Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1781,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.t (of order \(6\), degree \(2\), 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: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1781.1 | ||
Character | \(\chi\) | \(=\) | 2268.1781 |
Dual form | 2268.2.t.c.2105.1 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.11958 | − | 3.67122i | −0.947905 | − | 1.64182i | −0.749828 | − | 0.661633i | \(-0.769864\pi\) |
−0.198077 | − | 0.980186i | \(-0.563470\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.57575 | − | 0.604567i | −0.973543 | − | 0.228505i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.69031 | − | 2.70795i | −1.41418 | − | 0.816479i | −0.418404 | − | 0.908261i | \(-0.637410\pi\) |
−0.995779 | + | 0.0917822i | \(0.970744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.28169i | − | 1.18753i | −0.804640 | − | 0.593763i | \(-0.797642\pi\) | ||
0.804640 | − | 0.593763i | \(-0.202358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.26949 | − | 5.66292i | 0.792968 | − | 1.37346i | −0.131154 | − | 0.991362i | \(-0.541868\pi\) |
0.924121 | − | 0.382099i | \(-0.124799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.653566 | + | 0.377336i | −0.149938 | + | 0.0865669i | −0.573092 | − | 0.819491i | \(-0.694256\pi\) |
0.423154 | + | 0.906058i | \(0.360923\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.22399 | + | 1.86137i | −0.672249 | + | 0.388123i | −0.796928 | − | 0.604074i | \(-0.793543\pi\) |
0.124679 | + | 0.992197i | \(0.460210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.48524 | + | 11.2328i | −1.29705 | + | 2.24655i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.09363i | − | 0.760169i | −0.924952 | − | 0.380084i | \(-0.875895\pi\) | ||
0.924952 | − | 0.380084i | \(-0.124105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.17532 | + | 3.56532i | 1.10912 | + | 0.640350i | 0.938601 | − | 0.345004i | \(-0.112123\pi\) |
0.170518 | + | 0.985355i | \(0.445456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.24001 | + | 10.7376i | 0.547662 | + | 1.81498i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.90230 | − | 5.02693i | −0.477135 | − | 0.826423i | 0.522521 | − | 0.852626i | \(-0.324992\pi\) |
−0.999657 | + | 0.0262035i | \(0.991658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41012 | 0.220223 | 0.110112 | − | 0.993919i | \(-0.464879\pi\) | ||||
0.110112 | + | 0.993919i | \(0.464879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.23592 | 0.493474 | 0.246737 | − | 0.969083i | \(-0.420642\pi\) | ||||
0.246737 | + | 0.969083i | \(0.420642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.06551 | − | 3.57757i | −0.301286 | − | 0.521842i | 0.675142 | − | 0.737688i | \(-0.264082\pi\) |
−0.976427 | + | 0.215846i | \(0.930749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.26900 | + | 3.11443i | 0.895571 | + | 0.444918i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.34571 | + | 3.08635i | 0.734289 | + | 0.423942i | 0.819989 | − | 0.572379i | \(-0.193979\pi\) |
−0.0856999 | + | 0.996321i | \(0.527313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.9589i | 3.09578i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.610424 | − | 1.05728i | 0.0794704 | − | 0.137647i | −0.823551 | − | 0.567242i | \(-0.808010\pi\) |
0.903022 | + | 0.429595i | \(0.141344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.08007 | − | 1.77828i | 0.394362 | − | 0.227685i | −0.289686 | − | 0.957122i | \(-0.593551\pi\) |
0.684048 | + | 0.729437i | \(0.260218\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.7190 | + | 9.07538i | −1.94970 | + | 1.12566i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.22396 | + | 12.5123i | −0.882547 | + | 1.52862i | −0.0340481 | + | 0.999420i | \(0.510840\pi\) |
−0.848499 | + | 0.529197i | \(0.822493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.83088i | − | 0.454642i | −0.973820 | − | 0.227321i | \(-0.927003\pi\) | ||
0.973820 | − | 0.227321i | \(-0.0729967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.39512 | − | 4.84693i | −0.982575 | − | 0.567290i | −0.0795282 | − | 0.996833i | \(-0.525341\pi\) |
−0.903046 | + | 0.429543i | \(0.858675\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.4439 | + | 9.81063i | 1.19020 | + | 1.11802i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51308 | − | 4.35278i | −0.282743 | − | 0.489726i | 0.689316 | − | 0.724461i | \(-0.257911\pi\) |
−0.972059 | + | 0.234735i | \(0.924578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.771990 | −0.0847369 | −0.0423684 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423684 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −27.7198 | −3.00663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.04991 | + | 12.2108i | 0.747289 | + | 1.29434i | 0.949118 | + | 0.314922i | \(0.101978\pi\) |
−0.201828 | + | 0.979421i | \(0.564688\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.58857 | + | 11.0286i | −0.271355 | + | 1.15611i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.77057 | + | 1.59959i | 0.284255 | + | 0.164114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.12078i | 0.519936i | 0.965617 | + | 0.259968i | \(0.0837121\pi\) | ||||
−0.965617 | + | 0.259968i | \(0.916288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.33405 | − | 10.9709i | 0.630262 | − | 1.09165i | −0.357236 | − | 0.934014i | \(-0.616281\pi\) |
0.987498 | − | 0.157631i | \(-0.0503858\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3685 | + | 8.87301i | −1.51430 | + | 0.874283i | −0.514444 | + | 0.857524i | \(0.672002\pi\) |
−0.999860 | + | 0.0167594i | \(0.994665\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.70853 | − | 2.71847i | 0.455191 | − | 0.262805i | −0.254829 | − | 0.966986i | \(-0.582019\pi\) |
0.710020 | + | 0.704182i | \(0.248686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.01949 | − | 10.4261i | 0.576563 | − | 0.998636i | −0.419307 | − | 0.907845i | \(-0.637727\pi\) |
