Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, 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("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.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: | \(24.1467615712\) |
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 | 2881.1 | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.k.2305.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −1.76479 | + | 3.05671i | −0.789239 | + | 1.36700i | 0.137194 | + | 0.990544i | \(0.456192\pi\) |
−0.926433 | + | 0.376459i | \(0.877142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63986 | − | 0.176417i | 0.997774 | − | 0.0666792i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.16036 | + | 2.00981i | 0.349863 | + | 0.605981i | 0.986225 | − | 0.165410i | \(-0.0528948\pi\) |
−0.636362 | + | 0.771391i | \(0.719561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.35884 | − | 4.08563i | −0.654224 | − | 1.13315i | −0.982088 | − | 0.188424i | \(-0.939662\pi\) |
0.327864 | − | 0.944725i | \(-0.393671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.636946 | − | 1.10322i | 0.154482 | − | 0.267571i | −0.778388 | − | 0.627783i | \(-0.783962\pi\) |
0.932870 | + | 0.360212i | \(0.117296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.78386 | − | 4.82178i | −0.638661 | − | 1.10619i | −0.985727 | − | 0.168352i | \(-0.946155\pi\) |
0.347066 | − | 0.937841i | \(-0.387178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.64855 | − | 2.85537i | 0.343746 | − | 0.595386i | −0.641379 | − | 0.767224i | \(-0.721637\pi\) |
0.985125 | + | 0.171838i | \(0.0549707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.72899 | − | 6.45880i | −0.745798 | − | 1.29176i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.32116 | − | 7.48447i | 0.802419 | − | 1.38983i | −0.115601 | − | 0.993296i | \(-0.536879\pi\) |
0.918020 | − | 0.396535i | \(-0.129787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.51642 | −1.52959 | −0.764797 | − | 0.644272i | \(-0.777161\pi\) | ||||
−0.764797 | + | 0.644272i | \(0.777161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.11956 | + | 8.38064i | −0.696332 | + | 1.41659i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.84024 | − | 4.91943i | −0.466932 | − | 0.808750i | 0.532354 | − | 0.846522i | \(-0.321307\pi\) |
−0.999286 | + | 0.0377716i | \(0.987974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.66553 | − | 2.88478i | −0.260112 | − | 0.450528i | 0.706159 | − | 0.708053i | \(-0.250426\pi\) |
−0.966272 | + | 0.257525i | \(0.917093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0444165 | + | 0.0769317i | −0.00677346 | + | 0.0117320i | −0.869392 | − | 0.494123i | \(-0.835489\pi\) |
0.862619 | + | 0.505855i | \(0.168823\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.05213 | 1.02866 | 0.514330 | − | 0.857593i | \(-0.328041\pi\) | ||||
0.514330 | + | 0.857593i | \(0.328041\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.93775 | − | 0.931432i | 0.991108 | − | 0.133062i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.41816 | + | 5.92042i | −0.469520 | + | 0.813233i | −0.999393 | − | 0.0348444i | \(-0.988906\pi\) |
0.529873 | + | 0.848077i | \(0.322240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.19121 | −1.10450 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.99490 | −1.04085 | −0.520423 | − | 0.853908i | \(-0.674226\pi\) | ||||
−0.520423 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3553 | 1.70997 | 0.854985 | − | 0.518653i | \(-0.173566\pi\) | ||||
0.854985 | + | 0.518653i | \(0.173566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.6514 | 2.06536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.12804 | −0.748660 | −0.374330 | − | 0.927296i | \(-0.622127\pi\) | ||||
−0.374330 | + | 0.927296i | \(0.622127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.30202 | 0.154522 | 0.0772609 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772609 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.64529 | − | 11.5100i | 0.777772 | − | 1.34714i | −0.155451 | − | 0.987844i | \(-0.549683\pi\) |
0.933223 | − | 0.359297i | \(-0.116984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.41777 | + | 5.10092i | 0.389491 | + | 0.581303i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0281 | 1.12824 | 0.564122 | − | 0.825691i | \(-0.309215\pi\) | ||||
0.564122 | + | 0.825691i | \(0.309215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.90243 | + | 10.2233i | −0.647876 | + | 1.12215i | 0.335753 | + | 0.941950i | \(0.391009\pi\) |
−0.983629 | + | 0.180204i | \(0.942324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.24815 | + | 3.89392i | 0.243847 | + | 0.422355i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.561496 | − | 0.972540i | −0.0595185 | − | 0.103089i | 0.834731 | − | 0.550658i | \(-0.185623\pi\) |
−0.894249 | + | 0.447569i | \(0.852290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.94778 | − | 10.3694i | −0.728325 | − | 1.08700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.6517 | 2.01622 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50818 | + | 6.07635i | −0.356202 | + | 0.616960i | −0.987323 | − | 0.158724i | \(-0.949262\pi\) |
0.631121 | + | 0.775685i | \(0.282595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.87055 | − | 8.43605i | −0.484638 | − | 0.839418i | 0.515206 | − | 0.857066i | \(-0.327715\pi\) |
−0.999844 | + | 0.0176482i | \(0.994382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.14279 | − | 8.90757i | 0.506734 | − | 0.877689i | −0.493236 | − | 0.869896i | \(-0.664186\pi\) |
0.999970 | − | 0.00779301i | \(-0.00248062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.72201 | + | 4.71465i | 0.263146 | + | 0.455783i | 0.967076 | − | 0.254487i | \(-0.0819065\pi\) |
−0.703930 | + | 0.710269i | \(0.748573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.417404 | − | 0.722965i | 0.0399800 | − | 0.0692475i | −0.845343 | − | 0.534224i | \(-0.820604\pi\) |
