Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.3.h.f.65.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.00000 | 0.800000 | 0.400000 | − | 0.916515i | \(-0.369010\pi\) | ||||
0.400000 | + | 0.916515i | \(0.369010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.94427 | −1.27775 | −0.638877 | − | 0.769309i | \(-0.720601\pi\) | ||||
−0.638877 | + | 0.769309i | \(0.720601\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 0.406558 | 0.203279 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203279 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.8885i | 1.37604i | 0.725691 | + | 0.688021i | \(0.241520\pi\) | ||||
−0.725691 | + | 0.688021i | \(0.758480\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.94427 | − | 8.00000i | −0.596285 | − | 0.533333i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 17.8885i | − | 1.05227i | −0.850402 | − | 0.526134i | \(-0.823641\pi\) | ||
0.850402 | − | 0.526134i | \(-0.176359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000i | 1.05263i | 0.850289 | + | 0.526316i | \(0.176427\pi\) | ||||
−0.850289 | + | 0.526316i | \(0.823573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.0000 | + | 17.8885i | 0.952381 | + | 0.851835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.0000i | 0.695652i | 0.937559 | + | 0.347826i | \(0.113080\pi\) | ||||
−0.937559 | + | 0.347826i | \(0.886920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.00000 | −0.360000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.0000 | 1.79310 | 0.896552 | − | 0.442939i | \(-0.146064\pi\) | ||||
0.896552 | + | 0.442939i | \(0.146064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.8328 | 0.865575 | 0.432787 | − | 0.901496i | \(-0.357530\pi\) | ||||
0.432787 | + | 0.901496i | \(0.357530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0000 | − | 8.94427i | −0.303030 | − | 0.271039i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.7771 | −1.02220 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.6656i | 1.45042i | 0.688526 | + | 0.725211i | \(0.258258\pi\) | ||||
−0.688526 | + | 0.725211i | \(0.741742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 35.7771 | − | 40.0000i | 0.917361 | − | 1.02564i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.7771i | 0.872612i | 0.899798 | + | 0.436306i | \(0.143713\pi\) | ||||
−0.899798 | + | 0.436306i | \(0.856287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 36.0000i | − | 0.837209i | −0.908169 | − | 0.418605i | \(-0.862519\pi\) | ||
0.908169 | − | 0.418605i | \(-0.137481\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000 | + | 35.7771i | 0.0888889 | + | 0.795046i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 64.0000i | 1.36170i | 0.732422 | + | 0.680851i | \(0.238390\pi\) | ||||
−0.732422 | + | 0.680851i | \(0.761610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.0000 | 0.632653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.7771 | + | 40.0000i | −0.701512 | + | 0.784314i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.0000 | 0.377358 | 0.188679 | − | 0.982039i | \(-0.439579\pi\) | ||||
0.188679 | + | 0.982039i | \(0.439579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.8885 | 0.325246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.0000 | − | 44.7214i | 0.701754 | − | 0.784585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 102.859 | 1.74338 | 0.871688 | − | 0.490062i | \(-0.163026\pi\) | ||||
0.871688 | + | 0.490062i | \(0.163026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17.8885i | 0.293255i | 0.989192 | + | 0.146627i | \(0.0468418\pi\) | ||||
−0.989192 | + | 0.146627i | \(0.953158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.94427 | − | 80.0000i | −0.141973 | − | 1.26984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 71.5542i | 1.10083i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.0000i | 0.656716i | 0.944553 | + | 0.328358i | \(0.106495\pi\) | ||||
−0.944553 | + | 0.328358i | \(0.893505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 32.0000 | − | 35.7771i | 0.463768 | − | 0.518509i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.0000i | 1.12676i | 0.826198 | + | 0.563380i | \(0.190499\pi\) | ||||
−0.826198 | + | 0.563380i | \(0.809501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.0000 | −0.684932 | −0.342466 | − | 0.939530i | \(-0.611262\pi\) | ||||
−0.342466 | + | 0.939530i | \(0.611262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.1246 | + | 18.0000i | 0.268328 | + | 0.240000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −40.0000 | −0.519481 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −80.4984 | −1.01897 | −0.509484 | − | 0.860480i | \(-0.670164\pi\) | ||||
−0.509484 | + | 0.860480i | \(0.670164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −102.859 | −1.23927 | −0.619633 | − | 0.784891i | \(-0.712719\pi\) | ||||
−0.619633 | + | 0.784891i | \(0.712719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 71.5542i | − | 0.841814i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −116.276 | − | 104.000i | −1.33650 | − | 1.19540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 160.997i | − | 1.80895i | −0.426523 | − | 0.904477i | \(-0.640262\pi\) | ||
0.426523 | − | 0.904477i | \(-0.359738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 160.000i | − | 1.75824i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −60.0000 | − | 53.6656i | −0.645161 | − | 0.577050i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80.0000i | 0.842105i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.0000 | 0.515464 | 0.257732 | − | 0.966216i | \(-0.417025\pi\) | ||||
0.257732 | + | 0.966216i | \(0.417025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.47214 | + | 40.0000i | 0.0451731 | + | 0.404040i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −92.0000 | −0.910891 | −0.455446 | − | 0.890264i | \(-0.650520\pi\) | ||||
−0.455446 | + | 0.890264i | \(0.650520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −44.7214 | −0.434188 | −0.217094 | − | 0.976151i | \(-0.569658\pi\) | ||||
−0.217094 | + | 0.976151i | \(0.569658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 80.0000 | + | 71.5542i | 0.761905 | + | 0.681468i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −40.2492 | −0.376161 | −0.188080 | − | 0.982154i | \(-0.560227\pi\) | ||||
−0.188080 | + | 0.982154i | \(0.560227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 125.220i | − | 1.14881i | −0.818573 | − | 0.574403i | \(-0.805234\pi\) | ||
0.818573 | − | 0.574403i | \(-0.194766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 107.331 | − | 120.000i | 0.966948 | − | 1.08108i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 35.7771i | − | 0.316611i | −0.987390 | − | 0.158306i | \(-0.949397\pi\) | ||
0.987390 | − | 0.158306i | \(-0.0506031\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 64.0000i | 0.556522i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −160.000 | + | 17.8885i | −1.36752 | + | 0.152894i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 160.000i | 1.34454i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −101.000 | −0.834711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 71.5542 | − | 80.0000i | 0.581741 | − | 0.650407i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −136.000 | −1.08800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26.8328 | 0.211282 | 0.105641 | − | 0.994404i | \(-0.466311\pi\) | ||||
