Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(95,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("384.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.k (of order \(4\), 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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.163368480538624.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Root | \(0.204810 + 1.39930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.95 |
Dual form | 384.2.k.b.287.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.814141 | − | 1.52878i | 0.470045 | − | 0.882643i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.08397 | − | 2.08397i | −0.931979 | − | 0.931979i | 0.0658506 | − | 0.997829i | \(-0.479024\pi\) |
−0.997829 | + | 0.0658506i | \(0.979024\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14637 | −0.433285 | −0.216643 | − | 0.976251i | \(-0.569511\pi\) | ||||
−0.216643 | + | 0.976251i | \(0.569511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.67435 | − | 2.48929i | −0.558116 | − | 0.829763i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67435 | + | 1.67435i | −0.504835 | + | 0.504835i | −0.912937 | − | 0.408102i | \(-0.866191\pi\) |
0.408102 | + | 0.912937i | \(0.366191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.146365 | − | 0.146365i | −0.0405945 | − | 0.0405945i | 0.686518 | − | 0.727113i | \(-0.259138\pi\) |
−0.727113 | + | 0.686518i | \(0.759138\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.88258 | + | 1.48929i | −1.26068 | + | 0.384533i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.59722i | − | 1.35752i | −0.734358 | − | 0.678762i | \(-0.762517\pi\) | ||
0.734358 | − | 0.678762i | \(-0.237483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.48929 | + | 1.48929i | −0.341666 | + | 0.341666i | −0.856993 | − | 0.515327i | \(-0.827670\pi\) |
0.515327 | + | 0.856993i | \(0.327670\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.933303 | + | 1.75254i | −0.203663 | + | 0.382436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34870i | 0.698252i | 0.937076 | + | 0.349126i | \(0.113521\pi\) | ||||
−0.937076 | + | 0.349126i | \(0.886479\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.68585i | 0.737169i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.16874 | + | 0.533081i | −0.994724 | + | 0.102592i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51325 | − | 3.51325i | 0.652394 | − | 0.652394i | −0.301175 | − | 0.953569i | \(-0.597379\pi\) |
0.953569 | + | 0.301175i | \(0.0973788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.83221i | − | 1.04750i | −0.851873 | − | 0.523748i | \(-0.824533\pi\) | ||
0.851873 | − | 0.523748i | \(-0.175467\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.19656 | + | 3.92287i | 0.208294 | + | 0.682884i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.38899 | + | 2.38899i | 0.403813 | + | 0.403813i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.83221 | − | 4.83221i | 0.794411 | − | 0.794411i | −0.187797 | − | 0.982208i | \(-0.560135\pi\) |
0.982208 | + | 0.187797i | \(0.0601348\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.342923 | + | 0.104599i | −0.0549116 | + | 0.0167492i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.610042 | 0.0952726 | 0.0476363 | − | 0.998865i | \(-0.484831\pi\) | ||||
0.0476363 | + | 0.998865i | \(0.484831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48929 | + | 1.48929i | 0.227114 | + | 0.227114i | 0.811486 | − | 0.584372i | \(-0.198659\pi\) |
−0.584372 | + | 0.811486i | \(0.698659\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.69831 | + | 8.67689i | −0.253169 | + | 1.29347i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.41646 | 0.935936 | 0.467968 | − | 0.883745i | \(-0.344986\pi\) | ||||
0.467968 | + | 0.883745i | \(0.344986\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.68585 | −0.812264 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.55693 | − | 4.55693i | −1.19821 | − | 0.638097i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.164553 | − | 0.164553i | −0.0226031 | − | 0.0226031i | 0.695715 | − | 0.718318i | \(-0.255088\pi\) |
−0.718318 | + | 0.695715i | \(0.755088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.97858 | 0.940991 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.06431 | + | 3.48929i | 0.140971 | + | 0.462168i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.05051 | − | 9.05051i | 1.17828 | − | 1.17828i | 0.198093 | − | 0.980183i | \(-0.436525\pi\) |
0.980183 | − | 0.198093i | \(-0.0634749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.53948 | − | 4.53948i | −0.581221 | − | 0.581221i | 0.354018 | − | 0.935239i | \(-0.384815\pi\) |
−0.935239 | + | 0.354018i | \(0.884815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.91942 | + | 2.85363i | 0.241824 | + | 0.359524i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.610042i | 0.0756664i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.635654 | − | 0.635654i | 0.0776575 | − | 0.0776575i | −0.667211 | − | 0.744869i | \(-0.732512\pi\) |
0.744869 | + | 0.667211i | \(0.232512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.11943 | + | 2.72631i | 0.616307 | + | 0.328209i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.90659i | − | 0.819662i | −0.912162 | − | 0.409831i | \(-0.865588\pi\) | ||
0.912162 | − | 0.409831i | \(-0.134412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.07896i | − | 0.828530i | −0.910156 | − | 0.414265i | \(-0.864039\pi\) | ||
0.910156 | − | 0.414265i | \(-0.135961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.63485 | + | 3.00080i | 0.650657 | + | 0.346502i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.91942 | − | 1.91942i | 0.218738 | − | 0.218738i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.83221i | 1.10621i | 0.833111 | + | 0.553105i | \(0.186557\pi\) | ||||
−0.833111 | + | 0.553105i | \(0.813443\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39312 | + | 8.33587i | −0.377013 | + | 0.926208i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.09081 | + | 8.09081i | 0.888081 | + | 0.888081i | 0.994339 | − | 0.106257i | \(-0.0338867\pi\) |
−0.106257 | + | 0.994339i | \(0.533887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.6644 | + | 11.6644i | −1.26518 | + | 1.26518i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.51071 | − | 8.23127i | −0.269177 | − | 0.882485i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.490134 | 0.0519541 | 0.0259770 | − | 0.999663i | \(-0.491730\pi\) | ||||
0.0259770 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.167788 | + | 0.167788i | 0.0175890 | + | 0.0175890i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.91618 | − | 4.74824i | −0.924565 | − | 0.492370i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.20726 | 0.636851 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3503 | 1.25398 | 0.626990 | − | 0.779027i | \(-0.284287\pi\) | ||||
0.626990 | + | 0.779027i | \(0.284287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.97138 | + | 1.36449i | 0.700650 | + | 0.137137i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.29123 | + | 8.29123i | 0.825008 | + | 0.825008i | 0.986821 | − | 0.161813i | \(-0.0517343\pi\) |
−0.161813 | + | 0.986821i | \(0.551734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2253 | −1.20460 | −0.602299 | − | 0.798271i | \(-0.705748\pi\) | ||||
−0.602299 | + | 0.798271i | \(0.705748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.59722 | − | 1.70727i | 0.546233 | − | 0.166612i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.714641 | − | 0.714641i | 0.0690869 | − | 0.0690869i | −0.671719 | − | 0.740806i | \(-0.734444\pi\) |
0.740806 | + | 0.671719i | \(0.234444\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4966 | + | 12.4966i | 1.19696 | + | 1.19696i | 0.975072 | + | 0.221888i | \(0.0712221\pi\) |
