Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(9,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.bg (of order \(6\), degree \(2\), 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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 9.9 | ||
Character | \(\chi\) | \(=\) | 280.9 |
Dual form | 280.2.bg.a.249.9 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.76528 | − | 1.01918i | 1.01918 | − | 0.588426i | 0.105317 | − | 0.994439i | \(-0.466414\pi\) |
0.913868 | + | 0.406012i | \(0.133081\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.80516 | − | 1.31962i | −0.807293 | − | 0.590151i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.27974 | − | 1.34267i | 0.861662 | − | 0.507483i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.577473 | − | 1.00021i | 0.192491 | − | 0.333404i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.524037 | − | 0.907658i | −0.158003 | − | 0.273669i | 0.776145 | − | 0.630554i | \(-0.217172\pi\) |
−0.934148 | + | 0.356885i | \(0.883839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.15495i | − | 0.320324i | −0.987091 | − | 0.160162i | \(-0.948798\pi\) | ||
0.987091 | − | 0.160162i | \(-0.0512017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.53155 | − | 0.489703i | −1.17004 | − | 0.126441i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.90617 | − | 3.40993i | 1.43246 | − | 0.827030i | 0.435150 | − | 0.900358i | \(-0.356695\pi\) |
0.997308 | + | 0.0733282i | \(0.0233621\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.37560 | + | 4.11466i | −0.545000 | + | 0.943967i | 0.453607 | + | 0.891202i | \(0.350137\pi\) |
−0.998607 | + | 0.0527653i | \(0.983196\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.65595 | − | 4.69367i | 0.579576 | − | 1.02424i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76549 | − | 1.59666i | −0.576645 | − | 0.332926i | 0.183154 | − | 0.983084i | \(-0.441369\pi\) |
−0.759799 | + | 0.650158i | \(0.774703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.51721 | + | 4.76425i | 0.303443 | + | 0.952850i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.76090i | 0.723786i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.14130 | −0.954716 | −0.477358 | − | 0.878709i | \(-0.658405\pi\) | ||||
−0.477358 | + | 0.878709i | \(0.658405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.78686 | + | 4.82698i | 0.500534 | + | 0.866951i | 1.00000 | 0.000617170i | \(0.000196451\pi\) | |
−0.499465 | + | 0.866334i | \(0.666470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.85014 | − | 1.06818i | −0.322068 | − | 0.185946i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.88712 | − | 0.584648i | −0.995105 | − | 0.0988235i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.25885 | + | 2.45885i | 0.700150 | + | 0.404232i | 0.807403 | − | 0.590000i | \(-0.200872\pi\) |
−0.107253 | + | 0.994232i | \(0.534206\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.17710 | − | 2.03880i | −0.188487 | − | 0.326469i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.68948 | 1.51324 | 0.756621 | − | 0.653853i | \(-0.226849\pi\) | ||||
0.756621 | + | 0.653853i | \(0.226849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.44559i | 1.13544i | 0.823221 | + | 0.567721i | \(0.192175\pi\) | ||||
−0.823221 | + | 0.567721i | \(0.807825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.36233 | + | 1.04350i | −0.352155 | + | 0.155556i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.04651 | − | 4.64565i | −1.17370 | − | 0.677638i | −0.219154 | − | 0.975690i | \(-0.570330\pi\) |
−0.954550 | + | 0.298052i | \(0.903663\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.39445 | − | 6.12190i | 0.484922 | − | 0.874558i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.95070 | − | 12.0390i | 0.973292 | − | 1.68579i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.85078 | + | 2.80060i | −0.666305 | + | 0.384692i | −0.794675 | − | 0.607035i | \(-0.792359\pi\) |
0.128370 | + | 0.991726i | \(0.459026\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.251792 | + | 2.33000i | −0.0339516 | + | 0.314177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.68469i | 1.28277i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.43118 | + | 9.40708i | 0.707080 | + | 1.22470i | 0.965936 | + | 0.258782i | \(0.0833211\pi\) |
−0.258856 | + | 0.965916i | \(0.583346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.66722 | − | 2.88770i | 0.213465 | − | 0.369733i | −0.739331 | − | 0.673342i | \(-0.764858\pi\) |
0.952797 | + | 0.303609i | \(0.0981917\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0264698 | − | 3.05558i | −0.00333489 | − | 0.384967i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.52409 | + | 2.08486i | −0.189040 | + | 0.258595i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.72071 | + | 2.72551i | −0.576727 | + | 0.332973i | −0.759832 | − | 0.650120i | \(-0.774719\pi\) |
0.183105 | + | 0.983093i | \(0.441385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.50915 | −0.783609 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.10916 | −0.487668 | −0.243834 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243834 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.60213 | + | 3.23439i | −0.655680 | + | 0.378557i | −0.790629 | − | 0.612296i | \(-0.790246\pi\) |
0.134949 | + | 0.990853i | \(0.456913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.53395 | + | 6.86391i | 0.869946 | + | 0.792576i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.41336 | − | 1.36562i | −0.275028 | − | 0.155626i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.306372 | − | 0.530652i | 0.0344695 | − | 0.0597030i | −0.848276 | − | 0.529554i | \(-0.822359\pi\) |
0.882746 | + | 0.469851i | \(0.155692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.56547 | + | 9.63967i | 0.618385 | + | 1.07107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.275623i | − | 0.0302535i | −0.999886 | − | 0.0151268i | \(-0.995185\pi\) | ||
0.999886 | − | 0.0151268i | \(-0.00481518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.1614 | − | 1.63842i | −1.64449 | − | 0.177712i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.07583 | + | 5.23993i | −0.973031 | + | 0.561780i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.63232 | + | 14.9516i | −0.915024 | + | 1.58487i | −0.108158 | + | 0.994134i | \(0.534495\pi\) |
−0.806866 | + | 0.590735i | \(0.798838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.55072 | − | 2.63298i | −0.162559 | − | 0.276011i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.83916 | + | 5.68064i | 1.02027 | + | 0.589055i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.71812 | − | 4.29273i | 0.997058 | − | 0.440425i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.59854i | − | 0.771515i | −0.922600 | − | 0.385757i | \(-0.873940\pi\) | ||
0.922600 | − | 0.385757i | \(-0.126060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.21047 | −0.121657 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.282335 | + | 0.489019i | 0.0280934 | + | 0.0486592i | 0.879730 | − | 0.475473i | \(-0.157723\pi\) |
−0.851637 | + | 0.524132i | \(0.824390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4944 | + | 7.79097i | 1.32964 | + | 0.767667i | 0.985244 | − | 0.171157i | \(-0.0547506\pi\) |
0.344395 | + | 0.938825i | \(0.388084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.9883 | + | 4.96799i | −1.07235 | + | 0.484827i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1452 | − | 7.01205i | −1.17412 | − | 0.677880i | −0.219475 | − | 0.975618i | \(-0.570435\pi\) |
−0.954648 | + | 0.297738i | \(0.903768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.89890 | − | 13.6813i | −0.756577 | − | 1.31043i | −0.944586 | − | 0.328263i | \(-0.893537\pi\) |
0.188009 | − | 0.982167i | \(-0.439797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0241 | 0.951442 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 20.3625i | − | 1.91554i | −0.287536 | − | 0.957770i | \(-0.592836\pi\) | ||