0.105641 | + | 0.994404i | \(0.466311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −72.0000 | + | 80.4984i | −0.558140 | + | 0.624019i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 67.0820 | 0.512077 | 0.256038 | − | 0.966667i | \(-0.417583\pi\) | ||||
0.256038 | + | 0.966667i | \(0.417583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 178.885i | − | 1.34500i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 62.6099 | − | 88.0000i | 0.463777 | − | 0.651852i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 143.108i | 1.04459i | 0.852766 | + | 0.522293i | \(0.174923\pi\) | ||||
−0.852766 | + | 0.522293i | \(0.825077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 260.000i | 1.87050i | 0.353983 | + | 0.935252i | \(0.384827\pi\) | ||||
−0.353983 | + | 0.935252i | \(0.615173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 128.000 | − | 143.108i | 0.907801 | − | 1.01495i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 80.0000i | 0.559441i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 208.000 | 1.43448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −69.3181 | − | 62.0000i | −0.471552 | − | 0.421769i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −28.0000 | −0.187919 | −0.0939597 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939597 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 241.495 | 1.59931 | 0.799653 | − | 0.600462i | \(-0.205017\pi\) | ||||
0.799653 | + | 0.600462i | \(0.205017\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 160.000 | − | 17.8885i | 1.04575 | − | 0.116919i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 107.331 | 0.692460 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 53.6656i | − | 0.341819i | −0.985287 | − | 0.170910i | \(-0.945329\pi\) | ||
0.985287 | − | 0.170910i | \(-0.0546706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −44.7214 | − | 40.0000i | −0.281266 | − | 0.251572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 143.108i | − | 0.888872i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 124.000i | − | 0.760736i | −0.924835 | − | 0.380368i | \(-0.875797\pi\) | ||
0.924835 | − | 0.380368i | \(-0.124203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.0000 | − | 35.7771i | −0.242424 | − | 0.216831i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 16.0000i | − | 0.0958084i | −0.998852 | − | 0.0479042i | \(-0.984746\pi\) | ||
0.998852 | − | 0.0479042i | \(-0.0152542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −151.000 | −0.893491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −178.885 | + | 20.0000i | −1.04611 | + | 0.116959i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −140.000 | −0.809249 | −0.404624 | − | 0.914483i | \(-0.632598\pi\) | ||||
−0.404624 | + | 0.914483i | \(0.632598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 80.4984 | 0.459991 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −230.000 | − | 205.718i | −1.29944 | − | 1.16225i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 67.0820 | 0.374760 | 0.187380 | − | 0.982288i | \(-0.440000\pi\) | ||||
0.187380 | + | 0.982288i | \(0.440000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.220i | 0.691822i | 0.938267 | + | 0.345911i | \(0.112430\pi\) | ||||
−0.938267 | + | 0.345911i | \(0.887570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.7771 | − | 40.0000i | 0.195503 | − | 0.218579i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 214.663i | 1.16034i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 80.0000i | − | 0.427807i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −140.000 | + | 196.774i | −0.740741 | + | 1.04113i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.000i | 0.837696i | 0.908056 | + | 0.418848i | \(0.137566\pi\) | ||||
−0.908056 | + | 0.418848i | \(0.862434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 30.0000 | 0.155440 | 0.0777202 | − | 0.996975i | \(-0.475236\pi\) | ||||
0.0777202 | + | 0.996975i | \(0.475236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 143.108 | − | 160.000i | 0.733889 | − | 0.820513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 180.000 | 0.913706 | 0.456853 | − | 0.889542i | \(-0.348977\pi\) | ||||
0.456853 | + | 0.889542i | \(0.348977\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −259.384 | −1.30344 | −0.651718 | − | 0.758461i | \(-0.725952\pi\) | ||||
−0.651718 | + | 0.758461i | \(0.725952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 88.0000 | − | 98.3870i | 0.437811 | − | 0.489488i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −465.102 | −2.29114 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 143.108i | 0.698090i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −143.108 | + | 16.0000i | −0.691345 | + | 0.0772947i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 89.4427i | 0.427956i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 60.0000i | 0.284360i | 0.989841 | + | 0.142180i | \(0.0454112\pi\) | ||||
−0.989841 | + | 0.142180i | \(0.954589\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 160.000 | − | 178.885i | 0.751174 | − | 0.839838i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 144.000i | − | 0.669767i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −240.000 | −1.10599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 111.803 | + | 100.000i | 0.510518 | + | 0.456621i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 320.000 | 1.44796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −152.053 | −0.681850 | −0.340925 | − | 0.940090i | \(-0.610740\pi\) | ||||
−0.340925 | + | 0.940090i | \(0.610740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | − | 80.4984i | −0.0400000 | − | 0.357771i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 254.912 | 1.12296 | 0.561480 | − | 0.827491i | \(-0.310232\pi\) | ||||
0.561480 | + | 0.827491i | \(0.310232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 196.774i | 0.859275i | 0.903001 | + | 0.429638i | \(0.141359\pi\) | ||||
−0.903001 | + | 0.429638i | \(0.858641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 89.4427 | + | 80.0000i | 0.387198 | + | 0.346320i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 160.997i | − | 0.690974i | −0.938424 | − | 0.345487i | \(-0.887714\pi\) | ||
0.938424 | − | 0.345487i | \(-0.112286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 256.000i | 1.08936i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 180.000 | + | 160.997i | 0.759494 | + | 0.679312i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 320.000i | − | 1.33891i | −0.742852 | − | 0.669456i | \(-0.766527\pi\) | ||
0.742852 | − | 0.669456i | \(-0.233473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 318.000 | 1.31950 | 0.659751 | − | 0.751484i | \(-0.270662\pi\) | ||||
0.659751 | + | 0.751484i | \(0.270662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 212.426 | + | 118.000i | 0.874183 | + | 0.485597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 124.000 | 0.506122 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −357.771 | −1.44847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 230.000 | + | 205.718i | 0.923695 | + | 0.826178i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 147.580 | 0.587970 | 0.293985 | − | 0.955810i | \(-0.405018\pi\) | ||||
