2.67555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.33897 | −0.443377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 6.97474i | − 0.575267i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.14108i | 0.339250i | 0.985509 | + | 0.169625i | \(0.0542557\pi\) | ||||
−0.985509 | + | 0.169625i | \(0.945744\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6644 | −1.84440 | −0.922201 | − | 0.386712i | \(-0.873611\pi\) | ||||
−0.922201 | + | 0.386712i | \(0.873611\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.05320 | 0.246837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.47750i | 0.600607i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.93161i | 0.313777i | 0.987616 | + | 0.156888i | \(0.0501463\pi\) | ||||
−0.987616 | + | 0.156888i | \(0.949854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.03049 | −0.398944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.449555 | 0.0354299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.68897i | − 0.602247i | −0.953585 | − | 0.301123i | \(-0.902638\pi\) | ||||
0.953585 | − | 0.301123i | \(-0.0973616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.65685i | 0.751785i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.95458 | −0.306015 | −0.153007 | − | 0.988225i | \(-0.548896\pi\) | ||||
−0.153007 | + | 0.988225i | \(0.548896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.4844 | −1.72957 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.05320i | − 0.233484i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.6011i | − 1.71833i | −0.511699 | − | 0.859165i | \(-0.670984\pi\) | ||||
0.511699 | − | 0.859165i | \(-0.329016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.280920 | −0.0212355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65685 | −0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.2981i | 1.29292i | 0.762946 | + | 0.646462i | \(0.223752\pi\) | ||||
−0.762946 | + | 0.646462i | \(0.776248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.14953i | 0.605750i | 0.953030 | + | 0.302875i | \(0.0979465\pi\) | ||||
−0.953030 | + | 0.302875i | \(0.902054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.18944 | 0.383614 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2238 | 1.11928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.3990i | − 1.19922i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.158942i | 0.0115613i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1674 | 1.16983 | 0.584916 | − | 0.811094i | \(-0.301127\pi\) | ||||
0.584916 | + | 0.811094i | \(0.301127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1454 | −1.59406 | −0.797030 | − | 0.603940i | \(-0.793597\pi\) | ||||
−0.797030 | + | 0.603940i | \(0.793597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 10.7101i | − 0.766963i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2222i | 1.44077i | 0.693572 | + | 0.720387i | \(0.256036\pi\) | ||||
−0.693572 | + | 0.720387i | \(0.743964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0075 | 1.77274 | 0.886368 | − | 0.462981i | \(-0.153220\pi\) | ||||
0.886368 | + | 0.462981i | \(0.153220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.08532 | −0.0765527 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.471978i | 0.0331264i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.68119i | 0.326948i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.82843 | 0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.3990 | −1.13434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 26.0559i | − 1.79376i | −0.442273 | − | 0.896881i | \(-0.645828\pi\) | ||||
0.442273 | − | 0.896881i | \(-0.354172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.317883i | 0.0217810i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.6325 | −0.997930 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.661029 | 0.0448736 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 1.33897i | − 0.0904793i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1876i | 1.22343i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3465 | −1.22857 | −0.614286 | − | 0.789083i | \(-0.710556\pi\) | ||||
−0.614286 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.76744 | −0.117829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 0.163788i | − 0.0108710i | −0.999985 | − | 0.00543551i | \(-0.998270\pi\) | ||||
0.999985 | − | 0.00543551i | \(-0.00173019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 4.02756i | − 0.266148i | −0.991106 | − | 0.133074i | \(-0.957515\pi\) | ||||
0.991106 | − | 0.133074i | \(-0.0424849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.853690 | 0.0561687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7211 | 0.767874 | 0.383937 | − | 0.923359i | \(-0.374568\pi\) | ||||
0.383937 | + | 0.923359i | \(0.374568\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.08532i | 0.331730i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 9.69382i | − 0.629681i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.6517 | −0.883058 | −0.441529 | − | 0.897247i | \(-0.645564\pi\) | ||||
−0.441529 | + | 0.897247i | \(0.645564\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.13167 | −0.137313 | −0.0686565 | − | 0.997640i | \(-0.521871\pi\) | ||||
−0.0686565 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.5401i | 0.801158i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1876 | 1.15725 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.163788 | 0.0103797 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.27020i | − 0.395771i | −0.980225 | − | 0.197886i | \(-0.936593\pi\) | ||||