0.287536 | − | 0.957770i | \(-0.407164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.88518 | + | 6.53162i | 0.269044 | + | 0.609076i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.15519 | − | 0.666949i | −0.106797 | − | 0.0616595i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.88613 | − | 15.7038i | 0.814590 | − | 1.43957i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.95077 | − | 8.57499i | 0.450070 | − | 0.779544i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.1046 | − | 9.87536i | 1.54227 | − | 0.890432i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.54818 | − | 10.6024i | 0.317359 | − | 0.948306i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.358593i | 0.0318199i | 0.999873 | + | 0.0159100i | \(0.00506451\pi\) | ||||
−0.999873 | + | 0.0159100i | \(0.994935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.58843 | + | 13.1435i | 0.668124 | + | 1.15722i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.75572 | − | 13.4333i | 0.677620 | − | 1.17367i | −0.298075 | − | 0.954542i | \(-0.596345\pi\) |
0.975696 | − | 0.219130i | \(-0.0703220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.108891 | + | 12.5700i | 0.00944206 | + | 1.08996i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.96296 | − | 6.78903i | 0.427143 | − | 0.584307i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.729539 | − | 0.421199i | 0.0623287 | − | 0.0359855i | −0.468512 | − | 0.883457i | \(-0.655210\pi\) |
0.530841 | + | 0.847472i | \(0.321876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.97876 | −0.252655 | −0.126327 | − | 0.991989i | \(-0.540319\pi\) | ||||
−0.126327 | + | 0.991989i | \(0.540319\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9391 | −1.59496 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.04830 | + | 0.605233i | −0.0876628 | + | 0.0506122i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.28088 | + | 6.78456i | 0.770735 | + | 0.563427i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.247192 | − | 14.2664i | −0.0203881 | − | 1.17668i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.551451 | − | 0.955142i | 0.0451767 | − | 0.0782483i | −0.842553 | − | 0.538614i | \(-0.818948\pi\) |
0.887730 | + | 0.460365i | \(0.152282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.27624 | + | 10.8708i | 0.510753 | + | 0.884650i | 0.999922 | + | 0.0124612i | \(0.00396661\pi\) |
−0.489169 | + | 0.872189i | \(0.662700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.87657i | − | 0.636783i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.33904 | − | 12.3911i | 0.107555 | − | 0.995274i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2482 | − | 10.5356i | 1.45636 | − | 0.840831i | 0.457532 | − | 0.889193i | \(-0.348733\pi\) |
0.998830 | + | 0.0483621i | \(0.0154001\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.70865 | + | 9.88767i | −0.452725 | + | 0.784143i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.44840 | + | 0.0731866i | −0.665827 | + | 0.00576791i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9364 | − | 10.9329i | −1.48321 | − | 0.856332i | −0.483393 | − | 0.875404i | \(-0.660596\pi\) |
−0.999818 | + | 0.0190714i | \(0.993929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.93021 | + | 4.36972i | 0.150267 | + | 0.340182i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.1680i | 0.786821i | 0.919363 | + | 0.393411i | \(0.128705\pi\) | ||||
−0.919363 | + | 0.393411i | \(0.871295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6661 | 0.897392 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.74369 | + | 4.75220i | 0.209815 | + | 0.363410i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.691475 | − | 0.399223i | −0.0525719 | − | 0.0303524i | 0.473484 | − | 0.880803i | \(-0.342996\pi\) |
−0.526056 | + | 0.850450i | \(0.676330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.85569 | + | 8.82414i | 0.745020 | + | 0.667042i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.1751 | + | 11.0707i | 1.44129 | + | 0.832128i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.08777 | − | 10.5443i | −0.455021 | − | 0.788119i | 0.543668 | − | 0.839300i | \(-0.317035\pi\) |
−0.998689 | + | 0.0511806i | \(0.983702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00613 | −0.297773 | −0.148887 | − | 0.988854i | \(-0.547569\pi\) | ||||
−0.148887 | + | 0.988854i | \(0.547569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.79680i | − | 0.502434i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.44316 | − | 10.0587i | −0.326668 | − | 0.739528i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.19010 | − | 3.57386i | −0.452665 | − | 0.261346i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.04966 | + | 8.57389i | 0.367309 | + | 0.623658i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.33082 | + | 14.4294i | −0.602797 | + | 1.04407i | 0.389599 | + | 0.920985i | \(0.372614\pi\) |
−0.992396 | + | 0.123090i | \(0.960720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.43024 | + | 3.71250i | −0.462859 | + | 0.267232i | −0.713246 | − | 0.700914i | \(-0.752776\pi\) |
0.250387 | + | 0.968146i | \(0.419442\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.565581 | + | 5.23369i | −0.0405021 | + | 0.374792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.88883i | 0.134574i | 0.997734 | + | 0.0672869i | \(0.0214343\pi\) | ||||
−0.997734 | + | 0.0672869i | \(0.978566\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.61865 | − | 14.9279i | −0.610960 | − | 1.05821i | −0.991079 | − | 0.133276i | \(-0.957450\pi\) |
0.380119 | − | 0.924938i | \(-0.375883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.55558 | + | 9.62255i | −0.391861 | + | 0.678723i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.7208 | + | 6.90309i | −0.822642 | + | 0.484502i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.4911 | − | 12.7864i | −1.22163 | − | 0.893042i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.19399 | + | 1.84405i | −0.221998 | + | 0.128170i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.97960 | 0.344446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.25478 | −0.361754 | −0.180877 | − | 0.983506i | \(-0.557894\pi\) | ||||
−0.180877 | + | 0.983506i | \(0.557894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.25381 | + | 4.18799i | −0.497023 | + | 0.286956i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.82534 | − | 13.4405i | 0.670083 | − | 0.916634i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.8344 | + | 7.26243i | 0.871254 | + | 0.493006i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.59288 | + | 11.4192i | −0.445506 | + | 0.771639i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.93828 | − | 6.82131i | −0.264918 | − | 0.458851i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.2760i | 0.889027i | 0.895772 | + | 0.444513i | \(0.146623\pi\) | ||||
−0.895772 | + | 0.444513i | \(0.853377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.64141 | + | 1.23369i | 0.376094 | + | 0.0822459i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.2225 | − | 5.90197i | 0.678492 | − | 0.391727i | −0.120795 | − | 0.992677i | \(-0.538544\pi\) |
0.799286 | + | 0.600950i | \(0.205211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.74611 | − | 11.6846i | 0.445796 | − | 0.772141i | −0.552311 | − | 0.833638i | \(-0.686254\pi\) |
0.998107 | + | 0.0614969i | \(0.0195874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65206 | + | 0.0489625i | −0.371878 | + | 0.00322150i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.987785 | − | 0.570298i | −0.0647120 | − | 0.0373615i | 0.467295 | − | 0.884101i | \(-0.345229\pi\) |
−0.532007 | + | 0.846740i | \(0.678562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.39475 | + | 19.0045i | 0.547613 | + | 1.23971i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.24900i | − | 0.0811311i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.94796 | −0.190688 | −0.0953438 | − | 0.995444i | \(-0.530395\pi\) | ||||
