Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(257,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.e (of order \(2\), degree \(1\), 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: | \(20.9264843029\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.257 |
Dual form | 768.3.e.h.257.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.00000i | − | 0.800000i | −0.916515 | − | 0.400000i | \(-0.869010\pi\) | ||
0.916515 | − | 0.400000i | \(-0.130990\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 4.47214i | 0.406558i | 0.979121 | + | 0.203279i | \(0.0651598\pi\) | ||||
−0.979121 | + | 0.203279i | \(0.934840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.8885 | −1.37604 | −0.688021 | − | 0.725691i | \(-0.741520\pi\) | ||||
−0.688021 | + | 0.725691i | \(0.741520\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 20.0000 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.8885 | − | 20.0000i | 0.851835 | − | 0.952381i | ||||
\(22\) | 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 | ||||||||
\(27\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.0000i | 1.79310i | 0.442939 | + | 0.896552i | \(0.353936\pi\) | ||||
−0.442939 | + | 0.896552i | \(0.646064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.8328 | −0.865575 | −0.432787 | − | 0.901496i | \(-0.642470\pi\) | ||||
−0.432787 | + | 0.901496i | \(0.642470\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0000 | − | 8.94427i | −0.303030 | − | 0.271039i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.7771i | 1.02220i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.6656 | 1.45042 | 0.725211 | − | 0.688526i | \(-0.241742\pi\) | ||||
0.725211 | + | 0.688526i | \(0.241742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 35.7771 | − | 40.0000i | 0.917361 | − | 1.02564i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 35.7771i | − | 0.872612i | −0.899798 | − | 0.436306i | \(-0.856287\pi\) | ||
0.899798 | − | 0.436306i | \(-0.143713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.0000 | 0.837209 | 0.418605 | − | 0.908169i | \(-0.362519\pi\) | ||||
0.418605 | + | 0.908169i | \(0.362519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −35.7771 | + | 4.00000i | −0.795046 | + | 0.0888889i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 64.0000i | − | 1.36170i | −0.732422 | − | 0.680851i | \(-0.761610\pi\) | ||
0.732422 | − | 0.680851i | \(-0.238390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 31.0000 | 0.632653 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.0000 | + | 35.7771i | 0.784314 | + | 0.701512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 20.0000i | − | 0.377358i | −0.982039 | − | 0.188679i | \(-0.939579\pi\) | ||
0.982039 | − | 0.188679i | \(-0.0604206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.8885 | 0.325246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −40.0000 | + | 44.7214i | −0.701754 | + | 0.784585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 102.859i | 1.74338i | 0.490062 | + | 0.871688i | \(0.336974\pi\) | ||||
−0.490062 | + | 0.871688i | \(0.663026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.8885 | −0.293255 | −0.146627 | − | 0.989192i | \(-0.546842\pi\) | ||||
−0.146627 | + | 0.989192i | \(0.546842\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.94427 | + | 80.0000i | 0.141973 | + | 1.26984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 71.5542i | 1.10083i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.0000 | 0.656716 | 0.328358 | − | 0.944553i | \(-0.393505\pi\) | ||||
0.328358 | + | 0.944553i | \(0.393505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −35.7771 | − | 32.0000i | −0.518509 | − | 0.463768i | ||||
\(70\) | 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 | \(-0.388738\pi\) | ||||
0.342466 | + | 0.939530i | \(0.388738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.0000 | + | 20.1246i | −0.240000 | + | 0.268328i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 40.0000i | − | 0.519481i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.4984 | 1.01897 | 0.509484 | − | 0.860480i | \(-0.329836\pi\) | ||||
0.509484 | + | 0.860480i | \(0.329836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | + | 17.8885i | −0.975309 | + | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 102.859i | 1.23927i | 0.784891 | + | 0.619633i | \(0.212719\pi\) | ||||
−0.784891 | + | 0.619633i | \(0.787281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −71.5542 | −0.841814 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −116.276 | − | 104.000i | −1.33650 | − | 1.19540i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 160.997i | 1.80895i | 0.426523 | + | 0.904477i | \(0.359738\pi\) | ||||
−0.426523 | + | 0.904477i | \(0.640262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 160.000 | 1.75824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 53.6656 | − | 60.0000i | 0.577050 | − | 0.645161i | ||||
\(94\) | 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 | ||||||||
\(99\) | 40.0000 | − | 4.47214i | 0.404040 | − | 0.0451731i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.0000i | 0.910891i | 0.890264 | + | 0.455446i | \(0.150520\pi\) | ||||
−0.890264 | + | 0.455446i | \(0.849480\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − | 40.2492i | − | 0.376161i | −0.982154 | − | 0.188080i | \(-0.939773\pi\) | ||
0.982154 | − | 0.188080i | \(-0.0602266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 125.220 | 1.14881 | 0.574403 | − | 0.818573i | \(-0.305234\pi\) | ||||
0.574403 | + | 0.818573i | \(0.305234\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 64.0000 | 0.556522 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.8885 | + | 160.000i | 0.152894 | + | 1.36752i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 160.000i | 1.34454i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.000 | 0.834711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 80.0000 | + | 71.5542i | 0.650407 | + | 0.581741i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 136.000i | − | 1.08800i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −26.8328 | −0.211282 | −0.105641 | − | 0.994404i | \(-0.533689\pi\) | ||||
