Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(129,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
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("392.129");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 313.4 | ||
Root | \(-0.662827 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.313 |
Dual form | 392.3.o.b.129.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.20041 | − | 1.84776i | 1.06680 | − | 0.615920i | 0.139498 | − | 0.990222i | \(-0.455451\pi\) |
0.927307 | + | 0.374303i | \(0.122118\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.549104 | − | 0.317025i | −0.109821 | − | 0.0634051i | 0.444084 | − | 0.895985i | \(-0.353529\pi\) |
−0.553904 | + | 0.832580i | \(0.686863\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.32843 | − | 4.03295i | 0.258714 | − | 0.448106i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.65685 | − | 11.5300i | −0.605169 | − | 1.04818i | −0.992025 | − | 0.126043i | \(-0.959772\pi\) |
0.386856 | − | 0.922140i | \(-0.373561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21.5391i | − | 1.65685i | −0.560100 | − | 0.828425i | \(-0.689237\pi\) | ||
0.560100 | − | 0.828425i | \(-0.310763\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.34315 | −0.156210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.30262 | − | 3.06147i | 0.311919 | − | 0.180086i | −0.335866 | − | 0.941910i | \(-0.609029\pi\) |
0.647785 | + | 0.761823i | \(0.275696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.1003 | + | 9.87285i | 0.900014 | + | 0.519623i | 0.877205 | − | 0.480116i | \(-0.159406\pi\) |
0.0228094 | + | 0.999740i | \(0.492739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.3137 | − | 24.7921i | 0.622335 | − | 1.07792i | −0.366715 | − | 0.930333i | \(-0.619517\pi\) |
0.989050 | − | 0.147583i | \(-0.0471492\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.2990 | − | 21.3025i | −0.491960 | − | 0.852099i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.0502i | 0.594451i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.3137 | 1.28668 | 0.643340 | − | 0.765581i | \(-0.277548\pi\) | ||||
0.643340 | + | 0.765581i | \(0.277548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.1043 | + | 10.4525i | −0.584009 | + | 0.337178i | −0.762725 | − | 0.646723i | \(-0.776139\pi\) |
0.178716 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.6094 | − | 24.6005i | −1.29119 | − | 0.745470i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.9706 | − | 20.7336i | 0.323529 | − | 0.560368i | −0.657685 | − | 0.753293i | \(-0.728464\pi\) |
0.981213 | + | 0.192925i | \(0.0617974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.7990 | − | 68.9339i | −1.02049 | − | 1.76754i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.1061i | 1.70990i | 0.518707 | + | 0.854952i | \(0.326413\pi\) | ||||
−0.518707 | + | 0.854952i | \(0.673587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −46.0000 | −1.06977 | −0.534884 | − | 0.844926i | \(-0.679645\pi\) | ||||
−0.534884 | + | 0.844926i | \(0.679645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.55710 | + | 1.47634i | −0.0568244 | + | 0.0328076i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.909785 | + | 0.525265i | 0.0193571 | + | 0.0111758i | 0.509647 | − | 0.860383i | \(-0.329776\pi\) |
−0.490290 | + | 0.871559i | \(0.663109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3137 | − | 19.5959i | 0.221837 | − | 0.384234i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.68629 | + | 13.3130i | 0.145024 | + | 0.251190i | 0.929382 | − | 0.369119i | \(-0.120341\pi\) |
−0.784358 | + | 0.620309i | \(0.787007\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.44157i | 0.153483i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 72.9706 | 1.28019 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8959 | + | 7.44543i | −0.218574 | + | 0.126194i | −0.605290 | − | 0.796005i | \(-0.706943\pi\) |
0.386716 | + | 0.922199i | \(0.373609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 75.1626 | + | 43.3951i | 1.23217 | + | 0.711396i | 0.967483 | − | 0.252938i | \(-0.0813967\pi\) |
0.264691 | + | 0.964333i | \(0.414730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.82843 | + | 11.8272i | −0.105053 | + | 0.181957i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3137 | − | 21.3280i | −0.183787 | − | 0.318328i | 0.759380 | − | 0.650647i | \(-0.225502\pi\) |
−0.943167 | + | 0.332319i | \(0.892169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 105.793i | − | 1.53323i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45.0294 | −0.634217 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44.8058 | + | 25.8686i | −0.613778 | + | 0.354365i | −0.774443 | − | 0.632644i | \(-0.781970\pi\) |
0.160665 | + | 0.987009i | \(0.448636\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −78.7237 | − | 45.4511i | −1.04965 | − | 0.606015i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8579 | − | 29.1987i | 0.213391 | − | 0.369604i | −0.739383 | − | 0.673285i | \(-0.764883\pi\) |
0.952774 | + | 0.303682i | \(0.0982159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 50.6127 | + | 87.6638i | 0.624848 | + | 1.08227i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 77.3883i | − | 0.932389i | −0.884682 | − | 0.466195i | \(-0.845625\pi\) | ||
0.884682 | − | 0.466195i | \(-0.154375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.88225 | −0.0456735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 119.419 | − | 68.9467i | 1.37264 | − | 0.792491i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 68.2127 | + | 39.3826i | 0.766434 | + | 0.442501i | 0.831601 | − | 0.555373i | \(-0.187425\pi\) |
−0.0651668 | + | 0.997874i | \(0.520758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −38.6274 | + | 66.9046i | −0.415349 | + | 0.719405i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.25988 | − | 10.8424i | −0.0658935 | − | 0.114131i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 90.1781i | 0.929671i | 0.885397 | + | 0.464836i | \(0.153887\pi\) | ||||
−0.885397 | + | 0.464836i | \(0.846113\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −62.0000 | −0.626263 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112.281 | − | 64.8254i | 1.11169 | − | 0.641836i | 0.172425 | − | 0.985023i | \(-0.444840\pi\) |
0.939267 | + | 0.343187i | \(0.111506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −29.8077 | − | 17.2095i | −0.289395 | − | 0.167082i | 0.348274 | − | 0.937393i | \(-0.386768\pi\) |
−0.637669 | + | 0.770310i | \(0.720101\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −74.9411 | + | 129.802i | −0.700384 | + | 1.21310i | 0.267947 | + | 0.963434i | \(0.413655\pi\) |
−0.968332 | + | 0.249668i | \(0.919679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 33.6274 | + | 58.2444i | 0.308508 | + | 0.534352i | 0.978036 | − | 0.208435i | \(-0.0668369\pi\) |
−0.669528 | + | 0.742787i | \(0.733504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 88.4749i | − | 0.797071i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 70.2843 | 0.621985 | 0.310992 | − | 0.950412i | \(-0.399339\pi\) | ||||