−0.0953438 | + | 0.995444i | \(0.530395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.30655 | − | 9.19122i | −0.341825 | − | 0.592058i | 0.642947 | − | 0.765911i | \(-0.277712\pi\) |
−0.984772 | + | 0.173853i | \(0.944378\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.87810 | + | 5.70312i | 0.633680 | + | 0.365856i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.2061 | + | 6.57164i | −0.907595 | + | 0.419847i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.75220 | + | 2.74369i | 0.302375 | + | 0.174577i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.280910 | − | 0.486551i | −0.0178020 | − | 0.0308339i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3119 | −0.777120 | −0.388560 | − | 0.921423i | \(-0.627027\pi\) | ||||
−0.388560 | + | 0.921423i | \(0.627027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.34683i | 0.210413i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.4340 | + | 12.5600i | −1.78060 | + | 0.786537i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.3706 | − | 8.87421i | −0.958790 | − | 0.553558i | −0.0629896 | − | 0.998014i | \(-0.520064\pi\) |
−0.895800 | + | 0.444456i | \(0.853397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0105 | − | 0.112707i | 0.808433 | − | 0.00700327i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.96896 | + | 5.14239i | −0.183774 | + | 0.318306i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.61626 | + | 2.08785i | −0.222988 | + | 0.128742i | −0.607333 | − | 0.794447i | \(-0.707761\pi\) |
0.384345 | + | 0.923190i | \(0.374427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.4522 | + | 1.34565i | 0.764930 | + | 0.0826624i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.1917i | 2.15370i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1341 | + | 22.7489i | 0.800798 | + | 1.38702i | 0.919092 | + | 0.394044i | \(0.128924\pi\) |
−0.118294 | + | 0.992979i | \(0.537743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1537 | + | 22.7829i | −0.799031 | + | 1.38396i | 0.121216 | + | 0.992626i | \(0.461321\pi\) |
−0.920248 | + | 0.391337i | \(0.872013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.42093 | − | 3.06748i | −0.328090 | − | 0.185652i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.52923 | − | 3.87375i | 0.212821 | − | 0.233596i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1278 | + | 10.4661i | −1.08919 | + | 0.628845i | −0.933361 | − | 0.358938i | \(-0.883139\pi\) |
−0.155831 | + | 0.987784i | \(0.549806\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.43734 | 0.385393 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7097 | 0.937162 | 0.468581 | − | 0.883420i | \(-0.344765\pi\) | ||||
0.468581 | + | 0.883420i | \(0.344765\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.36062 | − | 5.40436i | 0.556431 | − | 0.321256i | −0.195281 | − | 0.980747i | \(-0.562562\pi\) |
0.751712 | + | 0.659492i | \(0.229228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.7801 | − | 17.4824i | 0.757028 | − | 1.03557i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.0895 | − | 13.0098i | 1.30390 | − | 0.767945i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7553 | − | 25.5569i | 0.867957 | − | 1.50335i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.74431 | − | 13.4135i | −0.453979 | − | 0.786316i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.91887i | 0.579467i | 0.957107 | + | 0.289733i | \(0.0935667\pi\) | ||||
−0.957107 | + | 0.289733i | \(0.906433\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.60960 | − | 24.1484i | 0.151937 | − | 1.40597i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41361 | − | 1.97085i | 0.198078 | − | 0.114360i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.84405 | + | 3.19399i | −0.106644 | + | 0.184713i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.99700 | + | 16.9740i | 0.576218 | + | 0.978367i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.996801 | + | 0.575504i | 0.0572647 | + | 0.0330618i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.82026 | + | 3.01268i | −0.390527 | + | 0.172506i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.64632i | 0.322252i | 0.986934 | + | 0.161126i | \(0.0515126\pi\) | ||||
−0.986934 | + | 0.161126i | \(0.948487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.7617 | 1.80686 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.00950 | − | 10.4088i | −0.340767 | − | 0.590226i | 0.643808 | − | 0.765187i | \(-0.277353\pi\) |
−0.984575 | + | 0.174961i | \(0.944020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.4358 | − | 9.48924i | −0.929009 | − | 0.536363i | −0.0425107 | − | 0.999096i | \(-0.513536\pi\) |
−0.886498 | + | 0.462733i | \(0.846869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.98442 | + | 5.55075i | −0.224497 | + | 0.312749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0347 | + | 6.37090i | 0.619772 | + | 0.357826i | 0.776780 | − | 0.629772i | \(-0.216852\pi\) |
−0.157008 | + | 0.987597i | \(0.550185\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.69423 | + | 4.66654i | 0.150848 | + | 0.261276i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.5863 | −1.59553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.4025i | 1.80292i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.50245 | − | 1.75230i | 0.305221 | − | 0.0972000i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.8875 | − | 16.1009i | −1.54218 | − | 0.890380i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.5816 | + | 0.212945i | −1.35523 | + | 0.0117400i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9192 | + | 20.6446i | −0.655137 | + | 1.13473i | 0.326722 | + | 0.945120i | \(0.394056\pi\) |
−0.981859 | + | 0.189611i | \(0.939277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.91873 | − | 2.83983i | 0.269545 | − | 0.155622i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.1183 | + | 1.30957i | 0.662092 | + | 0.0715492i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7427i | 1.29335i | 0.762767 | + | 0.646673i | \(0.223840\pi\) | ||||
−0.762767 | + | 0.646673i | \(0.776160\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.7531 | − | 35.9454i | −1.12715 | − | 1.95229i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.92083 | − | 5.05903i | 0.158172 | − | 0.273962i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.481244 | − | 18.5140i | −0.0259848 | − | 0.999662i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7501 | + | 8.58960i | 0.632602 | + | 0.462448i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.19579 | − | 1.26774i | 0.117876 | − | 0.0680558i | −0.439903 | − | 0.898045i | \(-0.644987\pi\) |
0.557779 | + | 0.829990i | \(0.311654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.9321 | −1.33459 | −0.667293 | − | 0.744795i | \(-0.732547\pi\) | ||||
−0.667293 | + | 0.744795i | \(0.732547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.34363 | 0.231846 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.03574 | − | 1.17533i | 0.108351 | − | 0.0625567i | −0.444845 | − | 0.895608i | \(-0.646741\pi\) |
0.553196 | + | 0.833051i | \(0.313408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.41770 | + | 5.42252i | 0.393690 | + | 0.287798i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.318602 | − | 36.7782i | −0.0168622 | − | 1.94651i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.1508 | + | 27.9740i | −0.852407 | + | 1.47641i | 0.0266238 | + | 0.999646i | \(0.491524\pi\) |
−0.879030 | + | 0.476766i | \(0.841809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.78693 | − | 3.09506i | −0.0940491 | − | 0.162898i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 20.1830i | − | 1.05933i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3809 | + | 1.55408i | 0.752732 | + | 0.0813442i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.54302 | − | 3.77762i | 0.341543 | − | 0.197190i | −0.319411 | − | 0.947616i | \(-0.603485\pi\) |