0.995870 | − | 0.0907919i | \(-0.0289398\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.05568i | − | 0.569670i | −0.958576 | − | 0.284835i | \(-0.908061\pi\) | ||
0.958576 | − | 0.284835i | \(-0.0919389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6670 | + | 7.89066i | 1.27446 | + | 0.735808i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.8450 | + | 12.6097i | −1.08583 | + | 1.15593i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.16603 | + | 15.8760i | 0.833276 | + | 1.44328i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.7881 | 3.02210 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5012 | 1.46424 | 0.732122 | − | 0.681173i | \(-0.238530\pi\) | ||||
0.732122 | + | 0.681173i | \(0.238530\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.46309 | − | 11.1944i | −0.564683 | − | 0.978060i | −0.997079 | − | 0.0763762i | \(-0.975665\pi\) |
0.432396 | − | 0.901684i | \(-0.357668\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.91155 | − | 0.576801i | 0.165752 | − | 0.0500150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0429778 | + | 0.0248133i | 0.00367184 | + | 0.00211994i | 0.501835 | − | 0.864963i | \(-0.332659\pi\) |
−0.498163 | + | 0.867083i | \(0.665992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.13230i | − | 0.180859i | −0.995903 | − | 0.0904296i | \(-0.971176\pi\) | ||
0.995903 | − | 0.0904296i | \(-0.0288240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.5946 | + | 20.0825i | −0.969590 | + | 1.67938i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.0286 | + | 8.67679i | −1.24806 | + | 0.720568i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.54458 | + | 4.35586i | −0.618076 | + | 0.356846i | −0.776120 | − | 0.630586i | \(-0.782815\pi\) |
0.158044 | + | 0.987432i | \(0.449481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.48389 | − | 11.2304i | 0.527651 | − | 0.913919i | −0.471829 | − | 0.881690i | \(-0.656406\pi\) |
0.999481 | − | 0.0322291i | \(-0.0102606\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 30.2279i | − | 2.42797i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.78620 | + | 1.03126i | 0.142554 | + | 0.0823036i | 0.569581 | − | 0.821935i | \(-0.307106\pi\) |
−0.427027 | + | 0.904239i | \(0.640439\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.42953 | − | 2.84532i | 0.743151 | − | 0.224242i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.36837 | − | 11.0303i | −0.498809 | − | 0.863963i | 0.501190 | − | 0.865337i | \(-0.332896\pi\) |
−0.999999 | + | 0.00137460i | \(0.999562\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.42324 | 0.419663 | 0.209831 | − | 0.977738i | \(-0.432709\pi\) | ||||
0.209831 | + | 0.977738i | \(0.432709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.33283 | −0.410218 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.71829 | + | 4.70822i | 0.206668 | + | 0.357959i | 0.950663 | − | 0.310226i | \(-0.100405\pi\) |
−0.743995 | + | 0.668185i | \(0.767071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.4953 | − | 25.0121i | 1.77608 | − | 1.89073i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.81355 | + | 1.62440i | 0.210294 | + | 0.121414i | 0.601448 | − | 0.798912i | \(-0.294591\pi\) |
−0.391154 | + | 0.920325i | \(0.627924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0236i | 1.26535i | 0.774416 | + | 0.632677i | \(0.218044\pi\) | ||||
−0.774416 | + | 0.632677i | \(0.781956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3033 | + | 21.3100i | −0.904558 | + | 1.56674i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.6699 | + | 17.7073i | −2.24280 | + | 1.29488i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.2007 | + | 11.0855i | −1.38931 | + | 0.802119i | −0.993238 | − | 0.116099i | \(-0.962961\pi\) |
−0.396074 | + | 0.918219i | \(0.629628\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.721359 | + | 1.24943i | −0.0519246 | + | 0.0899360i | −0.890819 | − | 0.454358i | \(-0.849869\pi\) |
0.838895 | + | 0.544293i | \(0.183202\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.2241i | − | 0.799686i | −0.916584 | − | 0.399843i | \(-0.869065\pi\) | ||
0.916584 | − | 0.399843i | \(-0.130935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.38720 | + | 1.37825i | 0.169224 | + | 0.0977016i | 0.582220 | − | 0.813031i | \(-0.302184\pi\) |
−0.412996 | + | 0.910733i | \(0.635518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.47488 | + | 10.5442i | −0.173702 | + | 0.740057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.98886 | − | 5.17685i | −0.208751 | − | 0.361567i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.08724 | 0.282720 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0295 | 1.10352 | 0.551758 | − | 0.834004i | \(-0.313957\pi\) | ||||
0.551758 | + | 0.834004i | \(0.313957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.85880 | − | 11.8798i | −0.467766 | − | 0.810194i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.7506 | − | 12.9168i | −0.933452 | − | 0.876848i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.2469 | − | 13.9989i | −1.63102 | − | 0.941670i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8747i | 1.06305i | 0.847044 | + | 0.531523i | \(0.178380\pi\) | ||||
−0.847044 | + | 0.531523i | \(0.821620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.32876 | + | 10.9617i | −0.420054 | + | 0.727556i | −0.995944 | − | 0.0899717i | \(-0.971322\pi\) |
0.575890 | + | 0.817527i | \(0.304656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.83444 | − | 1.05911i | 0.121223 | − | 0.0699883i | −0.438162 | − | 0.898896i | \(-0.644370\pi\) |
0.559386 | + | 0.828908i | \(0.311037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2245 | + | 8.78988i | −0.997392 | + | 0.575844i | −0.907476 | − | 0.420105i | \(-0.861993\pi\) |