0.310992 | + | 0.950412i | \(0.399339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.7194 | + | 9.07562i | −0.136691 | + | 0.0789184i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −86.8660 | − | 50.1521i | −0.742445 | − | 0.428651i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28.1274 | + | 48.7181i | −0.232458 | + | 0.402629i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 129.539 | + | 224.368i | 1.05316 | + | 1.82413i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.4476i | 0.251581i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −93.7645 | −0.738303 | −0.369152 | − | 0.929369i | \(-0.620352\pi\) | ||||
−0.369152 | + | 0.929369i | \(0.620352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −147.219 | + | 84.9969i | −1.14123 | + | 0.658891i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 126.636 | + | 73.1131i | 0.966684 | + | 0.558116i | 0.898224 | − | 0.439538i | \(-0.144858\pi\) |
0.0684606 | + | 0.997654i | \(0.478191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.08831 | − | 8.81321i | 0.0376912 | − | 0.0652831i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 74.8823 | + | 129.700i | 0.546586 | + | 0.946714i | 0.998505 | + | 0.0546556i | \(0.0174061\pi\) |
−0.451919 | + | 0.892059i | \(0.649261\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 120.249i | 0.865100i | 0.901610 | + | 0.432550i | \(0.142386\pi\) | ||||
−0.901610 | + | 0.432550i | \(0.857614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.88225 | 0.0275337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −248.346 | + | 143.382i | −1.73668 | + | 1.00267i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.4891 | − | 11.8294i | −0.141304 | − | 0.0815820i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.8823 | + | 29.2409i | −0.113304 | + | 0.196248i | −0.917100 | − | 0.398656i | \(-0.869477\pi\) |
0.803797 | + | 0.594904i | \(0.202810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −72.3137 | − | 125.251i | −0.478899 | − | 0.829477i | 0.520808 | − | 0.853674i | \(-0.325631\pi\) |
−0.999707 | + | 0.0241966i | \(0.992297\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 28.5136i | − | 0.186363i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2548 | 0.0855151 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 111.560 | − | 64.4089i | 0.710570 | − | 0.410248i | −0.100702 | − | 0.994917i | \(-0.532109\pi\) |
0.811272 | + | 0.584669i | \(0.198775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 49.1986 | + | 28.4048i | 0.309425 | + | 0.178647i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28.7157 | + | 49.7371i | −0.176170 | + | 0.305136i | −0.940566 | − | 0.339612i | \(-0.889704\pi\) |
0.764395 | + | 0.644748i | \(0.223038\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.5980 | + | 27.0165i | 0.0945332 | + | 0.163736i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 229.122i | 1.37199i | 0.727607 | + | 0.685994i | \(0.240633\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −294.931 | −1.74515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79.6335 | − | 45.9764i | 0.465693 | − | 0.268868i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −106.790 | − | 61.6552i | −0.617282 | − | 0.356388i | 0.158528 | − | 0.987355i | \(-0.449325\pi\) |
−0.775810 | + | 0.630966i | \(0.782659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.5147 | + | 47.6569i | −0.155450 | + | 0.269248i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 135.971 | + | 235.508i | 0.759612 | + | 1.31569i | 0.943049 | + | 0.332655i | \(0.107945\pi\) |
−0.183436 | + | 0.983032i | \(0.558722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 30.6333i | 0.169245i | 0.996413 | + | 0.0846225i | \(0.0269684\pi\) | ||||
−0.996413 | + | 0.0846225i | \(0.973032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 320.735 | 1.75265 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.1462 | + | 7.58994i | −0.0710604 | + | 0.0410267i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −70.5975 | − | 40.7595i | −0.377527 | − | 0.217965i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 34.7990 | − | 60.2736i | 0.182194 | − | 0.315569i | −0.760434 | − | 0.649416i | \(-0.775014\pi\) |
0.942627 | + | 0.333847i | \(0.108347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −139.711 | − | 241.986i | −0.723890 | − | 1.25381i | −0.959429 | − | 0.281949i | \(-0.909019\pi\) |
0.235540 | − | 0.971865i | \(-0.424314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 50.4692i | 0.258816i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 102.451 | 0.520055 | 0.260027 | − | 0.965601i | \(-0.416268\pi\) | ||||
0.260027 | + | 0.965601i | \(0.416268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 140.253 | − | 80.9750i | 0.704788 | − | 0.406910i | −0.104340 | − | 0.994542i | \(-0.533273\pi\) |
0.809128 | + | 0.587632i | \(0.199940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −78.8179 | − | 45.5055i | −0.392129 | − | 0.226396i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.2254 | − | 38.4955i | 0.108417 | − | 0.187783i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −66.6569 | − | 115.453i | −0.322014 | − | 0.557744i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 262.888i | − | 1.25784i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −51.0193 | −0.241798 | −0.120899 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120899 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −144.113 | + | 83.2036i | −0.676586 | + | 0.390627i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.2588 | + | 14.5832i | 0.117483 | + | 0.0678287i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −95.5980 | + | 165.581i | −0.436520 | + | 0.756076i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −65.9411 | − | 114.213i | −0.298376 | − | 0.516803i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 221.296i | − | 0.992358i | −0.868220 | − | 0.496179i | \(-0.834736\pi\) | ||
0.868220 | − | 0.496179i | \(-0.165264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −114.549 | −0.509108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 87.5093 | − | 50.5235i | 0.385504 | − | 0.222571i | −0.294706 | − | 0.955588i | \(-0.595222\pi\) |
0.680210 | + | 0.733017i | \(0.261889\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 147.391 | + | 85.0964i | 0.643630 | + | 0.371600i | 0.786011 | − | 0.618212i | \(-0.212143\pi\) |
−0.142382 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 225.510 | − | 390.594i | 0.967853 | − | 1.67637i | 0.266105 | − | 0.963944i | \(-0.414263\pi\) |
0.701747 | − | 0.712426i | \(-0.252404\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.333044 | − | 0.576850i | −0.00141721 | − | 0.00245468i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 124.597i | − | 0.525726i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 219.137 | 0.916892 | 0.458446 | − | 0.888722i | \(-0.348406\pi\) | ||||
0.458446 | + | 0.888722i | \(0.348406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 281.792 | − | 162.693i | 1.16926 | − | 0.675074i | 0.215757 | − | 0.976447i | \(-0.430778\pi\) |
