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 | 287.3 | ||
Root | \(-0.204810 - 1.39930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.287 |
Dual form | 384.2.k.a.95.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | −0.997829 | − | 0.0658506i | \(-0.979024\pi\) |
0.0658506 | + | 0.997829i | \(0.479024\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14637 | 0.433285 | 0.216643 | − | 0.976251i | \(-0.430489\pi\) | ||||
0.216643 | + | 0.976251i | \(0.430489\pi\) | |||||||
\(8\) | 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 | \(-0.133809\pi\) |
−0.408102 | + | 0.912937i | \(0.633809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.146365 | + | 0.146365i | −0.0405945 | + | 0.0405945i | −0.727113 | − | 0.686518i | \(-0.759138\pi\) |
0.686518 | + | 0.727113i | \(0.259138\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.88258 | + | 1.48929i | 1.26068 | + | 0.384533i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.59722i | 1.35752i | 0.734358 | + | 0.678762i | \(0.237483\pi\) | ||||
−0.734358 | + | 0.678762i | \(0.762517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48929 | + | 1.48929i | 0.341666 | + | 0.341666i | 0.856993 | − | 0.515327i | \(-0.172330\pi\) |
−0.515327 | + | 0.856993i | \(0.672330\pi\) | |||||||
\(20\) | 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 | 0.953569 | − | 0.301175i | \(-0.0973788\pi\) |
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(30\) | 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 | 0.982208 | − | 0.187797i | \(-0.0601348\pi\) |
−0.187797 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(38\) | 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 | \(-0.801341\pi\) |
0.584372 | + | 0.811486i | \(0.301341\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.69831 | − | 8.67689i | −0.253169 | − | 1.29347i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.41646 | −0.935936 | −0.467968 | − | 0.883745i | \(-0.655014\pi\) | ||||
−0.467968 | + | 0.883745i | \(0.655014\pi\) | |||||||
\(48\) | 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 | −0.718318 | − | 0.695715i | \(-0.755088\pi\) |
0.695715 | + | 0.718318i | \(0.255088\pi\) | |||||||
\(54\) | 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 | −0.980183 | − | 0.198093i | \(-0.936525\pi\) |
−0.198093 | − | 0.980183i | \(-0.563475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.53948 | + | 4.53948i | −0.581221 | + | 0.581221i | −0.935239 | − | 0.354018i | \(-0.884815\pi\) |
0.354018 | + | 0.935239i | \(0.384815\pi\) | |||||||
\(62\) | 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 | \(-0.267488\pi\) |
−0.744869 | + | 0.667211i | \(0.767488\pi\) | |||||||
\(68\) | 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 | \(0.135961\pi\) | ||||
−0.910156 | + | 0.414265i | \(0.864039\pi\) | |||||||
\(74\) | 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 | \(-0.966113\pi\) |
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(84\) | 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 | −0.161813 | − | 0.986821i | \(-0.551734\pi\) |
0.986821 | + | 0.161813i | \(0.0517343\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2253 | 1.20460 | 0.602299 | − | 0.798271i | \(-0.294252\pi\) | ||||
0.602299 | + | 0.798271i | \(0.294252\pi\) | |||||||
\(104\) | 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 | \(-0.265556\pi\) |
−0.740806 | + | 0.671719i | \(0.765556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4966 | − | 12.4966i | 1.19696 | − | 1.19696i | 0.221888 | − | 0.975072i | \(-0.428778\pi\) |
0.975072 | − | 0.221888i | \(-0.0712221\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.45330 | − | 11.3215i | 0.327772 | − | 1.07459i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.47731i | − | 0.515262i | −0.966243 | − | 0.257631i | \(-0.917058\pi\) | ||