0.660954 | + | 0.750426i | \(0.270152\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.59541 | − | 9.69153i | 0.291285 | − | 0.504521i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.29823 | + | 12.8977i | −0.378905 | + | 0.669613i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1708 | + | 14.5324i | 1.30329 | + | 0.752457i | 0.980968 | − | 0.194171i | \(-0.0622017\pi\) |
0.322327 | + | 0.946628i | \(0.395535\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.54225 | − | 22.3324i | −0.234561 | − | 1.15324i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.93792i | 0.305819i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.36318 | 0.480954 | 0.240477 | − | 0.970655i | \(-0.422696\pi\) | ||||
0.240477 | + | 0.970655i | \(0.422696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.365472 | + | 0.633016i | 0.0187237 | + | 0.0324304i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.67551 | − | 0.967354i | −0.0856143 | − | 0.0494295i | 0.456582 | − | 0.889682i | \(-0.349074\pi\) |
−0.542196 | + | 0.840252i | \(0.682407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.55441 | + | 5.64987i | 0.130185 | + | 0.287944i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.44717 | + | 4.29962i | 0.378561 | + | 0.218562i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.378695 | + | 0.655919i | 0.0192006 | + | 0.0332564i | 0.875466 | − | 0.483280i | \(-0.160555\pi\) |
−0.856265 | + | 0.516536i | \(0.827221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.7780 | −1.10136 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 31.6180i | − | 1.59492i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.25331 | + | 0.553618i | −0.0630608 | + | 0.0278555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.9755 | − | 16.7290i | −1.45424 | − | 0.839604i | −0.455519 | − | 0.890226i | \(-0.650546\pi\) |
−0.998718 | + | 0.0506216i | \(0.983880\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.0034 | + | 22.0786i | 0.650983 | + | 1.10531i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2506 | + | 26.4148i | −0.761577 | + | 1.31909i | 0.180460 | + | 0.983582i | \(0.442241\pi\) |
−0.942037 | + | 0.335508i | \(0.891092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.57490 | − | 3.21867i | 0.277705 | − | 0.160333i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.67413 | − | 24.7455i | 0.132878 | − | 1.22961i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.15410i | − | 0.255479i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.33683 | − | 16.1719i | −0.461676 | − | 0.799647i | 0.537368 | − | 0.843348i | \(-0.319419\pi\) |
−0.999045 | + | 0.0437007i | \(0.986085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.858559 | − | 1.48707i | 0.0423496 | − | 0.0733517i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.0123 | + | 14.1534i | 1.23078 | + | 0.696444i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.363717 | + | 0.497544i | −0.0178542 | + | 0.0244235i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.25834 | + | 3.03590i | −0.257502 | + | 0.148669i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.8449 | 1.70228 | 0.851142 | − | 0.524936i | \(-0.175911\pi\) | ||||
0.851142 | + | 0.524936i | \(0.175911\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.53106 | 0.269567 | 0.134784 | − | 0.990875i | \(-0.456966\pi\) | ||||
0.134784 | + | 0.990875i | \(0.456966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.29327 | + | 5.36547i | −0.451854 | + | 0.260878i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.2067 | + | 22.9649i | 1.22270 | + | 1.11396i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0764209 | − | 8.82175i | −0.00369826 | − | 0.426914i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.23369 | + | 2.13681i | −0.0595631 | + | 0.103166i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.28274 | − | 9.14998i | −0.254461 | − | 0.440739i | 0.710288 | − | 0.703911i | \(-0.248565\pi\) |
−0.964749 | + | 0.263172i | \(0.915231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.3654i | − | 0.690358i | −0.938537 | − | 0.345179i | \(-0.887818\pi\) | ||
0.938537 | − | 0.345179i | \(-0.112182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.2981 | + | 2.51771i | 1.11706 | + | 0.120715i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1394 | − | 7.58603i | 0.628542 | − | 0.362889i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8084 | − | 27.3809i | 0.754493 | − | 1.30682i | −0.191133 | − | 0.981564i | \(-0.561216\pi\) |
0.945626 | − | 0.325256i | \(-0.105451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.16300 | − | 6.93040i | −0.198238 | − | 0.330019i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3862 | − | 5.99650i | −0.493465 | − | 0.284902i | 0.232546 | − | 0.972585i | \(-0.425294\pi\) |
−0.726011 | + | 0.687683i | \(0.758628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.3132 | − | 15.5987i | 1.67400 | − | 0.739450i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.24812i | − | 0.106333i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.98107 | 0.235071 | 0.117536 | − | 0.993069i | \(-0.462501\pi\) | ||||
0.117536 | + | 0.993069i | \(0.462501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.07764 | − | 8.79473i | −0.239097 | − | 0.414128i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.1586 | + | 12.7933i | 1.04110 | + | 0.601081i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.675236 | + | 6.79930i | −0.0316556 | + | 0.318756i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.3640 | − | 13.4892i | −1.09292 | − | 0.631000i | −0.158570 | − | 0.987348i | \(-0.550689\pi\) |
−0.934353 | + | 0.356348i | \(0.884022\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.8244 | + | 22.2125i | 0.598592 | + | 1.03679i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.6886 | 1.05672 | 0.528358 | − | 0.849022i | \(-0.322808\pi\) | ||||
0.528358 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.0921i | − | 1.25908i | −0.776969 | − | 0.629539i | \(-0.783244\pi\) | ||
0.776969 | − | 0.629539i | \(-0.216756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.2650 | − | 23.2384i | −0.476027 | − | 1.07766i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.94459 | − | 2.27741i | −0.182534 | − | 0.105386i | 0.405949 | − | 0.913896i | \(-0.366941\pi\) |
−0.588483 | + | 0.808510i | \(0.700274\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.10255 | + | 12.5518i | −0.327965 | + | 0.579590i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.4754 | − | 37.1965i | 0.989534 | − | 1.71392i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.75805 | − | 3.90176i | 0.310735 | − | 0.179403i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.2075 | − | 5.07513i | −1.06483 | − | 0.232863i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.46907i | 0.296199i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.11469 | + | 7.12684i | 0.188005 | + | 0.325634i | 0.944585 | − | 0.328267i | \(-0.106465\pi\) |
−0.756580 | + | 0.653901i | \(0.773131\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.83983 | − | 4.91873i | 0.129485 | − | 0.224275i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.8392 | + | 8.73967i | −0.675206 | + | 0.397669i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0272 | + | 13.7166i | −0.455311 | + | 0.622838i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.4600 | + | 9.50316i | −0.745872 | + | 0.430629i | −0.824200 | − | 0.566298i | \(-0.808375\pi\) |
0.0783285 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.5706 | −2.01555 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2359 | 0.868102 | 0.434051 | − | 0.900888i | \(-0.357084\pi\) | ||||
0.434051 | + | 0.900888i | \(0.357084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.3654 | + | 17.5315i | −1.36759 | + | 0.789579i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.18509 | + | 1.59735i | 0.0982124 | + | 0.0717958i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.36783 | + | 5.51726i | −0.420204 | + | 0.247483i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.10526 | − | 10.5746i | 0.273309 | − | 0.473385i | −0.696398 | − | 0.717656i | \(-0.745215\pi\) |