0.953506 | + | 0.301373i | \(0.0974449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 198.864 | + | 114.814i | 0.818372 | + | 0.472487i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 212.652 | − | 368.324i | 0.860938 | − | 1.49119i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −142.995 | − | 247.675i | −0.574277 | − | 0.994677i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 260.063i | − | 1.03611i | −0.855348 | − | 0.518054i | \(-0.826657\pi\) | ||
0.855348 | − | 0.518054i | \(-0.173343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −381.137 | −1.50647 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.4248 | + | 7.17346i | −0.0487247 | + | 0.0281312i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 159.832 | + | 92.2792i | 0.621915 | + | 0.359063i | 0.777614 | − | 0.628742i | \(-0.216430\pi\) |
−0.155699 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 86.8823 | − | 150.484i | 0.332882 | − | 0.576569i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −123.426 | − | 213.781i | −0.469302 | − | 0.812855i | 0.530082 | − | 0.847946i | \(-0.322161\pi\) |
−0.999384 | + | 0.0350915i | \(0.988828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.74700i | − | 0.0367811i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 291.078 | 1.09018 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −91.0704 | + | 52.5795i | −0.338552 | + | 0.195463i | −0.659631 | − | 0.751589i | \(-0.729288\pi\) |
0.321080 | + | 0.947052i | \(0.395954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −62.1887 | − | 35.9047i | −0.229479 | − | 0.132489i | 0.380853 | − | 0.924636i | \(-0.375630\pi\) |
−0.610331 | + | 0.792146i | \(0.708964\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −163.745 | + | 283.615i | −0.595437 | + | 1.03133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −201.049 | − | 348.227i | −0.725808 | − | 1.25714i | −0.958641 | − | 0.284619i | \(-0.908133\pi\) |
0.232833 | − | 0.972517i | \(-0.425201\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 97.3516i | 0.348930i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.529 | 1.14423 | 0.572116 | − | 0.820173i | \(-0.306123\pi\) | ||||
0.572116 | + | 0.820173i | \(0.306123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −420.508 | + | 242.781i | −1.48590 | + | 0.857882i | −0.999871 | − | 0.0160633i | \(-0.994887\pi\) |
−0.486024 | + | 0.873945i | \(0.661553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −40.0684 | − | 23.1335i | −0.140591 | − | 0.0811702i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −125.755 | + | 217.814i | −0.435138 | + | 0.753681i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 166.627 | + | 288.607i | 0.572603 | + | 0.991777i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 480.218i | 1.63897i | 0.573100 | + | 0.819485i | \(0.305741\pi\) | ||||
−0.573100 | + | 0.819485i | \(0.694259\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.44156 | 0.0320053 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 185.059 | − | 106.844i | 0.623093 | − | 0.359743i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −533.998 | − | 308.304i | −1.78595 | − | 1.03112i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 239.563 | − | 414.936i | 0.790639 | − | 1.36943i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.5147 | − | 47.6569i | −0.0902122 | − | 0.156252i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.1876i | − | 0.0429564i | −0.999769 | − | 0.0214782i | \(-0.993163\pi\) | ||
0.999769 | − | 0.0214782i | \(-0.00683725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −127.196 | −0.411637 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 340.530 | − | 196.605i | 1.09495 | − | 0.632171i | 0.160062 | − | 0.987107i | \(-0.448831\pi\) |
0.934891 | + | 0.354936i | \(0.115497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −191.992 | − | 110.847i | −0.613394 | − | 0.354143i | 0.160898 | − | 0.986971i | \(-0.448561\pi\) |
−0.774293 | + | 0.632828i | \(0.781894\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 47.2843 | − | 81.8988i | 0.149162 | − | 0.258356i | −0.781756 | − | 0.623584i | \(-0.785676\pi\) |
0.930918 | + | 0.365229i | \(0.119009\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −248.392 | − | 430.227i | −0.778658 | − | 1.34868i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 553.893i | 1.72552i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 120.902 | 0.374308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −458.835 | + | 264.909i | −1.41180 | + | 0.815104i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 215.243 | + | 124.271i | 0.658236 | + | 0.380033i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95.1665 | − | 164.833i | 0.287512 | − | 0.497986i | −0.685703 | − | 0.727881i | \(-0.740505\pi\) |
0.973215 | + | 0.229896i | \(0.0738385\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −55.7452 | − | 96.5535i | −0.167403 | − | 0.289950i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.6150i | 0.0466120i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −430.735 | −1.27815 | −0.639073 | − | 0.769146i | \(-0.720682\pi\) | ||||
−0.639073 | + | 0.769146i | \(0.720682\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 224.939 | − | 129.868i | 0.663536 | − | 0.383093i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 241.035 | + | 139.162i | 0.706847 | + | 0.408098i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −33.5391 | + | 58.0914i | −0.0972148 | + | 0.168381i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 125.627 | + | 217.593i | 0.362039 | + | 0.627069i | 0.988296 | − | 0.152547i | \(-0.0487475\pi\) |
−0.626258 | + | 0.779616i | \(0.715414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 78.3487i | 0.224495i | 0.993680 | + | 0.112247i | \(0.0358049\pi\) | ||||
−0.993680 | + | 0.112247i | \(0.964195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 345.706 | 0.984916 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −38.0281 | + | 21.9555i | −0.107728 | + | 0.0621970i | −0.552896 | − | 0.833250i | \(-0.686477\pi\) |
0.445168 | + | 0.895447i | \(0.353144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7258 | + | 14.2755i | 0.0696503 | + | 0.0402126i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −273.215 | + | 473.223i | −0.761045 | + | 1.31817i | 0.181267 | + | 0.983434i | \(0.441980\pi\) |
−0.942312 | + | 0.334735i | \(0.891353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4462 | + | 25.0215i | 0.0400171 | + | 0.0693117i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 207.891i | 0.572702i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.8040 | 0.0898741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −416.996 | + | 240.753i | −1.13623 | + | 0.656002i | −0.945494 | − | 0.325640i | \(-0.894420\pi\) |
−0.190734 | + | 0.981642i | \(0.561087\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 282.735 | + | 163.237i | 0.766218 | + | 0.442376i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 216.421 | − | 374.853i | 0.580218 | − | 1.00497i | −0.415235 | − | 0.909714i | \(-0.636301\pi\) |