0.885323 | + | 0.464977i | \(0.153937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.44881 | − | 9.43761i | −0.512581 | − | 0.887815i | −0.999894 | − | 0.0145882i | \(-0.995356\pi\) |
0.487313 | − | 0.873227i | \(-0.337977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.81870 | + | 10.0783i | 0.542596 | + | 0.939804i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.48682 | − | 3.02472i | 0.136297 | − | 0.277276i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.80711 | − | 4.86205i | 0.255192 | − | 0.442005i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.67565 | 0.775974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.90354 | 0.878797 | 0.439399 | − | 0.898292i | \(-0.355192\pi\) | ||||
0.439399 | + | 0.898292i | \(0.355192\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.59220 | + | 14.8821i | −0.750704 | + | 1.30026i | 0.196778 | + | 0.980448i | \(0.436952\pi\) |
−0.947482 | + | 0.319809i | \(0.896381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.19964 | − | 12.2377i | −0.710999 | − | 1.06115i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.04696 | − | 13.9377i | −0.687498 | − | 1.19078i | −0.972645 | − | 0.232298i | \(-0.925376\pi\) |
0.285147 | − | 0.958484i | \(-0.407958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.11151 | − | 1.92519i | −0.0942768 | − | 0.163292i | 0.815030 | − | 0.579419i | \(-0.196721\pi\) |
−0.909307 | + | 0.416127i | \(0.863387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.47422 | − | 9.48163i | 0.457778 | − | 0.792894i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2519 | + | 26.4171i | 1.26660 | + | 2.19382i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.46846 | − | 6.00755i | 0.284147 | − | 0.492158i | −0.688255 | − | 0.725469i | \(-0.741623\pi\) |
0.972402 | + | 0.233312i | \(0.0749562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.75834 | + | 13.4378i | 0.631365 | + | 1.09356i | 0.987273 | + | 0.159035i | \(0.0508383\pi\) |
−0.355908 | + | 0.934521i | \(0.615828\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.0297 | − | 26.0322i | 1.20722 | − | 2.09096i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.802110 | 0.0640154 | 0.0320077 | − | 0.999488i | \(-0.489810\pi\) | ||||
0.0320077 | + | 0.999488i | \(0.489810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.84821 | − | 7.82862i | 0.303281 | − | 0.616982i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.77500 | − | 3.07438i | −0.139028 | − | 0.240804i | 0.788101 | − | 0.615546i | \(-0.211065\pi\) |
−0.927129 | + | 0.374742i | \(0.877731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.865131 | + | 1.49845i | 0.0669459 | + | 0.115954i | 0.897556 | − | 0.440901i | \(-0.145341\pi\) |
−0.830610 | + | 0.556855i | \(0.812008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.62823 | + | 8.01633i | −0.356018 | + | 0.616641i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.23458 | −0.169892 | −0.0849462 | − | 0.996386i | \(-0.527072\pi\) | ||||
−0.0849462 | + | 0.996386i | \(0.527072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.9835 | − | 16.3925i | −0.830272 | − | 1.23916i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.350412 | + | 0.606931i | −0.0261910 | + | 0.0453641i | −0.878824 | − | 0.477146i | \(-0.841671\pi\) |
0.852633 | + | 0.522511i | \(0.175004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6339 | −1.45938 | −0.729688 | − | 0.683780i | \(-0.760335\pi\) | ||||
−0.729688 | + | 0.683780i | \(0.760335\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0497 | 1.47408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.95636 | 0.216190 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0858 | 1.16393 | 0.581963 | − | 0.813215i | \(-0.302285\pi\) | ||||
0.581963 | + | 0.813215i | \(0.302285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.585463 | −0.0421426 | −0.0210713 | − | 0.999778i | \(-0.506708\pi\) | ||||
−0.0210713 | + | 0.999778i | \(0.506708\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2923 | 1.23203 | 0.616014 | − | 0.787735i | \(-0.288746\pi\) | ||||
0.616014 | + | 0.787735i | \(0.288746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2119 | − | 21.1517i | 0.865681 | − | 1.49940i | −0.000687656 | − | 1.00000i | \(-0.500219\pi\) |
0.866369 | − | 0.499404i | \(-0.166448\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0869 | − | 20.5203i | 0.707960 | − | 1.44024i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7573 | 0.821164 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.46058 | − | 11.1900i | 0.446888 | − | 0.774032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.58733 | + | 9.67754i | 0.384648 | + | 0.666230i | 0.991720 | − | 0.128417i | \(-0.0409895\pi\) |
−0.607072 | + | 0.794647i | \(0.707656\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.156772 | − | 0.271537i | −0.0106918 | − | 0.0185187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.4822 | + | 1.50244i | −1.52619 | + | 0.101992i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00981 | −0.404263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.32951 | − | 2.30277i | 0.0890303 | − | 0.154205i | −0.818071 | − | 0.575117i | \(-0.804957\pi\) |
0.907101 | + | 0.420912i | \(0.138290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.95786 | − | 10.3193i | −0.395437 | − | 0.684917i | 0.597720 | − | 0.801705i | \(-0.296073\pi\) |
−0.993157 | + | 0.116788i | \(0.962740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8064 | − | 25.6454i | 0.978434 | − | 1.69470i | 0.310330 | − | 0.950629i | \(-0.399561\pi\) |
0.668104 | − | 0.744068i | \(-0.267106\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.84417 | − | 3.19420i | −0.120816 | − | 0.209259i | 0.799274 | − | 0.600967i | \(-0.205218\pi\) |
−0.920090 | + | 0.391708i | \(0.871884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4456 | + | 21.5563i | −0.811859 | + | 1.40618i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.03590 | + | 13.9186i | 0.519799 | + | 0.900319i | 0.999735 | + | 0.0230153i | \(0.00732663\pi\) |