0.293985 | + | 0.955810i | \(0.405018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 71.5542i | 0.282823i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −143.108 | + | 160.000i | −0.561209 | + | 0.627451i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 107.331i | 0.417631i | 0.977955 | + | 0.208816i | \(0.0669609\pi\) | ||||
−0.977955 | + | 0.208816i | \(0.933039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 480.000i | − | 1.85328i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 52.0000 | + | 465.102i | 0.199234 | + | 1.78200i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 144.000i | 0.547529i | 0.961797 | + | 0.273764i | \(0.0882688\pi\) | ||||
−0.961797 | + | 0.273764i | \(0.911731\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 80.0000 | 0.301887 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −321.994 | + | 360.000i | −1.20597 | + | 1.34831i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 132.000 | 0.490706 | 0.245353 | − | 0.969434i | \(-0.421096\pi\) | ||||
0.245353 | + | 0.969434i | \(0.421096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 277.272 | 1.02315 | 0.511573 | − | 0.859240i | \(-0.329063\pi\) | ||||
0.511573 | + | 0.859240i | \(0.329063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −320.000 | + | 357.771i | −1.17216 | + | 1.31052i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −40.2492 | −0.146361 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 268.328i | 0.968694i | 0.874876 | + | 0.484347i | \(0.160943\pi\) | ||||
−0.874876 | + | 0.484347i | \(0.839057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.8328 | + | 240.000i | 0.0961750 | + | 0.860215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 196.774i | − | 0.700263i | −0.936701 | − | 0.350132i | \(-0.886137\pi\) | ||
0.936701 | − | 0.350132i | \(-0.113863\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 76.0000i | − | 0.268551i | −0.990944 | − | 0.134276i | \(-0.957129\pi\) | ||
0.990944 | − | 0.134276i | \(-0.0428707\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 160.000 | − | 178.885i | 0.561404 | − | 0.627668i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 320.000i | − | 1.11498i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0000 | −0.107266 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −111.803 | − | 100.000i | −0.384204 | − | 0.343643i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −140.000 | −0.477816 | −0.238908 | − | 0.971042i | \(-0.576789\pi\) | ||||
−0.238908 | + | 0.971042i | \(0.576789\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 411.437 | 1.39470 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 70.0000 | − | 98.3870i | 0.235690 | − | 0.331269i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −286.217 | −0.957246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 321.994i | 1.06975i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 205.718 | + | 184.000i | 0.678938 | + | 0.607261i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 71.5542i | 0.234604i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 244.000i | − | 0.794788i | −0.917648 | − | 0.397394i | \(-0.869915\pi\) | ||
0.917648 | − | 0.397394i | \(-0.130085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 100.000 | + | 89.4427i | 0.323625 | + | 0.289459i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 400.000i | − | 1.28617i | −0.765793 | − | 0.643087i | \(-0.777653\pi\) | ||
0.765793 | − | 0.643087i | \(-0.222347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −290.000 | −0.926518 | −0.463259 | − | 0.886223i | \(-0.653320\pi\) | ||||
−0.463259 | + | 0.886223i | \(0.653320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.7771 | − | 320.000i | −0.113578 | − | 1.01587i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 420.000 | 1.32492 | 0.662461 | − | 0.749097i | \(-0.269512\pi\) | ||||
0.662461 | + | 0.749097i | \(0.269512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 232.551 | 0.729000 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 90.0000 | + | 80.4984i | 0.280374 | + | 0.250774i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 357.771 | 1.10765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 160.997i | − | 0.495375i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −250.440 | + | 280.000i | −0.765870 | + | 0.856269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 572.433i | − | 1.73992i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 340.000i | 1.02719i | 0.858033 | + | 0.513595i | \(0.171687\pi\) | ||||
−0.858033 | + | 0.513595i | \(0.828313\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −480.000 | + | 53.6656i | −1.44144 | + | 0.161158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 176.000i | 0.525373i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 110.000 | 0.326409 | 0.163205 | − | 0.986592i | \(-0.447817\pi\) | ||||
0.163205 | + | 0.986592i | \(0.447817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −71.5542 | + | 80.0000i | −0.211074 | + | 0.235988i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.000 | 0.351906 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 160.997 | 0.469379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 128.000 | − | 143.108i | 0.371014 | − | 0.414807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 147.580 | 0.425304 | 0.212652 | − | 0.977128i | \(-0.431790\pi\) | ||||
0.212652 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8885i | 0.0512566i | 0.999672 | + | 0.0256283i | \(0.00815863\pi\) | ||||
−0.999672 | + | 0.0256283i | \(0.991841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 393.548 | + | 280.000i | 1.12122 | + | 0.797721i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 214.663i | − | 0.608109i | −0.952655 | − | 0.304055i | \(-0.901659\pi\) | ||
0.952655 | − | 0.304055i | \(-0.0983405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 320.000i | 0.901408i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 320.000 | − | 357.771i | 0.896359 | − | 1.00216i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 560.000i | − | 1.55989i | −0.625849 | − | 0.779944i | \(-0.715247\pi\) | ||
0.625849 | − | 0.779944i | \(-0.284753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.0000 | −0.108033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 225.843 | + | 202.000i | 0.622157 | + | 0.556474i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −200.000 | −0.547945 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −617.155 | −1.68162 | −0.840810 | − | 0.541330i | \(-0.817921\pi\) | ||||
−0.840810 | + | 0.541330i | \(0.817921\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −320.000 | + | 35.7771i | −0.867209 | + | 0.0969569i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −178.885 | −0.482171 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 375.659i | − | 1.00713i | −0.863957 | − | 0.503565i | \(-0.832021\pi\) | ||