0.980225 | − | 0.197886i | \(-0.0634075\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 15.1917i | − 0.955096i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.48946 | −0.343763 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0853 | 0.940997 | 0.470498 | − | 0.882401i | \(-0.344074\pi\) | ||||
0.470498 | + | 0.882401i | \(0.344074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.34583i | − 0.0836255i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.96951i | 0.183808i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.1706 | −1.61375 | −0.806875 | − | 0.590722i | \(-0.798843\pi\) | ||||
−0.806875 | + | 0.590722i | \(0.798843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.04449 | 0.555599 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 14.3990i | − 0.881206i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1580i | 0.741286i | 0.928775 | + | 0.370643i | \(0.120863\pi\) | ||||
−0.928775 | + | 0.370643i | \(0.879137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6644 | 0.647815 | 0.323907 | − | 0.946089i | \(-0.395003\pi\) | ||||
0.323907 | + | 0.946089i | \(0.395003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.946795 | −0.0573027 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.49307i | 0.572453i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.76421i | − 0.226170i | −0.993585 | − | 0.113085i | \(-0.963927\pi\) | ||||
0.993585 | − | 0.113085i | \(-0.0360732\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.15894 | 0.248989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4496 | −0.623368 | −0.311684 | − | 0.950186i | \(-0.600893\pi\) | ||||
−0.311684 | + | 0.950186i | \(0.600893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.6569i | − 1.04959i | −0.851228 | − | 0.524796i | \(-0.824142\pi\) | ||||
0.851228 | − | 0.524796i | \(-0.175858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.48946i | 0.325167i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.413828 | 0.0244275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.67794 | −0.451644 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 0.571533i | − 0.0335038i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 30.7465i | − 1.79623i | −0.439762 | − | 0.898114i | \(-0.644937\pi\) | ||||
0.439762 | − | 0.898114i | \(-0.355063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1706 | 0.592158 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.37109 | 0.311662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.8486i | 0.974379i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.29355i | 0.0745590i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1158 | −0.581138 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.33026 | −0.534249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.2981i | − 1.21555i | −0.794110 | − | 0.607775i | \(-0.792062\pi\) | ||||
0.794110 | − | 0.607775i | \(-0.207938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 11.3507i | − 0.645717i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.77883 | 0.100868 | 0.0504342 | − | 0.998727i | \(-0.483939\pi\) | ||||
0.0504342 | + | 0.998727i | \(0.483939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70320 | 0.152794 | 0.0763971 | − | 0.997077i | \(-0.475658\pi\) | ||||
0.0763971 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 0.285766i | − 0.0161011i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 22.0653i | − 1.23931i | −0.784874 | − | 0.619655i | \(-0.787272\pi\) | ||||
0.784874 | − | 0.619655i | \(-0.212728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9495 | 0.892999 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02109 | −0.0569916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.32206i | − 0.518693i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 10.5284i | − 0.584011i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.04313 | 0.112985 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.449555 | 0.0247848 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 21.8431i | − 1.20060i | −0.799774 | − | 0.600302i | \(-0.795047\pi\) | ||||
0.799774 | − | 0.600302i | \(-0.204953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.46742i | − 0.464012i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.95133 | 0.106613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.8738 | 1.02812 | 0.514062 | − | 0.857753i | \(-0.328140\pi\) | ||||
0.514062 | + | 0.857753i | \(0.328140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.53488i | 0.191988i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 22.3380i | − 1.20967i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.22117 | 0.119932 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.08532 | −0.273785 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0490i | 1.50575i | 0.658163 | + | 0.752875i | \(0.271334\pi\) | ||||
−0.658163 | + | 0.752875i | \(0.728666\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 16.9307i | − 0.906279i | −0.891440 | − | 0.453139i | \(-0.850304\pi\) | ||||
0.891440 | − | 0.453139i | \(-0.149696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.95687 | −0.317954 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6202 | −0.671705 | −0.335853 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335853 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 0.571533i | − 0.0303338i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.485281i | 0.0256838i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.0867 | −1.42958 | −0.714790 | − | 0.699339i | \(-0.753478\pi\) | ||||