0.221888 | + | 0.975072i | \(0.428778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.45330 | − | 11.3215i | −0.327772 | − | 1.07459i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.47731i | 0.515262i | 0.966243 | + | 0.257631i | \(0.0829419\pi\) | ||||
−0.966243 | + | 0.257631i | \(0.917058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.97858 | − | 6.97858i | 0.650756 | − | 0.650756i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.119279 | + | 0.609413i | −0.0110274 | + | 0.0563402i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.41646i | 0.588196i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.39312i | 0.490283i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.496660 | − | 0.932621i | 0.0447824 | − | 0.0840916i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.73865 | + | 2.73865i | −0.244953 | + | 0.244953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.20390i | 0.639243i | 0.947545 | + | 0.319622i | \(0.103556\pi\) | ||||
−0.947545 | + | 0.319622i | \(0.896444\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.48929 | − | 1.06431i | 0.307215 | − | 0.0937069i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.05051 | − | 9.05051i | −0.790747 | − | 0.790747i | 0.190869 | − | 0.981616i | \(-0.438870\pi\) |
−0.981616 | + | 0.190869i | \(0.938870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70727 | − | 1.70727i | 0.148039 | − | 0.148039i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.8824 | + | 9.66056i | 1.02267 | + | 0.831448i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.4430 | 1.14851 | 0.574255 | − | 0.818677i | \(-0.305292\pi\) | ||||
0.574255 | + | 0.818677i | \(0.305292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.63565 | − | 8.63565i | −0.732467 | − | 0.732467i | 0.238641 | − | 0.971108i | \(-0.423298\pi\) |
−0.971108 | + | 0.238641i | \(0.923298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.22390 | − | 9.80936i | 0.439932 | − | 0.826097i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.490134 | 0.0409870 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.6430 | −1.21603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.62908 | + | 8.69242i | −0.381800 | + | 0.716939i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6399 | − | 11.6399i | −0.953580 | − | 0.953580i | 0.0453896 | − | 0.998969i | \(-0.485547\pi\) |
−0.998969 | + | 0.0453896i | \(0.985547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.810789 | −0.0659811 | −0.0329905 | − | 0.999456i | \(-0.510503\pi\) | ||||
−0.0329905 | + | 0.999456i | \(0.510503\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.9331 | + | 9.37169i | −1.12642 | + | 0.757656i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.1541 | + | 12.1541i | −0.976244 | + | 0.976244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.51806 | − | 5.51806i | −0.440389 | − | 0.440389i | 0.451754 | − | 0.892143i | \(-0.350799\pi\) |
−0.892143 | + | 0.451754i | \(0.850799\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.385535 | + | 0.117596i | −0.0305749 | + | 0.00932599i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.83883i | − | 0.302542i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0748 | + | 10.0748i | −0.789115 | + | 0.789115i | −0.981349 | − | 0.192234i | \(-0.938427\pi\) |
0.192234 | + | 0.981349i | \(0.438427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.68155 | − | 10.6687i | 0.442308 | − | 0.830559i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.36843i | − | 0.183275i | −0.995792 | − | 0.0916373i | \(-0.970790\pi\) | ||
0.995792 | − | 0.0916373i | \(-0.0292100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9572i | − | 0.996704i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.20086 | + | 1.21368i | 0.474191 | + | 0.0928125i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.22347 | + | 5.22347i | −0.397133 | + | 0.397133i | −0.877221 | − | 0.480088i | \(-0.840605\pi\) |
0.480088 | + | 0.877221i | \(0.340605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.22533i | − | 0.319405i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.46787 | − | 21.2047i | −0.486155 | − | 1.59384i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.13110 | − | 7.13110i | −0.533003 | − | 0.533003i | 0.388462 | − | 0.921465i | \(-0.373007\pi\) |
−0.921465 | + | 0.388462i | \(0.873007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.73183 | − | 6.73183i | 0.500373 | − | 0.500373i | −0.411181 | − | 0.911554i | \(-0.634884\pi\) |
0.911554 | + | 0.411181i | \(0.134884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.6357 | + | 3.24410i | −0.786210 | + | 0.239811i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.1403 | −1.48075 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.37169 | + | 9.37169i | 0.685326 | + | 0.685326i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.92526 | − | 0.611106i | 0.430999 | − | 0.0444514i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.5284 | −1.84717 | −0.923584 | − | 0.383396i | \(-0.874754\pi\) | ||||
−0.923584 | + | 0.383396i | \(0.874754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.07896 | 0.653518 | 0.326759 | − | 0.945108i | \(-0.394043\pi\) | ||||
0.326759 | + | 0.945108i | \(0.394043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.932621 | + | 0.496660i | 0.0667864 | + | 0.0355666i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.18414 | − | 3.18414i | −0.226861 | − | 0.226861i | 0.584519 | − | 0.811380i | \(-0.301283\pi\) |
−0.811380 | + | 0.584519i | \(0.801283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5542 | 1.38616 | 0.693079 | − | 0.720861i | \(-0.256254\pi\) | ||||
0.693079 | + | 0.720861i | \(0.256254\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.454264 | − | 1.48929i | −0.0320413 | − | 0.105046i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.02747 | + | 4.02747i | −0.282673 | + | 0.282673i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.27131 | − | 1.27131i | −0.0887920 | − | 0.0887920i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.33587 | − | 5.60688i | 0.579383 | − | 0.389705i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.98718i | − | 0.344970i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3429 | − | 10.3429i | 0.712036 | − | 0.712036i | −0.254925 | − | 0.966961i | \(-0.582051\pi\) |
0.966961 | + | 0.254925i | \(0.0820507\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.5587 | − | 5.62294i | −0.723468 | − | 0.385277i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6.20726i | − | 0.423332i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.68585i | 0.453865i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.8222 | − | 5.76327i | −0.731296 | − | 0.389446i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.819240 | + | 0.819240i | −0.0551080 | + | 0.0551080i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.6184i | − | 1.51464i | −0.653042 | − | 0.757321i | \(-0.726508\pi\) | ||
0.653042 | − | 0.757321i | \(-0.273492\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.17513 | − | 6.17139i | 0.611676 | − | 0.411426i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.46515 | − | 1.46515i | −0.0972455 | − | 0.0972455i | 0.656810 | − | 0.754056i | \(-0.271905\pi\) |
−0.754056 | + | 0.656810i | \(0.771905\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.51806 | − | 7.51806i | 0.496807 | − | 0.496807i | −0.413635 | − | 0.910443i | \(-0.635741\pi\) |
0.910443 | + | 0.413635i | \(0.135741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.37169 | − | 4.49704i | −0.0902507 | − | 0.295884i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3820 | −1.20424 | −0.602121 | − | 0.798405i | \(-0.705678\pi\) | ||||