0.995453 | − | 0.0952531i | \(-0.0303660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 58.1076 | + | 100.645i | 0.154954 | + | 0.268388i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 803.702i | − | 2.13184i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −512.607 | −1.35253 | −0.676263 | − | 0.736660i | \(-0.736402\pi\) | ||||
−0.676263 | + | 0.736660i | \(0.736402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −300.085 | + | 173.254i | −0.787625 | + | 0.454735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −564.559 | − | 325.948i | −1.47405 | − | 0.851040i | −0.474472 | − | 0.880270i | \(-0.657361\pi\) |
−0.999573 | + | 0.0292301i | \(0.990694\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −107.108 | + | 185.516i | −0.276764 | + | 0.479369i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 261.676 | + | 453.236i | 0.672689 | + | 1.16513i | 0.977139 | + | 0.212604i | \(0.0681943\pi\) |
−0.304449 | + | 0.952529i | \(0.598472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 175.284i | − | 0.448296i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 540.382 | 1.37502 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.5134 | + | 10.6887i | −0.0468695 | + | 0.0270601i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.7276 | + | 7.92563i | 0.0345783 | + | 0.0199638i | 0.517190 | − | 0.855871i | \(-0.326978\pi\) |
−0.482611 | + | 0.875835i | \(0.660312\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.88730 | + | 10.1971i | −0.0146816 | + | 0.0254292i | −0.873273 | − | 0.487232i | \(-0.838007\pi\) |
0.858591 | + | 0.512661i | \(0.171340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 225.137 | + | 389.949i | 0.558653 | + | 0.967615i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 64.1820i | − | 0.158474i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −318.745 | −0.783158 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 426.503 | − | 246.241i | 1.04279 | − | 0.602057i | 0.122171 | − | 0.992509i | \(-0.461014\pi\) |
0.920623 | + | 0.390452i | \(0.127681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 479.308 | + | 276.729i | 1.16620 | + | 0.673306i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.5341 | + | 42.4942i | −0.0591182 | + | 0.102396i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 222.191 | + | 384.846i | 0.532832 | + | 0.922892i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 276.946i | 0.660970i | 0.943811 | + | 0.330485i | \(0.107212\pi\) | ||||
−0.943811 | + | 0.330485i | \(0.892788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3532 | 0.0340932 | 0.0170466 | − | 0.999855i | \(-0.494574\pi\) | ||||
0.0170466 | + | 0.999855i | \(0.494574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.23674 | − | 2.44608i | 0.0100159 | − | 0.00578270i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −130.434 | − | 75.3059i | −0.306903 | − | 0.177190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −529.872 | + | 917.765i | −1.23513 | + | 2.13931i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −125.235 | − | 216.914i | −0.290570 | − | 0.503281i | 0.683375 | − | 0.730068i | \(-0.260511\pi\) |
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 656.534i | − | 1.51625i | −0.652112 | − | 0.758123i | \(-0.726117\pi\) | ||
0.652112 | − | 0.758123i | \(-0.273883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −87.4315 | −0.200992 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 489.537 | − | 282.634i | 1.12022 | − | 0.646760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 308.650 | + | 178.199i | 0.703075 | + | 0.405921i | 0.808492 | − | 0.588508i | \(-0.200284\pi\) |
−0.105417 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −126.892 | + | 219.784i | −0.286439 | + | 0.496126i | −0.972957 | − | 0.230986i | \(-0.925805\pi\) |
0.686518 | + | 0.727112i | \(0.259138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.9706 | − | 43.2503i | −0.0561136 | − | 0.0971916i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 124.777i | 0.279144i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −107.921 | −0.240358 | −0.120179 | − | 0.992752i | \(-0.538347\pi\) | ||||
−0.120179 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 808.324 | − | 466.686i | 1.79229 | − | 1.03478i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −462.867 | − | 267.237i | −1.02178 | − | 0.589926i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −71.9949 | + | 124.699i | −0.157538 | + | 0.272864i | −0.933980 | − | 0.357324i | \(-0.883689\pi\) |
0.776442 | + | 0.630189i | \(0.217022\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 49.1371 | + | 85.1079i | 0.107052 | + | 0.185420i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 380.728i | 0.825875i | 0.910759 | + | 0.412938i | \(0.135497\pi\) | ||||
−0.910759 | + | 0.412938i | \(0.864503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −227.990 | −0.492419 | −0.246209 | − | 0.969217i | \(-0.579185\pi\) | ||||
−0.246209 | + | 0.969217i | \(0.579185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.4209 | − | 24.4917i | 0.0912278 | − | 0.0526704i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 435.539 | + | 251.458i | 0.932631 | + | 0.538455i | 0.887643 | − | 0.460533i | \(-0.152342\pi\) |
0.0449884 | + | 0.998988i | \(0.485675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 238.024 | − | 412.270i | 0.505360 | − | 0.875309i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 306.215 | + | 530.380i | 0.647390 | + | 1.12131i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 485.704i | − | 1.02254i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 71.5879 | 0.150079 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −184.149 | + | 106.318i | −0.384444 | + | 0.221959i | −0.679750 | − | 0.733444i | \(-0.737912\pi\) |
0.295306 | + | 0.955403i | \(0.404578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −446.583 | − | 257.835i | −0.928446 | − | 0.536039i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.5887 | − | 49.5172i | 0.0589459 | − | 0.102097i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 60.7056 | + | 105.145i | 0.124652 | + | 0.215904i | 0.921597 | − | 0.388148i | \(-0.126885\pi\) |
−0.796945 | + | 0.604052i | \(0.793552\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 212.239i | 0.434027i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −130.353 | −0.265485 | −0.132743 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 197.860 | − | 114.235i | 0.401339 | − | 0.231713i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.0444 | + | 19.6556i | 0.0687767 | + | 0.0397082i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −78.9899 | + | 136.815i | −0.158296 | + | 0.274177i | −0.934254 | − | 0.356607i | \(-0.883933\pi\) |
0.775958 | + | 0.630785i | \(0.217267\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 423.362 | + | 733.285i | 0.845035 | + | 1.46364i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 323.502i | − | 0.643146i | −0.946885 | − | 0.321573i | \(-0.895788\pi\) | ||
0.946885 | − | 0.321573i | \(-0.104212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −82.2052 | −0.162783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −943.901 | + | 544.961i | −1.86174 | + | 1.07487i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −437.969 | − | 252.862i | −0.860450 | − | 0.496781i | 0.00371263 | − | 0.999993i | \(-0.498818\pi\) |