−0.479936 | + | 0.877304i | \(0.659340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.24933 | − | 3.89596i | −0.144892 | − | 0.250961i | 0.784440 | − | 0.620204i | \(-0.212950\pi\) |
−0.929333 | + | 0.369243i | \(0.879617\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.39658 | + | 22.8505i | −0.600326 | + | 1.45986i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1333 | + | 22.7476i | −0.835654 | + | 1.44740i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2696 | −1.09005 | −0.545023 | − | 0.838421i | \(-0.683479\pi\) | ||||
−0.545023 | + | 0.838421i | \(0.683479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.65167 | 0.481057 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.41087 | − | 4.17574i | 0.150386 | − | 0.260476i | −0.780984 | − | 0.624552i | \(-0.785282\pi\) |
0.931369 | + | 0.364076i | \(0.118615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.36571 | − | 12.4856i | −0.519820 | − | 0.775815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0452 | − | 24.3270i | −0.866062 | − | 1.50006i | −0.865988 | − | 0.500064i | \(-0.833310\pi\) |
−7.41948e−5 | − | 1.00000i | \(-0.500024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0647 | − | 20.8966i | −0.741128 | − | 1.28367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4126 | + | 21.4993i | −0.756810 | + | 1.31083i | 0.187659 | + | 0.982234i | \(0.439910\pi\) |
−0.944469 | + | 0.328599i | \(0.893423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.79671 | + | 8.30815i | 0.291379 | + | 0.504684i | 0.974136 | − | 0.225962i | \(-0.0725524\pi\) |
−0.682757 | + | 0.730646i | \(0.739219\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.65398 | − | 14.9891i | 0.521854 | − | 0.903878i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.46914 | − | 14.6690i | −0.508862 | − | 0.881374i | −0.999947 | − | 0.0102629i | \(-0.996733\pi\) |
0.491086 | − | 0.871111i | \(-0.336600\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.4291 | + | 19.7958i | −0.681805 | + | 1.18092i | 0.292625 | + | 0.956227i | \(0.405471\pi\) |
−0.974430 | + | 0.224693i | \(0.927862\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.35621 | −0.496725 | −0.248363 | − | 0.968667i | \(-0.579892\pi\) | ||||
−0.248363 | + | 0.968667i | \(0.579892\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.90570 | − | 7.32161i | −0.289574 | − | 0.432181i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.68860 | + | 13.3170i | 0.452271 | + | 0.783356i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.16141 | + | 3.74368i | 0.126271 | + | 0.218708i | 0.922229 | − | 0.386644i | \(-0.126366\pi\) |
−0.795958 | + | 0.605352i | \(0.793032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1093 | − | 24.4381i | 0.821477 | − | 1.42284i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.5546 | −0.899548 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.103682 | + | 0.210925i | −0.00597610 | + | 0.0121575i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.5693 | + | 40.8233i | −1.34958 | + | 2.33753i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.22888 | 0.526720 | 0.263360 | − | 0.964698i | \(-0.415169\pi\) | ||||
0.263360 | + | 0.964698i | \(0.415169\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1073 | −1.08348 | −0.541738 | − | 0.840548i | \(-0.682233\pi\) | ||||
−0.541738 | + | 0.840548i | \(0.682233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.67903 | 0.320997 | 0.160499 | − | 0.987036i | \(-0.448690\pi\) | ||||
0.160499 | + | 0.987036i | \(0.448690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.2681 | 1.58770 | 0.793848 | − | 0.608116i | \(-0.208075\pi\) | ||||
0.793848 | + | 0.608116i | \(0.208075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0565 | 1.12295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.09266 | −0.394646 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.5922 | + | 30.4705i | −0.975838 | + | 1.69020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.6167 | − | 1.24411i | 1.02637 | − | 0.0685902i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.68091 | 0.367216 | 0.183608 | − | 0.983000i | \(-0.441222\pi\) | ||||
0.183608 | + | 0.983000i | \(0.441222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.8147 | − | 18.7317i | 0.590872 | − | 1.02342i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.49421 | − | 6.05215i | −0.190342 | − | 0.329681i | 0.755022 | − | 0.655700i | \(-0.227626\pi\) |
−0.945363 | + | 0.326018i | \(0.894293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.88215 | − | 17.1164i | −0.535148 | − | 0.926904i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1504 | − | 3.68279i | 0.980030 | − | 0.198852i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.28821 | 0.444934 | 0.222467 | − | 0.974940i | \(-0.428589\pi\) | ||||
0.222467 | + | 0.974940i | \(0.428589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.05373 | − | 5.28921i | 0.163462 | − | 0.283125i | −0.772646 | − | 0.634837i | \(-0.781067\pi\) |
0.936108 | + | 0.351712i | \(0.114400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3604 | − | 23.1409i | −0.711104 | − | 1.23167i | −0.964443 | − | 0.264290i | \(-0.914862\pi\) |
0.253340 | − | 0.967377i | \(-0.418471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.29780 | + | 3.97991i | −0.121955 | + | 0.211232i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.45603 | + | 4.25397i | 0.129624 | + | 0.224516i | 0.923531 | − | 0.383523i | \(-0.125289\pi\) |
−0.793907 | + | 0.608040i | \(0.791956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.99972 | + | 10.3918i | −0.315775 | + | 0.546938i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.4551 | + | 40.6255i | 1.22770 | + | 2.12643i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.3532 | − | 26.5925i | −0.801430 | − | 1.38812i | −0.918675 | − | 0.395015i | \(-0.870740\pi\) |