0.863957 | − | 0.503565i | \(-0.167979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 304.105 | + | 272.000i | 0.810947 | + | 0.725333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 930.204i | 2.46739i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 260.000i | − | 0.686016i | −0.939333 | − | 0.343008i | \(-0.888554\pi\) | ||
0.939333 | − | 0.343008i | \(-0.111446\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −60.0000 | − | 53.6656i | −0.157480 | − | 0.140855i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 544.000i | − | 1.42037i | −0.704017 | − | 0.710183i | \(-0.748612\pi\) | ||
0.704017 | − | 0.710183i | \(-0.251388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −160.000 | −0.415584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 321.994 | − | 36.0000i | 0.832025 | − | 0.0930233i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −332.000 | −0.853470 | −0.426735 | − | 0.904377i | \(-0.640336\pi\) | ||||
−0.426735 | + | 0.904377i | \(0.640336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 286.217 | 0.732012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −150.000 | − | 134.164i | −0.381679 | − | 0.341384i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −321.994 | −0.815174 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 268.328i | − | 0.675890i | −0.941166 | − | 0.337945i | \(-0.890268\pi\) | ||
0.941166 | − | 0.337945i | \(-0.109732\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −357.771 | + | 400.000i | −0.896669 | + | 1.00251i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 160.997i | 0.401489i | 0.979644 | + | 0.200744i | \(0.0643360\pi\) | ||||
−0.979644 | + | 0.200744i | \(0.935664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 480.000i | 1.19107i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −316.000 | + | 71.5542i | −0.780247 | + | 0.176677i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 240.000i | 0.589681i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 178.000 | 0.435208 | 0.217604 | − | 0.976037i | \(-0.430176\pi\) | ||||
0.217604 | + | 0.976037i | \(0.430176\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 286.217 | − | 320.000i | 0.696391 | − | 0.778589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −920.000 | −2.22760 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −411.437 | −0.991413 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 520.000 | − | 581.378i | 1.24700 | − | 1.39419i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −245.967 | −0.587035 | −0.293517 | − | 0.955954i | \(-0.594826\pi\) | ||||
−0.293517 | + | 0.955954i | \(0.594826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 53.6656i | 0.127472i | 0.997967 | + | 0.0637359i | \(0.0203015\pi\) | ||||
−0.997967 | + | 0.0637359i | \(0.979698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −572.433 | + | 64.0000i | −1.35327 | + | 0.151300i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 160.997i | 0.378816i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 160.000i | − | 0.374707i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 160.000 | − | 178.885i | 0.372960 | − | 0.416982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 320.000i | − | 0.742459i | −0.928541 | − | 0.371230i | \(-0.878936\pi\) | ||
0.928541 | − | 0.371230i | \(-0.121064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 530.000 | 1.22402 | 0.612009 | − | 0.790851i | \(-0.290362\pi\) | ||||
0.612009 | + | 0.790851i | \(0.290362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −465.102 | − | 416.000i | −1.06920 | − | 0.956322i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −320.000 | −0.732265 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −474.046 | −1.07983 | −0.539916 | − | 0.841719i | \(-0.681544\pi\) | ||||
−0.539916 | + | 0.841719i | \(0.681544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.0000 | + | 277.272i | 0.0702948 | + | 0.628736i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 505.351 | 1.14075 | 0.570374 | − | 0.821385i | \(-0.306798\pi\) | ||||
0.570374 | + | 0.821385i | \(0.306798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 643.988i | − | 1.44716i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 62.6099 | + | 56.0000i | 0.140067 | + | 0.125280i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 268.328i | 0.597613i | 0.954314 | + | 0.298806i | \(0.0965885\pi\) | ||||
−0.954314 | + | 0.298806i | \(0.903412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 160.000i | 0.354767i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −540.000 | − | 482.991i | −1.19205 | − | 1.06620i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 640.000i | − | 1.40659i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 210.000 | 0.459519 | 0.229759 | − | 0.973247i | \(-0.426206\pi\) | ||||
0.229759 | + | 0.973247i | \(0.426206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −393.548 | − | 280.000i | −0.857403 | − | 0.610022i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 372.000 | 0.806941 | 0.403471 | − | 0.914993i | \(-0.367804\pi\) | ||||
0.403471 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 169.941 | 0.367044 | 0.183522 | − | 0.983016i | \(-0.441250\pi\) | ||||
0.183522 | + | 0.983016i | \(0.441250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −240.000 | − | 214.663i | −0.516129 | − | 0.461640i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −460.630 | −0.986360 | −0.493180 | − | 0.869927i | \(-0.664166\pi\) | ||||
−0.493180 | + | 0.869927i | \(0.664166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 393.548i | − | 0.839121i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −107.331 | + | 120.000i | −0.227880 | + | 0.254777i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 160.997i | − | 0.340374i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 180.000i | − | 0.378947i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.0000 | + | 178.885i | 0.0419287 | + | 0.375022i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 320.000i | 0.668058i | 0.942563 | + | 0.334029i | \(0.108408\pi\) | ||||
−0.942563 | + | 0.334029i | \(0.891592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −960.000 | −1.99584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −286.217 | + | 320.000i | −0.592581 | + | 0.662526i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 200.000 | 0.412371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 62.6099 | 0.128562 | 0.0642812 | − | 0.997932i | \(-0.479525\pi\) | ||||
0.0642812 | + | 0.997932i | \(0.479525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −248.000 | + | 277.272i | −0.507157 | + | 0.567019i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 889.955 | 1.81254 | 0.906268 | − | 0.422704i | \(-0.138919\pi\) | ||||
0.906268 | + | 0.422704i | \(0.138919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 930.204i | − | 1.88682i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.8885 | + | 160.000i | 0.0361385 | + | 0.323232i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 715.542i | − | 1.43972i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 100.000i | − | 0.200401i | −0.994967 | − | 0.100200i | \(-0.968052\pi\) | ||
0.994967 | − | 0.100200i | \(-0.0319484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.0000 | + | 35.7771i | −0.0638723 | + | 0.0714114i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.0000i | − | 0.0318091i | −0.999874 | − | 0.0159046i | \(-0.994937\pi\) | ||