−0.864163 | + | 0.503212i | \(0.832152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −158.461 | + | 274.462i | −0.308891 | + | 0.535014i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.9117 | + | 18.8996i | 0.0211877 | + | 0.0366982i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.9864i | − | 0.0270531i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −455.696 | −0.878026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −716.925 | + | 413.917i | −1.37606 | + | 0.794466i | −0.991682 | − | 0.128712i | \(-0.958916\pi\) |
−0.384373 | + | 0.923178i | \(0.625582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −98.9920 | − | 57.1531i | −0.189277 | − | 0.109279i | 0.402367 | − | 0.915479i | \(-0.368188\pi\) |
−0.591644 | + | 0.806199i | \(0.701521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −64.0000 | + | 110.851i | −0.121442 | + | 0.210344i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −145.265 | − | 251.605i | −0.274602 | − | 0.475625i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 69.3446i | 0.130592i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1510.02 | 2.83306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 82.3009 | − | 47.5165i | 0.153834 | − | 0.0888158i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 870.324 | + | 502.482i | 1.62071 | + | 0.935720i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −264.549 | + | 458.213i | −0.489000 | + | 0.846974i | −0.999920 | − | 0.0126550i | \(-0.995972\pi\) |
0.510920 | + | 0.859629i | \(0.329305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 56.6030 | + | 98.0393i | 0.104241 | + | 0.180551i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 42.6430i | − | 0.0782440i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −281.314 | −0.514285 | −0.257142 | − | 0.966374i | \(-0.582781\pi\) | ||||
−0.257142 | + | 0.966374i | \(0.582781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 350.021 | − | 202.085i | 0.637561 | − | 0.368096i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 638.075 | + | 368.392i | 1.15803 | + | 0.668589i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.0488 | + | 48.5819i | −0.0505383 | + | 0.0875350i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 99.2355 | + | 171.881i | 0.178161 | + | 0.308583i | 0.941251 | − | 0.337709i | \(-0.109652\pi\) |
−0.763090 | + | 0.646292i | \(0.776319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 990.797i | 1.77244i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −301.255 | −0.536996 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −85.1245 | + | 49.1467i | −0.151198 | + | 0.0872942i | −0.573690 | − | 0.819072i | \(-0.694489\pi\) |
0.422492 | + | 0.906367i | \(0.361155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.5934 | − | 22.2819i | −0.0683069 | − | 0.0394370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 354.515 | − | 614.038i | 0.623049 | − | 1.07915i | −0.365866 | − | 0.930668i | \(-0.619227\pi\) |
0.988915 | − | 0.148484i | \(-0.0474395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −231.059 | − | 400.206i | −0.404657 | − | 0.700886i | 0.589625 | − | 0.807677i | \(-0.299276\pi\) |
−0.994281 | + | 0.106792i | \(0.965942\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 257.201i | − | 0.448867i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −704.177 | −1.22465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −507.985 | + | 293.285i | −0.880391 | + | 0.508294i | −0.870787 | − | 0.491660i | \(-0.836390\pi\) |
−0.00960341 | + | 0.999954i | \(0.503057\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −894.264 | − | 516.303i | −1.54450 | − | 0.891716i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 102.333 | − | 177.246i | 0.175528 | − | 0.304024i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.7990 | + | 55.0775i | 0.0543572 | + | 0.0941495i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 441.613i | 0.752322i | 0.926554 | + | 0.376161i | \(0.122756\pi\) | ||||
−0.926554 | + | 0.376161i | \(0.877244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −412.784 | −0.700821 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 327.885 | − | 189.304i | 0.554797 | − | 0.320312i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −75.3672 | − | 43.5133i | −0.127095 | − | 0.0733782i | 0.435105 | − | 0.900380i | \(-0.356711\pi\) |
−0.562199 | + | 0.827002i | \(0.690045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 299.245 | − | 518.307i | 0.501247 | − | 0.868186i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −242.054 | − | 419.250i | −0.404097 | − | 0.699916i | 0.590119 | − | 0.807316i | \(-0.299081\pi\) |
−0.994216 | + | 0.107400i | \(0.965747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 904.895i | 1.50565i | 0.658221 | + | 0.752825i | \(0.271309\pi\) | ||||
−0.658221 | + | 0.752825i | \(0.728691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −114.686 | −0.190193 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.8898 | − | 17.8342i | 0.0510574 | − | 0.0294780i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −814.913 | − | 470.490i | −1.34253 | − | 0.775107i | −0.355348 | − | 0.934734i | \(-0.615638\pi\) |
−0.987177 | + | 0.159627i | \(0.948971\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3137 | − | 19.5959i | 0.0185167 | − | 0.0320719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −120.314 | − | 208.389i | −0.196270 | − | 0.339950i | 0.751046 | − | 0.660250i | \(-0.229550\pi\) |
−0.947316 | + | 0.320300i | \(0.896216\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 164.269i | − | 0.267104i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 781.716 | 1.26696 | 0.633481 | − | 0.773758i | \(-0.281625\pi\) | ||||
0.633481 | + | 0.773758i | \(0.281625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.65912 | + | 4.99935i | −0.0139889 | + | 0.00807649i | −0.506978 | − | 0.861959i | \(-0.669238\pi\) |
0.492989 | + | 0.870035i | \(0.335904\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 397.917 | + | 229.738i | 0.640768 | + | 0.369948i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −297.505 | + | 515.294i | −0.476008 | + | 0.824470i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −485.754 | − | 841.351i | −0.774728 | − | 1.34187i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 146.590i | − | 0.233052i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 908.538 | 1.43984 | 0.719919 | − | 0.694058i | \(-0.244179\pi\) | ||||
0.719919 | + | 0.694058i | \(0.244179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −163.283 | + | 94.2714i | −0.257951 | + | 0.148928i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.4865 | + | 29.7257i | 0.0810810 | + | 0.0468122i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −104.848 | + | 181.602i | −0.164081 | + | 0.284197i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −96.7300 | − | 167.541i | −0.150905 | − | 0.261375i | 0.780656 | − | 0.624962i | \(-0.214885\pi\) |