0.117245 | − | 0.993103i | \(-0.462594\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.97901 | + | 16.2321i | −0.414250 | + | 0.842730i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.29190 | + | 14.3620i | −0.429338 | + | 0.743635i | −0.996815 | − | 0.0797543i | \(-0.974586\pi\) |
0.567477 | + | 0.823390i | \(0.307920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.7716 | −2.09985 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.08857 | −0.210016 | −0.105008 | − | 0.994471i | \(-0.533487\pi\) | ||||
−0.105008 | + | 0.994471i | \(0.533487\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1769 | + | 26.2871i | −0.775503 | + | 1.34321i | 0.159009 | + | 0.987277i | \(0.449170\pi\) |
−0.934511 | + | 0.355933i | \(0.884163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.6237 | + | 1.44507i | −1.10205 | + | 0.0736474i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.73382 | − | 3.00307i | −0.0879082 | − | 0.152261i | 0.818719 | − | 0.574195i | \(-0.194685\pi\) |
−0.906627 | + | 0.421934i | \(0.861352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.10007 | − | 3.63743i | −0.106205 | − | 0.183953i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.6974 | + | 30.6529i | −0.890455 | + | 1.54231i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.04243 | − | 12.1979i | −0.353450 | − | 0.612193i | 0.633402 | − | 0.773823i | \(-0.281658\pi\) |
−0.986851 | + | 0.161630i | \(0.948325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.46593 | + | 9.46726i | −0.272955 | + | 0.472772i | −0.969617 | − | 0.244627i | \(-0.921334\pi\) |
0.696662 | + | 0.717400i | \(0.254668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.0888 | + | 34.7949i | 1.00070 | + | 1.73326i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.59142 | − | 11.4167i | 0.326725 | − | 0.565904i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.9879 | 0.790553 | 0.395276 | − | 0.918562i | \(-0.370649\pi\) | ||||
0.395276 | + | 0.918562i | \(0.370649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.1054 | + | 1.41043i | −1.03853 | + | 0.0694029i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.8331 | − | 36.0841i | −1.02266 | − | 1.77130i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.56197 | − | 6.16951i | −0.174014 | − | 0.301400i | 0.765806 | − | 0.643072i | \(-0.222340\pi\) |
−0.939819 | + | 0.341671i | \(0.889007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6326 | + | 28.8086i | −0.810625 | + | 1.40404i | 0.101802 | + | 0.994805i | \(0.467539\pi\) |
−0.912427 | + | 0.409239i | \(0.865794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.50066 | −0.460849 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.2561 | − | 2.35610i | 1.70616 | − | 0.114019i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.62382 | + | 4.54459i | −0.126385 | + | 0.218905i | −0.922273 | − | 0.386538i | \(-0.873671\pi\) |
0.795889 | + | 0.605443i | \(0.207004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.1053 | 1.06231 | 0.531156 | − | 0.847274i | \(-0.321758\pi\) | ||||
0.531156 | + | 0.847274i | \(0.321758\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.3573 | −0.878149 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.6165 | −1.65216 | −0.826079 | − | 0.563555i | \(-0.809433\pi\) | ||||
−0.826079 | + | 0.563555i | \(0.809433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.40923 | −0.209489 | −0.104744 | − | 0.994499i | \(-0.533402\pi\) | ||||
−0.104744 | + | 0.994499i | \(0.533402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.96370 | 0.187897 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6336 | 0.926568 | 0.463284 | − | 0.886210i | \(-0.346671\pi\) | ||||
0.463284 | + | 0.886210i | \(0.346671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.86525 | − | 6.69481i | 0.182007 | − | 0.315246i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.9575 | − | 2.93759i | 2.06076 | − | 0.137716i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.8392 | −1.44259 | −0.721297 | − | 0.692626i | \(-0.756454\pi\) | ||||
−0.721297 | + | 0.692626i | \(0.756454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6297 | − | 23.6074i | 0.634800 | − | 1.09951i | −0.351757 | − | 0.936091i | \(-0.614416\pi\) |
0.986557 | − | 0.163415i | \(-0.0522510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.959750 | + | 1.66234i | 0.0446034 | + | 0.0772553i | 0.887465 | − | 0.460875i | \(-0.152464\pi\) |
−0.842862 | + | 0.538130i | \(0.819131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.88655 | + | 8.46376i | 0.226123 | + | 0.391656i | 0.956656 | − | 0.291221i | \(-0.0940616\pi\) |
−0.730533 | + | 0.682877i | \(0.760728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.1772 | + | 1.08109i | −0.746994 | + | 0.0499201i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.206158 | −0.00947913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7619 | + | 35.9607i | −0.952623 | + | 1.64999i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.68809 | − | 13.3162i | −0.351278 | − | 0.608431i | 0.635196 | − | 0.772351i | \(-0.280919\pi\) |
−0.986474 | + | 0.163920i | \(0.947586\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3993 | + | 23.2083i | −0.610956 | + | 1.05821i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3824 | − | 21.4470i | −0.562258 | − | 0.973859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.18342 | + | 8.97794i | −0.234883 | + | 0.406829i | −0.959239 | − | 0.282597i | \(-0.908804\pi\) |
0.724356 | + | 0.689427i | \(0.242137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.94718 | − | 12.0329i | −0.313522 | − | 0.543035i | 0.665600 | − | 0.746308i | \(-0.268175\pi\) |
−0.979122 | + | 0.203273i | \(0.934842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.50469 | − | 9.53440i | −0.247919 | − | 0.429408i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.43717 | − | 0.229699i | 0.154178 | − | 0.0103034i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.70488 | + | 2.95294i | −0.0763210 | + | 0.132192i | −0.901660 | − | 0.432446i | \(-0.857651\pi\) |