0.966243 | − | 0.257631i | \(-0.0829419\pi\) | |||||||
\(114\) | 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 | \(-0.561130\pi\) |
0.981616 | + | 0.190869i | \(0.0611304\pi\) | |||||||
\(132\) | 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 | \(-0.576702\pi\) |
0.971108 | + | 0.238641i | \(0.0767020\pi\) | |||||||
\(140\) | 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 | −0.998969 | − | 0.0453896i | \(-0.985547\pi\) |
0.0453896 | + | 0.998969i | \(0.485547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.810789 | 0.0659811 | 0.0329905 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329905 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(152\) | 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 | −0.892143 | − | 0.451754i | \(-0.850799\pi\) |
0.451754 | + | 0.892143i | \(0.350799\pi\) | |||||||
\(158\) | 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 | \(-0.0615732\pi\) |
−0.192234 | + | 0.981349i | \(0.561573\pi\) | |||||||
\(164\) | 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 | 0.480088 | − | 0.877221i | \(-0.340605\pi\) |
−0.877221 | + | 0.480088i | \(0.840605\pi\) | |||||||
\(174\) | 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 | \(-0.626993\pi\) |
0.921465 | + | 0.388462i | \(0.126993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.73183 | + | 6.73183i | 0.500373 | + | 0.500373i | 0.911554 | − | 0.411181i | \(-0.134884\pi\) |
−0.411181 | + | 0.911554i | \(0.634884\pi\) | |||||||
\(182\) | 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 | \(-0.125246\pi\) | ||||
0.923584 | + | 0.383396i | \(0.125246\pi\) | |||||||
\(192\) | 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 | −0.811380 | − | 0.584519i | \(-0.801283\pi\) |
0.584519 | + | 0.811380i | \(0.301283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5542 | −1.38616 | −0.693079 | − | 0.720861i | \(-0.743746\pi\) | ||||
−0.693079 | + | 0.720861i | \(0.743746\pi\) | |||||||
\(200\) | 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 | \(-0.417949\pi\) |
−0.966961 | + | 0.254925i | \(0.917949\pi\) | |||||||
\(212\) | 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 | \(-0.728095\pi\) |
0.754056 | + | 0.656810i | \(0.228095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.51806 | + | 7.51806i | 0.496807 | + | 0.496807i | 0.910443 | − | 0.413635i | \(-0.135741\pi\) |
−0.413635 | + | 0.910443i | \(0.635741\pi\) | |||||||
\(230\) | 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 | \(-0.355806\pi\) | ||||
0.437664 | + | 0.899139i | \(0.355806\pi\) | |||||||
\(240\) | 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 | \(-0.174973\pi\) |
−0.522427 | + | 0.852684i | \(0.674973\pi\) | |||||||
\(252\) | 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 | \(-0.868924\pi\) | ||
0.916407 | − | 0.400248i | \(-0.131076\pi\) | |||||||
\(258\) | 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 | 0.477423 | − | 0.878674i | \(-0.341571\pi\) |
−0.878674 | + | 0.477423i | \(0.841571\pi\) | |||||||
\(270\) | 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 | 0.192664 | − | 0.981265i | \(-0.438287\pi\) |
−0.981265 | + | 0.192664i | \(0.938287\pi\) | |||||||
\(278\) | 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 | −0.0666843 | + | 0.997774i | \(0.521242\pi\) |
−0.997774 | + | 0.0666843i | \(0.978758\pi\) | |||||||
\(284\) | 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 | −0.687725 | − | 0.725972i | \(-0.741390\pi\) |
0.725972 | + | 0.687725i | \(0.241390\pi\) | |||||||
\(294\) | 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 | \(-0.262480\pi\) |
−0.734279 | + | 0.678848i | \(0.762480\pi\) | |||||||