−0.931560 | + | 0.363587i | \(0.881552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 362.412i | 0.563627i | 0.959469 | + | 0.281814i | \(0.0909360\pi\) | ||||
−0.959469 | + | 0.281814i | \(0.909064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 107.785 | 0.167108 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 311.444 | − | 179.812i | 0.481366 | − | 0.277917i | −0.239619 | − | 0.970867i | \(-0.577023\pi\) |
0.720986 | + | 0.692950i | \(0.243689\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 171.692 | + | 99.1263i | 0.264548 | + | 0.152737i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 357.843 | − | 619.802i | 0.547998 | − | 0.949160i | −0.450414 | − | 0.892820i | \(-0.648723\pi\) |
0.998412 | − | 0.0563404i | \(-0.0179432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.3574 | − | 80.2934i | −0.0707747 | − | 0.122585i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 240.933i | 0.366717i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −390.431 | −0.592459 | −0.296230 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296230 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −303.520 | + | 175.237i | −0.459183 | + | 0.265109i | −0.711700 | − | 0.702483i | \(-0.752075\pi\) |
0.252518 | + | 0.967592i | \(0.418741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −422.078 | − | 243.687i | −0.636618 | − | 0.367551i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 534.098 | − | 925.084i | 0.800746 | − | 1.38693i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −408.902 | − | 708.238i | −0.611213 | − | 1.05865i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1155.50i | − | 1.72206i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 487.214 | 0.723944 | 0.361972 | − | 0.932189i | \(-0.382104\pi\) | ||||
0.361972 | + | 0.932189i | \(0.382104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 341.908 | − | 197.401i | 0.506531 | − | 0.292446i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 391.220 | + | 225.871i | 0.577873 | + | 0.333635i | 0.760288 | − | 0.649586i | \(-0.225058\pi\) |
−0.182414 | + | 0.983222i | \(0.558391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 186.711 | − | 323.392i | 0.274171 | − | 0.474879i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 112.373 | + | 194.635i | 0.164528 | + | 0.284971i | 0.936488 | − | 0.350701i | \(-0.114057\pi\) |
−0.771960 | + | 0.635672i | \(0.780723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 94.9583i | − | 0.138625i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 628.950 | 0.915503 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 286.751 | − | 165.555i | 0.416184 | − | 0.240284i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.5715 | − | 28.0427i | −0.0702915 | − | 0.0405828i | 0.464442 | − | 0.885603i | \(-0.346255\pi\) |
−0.534734 | + | 0.845021i | \(0.679588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.1219 | − | 66.0291i | 0.0548517 | − | 0.0950059i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 214.627 | + | 371.746i | 0.307930 | + | 0.533351i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1666.75i | − | 2.38448i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −769.647 | −1.09793 | −0.548963 | − | 0.835846i | \(-0.684977\pi\) | ||||
−0.548963 | + | 0.835846i | \(0.684977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 409.400 | − | 236.367i | 0.582361 | − | 0.336226i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.13176 | − | 1.23077i | −0.00302377 | − | 0.00174578i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −232.980 | + | 403.533i | −0.328603 | + | 0.569158i | −0.982235 | − | 0.187655i | \(-0.939911\pi\) |
0.653632 | + | 0.756813i | \(0.273245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −78.5046 | − | 135.974i | −0.110414 | − | 0.191243i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 598.456i | 0.839350i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 181.823 | 0.254298 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 701.329 | − | 404.913i | 0.978144 | − | 0.564732i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 910.957 | + | 525.942i | 1.26698 | + | 0.731490i | 0.974415 | − | 0.224756i | \(-0.0721584\pi\) |
0.292563 | + | 0.956246i | \(0.405492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 601.235 | − | 1041.37i | 0.831583 | − | 1.44034i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −458.921 | − | 794.874i | −0.632994 | − | 1.09638i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 161.080i | − | 0.221568i | −0.993845 | − | 0.110784i | \(-0.964664\pi\) | ||
0.993845 | − | 0.110784i | \(-0.0353361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −62.4315 | −0.0856399 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −243.920 | + | 140.828i | −0.333680 | + | 0.192650i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1245.95 | + | 719.349i | 1.69979 | + | 0.981376i | 0.945945 | + | 0.324327i | \(0.105138\pi\) |
0.753848 | + | 0.657049i | \(0.228195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −163.941 | + | 283.954i | −0.222444 | + | 0.385284i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −568.696 | − | 985.010i | −0.769547 | − | 1.33290i | −0.937809 | − | 0.347153i | \(-0.887149\pi\) |
0.168261 | − | 0.985742i | \(-0.446185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1571.72i | − | 2.12108i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −745.882 | −1.00388 | −0.501940 | − | 0.864903i | \(-0.667380\pi\) | ||||
−0.501940 | + | 0.864903i | \(0.667380\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.5402 | − | 10.7042i | 0.0248862 | − | 0.0143681i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −312.103 | − | 180.193i | −0.417809 | − | 0.241222i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 76.9411 | − | 133.266i | 0.102452 | − | 0.177451i | −0.810243 | − | 0.586095i | \(-0.800665\pi\) |
0.912694 | + | 0.408643i | \(0.133998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −480.534 | − | 832.309i | −0.638159 | − | 1.10532i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 91.7011i | 0.121458i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −119.137 | −0.157381 | −0.0786903 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786903 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1219.80 | + | 704.250i | −1.60711 | + | 0.927865i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1199.62 | − | 692.600i | −1.57637 | − | 0.910119i | −0.995360 | − | 0.0962239i | \(-0.969324\pi\) |
−0.581012 | − | 0.813895i | \(-0.697343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.03954 | + | 15.6569i | −0.0118164 | + | 0.0204666i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 160.368 | + | 277.765i | 0.209084 | + | 0.362144i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 55.9020i | 0.0726945i | 0.999339 | + | 0.0363472i | \(0.0115722\pi\) | ||||
−0.999339 | + | 0.0363472i | \(0.988428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 682.039 | 0.884616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 155.676 | − | 89.8797i | 0.201392 | − | 0.116274i | −0.395912 | − | 0.918288i | \(-0.629572\pi\) |