0.969707 | + | 0.244271i | \(0.0785485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3630 | + | 17.9493i | 0.462986 | + | 0.801916i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.17917i | 0.0971646i | 0.998819 | + | 0.0485823i | \(0.0154703\pi\) | ||||
−0.998819 | + | 0.0485823i | \(0.984530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.135658 | − | 1.25533i | 0.00603671 | − | 0.0558616i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.5939 | − | 11.8899i | 0.914608 | − | 0.528049i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.22006 | − | 10.7735i | 0.275699 | − | 0.477525i | −0.694612 | − | 0.719384i | \(-0.744424\pi\) |
0.970311 | + | 0.241859i | \(0.0777573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.42868 | + | 14.8954i | −0.372863 | + | 0.658935i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.4748 | − | 8.93439i | −0.683230 | − | 0.394463i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.0784 | − | 31.8714i | −0.620368 | − | 1.40442i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.73797i | 0.428275i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.62753 | −0.0714405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.42724 | − | 16.3285i | −0.413015 | − | 0.715363i | 0.582203 | − | 0.813044i | \(-0.302191\pi\) |
−0.995218 | + | 0.0976807i | \(0.968858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4600 | + | 9.50316i | 0.719744 | + | 0.415544i | 0.814658 | − | 0.579941i | \(-0.196924\pi\) |
−0.0949146 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.3915 | + | 5.53230i | 1.15182 | + | 0.241449i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.9193 | + | 19.0060i | 1.43399 | + | 0.827914i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.40137 | − | 11.0875i | −0.278321 | − | 0.482065i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5454 | 0.544426 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.1908i | − | 0.484728i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6709 | + | 28.6849i | 0.547809 | + | 1.24016i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.4932 | − | 12.4091i | −0.927500 | − | 0.535493i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.33541 | + | 0.127100i | −0.315958 | + | 0.00547457i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.1810 | + | 21.0982i | −0.523703 | + | 0.907081i | 0.475916 | + | 0.879491i | \(0.342117\pi\) |
−0.999619 | + | 0.0275900i | \(0.991217\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.07193 | + | 4.08298i | −0.303486 | + | 0.175218i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.79531 | + | 35.1205i | −0.162573 | + | 1.50440i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.44667i | − | 0.147369i | −0.997282 | − | 0.0736845i | \(-0.976524\pi\) | ||
0.997282 | − | 0.0736845i | \(-0.0234758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.92554 | − | 3.33514i | −0.0821802 | − | 0.142340i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.2137 | − | 21.1547i | 0.520320 | − | 0.901220i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0140433 | − | 1.62111i | −0.000597181 | − | 0.0689365i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.0951 | − | 13.2279i | −0.768092 | − | 0.561495i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.3606 | + | 19.2607i | −1.41353 | + | 0.816104i | −0.995719 | − | 0.0924287i | \(-0.970537\pi\) |
−0.417814 | + | 0.908533i | \(0.637204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.59925 | 0.363709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.5697 | −0.615132 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.32476 | − | 5.38365i | 0.392992 | − | 0.226894i | −0.290464 | − | 0.956886i | \(-0.593810\pi\) |
0.683456 | + | 0.729992i | \(0.260476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.8707 | + | 36.7575i | −1.13046 | + | 1.54640i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.6308 | + | 14.5034i | 1.07639 | + | 0.609084i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.6853 | + | 20.2395i | −0.489873 | + | 0.848486i | −0.999932 | − | 0.0116540i | \(-0.996290\pi\) |
0.510059 | + | 0.860140i | \(0.329624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.78226 | + | 10.0152i | 0.241980 | + | 0.419122i | 0.961278 | − | 0.275580i | \(-0.0888698\pi\) |
−0.719298 | + | 0.694701i | \(0.755536\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.9625i | 1.41881i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.41103 | − | 15.5980i | 0.142250 | − | 0.650480i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.87268 | + | 1.08119i | −0.0779608 | + | 0.0450107i | −0.538474 | − | 0.842642i | \(-0.680999\pi\) |
0.460513 | + | 0.887653i | \(0.347666\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.56745 | + | 13.1072i | −0.314492 | + | 0.544717i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.370072 | − | 0.628349i | −0.0153532 | − | 0.0260683i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.08397 | + | 2.93523i | 0.210556 | + | 0.121565i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.20519 | + | 2.72836i | 0.0498283 | + | 0.112804i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.65367i | 0.0682544i | 0.999417 | + | 0.0341272i | \(0.0108651\pi\) | ||||
−0.999417 | + | 0.0341272i | \(0.989135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4818 | −1.09116 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.92507 | + | 3.33432i | 0.0791868 | + | 0.137155i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1592 | + | 12.7936i | 0.909971 | + | 0.525372i | 0.880422 | − | 0.474191i | \(-0.157260\pi\) |
0.0295491 | + | 0.999563i | \(0.490593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.7640 | + | 16.6216i | −1.50718 | + | 0.681421i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.4286 | − | 17.5680i | −1.24536 | − | 0.719010i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.88867 | + | 10.1995i | 0.240604 | + | 0.416739i | 0.960887 | − | 0.276942i | \(-0.0893210\pi\) |
−0.720282 | + | 0.693681i | \(0.755988\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5454 | 0.756484 | 0.378242 | − | 0.925707i | \(-0.376529\pi\) | ||||
0.378242 | + | 0.925707i | \(0.376529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.29562i | 0.256377i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.2527 | + | 8.94610i | −0.823387 | + | 0.363711i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.18915 | + | 3.57331i | 0.251210 | + | 0.145036i | 0.620318 | − | 0.784350i | \(-0.287003\pi\) |
−0.369108 | + | 0.929386i | \(0.620337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6550 | + | 24.1316i | −0.553330 | + | 0.977861i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.36547 | + | 9.29327i | −0.217064 | + | 0.375966i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.8182 | − | 10.2873i | 0.719669 | − | 0.415501i | −0.0949620 | − | 0.995481i | \(-0.530273\pi\) |
0.814631 | + | 0.579980i | \(0.196940\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −43.9083 | − | 4.74497i | −1.77055 | − | 0.191336i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.4857i | 1.79093i | 0.445134 | + | 0.895464i | \(0.353156\pi\) | ||||
−0.445134 | + | 0.895464i | \(0.646844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4068 | − | 24.9533i | −0.579058 | − | 1.00296i | −0.995588 | − | 0.0938359i | \(-0.970087\pi\) |
0.416530 | − | 0.909122i | \(-0.363246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.00487 | − | 10.4007i | 0.240967 | − | 0.417367i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.395683 | + | 45.6762i | 0.0158527 | + | 1.82998i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.3961 | + | 14.4568i | −0.815845 | + | 0.578270i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.79038 | − | 5.07513i | 0.351054 | − | 0.202681i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.5380 | 1.33725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 48.6854 | 1.93813 | 0.969067 | − | 0.246796i | \(-0.0793777\pi\) | ||||