−0.0899163 | + | 0.995949i | \(0.528660\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.75603 | + | 15.1659i | −0.571181 | + | 0.989314i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.9539i | − | 1.54945i | −0.632300 | − | 0.774724i | \(-0.717889\pi\) | ||
0.632300 | − | 0.774724i | \(-0.282111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9257 | − | 8.61736i | −0.961449 | − | 0.555093i | −0.0648302 | − | 0.997896i | \(-0.520651\pi\) |
−0.896619 | + | 0.442804i | \(0.853984\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.85389 | − | 29.6162i | −0.118441 | − | 1.89211i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.61564 | + | 2.79836i | 0.102800 | + | 0.178056i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5019 | −0.852231 | −0.426116 | − | 0.904669i | \(-0.640118\pi\) | ||||
−0.426116 | + | 0.904669i | \(0.640118\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1621 | 1.26758 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.42572 | − | 5.93352i | −0.213691 | − | 0.370123i | 0.739176 | − | 0.673512i | \(-0.235215\pi\) |
−0.952867 | + | 0.303389i | \(0.901882\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.43649 | + | 14.7028i | 0.275670 | + | 0.913586i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.36275 | − | 2.51883i | −0.269018 | − | 0.155318i | 0.359423 | − | 0.933175i | \(-0.382974\pi\) |
−0.628442 | + | 0.777857i | \(0.716307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 26.1670i | − | 1.60743i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.33996 | − | 14.4452i | 0.508496 | − | 0.880741i | −0.491455 | − | 0.870903i | \(-0.663535\pi\) |
0.999952 | − | 0.00983842i | \(-0.00313172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0754 | − | 6.39439i | 0.672784 | − | 0.388432i | −0.124347 | − | 0.992239i | \(-0.539684\pi\) |
0.797131 | + | 0.603807i | \(0.206350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.8356 | − | 35.1235i | 3.66853 | − | 2.11802i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.661620 | + | 1.14596i | −0.0397529 | + | 0.0688541i | −0.885217 | − | 0.465178i | \(-0.845990\pi\) |
0.845464 | + | 0.534032i | \(0.179324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.42530i | 0.323646i | 0.986820 | + | 0.161823i | \(0.0517374\pi\) | ||||
−0.986820 | + | 0.161823i | \(0.948263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.92389 | + | 3.42016i | 0.352139 | + | 0.203307i | 0.665627 | − | 0.746285i | \(-0.268164\pi\) |
−0.313488 | + | 0.949592i | \(0.601498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.63211 | − | 0.852511i | −0.214397 | − | 0.0503221i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8791 | − | 22.3073i | −0.757596 | − | 1.31220i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.19467 | −0.128214 | −0.0641070 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641070 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.17537 | −0.301322 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.96981 | + | 13.8041i | 0.460906 | + | 0.798313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.33493 | − | 1.95633i | −0.480418 | − | 0.112761i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0569 | − | 7.53840i | −0.747636 | − | 0.431648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.6442i | − | 1.29237i | −0.763180 | − | 0.646186i | \(-0.776363\pi\) | ||
0.763180 | − | 0.646186i | \(-0.223637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0582 | + | 19.1534i | −0.627056 | + | 1.08609i | 0.361084 | + | 0.932533i | \(0.382407\pi\) |
−0.988139 | + | 0.153559i | \(0.950927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.97360 | − | 1.13946i | 0.111554 | − | 0.0644060i | −0.443185 | − | 0.896430i | \(-0.646151\pi\) |
0.554739 | + | 0.832024i | \(0.312818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00423 | + | 3.46655i | −0.337231 | + | 0.194701i | −0.659047 | − | 0.752102i | \(-0.729040\pi\) |
0.321816 | + | 0.946802i | \(0.395707\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0854 | + | 19.2004i | −0.620662 | + | 1.07502i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.93479i | 0.274579i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 48.0952 | + | 27.7678i | 2.66784 | + | 1.54028i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.15736 | + | 10.4637i | 0.174071 | + | 0.576881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.39474 | + | 2.41577i | 0.0766621 | + | 0.132783i | 0.901808 | − | 0.432137i | \(-0.142240\pi\) |
−0.825146 | + | 0.564920i | \(0.808907\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 61.2471 | 3.34628 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.827607 | −0.0450826 | −0.0225413 | − | 0.999746i | \(-0.507176\pi\) | ||||
−0.0225413 | + | 0.999746i | \(0.507176\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3094 | − | 33.4449i | −1.04567 | − | 1.81115i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2645 | − | 11.8120i | −0.770211 | − | 0.637789i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.36055 | + | 3.67227i | 0.341452 | + | 0.197138i | 0.660914 | − | 0.750462i | \(-0.270169\pi\) |
−0.319462 | + | 0.947599i | \(0.603502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.25225i | − | 0.334675i | −0.985900 | − | 0.167338i | \(-0.946483\pi\) | ||
0.985900 | − | 0.167338i | \(-0.0535170\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.85218 | − | 11.8683i | 0.364705 | − | 0.631687i | −0.624024 | − | 0.781405i | \(-0.714503\pi\) |
0.988729 | + | 0.149718i | \(0.0478367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0640 | + | 8.11986i | −0.746440 | + | 0.430958i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.65240 | + | 2.68606i | −0.245544 | + | 0.141765i | −0.617722 | − | 0.786396i | \(-0.711944\pi\) |