0.825339 | + | 0.564638i | \(0.190984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.8911 | 1.95701 | 0.978504 | − | 0.206227i | \(-0.0661185\pi\) | ||||
0.978504 | + | 0.206227i | \(0.0661185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.3821 | 1.52998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.6674 | − | 34.0649i | 0.871742 | − | 1.50990i | 0.0115483 | − | 0.999933i | \(-0.496324\pi\) |
0.860193 | − | 0.509968i | \(-0.170343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5121 | − | 31.5571i | 0.686215 | − | 1.39600i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.1519 | + | 31.4400i | 0.799869 | + | 1.38541i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.18305 | + | 14.1735i | 0.359890 | + | 0.623348i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.4779 | + | 21.6124i | −0.546669 | + | 0.946858i | 0.451831 | + | 0.892104i | \(0.350771\pi\) |
−0.998500 | + | 0.0547547i | \(0.982562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.1575 | + | 26.2536i | 0.662792 | + | 1.14799i | 0.979879 | + | 0.199594i | \(0.0639622\pi\) |
−0.317086 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.42449 | + | 9.39550i | −0.236295 | + | 0.409274i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.06457 | + | 10.5041i | 0.263677 | + | 0.456702i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.85744 | + | 13.6095i | −0.340343 | + | 0.589492i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2151 | −0.830742 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.92233 | + | 12.8628i | 0.427385 | + | 0.554039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2812 | − | 24.7357i | −0.613996 | − | 1.06347i | −0.990560 | − | 0.137082i | \(-0.956228\pi\) |
0.376563 | − | 0.926391i | \(-0.377106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.47326 | + | 2.55177i | 0.0631077 | + | 0.109306i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.89233 | + | 6.74171i | −0.166424 | + | 0.288255i | −0.937160 | − | 0.348900i | \(-0.886555\pi\) |
0.770736 | + | 0.637154i | \(0.219889\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.1179 | −2.04989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.4727 | − | 1.76912i | 1.12573 | − | 0.0752305i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2470 | − | 40.2650i | 0.985008 | − | 1.70608i | 0.343108 | − | 0.939296i | \(-0.388520\pi\) |
0.641900 | − | 0.766788i | \(-0.278146\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.419086 | 0.0177254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.9826 | 1.17933 | 0.589663 | − | 0.807650i | \(-0.299261\pi\) | ||||
0.589663 | + | 0.807650i | \(0.299261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.4641 | 1.61820 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.89957 | −0.373090 | −0.186545 | − | 0.982446i | \(-0.559729\pi\) | ||||
−0.186545 | + | 0.982446i | \(0.559729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.3304 | 1.35298 | 0.676492 | − | 0.736450i | \(-0.263500\pi\) | ||||
0.676492 | + | 0.736450i | \(0.263500\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.5897 | −1.02546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.8414 | + | 29.1701i | −0.701115 | + | 1.21437i | 0.266960 | + | 0.963707i | \(0.413981\pi\) |
−0.968075 | + | 0.250659i | \(0.919353\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.7780 | + | 28.0294i | −0.571610 | + | 1.16286i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.8652 | −0.657071 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.24076 | + | 2.14907i | −0.0512118 | + | 0.0887015i | −0.890495 | − | 0.454993i | \(-0.849642\pi\) |
0.839283 | + | 0.543695i | \(0.182975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.7085 | + | 41.0643i | 0.976891 | + | 1.69202i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0903 | + | 26.1371i | 0.619684 | + | 1.07332i | 0.989543 | + | 0.144236i | \(0.0460725\pi\) |
−0.369859 | + | 0.929088i | \(0.620594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.62177 | + | 9.88280i | 0.271466 | + | 0.405155i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.4083 | −0.670424 | −0.335212 | − | 0.942143i | \(-0.608808\pi\) | ||||
−0.335212 | + | 0.942143i | \(0.608808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.96998 | + | 5.14416i | −0.121148 | + | 0.209835i | −0.920221 | − | 0.391400i | \(-0.871991\pi\) |
0.799073 | + | 0.601235i | \(0.205324\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.90793 | + | 17.1610i | 0.402815 | + | 0.697695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.97573 | + | 5.15412i | −0.120781 | + | 0.209199i | −0.920076 | − | 0.391740i | \(-0.871873\pi\) |
0.799295 | + | 0.600939i | \(0.205207\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6348 | − | 28.8124i | −0.672974 | − | 1.16562i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5920 | − | 27.0062i | 0.629756 | − | 1.09077i | −0.357845 | − | 0.933781i | \(-0.616488\pi\) |
0.987601 | − | 0.156988i | \(-0.0501783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1437 | + | 19.3014i | 0.448627 | + | 0.777045i | 0.998297 | − | 0.0583367i | \(-0.0185797\pi\) |
−0.549670 | + | 0.835382i | \(0.685246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2943 | + | 29.9547i | 0.695118 | + | 1.20398i | 0.970141 | + | 0.242543i | \(0.0779814\pi\) |
−0.275022 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.65384 | − | 2.46831i | −0.0662599 | − | 0.0988909i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.33422 | − | 5.77504i | 0.133369 | − | 0.231002i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.23631 | −0.288530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2933 | 1.04672 | 0.523360 | − | 0.852112i | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852112i | \(0.324678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.4777 | + | 30.2723i | −0.693582 | + | 1.20132i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.1705 | − | 26.1480i | −0.799185 | − | 1.03602i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.2673 | − | 28.1758i | −0.642519 | − | 1.11288i | −0.984869 | − | 0.173303i | \(-0.944556\pi\) |