−0.602121 | + | 0.798405i | \(0.705678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3717 | − | 13.3717i | −0.872273 | − | 0.872273i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0313 | + | 8.00481i | 0.976388 | + | 0.519968i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5322 | −0.875328 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.87819 | 0.314232 | 0.157116 | − | 0.987580i | \(-0.449780\pi\) | ||||
0.157116 | + | 0.987580i | \(0.449780\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.98126 | + | 11.9739i | 0.640298 | + | 0.768127i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.8491 | + | 11.8491i | 0.757013 | + | 0.757013i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.435961 | 0.0277395 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.9561 | − | 5.78202i | 1.20130 | − | 0.366421i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.23224 | + | 5.23224i | −0.330256 | + | 0.330256i | −0.852684 | − | 0.522427i | \(-0.825027\pi\) |
0.522427 | + | 0.852684i | \(0.325027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.60688 | − | 5.60688i | −0.352502 | − | 0.352502i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.33587 | + | 27.3288i | 0.522013 | + | 1.71140i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8329i | 0.800495i | 0.916407 | + | 0.400248i | \(0.131076\pi\) | ||||
−0.916407 | + | 0.400248i | \(0.868924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.53948 | + | 5.53948i | −0.344207 | + | 0.344207i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.6279 | − | 2.86309i | −0.905444 | − | 0.177221i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.3152i | 1.74599i | 0.487729 | + | 0.872995i | \(0.337825\pi\) | ||||
−0.487729 | + | 0.872995i | \(0.662175\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.685846i | 0.0421312i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.399038 | − | 0.749307i | 0.0244207 | − | 0.0458569i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.58101 | + | 6.58101i | −0.401251 | + | 0.401251i | −0.878674 | − | 0.477423i | \(-0.841571\pi\) |
0.477423 | + | 0.878674i | \(0.341571\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.66129i | 0.526136i | 0.964777 | + | 0.263068i | \(0.0847343\pi\) | ||||
−0.964777 | + | 0.263068i | \(0.915266\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.393115 | − | 0.119908i | 0.0237924 | − | 0.00725719i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.17139 | − | 6.17139i | −0.372149 | − | 0.372149i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.1249 | + | 13.1249i | −0.788601 | + | 0.788601i | −0.981265 | − | 0.192664i | \(-0.938287\pi\) |
0.192664 | + | 0.981265i | \(0.438287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5181 | + | 9.76515i | −0.869173 | + | 0.584624i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1560 | 1.56033 | 0.780167 | − | 0.625571i | \(-0.215134\pi\) | ||||
0.780167 | + | 0.625571i | \(0.215134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9070 | + | 17.9070i | 1.06446 | + | 1.06446i | 0.997774 | + | 0.0666843i | \(0.0212420\pi\) |
0.0666843 | + | 0.997774i | \(0.478758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.05359 | − | 9.48955i | 0.299349 | − | 0.562112i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.699331 | −0.0412802 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3288 | −0.842873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0549 | − | 18.8809i | 0.589426 | − | 1.10682i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.654687 | + | 0.654687i | 0.0382472 | + | 0.0382472i | 0.725972 | − | 0.687725i | \(-0.241390\pi\) |
−0.687725 | + | 0.725972i | \(0.741390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.7220 | −2.19626 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.76170 | − | 9.54683i | 0.450379 | − | 0.553963i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.490134 | − | 0.490134i | 0.0283452 | − | 0.0283452i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.70727 | − | 1.70727i | −0.0984054 | − | 0.0984054i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.4257 | − | 5.92525i | 1.11598 | − | 0.340397i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.9203i | 1.08337i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.971231 | − | 0.971231i | 0.0554311 | − | 0.0554311i | −0.678848 | − | 0.734279i | \(-0.737520\pi\) |
0.734279 | + | 0.678848i | \(0.237520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.95314 | + | 18.6899i | −0.566214 | + | 1.06323i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 33.1343i | − | 1.87887i | −0.342723 | − | 0.939437i | \(-0.611349\pi\) | ||
0.342723 | − | 0.939437i | \(-0.388651\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2285i | 0.747717i | 0.927486 | + | 0.373858i | \(0.121965\pi\) | ||||
−0.927486 | + | 0.373858i | \(0.878035\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.94688 | − | 9.94688i | 0.109694 | − | 0.560443i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.89038 | − | 7.89038i | 0.443168 | − | 0.443168i | −0.449907 | − | 0.893075i | \(-0.648543\pi\) |
0.893075 | + | 0.449907i | \(0.148543\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7648i | 0.658703i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.510711 | − | 1.67435i | −0.0285051 | − | 0.0934530i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.33587 | + | 8.33587i | 0.463820 | + | 0.463820i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.539481 | − | 0.539481i | 0.0299250 | − | 0.0299250i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.2787 | − | 8.93060i | 1.61911 | − | 0.493864i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.35561 | −0.405528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.02877 | + | 3.02877i | 0.166476 | + | 0.166476i | 0.785429 | − | 0.618952i | \(-0.212443\pi\) |
−0.618952 | + | 0.785429i | \(0.712443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.1196 | − | 3.93796i | −1.10255 | − | 0.215799i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.64937 | −0.144750 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2285 | 0.829547 | 0.414774 | − | 0.909925i | \(-0.363861\pi\) | ||||
0.414774 | + | 0.909925i | \(0.363861\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.37361 | + | 4.45930i | 0.454792 | + | 0.242196i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.76515 | + | 9.76515i | 0.528813 | + | 0.528813i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5426 | 0.785227 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.98718 | − | 16.3503i | −0.268501 | − | 0.880269i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2175 | − | 16.2175i | 0.870600 | − | 0.870600i | −0.121938 | − | 0.992538i | \(-0.538911\pi\) |
0.992538 | + | 0.121938i | \(0.0389108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.14637 | + | 6.14637i | 0.329007 | + | 0.329007i | 0.852209 | − | 0.523202i | \(-0.175263\pi\) |
−0.523202 | + | 0.852209i | \(0.675263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.834549 | + | 0.678500i | 0.0445449 | + | 0.0362156i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9507i | 1.22154i | 0.791806 | + | 0.610772i | \(0.209141\pi\) | ||||
−0.791806 | + | 0.610772i | \(0.790859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.3931 | + | 14.3931i | −0.763907 | + | 0.763907i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.80936 | + | 5.22390i | 0.519167 | + | 0.276478i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.3408i | − | 0.967993i | −0.875070 | − | 0.483996i | \(-0.839185\pi\) | ||
0.875070 | − | 0.483996i | \(-0.160815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5640i | 0.766528i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.24490 | + | 4.39076i | 0.432745 | + | 0.230455i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.7523 | + | 14.7523i | −0.772172 | + | 0.772172i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.86833i | − | 0.149725i | −0.997194 | − | 0.0748627i | \(-0.976148\pi\) | ||