0.969067 | + | 0.246796i | \(0.0793777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.27615 | + | 5.35559i | −0.368694 | + | 0.212866i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.473205 | − | 0.647317i | 0.0187786 | − | 0.0256880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.07046 | − | 3.92041i | −0.280142 | − | 0.155332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.37293 | + | 4.11003i | −0.0938716 | + | 0.162590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1248 | − | 31.3931i | −0.715888 | − | 1.23995i | −0.962616 | − | 0.270869i | \(-0.912689\pi\) |
0.246729 | − | 0.969085i | \(-0.420644\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.4717i | − | 0.689015i | −0.938784 | − | 0.344507i | \(-0.888046\pi\) | ||
0.938784 | − | 0.344507i | \(-0.111954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.64613 | − | 33.7400i | 0.143566 | − | 1.32851i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.77643 | + | 3.33502i | −0.227095 | + | 0.131113i | −0.609231 | − | 0.792993i | \(-0.708522\pi\) |
0.382136 | + | 0.924106i | \(0.375188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.69227 | − | 9.85931i | 0.223441 | − | 0.387012i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.0580 | − | 0.260386i | 1.17807 | − | 0.0102053i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.8781 | − | 8.01251i | −0.543091 | − | 0.313554i | 0.203240 | − | 0.979129i | \(-0.434853\pi\) |
−0.746331 | + | 0.665575i | \(0.768186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.7272 | + | 14.0147i | −1.23968 | + | 0.547599i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.47109i | 0.291475i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3934 | −0.482780 | −0.241390 | − | 0.970428i | \(-0.577603\pi\) | ||||
−0.241390 | + | 0.970428i | \(0.577603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.15660 | − | 10.6635i | −0.239464 | − | 0.414763i | 0.721097 | − | 0.692834i | \(-0.243638\pi\) |
−0.960561 | + | 0.278071i | \(0.910305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.9043 | − | 8.02767i | −0.540000 | − | 0.311769i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.3911 | − | 22.8346i | 0.635618 | − | 0.885487i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2182 | + | 8.20890i | 0.550532 | + | 0.317850i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.5307 | + | 23.4358i | 0.523127 | + | 0.906082i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.49473 | −0.134913 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.3139i | − | 0.397572i | −0.980043 | − | 0.198786i | \(-0.936300\pi\) | ||
0.980043 | − | 0.198786i | \(-0.0636998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.9179 | + | 5.70609i | −0.689659 | + | 0.219627i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.3265 | + | 15.1996i | 1.01181 | + | 0.584168i | 0.911721 | − | 0.410811i | \(-0.134754\pi\) |
0.100088 | + | 0.994979i | \(0.468088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2024 | − | 17.3227i | −0.391531 | − | 0.664785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0304 | − | 20.8372i | 0.461005 | − | 0.798484i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.3400 | + | 12.8980i | −0.854817 | + | 0.493529i | −0.862273 | − | 0.506444i | \(-0.830960\pi\) |
0.00745650 | + | 0.999972i | \(0.497626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.87276 | − | 0.202380i | −0.0715544 | − | 0.00773255i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 27.5021i | − | 1.04927i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.23454 | + | 5.60238i | 0.123226 | + | 0.213434i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.82266 | − | 13.5492i | 0.297588 | − | 0.515437i | −0.677996 | − | 0.735066i | \(-0.737151\pi\) |
0.975584 | + | 0.219629i | \(0.0704845\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.75955 | + | 1.62526i | −0.104827 | + | 0.0617386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.37714 | + | 3.93082i | 0.203966 | + | 0.149105i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 57.2278 | − | 33.0405i | 2.16766 | − | 1.25150i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.32496 | −0.0879379 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3083 | 1.14473 | 0.572365 | − | 0.819999i | \(-0.306026\pi\) | ||||
0.572365 | + | 0.819999i | \(0.306026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.2346 | + | 11.6825i | −0.763163 | + | 0.440612i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.1881 | + | 24.9924i | 1.28760 | + | 0.941268i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.30025 | + | 0.735754i | 0.0489008 | + | 0.0276709i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.3543 | − | 35.2547i | 0.764423 | − | 1.32402i | −0.176129 | − | 0.984367i | \(-0.556357\pi\) |
0.940551 | − | 0.339652i | \(-0.110309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.353843 | − | 0.612874i | −0.0132701 | − | 0.0229846i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 17.7986i | − | 0.666564i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.69102 | + | 0.290806i | 0.100638 | + | 0.0108755i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.20397 | + | 3.00451i | −0.194346 | + | 0.112206i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.63458 | − | 9.75938i | 0.210134 | − | 0.363963i | −0.741622 | − | 0.670818i | \(-0.765943\pi\) |
0.951756 | + | 0.306855i | \(0.0992765\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.2244 | − | 0.357118i | 1.53528 | − | 0.0132998i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.7351 | − | 10.8167i | −0.696765 | − | 0.402278i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.80045 | − | 24.4944i | −0.289701 | − | 0.909701i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5742i | 0.948495i | 0.880392 | + | 0.474248i | \(0.157280\pi\) | ||||
−0.880392 | + | 0.474248i | \(0.842720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.1427 | −0.375655 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.3889 | + | 43.9749i | 0.939044 | + | 1.62647i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.81251 | + | 3.93320i | 0.251626 | + | 0.145276i | 0.620508 | − | 0.784200i | \(-0.286926\pi\) |
−0.368883 | + | 0.929476i | \(0.620260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.3800 | + | 26.0794i | −0.677958 | + | 0.961954i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.94765 | + | 2.85653i | 0.182249 | + | 0.105222i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.02574 | + | 12.1689i | 0.258446 | + | 0.447641i | 0.965826 | − | 0.259192i | \(-0.0834563\pi\) |
−0.707380 | + | 0.706834i | \(0.750123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.1853 | 0.410902 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.3464i | − | 0.416258i | −0.978101 | − | 0.208129i | \(-0.933263\pi\) | ||
0.978101 | − | 0.208129i | \(-0.0667374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.25588 | + | 0.996479i | −0.0826491 | + | 0.0365082i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.275681 | − | 0.159165i | −0.0100866 | − | 0.00582353i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.1029 | + | 0.321414i | −1.35571 | + | 0.0117442i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0968 | − | 41.7369i | 0.879306 | − | 1.52300i | 0.0272012 | − | 0.999630i | \(-0.491341\pi\) |
0.852104 | − | 0.523372i | \(-0.175326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.7339 | + | 12.5481i | −0.792028 | + | 0.457278i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.01564 | − | 27.9057i | 0.109750 | − | 1.01559i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 20.3236i | − | 0.738676i | −0.929295 | − | 0.369338i | \(-0.879585\pi\) | ||
0.929295 | − | 0.369338i | \(-0.120415\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.41103 | + | 5.90808i | 0.123813 | + | 0.214450i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.46441 | + | 6.00054i | −0.125585 | + | 0.217519i | −0.921961 | − | 0.387282i | \(-0.873414\pi\) |