0.342349 | − | 0.939573i | \(-0.388777\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.21987 | − | 9.04107i | −0.205851 | − | 0.356545i | 0.744552 | − | 0.667564i | \(-0.232663\pi\) |
−0.950404 | + | 0.311019i | \(0.899330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.685824 | − | 1.18788i | 0.0269625 | − | 0.0467005i | −0.852229 | − | 0.523168i | \(-0.824750\pi\) |
0.879192 | + | 0.476468i | \(0.158083\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.27699 | − | 16.0682i | −0.364154 | − | 0.630733i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.62567 | + | 6.27985i | −0.141883 | + | 0.245749i | −0.928206 | − | 0.372067i | \(-0.878649\pi\) |
0.786322 | + | 0.617816i | \(0.211982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.3269 | − | 52.5277i | −1.18497 | − | 2.05243i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.3187 | + | 23.0686i | −0.518822 | + | 0.898626i | 0.480939 | + | 0.876754i | \(0.340296\pi\) |
−0.999761 | + | 0.0218722i | \(0.993037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.8199 | −1.35434 | −0.677168 | − | 0.735828i | \(-0.736793\pi\) | ||||
−0.677168 | + | 0.735828i | \(0.736793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51.8779 | − | 3.46689i | 2.01174 | − | 0.134440i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2473 | − | 24.6770i | −0.551657 | − | 0.955498i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4970 | + | 26.8416i | 0.598255 | + | 1.03621i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.23841 | − | 14.2693i | 0.317567 | − | 0.550043i | −0.662412 | − | 0.749139i | \(-0.730467\pi\) |
0.979980 | + | 0.199096i | \(0.0638007\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.1654 | 0.813450 | 0.406725 | − | 0.913551i | \(-0.366671\pi\) | ||||
0.406725 | + | 0.913551i | \(0.366671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.18916 | + | 16.6596i | −0.314271 | + | 0.639339i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0756 | − | 24.3796i | 0.538587 | − | 0.932859i | −0.460394 | − | 0.887715i | \(-0.652292\pi\) |
0.998980 | − | 0.0451447i | \(-0.0143749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.8049 | 2.17040 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.2515 | 1.22869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0796 | −0.725822 | −0.362911 | − | 0.931824i | \(-0.618217\pi\) | ||||
−0.362911 | + | 0.931824i | \(0.618217\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.84632 | 0.297628 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.24341 | −0.160731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8508 | −0.900834 | −0.450417 | − | 0.892818i | \(-0.648725\pi\) | ||||
−0.450417 | + | 0.892818i | \(0.648725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8136 | + | 27.3900i | −0.596422 | + | 1.03303i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.3459 | − | 21.4108i | −0.539532 | − | 0.805235i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0986 | 0.754817 | 0.377409 | − | 0.926047i | \(-0.376815\pi\) | ||||
0.377409 | + | 0.926047i | \(0.376815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.0397 | + | 24.3175i | −0.525792 | + | 0.910698i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.3217 | + | 33.4662i | 0.722592 | + | 1.25157i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.29246 | − | 5.70270i | −0.122788 | − | 0.212675i | 0.798078 | − | 0.602554i | \(-0.205850\pi\) |
−0.920866 | + | 0.389879i | \(0.872517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0048 | − | 24.4220i | 0.447082 | − | 0.909524i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −64.4542 | −2.39377 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2342 | + | 31.5826i | −0.676269 | + | 1.17133i | 0.299827 | + | 0.953994i | \(0.403071\pi\) |
−0.976096 | + | 0.217339i | \(0.930262\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0565818 | + | 0.0980026i | 0.00209276 | + | 0.00362476i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.6824 | + | 20.2345i | −0.431498 | + | 0.747377i | −0.997003 | − | 0.0773684i | \(-0.975348\pi\) |
0.565504 | + | 0.824745i | \(0.308682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.11077 | − | 12.3162i | −0.261928 | − | 0.453673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.4596 | + | 25.0448i | −0.531906 | + | 0.921288i | 0.467400 | + | 0.884046i | \(0.345191\pi\) |
−0.999306 | + | 0.0372422i | \(0.988143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.6794 | + | 20.2292i | 0.428474 | + | 0.742139i | 0.996738 | − | 0.0807074i | \(-0.0257179\pi\) |
−0.568264 | + | 0.822847i | \(0.692385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2422 | + | 21.2042i | 0.448521 | + | 0.776860i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.01747 | + | 11.9658i | 0.292952 | + | 0.437222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.856616 | + | 1.48370i | −0.0312584 | + | 0.0541411i | −0.881231 | − | 0.472685i | \(-0.843285\pi\) |
0.849973 | + | 0.526826i | \(0.176618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.7675 | −1.99319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4587 | 1.03435 | 0.517175 | − | 0.855880i | \(-0.326984\pi\) | ||||
0.517175 | + | 0.855880i | \(0.326984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0525 | + | 29.5358i | −0.618154 | + | 1.07067i | 0.371669 | + | 0.928365i | \(0.378786\pi\) |