−0.105641 | + | 0.994404i | \(0.533689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −72.0000 | + | 80.4984i | −0.558140 | + | 0.624019i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 67.0820i | − | 0.512077i | −0.966667 | − | 0.256038i | \(-0.917583\pi\) | ||
0.966667 | − | 0.256038i | \(-0.0824173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −178.885 | −1.34500 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 62.6099 | − | 88.0000i | 0.463777 | − | 0.651852i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 143.108i | − | 1.04459i | −0.852766 | − | 0.522293i | \(-0.825077\pi\) | ||
0.852766 | − | 0.522293i | \(-0.174923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −260.000 | −1.87050 | −0.935252 | − | 0.353983i | \(-0.884827\pi\) | ||||
−0.935252 | + | 0.353983i | \(0.884827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 143.108 | + | 128.000i | 1.01495 | + | 0.907801i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 80.0000i | − | 0.559441i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 208.000 | 1.43448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −62.0000 | + | 69.3181i | −0.421769 | + | 0.471552i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28.0000i | 0.187919i | 0.995576 | + | 0.0939597i | \(0.0299525\pi\) | ||||
−0.995576 | + | 0.0939597i | \(0.970048\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 107.331i | 0.692460i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 53.6656 | 0.341819 | 0.170910 | − | 0.985287i | \(-0.445329\pi\) | ||||
0.170910 | + | 0.985287i | \(0.445329\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 44.7214 | + | 40.0000i | 0.281266 | + | 0.251572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 143.108i | − | 0.888872i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −124.000 | −0.760736 | −0.380368 | − | 0.924835i | \(-0.624203\pi\) | ||||
−0.380368 | + | 0.924835i | \(0.624203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −35.7771 | + | 40.0000i | −0.216831 | + | 0.242424i | ||||
\(166\) | 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 | ||||||||
\(171\) | −20.0000 | − | 178.885i | −0.116959 | − | 1.04611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 140.000i | − | 0.809249i | −0.914483 | − | 0.404624i | \(-0.867402\pi\) | ||
0.914483 | − | 0.404624i | \(-0.132598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −80.4984 | −0.459991 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −230.000 | − | 205.718i | −1.29944 | − | 1.16225i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 67.0820i | − | 0.374760i | −0.982288 | − | 0.187380i | \(-0.940000\pi\) | ||
0.982288 | − | 0.187380i | \(-0.0599996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.220 | 0.691822 | 0.345911 | − | 0.938267i | \(-0.387570\pi\) | ||||
0.345911 | + | 0.938267i | \(0.387570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.7771 | − | 40.0000i | 0.195503 | − | 0.218579i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 214.663i | − | 1.16034i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 80.0000 | 0.427807 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −196.774 | − | 140.000i | −1.04113 | − | 0.740741i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 160.000i | − | 0.837696i | −0.908056 | − | 0.418848i | \(-0.862434\pi\) | ||
0.908056 | − | 0.418848i | \(-0.137566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 30.0000 | 0.155440 | 0.0777202 | − | 0.996975i | \(-0.475236\pi\) | ||||
0.0777202 | + | 0.996975i | \(0.475236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −160.000 | − | 143.108i | −0.820513 | − | 0.733889i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 180.000i | − | 0.913706i | −0.889542 | − | 0.456853i | \(-0.848977\pi\) | ||
0.889542 | − | 0.456853i | \(-0.151023\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | − | 465.102i | − | 2.29114i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −143.108 | −0.698090 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 143.108 | − | 16.0000i | 0.691345 | − | 0.0772947i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 89.4427i | 0.427956i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 60.0000 | 0.284360 | 0.142180 | − | 0.989841i | \(-0.454589\pi\) | ||||
0.142180 | + | 0.989841i | \(0.454589\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −178.885 | − | 160.000i | −0.839838 | − | 0.751174i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 144.000i | − | 0.669767i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 240.000 | 1.10599 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −100.000 | + | 111.803i | −0.456621 | + | 0.510518i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 320.000i | 1.44796i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 152.053 | 0.681850 | 0.340925 | − | 0.940090i | \(-0.389260\pi\) | ||||
0.340925 | + | 0.940090i | \(0.389260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | − | 80.4984i | −0.0400000 | − | 0.357771i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 254.912i | − | 1.12296i | −0.827491 | − | 0.561480i | \(-0.810232\pi\) | ||
0.827491 | − | 0.561480i | \(-0.189768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 196.774 | 0.859275 | 0.429638 | − | 0.903001i | \(-0.358641\pi\) | ||||
0.429638 | + | 0.903001i | \(0.358641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 89.4427 | + | 80.0000i | 0.387198 | + | 0.346320i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 160.997i | 0.690974i | 0.938424 | + | 0.345487i | \(0.112286\pi\) | ||||
−0.938424 | + | 0.345487i | \(0.887714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −256.000 | −1.08936 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −160.997 | + | 180.000i | −0.679312 | + | 0.759494i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 320.000i | 1.33891i | 0.742852 | + | 0.669456i | \(0.233473\pi\) | ||||
−0.742852 | + | 0.669456i | \(0.766527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 318.000 | 1.31950 | 0.659751 | − | 0.751484i | \(-0.270662\pi\) | ||||