0.796377 | + | 0.604801i | \(0.206747\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.3770 | − | 20.5842i | −1.31693 | − | 0.745197i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.3941 | + | 14.2185i | −0.375798 | + | 0.514070i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.8647 | − | 6.27272i | 0.392300 | − | 0.226495i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.5653 | 1.17434 | 0.587168 | − | 0.809465i | \(-0.300243\pi\) | ||||
0.587168 | + | 0.809465i | \(0.300243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.1778 | −1.30291 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.2562 | − | 15.7364i | 0.980338 | − | 0.565998i | 0.0779655 | − | 0.996956i | \(-0.475158\pi\) |
0.902372 | + | 0.430958i | \(0.141824\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.7687 | + | 20.6008i | −0.674191 | + | 0.740004i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.8523 | − | 13.4591i | 0.819821 | − | 0.482841i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.0183 | + | 39.8689i | −0.824717 | + | 1.42845i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.15335 | + | 3.72971i | 0.0770529 | + | 0.133460i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 19.3359i | − | 0.691010i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.8438 | − | 5.06220i | −1.67193 | − | 0.180678i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7737 | − | 22.9633i | 1.41778 | − | 0.818555i | 0.421675 | − | 0.906747i | \(-0.361442\pi\) |
0.996103 | + | 0.0881921i | \(0.0281089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.25581 | + | 7.37128i | −0.151511 | + | 0.262424i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.3402 | − | 46.4212i | −0.972104 | − | 1.65055i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.33514 | − | 1.92554i | −0.118434 | − | 0.0683781i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.3530 | − | 10.3156i | 0.828245 | − | 0.365857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 13.5988i | − | 0.481696i | −0.970563 | − | 0.240848i | \(-0.922575\pi\) | ||
0.970563 | − | 0.240848i | \(-0.0774255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.3654 | −2.24171 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.96986 | + | 17.2683i | 0.352268 | + | 0.610145i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.87144 | + | 3.38988i | 0.207199 | + | 0.119626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.3473 | + | 11.0165i | 0.540921 | + | 0.388282i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.3706 | + | 26.7721i | 1.63232 | + | 0.942421i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.53756 | + | 14.7875i | 0.300165 | + | 0.519900i | 0.976173 | − | 0.216994i | \(-0.0696251\pi\) |
−0.676009 | + | 0.736894i | \(0.736292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.7020 | −1.25367 | −0.626833 | − | 0.779153i | \(-0.715649\pi\) | ||||
−0.626833 | + | 0.779153i | \(0.715649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.6242i | 1.88068i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.7559 | + | 44.7245i | 0.692019 | + | 1.56663i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.6360 | − | 17.6877i | −1.07182 | − | 0.618815i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.52903 | + | 0.0305712i | −0.123314 | + | 0.00106824i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.23349 | − | 14.2608i | 0.287351 | − | 0.497706i | −0.685826 | − | 0.727766i | \(-0.740559\pi\) |
0.973177 | + | 0.230060i | \(0.0738922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.1493 | − | 14.5200i | 0.876651 | − | 0.506135i | 0.00709835 | − | 0.999975i | \(-0.497741\pi\) |
0.869553 | + | 0.493840i | \(0.164407\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.28201 | − | 10.4352i | 0.0794495 | − | 0.363307i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.8903i | 1.66531i | 0.553794 | + | 0.832654i | \(0.313179\pi\) | ||||
−0.553794 | + | 0.832654i | \(0.686821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0593 | + | 20.8873i | 0.418836 | + | 0.725446i | 0.995823 | − | 0.0913081i | \(-0.0291048\pi\) |
−0.576986 | + | 0.816754i | \(0.695771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.3337 | + | 36.9511i | −0.740058 | + | 1.28182i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.827043 | − | 47.7319i | −0.0286553 | − | 1.65381i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.4178 | − | 18.3548i | 0.464344 | − | 0.635195i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.1538 | + | 10.4811i | −0.627487 | + | 0.362280i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1230 | −0.867343 | −0.433672 | − | 0.901071i | \(-0.642782\pi\) | ||||
−0.433672 | + | 0.901071i | \(0.642782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.56701 | −0.0885175 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.7320 | − | 16.0111i | 0.955141 | − | 0.551451i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.0592 | − | 15.3948i | −0.724458 | − | 0.529597i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.226930 | − | 26.1960i | −0.00779742 | − | 0.900106i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.0161 | − | 19.0804i | 0.378071 | − | 0.654838i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.85186 | − | 13.5998i | −0.269158 | − | 0.466196i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78647i | 0.0954069i | 0.998862 | + | 0.0477035i | \(0.0151902\pi\) | ||||
−0.998862 | + | 0.0477035i | \(0.984810\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.31830 | − | 12.1991i | 0.0450850 | − | 0.417201i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.2071 | + | 16.8627i | −0.997694 | + | 0.576019i | −0.907565 | − | 0.419911i | \(-0.862061\pi\) |
−0.0901287 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.55853 | − | 16.5559i | 0.326133 | − | 0.564879i | −0.655608 | − | 0.755101i | \(-0.727588\pi\) |
0.981741 | + | 0.190223i | \(0.0609210\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.7348 | − | 45.4792i | 0.877038 | − | 1.54993i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6167 | + | 16.5218i | 0.974122 | + | 0.562410i | 0.900490 | − | 0.434876i | \(-0.143208\pi\) |
0.0736318 | + | 0.997285i | \(0.476541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.721401 | + | 1.63315i | 0.0245284 | + | 0.0555286i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 60.1533i | − | 2.04291i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.642200 | −0.0217852 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14781 | + | 5.45217i | 0.106659 | + | 0.184740i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.60015 | − | 4.38795i | −0.257226 | − | 0.148510i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.14661 | − | 28.9347i | −0.207793 | − | 0.978173i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.160302 | − | 0.0925506i | −0.00541303 | − | 0.00312521i | 0.497291 | − | 0.867584i | \(-0.334328\pi\) |
−0.502704 | + | 0.864459i | \(0.667661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1092 | + | 17.5096i | 0.340974 | + | 0.590583i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.7063 | 1.47250 | 0.736252 | − | 0.676708i | \(-0.236594\pi\) | ||||
0.736252 | + | 0.676708i | \(0.236594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.70129i | − | 0.158211i | −0.996866 | − | 0.0791055i | \(-0.974794\pi\) | ||
0.996866 | − | 0.0791055i | \(-0.0252064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0050 | − | 45.2883i | −0.672460 | − | 1.52235i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.0933 | − | 14.4876i | −0.842550 | − | 0.486447i | 0.0155799 | − | 0.999879i | \(-0.495041\pi\) |