0.997194 | − | 0.0748627i | \(-0.0238519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.02142 | − | 1.51857i | −0.0531731 | − | 0.0790536i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.188638 | + | 0.188638i | 0.00979359 | + | 0.00979359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.2253 | − | 17.2253i | 0.891894 | − | 0.891894i | −0.102808 | − | 0.994701i | \(-0.532783\pi\) |
0.994701 | + | 0.102808i | \(0.0327826\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.95715 | + | 6.41646i | 0.101067 | + | 0.331344i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.02844 | −0.0529672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.83956 | − | 5.83956i | −0.299958 | − | 0.299958i | 0.541039 | − | 0.840997i | \(-0.318031\pi\) |
−0.840997 | + | 0.541039i | \(0.818031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0132 | + | 5.86499i | 0.564223 | + | 0.300473i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.7659 | 1.57206 | 0.786031 | − | 0.618187i | \(-0.212133\pi\) | ||||
0.786031 | + | 0.618187i | \(0.212133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.21368 | − | 6.20086i | 0.0616949 | − | 0.315207i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.0299 | + | 11.0299i | 0.559237 | + | 0.559237i | 0.929090 | − | 0.369853i | \(-0.120592\pi\) |
−0.369853 | + | 0.929090i | \(0.620592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7434 | 0.947894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.2047 | + | 6.46787i | −1.06963 | + | 0.326261i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.4900 | − | 20.4900i | 1.03096 | − | 1.03096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.75325 | + | 1.75325i | 0.0879931 | + | 0.0879931i | 0.749733 | − | 0.661740i | \(-0.230182\pi\) |
−0.661740 | + | 0.749733i | \(0.730182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.22008 | − | 4.00000i | −0.0610806 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.4693i | − | 1.22194i | −0.791654 | − | 0.610970i | \(-0.790780\pi\) | ||
0.791654 | − | 0.610970i | \(-0.209220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.853635 | + | 0.853635i | −0.0425226 | + | 0.0425226i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.4428 | − | 10.3005i | 1.21457 | − | 0.511838i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1816i | 0.802093i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.78623i | − | 0.434451i | −0.976121 | − | 0.217226i | \(-0.930299\pi\) | ||
0.976121 | − | 0.217226i | \(-0.0697007\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9445 | − | 20.5513i | 0.539851 | − | 1.01372i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.3752 | + | 10.3752i | −0.510530 | + | 0.510530i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 33.7220i | − | 1.65535i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.2327 | + | 6.17139i | −0.990798 | + | 0.302214i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.52202 | − | 3.52202i | −0.172062 | − | 0.172062i | 0.615823 | − | 0.787885i | \(-0.288824\pi\) |
−0.787885 | + | 0.615823i | \(0.788824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2253 | + | 11.2253i | −0.547089 | + | 0.547089i | −0.925598 | − | 0.378509i | \(-0.876437\pi\) |
0.378509 | + | 0.925598i | \(0.376437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7434 | − | 15.9724i | −0.522361 | − | 0.776605i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6305 | 1.00073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.20390 | + | 5.20390i | 0.251835 | + | 0.251835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.399038 | − | 0.749307i | 0.0192657 | − | 0.0361769i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1336 | 0.584454 | 0.292227 | − | 0.956349i | \(-0.405604\pi\) | ||||
0.292227 | + | 0.956349i | \(0.405604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1495 | −0.583868 | −0.291934 | − | 0.956439i | \(-0.594299\pi\) | ||||
−0.291934 | + | 0.956439i | \(0.594299\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.9215 | + | 22.3860i | −0.571591 | + | 1.07332i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.98718 | − | 4.98718i | −0.238569 | − | 0.238569i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.1035 | 1.29358 | 0.646790 | − | 0.762668i | \(-0.276111\pi\) | ||||
0.646790 | + | 0.762668i | \(0.276111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.52009 | + | 14.1537i | 0.453337 | + | 0.673986i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.8412 | + | 28.8412i | −1.37029 | + | 1.37029i | −0.510276 | + | 0.860011i | \(0.670457\pi\) |
−0.860011 | + | 0.510276i | \(0.829543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.02142 | − | 1.02142i | −0.0484201 | − | 0.0484201i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.2714 | + | 8.31836i | −1.28990 | + | 0.393445i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.67586i | − | 0.456632i | −0.973587 | − | 0.228316i | \(-0.926678\pi\) | ||
0.973587 | − | 0.228316i | \(-0.0733220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.02142 | + | 1.02142i | −0.0480969 | + | 0.0480969i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.660097 | + | 1.23952i | −0.0310140 | + | 0.0582377i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.699331i | − | 0.0327851i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20077i | 0.196504i | 0.995162 | + | 0.0982518i | \(0.0313251\pi\) | ||||
−0.995162 | + | 0.0982518i | \(0.968675\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.98377 | + | 28.9305i | 0.139271 | + | 1.35036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5406 | − | 27.5406i | 1.28269 | − | 1.28269i | 0.343565 | − | 0.939129i | \(-0.388366\pi\) |
0.939129 | − | 0.343565i | \(-0.111634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.4109i | 1.73863i | 0.494255 | + | 0.869317i | \(0.335441\pi\) | ||||
−0.494255 | + | 0.869317i | \(0.664559\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.68585 | + | 28.4762i | 0.402796 | + | 1.32055i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.9168 | − | 16.9168i | −0.782817 | − | 0.782817i | 0.197489 | − | 0.980305i | \(-0.436721\pi\) |
−0.980305 | + | 0.197489i | \(0.936721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.728692 | + | 0.728692i | −0.0336479 | + | 0.0336479i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.9284 | + | 3.94343i | −0.595709 | + | 0.181704i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.98718 | −0.229311 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.48929 | − | 5.48929i | −0.251866 | − | 0.251866i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.134101 | + | 0.685139i | −0.00614005 | + | 0.0313703i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.5500 | 0.847573 | 0.423786 | − | 0.905762i | \(-0.360701\pi\) | ||||
0.423786 | + | 0.905762i | \(0.360701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.41454 | −0.0644974 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.86873 | − | 3.12535i | −0.267037 | − | 0.142208i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.7376 | − | 25.7376i | −1.16868 | − | 1.16868i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.9259 | −1.85453 | −0.927264 | − | 0.374408i | \(-0.877846\pi\) | ||||
−0.927264 | + | 0.374408i | \(0.877846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.19983 | + | 23.6044i | 0.325587 | + | 1.06743i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.04360 | + | 5.04360i | −0.227615 | + | 0.227615i | −0.811696 | − | 0.584081i | \(-0.801455\pi\) |