0.659751 | + | 0.751484i | \(0.270662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 118.000 | − | 212.426i | 0.485597 | − | 0.874183i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 124.000i | − | 0.506122i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −357.771 | −1.44847 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −230.000 | − | 205.718i | −0.923695 | − | 0.826178i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 147.580i | 0.587970i | 0.955810 | + | 0.293985i | \(0.0949816\pi\) | ||||
−0.955810 | + | 0.293985i | \(0.905018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −71.5542 | −0.282823 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | −480.000 | −1.85328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 465.102 | − | 52.0000i | 1.78200 | − | 0.199234i | ||||
\(262\) | 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 | ||||||||
\(267\) | −360.000 | − | 321.994i | −1.34831 | − | 1.20597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 132.000i | 0.490706i | 0.969434 | + | 0.245353i | \(0.0789039\pi\) | ||||
−0.969434 | + | 0.245353i | \(0.921096\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −277.272 | −1.02315 | −0.511573 | − | 0.859240i | \(-0.670937\pi\) | ||||
−0.511573 | + | 0.859240i | \(0.670937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −320.000 | + | 357.771i | −1.17216 | + | 1.31052i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 40.2492i | 0.146361i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 268.328 | 0.968694 | 0.484347 | − | 0.874876i | \(-0.339057\pi\) | ||||
0.484347 | + | 0.874876i | \(0.339057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.8328 | + | 240.000i | 0.0961750 | + | 0.860215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196.774i | 0.700263i | 0.936701 | + | 0.350132i | \(0.113863\pi\) | ||||
−0.936701 | + | 0.350132i | \(0.886137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 76.0000 | 0.268551 | 0.134276 | − | 0.990944i | \(-0.457129\pi\) | ||||
0.134276 | + | 0.990944i | \(0.457129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 178.885 | + | 160.000i | 0.627668 | + | 0.561404i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 320.000i | 1.11498i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0000 | −0.107266 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −100.000 | + | 111.803i | −0.343643 | + | 0.384204i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 140.000i | 0.477816i | 0.971042 | + | 0.238908i | \(0.0767894\pi\) | ||||
−0.971042 | + | 0.238908i | \(0.923211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 411.437 | 1.39470 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −70.0000 | + | 98.3870i | −0.235690 | + | 0.331269i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 286.217i | − | 0.957246i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −321.994 | −1.06975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −205.718 | − | 184.000i | −0.678938 | − | 0.607261i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 71.5542i | 0.234604i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −244.000 | −0.794788 | −0.397394 | − | 0.917648i | \(-0.630085\pi\) | ||||
−0.397394 | + | 0.917648i | \(0.630085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 89.4427 | − | 100.000i | 0.289459 | − | 0.323625i | ||||
\(310\) | 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 | \(-0.346680\pi\) | ||||
0.463259 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 320.000 | − | 35.7771i | 1.01587 | − | 0.113578i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 420.000i | 1.32492i | 0.749097 | + | 0.662461i | \(0.230488\pi\) | ||||
−0.749097 | + | 0.662461i | \(0.769512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −232.551 | −0.729000 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 90.0000 | + | 80.4984i | 0.280374 | + | 0.250774i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 357.771i | − | 1.10765i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −160.997 | −0.495375 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −250.440 | + | 280.000i | −0.765870 | + | 0.856269i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 572.433i | 1.73992i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −340.000 | −1.02719 | −0.513595 | − | 0.858033i | \(-0.671687\pi\) | ||||
−0.513595 | + | 0.858033i | \(0.671687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −53.6656 | − | 480.000i | −0.161158 | − | 1.44144i | ||||
\(334\) | 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 | ||||||||
\(339\) | 80.0000 | + | 71.5542i | 0.235988 | + | 0.211074i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 120.000i | − | 0.351906i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 160.997 | 0.469379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −128.000 | + | 143.108i | −0.371014 | + | 0.414807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 147.580i | 0.425304i | 0.977128 | + | 0.212652i | \(0.0682101\pi\) | ||||
−0.977128 | + | 0.212652i | \(0.931790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8885 | −0.0512566 | −0.0256283 | − | 0.999672i | \(-0.508159\pi\) | ||||
−0.0256283 | + | 0.999672i | \(0.508159\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 320.000 | 0.901408 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −357.771 | − | 320.000i | −1.00216 | − | 0.896359i | ||||
\(358\) | 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 | ||||||||
\(363\) | −202.000 | + | 225.843i | −0.556474 | + | 0.622157i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 200.000i | − | 0.547945i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 617.155 | 1.68162 | 0.840810 | − | 0.541330i | \(-0.182079\pi\) | ||||
0.840810 | + | 0.541330i | \(0.182079\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −320.000 | + | 35.7771i | −0.867209 | + | 0.0969569i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 178.885i | 0.482171i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −375.659 | −1.00713 | −0.503565 | − | 0.863957i | \(-0.667979\pi\) | ||||