−0.858130 | + | 0.513432i | \(0.828374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.481473 | + | 0.817499i | 0.0161481 | + | 0.0274180i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.83302 | − | 10.1031i | 0.195413 | − | 0.338466i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2305 | − | 22.0724i | 1.27934 | − | 0.738625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.92508 | + | 27.0677i | −0.0977748 | + | 0.904774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.51771i | 0.251009i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.3281 | − | 24.8170i | −0.477868 | − | 0.827692i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.0997 | + | 33.0816i | −0.636303 | + | 1.10211i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.9471 | + | 19.7751i | 1.16297 | + | 0.658074i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.23171 | + | 5.28656i | 0.240390 | + | 0.175731i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.1475 | + | 17.9830i | −1.03424 | + | 0.597117i | −0.918196 | − | 0.396127i | \(-0.870354\pi\) |
−0.116041 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.652164 | 0.0216309 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1414 | 0.965499 | 0.482749 | − | 0.875759i | \(-0.339638\pi\) | ||||
0.482749 | + | 0.875759i | \(0.339638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.250171 | + | 0.144436i | −0.00827946 | + | 0.00478015i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.96919 | + | 12.2693i | −0.296512 | + | 0.405611i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.355502 | − | 41.0379i | −0.0117397 | − | 1.35519i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8007 | − | 23.9035i | 0.455243 | − | 0.788503i | −0.543459 | − | 0.839435i | \(-0.682886\pi\) |
0.998702 | + | 0.0509320i | \(0.0162192\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.75464 | + | 9.96733i | 0.189622 | + | 0.328435i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.74585i | 0.156212i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.25298 | + | 24.0208i | −0.172717 | + | 0.789799i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5853 | − | 8.99815i | 0.511887 | − | 0.295538i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.7143 | − | 35.8783i | 0.679616 | − | 1.17713i | −0.295481 | − | 0.955349i | \(-0.595480\pi\) |
0.975097 | − | 0.221780i | \(-0.0711867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.1257 | + | 28.5102i | 0.561271 | + | 0.934384i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2169 | − | 12.2496i | −0.694609 | − | 0.401033i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.45800 | + | 14.6200i | 0.211199 | + | 0.478124i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.6450i | 0.576438i | 0.957564 | + | 0.288219i | \(0.0930632\pi\) | ||||
−0.957564 | + | 0.288219i | \(0.906937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.6851 | −1.26244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0502 | − | 20.8716i | −0.392827 | − | 0.680396i | 0.599995 | − | 0.800004i | \(-0.295169\pi\) |
−0.992821 | + | 0.119609i | \(0.961836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.7962 | − | 15.4708i | −0.872603 | − | 0.503798i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.19880 | − | 22.1409i | 0.0715270 | − | 0.720243i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.34994 | − | 4.82084i | −0.271337 | − | 0.156656i | 0.358158 | − | 0.933661i | \(-0.383405\pi\) |
−0.629495 | + | 0.777005i | \(0.716738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.73555 | + | 6.47016i | 0.121261 | + | 0.210030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9725 | 0.842216 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.3033i | − | 0.398544i | −0.979944 | − | 0.199272i | \(-0.936142\pi\) | ||
0.979944 | − | 0.199272i | \(-0.0638577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.0798 | − | 15.0539i | 1.10280 | − | 0.487132i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.51213 | + | 5.49183i | 0.307484 | + | 0.177526i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.09763 | − | 1.93976i | 0.0354442 | − | 0.0626381i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0331498 | + | 0.0574172i | −0.00106935 | + | 0.00185217i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.0271 | + | 8.09853i | −0.452016 | + | 0.260972i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5067 | + | 1.78380i | 0.531370 | + | 0.0574227i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.7098i | 0.505193i | 0.967572 | + | 0.252597i | \(0.0812846\pi\) | ||||
−0.967572 | + | 0.252597i | \(0.918715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.0241 | + | 57.1995i | 1.06089 | + | 1.83751i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.35791 | − | 4.08402i | 0.0756689 | − | 0.131062i | −0.825708 | − | 0.564098i | \(-0.809224\pi\) |
0.901377 | + | 0.433035i | \(0.142557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.79080 | + | 3.99950i | −0.217703 | + | 0.128218i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.92744 | − | 8.70130i | 0.253881 | − | 0.278665i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.1247 | + | 14.5057i | −0.803809 | + | 0.464079i | −0.844801 | − | 0.535080i | \(-0.820281\pi\) |
0.0409922 | + | 0.999159i | \(0.486948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0946 | 0.578306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.2456 | −0.582537 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6697 | + | 14.8204i | −0.818735 | + | 0.472697i | −0.849980 | − | 0.526815i | \(-0.823386\pi\) |
0.0312448 | + | 0.999512i | \(0.490053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.49254 | − | 3.40965i | 0.0794189 | − | 0.108640i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.1763 | + | 25.4290i | −1.37432 | + | 0.809415i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.8881 | − | 20.5907i | 0.378018 | − | 0.654746i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5139 | − | 33.7991i | −0.619879 | − | 1.07366i | −0.989507 | − | 0.144483i | \(-0.953848\pi\) |
0.369628 | − | 0.929180i | \(-0.379485\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 48.5913i | 1.54200i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.14114 | + | 38.3207i | −0.131283 | + | 1.21485i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7136 | + | 6.18548i | −0.339302 | + | 0.195896i | −0.659963 | − | 0.751298i | \(-0.729428\pi\) |
0.320661 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.24747 | + | 16.0171i | −0.292577 | + | 0.506758i |
(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 | 280.2.bg.a.9.9 | yes | 24 | |
4.3 | odd | 2 | 560.2.bw.f.289.4 | 24 | |||
5.2 | odd | 4 | 1400.2.q.o.401.2 | 12 | |||
5.3 | odd | 4 | 1400.2.q.n.401.5 | 12 | |||
5.4 | even | 2 | inner | 280.2.bg.a.9.4 | ✓ | 24 | |
7.2 | even | 3 | 1960.2.g.f.1569.9 | 12 | |||
7.4 | even | 3 | inner | 280.2.bg.a.249.4 | yes | 24 | |
7.5 | odd | 6 | 1960.2.g.e.1569.4 | 12 | |||
20.19 | odd | 2 | 560.2.bw.f.289.9 | 24 | |||
28.11 | odd | 6 | 560.2.bw.f.529.9 | 24 | |||
35.2 | odd | 12 | 9800.2.a.cv.1.5 | 6 | |||
35.4 | even | 6 | inner | 280.2.bg.a.249.9 | yes | 24 | |
35.9 | even | 6 | 1960.2.g.f.1569.4 | 12 | |||
35.12 | even | 12 | 9800.2.a.cy.1.2 | 6 | |||
35.18 | odd | 12 | 1400.2.q.n.1201.5 | 12 | |||
35.19 | odd | 6 | 1960.2.g.e.1569.9 | 12 | |||
35.23 | odd | 12 | 9800.2.a.cx.1.2 | 6 | |||
35.32 | odd | 12 | 1400.2.q.o.1201.2 | 12 | |||
35.33 | even | 12 | 9800.2.a.cw.1.5 | 6 | |||
140.39 | odd | 6 | 560.2.bw.f.529.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.4 | ✓ | 24 | 5.4 | even | 2 | inner | |
280.2.bg.a.9.9 | yes | 24 | 1.1 | even | 1 | trivial | |
280.2.bg.a.249.4 | yes | 24 | 7.4 | even | 3 | inner | |
280.2.bg.a.249.9 | yes | 24 | 35.4 | even | 6 | inner | |
560.2.bw.f.289.4 | 24 | 4.3 | odd | 2 | |||
560.2.bw.f.289.9 | 24 | 20.19 | odd | 2 | |||
560.2.bw.f.529.4 | 24 | 140.39 | odd | 6 | |||
560.2.bw.f.529.9 | 24 | 28.11 | odd | 6 | |||
1400.2.q.n.401.5 | 12 | 5.3 | odd | 4 | |||
1400.2.q.n.1201.5 | 12 | 35.18 | odd | 12 | |||
1400.2.q.o.401.2 | 12 | 5.2 | odd | 4 | |||
1400.2.q.o.1201.2 | 12 | 35.32 | odd | 12 | |||
1960.2.g.e.1569.4 | 12 | 7.5 | odd | 6 | |||
1960.2.g.e.1569.9 | 12 | 35.19 | odd | 6 | |||
1960.2.g.f.1569.4 | 12 | 35.9 | even | 6 | |||
1960.2.g.f.1569.9 | 12 | 7.2 | even | 3 | |||
9800.2.a.cv.1.5 | 6 | 35.2 | odd | 12 | |||
9800.2.a.cw.1.5 | 6 | 35.33 | even | 12 | |||
9800.2.a.cx.1.2 | 6 | 35.23 | odd | 12 | |||
9800.2.a.cy.1.2 | 6 | 35.12 | even | 12 |