\(308\) | 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 | \(-0.878035\pi\) | ||
0.927486 | − | 0.373858i | \(-0.121965\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.94688 | − | 9.94688i | −0.109694 | − | 0.560443i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.89038 | + | 7.89038i | 0.443168 | + | 0.443168i | 0.893075 | − | 0.449907i | \(-0.148543\pi\) |
−0.449907 | + | 0.893075i | \(0.648543\pi\) | |||||||
\(318\) | 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 | \(-0.787557\pi\) |
0.618952 | + | 0.785429i | \(0.287557\pi\) | |||||||
\(332\) | 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 | \(-0.461089\pi\) |
−0.992538 | + | 0.121938i | \(0.961089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.14637 | − | 6.14637i | 0.329007 | − | 0.329007i | −0.523202 | − | 0.852209i | \(-0.675263\pi\) |
0.852209 | + | 0.523202i | \(0.175263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.834549 | + | 0.678500i | −0.0445449 | + | 0.0362156i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.9507i | − | 1.22154i | −0.791806 | − | 0.610772i | \(-0.790859\pi\) | ||
0.791806 | − | 0.610772i | \(-0.209141\pi\) | |||||||
\(354\) | 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 | 0.994701 | − | 0.102808i | \(-0.0327826\pi\) |
−0.102808 | + | 0.994701i | \(0.532783\pi\) | |||||||
\(374\) | 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 | \(-0.681969\pi\) |
0.840997 | + | 0.541039i | \(0.181969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0132 | − | 5.86499i | 0.564223 | − | 0.300473i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.7659 | −1.57206 | −0.786031 | − | 0.618187i | \(-0.787867\pi\) | ||||
−0.786031 | + | 0.618187i | \(0.787867\pi\) | |||||||
\(384\) | 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 | −0.369853 | − | 0.929090i | \(-0.620592\pi\) |
0.929090 | + | 0.369853i | \(0.120592\pi\) | |||||||
\(390\) | 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 | −0.661740 | − | 0.749733i | \(-0.730182\pi\) |
0.749733 | + | 0.661740i | \(0.230182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.22008 | − | 4.00000i | 0.0610806 | − | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4693i | 1.22194i | 0.791654 | + | 0.610970i | \(0.209220\pi\) | ||||
−0.791654 | + | 0.610970i | \(0.790780\pi\) | |||||||
\(402\) | 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 | \(0.0697007\pi\) | ||||
−0.976121 | + | 0.217226i | \(0.930299\pi\) | |||||||
\(410\) | 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 | \(-0.711176\pi\) |
0.787885 | + | 0.615823i | \(0.211176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.2253 | − | 11.2253i | −0.547089 | − | 0.547089i | 0.378509 | − | 0.925598i | \(-0.376437\pi\) |
−0.925598 | + | 0.378509i | \(0.876437\pi\) | |||||||
\(422\) | 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 | \(-0.594396\pi\) | ||||
−0.292227 | + | 0.956349i | \(0.594396\pi\) | |||||||
\(432\) | 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 | \(-0.723889\pi\) | ||||
−0.646790 | + | 0.762668i | \(0.723889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.52009 | − | 14.1537i | 0.453337 | − | 0.673986i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8412 | + | 28.8412i | 1.37029 | + | 1.37029i | 0.860011 | + | 0.510276i | \(0.170457\pi\) |
0.510276 | + | 0.860011i | \(0.329543\pi\) | |||||||
\(444\) | 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 | \(0.0733220\pi\) | ||||
−0.973587 | + | 0.228316i | \(0.926678\pi\) | |||||||
\(450\) | 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 | \(-0.968675\pi\) | ||