−0.503565 | + | 0.863957i | \(0.667979\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 304.105 | + | 272.000i | 0.810947 | + | 0.725333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 930.204i | − | 2.46739i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 260.000 | 0.686016 | 0.343008 | − | 0.939333i | \(-0.388554\pi\) | ||||
0.343008 | + | 0.939333i | \(0.388554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.6656 | − | 60.0000i | 0.140855 | − | 0.157480i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 544.000i | 1.42037i | 0.704017 | + | 0.710183i | \(0.251388\pi\) | ||||
−0.704017 | + | 0.710183i | \(0.748612\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −160.000 | −0.415584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36.0000 | − | 321.994i | −0.0930233 | − | 0.832025i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 332.000i | 0.853470i | 0.904377 | + | 0.426735i | \(0.140336\pi\) | ||||
−0.904377 | + | 0.426735i | \(0.859664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 286.217 | 0.732012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 150.000 | + | 134.164i | 0.381679 | + | 0.341384i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 321.994i | − | 0.815174i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.328 | 0.675890 | 0.337945 | − | 0.941166i | \(-0.390268\pi\) | ||||
0.337945 | + | 0.941166i | \(0.390268\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 480.000 | 1.19107 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 71.5542 | + | 316.000i | 0.176677 | + | 0.780247i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 240.000i | 0.589681i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −178.000 | −0.435208 | −0.217604 | − | 0.976037i | \(-0.569824\pi\) | ||||
−0.217604 | + | 0.976037i | \(0.569824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 320.000 | + | 286.217i | 0.778589 | + | 0.696391i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 920.000i | − | 2.22760i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 411.437 | 0.991413 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 520.000 | − | 581.378i | 1.24700 | − | 1.39419i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 245.967i | 0.587035i | 0.955954 | + | 0.293517i | \(0.0948258\pi\) | ||||
−0.955954 | + | 0.293517i | \(0.905174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 53.6656 | 0.127472 | 0.0637359 | − | 0.997967i | \(-0.479698\pi\) | ||||
0.0637359 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −572.433 | + | 64.0000i | −1.35327 | + | 0.151300i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 160.997i | − | 0.378816i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 160.000 | 0.374707 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 178.885 | + | 160.000i | 0.416982 | + | 0.372960i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 320.000i | 0.742459i | 0.928541 | + | 0.371230i | \(0.121064\pi\) | ||||
−0.928541 | + | 0.371230i | \(0.878936\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 530.000 | 1.22402 | 0.612009 | − | 0.790851i | \(-0.290362\pi\) | ||||
0.612009 | + | 0.790851i | \(0.290362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −416.000 | + | 465.102i | −0.956322 | + | 1.06920i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 320.000i | 0.732265i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 505.351i | 1.14075i | 0.821385 | + | 0.570374i | \(0.193202\pi\) | ||||
−0.821385 | + | 0.570374i | \(0.806798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 643.988 | 1.44716 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 160.000 | 0.354767 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −482.991 | + | 540.000i | −1.06620 | + | 1.19205i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 640.000i | − | 1.40659i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −210.000 | −0.459519 | −0.229759 | − | 0.973247i | \(-0.573794\pi\) | ||||
−0.229759 | + | 0.973247i | \(0.573794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 280.000 | − | 393.548i | 0.610022 | − | 0.857403i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 372.000i | 0.806941i | 0.914993 | + | 0.403471i | \(0.132196\pi\) | ||||
−0.914993 | + | 0.403471i | \(0.867804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −169.941 | −0.367044 | −0.183522 | − | 0.983016i | \(-0.558750\pi\) | ||||
−0.183522 | + | 0.983016i | \(0.558750\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −240.000 | − | 214.663i | −0.516129 | − | 0.461640i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 460.630i | 0.986360i | 0.869927 | + | 0.493180i | \(0.164166\pi\) | ||||
−0.869927 | + | 0.493180i | \(0.835834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −393.548 | −0.839121 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −107.331 | + | 120.000i | −0.227880 | + | 0.254777i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 160.997i | 0.340374i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 180.000 | 0.378947 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −178.885 | + | 20.0000i | −0.375022 | + | 0.0419287i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 320.000i | − | 0.668058i | −0.942563 | − | 0.334029i | \(-0.891592\pi\) | ||
0.942563 | − | 0.334029i | \(-0.108408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −960.000 | −1.99584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 320.000 | + | 286.217i | 0.662526 | + | 0.592581i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 200.000i | − | 0.412371i | ||||||
\(486\) | 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 | ||||||||
\(491\) | 889.955i | 1.81254i | 0.422704 | + | 0.906268i | \(0.361081\pi\) | ||||
−0.422704 | + | 0.906268i | \(0.638919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 930.204 | 1.88682 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.8885 | − | 160.000i | −0.0361385 | − | 0.323232i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 715.542i | − | 1.43972i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −100.000 | −0.200401 | −0.100200 | − | 0.994967i | \(-0.531948\pi\) | ||||