−0.989822 | + | 0.142308i | \(0.954548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.974346 | − | 1.98216i | 0.0352737 | − | 0.0717592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.8587 | + | 32.6642i | 0.680947 | + | 1.17943i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.48467 | + | 4.30357i | 0.0895995 | + | 0.155191i | 0.907342 | − | 0.420394i | \(-0.138108\pi\) |
−0.817742 | + | 0.575584i | \(0.804775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.74814 | − | 9.95607i | 0.206746 | − | 0.358095i | −0.743941 | − | 0.668245i | \(-0.767046\pi\) |
0.950688 | + | 0.310150i | \(0.100379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.7576 | + | 55.0058i | 1.14077 | + | 1.97587i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.27320 | + | 16.0617i | −0.332247 | + | 0.575469i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.51082 | + | 2.61682i | 0.0540615 | + | 0.0936373i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.41556 | + | 2.45182i | −0.0505235 | + | 0.0875092i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.6011 | −1.73244 | −0.866221 | − | 0.499661i | \(-0.833458\pi\) | ||||
−0.866221 | + | 0.499661i | \(0.833458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0491 | − | 23.9527i | −0.570639 | − | 0.851661i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.5030 | − | 54.5647i | −1.11870 | − | 1.93765i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.8556 | − | 29.1947i | −0.597056 | − | 1.03413i | −0.993253 | − | 0.115965i | \(-0.963004\pi\) |
0.396198 | − | 0.918165i | \(-0.370330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49183 | − | 7.78007i | 0.158909 | − | 0.275239i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.8438 | 1.08846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.1385 | + | 25.5788i | 0.604054 | + | 0.901533i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.93617 | − | 13.7459i | 0.279021 | − | 0.483278i | −0.692121 | − | 0.721782i | \(-0.743323\pi\) |
0.971142 | + | 0.238503i | \(0.0766568\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.2524 | −0.956963 | −0.478481 | − | 0.878098i | \(-0.658813\pi\) | ||||
−0.478481 | + | 0.878098i | \(0.658813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.5300 | 0.438907 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.494597 | 0.0173038 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.3389 | −0.849433 | −0.424717 | − | 0.905326i | \(-0.639626\pi\) | ||||
−0.424717 | + | 0.905326i | \(0.639626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5380 | 0.402188 | 0.201094 | − | 0.979572i | \(-0.435550\pi\) | ||||
0.201094 | + | 0.979572i | \(0.435550\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.8582 | −1.21214 | −0.606069 | − | 0.795412i | \(-0.707255\pi\) | ||||
−0.606069 | + | 0.795412i | \(0.707255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.64018 | + | 13.2332i | −0.265354 | + | 0.459607i | −0.967656 | − | 0.252272i | \(-0.918822\pi\) |
0.702302 | + | 0.711879i | \(0.252156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.39140 | − | 8.24716i | 0.117505 | − | 0.285747i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.10711 | −0.211345 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.39990 | + | 14.5490i | −0.289997 | + | 0.502289i | −0.973809 | − | 0.227369i | \(-0.926988\pi\) |
0.683812 | + | 0.729658i | \(0.260321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8448 | − | 39.5684i | −0.787753 | − | 1.36443i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.3357 | − | 28.2943i | −0.561967 | − | 0.973355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.55263 | − | 13.3304i | 0.225151 | − | 0.458037i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.7291 | −0.642024 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4270 | + | 19.7921i | −0.391253 | + | 0.677670i | −0.992615 | − | 0.121306i | \(-0.961292\pi\) |
0.601362 | + | 0.798977i | \(0.294625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5871 | − | 30.4618i | −0.600765 | − | 1.04056i | −0.992705 | − | 0.120565i | \(-0.961529\pi\) |
0.391940 | − | 0.919991i | \(-0.371804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.28520 | − | 9.15424i | 0.180329 | − | 0.312339i | −0.761664 | − | 0.647973i | \(-0.775617\pi\) |
0.941993 | + | 0.335634i | \(0.108950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.29326 | − | 12.6323i | −0.248265 | − | 0.430008i | 0.714779 | − | 0.699350i | \(-0.246527\pi\) |
−0.963045 | + | 0.269342i | \(0.913194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.94358 | − | 6.83048i | 0.134086 | − | 0.232243i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6362 | + | 20.1545i | 0.394731 | + | 0.683694i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.4551 | + | 25.0369i | 0.489791 | + | 0.848343i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.9025 | − | 1.53053i | 0.774247 | − | 0.0517413i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.65914 | + | 9.80192i | −0.191096 | + | 0.330987i | −0.945614 | − | 0.325292i | \(-0.894537\pi\) |
0.754518 | + | 0.656279i | \(0.227871\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.733220 | 0.0247028 | 0.0123514 | − | 0.999924i | \(-0.496068\pi\) | ||||
0.0123514 | + | 0.999924i | \(0.496068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1726 | 0.476944 | 0.238472 | − | 0.971149i | \(-0.423353\pi\) | ||||
0.238472 | + | 0.971149i | \(0.423353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.8162 | − | 29.1266i | 0.564634 | − | 0.977975i | −0.432449 | − | 0.901658i | \(-0.642351\pi\) |
0.997084 | − | 0.0763170i | \(-0.0243161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.1440 | − | 1.74715i | 0.876842 | − | 0.0585975i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.6321 | − | 34.0038i | −0.656964 | − | 1.13790i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.23681 | − | 2.14221i | −0.0413419 | − | 0.0716063i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.8008 | + | 63.7408i | −1.22737 | + | 2.12588i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.35436 | + | 7.54198i | 0.145065 | + | 0.251260i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.6498 | − | 60.0152i | 1.15180 | − | 1.99497i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.79255 | + | 8.30094i | 0.159134 | + | 0.275628i | 0.934557 | − | 0.355814i | \(-0.115796\pi\) |