0.995162 | − | 0.0982518i | \(-0.0313251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.98377 | + | 28.9305i | −0.139271 | + | 1.35036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.5406 | + | 27.5406i | 1.28269 | + | 1.28269i | 0.939129 | + | 0.343565i | \(0.111634\pi\) |
0.343565 | + | 0.939129i | \(0.388366\pi\) | |||||||
\(462\) | 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 | \(-0.563279\pi\) |
0.980305 | + | 0.197489i | \(0.0632785\pi\) | |||||||
\(468\) | 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 | \(-0.639299\pi\) | ||||
−0.423786 | + | 0.905762i | \(0.639299\pi\) | |||||||
\(480\) | 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 | \(-0.122154\pi\) | ||||
0.927264 | + | 0.374408i | \(0.122154\pi\) | |||||||
\(488\) | 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 | \(-0.198545\pi\) |
−0.584081 | + | 0.811696i | \(0.698545\pi\) | |||||||
\(492\) | 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 | \(-0.368217\pi\) |
−0.915515 | + | 0.402283i | \(0.868217\pi\) | |||||||
\(500\) | 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 | 0.445756 | − | 0.895155i | \(-0.352935\pi\) |
−0.895155 | + | 0.445756i | \(0.852935\pi\) | |||||||
\(510\) | 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 | \(-0.586603\pi\) |
0.963216 | + | 0.268727i | \(0.0866030\pi\) | |||||||
\(524\) | 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 | 0.107184 | − | 0.994239i | \(-0.465817\pi\) |
0.994239 | − | 0.107184i | \(-0.0341833\pi\) | |||||||
\(542\) | 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 | −0.983711 | − | 0.179758i | \(-0.942468\pi\) |
−0.179758 | − | 0.983711i | \(-0.557532\pi\) | |||||||
\(548\) | 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 | 0.993228 | + | 0.116184i | \(0.0370662\pi\) |
0.116184 | + | 0.993228i | \(0.462934\pi\) | |||||||
\(558\) | 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 | −0.0570880 | + | 0.998369i | \(0.518182\pi\) |
−0.998369 | + | 0.0570880i | \(0.981818\pi\) | |||||||
\(564\) | 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 | \(-0.792381\pi\) |
0.606979 | + | 0.794718i | \(0.292381\pi\) | |||||||
\(572\) | 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 | \(-0.136295\pi\) |
−0.415220 | + | 0.909721i | \(0.636295\pi\) | |||||||
\(588\) | 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 | \(0.0214334\pi\) | ||||
−0.997734 | + | 0.0672843i | \(0.978567\pi\) | |||||||
\(594\) | 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 | \(0.159689\pi\) | ||||
−0.876776 | + | 0.480898i | \(0.840311\pi\) | |||||||
\(602\) | 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 | 0.0999189 | − | 0.994996i | \(-0.468142\pi\) |
−0.994996 | + | 0.0999189i | \(0.968142\pi\) | |||||||
\(614\) | 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 | \(-0.679637\pi\) |
0.844939 | + | 0.534863i | \(0.179637\pi\) | |||||||
\(620\) | 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 | \(-0.514376\pi\) | ||||
−0.0451473 | + | 0.998980i | \(0.514376\pi\) | |||||||
\(632\) | 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 | \(0.129717\pi\) | ||||
−0.918108 | + | 0.396331i | \(0.870283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0748 | + | 14.0748i | 0.555054 | + | 0.555054i | 0.927895 | − | 0.372841i | \(-0.121616\pi\) |
−0.372841 | + | 0.927895i | \(0.621616\pi\) | |||||||
\(644\) | 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 | 0.584389 | − | 0.811474i | \(-0.301334\pi\) |
−0.811474 | + | 0.584389i | \(0.801334\pi\) | |||||||
\(654\) | 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 | \(-0.701656\pi\) |
0.805948 | + | 0.591986i | \(0.201656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.86833 | + | 5.86833i | 0.228251 | + | 0.228251i | 0.811962 | − | 0.583710i | \(-0.198400\pi\) |
−0.583710 | + | 0.811962i | \(0.698400\pi\) | |||||||