−0.714790 | + | 0.699339i | \(0.753478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.67794 | 0.509365 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 17.8486i | − 0.936808i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40738i | 0.126008i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.4937 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.60365 | 0.135541 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 0.799555i | − 0.0415108i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.46190i | 0.0756943i | 0.999284 | + | 0.0378471i | \(0.0120500\pi\) | ||||
−0.999284 | + | 0.0378471i | \(0.987950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1674 | 0.628322 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.6890 | −0.911028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9871i | 1.28350i | 0.766913 | + | 0.641751i | \(0.221792\pi\) | ||||
−0.766913 | + | 0.641751i | \(0.778208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.49791i | 0.0767404i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.0958 | 1.58892 | 0.794460 | − | 0.607316i | \(-0.207754\pi\) | ||||
0.794460 | + | 0.607316i | \(0.207754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.53488 | −0.0782245 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.13853i | 0.413705i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.62218i | 0.183652i | 0.995775 | + | 0.0918260i | \(0.0292704\pi\) | ||||
−0.995775 | + | 0.0918260i | \(0.970730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.63577 | 0.436729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.7422 | −0.743644 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.4288i | 0.876940i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.20959i | − 0.361839i | −0.983498 | − | 0.180920i | \(-0.942093\pi\) | ||||
0.983498 | − | 0.180920i | \(-0.0579074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.485281 | 0.0242945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2660 | 0.762349 | 0.381174 | − | 0.924503i | \(-0.375520\pi\) | ||||
0.381174 | + | 0.924503i | \(0.375520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.7743i | 1.23410i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.79793i | − 0.0893400i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.4792 | −2.25432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3779 | 0.562603 | 0.281302 | − | 0.959619i | \(-0.409234\pi\) | ||||
0.281302 | + | 0.959619i | \(0.409234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 13.7954i | − 0.680476i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 0.899110i | − 0.0442423i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.294481 | −0.0144555 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.42847 | −0.167893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9618i | 1.61029i | 0.593077 | + | 0.805146i | \(0.297913\pi\) | ||||
−0.593077 | + | 0.805146i | \(0.702087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9119i | 1.21413i | 0.794652 | + | 0.607065i | \(0.207653\pi\) | ||||
−0.794652 | + | 0.607065i | \(0.792347\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.39635 | −0.261761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.824818i | 0.0399157i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.9949i | 1.54473i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3211 | 0.497151 | 0.248576 | − | 0.968612i | \(-0.420038\pi\) | ||||
0.248576 | + | 0.968612i | \(0.420038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3137 | 0.735930 | 0.367965 | − | 0.929840i | \(-0.380055\pi\) | ||||
0.367965 | + | 0.929840i | \(0.380055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 5.33897i | − 0.255984i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.63577i | − 0.413105i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5735 | 1.07738 | 0.538688 | − | 0.842505i | \(-0.318920\pi\) | ||||
0.538688 | + | 0.842505i | \(0.318920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.97474 | 0.332130 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.5334i | 1.59322i | 0.604494 | + | 0.796610i | \(0.293375\pi\) | ||||
−0.604494 | + | 0.796610i | \(0.706625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.8885i | 1.22723i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.14108 | −0.195866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75506 | −0.0828266 | −0.0414133 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414133 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 13.9844i | − 0.658501i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 22.6644i | − 1.06487i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.70227 | 0.0798039 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7422 | 1.25095 | 0.625473 | − | 0.780246i | \(-0.284906\pi\) | ||||
0.625473 | + | 0.780246i | \(0.284906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.05320i | 0.142511i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0662i | 0.608555i | 0.952584 | + | 0.304277i | \(0.0984149\pi\) | ||||
−0.952584 | + | 0.304277i | \(0.901585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4474 | 1.36854 | 0.684268 | − | 0.729231i | \(-0.260122\pi\) | ||||
0.684268 | + | 0.729231i | \(0.260122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.47750 | −0.346761 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7040i | 1.28199i | 0.767545 | + | 0.640995i | \(0.221478\pi\) | ||||
−0.767545 | + | 0.640995i | \(0.778522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 0.172503i | − 0.00796544i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.93161 | −0.181159 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.7127 | 2.00991 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.39635i | 0.247602i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.03049i | − 0.230331i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.5499 | −1.62432 | −0.812159 | − | 0.583436i | \(-0.801708\pi\) | ||||