−0.100200 | + | 0.994967i | \(0.531948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.7771 | + | 32.0000i | 0.0714114 | + | 0.0638723i | ||||
\(502\) | 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 | ||||||||
\(507\) | −302.000 | + | 337.646i | −0.595661 | + | 0.665969i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 332.000i | − | 0.652259i | −0.945325 | − | 0.326130i | \(-0.894255\pi\) | ||
0.945325 | − | 0.326130i | \(-0.105745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −447.214 | −0.875173 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 440.000 | + | 313.050i | 0.857700 | + | 0.610233i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 178.885i | 0.347350i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 286.217 | 0.553611 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 313.050 | + | 280.000i | 0.603178 | + | 0.539499i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 214.663i | − | 0.412020i | −0.978550 | − | 0.206010i | \(-0.933952\pi\) | ||
0.978550 | − | 0.206010i | \(-0.0660480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −76.0000 | −0.145315 | −0.0726577 | − | 0.997357i | \(-0.523148\pi\) | ||||
−0.0726577 | + | 0.997357i | \(0.523148\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 160.997 | − | 180.000i | 0.306661 | − | 0.342857i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 480.000i | 0.910816i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 273.000 | 0.516068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 920.000 | − | 102.859i | 1.73258 | − | 0.193708i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 640.000i | 1.20075i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −160.997 | −0.300929 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 150.000 | + | 134.164i | 0.279330 | + | 0.249840i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 138.636i | 0.257210i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1019.65 | −1.88474 | −0.942372 | − | 0.334566i | \(-0.891410\pi\) | ||||
−0.942372 | + | 0.334566i | \(0.891410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −250.440 | + | 280.000i | −0.461215 | + | 0.515654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 500.879i | − | 0.919044i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 244.000 | 0.446069 | 0.223035 | − | 0.974810i | \(-0.428404\pi\) | ||||
0.223035 | + | 0.974810i | \(0.428404\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.8885 | + | 160.000i | 0.0325839 | + | 0.291439i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1040.00i | 1.88748i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −720.000 | −1.30199 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 480.000 | + | 429.325i | 0.864865 | + | 0.773559i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 60.0000i | − | 0.107720i | −0.998548 | − | 0.0538600i | \(-0.982848\pi\) | ||
0.998548 | − | 0.0538600i | \(-0.0171525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −643.988 | −1.15204 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −160.000 | + | 178.885i | −0.285205 | + | 0.318869i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 111.803i | − | 0.198585i | −0.995058 | − | 0.0992925i | \(-0.968342\pi\) | ||
0.995058 | − | 0.0992925i | \(-0.0316580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −143.108 | −0.253289 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 706.597 | − | 160.000i | 1.24620 | − | 0.282187i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 858.650i | 1.50905i | 0.656271 | + | 0.754526i | \(0.272133\pi\) | ||||
−0.656271 | + | 0.754526i | \(0.727867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 940.000 | 1.64623 | 0.823117 | − | 0.567871i | \(-0.192233\pi\) | ||||
0.823117 | + | 0.567871i | \(0.192233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 357.771 | + | 320.000i | 0.624382 | + | 0.558464i | ||||
\(574\) | 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 | ||||||||
\(579\) | −60.0000 | + | 67.0820i | −0.103627 | + | 0.115858i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 920.000i | − | 1.58348i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 89.4427 | 0.153418 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 640.000 | − | 71.5542i | 1.09402 | − | 0.122315i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 469.574i | − | 0.799956i | −0.916525 | − | 0.399978i | \(-0.869018\pi\) | ||
0.916525 | − | 0.399978i | \(-0.130982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −536.656 | −0.911131 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 640.000 | 1.07563 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 518.768 | − | 580.000i | 0.868958 | − | 0.971524i | ||||
\(598\) | 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 | \(-0.580841\pi\) | ||||
−0.251248 | + | 0.967923i | \(0.580841\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.0000 | − | 393.548i | −0.0729685 | − | 0.652650i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 404.000i | − | 0.667769i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.7214 | 0.0736760 | 0.0368380 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368380 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1040.00 | + | 930.204i | 1.70772 | + | 1.52743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1144.87i | 1.87376i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −447.214 | −0.729549 | −0.364775 | − | 0.931096i | \(-0.618854\pi\) | ||||
−0.364775 | + | 0.931096i | \(0.618854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 286.217 | − | 320.000i | 0.465393 | − | 0.520325i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 447.214i | − | 0.724819i | −0.932019 | − | 0.362410i | \(-0.881954\pi\) | ||
0.932019 | − | 0.362410i | \(-0.118046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 780.000 | 1.26010 | 0.630048 | − | 0.776556i | \(-0.283035\pi\) | ||||
0.630048 | + | 0.776556i | \(0.283035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −250.440 | + | 352.000i | −0.403284 | + | 0.566828i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1440.00i | − | 2.31140i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −200.000 | − | 178.885i | −0.318979 | − | 0.285304i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 960.000i | − | 1.52623i | ||||||