0.597305 | + | 0.802014i | \(0.296238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 445.328 | + | 257.110i | 0.574617 | + | 0.331755i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −692.146 | + | 1198.83i | −0.888506 | + | 1.53894i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 299.754 | + | 519.190i | 0.383808 | + | 0.664776i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 598.892i | 0.764868i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −81.6771 | −0.104047 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 180.448 | − | 104.182i | 0.229286 | − | 0.132378i | −0.380957 | − | 0.924593i | \(-0.624405\pi\) |
0.610242 | + | 0.792215i | \(0.291072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −790.031 | − | 456.125i | −1.00131 | − | 0.578105i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 934.690 | − | 1618.93i | 1.17868 | − | 2.04153i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.0101 | − | 31.1944i | −0.0226542 | − | 0.0392383i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 237.327i | − | 0.297776i | −0.988854 | − | 0.148888i | \(-0.952431\pi\) | ||
0.988854 | − | 0.148888i | \(-0.0475694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.43232 | 0.00805047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 317.656 | − | 183.399i | 0.396575 | − | 0.228963i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 596.531 | + | 344.407i | 0.742878 | + | 0.428901i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −194.309 | + | 336.552i | −0.240779 | + | 0.417041i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −256.897 | − | 444.958i | −0.317548 | − | 0.550010i | 0.662428 | − | 0.749126i | \(-0.269526\pi\) |
−0.979976 | + | 0.199116i | \(0.936193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 452.373i | 0.557797i | 0.960321 | + | 0.278898i | \(0.0899692\pi\) | ||||
−0.960321 | + | 0.278898i | \(0.910031\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −265.373 | −0.326412 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.5358 | − | 18.2072i | 0.0386943 | − | 0.0223402i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −786.612 | − | 454.151i | −0.962806 | − | 0.555876i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 720.519 | − | 1247.98i | 0.877611 | − | 1.52007i | 0.0236566 | − | 0.999720i | \(-0.492469\pi\) |
0.853955 | − | 0.520347i | \(-0.174197\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 801.828 | + | 1388.81i | 0.974275 | + | 1.68749i | 0.682307 | + | 0.731066i | \(0.260977\pi\) |
0.291968 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1210.25i | 1.46697i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 933.549 | 1.12884 | 0.564419 | − | 0.825488i | \(-0.309100\pi\) | ||||
0.564419 | + | 0.825488i | \(0.309100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −362.699 | + | 209.404i | −0.437514 | + | 0.252599i | −0.702543 | − | 0.711642i | \(-0.747952\pi\) |
0.265029 | + | 0.964241i | \(0.414619\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1286.88 | − | 742.979i | −1.54859 | − | 0.894079i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 72.6375 | − | 125.812i | 0.0869910 | − | 0.150673i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −167.765 | − | 290.577i | −0.200435 | − | 0.347164i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 995.689i | 1.18676i | 0.804924 | + | 0.593378i | \(0.202206\pi\) | ||||
−0.804924 | + | 0.593378i | \(0.797794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 551.313 | 0.655544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1029.03 | − | 594.108i | 1.22067 | − | 0.704755i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 161.948 | + | 93.5006i | 0.191654 | + | 0.110652i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −897.200 | + | 1554.00i | −1.05677 | + | 1.83038i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −342.686 | − | 593.550i | −0.402687 | − | 0.697474i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 315.117i | − | 0.369422i | −0.982793 | − | 0.184711i | \(-0.940865\pi\) | ||
0.982793 | − | 0.184711i | \(-0.0591349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −58.3027 | −0.0681903 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −189.042 | + | 109.144i | −0.220586 | + | 0.127355i | −0.606222 | − | 0.795296i | \(-0.707316\pi\) |
0.385636 | + | 0.922651i | \(0.373982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1248.60 | + | 720.879i | 1.45355 | + | 0.839208i | 0.998681 | − | 0.0513505i | \(-0.0163526\pi\) |
0.454870 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −437.437 | + | 757.662i | −0.506879 | + | 0.877940i | 0.493089 | + | 0.869979i | \(0.335868\pi\) |
−0.999968 | + | 0.00796139i | \(0.997466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.0925 | + | 67.7102i | 0.0451936 | + | 0.0782777i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 929.459i | 1.07204i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −448.881 | −0.516549 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −459.384 | + | 265.226i | −0.527422 | + | 0.304507i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 363.684 | + | 209.973i | 0.416591 | + | 0.240519i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −851.323 | + | 1474.53i | −0.970722 | + | 1.68134i | −0.277336 | + | 0.960773i | \(0.589451\pi\) |
−0.693386 | + | 0.720566i | \(0.743882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 887.328 | + | 1536.90i | 1.00947 | + | 1.74846i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1018.58i | 1.15617i | 0.815978 | + | 0.578083i | \(0.196199\pi\) | ||||
−0.815978 | + | 0.578083i | \(0.803801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1646.04 | 1.86414 | 0.932071 | − | 0.362276i | \(-0.118000\pi\) | ||||
0.932071 | + | 0.362276i | \(0.118000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.2169 | − | 17.4457i | 0.0341434 | − | 0.0197127i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −596.343 | − | 344.299i | −0.672314 | − | 0.388161i | 0.124639 | − | 0.992202i | \(-0.460223\pi\) |
−0.796953 | + | 0.604041i | \(0.793556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 673.843 | − | 1167.13i | 0.756277 | − | 1.30991i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3717 | + | 17.9643i | 0.0116145 | + | 0.0201168i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 172.424i | − | 0.192653i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2278.68 | −2.54034 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −675.537 | + | 390.022i | −0.751432 | + | 0.433839i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 81.5149 | + | 47.0627i | 0.0904716 | + | 0.0522338i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.71154 | − | 16.8209i | 0.0107310 | − | 0.0185866i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 106.009 | + | 183.613i | 0.116879 | + | 0.202440i | 0.918529 | − | 0.395353i | \(-0.129378\pi\) |
−0.801650 | + | 0.597793i | \(0.796044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 603.765i | − | 0.664208i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −601.882 | −0.660683 | −0.330342 | − | 0.943861i | \(-0.607164\pi\) | ||||