−0.775423 | + | 0.631443i | \(0.782463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.37499 | + | 16.2380i | −0.310607 | + | 0.537988i | −0.978494 | − | 0.206275i | \(-0.933866\pi\) |
0.667887 | + | 0.744263i | \(0.267199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.3959 | −0.906672 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.0568 | + | 40.8026i | −0.662333 | + | 1.34742i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2895 | − | 36.8745i | −0.702276 | − | 1.21638i | −0.967666 | − | 0.252236i | \(-0.918834\pi\) |
0.265390 | − | 0.964141i | \(-0.414499\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.07126 | − | 5.31958i | −0.101092 | − | 0.175096i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.1824 | + | 36.6890i | −0.696474 | + | 1.20633i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.1524 | −1.25174 | −0.625869 | − | 0.779928i | \(-0.715256\pi\) | ||||
−0.625869 | + | 0.779928i | \(0.715256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8049 | − | 30.8594i | −0.780173 | − | 1.01137i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.21736 | + | 9.03673i | −0.170626 | + | 0.295533i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.48960 | 0.212006 | 0.106003 | − | 0.994366i | \(-0.466195\pi\) | ||||
0.106003 | + | 0.994366i | \(0.466195\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.466471 | 0.0152065 | 0.00760326 | − | 0.999971i | \(-0.497580\pi\) | ||||
0.00760326 | + | 0.999971i | \(0.497580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9828 | −0.357650 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1115 | −0.491058 | −0.245529 | − | 0.969389i | \(-0.578962\pi\) | ||||
−0.245529 | + | 0.969389i | \(0.578962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.7006 | −2.03535 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.6802 | −0.637503 | −0.318751 | − | 0.947838i | \(-0.603264\pi\) | ||||
−0.318751 | + | 0.947838i | \(0.603264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.3881 | + | 49.1696i | −0.918616 | + | 1.59109i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.7017 | − | 35.3741i | −0.765368 | − | 1.14229i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.5293 | 1.33966 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03322 | − | 1.78959i | 0.0332606 | − | 0.0576090i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.83228 | − | 15.2980i | −0.284027 | − | 0.491949i | 0.688346 | − | 0.725383i | \(-0.258337\pi\) |
−0.972373 | + | 0.233433i | \(0.925004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7523 | − | 20.3555i | −0.377148 | − | 0.653240i | 0.613498 | − | 0.789697i | \(-0.289762\pi\) |
−0.990646 | + | 0.136456i | \(0.956429\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.27386 | − | 4.88614i | −0.104955 | − | 0.156642i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.43379 | 0.173842 | 0.0869211 | − | 0.996215i | \(-0.472297\pi\) | ||||
0.0869211 | + | 0.996215i | \(0.472297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.30308 | − | 2.25700i | 0.0416466 | − | 0.0721341i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.05345 | + | 1.82463i | 0.0335998 | + | 0.0581966i | 0.882336 | − | 0.470619i | \(-0.155969\pi\) |
−0.848736 | + | 0.528816i | \(0.822636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.5174 | + | 52.8577i | −0.972366 | + | 1.68419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.146446 | + | 0.253651i | 0.00465670 | + | 0.00806564i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.91172 | + | 15.4356i | −0.283090 | + | 0.490327i | −0.972144 | − | 0.234383i | \(-0.924693\pi\) |
0.689054 | + | 0.724710i | \(0.258026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.1031 | + | 74.6567i | 1.36646 | + | 2.36678i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.2477 | + | 31.6060i | 0.577911 | + | 1.00097i | 0.995719 | + | 0.0924360i | \(0.0294653\pi\) |
−0.417807 | + | 0.908536i | \(0.637201\pi\) | |||||||
\(998\) | 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 | 3024.2.q.k.2881.1 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.529.4 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.1369.1 | 22 | |||
7.2 | even | 3 | 3024.2.t.l.289.11 | 22 | |||
9.4 | even | 3 | 3024.2.t.l.1873.11 | 22 | |||
9.5 | odd | 6 | 1008.2.t.k.193.5 | 22 | |||
12.11 | even | 2 | 504.2.q.d.25.8 | ✓ | 22 | ||
21.2 | odd | 6 | 1008.2.t.k.961.5 | 22 | |||
28.23 | odd | 6 | 1512.2.t.d.289.11 | 22 | |||
36.23 | even | 6 | 504.2.t.d.193.7 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.t.d.361.11 | 22 | |||
63.23 | odd | 6 | 1008.2.q.k.625.4 | 22 | |||
63.58 | even | 3 | inner | 3024.2.q.k.2305.1 | 22 | ||
84.23 | even | 6 | 504.2.t.d.457.7 | yes | 22 | ||
252.23 | even | 6 | 504.2.q.d.121.8 | yes | 22 | ||
252.247 | odd | 6 | 1512.2.q.c.793.1 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.8 | ✓ | 22 | 12.11 | even | 2 | ||
504.2.q.d.121.8 | yes | 22 | 252.23 | even | 6 | ||
504.2.t.d.193.7 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.457.7 | yes | 22 | 84.23 | even | 6 | ||
1008.2.q.k.529.4 | 22 | 3.2 | odd | 2 | |||
1008.2.q.k.625.4 | 22 | 63.23 | odd | 6 | |||
1008.2.t.k.193.5 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.961.5 | 22 | 21.2 | odd | 6 | |||
1512.2.q.c.793.1 | 22 | 252.247 | odd | 6 | |||
1512.2.q.c.1369.1 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.289.11 | 22 | 28.23 | odd | 6 | |||
1512.2.t.d.361.11 | 22 | 36.31 | odd | 6 | |||
3024.2.q.k.2305.1 | 22 | 63.58 | even | 3 | inner | ||
3024.2.q.k.2881.1 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.289.11 | 22 | 7.2 | even | 3 | |||
3024.2.t.l.1873.11 | 22 | 9.4 | even | 3 |