\(630\) | 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 | ||||||||
\(635\) | 107.331i | 0.169026i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −554.545 | −0.870557 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −844.000 | −1.31260 | −0.656299 | − | 0.754501i | \(-0.727879\pi\) | ||||
−0.656299 | + | 0.754501i | \(0.727879\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 321.994 | + | 288.000i | 0.499215 | + | 0.446512i | ||||
\(646\) | 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 | ||||||||
\(651\) | −480.000 | + | 536.656i | −0.737327 | + | 0.824357i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 660.000i | 1.01072i | 0.862909 | + | 0.505360i | \(0.168640\pi\) | ||||
−0.862909 | + | 0.505360i | \(0.831360\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −268.328 | −0.409661 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.0000 | − | 447.214i | −0.0761035 | − | 0.680690i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 210.190i | − | 0.318954i | −0.987202 | − | 0.159477i | \(-0.949019\pi\) | ||
0.987202 | − | 0.159477i | \(-0.0509807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 769.207 | 1.16370 | 0.581851 | − | 0.813295i | \(-0.302329\pi\) | ||||
0.581851 | + | 0.813295i | \(0.302329\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −715.542 | − | 640.000i | −1.07925 | − | 0.965309i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 715.542i | 1.07600i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −832.000 | −1.24738 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −304.105 | + | 340.000i | −0.454567 | + | 0.508221i | ||||
\(670\) | 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 | ||||||||
\(675\) | 198.000 | + | 140.872i | 0.293333 | + | 0.208700i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 260.000i | − | 0.384047i | −0.981390 | − | 0.192024i | \(-0.938495\pi\) | ||
0.981390 | − | 0.192024i | \(-0.0615050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −447.214 | −0.658636 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 570.000 | + | 509.823i | 0.837004 | + | 0.748639i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 934.676i | 1.36849i | 0.729254 | + | 0.684243i | \(0.239867\pi\) | ||||
−0.729254 | + | 0.684243i | \(0.760133\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −572.433 | −0.835669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −393.548 | + | 440.000i | −0.572850 | + | 0.640466i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 357.771i | 0.519261i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 100.000 | 0.144718 | 0.0723589 | − | 0.997379i | \(-0.476947\pi\) | ||||
0.0723589 | + | 0.997379i | \(0.476947\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −357.771 | + | 40.0000i | −0.516264 | + | 0.0577201i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1040.00i | 1.49640i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −640.000 | −0.918221 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −360.000 | − | 321.994i | −0.515021 | − | 0.460649i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1028.00i | 1.46648i | 0.679972 | + | 0.733238i | \(0.261992\pi\) | ||||
−0.679972 | + | 0.733238i | \(0.738008\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1073.31 | 1.52676 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 512.000 | − | 572.433i | 0.726241 | − | 0.811962i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 822.873i | − | 1.16389i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 912.316 | 1.28676 | 0.643382 | − | 0.765545i | \(-0.277531\pi\) | ||||
0.643382 | + | 0.765545i | \(0.277531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −80.4984 | − | 720.000i | −0.113219 | − | 1.01266i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 429.325i | − | 0.602139i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −320.000 | −0.447552 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −715.542 | − | 640.000i | −0.997966 | − | 0.892608i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 480.000i | 0.667594i | 0.942645 | + | 0.333797i | \(0.108330\pi\) | ||||
−0.942645 | + | 0.333797i | \(0.891670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 400.000 | 0.554785 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −636.000 | + | 711.070i | −0.879668 | + | 0.983499i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 468.000i | 0.645517i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | − | 643.988i | − | 0.880968i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1126.98 | 1.53749 | 0.768744 | − | 0.639557i | \(-0.220882\pi\) | ||||
0.768744 | + | 0.639557i | \(0.220882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 277.272 | + | 248.000i | 0.377241 | + | 0.337415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 196.774i | 0.266993i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1020.00 | 1.38024 | 0.690122 | − | 0.723693i | \(-0.257557\pi\) | ||||
0.690122 | + | 0.723693i | \(0.257557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 715.542 | − | 800.000i | 0.965643 | − | 1.07962i | ||||
\(742\) | 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 | ||||||||
\(747\) | 920.000 | − | 102.859i | 1.23159 | − | 0.137696i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 360.000i | 0.480641i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1296.92 | 1.72692 | 0.863462 | − | 0.504414i | \(-0.168292\pi\) | ||||
0.863462 | + | 0.504414i | \(0.168292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −330.000 | − | 295.161i | −0.438247 | − | 0.391980i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 965.981i | − | 1.27945i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 983.870 | 1.29970 | 0.649848 | − | 0.760064i | \(-0.274833\pi\) | ||||
0.649848 | + | 0.760064i | \(0.274833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 143.108 | − | 160.000i | 0.188549 | − | 0.210804i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 107.331i | 0.141040i | 0.997510 | + | 0.0705199i | \(0.0224658\pi\) | ||||