−0.812159 | + | 0.583436i | \(0.801708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.4393 | 2.29984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.449555i | 0.0204555i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.02758i | 0.0466599i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.86632 | 0.447086 | 0.223543 | − | 0.974694i | \(-0.428238\pi\) | ||||
0.223543 | + | 0.974694i | \(0.428238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.68897 | 0.347707 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.635767i | 0.0286917i | 0.999897 | + | 0.0143459i | \(0.00456659\pi\) | ||||
−0.999897 | + | 0.0143459i | \(0.995433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.06651i | 0.408335i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.65685 | −0.434043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0505249 | −0.00226635 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3.82750i | − 0.171342i | −0.996323 | − | 0.0856712i | \(-0.972697\pi\) | ||||
0.996323 | − | 0.0856712i | \(-0.0273034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.95458i | − 0.176678i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.6719 | 1.05548 | 0.527739 | − | 0.849407i | \(-0.323040\pi\) | ||||
0.527739 | + | 0.849407i | \(0.323040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1876 | 0.809336 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 22.4844i | − 0.998565i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.7970i | 1.54235i | 0.636623 | + | 0.771175i | \(0.280331\pi\) | ||||
−0.636623 | + | 0.771175i | \(0.719669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.212818 | 0.00941453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.05320 | 0.134802 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.4077i | 0.899273i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 15.1917i | − 0.668132i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.6011 | 0.992078 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4889 | 0.634770 | 0.317385 | − | 0.948297i | \(-0.397195\pi\) | ||||
0.317385 | + | 0.948297i | \(0.397195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.5742i | 1.20574i | 0.797841 | + | 0.602868i | \(0.205975\pi\) | ||||
−0.797841 | + | 0.602868i | \(0.794025\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 0.280920i | − 0.0122603i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6981 | 0.553138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.65685i | − 0.245487i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.5096i | 0.671796i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.83585 | 0.0793706 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.2981 | −0.746470 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 37.4619i | − 1.61360i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1982i | 0.610428i | 0.952284 | + | 0.305214i | \(0.0987280\pi\) | ||||
−0.952284 | + | 0.305214i | \(0.901272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.14953 | −0.349730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.67340 | −0.157351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10.1807i | − 0.435295i | −0.976027 | − | 0.217648i | \(-0.930162\pi\) | ||||
0.976027 | − | 0.217648i | \(-0.0698384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.18944i | 0.221480i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.06651 | 0.386246 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54075 | 0.0655194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.2238i | 0.646216i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.44432i | 0.0611979i | 0.999532 | + | 0.0305990i | \(0.00974147\pi\) | ||||
−0.999532 | + | 0.0305990i | \(0.990259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.4802 | −2.05049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3990 | 0.692368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9.48585i | − 0.399781i | −0.979818 | − | 0.199890i | \(-0.935941\pi\) | ||||
0.979818 | − | 0.199890i | \(-0.0640586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.35547i | − 0.267377i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.158942 | −0.00667492 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.98711 | −0.376759 | −0.188380 | − | 0.982096i | \(-0.560324\pi\) | ||||
−0.188380 | + | 0.982096i | \(0.560324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 12.9706i | − 0.542801i | −0.962466 | − | 0.271401i | \(-0.912513\pi\) | ||||
0.962466 | − | 0.271401i | \(-0.0874868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1674i | 0.675403i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.99907 | −0.208476 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5013 | 1.22815 | 0.614077 | − | 0.789246i | \(-0.289528\pi\) | ||||
0.614077 | + | 0.789246i | \(0.289528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 22.1454i | − 0.920331i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0260328i | 0.00108002i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.0192 | −1.11902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.7101 | 0.442806 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.57988i | − 0.106483i | −0.998582 | − | 0.0532416i | \(-0.983045\pi\) | ||||
0.998582 | − | 0.0532416i | \(-0.0169553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 12.6981i | − 0.523216i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2222 | −0.831831 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.4338 | 1.45509 | 0.727546 | − | 0.686058i | \(-0.240661\pi\) | ||||