0.584081 | + | 0.811696i | \(0.301455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6644 | − | 19.6644i | −0.885641 | − | 0.885641i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.6846 | − | 17.3717i | −0.525182 | − | 0.780800i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.91748i | 0.355147i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4647 | − | 11.4647i | 0.513232 | − | 0.513232i | −0.402283 | − | 0.915515i | \(-0.631783\pi\) |
0.915515 | + | 0.402283i | \(0.131783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.62081 | − | 1.92824i | −0.161766 | − | 0.0861472i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.7159i | 1.45873i | 0.684125 | + | 0.729365i | \(0.260184\pi\) | ||||
−0.684125 | + | 0.729365i | \(0.739816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 34.5573i | − | 1.53778i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.8087 | − | 10.5490i | −0.879734 | − | 0.468495i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1389 | + | 10.1389i | −0.449399 | + | 0.449399i | −0.895155 | − | 0.445756i | \(-0.852935\pi\) |
0.445756 | + | 0.895155i | \(0.352935\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.11508i | 0.358990i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.90383 | − | 8.49165i | 0.304811 | − | 0.374916i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.4772 | + | 25.4772i | 1.12266 | + | 1.12266i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7434 | + | 10.7434i | −0.472494 | + | 0.472494i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.73290 | + | 12.2382i | 0.163856 | + | 0.537197i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.08735 | 0.266692 | 0.133346 | − | 0.991070i | \(-0.457428\pi\) | ||||
0.133346 | + | 0.991070i | \(0.457428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8824 | − | 15.8824i | −0.694489 | − | 0.694489i | 0.268727 | − | 0.963216i | \(-0.413397\pi\) |
−0.963216 | + | 0.268727i | \(0.913397\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.45960 | − | 3.44001i | −0.281920 | − | 0.150134i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.6442 | −1.42200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.7862 | 0.512445 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −37.6831 | − | 7.37563i | −1.63531 | − | 0.320075i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0892891 | − | 0.0892891i | −0.00386754 | − | 0.00386754i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.97858 | −0.128775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.7076 | + | 5.09617i | −0.720987 | + | 0.219916i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.52009 | − | 9.52009i | 0.410059 | − | 0.410059i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.6184 | + | 25.6184i | 1.10142 | + | 1.10142i | 0.994239 | + | 0.107184i | \(0.0341833\pi\) |
0.107184 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.81084 | − | 15.7722i | −0.206453 | − | 0.676848i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 52.0852i | − | 2.23108i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.2113 | − | 27.2113i | 1.16347 | − | 1.16347i | 0.179758 | − | 0.983711i | \(-0.442468\pi\) |
0.983711 | − | 0.179758i | \(-0.0575315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.69941 | + | 18.9007i | −0.157887 | + | 0.806664i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4645i | 0.445802i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 11.2713i | − | 0.479305i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.3971 | + | 30.7902i | −0.696018 | + | 1.30697i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.1831 | − | 26.1831i | 1.10941 | − | 1.10941i | 0.116184 | − | 0.993228i | \(-0.462934\pi\) |
0.993228 | − | 0.116184i | \(-0.0370662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.435961i | − | 0.0184392i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9572 | − | 6.69739i | 0.927032 | − | 0.282764i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0435 | + | 25.0435i | 1.05546 | + | 1.05546i | 0.998369 | + | 0.0570880i | \(0.0181816\pi\) |
0.0570880 | + | 0.998369i | \(0.481818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.4145 | − | 11.4145i | 0.480213 | − | 0.480213i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.88975 | − | 9.55596i | 0.163354 | − | 0.401312i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.5449 | −0.525911 | −0.262955 | − | 0.964808i | \(-0.584697\pi\) | ||||
−0.262955 | + | 0.964808i | \(0.584697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.48615 | + | 4.48615i | 0.187740 | + | 0.187740i | 0.794718 | − | 0.606979i | \(-0.207619\pi\) |
−0.606979 | + | 0.794718i | \(0.707619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.7837 | + | 39.0273i | −0.868251 | + | 1.63039i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.3428 | −0.514730 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.48508 | 0.186716 | 0.0933581 | − | 0.995633i | \(-0.470240\pi\) | ||||
0.0933581 | + | 0.995633i | \(0.470240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.39156 | − | 13.8798i | 0.307183 | − | 0.576823i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.27502 | − | 9.27502i | −0.384793 | − | 0.384793i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.551038 | 0.0228217 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.51857 | − | 1.02142i | 0.0627852 | − | 0.0422306i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.9808 | + | 11.9808i | −0.494501 | + | 0.494501i | −0.909721 | − | 0.415220i | \(-0.863705\pi\) |
0.415220 | + | 0.909721i | \(0.363705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.68585 | + | 8.68585i | 0.357894 | + | 0.357894i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.46020 | + | 2.27552i | −0.306872 | + | 0.0936023i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.27696i | − | 0.134569i | −0.997734 | − | 0.0672843i | \(-0.978567\pi\) | ||
0.997734 | − | 0.0672843i | \(-0.0214334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.3717 | − | 13.3717i | 0.548186 | − | 0.548186i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.9199 | − | 29.8941i | 0.651556 | − | 1.22348i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 38.9889i | − | 1.59304i | −0.604611 | − | 0.796521i | \(-0.706671\pi\) | ||
0.604611 | − | 0.796521i | \(-0.293329\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.5787i | − | 0.961797i | −0.876776 | − | 0.480898i | \(-0.840311\pi\) | ||
0.876776 | − | 0.480898i | \(-0.159689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.64663 | − | 0.518020i | −0.107779 | − | 0.0210954i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2391 | − | 11.2391i | 0.456934 | − | 0.456934i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.2829i | − | 0.904434i | −0.891908 | − | 0.452217i | \(-0.850633\pi\) | ||
0.891908 | − | 0.452217i | \(-0.149367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.87819 | + | 9.43605i | 0.116630 | + | 0.382368i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.939148 | − | 0.939148i | −0.0379939 | − | 0.0379939i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1611 | + | 22.1611i | −0.895077 | + | 0.895077i | −0.994996 | − | 0.0999189i | \(-0.968142\pi\) |
0.0999189 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.97858 | + | 0.908529i | −0.120108 | + | 0.0366354i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.7376 | −1.03616 | −0.518078 | − | 0.855334i | \(-0.673352\pi\) | ||||
−0.518078 | + | 0.855334i | \(0.673352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.71462 | − | 7.71462i | −0.310077 | − | 0.310077i | 0.534863 | − | 0.844939i | \(-0.320363\pi\) |
−0.844939 | + | 0.534863i | \(0.820363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.78513 | − | 17.3085i | −0.0716347 | − | 0.694567i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.561872 | −0.0225109 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.8438 | 1.19375 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.62430 | − | 4.06027i | −0.304485 | − | 0.162151i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.0469 | − | 27.0469i | −1.07843 | − | 1.07843i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.26817 | 0.0902945 | 0.0451473 | − | 0.998980i | \(-0.485624\pi\) | ||||