−0.997510 | + | 0.0705199i | \(0.977534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1120.00 | −1.46789 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 71.5542 | + | 640.000i | 0.0935349 | + | 0.836601i | ||||
\(766\) | 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 | ||||||||
\(771\) | −240.000 | − | 214.663i | −0.311284 | − | 0.278421i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1180.00i | 1.52652i | 0.646091 | + | 0.763260i | \(0.276402\pi\) | ||||
−0.646091 | + | 0.763260i | \(0.723598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −241.495 | −0.311607 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 960.000 | − | 1073.31i | 1.23552 | − | 1.38135i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 715.542i | − | 0.918539i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −357.771 | −0.458093 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −813.929 | + | 1144.00i | −1.03950 | + | 1.46105i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 214.663i | − | 0.273455i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1244.00 | −1.58069 | −0.790343 | − | 0.612665i | \(-0.790098\pi\) | ||||
−0.790343 | + | 0.612665i | \(0.790098\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −321.994 | − | 288.000i | −0.408104 | − | 0.365019i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 320.000i | 0.404551i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 320.000 | 0.403531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 160.000 | − | 178.885i | 0.201258 | − | 0.225013i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 580.000i | 0.727729i | 0.931452 | + | 0.363864i | \(0.118543\pi\) | ||||
−0.931452 | + | 0.363864i | \(0.881457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1144.87 | −1.43287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1440.00 | − | 160.997i | 1.79775 | − | 0.200995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 223.607i | 0.278464i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −572.433 | −0.711097 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −295.161 | − | 264.000i | −0.365751 | − | 0.327138i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 250.440i | − | 0.309567i | −0.987948 | − | 0.154783i | \(-0.950532\pi\) | ||
0.987948 | − | 0.154783i | \(-0.0494680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 980.000 | 1.20838 | 0.604192 | − | 0.796839i | \(-0.293496\pi\) | ||||
0.604192 | + | 0.796839i | \(0.293496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 554.545 | − | 620.000i | 0.682097 | − | 0.762608i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 496.000i | 0.608589i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 720.000 | 0.881273 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −160.000 | − | 1431.08i | −0.195360 | − | 1.74735i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 932.000i | − | 1.13520i | −0.823304 | − | 0.567600i | \(-0.807872\pi\) | ||
0.823304 | − | 0.567600i | \(-0.192128\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − | 1542.89i | − | 1.86564i | −0.360339 | − | 0.932822i | \(-0.617339\pi\) | ||
0.360339 | − | 0.932822i | \(-0.382661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 482.991 | 0.582618 | 0.291309 | − | 0.956629i | \(-0.405909\pi\) | ||||
0.291309 | + | 0.956629i | \(0.405909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −536.656 | + | 600.000i | −0.645796 | + | 0.722022i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 554.545i | − | 0.665720i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −64.0000 | −0.0766467 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −590.322 | − | 420.000i | −0.705283 | − | 0.501792i | ||||
\(838\) | 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 | ||||||||
\(843\) | −440.000 | − | 393.548i | −0.521945 | − | 0.466842i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 604.000i | − | 0.714793i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −903.371 | −1.06655 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −152.000 | + | 169.941i | −0.179034 | + | 0.200166i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 858.650i | 1.00899i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −948.093 | −1.11148 | −0.555740 | − | 0.831356i | \(-0.687565\pi\) | ||||
−0.555740 | + | 0.831356i | \(0.687565\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −715.542 | + | 80.0000i | −0.836891 | + | 0.0935673i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 858.650i | − | 1.00193i | −0.865469 | − | 0.500963i | \(-0.832979\pi\) | ||
0.865469 | − | 0.500963i | \(-0.167021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1340.00 | −1.55995 | −0.779977 | − | 0.625809i | \(-0.784769\pi\) | ||||
−0.779977 | + | 0.625809i | \(0.784769\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −715.542 | − | 640.000i | −0.831059 | − | 0.743322i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 224.000i | − | 0.259560i | −0.991543 | − | 0.129780i | \(-0.958573\pi\) | ||
0.991543 | − | 0.129780i | \(-0.0414271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −560.000 | −0.647399 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 62.0000 | − | 69.3181i | 0.0715110 | − | 0.0799517i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 360.000i | 0.414269i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −787.096 | −0.903669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −50.0000 | − | 447.214i | −0.0572738 | − | 0.512272i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1216.42i | 1.39020i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −948.093 | −1.08106 | −0.540532 | − | 0.841324i | \(-0.681777\pi\) | ||||
−0.540532 | + | 0.841324i | \(0.681777\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −1164.00 | −1.31823 | −0.659117 | − | 0.752041i | \(-0.729070\pi\) | ||||
−0.659117 | + | 0.752041i | \(0.729070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −822.873 | + | 920.000i | −0.929800 | + | 1.03955i | ||||
\(886\) | 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 | ||||||||