0.727546 | + | 0.686058i | \(0.240661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 0.872503i | − 0.0357691i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.0075i | 1.02349i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.1632 | −1.10986 | −0.554930 | − | 0.831897i | \(-0.687255\pi\) | ||||
−0.554930 | + | 0.831897i | \(0.687255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.33897 | 0.217781 | 0.108891 | − | 0.994054i | \(-0.465270\pi\) | ||||
0.108891 | + | 0.994054i | \(0.465270\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.08532i | − 0.0441977i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.0906i | 1.30467i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1084 | −0.653820 | −0.326910 | − | 0.945055i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945055i | \(0.606007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.471978 | −0.0191255 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.8486i | 0.681621i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 0.617903i | − 0.0249569i | −0.999922 | − | 0.0124784i | \(-0.996028\pi\) | ||||
0.999922 | − | 0.0124784i | \(-0.00397211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.68119 | −0.188764 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.80641 | −0.354533 | −0.177266 | − | 0.984163i | \(-0.556725\pi\) | ||||
−0.177266 | + | 0.984163i | \(0.556725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 2.72847i | − 0.109666i | −0.998496 | − | 0.0548332i | \(-0.982537\pi\) | ||||
0.998496 | − | 0.0548332i | \(-0.0174627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843i | 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.28861 | 0.0916910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0390 | −0.521559 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 16.3990i | − 0.654914i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 25.8528i | − 1.03082i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.7864 | 1.54406 | 0.772030 | − | 0.635586i | \(-0.219241\pi\) | ||||
0.772030 | + | 0.635586i | \(0.219241\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.0559 | 1.03563 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 2.69315i | − 0.106874i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.5476i | 1.64618i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.317883 | −0.0125753 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1091 | 1.30773 | 0.653865 | − | 0.756611i | \(-0.273146\pi\) | ||||
0.653865 | + | 0.756611i | \(0.273146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27.2797i | − 1.07581i | −0.843006 | − | 0.537904i | \(-0.819216\pi\) | ||||
0.843006 | − | 0.537904i | \(-0.180784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 14.6325i | − 0.576155i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.8477 | 1.64520 | 0.822601 | − | 0.568620i | \(-0.192522\pi\) | ||||
0.822601 | + | 0.568620i | \(0.192522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.3835 | −1.19266 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.661029i | 0.0259078i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8937i | 0.817634i | 0.912616 | + | 0.408817i | \(0.134059\pi\) | ||||
−0.912616 | + | 0.408817i | \(0.865941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.5054 | 1.03565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.33897 | 0.0522382 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.15142i | 0.122762i | 0.998114 | + | 0.0613809i | \(0.0195504\pi\) | ||||
−0.998114 | + | 0.0613809i | \(0.980450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 25.5527i | − 0.993886i | −0.867783 | − | 0.496943i | \(-0.834456\pi\) | ||||
0.867783 | − | 0.496943i | \(-0.165544\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.1876 | −0.706346 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.872503 | −0.0338342 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.39903i | 0.325212i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 18.3465i | − 0.709317i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.8729 | 1.07602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7981 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.76744i | − 0.0680287i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 41.0423i | − 1.57738i | −0.614789 | − | 0.788692i | \(-0.710759\pi\) | ||||
0.614789 | − | 0.788692i | \(-0.289241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0908404 | 0.00348613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.163788 | 0.00627639 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.5784i | 1.01699i | 0.861064 | + | 0.508497i | \(0.169799\pi\) | ||||
−0.861064 | + | 0.508497i | \(0.830201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.8032i | 0.947680i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.02756 | 0.153661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.9660 | 1.14161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 14.7899i | − 0.562633i | −0.959615 | − | 0.281316i | \(-0.909229\pi\) | ||||
0.959615 | − | 0.281316i | \(-0.0907710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.853690i | 0.0324290i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.16415 | 0.233820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.94948 | 0.301108 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.7211i | 0.443332i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 25.9245i | − 0.979155i | −0.871960 | − | 0.489577i | \(-0.837151\pi\) | ||||