0.372178 | + | 0.928161i | \(0.378611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.21523 | + | 15.9613i | −0.485012 | + | 0.840066i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.0938i | 2.15095i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.2376 | + | 13.9936i | 1.26519 | + | 0.730461i | 0.974075 | − | 0.226226i | \(-0.0726387\pi\) |
0.291120 | + | 0.956687i | \(0.405972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9033 | − | 11.1815i | −0.617989 | − | 0.580515i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4260 | − | 31.9148i | −0.954062 | − | 1.65248i | −0.736499 | − | 0.676438i | \(-0.763523\pi\) |
−0.217563 | − | 0.976046i | \(-0.569811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.5277 | −0.902720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.49138 | 0.0766072 | 0.0383036 | − | 0.999266i | \(-0.487805\pi\) | ||||
0.0383036 | + | 0.999266i | \(0.487805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.60947 | − | 4.51973i | −0.133338 | − | 0.230948i | 0.791624 | − | 0.611009i | \(-0.209236\pi\) |
−0.924961 | + | 0.380062i | \(0.875903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8802 | − | 59.1364i | 0.707400 | − | 3.01387i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5661 | − | 6.67772i | −0.586427 | − | 0.338574i | 0.177257 | − | 0.984165i | \(-0.443278\pi\) |
−0.763683 | + | 0.645591i | \(0.776611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.3430i | 1.23108i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.6533 | + | 18.4521i | −0.536027 | + | 0.928427i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0192 | + | 8.09397i | −0.703602 | + | 0.406225i | −0.808687 | − | 0.588239i | \(-0.799822\pi\) |
0.105086 | + | 0.994463i | \(0.466488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4857 | + | 14.7142i | −1.27270 | + | 0.734791i | −0.975495 | − | 0.220023i | \(-0.929387\pi\) |
−0.297201 | + | 0.954815i | \(0.596053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2656 | − | 26.4408i | 0.760433 | − | 1.31711i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.4372i | 1.55828i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0506 | + | 13.8856i | 1.18923 | + | 0.686600i | 0.958131 | − | 0.286331i | \(-0.0924356\pi\) |
0.231096 | + | 0.972931i | \(0.425769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.21150 | + | 2.35426i | −0.108821 | + | 0.115846i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.63629 | + | 2.83414i | 0.0803225 | + | 0.139123i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.49790 | −0.122030 | −0.0610152 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610152 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.8438 | 1.84439 | 0.922197 | − | 0.386721i | \(-0.126392\pi\) | ||||
0.922197 | + | 0.386721i | \(0.126392\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.4069 | + | 73.4508i | 2.05703 | + | 3.56289i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.00858 | + | 2.71830i | −0.435956 | + | 0.131548i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.420534 | + | 0.242795i | 0.0202564 | + | 0.0116950i | 0.510094 | − | 0.860119i | \(-0.329611\pi\) |
−0.489838 | + | 0.871814i | \(0.662944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.6844i | − | 0.994030i | −0.867742 | − | 0.497015i | \(-0.834429\pi\) | ||
0.867742 | − | 0.497015i | \(-0.165571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.40473 | − | 2.43306i | 0.0671972 | − | 0.116389i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.5976 | − | 9.58265i | 0.792162 | − | 0.457355i | −0.0485610 | − | 0.998820i | \(-0.515464\pi\) |
0.840723 | + | 0.541465i | \(0.182130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6860 | − | 6.16955i | 0.507706 | − | 0.293124i | −0.224184 | − | 0.974547i | \(-0.571972\pi\) |
0.731890 | + | 0.681422i | \(0.238638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.8857 | − | 51.7636i | 1.41672 | − | 2.45383i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9016i | 1.45834i | 0.684334 | + | 0.729168i | \(0.260093\pi\) | ||||
−0.684334 | + | 0.729168i | \(0.739907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.61390 | − | 3.81854i | −0.311436 | − | 0.179808i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.9749 | − | 13.8727i | 2.15534 | − | 0.650363i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5836 | − | 25.2595i | −0.682191 | − | 1.18159i | −0.974311 | − | 0.225207i | \(-0.927694\pi\) |
0.292120 | − | 0.956382i | \(-0.405639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.55436 | 0.165543 | 0.0827715 | − | 0.996569i | \(-0.473623\pi\) | ||||
0.0827715 | + | 0.996569i | \(0.473623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3960 | 1.13378 | 0.566889 | − | 0.823794i | \(-0.308147\pi\) | ||||
0.566889 | + | 0.823794i | \(0.308147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.2411 | + | 31.5946i | 0.844100 | + | 1.46202i | 0.886401 | + | 0.462918i | \(0.153198\pi\) |
−0.0423013 | + | 0.999105i | \(0.513469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.1716 | − | 27.8611i | 1.20849 | − | 1.28651i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.1775 | − | 8.76273i | −0.697862 | − | 0.402911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 9.78847i | − | 0.449126i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.9775 | − | 24.2097i | 0.638648 | − | 1.10617i | −0.347082 | − | 0.937835i | \(-0.612827\pi\) |
0.985730 | − | 0.168336i | \(-0.0538393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.5237 | + | 12.4267i | −0.981398 | + | 0.566611i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.7995 | − | 10.8539i | 0.853642 | − | 0.492850i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5796 | − | 28.7166i | 0.751292 | − | 1.30128i | −0.195905 | − | 0.980623i | \(-0.562764\pi\) |
0.947197 | − | 0.320653i | \(-0.103902\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.1613i | 1.49655i | 0.663388 | + | 0.748275i | \(0.269118\pi\) | ||||