0.999874 | − | 0.0159046i | \(-0.00506280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −368.000 | −0.728713 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 337.646 | + | 302.000i | 0.665969 | + | 0.595661i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −332.000 | −0.652259 | −0.326130 | − | 0.945325i | \(-0.605745\pi\) | ||||
−0.326130 | + | 0.945325i | \(0.605745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 447.214 | 0.875173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 440.000 | + | 313.050i | 0.857700 | + | 0.610233i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −178.885 | −0.347350 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 286.217i | 0.553611i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 313.050 | + | 280.000i | 0.603178 | + | 0.539499i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 214.663i | 0.412020i | 0.978550 | + | 0.206010i | \(0.0660480\pi\) | ||||
−0.978550 | + | 0.206010i | \(0.933952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 76.0000i | 0.145315i | 0.997357 | + | 0.0726577i | \(0.0231481\pi\) | ||||
−0.997357 | + | 0.0726577i | \(0.976852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −180.000 | − | 160.997i | −0.342857 | − | 0.306661i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 480.000i | − | 0.910816i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 273.000 | 0.516068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 102.859 | + | 920.000i | 0.193708 | + | 1.73258i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −640.000 | −1.20075 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −160.997 | −0.300929 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −150.000 | − | 134.164i | −0.279330 | − | 0.249840i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 138.636 | 0.257210 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1019.65i | 1.88474i | 0.334566 | + | 0.942372i | \(0.391410\pi\) | ||||
−0.334566 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 250.440 | − | 280.000i | 0.461215 | − | 0.515654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 500.879i | − | 0.919044i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 244.000i | 0.446069i | 0.974810 | + | 0.223035i | \(0.0715963\pi\) | ||||
−0.974810 | + | 0.223035i | \(0.928404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −160.000 | + | 17.8885i | −0.291439 | + | 0.0325839i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1040.00i | 1.88748i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 720.000 | 1.30199 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 429.325 | − | 480.000i | 0.773559 | − | 0.864865i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −60.0000 | −0.107720 | −0.0538600 | − | 0.998548i | \(-0.517152\pi\) | ||||
−0.0538600 | + | 0.998548i | \(0.517152\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 643.988 | 1.15204 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −160.000 | + | 178.885i | −0.285205 | + | 0.318869i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 111.803 | 0.198585 | 0.0992925 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992925 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 143.108i | − | 0.253289i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 706.597 | − | 160.000i | 1.24620 | − | 0.282187i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 858.650i | − | 1.50905i | −0.656271 | − | 0.754526i | \(-0.727867\pi\) | ||
0.656271 | − | 0.754526i | \(-0.272133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 940.000i | − | 1.64623i | −0.567871 | − | 0.823117i | \(-0.692233\pi\) | ||
0.567871 | − | 0.823117i | \(-0.307767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 320.000 | − | 357.771i | 0.558464 | − | 0.624382i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 144.000i | − | 0.250435i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −370.000 | −0.641248 | −0.320624 | − | 0.947207i | \(-0.603893\pi\) | ||||
−0.320624 | + | 0.947207i | \(0.603893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −67.0820 | − | 60.0000i | −0.115858 | − | 0.103627i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 920.000 | 1.58348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 89.4427 | 0.153418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −640.000 | + | 71.5542i | −1.09402 | + | 0.122315i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −469.574 | −0.799956 | −0.399978 | − | 0.916525i | \(-0.630982\pi\) | ||||
−0.399978 | + | 0.916525i | \(0.630982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 536.656i | 0.911131i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −402.492 | − | 360.000i | −0.681036 | − | 0.609137i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 572.433i | 0.965318i | 0.875808 | + | 0.482659i | \(0.160329\pi\) | ||||
−0.875808 | + | 0.482659i | \(0.839671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 640.000i | 1.07563i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 580.000 | + | 518.768i | 0.971524 | + | 0.868958i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 560.000i | − | 0.934891i | −0.884022 | − | 0.467446i | \(-0.845174\pi\) | ||
0.884022 | − | 0.467446i | \(-0.154826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 302.000 | 0.502496 | 0.251248 | − | 0.967923i | \(-0.419159\pi\) | ||||
0.251248 | + | 0.967923i | \(0.419159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −393.548 | + | 44.0000i | −0.652650 | + | 0.0729685i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −404.000 | −0.667769 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.7214 | −0.0736760 | −0.0368380 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368380 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1040.00 | + | 930.204i | 1.70772 | + | 1.52743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1144.87 | −1.87376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 447.214i | − | 0.729549i | −0.931096 | − | 0.364775i | \(-0.881146\pi\) | ||
0.931096 | − | 0.364775i | \(-0.118854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 286.217 | − | 320.000i | 0.465393 | − | 0.520325i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 447.214i | 0.724819i | 0.932019 | + | 0.362410i | \(0.118046\pi\) | ||||
−0.932019 | + | 0.362410i | \(0.881954\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 780.000i | − | 1.26010i | −0.776556 | − | 0.630048i | \(-0.783035\pi\) | ||
0.776556 | − | 0.630048i | \(-0.216965\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 352.000 | + | 250.440i | 0.566828 | + | 0.403284i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1440.00i | 2.31140i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 178.885 | − | 200.000i | 0.285304 | − | 0.318979i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 960.000 | 1.52623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −80.4984 | −0.127573 | −0.0637864 | − | 0.997964i | \(-0.520318\pi\) | ||||