0.0451473 | + | 0.998980i | \(0.485624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.39147 | − | 24.2327i | −0.293785 | − | 0.963162i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.0127 | − | 15.0127i | 0.595761 | − | 0.595761i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.832212 | + | 0.832212i | 0.0329734 | + | 0.0329734i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.1925 | + | 11.5640i | −0.680125 | + | 0.457466i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.0686i | − | 0.792662i | −0.918108 | − | 0.396331i | \(-0.870283\pi\) | ||
0.918108 | − | 0.396331i | \(-0.129717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0748 | + | 14.0748i | −0.555054 | + | 0.555054i | −0.927895 | − | 0.372841i | \(-0.878384\pi\) |
0.372841 | + | 0.927895i | \(0.378384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.48955 | − | 5.05359i | −0.373651 | − | 0.198985i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.95003i | 0.0766638i | 0.999265 | + | 0.0383319i | \(0.0122044\pi\) | ||||
−0.999265 | + | 0.0383319i | \(0.987796\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3074i | 1.18967i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.2212 | + | 5.44322i | 0.400600 | + | 0.213337i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.80289 | + | 5.80289i | −0.227085 | + | 0.227085i | −0.811474 | − | 0.584389i | \(-0.801334\pi\) |
0.584389 | + | 0.811474i | \(0.301334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.7220i | 1.47392i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.6216 | + | 11.8526i | −0.687483 | + | 0.462416i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.49262 | − | 5.49262i | −0.213962 | − | 0.213962i | 0.591986 | − | 0.805948i | \(-0.298344\pi\) |
−0.805948 | + | 0.591986i | \(0.798344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.86833 | − | 5.86833i | 0.228251 | − | 0.228251i | −0.583710 | − | 0.811962i | \(-0.698400\pi\) |
0.811962 | + | 0.583710i | \(0.198400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.585462 | + | 1.91942i | 0.0227375 | + | 0.0745439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.11579 | −0.275938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7648 | + | 11.7648i | 0.455535 | + | 0.455535i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.5787 | − | 18.4146i | −1.33689 | − | 0.711950i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2013 | 0.586841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.8929 | −0.882456 | −0.441228 | − | 0.897395i | \(-0.645457\pi\) | ||||
−0.441228 | + | 0.897395i | \(0.645457\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.96486 | − | 19.0512i | −0.0756273 | − | 0.733280i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.7685 | + | 13.7685i | 0.529168 | + | 0.529168i | 0.920324 | − | 0.391156i | \(-0.127925\pi\) |
−0.391156 | + | 0.920324i | \(0.627925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1579 | −0.543331 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.43274 | + | 1.04706i | −0.131543 | + | 0.0401233i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.72238 | − | 5.72238i | 0.218961 | − | 0.218961i | −0.589100 | − | 0.808060i | \(-0.700517\pi\) |
0.808060 | + | 0.589100i | \(0.200517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.0147 | − | 28.0147i | −1.07039 | − | 1.07039i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.37271 | − | 17.6142i | −0.204982 | − | 0.672025i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0481697i | 0.00183512i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.2327 | + | 24.2327i | −0.921854 | + | 0.921854i | −0.997160 | − | 0.0753061i | \(-0.976007\pi\) |
0.0753061 | + | 0.997160i | \(0.476007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.99175 | − | 1.56421i | −0.303581 | − | 0.0594194i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.9929i | 1.36529i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.41454i | − | 0.129335i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.9655 | + | 28.1020i | −0.566048 | + | 1.06292i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.9100 | − | 10.9100i | 0.412064 | − | 0.412064i | −0.470393 | − | 0.882457i | \(-0.655888\pi\) |
0.882457 | + | 0.470393i | \(0.155888\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3931i | 0.542847i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.3288 | + | 9.55596i | −1.17991 | + | 0.359898i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.50478 | − | 9.50478i | −0.357464 | − | 0.357464i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0031 | − | 14.0031i | 0.525899 | − | 0.525899i | −0.393448 | − | 0.919347i | \(-0.628718\pi\) |
0.919347 | + | 0.393448i | \(0.128718\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.4752 | − | 16.4625i | 0.917892 | − | 0.617394i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.5303 | 0.731416 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.02142 | − | 1.02142i | −0.0381990 | − | 0.0381990i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.0172 | + | 20.6879i | −0.411443 | + | 0.772602i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0665 | 1.12129 | 0.560646 | − | 0.828055i | \(-0.310553\pi\) | ||||
0.560646 | + | 0.828055i | \(0.310553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0147 | 0.521934 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.97154 | − | 7.45769i | 0.147703 | − | 0.277355i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.9493 | + | 12.9493i | 0.480925 | + | 0.480925i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.48194 | 0.351666 | 0.175833 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175833 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4316 | − | 5.51071i | 0.978950 | − | 0.204100i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.33587 | − | 8.33587i | 0.308313 | − | 0.308313i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4752 | + | 29.4752i | 1.08869 | + | 1.08869i | 0.995663 | + | 0.0930283i | \(0.0296547\pi\) |
0.0930283 | + | 0.995663i | \(0.470345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.7616 | − | 8.46787i | 1.02400 | − | 0.312342i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.12861i | 0.0784085i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.1077 | + | 22.1077i | −0.813246 | + | 0.813246i | −0.985119 | − | 0.171873i | \(-0.945018\pi\) |
0.171873 | + | 0.985119i | \(0.445018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.354934 | − | 0.666489i | 0.0130388 | − | 0.0244841i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.908529i | 0.0333307i | 0.999861 | + | 0.0166653i | \(0.00530499\pi\) | ||||
−0.999861 | + | 0.0166653i | \(0.994695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.5145i | 1.77743i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.59352 | − | 33.6872i | 0.241244 | − | 1.23255i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.819240 | + | 0.819240i | −0.0299344 | + | 0.0299344i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 39.1182i | − | 1.42744i | −0.700429 | − | 0.713722i | \(-0.747008\pi\) | ||
0.700429 | − | 0.713722i | \(-0.252992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.73917 | + | 12.2587i | 0.136263 | + | 0.446733i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.68966 | + | 1.68966i | 0.0614930 | + | 0.0614930i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.97544 | − | 8.97544i | 0.326218 | − | 0.326218i | −0.524928 | − | 0.851146i | \(-0.675908\pi\) |