−0.663388 | + | 0.748275i | \(0.730882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.1819 | − | 13.3841i | −1.04406 | − | 0.602790i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.31603 | + | 9.86741i | −0.103888 | + | 0.442614i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5140 | − | 30.3351i | −0.784034 | − | 1.35799i | −0.929574 | − | 0.368635i | \(-0.879825\pi\) |
0.145540 | − | 0.989352i | \(-0.453508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.8096 | −0.749502 | −0.374751 | − | 0.927126i | \(-0.622272\pi\) | ||||
−0.374751 | + | 0.927126i | \(0.622272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.7021 | −2.38971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.16560 | − | 10.6791i | −0.273286 | − | 0.473344i | 0.696416 | − | 0.717639i | \(-0.254777\pi\) |
−0.969701 | + | 0.244294i | \(0.921444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.6935 | + | 17.5599i | 0.826950 | + | 0.776804i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 65.1495 | + | 37.6141i | 2.87083 | + | 1.65748i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.3732i | 0.983974i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6147 | − | 21.8494i | 0.552662 | − | 0.957238i | −0.445420 | − | 0.895322i | \(-0.646946\pi\) |
0.998081 | − | 0.0619160i | \(-0.0197211\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.11226 | − | 1.79687i | 0.136090 | − | 0.0785715i | −0.430409 | − | 0.902634i | \(-0.641631\pi\) |
0.566499 | + | 0.824062i | \(0.308297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.3803 | − | 23.3136i | 1.75899 | − | 1.01555i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.57058 | + | 7.91648i | −0.198721 | + | 0.344195i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.03768i | − | 0.261521i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.9602 | − | 11.5240i | −0.862955 | − | 0.498227i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.9698 | − | 31.5838i | −0.903235 | − | 1.36041i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.49278 | − | 7.78172i | −0.193160 | − | 0.334562i | 0.753136 | − | 0.657865i | \(-0.228540\pi\) |
−0.946296 | + | 0.323303i | \(0.895207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −51.0352 | −2.18611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.5987 | 0.624197 | 0.312098 | − | 0.950050i | \(-0.398968\pi\) | ||||
0.312098 | + | 0.950050i | \(0.398968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.54468 | + | 2.67546i | 0.0658055 | + | 0.113978i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.84152 | + | 12.7310i | 0.163358 | + | 0.541377i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.2691 | − | 21.5173i | −1.57914 | − | 0.911717i | −0.994979 | − | 0.100079i | \(-0.968090\pi\) |
−0.584161 | − | 0.811638i | \(-0.698576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.8552i | − | 0.586013i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.77840 | + | 10.0085i | −0.243530 | + | 0.421807i | −0.961717 | − | 0.274043i | \(-0.911639\pi\) |
0.718187 | + | 0.695850i | \(0.244972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.2317 | + | 12.8355i | −0.935296 | + | 0.539993i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.2224 | + | 23.2224i | −1.68621 | + | 0.973534i | −0.728834 | + | 0.684691i | \(0.759937\pi\) |
−0.957376 | + | 0.288843i | \(0.906729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.74762 | − | 13.4193i | 0.324228 | − | 0.561579i | −0.657128 | − | 0.753779i | \(-0.728229\pi\) |
0.981356 | + | 0.192200i | \(0.0615622\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 48.2858i | − | 2.01366i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.22582 | − | 3.59448i | −0.259184 | − | 0.149640i | 0.364778 | − | 0.931094i | \(-0.381145\pi\) |
−0.623962 | + | 0.781454i | \(0.714478\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.98845 | + | 0.466719i | 0.0824950 | + | 0.0193628i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.7154 | − | 28.9519i | −0.692280 | − | 1.19906i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.7271 | −1.59844 | −0.799220 | − | 0.601039i | \(-0.794754\pi\) | ||||
−0.799220 | + | 0.601039i | \(0.794754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.38130 | −0.221733 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.72502 | − | 4.71988i | −0.111903 | − | 0.193822i | 0.804634 | − | 0.593771i | \(-0.202361\pi\) |
−0.916538 | + | 0.399948i | \(0.869028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 71.3993 | + | 16.7585i | 2.92709 | + | 0.687030i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5032 | + | 8.95077i | 0.633443 | + | 0.365719i | 0.782084 | − | 0.623173i | \(-0.214157\pi\) |
−0.148641 | + | 0.988891i | \(0.547490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5691i | 0.594288i | 0.954833 | + | 0.297144i | \(0.0960341\pi\) | ||||
−0.954833 | + | 0.297144i | \(0.903966\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 38.8563 | − | 67.3010i | 1.57973 | − | 2.73618i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.0544 | − | 23.7028i | 1.66635 | − | 0.962066i | 0.696766 | − | 0.717298i | \(-0.254622\pi\) |
0.969582 | − | 0.244768i | \(-0.0787118\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.3180 | + | 8.84387i | −0.619701 | + | 0.357785i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.520565 | − | 0.901645i | 0.0210254 | − | 0.0364171i | −0.855321 | − | 0.518098i | \(-0.826640\pi\) |
0.876347 | + | 0.481681i | \(0.159974\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.13220i | 0.287131i | 0.989641 | + | 0.143566i | \(0.0458568\pi\) | ||||
−0.989641 | + | 0.143566i | \(0.954143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.4034 | + | 7.73848i | 0.538730 | + | 0.311036i | 0.744564 | − | 0.667551i | \(-0.232657\pi\) |