−0.330342 | + | 0.943861i | \(0.607164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −892.288 | + | 515.163i | −0.977314 | + | 0.564253i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −176.117 | − | 101.681i | −0.192477 | − | 0.111127i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −559.171 | + | 968.512i | −0.608456 | + | 1.05388i | 0.383039 | + | 0.923732i | \(0.374877\pi\) |
−0.991495 | + | 0.130144i | \(0.958456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.3675 | − | 42.2058i | −0.0264577 | − | 0.0458261i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 969.892i | 1.05080i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −588.903 | −0.636652 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −138.810 | + | 80.1421i | −0.149741 | + | 0.0864532i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 348.062 | + | 200.954i | 0.374663 | + | 0.216312i | 0.675494 | − | 0.737366i | \(-0.263931\pi\) |
−0.300831 | + | 0.953678i | \(0.597264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 726.558 | − | 1258.44i | 0.778734 | − | 1.34881i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.8436 | + | 44.7624i | 0.0276402 | + | 0.0478742i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1597.84i | − | 1.70527i | −0.522507 | − | 0.852635i | \(-0.675003\pi\) | ||
0.522507 | − | 0.852635i | \(-0.324997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −819.273 | −0.872496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1331.70 | + | 768.857i | −1.41520 | + | 0.817064i | −0.995872 | − | 0.0907721i | \(-0.971067\pi\) |
−0.419325 | + | 0.907836i | \(0.637733\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1738.07 | + | 1003.48i | 1.84313 | + | 1.06413i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 160.137 | − | 277.366i | 0.169099 | − | 0.292889i | −0.769004 | − | 0.639244i | \(-0.779247\pi\) |
0.938103 | + | 0.346355i | \(0.112581\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 557.186 | + | 965.074i | 0.587129 | + | 1.01694i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 349.480i | − | 0.367487i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −734.861 | −0.771103 | −0.385552 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385552 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.2165 | + | 22.0643i | −0.0400173 | + | 0.0231040i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1589.91 | − | 917.937i | −1.66135 | − | 0.959182i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −261.990 | + | 453.781i | −0.272623 | + | 0.472196i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 348.990 | + | 604.468i | 0.362399 | + | 0.627693i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 177.167i | 0.183593i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1446.98 | 1.49636 | 0.748179 | − | 0.663497i | \(-0.230928\pi\) | ||||
0.748179 | + | 0.663497i | \(0.230928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 386.935 | − | 223.397i | 0.399314 | − | 0.230544i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −836.653 | − | 483.042i | −0.861641 | − | 0.497469i | 0.00292046 | − | 0.999996i | \(-0.499070\pi\) |
−0.864561 | + | 0.502527i | \(0.832404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −978.975 | + | 1695.63i | −1.00408 | + | 1.73911i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 304.803 | + | 527.935i | 0.311979 | + | 0.540363i | 0.978791 | − | 0.204863i | \(-0.0656749\pi\) |
−0.666812 | + | 0.745226i | \(0.732342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1048.66i | − | 1.07115i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 313.196 | 0.319262 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1106.15 | − | 638.635i | 1.12528 | − | 0.649679i | 0.182534 | − | 0.983199i | \(-0.441570\pi\) |
0.942743 | + | 0.333520i | \(0.108237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.2561 | − | 32.4795i | −0.0571128 | − | 0.0329741i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −658.431 | + | 1140.44i | −0.665754 | + | 1.15312i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 834.994 | + | 1446.25i | 0.842577 | + | 1.45939i | 0.887709 | + | 0.460406i | \(0.152296\pi\) |
−0.0451314 | + | 0.998981i | \(0.514371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 703.379i | − | 0.708338i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −102.685 | −0.103201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 684.118 | − | 394.976i | 0.686177 | − | 0.396164i | −0.116001 | − | 0.993249i | \(-0.537008\pi\) |
0.802178 | + | 0.597085i | \(0.203674\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 332.778 | + | 192.130i | 0.333111 | + | 0.192322i |
(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 | 392.3.o.b.313.4 | 8 | ||
4.3 | odd | 2 | 784.3.s.f.705.1 | 8 | |||
7.2 | even | 3 | 56.3.c.a.41.4 | yes | 4 | ||
7.3 | odd | 6 | inner | 392.3.o.b.129.4 | 8 | ||
7.4 | even | 3 | inner | 392.3.o.b.129.1 | 8 | ||
7.5 | odd | 6 | 56.3.c.a.41.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 392.3.o.b.313.1 | 8 | ||
21.2 | odd | 6 | 504.3.f.a.433.2 | 4 | |||
21.5 | even | 6 | 504.3.f.a.433.3 | 4 | |||
28.3 | even | 6 | 784.3.s.f.129.1 | 8 | |||
28.11 | odd | 6 | 784.3.s.f.129.4 | 8 | |||
28.19 | even | 6 | 112.3.c.c.97.4 | 4 | |||
28.23 | odd | 6 | 112.3.c.c.97.1 | 4 | |||
28.27 | even | 2 | 784.3.s.f.705.4 | 8 | |||
35.2 | odd | 12 | 1400.3.p.a.1049.7 | 8 | |||
35.9 | even | 6 | 1400.3.f.a.601.1 | 4 | |||
35.12 | even | 12 | 1400.3.p.a.1049.1 | 8 | |||
35.19 | odd | 6 | 1400.3.f.a.601.4 | 4 | |||
35.23 | odd | 12 | 1400.3.p.a.1049.2 | 8 | |||
35.33 | even | 12 | 1400.3.p.a.1049.8 | 8 | |||
56.5 | odd | 6 | 448.3.c.f.321.4 | 4 | |||
56.19 | even | 6 | 448.3.c.e.321.1 | 4 | |||
56.37 | even | 6 | 448.3.c.f.321.1 | 4 | |||
56.51 | odd | 6 | 448.3.c.e.321.4 | 4 | |||
84.23 | even | 6 | 1008.3.f.h.433.2 | 4 | |||
84.47 | odd | 6 | 1008.3.f.h.433.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.c.a.41.1 | ✓ | 4 | 7.5 | odd | 6 | ||
56.3.c.a.41.4 | yes | 4 | 7.2 | even | 3 | ||
112.3.c.c.97.1 | 4 | 28.23 | odd | 6 | |||
112.3.c.c.97.4 | 4 | 28.19 | even | 6 | |||
392.3.o.b.129.1 | 8 | 7.4 | even | 3 | inner | ||
392.3.o.b.129.4 | 8 | 7.3 | odd | 6 | inner | ||
392.3.o.b.313.1 | 8 | 7.6 | odd | 2 | inner | ||
392.3.o.b.313.4 | 8 | 1.1 | even | 1 | trivial | ||
448.3.c.e.321.1 | 4 | 56.19 | even | 6 | |||
448.3.c.e.321.4 | 4 | 56.51 | odd | 6 | |||
448.3.c.f.321.1 | 4 | 56.37 | even | 6 | |||
448.3.c.f.321.4 | 4 | 56.5 | odd | 6 | |||
504.3.f.a.433.2 | 4 | 21.2 | odd | 6 | |||
504.3.f.a.433.3 | 4 | 21.5 | even | 6 | |||
784.3.s.f.129.1 | 8 | 28.3 | even | 6 | |||
784.3.s.f.129.4 | 8 | 28.11 | odd | 6 | |||
784.3.s.f.705.1 | 8 | 4.3 | odd | 2 | |||
784.3.s.f.705.4 | 8 | 28.27 | even | 2 | |||
1008.3.f.h.433.2 | 4 | 84.23 | even | 6 | |||
1008.3.f.h.433.3 | 4 | 84.47 | odd | 6 | |||
1400.3.f.a.601.1 | 4 | 35.9 | even | 6 | |||
1400.3.f.a.601.4 | 4 | 35.19 | odd | 6 | |||
1400.3.p.a.1049.1 | 8 | 35.12 | even | 12 | |||
1400.3.p.a.1049.2 | 8 | 35.23 | odd | 12 | |||
1400.3.p.a.1049.7 | 8 | 35.2 | odd | 12 | |||
1400.3.p.a.1049.8 | 8 | 35.33 | even | 12 |