0.851146 | + | 0.524928i | \(0.175908\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1365 | + | 4.00691i | −0.476825 | + | 0.145442i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6766 | 1.11202 | 0.556012 | − | 0.831174i | \(-0.312331\pi\) | ||||
0.556012 | + | 0.831174i | \(0.312331\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.3257 | − | 14.3257i | −0.518626 | − | 0.518626i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.5664 | + | 9.50581i | 1.75592 | + | 0.343683i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.64937 | −0.0956630 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.7795 | −1.50661 | −0.753304 | − | 0.657673i | \(-0.771541\pi\) | ||||
−0.753304 | + | 0.657673i | \(0.771541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6187 | + | 10.4478i | 0.706551 | + | 0.376268i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.6074 | + | 17.6074i | 0.633293 | + | 0.633293i | 0.948892 | − | 0.315599i | \(-0.102206\pi\) |
−0.315599 | + | 0.948892i | \(0.602206\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.4966 | 0.772182 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.95874 | + | 12.9786i | 0.142019 | + | 0.465604i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.908529 | + | 0.908529i | −0.0325514 | + | 0.0325514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.5640 | + | 11.5640i | 0.413794 | + | 0.413794i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.2862 | + | 20.0319i | −0.582022 | + | 0.715882i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.9989i | 0.820866i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.69006 | + | 1.69006i | −0.0602440 | + | 0.0602440i | −0.736587 | − | 0.676343i | \(-0.763564\pi\) |
0.676343 | + | 0.736587i | \(0.263564\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43.2878 | + | 23.0526i | 1.54108 | + | 0.820693i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.27900i | − | 0.223255i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.32885i | 0.0471887i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.04851 | + | 0.558376i | 0.0371868 | + | 0.0198035i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.76177 | + | 5.76177i | −0.204092 | + | 0.204092i | −0.801751 | − | 0.597658i | \(-0.796098\pi\) |
0.597658 | + | 0.801751i | \(0.296098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 35.9143i | − | 1.27056i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.820654 | − | 1.22008i | −0.0289964 | − | 0.0431096i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8526 | + | 11.8526i | 0.418271 | + | 0.418271i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | + | 8.00000i | −0.281963 | + | 0.281963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.70306 | + | 15.4188i | 0.165555 | + | 0.542767i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.1012 | −0.495771 | −0.247885 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247885 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.2327 | + | 16.2327i | 0.570006 | + | 0.570006i | 0.932130 | − | 0.362124i | \(-0.117948\pi\) |
−0.362124 | + | 0.932130i | \(0.617948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2412 | + | 7.05151i | 0.464390 | + | 0.247307i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.9909 | 1.47088 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.43596 | −0.155195 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.136737 | − | 0.698610i | 0.00477799 | − | 0.0244114i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2853 | + | 17.2853i | 0.603262 | + | 0.603262i | 0.941177 | − | 0.337915i | \(-0.109722\pi\) |
−0.337915 | + | 0.941177i | \(0.609722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.35341 | 0.256324 | 0.128162 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128162 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.4591 | + | 4.41033i | −0.503401 | + | 0.153548i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.224507 | + | 0.224507i | −0.00780688 | + | 0.00780688i | −0.710999 | − | 0.703193i | \(-0.751757\pi\) |
0.703193 | + | 0.710999i | \(0.251757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.5181 | − | 29.5181i | −1.02520 | − | 1.02520i | −0.999674 | − | 0.0255305i | \(-0.991873\pi\) |
−0.0255305 | − | 0.999674i | \(-0.508127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.37962 | + | 30.7507i | 0.325375 | + | 1.06673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.8249i | 1.10267i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.93573 | + | 4.93573i | −0.170808 | + | 0.170808i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.10904 | + | 30.1452i | 0.107464 | + | 1.04197i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 14.0224i | − | 0.484106i | −0.970263 | − | 0.242053i | \(-0.922179\pi\) | ||
0.970263 | − | 0.242053i | \(-0.0778208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.31415i | 0.148764i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.2946 | − | 39.9868i | 0.733427 | − | 1.37722i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.0023 | + | 27.0023i | −0.928907 | + | 0.928907i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.18248i | − | 0.212433i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.9546 | − | 12.7970i | 1.43988 | − | 0.439193i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.1816 | + | 16.1816i | 0.554698 | + | 0.554698i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.55417 | − | 8.55417i | 0.292889 | − | 0.292889i | −0.545331 | − | 0.838221i | \(-0.683596\pi\) |
0.838221 | + | 0.545331i | \(0.183596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3931 | − | 15.4517i | −0.355437 | − | 0.528436i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.5095 | 1.48626 | 0.743128 | − | 0.669149i | \(-0.233341\pi\) | ||||
0.743128 | + | 0.669149i | \(0.233341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.70306 | + | 8.70306i | 0.296945 | + | 0.296945i | 0.839816 | − | 0.542871i | \(-0.182663\pi\) |
−0.542871 | + | 0.839816i | \(0.682663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.569354 | + | 1.06912i | −0.0194035 | + | 0.0364357i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.9270 | −0.916607 | −0.458303 | − | 0.888796i | \(-0.651543\pi\) | ||||
−0.458303 | + | 0.888796i | \(0.651543\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.7711 | 0.740239 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.6657 | + | 21.9057i | −0.396188 | + | 0.743956i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.4625 | − | 16.4625i | −0.558454 | − | 0.558454i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.186076 | −0.00630493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6787 | − | 30.7434i | −0.699866 | − | 1.04051i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.13950 | − | 3.13950i | 0.106134 | − | 0.106134i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.7251 | − | 39.7251i | −1.34142 | − | 1.34142i | −0.894646 | − | 0.446775i | \(-0.852573\pi\) |
−0.446775 | − | 0.894646i | \(-0.647427\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.53388 | − | 0.467866i | 0.0517365 | − | 0.0157807i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.63848i | − | 0.0552018i | −0.999619 | − | 0.0276009i | \(-0.991213\pi\) | ||
0.999619 | − | 0.0276009i | \(-0.00878675\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.7967 | − | 31.7967i | 1.07004 | − | 1.07004i | 0.0726900 | − | 0.997355i | \(-0.476842\pi\) |
0.997355 | − | 0.0726900i | \(-0.0231584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −30.7110 | + | 57.6687i | −1.03234 | + | 1.93851i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.8573i | − | 1.00251i | −0.865299 | − | 0.501256i | \(-0.832872\pi\) | ||