−0.205834 | + | 0.978587i | \(0.565991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7766 | − | 35.7142i | −0.431754 | − | 1.43086i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −39.1905 | − | 67.8799i | −1.56762 | − | 2.71519i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.9562 | −1.51341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1168 | 0.522170 | 0.261085 | − | 0.965316i | \(-0.415920\pi\) | ||||
0.261085 | + | 0.965316i | \(0.415920\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.9756 | − | 60.5795i | −1.38796 | − | 2.40403i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.3350 | − | 26.8419i | 0.528352 | − | 1.06351i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1902 | + | 15.6983i | 1.07395 | + | 0.620045i | 0.929258 | − | 0.369432i | \(-0.120448\pi\) |
0.144691 | + | 0.989477i | \(0.453781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.4443i | 1.59497i | 0.603340 | + | 0.797484i | \(0.293836\pi\) | ||||
−0.603340 | + | 0.797484i | \(0.706164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.1498 | + | 24.5081i | −0.556284 | + | 0.963513i | 0.441518 | + | 0.897252i | \(0.354440\pi\) |
−0.997802 | + | 0.0662602i | \(0.978893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.72616 | + | 3.30600i | −0.224771 | + | 0.129772i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.6570 | − | 14.2357i | 0.964902 | − | 0.557087i | 0.0672240 | − | 0.997738i | \(-0.478586\pi\) |
0.897678 | + | 0.440651i | \(0.145252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.3981 | + | 47.4549i | −1.07053 | + | 1.85422i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.79499i | − | 0.0699229i | −0.999389 | − | 0.0349615i | \(-0.988869\pi\) | ||
0.999389 | − | 0.0349615i | \(-0.0111308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.4029 | + | 14.0890i | 0.949163 | + | 0.547999i | 0.892821 | − | 0.450412i | \(-0.148723\pi\) |
0.0563422 | + | 0.998412i | \(0.482056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.16924 | − | 5.79514i | −0.239233 | − | 0.224726i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.61978 | + | 13.1978i | 0.295039 | + | 0.511023i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.2620 | −0.743600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.2923 | −1.51461 | −0.757304 | − | 0.653062i | \(-0.773484\pi\) | ||||
−0.757304 | + | 0.653062i | \(0.773484\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.57377 | − | 7.92200i | −0.175784 | − | 0.304467i | 0.764648 | − | 0.644448i | \(-0.222913\pi\) |
−0.940432 | + | 0.339981i | \(0.889579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.09585 | − | 13.1899i | 0.118808 | − | 0.506180i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.8532 | − | 15.5037i | −1.02751 | − | 0.593233i | −0.111240 | − | 0.993794i | \(-0.535482\pi\) |
−0.916270 | + | 0.400561i | \(0.868815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.210375i | − | 0.00803801i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.2148 | − | 22.8886i | 0.503442 | − | 0.871988i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.48927 | + | 4.32393i | −0.284905 | + | 0.164490i | −0.635642 | − | 0.771984i | \(-0.719265\pi\) |
0.350737 | + | 0.936474i | \(0.385931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.82814 | + | 4.51958i | −0.296938 | + | 0.171437i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.61037 | − | 7.98539i | 0.174630 | − | 0.302468i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.2714i | 1.74765i | 0.486243 | + | 0.873824i | \(0.338367\pi\) | ||||
−0.486243 | + | 0.873824i | \(0.661633\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.79369 | + | 2.19029i | 0.143082 | + | 0.0826083i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.9476 | + | 24.4290i | −0.863033 | + | 0.918746i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.37490 | + | 2.38140i | 0.0516355 | + | 0.0894353i | 0.890688 | − | 0.454615i | \(-0.150223\pi\) |
−0.839052 | + | 0.544051i | \(0.816890\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.5456 | −0.994139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 98.3028 | 3.67632 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6349 | − | 27.0805i | −0.583084 | − | 1.00993i | −0.995111 | − | 0.0987597i | \(-0.968512\pi\) |
0.412027 | − | 0.911172i | \(-0.364821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.9498 | − | 13.5634i | 1.67402 | − | 0.505127i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.9828 | + | 26.5482i | 1.70776 | + | 0.985975i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.77834i | − | 0.177219i | −0.996066 | − | 0.0886093i | \(-0.971758\pi\) | ||
0.996066 | − | 0.0886093i | \(-0.0282423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.5798 | − | 18.3248i | 0.391309 | − | 0.677767i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.72950 | − | 2.73058i | 0.174688 | − | 0.100856i | −0.410106 | − | 0.912038i | \(-0.634508\pi\) |
0.584795 | + | 0.811181i | \(0.301175\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67.7653 | − | 39.1243i | 2.49617 | − | 1.44116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.9108 | + | 27.5584i | −0.585289 | + | 1.01375i | 0.409550 | + | 0.912288i | \(0.365686\pi\) |
−0.994839 | + | 0.101463i | \(0.967648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.255254i | 0.00936435i | 0.999989 | + | 0.00468217i | \(0.00149039\pi\) | ||||
−0.999989 | + | 0.00468217i | \(0.998510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.9827 | + | 18.4652i | 1.17175 | + | 0.676513i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.7715 | + | 4.15549i | −0.503200 | + | 0.151838i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.69027 | + | 8.12379i | 0.171150 | + | 0.296441i | 0.938822 | − | 0.344402i | \(-0.111918\pi\) |
−0.767672 | + | 0.640843i | \(0.778585\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54.9725 | −2.00065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3629 | −0.449338 | −0.224669 | − | 0.974435i | \(-0.572130\pi\) | ||||