−0.0637864 | + | 0.997964i | \(0.520318\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 120.000 | − | 134.164i | 0.189573 | − | 0.211950i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 107.331 | 0.169026 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 554.545i | 0.870557i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −715.542 | + | 80.0000i | −1.11978 | + | 0.125196i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 661.876i | 1.03257i | 0.856417 | + | 0.516284i | \(0.172685\pi\) | ||||
−0.856417 | + | 0.516284i | \(0.827315\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 844.000i | − | 1.31260i | −0.754501 | − | 0.656299i | \(-0.772121\pi\) | ||
0.754501 | − | 0.656299i | \(-0.227879\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −288.000 | + | 321.994i | −0.446512 | + | 0.499215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.0000i | − | 0.0247295i | −0.999924 | − | 0.0123648i | \(-0.996064\pi\) | ||
0.999924 | − | 0.0123648i | \(-0.00393593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 460.000 | 0.708783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 536.656 | + | 480.000i | 0.824357 | + | 0.737327i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 660.000 | 1.01072 | 0.505360 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505360 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 268.328 | 0.409661 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.0000 | − | 447.214i | −0.0761035 | − | 0.680690i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 210.190 | 0.318954 | 0.159477 | − | 0.987202i | \(-0.449019\pi\) | ||||
0.159477 | + | 0.987202i | \(0.449019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 769.207i | 1.16370i | 0.813295 | + | 0.581851i | \(0.197671\pi\) | ||||
−0.813295 | + | 0.581851i | \(0.802329\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −715.542 | − | 640.000i | −1.07925 | − | 0.965309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 715.542i | − | 1.07600i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 832.000i | 1.24738i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 340.000 | + | 304.105i | 0.508221 | + | 0.454567i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 80.0000i | 0.119225i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −910.000 | −1.35215 | −0.676077 | − | 0.736831i | \(-0.736321\pi\) | ||||
−0.676077 | + | 0.736831i | \(0.736321\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −140.872 | + | 198.000i | −0.208700 | + | 0.293333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 260.000 | 0.384047 | 0.192024 | − | 0.981390i | \(-0.438495\pi\) | ||||
0.192024 | + | 0.981390i | \(0.438495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −447.214 | −0.658636 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −570.000 | − | 509.823i | −0.837004 | − | 0.748639i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 934.676 | 1.36849 | 0.684243 | − | 0.729254i | \(-0.260133\pi\) | ||||
0.684243 | + | 0.729254i | \(0.260133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 572.433i | 0.835669i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 393.548 | − | 440.000i | 0.572850 | − | 0.640466i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 357.771i | 0.519261i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 100.000i | 0.144718i | 0.997379 | + | 0.0723589i | \(0.0230527\pi\) | ||||
−0.997379 | + | 0.0723589i | \(0.976947\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.0000 | − | 357.771i | −0.0577201 | − | 0.516264i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1040.00i | 1.49640i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 640.000 | 0.918221 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −321.994 | + | 360.000i | −0.460649 | + | 0.515021i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1028.00 | 1.46648 | 0.733238 | − | 0.679972i | \(-0.238008\pi\) | ||||
0.733238 | + | 0.679972i | \(0.238008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1073.31 | −1.52676 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 512.000 | − | 572.433i | 0.726241 | − | 0.811962i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 822.873 | 1.16389 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 912.316i | 1.28676i | 0.765545 | + | 0.643382i | \(0.222469\pi\) | ||||
−0.765545 | + | 0.643382i | \(0.777531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −80.4984 | − | 720.000i | −0.113219 | − | 1.01266i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 429.325i | 0.602139i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.000i | 0.447552i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −640.000 | + | 715.542i | −0.892608 | + | 0.997966i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 480.000i | − | 0.667594i | −0.942645 | − | 0.333797i | \(-0.891670\pi\) | ||
0.942645 | − | 0.333797i | \(-0.108330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 400.000 | 0.554785 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −711.070 | − | 636.000i | −0.983499 | − | 0.879668i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −468.000 | −0.645517 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 241.495 | 0.332181 | 0.166090 | − | 0.986111i | \(-0.446886\pi\) | ||||
0.166090 | + | 0.986111i | \(0.446886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −239.000 | − | 688.709i | −0.327846 | − | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −643.988 | −0.880968 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1126.98i | − | 1.53749i | −0.639557 | − | 0.768744i | \(-0.720882\pi\) | ||
0.639557 | − | 0.768744i | \(-0.279118\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −277.272 | − | 248.000i | −0.377241 | − | 0.337415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 196.774i | 0.266993i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1020.00i | 1.38024i | 0.723693 | + | 0.690122i | \(0.242443\pi\) | ||||
−0.723693 | + | 0.690122i | \(0.757557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 800.000 | + | 715.542i | 1.07962 | + | 0.965643i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 176.000i | 0.236878i | 0.992961 | + | 0.118439i | \(0.0377889\pi\) | ||||
−0.992961 | + | 0.118439i | \(0.962211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −112.000 | −0.150336 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −102.859 | − | 920.000i | −0.137696 | − | 1.23159i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 360.000 | 0.480641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1296.92 | −1.72692 | −0.863462 | − | 0.504414i | \(-0.831708\pi\) | ||||
−0.863462 | + | 0.504414i | \(0.831708\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −330.000 | − | 295.161i | −0.438247 | − | 0.391980i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 965.981 | 1.27945 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 983.870i | 1.29970i | 0.760064 | + | 0.649848i | \(0.225167\pi\) | ||||
−0.760064 | + | 0.649848i | \(0.774833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 143.108 | − | 160.000i | 0.188549 | − | 0.210804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 107.331i | − | 0.141040i | −0.997510 | − | 0.0705199i | \(-0.977534\pi\) | ||