\(662\) | 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 | −0.391156 | − | 0.920324i | \(-0.627925\pi\) |
0.920324 | + | 0.391156i | \(0.127925\pi\) | |||||||
\(678\) | 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 | \(-0.299483\pi\) |
−0.808060 | + | 0.589100i | \(0.799483\pi\) | |||||||
\(684\) | 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 | \(-0.0239934\pi\) |
−0.0753061 | + | 0.997160i | \(0.523993\pi\) | |||||||
\(692\) | 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 | 0.882457 | − | 0.470393i | \(-0.155888\pi\) |
−0.470393 | + | 0.882457i | \(0.655888\pi\) | |||||||
\(702\) | 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 | 0.919347 | − | 0.393448i | \(-0.128718\pi\) |
−0.393448 | + | 0.919347i | \(0.628718\pi\) | |||||||
\(710\) | 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 | \(-0.689447\pi\) | ||||
−0.560646 | + | 0.828055i | \(0.689447\pi\) | |||||||
\(720\) | 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 | \(-0.556262\pi\) | ||||
−0.175833 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(728\) | 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 | 0.0930283 | − | 0.995663i | \(-0.470345\pi\) |
0.995663 | − | 0.0930283i | \(-0.0296547\pi\) | |||||||
\(734\) | 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 | \(-0.0549819\pi\) |
−0.171873 | + | 0.985119i | \(0.554982\pi\) | |||||||
\(740\) | 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 | 0.851146 | − | 0.524928i | \(-0.175908\pi\) |
−0.524928 | + | 0.851146i | \(0.675908\pi\) | |||||||
\(758\) | 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 | −0.315599 | − | 0.948892i | \(-0.602206\pi\) |
0.948892 | + | 0.315599i | \(0.102206\pi\) | |||||||
\(774\) | 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 | \(-0.236436\pi\) |
−0.676343 | + | 0.736587i | \(0.736436\pi\) | |||||||
\(788\) | 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 | 0.597658 | − | 0.801751i | \(-0.296098\pi\) |
−0.801751 | + | 0.597658i | \(0.796098\pi\) | |||||||
\(798\) | 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 | \(-0.882052\pi\) |
0.362124 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(812\) | 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 | −0.337915 | − | 0.941177i | \(-0.609722\pi\) |
0.941177 | + | 0.337915i | \(0.109722\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.35341 | −0.256324 | −0.128162 | − | 0.991753i | \(-0.540908\pi\) | ||||
−0.128162 | + | 0.991753i | \(0.540908\pi\) | |||||||
\(824\) | 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 | \(-0.248243\pi\) |
−0.703193 | + | 0.710999i | \(0.748243\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.5181 | + | 29.5181i | −1.02520 | + | 1.02520i | −0.0255305 | + | 0.999674i | \(0.508127\pi\) |
−0.999674 | + | 0.0255305i | \(0.991873\pi\) | |||||||
\(830\) | 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 | 0.838221 | − | 0.545331i | \(-0.183596\pi\) |
−0.545331 | + | 0.838221i | \(0.683596\pi\) | |||||||
\(854\) | 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 | \(-0.817337\pi\) |
0.542871 | + | 0.839816i | \(0.317337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.569354 | − | 1.06912i | −0.0194035 | − | 0.0364357i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9270 | 0.916607 | 0.458303 | − | 0.888796i | \(-0.348457\pi\) | ||||
0.458303 | + | 0.888796i | \(0.348457\pi\) | |||||||
\(864\) | 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 | −0.446775 | + | 0.894646i | \(0.647427\pi\) |
−0.894646 | + | 0.446775i | \(0.852573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.53388 | − | 0.467866i | −0.0517365 | − | 0.0157807i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.63848i | 0.0552018i | 0.999619 | + | 0.0276009i | \(0.00878675\pi\) | ||||