−0.224669 | + | 0.974435i | \(0.572130\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.986597 | + | 1.70884i | 0.0357641 | + | 0.0619452i | 0.883353 | − | 0.468708i | \(-0.155280\pi\) |
−0.847589 | + | 0.530653i | \(0.821947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.8080 | + | 23.2158i | −0.789502 | + | 0.840468i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.52696 | − | 2.61364i | −0.163459 | − | 0.0943731i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.9083i | 1.40307i | 0.712636 | + | 0.701534i | \(0.247501\pi\) | ||||
−0.712636 | + | 0.701534i | \(0.752499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2184 | − | 31.5552i | 0.655269 | − | 1.13496i | −0.326557 | − | 0.945178i | \(-0.605888\pi\) |
0.981826 | − | 0.189782i | \(-0.0607782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −80.0968 | + | 46.2439i | −2.87716 | + | 1.66113i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.921605 | + | 0.532089i | −0.0330199 | + | 0.0190641i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.3739 | + | 17.9680i | −0.371206 | + | 0.642947i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8.74337i | − | 0.312064i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5338 | − | 14.7420i | −0.910183 | − | 0.525494i | −0.0296927 | − | 0.999559i | \(-0.509453\pi\) |
−0.880490 | + | 0.474065i | \(0.842786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.66106 | + | 15.5979i | −0.130172 | + | 0.554599i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.61402 | − | 13.1879i | −0.270382 | − | 0.468315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2311 | −0.610357 | −0.305179 | − | 0.952295i | \(-0.598716\pi\) | ||||
−0.305179 | + | 0.952295i | \(0.598716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.0127 | −0.955640 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.2505 | + | 45.4672i | 0.926360 | + | 1.60450i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.4324 | − | 28.5870i | −1.07260 | − | 1.00756i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.8129 | + | 18.3672i | 1.11848 | + | 0.645756i | 0.941013 | − | 0.338371i | \(-0.109876\pi\) |
0.177469 | + | 0.984126i | \(0.443209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.7198i | − | 0.376425i | −0.982128 | − | 0.188212i | \(-0.939731\pi\) | ||
0.982128 | − | 0.188212i | \(-0.0602693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.9965 | + | 46.7594i | −0.945647 | + | 1.63791i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.11489 | + | 1.22103i | −0.0739906 | + | 0.0427185i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4865 | − | 12.4052i | 0.749884 | − | 0.432946i | −0.0757677 | − | 0.997125i | \(-0.524141\pi\) |
0.825652 | + | 0.564179i | \(0.190807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3320 | + | 28.2879i | −0.569298 | + | 0.986054i | 0.427337 | + | 0.904092i | \(0.359452\pi\) |
−0.996636 | + | 0.0819613i | \(0.973882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0080i | 0.695747i | 0.937541 | + | 0.347874i | \(0.113096\pi\) | ||||
−0.937541 | + | 0.347874i | \(0.886904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.2288 | − | 18.6073i | −1.11935 | − | 0.646259i | −0.178117 | − | 0.984009i | \(-0.557001\pi\) |
−0.941236 | + | 0.337751i | \(0.890334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.1332 | − | 25.3183i | 1.32124 | − | 0.877226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4950 | − | 19.9099i | −0.397800 | − | 0.689010i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.4001 | 0.669767 | 0.334883 | − | 0.942260i | \(-0.391303\pi\) | ||||
0.334883 | + | 0.942260i | \(0.391303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2422 | 0.422143 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.3034 | + | 19.5780i | 0.388848 | + | 0.673504i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0113 | − | 46.4342i | −0.481434 | − | 1.59550i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7140 | + | 10.8045i | 0.641508 | + | 0.370375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.5850i | − | 0.499380i | −0.968326 | − | 0.249690i | \(-0.919671\pi\) | ||
0.968326 | − | 0.249690i | \(-0.0803287\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.6910 | + | 34.1058i | −0.672632 | + | 1.16503i | 0.304523 | + | 0.952505i | \(0.401503\pi\) |
−0.977155 | + | 0.212528i | \(0.931830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6526 | + | 10.7691i | −0.636420 | + | 0.367437i | −0.783234 | − | 0.621727i | \(-0.786431\pi\) |
0.146814 | + | 0.989164i | \(0.453098\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0611 | + | 16.2011i | −0.955211 | + | 0.551491i | −0.894696 | − | 0.446676i | \(-0.852608\pi\) |
−0.0605152 | + | 0.998167i | \(0.519274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5233 | − | 19.9589i | 0.391803 | − | 0.678622i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.2212i | 0.923415i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.5736 | + | 30.9307i | 1.81527 | + | 1.04805i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −87.0299 | − | 20.4272i | −2.94215 | − | 0.690565i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.55934 | − | 2.70086i | −0.0526553 | − | 0.0912016i | 0.838496 | − | 0.544907i | \(-0.183435\pi\) |
−0.891152 | + | 0.453706i | \(0.850102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.7998 | 1.17243 | 0.586217 | − | 0.810154i | \(-0.300616\pi\) | ||||
0.586217 | + | 0.810154i | \(0.300616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.1569 | −1.14947 | −0.574736 | − | 0.818339i | \(-0.694895\pi\) | ||||
−0.574736 | + | 0.818339i | \(0.694895\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1531 | − | 47.0306i | −0.911713 | − | 1.57913i | −0.811644 | − | 0.584152i | \(-0.801427\pi\) |