0.871960 | − | 0.489577i | \(-0.162849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8528 | −0.975055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.08532 | −0.191524 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.60782i | − 0.0604685i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 20.6082i | − 0.773958i | −0.922089 | − | 0.386979i | \(-0.873519\pi\) | ||||
0.922089 | − | 0.386979i | \(-0.126481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.69382 | 0.363547 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.7633 | 0.440538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 57.5247i | − 2.15130i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 13.6517i | − 0.509834i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.0949 | 1.64446 | 0.822230 | − | 0.569155i | \(-0.192730\pi\) | ||||
0.822230 | + | 0.569155i | \(0.192730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.80409 | 0.0671880 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.13167i | − 0.0792777i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 5.24842i | − 0.194921i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.23457 | −0.342491 | −0.171246 | − | 0.985228i | \(-0.554779\pi\) | ||||
−0.171246 | + | 0.985228i | \(0.554779\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.8486i | 0.919058i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 25.8467i | − 0.954670i | −0.878721 | − | 0.477335i | \(-0.841603\pi\) | ||||
0.878721 | − | 0.477335i | \(-0.158397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.5401 | −0.462549 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.82936 | −0.214727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0403i | 0.884337i | 0.896932 | + | 0.442169i | \(0.145791\pi\) | ||||
−0.896932 | + | 0.442169i | \(0.854209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.1876i | 0.668137i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.8748 | −0.655762 | −0.327881 | − | 0.944719i | \(-0.606335\pi\) | ||||
−0.327881 | + | 0.944719i | \(0.606335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44538 | 0.272778 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.163788i | 0.00599271i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 0.162293i | − 0.00593007i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0731 | −1.27984 | −0.639918 | − | 0.768443i | \(-0.721032\pi\) | ||||
−0.639918 | + | 0.768443i | \(0.721032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.27020 | 0.228499 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.7490i | 1.48301i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 46.3962i | − 1.68630i | −0.537679 | − | 0.843150i | \(-0.680699\pi\) | ||||
0.537679 | − | 0.843150i | \(-0.319301\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.1917 | 0.551425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5531 | 0.382550 | 0.191275 | − | 0.981536i | \(-0.438738\pi\) | ||||
0.191275 | + | 0.981536i | \(0.438738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.324738i | 0.0117563i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.48946i | − 0.198472i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6972 | 1.21673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2068 | −1.26959 | −0.634795 | − | 0.772681i | \(-0.718915\pi\) | ||||
−0.634795 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0853i | 0.543285i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.4212i | 0.986271i | 0.869952 | + | 0.493136i | \(0.164149\pi\) | ||||
−0.869952 | + | 0.493136i | \(0.835851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.35067 | −0.264044 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.34583 | 0.0482812 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 7.94948i | − 0.284820i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.70738i | 0.0610948i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.96951 | −0.106121 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.06877 | 0.252295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.46058i | 0.337233i | 0.985682 | + | 0.168617i | \(0.0539300\pi\) | ||||
−0.985682 | + | 0.168617i | \(0.946070\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 26.1706i | − 0.931700i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.561839 | −0.0199767 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.9128 | −1.09775 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.04449i | 0.320775i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 19.1791i | − 0.679359i | −0.940541 | − | 0.339680i | \(-0.889681\pi\) | ||||
0.940541 | − | 0.339680i | \(-0.110319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63577 | 0.305511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3990 | 0.508765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.19173i | − 0.253791i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 0.808269i | − 0.0284878i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.1580 | −0.427982 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.1578 | 1.51735 | 0.758673 | − | 0.651472i | \(-0.225848\pi\) | ||||
0.758673 | + | 0.651472i | \(0.225848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.87518i | − 0.136076i | −0.997683 | − | 0.0680380i | \(-0.978326\pi\) | ||||
0.997683 | − | 0.0680380i | \(-0.0216739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6644i | 0.374016i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.8243 | −0.484242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.8486 | 0.869342 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 0.946795i | − 0.0330837i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.62084i | 0.196169i | 0.995178 | + | 0.0980843i | \(0.0312715\pi\) | ||||