−0.999619 | + | 0.0276009i | \(0.991213\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7967 | − | 31.7967i | −1.07004 | − | 1.07004i | −0.997355 | − | 0.0726900i | \(-0.976842\pi\) |
−0.0726900 | − | 0.997355i | \(-0.523158\pi\) | |||||||
\(884\) | 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 | \(-0.841831\pi\) |
0.476705 | + | 0.879063i | \(0.341831\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.75686 | + | 34.5217i | 0.224111 | + | 1.14501i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.53816 | −0.150356 | −0.0751780 | − | 0.997170i | \(-0.523952\pi\) | ||||
−0.0751780 | + | 0.997170i | \(0.523952\pi\) | |||||||
\(912\) | 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 | \(-0.312741\pi\) | ||||
0.554942 | + | 0.831889i | \(0.312741\pi\) | |||||||
\(920\) | 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 | \(-0.852867\pi\) | ||
0.895060 | − | 0.445946i | \(-0.147133\pi\) | |||||||
\(930\) | 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 | \(0.117836\pi\) | ||||
−0.932257 | + | 0.361796i | \(0.882164\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.2234 | + | 10.7698i | −0.659967 | + | 0.351460i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.35208 | + | 7.35208i | 0.239671 | + | 0.239671i | 0.816714 | − | 0.577043i | \(-0.195793\pi\) |
−0.577043 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(942\) | 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 | \(-0.681523\pi\) |
0.841755 | + | 0.539860i | \(0.181523\pi\) | |||||||
\(948\) | 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 | \(-0.622257\pi\) | ||||
−0.374708 | + | 0.927143i | \(0.622257\pi\) | |||||||
\(968\) | 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 | \(-0.205276\pi\) |
−0.601114 | + | 0.799163i | \(0.705276\pi\) | |||||||
\(972\) | 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 | \(-0.951769\pi\) | ||
0.988542 | − | 0.150943i | \(-0.0482310\pi\) | |||||||
\(978\) | 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 | 0.655163 | − | 0.755488i | \(-0.272600\pi\) |
−0.755488 | + | 0.655163i | \(0.772600\pi\) | |||||||
\(998\) | 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.a.287.3 | 12 | ||
3.2 | odd | 2 | inner | 384.2.k.a.287.1 | 12 | ||
4.3 | odd | 2 | 384.2.k.b.287.4 | 12 | |||
8.3 | odd | 2 | 48.2.k.a.11.1 | ✓ | 12 | ||
8.5 | even | 2 | 192.2.k.a.143.4 | 12 | |||
12.11 | even | 2 | 384.2.k.b.287.6 | 12 | |||
16.3 | odd | 4 | inner | 384.2.k.a.95.1 | 12 | ||
16.5 | even | 4 | 48.2.k.a.35.6 | yes | 12 | ||
16.11 | odd | 4 | 192.2.k.a.47.6 | 12 | |||
16.13 | even | 4 | 384.2.k.b.95.6 | 12 | |||
24.5 | odd | 2 | 192.2.k.a.143.6 | 12 | |||
24.11 | even | 2 | 48.2.k.a.11.6 | yes | 12 | ||
48.5 | odd | 4 | 48.2.k.a.35.1 | yes | 12 | ||
48.11 | even | 4 | 192.2.k.a.47.4 | 12 | |||
48.29 | odd | 4 | 384.2.k.b.95.4 | 12 | |||
48.35 | even | 4 | inner | 384.2.k.a.95.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.k.a.11.1 | ✓ | 12 | 8.3 | odd | 2 | ||
48.2.k.a.11.6 | yes | 12 | 24.11 | even | 2 | ||
48.2.k.a.35.1 | yes | 12 | 48.5 | odd | 4 | ||
48.2.k.a.35.6 | yes | 12 | 16.5 | even | 4 | ||
192.2.k.a.47.4 | 12 | 48.11 | even | 4 | |||
192.2.k.a.47.6 | 12 | 16.11 | odd | 4 | |||
192.2.k.a.143.4 | 12 | 8.5 | even | 2 | |||
192.2.k.a.143.6 | 12 | 24.5 | odd | 2 | |||
384.2.k.a.95.1 | 12 | 16.3 | odd | 4 | inner | ||
384.2.k.a.95.3 | 12 | 48.35 | even | 4 | inner | ||
384.2.k.a.287.1 | 12 | 3.2 | odd | 2 | inner | ||
384.2.k.a.287.3 | 12 | 1.1 | even | 1 | trivial | ||
384.2.k.b.95.4 | 12 | 48.29 | odd | 4 | |||
384.2.k.b.95.6 | 12 | 16.13 | even | 4 | |||
384.2.k.b.287.4 | 12 | 4.3 | odd | 2 | |||
384.2.k.b.287.6 | 12 | 12.11 | even | 2 |