\(891\) | −80.0000 | − | 353.299i | −0.0897868 | − | 0.396519i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1280.00i | − | 1.43337i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −268.328 | −0.299808 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 640.000 | + | 572.433i | 0.713489 | + | 0.638164i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1395.31i | − | 1.55206i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −357.771 | −0.397082 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 643.988 | − | 720.000i | 0.713165 | − | 0.797342i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 500.879i | − | 0.553458i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −764.000 | −0.842337 | −0.421169 | − | 0.906982i | \(-0.638380\pi\) | ||||
−0.421169 | + | 0.906982i | \(0.638380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 822.873 | − | 92.0000i | 0.905251 | − | 0.101210i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1280.00i | − | 1.40505i | −0.711659 | − | 0.702525i | \(-0.752056\pi\) | ||
0.711659 | − | 0.702525i | \(-0.247944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −460.000 | −0.503834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −160.000 | − | 143.108i | −0.174863 | − | 0.156403i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 600.000i | 0.654308i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − | 1431.08i | − | 1.55047i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 482.991 | 0.522152 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 620.000 | 0.665951 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 894.427 | + | 800.000i | 0.958657 | + | 0.857449i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 320.000i | − | 0.342246i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 510.000 | 0.544290 | 0.272145 | − | 0.962256i | \(-0.412267\pi\) | ||||
0.272145 | + | 0.962256i | \(0.412267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −580.000 | + | 648.460i | −0.617678 | + | 0.690585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 812.000i | − | 0.862912i | −0.902134 | − | 0.431456i | \(-0.858000\pi\) | ||
0.902134 | − | 0.431456i | \(-0.142000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 572.433 | 0.607034 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −560.000 | + | 787.096i | −0.592593 | + | 0.832906i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1569.72i | − | 1.65757i | −0.559566 | − | 0.828785i | \(-0.689032\pi\) | ||
0.559566 | − | 0.828785i | \(-0.310968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −894.427 | −0.942494 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −939.149 | − | 840.000i | −0.987538 | − | 0.883281i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1073.31i | 1.12625i | 0.826373 | + | 0.563123i | \(0.190400\pi\) | ||||
−0.826373 | + | 0.563123i | \(0.809600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −640.000 | −0.670157 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 465.102 | − | 520.000i | 0.486000 | − | 0.543365i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1280.00i | 1.33472i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −241.000 | −0.250780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −360.000 | + | 40.2492i | −0.373832 | + | 0.0417957i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 120.000i | − | 0.124352i | ||||||
\(966\) | 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 | ||||||||
\(971\) | 791.568i | 0.815209i | 0.913159 | + | 0.407605i | \(0.133636\pi\) | ||||
−0.913159 | + | 0.407605i | \(0.866364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2325.51 | 2.39004 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | −720.000 | −0.735444 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −125.220 | − | 1120.00i | −0.127645 | − | 1.14169i | ||||
\(982\) | 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 | ||||||||
\(987\) | −1280.00 | − | 1144.87i | −1.29686 | − | 1.15995i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 576.000i | 0.582406i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1368.47 | 1.38090 | 0.690451 | − | 0.723379i | \(-0.257412\pi\) | ||||
0.690451 | + | 0.723379i | \(0.257412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 680.000 | − | 760.263i | 0.684794 | − | 0.765622i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1037.54i | 1.04275i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1234.31 | −1.23802 | −0.619012 | − | 0.785382i | \(-0.712467\pi\) | ||||
−0.619012 | + | 0.785382i | \(0.712467\pi\) | |||||||
\(998\) | 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 | 768.3.e.h.257.3 | 4 | ||
3.2 | odd | 2 | inner | 768.3.e.h.257.2 | 4 | ||
4.3 | odd | 2 | 768.3.e.m.257.1 | 4 | |||
8.3 | odd | 2 | inner | 768.3.e.h.257.4 | 4 | ||
8.5 | even | 2 | 768.3.e.m.257.2 | 4 | |||
12.11 | even | 2 | 768.3.e.m.257.4 | 4 | |||
16.3 | odd | 4 | 384.3.h.e.65.4 | yes | 4 | ||
16.5 | even | 4 | 384.3.h.f.65.4 | yes | 4 | ||
16.11 | odd | 4 | 384.3.h.f.65.1 | yes | 4 | ||
16.13 | even | 4 | 384.3.h.e.65.1 | ✓ | 4 | ||
24.5 | odd | 2 | 768.3.e.m.257.3 | 4 | |||
24.11 | even | 2 | inner | 768.3.e.h.257.1 | 4 | ||
48.5 | odd | 4 | 384.3.h.e.65.2 | yes | 4 | ||
48.11 | even | 4 | 384.3.h.e.65.3 | yes | 4 | ||
48.29 | odd | 4 | 384.3.h.f.65.3 | yes | 4 | ||
48.35 | even | 4 | 384.3.h.f.65.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.h.e.65.1 | ✓ | 4 | 16.13 | even | 4 | ||
384.3.h.e.65.2 | yes | 4 | 48.5 | odd | 4 | ||
384.3.h.e.65.3 | yes | 4 | 48.11 | even | 4 | ||
384.3.h.e.65.4 | yes | 4 | 16.3 | odd | 4 | ||
384.3.h.f.65.1 | yes | 4 | 16.11 | odd | 4 | ||
384.3.h.f.65.2 | yes | 4 | 48.35 | even | 4 | ||
384.3.h.f.65.3 | yes | 4 | 48.29 | odd | 4 | ||
384.3.h.f.65.4 | yes | 4 | 16.5 | even | 4 | ||
768.3.e.h.257.1 | 4 | 24.11 | even | 2 | inner | ||
768.3.e.h.257.2 | 4 | 3.2 | odd | 2 | inner | ||
768.3.e.h.257.3 | 4 | 1.1 | even | 1 | trivial | ||
768.3.e.h.257.4 | 4 | 8.3 | odd | 2 | inner | ||
768.3.e.m.257.1 | 4 | 4.3 | odd | 2 | |||
768.3.e.m.257.2 | 4 | 8.5 | even | 2 | |||
768.3.e.m.257.3 | 4 | 24.5 | odd | 2 | |||
768.3.e.m.257.4 | 4 | 12.11 | even | 2 |