0.997510 | − | 0.0705199i | \(-0.0224658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1120.00i | 1.46789i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 640.000 | − | 71.5542i | 0.836601 | − | 0.0935349i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1840.00i | 2.39896i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1378.00 | −1.79194 | −0.895969 | − | 0.444117i | \(-0.853517\pi\) | ||||
−0.895969 | + | 0.444117i | \(0.853517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 214.663 | − | 240.000i | 0.278421 | − | 0.311284i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1180.00 | −1.52652 | −0.763260 | − | 0.646091i | \(-0.776402\pi\) | ||||
−0.763260 | + | 0.646091i | \(0.776402\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −241.495 | −0.311607 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −960.000 | + | 1073.31i | −1.23552 | + | 1.38135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −715.542 | −0.918539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 357.771i | 0.458093i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 813.929 | − | 1144.00i | 1.03950 | − | 1.46105i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 214.663i | − | 0.273455i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1244.00i | − | 1.58069i | −0.612665 | − | 0.790343i | \(-0.709902\pi\) | ||
0.612665 | − | 0.790343i | \(-0.290098\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 288.000 | − | 321.994i | 0.365019 | − | 0.408104i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 320.000i | 0.404551i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −320.000 | −0.403531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −178.885 | − | 160.000i | −0.225013 | − | 0.201258i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 580.000 | 0.727729 | 0.363864 | − | 0.931452i | \(-0.381457\pi\) | ||||
0.363864 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1144.87 | 1.43287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1440.00 | − | 160.997i | 1.79775 | − | 0.200995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −223.607 | −0.278464 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 572.433i | − | 0.711097i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −295.161 | − | 264.000i | −0.365751 | − | 0.327138i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 250.440i | 0.309567i | 0.987948 | + | 0.154783i | \(0.0494680\pi\) | ||||
−0.987948 | + | 0.154783i | \(0.950532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 980.000i | − | 1.20838i | −0.796839 | − | 0.604192i | \(-0.793496\pi\) | ||
0.796839 | − | 0.604192i | \(-0.206504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −620.000 | − | 554.545i | −0.762608 | − | 0.682097i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 496.000i | − | 0.608589i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 720.000 | 0.881273 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1431.08 | − | 160.000i | 1.74735 | − | 0.195360i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 932.000 | 1.13520 | 0.567600 | − | 0.823304i | \(-0.307872\pi\) | ||||
0.567600 | + | 0.823304i | \(0.307872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1565.25 | 1.90188 | 0.950940 | − | 0.309375i | \(-0.100120\pi\) | ||||
0.950940 | + | 0.309375i | \(0.100120\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 90.0000 | + | 80.4984i | 0.109091 | + | 0.0975739i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1542.89 | −1.86564 | −0.932822 | − | 0.360339i | \(-0.882661\pi\) | ||||
−0.932822 | + | 0.360339i | \(0.882661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 482.991i | − | 0.582618i | −0.956629 | − | 0.291309i | \(-0.905909\pi\) | ||
0.956629 | − | 0.291309i | \(-0.0940909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 536.656 | − | 600.000i | 0.645796 | − | 0.722022i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 554.545i | − | 0.665720i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 64.0000i | − | 0.0766467i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 420.000 | − | 590.322i | 0.501792 | − | 0.705283i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1360.00i | 1.62098i | 0.585754 | + | 0.810489i | \(0.300798\pi\) | ||||
−0.585754 | + | 0.810489i | \(0.699202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1863.00 | 2.21522 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −393.548 | + | 440.000i | −0.466842 | + | 0.521945i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −604.000 | −0.714793 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 903.371 | 1.06655 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −152.000 | + | 169.941i | −0.179034 | + | 0.200166i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −858.650 | −1.00899 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 948.093i | − | 1.11148i | −0.831356 | − | 0.555740i | \(-0.812435\pi\) | ||
0.831356 | − | 0.555740i | \(-0.187565\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −715.542 | + | 80.0000i | −0.836891 | + | 0.0935673i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 858.650i | 1.00193i | 0.865469 | + | 0.500963i | \(0.167021\pi\) | ||||
−0.865469 | + | 0.500963i | \(0.832979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1340.00i | 1.55995i | 0.625809 | + | 0.779977i | \(0.284769\pi\) | ||||
−0.625809 | + | 0.779977i | \(0.715231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −640.000 | + | 715.542i | −0.743322 | + | 0.831059i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 224.000i | 0.259560i | 0.991543 | + | 0.129780i | \(0.0414271\pi\) | ||||
−0.991543 | + | 0.129780i | \(0.958573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −560.000 | −0.647399 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 69.3181 | + | 62.0000i | 0.0799517 | + | 0.0715110i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −360.000 | −0.414269 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −787.096 | −0.903669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.0000 | + | 447.214i | 0.0572738 | + | 0.512272i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1216.42 | 1.39020 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 948.093i | 1.08106i | 0.841324 | + | 0.540532i | \(0.181777\pi\) | ||||
−0.841324 | + | 0.540532i | \(0.818223\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 313.050 | + | 280.000i | 0.356143 | + | 0.318544i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1538.41i | − | 1.74621i | −0.487528 | − | 0.873107i | \(-0.662101\pi\) | ||
0.487528 | − | 0.873107i | \(-0.337899\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1164.00i | − | 1.31823i | −0.752041 | − | 0.659117i | \(-0.770930\pi\) | ||
0.752041 | − | 0.659117i | \(-0.229070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −920.000 | − | 822.873i | −1.03955 | − | 0.929800i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 336.000i | − | 0.378805i | −0.981900 | − | 0.189402i | \(-0.939345\pi\) | ||