−0.100068 | − | 0.994981i | \(-0.531906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42.5030 | − | 9.97608i | −1.42550 | − | 0.334587i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.69990 | + | 1.55879i | 0.0903486 | + | 0.0521628i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.7722i | − | 0.460354i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.5951 | − | 25.2795i | 0.486774 | − | 0.843118i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9555 | − | 20.1816i | 1.16454 | − | 0.672345i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 62.4974 | − | 36.0829i | 2.07748 | − | 1.19944i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.9908 | − | 34.6251i | 0.663784 | − | 1.14971i | −0.315830 | − | 0.948816i | \(-0.602283\pi\) |
0.979614 | − | 0.200891i | \(-0.0643837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7332i | 0.620658i | 0.950629 | + | 0.310329i | \(0.100439\pi\) | ||||
−0.950629 | + | 0.310329i | \(0.899561\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.62087 | + | 2.09051i | 0.119833 | + | 0.0691859i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.87956 | + | 32.7414i | 0.326252 | + | 1.08122i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0939 | + | 43.4639i | 0.827771 | + | 1.43374i | 0.899783 | + | 0.436338i | \(0.143725\pi\) |
−0.0720116 | + | 0.997404i | \(0.522942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.4026 | −0.539899 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75.2885 | 2.47547 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9979 | + | 36.3695i | 0.688920 | + | 1.19324i | 0.972188 | + | 0.234203i | \(0.0752482\pi\) |
−0.283268 | + | 0.959041i | \(0.591419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.27239 | + | 0.330037i | −0.172796 | + | 0.0108165i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 130.015 | + | 75.0639i | 4.25193 | + | 2.45485i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.8226i | 0.680243i | 0.940381 | + | 0.340122i | \(0.110468\pi\) | ||||
−0.940381 | + | 0.340122i | \(0.889532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.7306 | + | 44.5667i | −0.838793 | + | 1.45283i | 0.0521115 | + | 0.998641i | \(0.483405\pi\) |
−0.890904 | + | 0.454191i | \(0.849928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.54621 | + | 2.62476i | −0.148045 | + | 0.0854738i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.3121 | + | 18.0781i | −1.01751 | + | 0.587458i | −0.913381 | − | 0.407106i | \(-0.866538\pi\) |
−0.104127 | + | 0.994564i | \(0.533205\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.7530 | + | 35.9453i | −0.673671 | + | 1.16683i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.5525i | − | 0.730548i | −0.930900 | − | 0.365274i | \(-0.880975\pi\) | ||
0.930900 | − | 0.365274i | \(-0.119025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81.3947 | + | 46.9933i | 2.63387 | + | 1.52067i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0956990 | − | 0.0898958i | −0.00309028 | − | 0.00290289i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.92301 | + | 17.1872i | 0.320097 | + | 0.554424i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.11591 | 0.196878 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.9250 | −1.25174 | −0.625872 | − | 0.779926i | \(-0.715257\pi\) | ||||
−0.625872 | + | 0.779926i | \(0.715257\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.69001 | + | 15.0515i | 0.278876 | + | 0.483027i | 0.971106 | − | 0.238650i | \(-0.0767049\pi\) |
−0.692230 | + | 0.721677i | \(0.743372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.28912 | + | 5.49227i | −0.0413272 | + | 0.176074i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.8075 | − | 28.1790i | −1.56149 | − | 0.901526i | −0.997107 | − | 0.0760123i | \(-0.975781\pi\) |
−0.564382 | − | 0.825514i | \(-0.690885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 76.3634i | − | 2.44058i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.03208 | − | 13.9120i | 0.256184 | − | 0.443723i | −0.709033 | − | 0.705176i | \(-0.750868\pi\) |
0.965216 | + | 0.261453i | \(0.0842015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.2062 | + | 23.7904i | −1.31294 | + | 0.758026i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.4326 | + | 6.02326i | −0.331737 | + | 0.191528i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.7654 | + | 29.0385i | −0.532570 | + | 0.922438i | 0.466707 | + | 0.884412i | \(0.345440\pi\) |
−0.999277 | + | 0.0380259i | \(0.987893\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11.6852i | − | 0.370447i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.65835 | + | 3.26685i | 0.179202 | + | 0.103462i | 0.586917 | − | 0.809647i | \(-0.300341\pi\) |
−0.407716 | + | 0.913109i | \(0.633675\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2268.2.t.c.1781.1 | ✓ | 32 | |
3.2 | odd | 2 | inner | 2268.2.t.c.1781.16 | yes | 32 | |
7.5 | odd | 6 | inner | 2268.2.t.c.2105.16 | yes | 32 | |
9.2 | odd | 6 | 2268.2.bm.j.1025.1 | 32 | |||
9.4 | even | 3 | 2268.2.w.j.269.1 | 32 | |||
9.5 | odd | 6 | 2268.2.w.j.269.16 | 32 | |||
9.7 | even | 3 | 2268.2.bm.j.1025.16 | 32 | |||
21.5 | even | 6 | inner | 2268.2.t.c.2105.1 | yes | 32 | |
63.5 | even | 6 | 2268.2.bm.j.593.16 | 32 | |||
63.40 | odd | 6 | 2268.2.bm.j.593.1 | 32 | |||
63.47 | even | 6 | 2268.2.w.j.1349.1 | 32 | |||
63.61 | odd | 6 | 2268.2.w.j.1349.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2268.2.t.c.1781.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
2268.2.t.c.1781.16 | yes | 32 | 3.2 | odd | 2 | inner | |
2268.2.t.c.2105.1 | yes | 32 | 21.5 | even | 6 | inner | |
2268.2.t.c.2105.16 | yes | 32 | 7.5 | odd | 6 | inner | |
2268.2.w.j.269.1 | 32 | 9.4 | even | 3 | |||
2268.2.w.j.269.16 | 32 | 9.5 | odd | 6 | |||
2268.2.w.j.1349.1 | 32 | 63.47 | even | 6 | |||
2268.2.w.j.1349.16 | 32 | 63.61 | odd | 6 | |||
2268.2.bm.j.593.1 | 32 | 63.40 | odd | 6 | |||
2268.2.bm.j.593.16 | 32 | 63.5 | even | 6 | |||
2268.2.bm.j.1025.1 | 32 | 9.2 | odd | 6 | |||
2268.2.bm.j.1025.16 | 32 | 9.7 | even | 3 |