0.865299 | − | 0.501256i | \(-0.167128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.25831i | − | 0.276975i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.27590 | − | 19.6384i | −0.277253 | − | 0.657912i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.55596 | + | 9.55596i | −0.319778 | + | 0.319778i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.7220i | 0.993496i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.350269 | − | 1.14835i | −0.0116952 | − | 0.0383421i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.4900 | − | 20.4900i | −0.683380 | − | 0.683380i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.921039 | + | 0.921039i | −0.0306842 | + | 0.0306842i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.00000 | + | 1.22008i | −0.133112 | + | 0.0406019i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.0578 | −0.932674 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1176 | + | 12.1176i | 0.402358 | + | 0.402358i | 0.879063 | − | 0.476705i | \(-0.158169\pi\) |
−0.476705 | + | 0.879063i | \(0.658169\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.75686 | − | 34.5217i | 0.224111 | − | 1.14501i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.53816 | 0.150356 | 0.0751780 | − | 0.997170i | \(-0.476048\pi\) | ||||
0.0751780 | + | 0.997170i | \(0.476048\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.0937 | −0.896669 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.9250 | + | 15.4038i | 0.956230 | + | 0.509233i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.3752 | + | 10.3752i | 0.342619 | + | 0.342619i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.6461 | −1.10988 | −0.554942 | − | 0.831889i | \(-0.687259\pi\) | ||||
−0.554942 | + | 0.831889i | \(0.687259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.694081 | − | 2.27552i | −0.0228707 | − | 0.0749809i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.01089 | + | 1.01089i | −0.0332737 | + | 0.0332737i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.8108 | + | 17.8108i | 0.585615 | + | 0.585615i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.4695 | + | 30.4324i | 0.672305 | + | 0.999530i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.1844i | 0.891891i | 0.895060 | + | 0.445946i | \(0.147133\pi\) | ||||
−0.895060 | + | 0.445946i | \(0.852867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.46787 | − | 8.46787i | 0.277523 | − | 0.277523i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.6551 | − | 26.9760i | −1.65837 | − | 0.883154i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 39.0606i | − | 1.27742i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.1495i | − | 0.723593i | −0.932257 | − | 0.361796i | \(-0.882164\pi\) | ||
0.932257 | − | 0.361796i | \(-0.117836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.2234 | + | 10.7698i | 0.659967 | + | 0.351460i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.35208 | − | 7.35208i | 0.239671 | − | 0.239671i | −0.577043 | − | 0.816714i | \(-0.695793\pi\) |
0.816714 | + | 0.577043i | \(0.195793\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.04285i | 0.0665242i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.6216 | − | 11.0745i | −0.443110 | − | 0.360254i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.29033 | − | 9.29033i | −0.301895 | − | 0.301895i | 0.539860 | − | 0.841755i | \(-0.318477\pi\) |
−0.841755 | + | 0.539860i | \(0.818477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.03612 | + | 1.03612i | −0.0336337 | + | 0.0336337i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.63879 | − | 18.4866i | −0.182850 | − | 0.599468i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.6413 | 0.409491 | 0.204745 | − | 0.978815i | \(-0.434363\pi\) | ||||
0.204745 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.2003 | + | 53.2003i | 1.72152 | + | 1.72152i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.9858 | + | 9.57821i | 0.581399 | + | 0.309620i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.4105 | −0.497632 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.01469 | −0.0972482 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.97550 | − | 0.582390i | −0.0958843 | − | 0.0187672i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9203 | − | 18.9203i | −0.609065 | − | 0.609065i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3043 | 0.749415 | 0.374708 | − | 0.927143i | \(-0.377743\pi\) | ||||
0.374708 | + | 0.927143i | \(0.377743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.5303 | − | 5.95715i | 0.627404 | − | 0.191371i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.17139 | + | 6.17139i | −0.198049 | + | 0.198049i | −0.799163 | − | 0.601114i | \(-0.794724\pi\) |
0.601114 | + | 0.799163i | \(0.294724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.89962 | + | 9.89962i | 0.317367 | + | 0.317367i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.385535 | − | 1.26396i | −0.0123470 | − | 0.0404792i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.43605i | 0.301886i | 0.988542 | + | 0.150943i | \(0.0482310\pi\) | ||||
−0.988542 | + | 0.150943i | \(0.951769\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.820654 | + | 0.820654i | −0.0262282 | + | 0.0262282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.1840 | − | 52.0315i | 0.325150 | − | 1.66124i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.8750i | 0.825285i | 0.910893 | + | 0.412643i | \(0.135394\pi\) | ||||
−0.910893 | + | 0.412643i | \(0.864606\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2713i | 0.422859i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.98850 | + | 11.2451i | −0.190616 | + | 0.357936i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.98718 | + | 4.98718i | −0.158583 | + | 0.158583i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5886i | 0.749316i | 0.927163 | + | 0.374658i | \(0.122240\pi\) | ||||
−0.927163 | + | 0.374658i | \(0.877760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.09617 | − | 2.16448i | 0.225190 | − | 0.0686878i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.7503 | − | 40.7503i | −1.29187 | − | 1.29187i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.16779 | + | 3.16779i | −0.100325 | + | 0.100325i | −0.755488 | − | 0.655163i | \(-0.772600\pi\) |
0.655163 | + | 0.755488i | \(0.272600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.4005 | + | 27.5524i | −0.708719 | + | 0.871719i |
(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 | 384.2.k.b.95.4 | 12 | ||
3.2 | odd | 2 | inner | 384.2.k.b.95.6 | 12 | ||
4.3 | odd | 2 | 384.2.k.a.95.3 | 12 | |||
8.3 | odd | 2 | 192.2.k.a.47.4 | 12 | |||
8.5 | even | 2 | 48.2.k.a.35.1 | yes | 12 | ||
12.11 | even | 2 | 384.2.k.a.95.1 | 12 | |||
16.3 | odd | 4 | 48.2.k.a.11.6 | yes | 12 | ||
16.5 | even | 4 | 384.2.k.a.287.1 | 12 | |||
16.11 | odd | 4 | inner | 384.2.k.b.287.6 | 12 | ||
16.13 | even | 4 | 192.2.k.a.143.6 | 12 | |||
24.5 | odd | 2 | 48.2.k.a.35.6 | yes | 12 | ||
24.11 | even | 2 | 192.2.k.a.47.6 | 12 | |||
48.5 | odd | 4 | 384.2.k.a.287.3 | 12 | |||
48.11 | even | 4 | inner | 384.2.k.b.287.4 | 12 | ||
48.29 | odd | 4 | 192.2.k.a.143.4 | 12 | |||
48.35 | even | 4 | 48.2.k.a.11.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.1 | ✓ | 12 | 48.35 | even | 4 | ||
48.2.k.a.11.6 | yes | 12 | 16.3 | odd | 4 | ||
48.2.k.a.35.1 | yes | 12 | 8.5 | even | 2 | ||
48.2.k.a.35.6 | yes | 12 | 24.5 | odd | 2 | ||
192.2.k.a.47.4 | 12 | 8.3 | odd | 2 | |||
192.2.k.a.47.6 | 12 | 24.11 | even | 2 | |||
192.2.k.a.143.4 | 12 | 48.29 | odd | 4 | |||
192.2.k.a.143.6 | 12 | 16.13 | even | 4 | |||
384.2.k.a.95.1 | 12 | 12.11 | even | 2 | |||
384.2.k.a.95.3 | 12 | 4.3 | odd | 2 | |||
384.2.k.a.287.1 | 12 | 16.5 | even | 4 | |||
384.2.k.a.287.3 | 12 | 48.5 | odd | 4 | |||
384.2.k.b.95.4 | 12 | 1.1 | even | 1 | trivial | ||
384.2.k.b.95.6 | 12 | 3.2 | odd | 2 | inner | ||
384.2.k.b.287.4 | 12 | 48.11 | even | 4 | inner | ||
384.2.k.b.287.6 | 12 | 16.11 | odd | 4 | inner |