−0.995178 | + | 0.0980843i | \(0.968729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.5255 | −1.34291 | −0.671457 | − | 0.741043i | \(-0.734331\pi\) | ||||
−0.671457 | + | 0.741043i | \(0.734331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.49307 | −0.330506 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.23674i | 0.147326i | 0.997283 | + | 0.0736629i | \(0.0234689\pi\) | ||||
−0.997283 | + | 0.0736629i | \(0.976531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3128i | 1.22646i | 0.789903 | + | 0.613231i | \(0.210131\pi\) | ||||
−0.789903 | + | 0.613231i | \(0.789869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.76421 | 0.130579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.2953 | 0.737838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.11007i | 0.246054i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.15894i | 0.143754i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.6005 | −1.36716 | −0.683580 | − | 0.729876i | \(-0.739578\pi\) | ||||
−0.683580 | + | 0.729876i | \(0.739578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.1820 | 0.695932 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 10.4496i | − 0.359902i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.4253i | 1.39067i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.83688 | 0.0974765 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 23.9495i | − 0.820977i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8683i | 0.372124i | 0.982538 | + | 0.186062i | \(0.0595725\pi\) | ||||
−0.982538 | + | 0.186062i | \(0.940428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48946 | −0.187735 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.0082 | 1.16170 | 0.580849 | − | 0.814011i | \(-0.302721\pi\) | ||||
0.580849 | + | 0.814011i | \(0.302721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9973i | 0.443463i | 0.975108 | + | 0.221731i | \(0.0711708\pi\) | ||||
−0.975108 | + | 0.221731i | \(0.928829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.413828i | 0.0141032i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8307 | 0.879289 | 0.439644 | − | 0.898172i | \(-0.355104\pi\) | ||||
0.439644 | + | 0.898172i | \(0.355104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.6353 | −1.38164 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 7.67794i | − 0.260757i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 52.0663i | − 1.76623i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.46512 | 0.219062 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.571533 | 0.0193435 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.93391i | 0.0653780i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.2150i | 1.52680i | 0.645926 | + | 0.763400i | \(0.276472\pi\) | ||||
−0.645926 | + | 0.763400i | \(0.723528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.7465 | 1.03705 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.7403 | −1.17043 | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||||
−0.585215 | + | 0.810878i | \(0.698990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.9366i | 1.64685i | 0.567427 | + | 0.823424i | \(0.307939\pi\) | ||||
−0.567427 | + | 0.823424i | \(0.692061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1706i | 0.341882i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9284 | 0.769860 | 0.384930 | − | 0.922946i | \(-0.374226\pi\) | ||||
0.384930 | + | 0.922946i | \(0.374226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.238081 | −0.00798497 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.37109i | 0.179938i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.63577i | − 0.288985i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.1009 | 1.03959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8486 | −0.562558 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.3500i | 0.411896i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 15.3591i | − 0.511687i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.29355 | −0.0430467 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.6523 | 0.487059 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.1680i | 0.769280i | 0.923067 | + | 0.384640i | \(0.125674\pi\) | ||||
−0.923067 | + | 0.384640i | \(0.874326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 10.1158i | − 0.335520i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4078 | −0.974324 | −0.487162 | − | 0.873312i | \(-0.661968\pi\) | ||||
−0.487162 | + | 0.873312i | \(0.661968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.879722 | 0.0291146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 9.33026i | − 0.308449i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.34315i | − 0.0773775i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.86029 | −0.226300 | −0.113150 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113150 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.2981 | 0.701798 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.89359i | − 0.0623283i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.9656i | 0.492067i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3507 | 0.372805 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1385 | 0.529488 | 0.264744 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264744 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 21.2953i | − 0.697925i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.77883i | 0.0582363i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.4844 | −0.964241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7669 | 1.13579 | 0.567893 | − | 0.823102i | \(-0.307759\pi\) | ||||