0.981900 | − | 0.189402i | \(-0.0606551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −240.000 | −0.269966 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −353.299 | + | 80.0000i | −0.396519 | + | 0.0897868i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1280.00 | −1.43337 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 268.328 | 0.299808 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 640.000 | + | 572.433i | 0.713489 | + | 0.638164i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1395.31 | 1.55206 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 357.771i | − | 0.397082i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 643.988 | − | 720.000i | 0.713165 | − | 0.797342i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 500.879i | 0.553458i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 764.000i | 0.842337i | 0.906982 | + | 0.421169i | \(0.138380\pi\) | ||||
−0.906982 | + | 0.421169i | \(0.861620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −92.0000 | − | 822.873i | −0.101210 | − | 0.905251i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1280.00i | 1.40505i | 0.711659 | + | 0.702525i | \(0.247944\pi\) | ||||
−0.711659 | + | 0.702525i | \(0.752056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −460.000 | −0.503834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 143.108 | − | 160.000i | 0.156403 | − | 0.174863i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −600.000 | −0.654308 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 849.706 | 0.924598 | 0.462299 | − | 0.886724i | \(-0.347025\pi\) | ||||
0.462299 | + | 0.886724i | \(0.347025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −488.000 | + | 545.601i | −0.529859 | + | 0.592400i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1431.08 | −1.55047 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 482.991i | − | 0.522152i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −44.7214 | − | 400.000i | −0.0482431 | − | 0.431499i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 375.659i | 0.404370i | 0.979347 | + | 0.202185i | \(0.0648042\pi\) | ||||
−0.979347 | + | 0.202185i | \(0.935196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 620.000i | 0.665951i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −800.000 | + | 894.427i | −0.857449 | + | 0.958657i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 320.000i | − | 0.342246i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −510.000 | −0.544290 | −0.272145 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272145 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 648.460 | + | 580.000i | 0.690585 | + | 0.617678i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −812.000 | −0.862912 | −0.431456 | − | 0.902134i | \(-0.642000\pi\) | ||||
−0.431456 | + | 0.902134i | \(0.642000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −572.433 | −0.607034 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −560.000 | + | 787.096i | −0.592593 | + | 0.832906i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1569.72 | 1.65757 | 0.828785 | − | 0.559566i | \(-0.189032\pi\) | ||||
0.828785 | + | 0.559566i | \(0.189032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 894.427i | − | 0.942494i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −939.149 | − | 840.000i | −0.987538 | − | 0.883281i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1073.31i | − | 1.12625i | −0.826373 | − | 0.563123i | \(-0.809600\pi\) | ||
0.826373 | − | 0.563123i | \(-0.190400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 640.000i | 0.670157i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −520.000 | − | 465.102i | −0.543365 | − | 0.486000i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1280.00i | − | 1.33472i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −241.000 | −0.250780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.2492 | − | 360.000i | −0.0417957 | − | 0.373832i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 120.000 | 0.124352 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 420.381 | 0.434727 | 0.217363 | − | 0.976091i | \(-0.430254\pi\) | ||||
0.217363 | + | 0.976091i | \(0.430254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −800.000 | − | 715.542i | −0.825593 | − | 0.738433i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 791.568 | 0.815209 | 0.407605 | − | 0.913159i | \(-0.366364\pi\) | ||||
0.407605 | + | 0.913159i | \(0.366364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2325.51i | − | 2.39004i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −321.994 | + | 360.000i | −0.330250 | + | 0.369231i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 661.876i | − | 0.677458i | −0.940884 | − | 0.338729i | \(-0.890003\pi\) | ||
0.940884 | − | 0.338729i | \(-0.109997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 720.000i | − | 0.735444i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1120.00 | − | 125.220i | 1.14169 | − | 0.127645i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1776.00i | 1.80671i | 0.428889 | + | 0.903357i | \(0.358905\pi\) | ||||
−0.428889 | + | 0.903357i | \(0.641095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 720.000 | 0.730964 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1144.87 | + | 1280.00i | −1.15995 | + | 1.29686i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 576.000 | 0.582406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1368.47 | −1.38090 | −0.690451 | − | 0.723379i | \(-0.742588\pi\) | ||||
−0.690451 | + | 0.723379i | \(0.742588\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 680.000 | − | 760.263i | 0.684794 | − | 0.765622i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1037.54 | −1.04275 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1234.31i | − | 1.23802i | −0.785382 | − | 0.619012i | \(-0.787533\pi\) | ||
0.785382 | − | 0.619012i | \(-0.212467\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1180.64 | + | 840.000i | 1.18183 | + | 0.840841i |
(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 | 384.3.h.f.65.1 | yes | 4 | |
3.2 | odd | 2 | 384.3.h.e.65.3 | yes | 4 | ||
4.3 | odd | 2 | inner | 384.3.h.f.65.4 | yes | 4 | |
8.3 | odd | 2 | 384.3.h.e.65.1 | ✓ | 4 | ||
8.5 | even | 2 | 384.3.h.e.65.4 | yes | 4 | ||
12.11 | even | 2 | 384.3.h.e.65.2 | yes | 4 | ||
16.3 | odd | 4 | 768.3.e.h.257.3 | 4 | |||
16.5 | even | 4 | 768.3.e.h.257.4 | 4 | |||
16.11 | odd | 4 | 768.3.e.m.257.2 | 4 | |||
16.13 | even | 4 | 768.3.e.m.257.1 | 4 | |||
24.5 | odd | 2 | inner | 384.3.h.f.65.2 | yes | 4 | |
24.11 | even | 2 | inner | 384.3.h.f.65.3 | yes | 4 | |
48.5 | odd | 4 | 768.3.e.h.257.1 | 4 | |||
48.11 | even | 4 | 768.3.e.m.257.3 | 4 | |||
48.29 | odd | 4 | 768.3.e.m.257.4 | 4 | |||
48.35 | even | 4 | 768.3.e.h.257.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.h.e.65.1 | ✓ | 4 | 8.3 | odd | 2 | ||
384.3.h.e.65.2 | yes | 4 | 12.11 | even | 2 | ||
384.3.h.e.65.3 | yes | 4 | 3.2 | odd | 2 | ||
384.3.h.e.65.4 | yes | 4 | 8.5 | even | 2 | ||
384.3.h.f.65.1 | yes | 4 | 1.1 | even | 1 | trivial | |
384.3.h.f.65.2 | yes | 4 | 24.5 | odd | 2 | inner | |
384.3.h.f.65.3 | yes | 4 | 24.11 | even | 2 | inner | |
384.3.h.f.65.4 | yes | 4 | 4.3 | odd | 2 | inner | |
768.3.e.h.257.1 | 4 | 48.5 | odd | 4 | |||
768.3.e.h.257.2 | 4 | 48.35 | even | 4 | |||
768.3.e.h.257.3 | 4 | 16.3 | odd | 4 | |||
768.3.e.h.257.4 | 4 | 16.5 | even | 4 | |||
768.3.e.m.257.1 | 4 | 16.13 | even | 4 | |||
768.3.e.m.257.2 | 4 | 16.11 | odd | 4 | |||
768.3.e.m.257.3 | 4 | 48.11 | even | 4 | |||
768.3.e.m.257.4 | 4 | 48.29 | odd | 4 |