0.567893 | + | 0.823102i | \(0.307759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.70320i | 0.0882157i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 52.7024i | − 1.71805i | −0.511934 | − | 0.859025i | \(-0.671071\pi\) | ||||
0.511934 | − | 0.859025i | \(-0.328929\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.36423 | 0.239812 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.285766 | 0.00929598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 26.1972i | − 0.851296i | −0.904889 | − | 0.425648i | \(-0.860046\pi\) | ||||
0.904889 | − | 0.425648i | \(-0.139954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.97608i | 0.258915i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0653 | 0.715516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1752 | 0.362000 | 0.181000 | − | 0.983483i | \(-0.442067\pi\) | ||||
0.181000 | + | 0.983483i | \(0.442067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 29.0679i | − 0.940615i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9495i | 0.515573i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.19266 | 0.0708047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7032 | −0.442039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.02109i | − 0.0329041i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.8159i | 1.28172i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8452 | −0.413075 | −0.206537 | − | 0.978439i | \(-0.566220\pi\) | ||||
−0.206537 | + | 0.978439i | \(0.566220\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.32206 | 0.299468 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 8.40774i | − 0.269817i | −0.990858 | − | 0.134909i | \(-0.956926\pi\) | ||||
0.990858 | − | 0.134909i | \(-0.0430741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 0.544926i | − 0.0174695i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.5284 | 0.337179 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.4156 | −1.29301 | −0.646504 | − | 0.762910i | \(-0.723770\pi\) | ||||
−0.646504 | + | 0.762910i | \(0.723770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 77.3385i | − 2.47175i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.04313i | 0.0652320i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.9202 | −0.443985 | −0.221993 | − | 0.975048i | \(-0.571256\pi\) | ||||
−0.221993 | + | 0.975048i | \(0.571256\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.3582 | 1.15847 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.449555i | 0.0143095i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.0192i | 0.731969i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0309 | −1.30339 | −0.651695 | − | 0.758481i | \(-0.725942\pi\) | ||||
−0.651695 | + | 0.758481i | \(0.725942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.8431 | 0.693169 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 44.9618i | − 1.42539i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.6427i | − 1.22383i | −0.790925 | − | 0.611913i | \(-0.790400\pi\) | ||||
0.790925 | − | 0.611913i | \(-0.209600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.46742 | 0.267897 |
(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 | 3072.2.d.i.1537.5 | 8 | ||
4.3 | odd | 2 | 3072.2.d.f.1537.1 | 8 | |||
8.3 | odd | 2 | 3072.2.d.f.1537.8 | 8 | |||
8.5 | even | 2 | inner | 3072.2.d.i.1537.4 | 8 | ||
16.3 | odd | 4 | 3072.2.a.t.1.1 | 4 | |||
16.5 | even | 4 | 3072.2.a.o.1.4 | 4 | |||
16.11 | odd | 4 | 3072.2.a.i.1.4 | 4 | |||
16.13 | even | 4 | 3072.2.a.n.1.1 | 4 | |||
32.3 | odd | 8 | 48.2.j.a.37.1 | yes | 8 | ||
32.5 | even | 8 | 192.2.j.a.145.2 | 8 | |||
32.11 | odd | 8 | 384.2.j.b.289.1 | 8 | |||
32.13 | even | 8 | 384.2.j.a.97.3 | 8 | |||
32.19 | odd | 8 | 384.2.j.b.97.1 | 8 | |||
32.21 | even | 8 | 384.2.j.a.289.3 | 8 | |||
32.27 | odd | 8 | 48.2.j.a.13.1 | ✓ | 8 | ||
32.29 | even | 8 | 192.2.j.a.49.2 | 8 | |||
48.5 | odd | 4 | 9216.2.a.bn.1.1 | 4 | |||
48.11 | even | 4 | 9216.2.a.bo.1.1 | 4 | |||
48.29 | odd | 4 | 9216.2.a.x.1.4 | 4 | |||
48.35 | even | 4 | 9216.2.a.y.1.4 | 4 | |||
96.5 | odd | 8 | 576.2.k.b.145.2 | 8 | |||
96.11 | even | 8 | 1152.2.k.c.289.3 | 8 | |||
96.29 | odd | 8 | 576.2.k.b.433.2 | 8 | |||
96.35 | even | 8 | 144.2.k.b.37.4 | 8 | |||
96.53 | odd | 8 | 1152.2.k.f.289.3 | 8 | |||
96.59 | even | 8 | 144.2.k.b.109.4 | 8 | |||
96.77 | odd | 8 | 1152.2.k.f.865.3 | 8 | |||
96.83 | even | 8 | 1152.2.k.c.865.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.1 | ✓ | 8 | 32.27 | odd | 8 | ||
48.2.j.a.37.1 | yes | 8 | 32.3 | odd | 8 | ||
144.2.k.b.37.4 | 8 | 96.35 | even | 8 | |||
144.2.k.b.109.4 | 8 | 96.59 | even | 8 | |||
192.2.j.a.49.2 | 8 | 32.29 | even | 8 | |||
192.2.j.a.145.2 | 8 | 32.5 | even | 8 | |||
384.2.j.a.97.3 | 8 | 32.13 | even | 8 | |||
384.2.j.a.289.3 | 8 | 32.21 | even | 8 | |||
384.2.j.b.97.1 | 8 | 32.19 | odd | 8 | |||
384.2.j.b.289.1 | 8 | 32.11 | odd | 8 | |||
576.2.k.b.145.2 | 8 | 96.5 | odd | 8 | |||
576.2.k.b.433.2 | 8 | 96.29 | odd | 8 | |||
1152.2.k.c.289.3 | 8 | 96.11 | even | 8 | |||
1152.2.k.c.865.3 | 8 | 96.83 | even | 8 | |||
1152.2.k.f.289.3 | 8 | 96.53 | odd | 8 | |||
1152.2.k.f.865.3 | 8 | 96.77 | odd | 8 | |||
3072.2.a.i.1.4 | 4 | 16.11 | odd | 4 | |||
3072.2.a.n.1.1 | 4 | 16.13 | even | 4 | |||
3072.2.a.o.1.4 | 4 | 16.5 | even | 4 | |||
3072.2.a.t.1.1 | 4 | 16.3 | odd | 4 | |||
3072.2.d.f.1537.1 | 8 | 4.3 | odd | 2 | |||
3072.2.d.f.1537.8 | 8 | 8.3 | odd | 2 | |||
3072.2.d.i.1537.4 | 8 | 8.5 | even | 2 | inner | ||
3072.2.d.i.1537.5 | 8 | 1.1 | even | 1 | trivial | ||
9216.2.a.x.1.4 | 4 | 48.29 | odd | 4 | |||
9216.2.a.y.1.4 | 4 | 48.35 | even | 4 | |||
9216.2.a.bn.1.1 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bo.1.1 | 4 | 48.11 | even | 4 |