Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(683,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.683");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 683.15 | ||
Character | \(\chi\) | \(=\) | 684.683 |
Dual form | 684.3.b.a.683.13 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58380 | + | 1.22130i | −0.791901 | + | 0.610649i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.01686 | − | 3.86859i | 0.254215 | − | 0.967148i | ||||
\(5\) | 8.58011i | 1.71602i | 0.513631 | + | 0.858011i | \(0.328300\pi\) | ||||
−0.513631 | + | 0.858011i | \(0.671700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.97492i | 0.282131i | 0.990000 | + | 0.141065i | \(0.0450528\pi\) | ||||
−0.990000 | + | 0.141065i | \(0.954947\pi\) | |||||||
\(8\) | 3.11420 | + | 7.36897i | 0.389275 | + | 0.921121i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.4789 | − | 13.5892i | −1.04789 | − | 1.35892i | ||||
\(11\) | −19.5235 | −1.77487 | −0.887433 | − | 0.460936i | \(-0.847514\pi\) | ||||
−0.887433 | + | 0.460936i | \(0.847514\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.4277i | − | 1.41751i | −0.705452 | − | 0.708757i | \(-0.749256\pi\) | ||
0.705452 | − | 0.708757i | \(-0.250744\pi\) | |||||||
\(14\) | −2.41196 | − | 3.12788i | −0.172283 | − | 0.223420i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.9320 | − | 7.86762i | −0.870750 | − | 0.491726i | ||||
\(17\) | − | 22.2232i | − | 1.30725i | −0.756820 | − | 0.653623i | \(-0.773248\pi\) | ||
0.756820 | − | 0.653623i | \(-0.226752\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.8565 | − | 2.33061i | 0.992448 | − | 0.122664i | ||||
\(20\) | 33.1929 | + | 8.72476i | 1.65965 | + | 0.436238i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 30.9214 | − | 23.8441i | 1.40552 | − | 1.08382i | ||||
\(23\) | −15.3015 | −0.665281 | −0.332641 | − | 0.943054i | \(-0.607940\pi\) | ||||
−0.332641 | + | 0.943054i | \(0.607940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −48.6183 | −1.94473 | ||||||||
\(26\) | 22.5057 | + | 29.1858i | 0.865604 | + | 1.12253i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.64014 | + | 2.00821i | 0.272862 | + | 0.0717218i | ||||
\(29\) | 38.6261 | 1.33193 | 0.665967 | − | 0.745981i | \(-0.268019\pi\) | ||||
0.665967 | + | 0.745981i | \(0.268019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −45.2889 | −1.46093 | −0.730465 | − | 0.682950i | \(-0.760697\pi\) | ||||
−0.730465 | + | 0.682950i | \(0.760697\pi\) | |||||||
\(32\) | 31.6742 | − | 4.55437i | 0.989820 | − | 0.142324i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 27.1412 | + | 35.1971i | 0.798269 | + | 1.03521i | ||||
\(35\) | −16.9450 | −0.484143 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.92063i | − | 0.268125i | −0.990973 | − | 0.134063i | \(-0.957198\pi\) | ||
0.990973 | − | 0.134063i | \(-0.0428023\pi\) | |||||||
\(38\) | −27.0186 | + | 26.7207i | −0.711016 | + | 0.703176i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −63.2266 | + | 26.7202i | −1.58066 | + | 0.668005i | ||||
\(41\) | 36.5718 | 0.891996 | 0.445998 | − | 0.895034i | \(-0.352849\pi\) | ||||
0.445998 | + | 0.895034i | \(0.352849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 25.5525i | 0.594244i | 0.954840 | + | 0.297122i | \(0.0960267\pi\) | ||||
−0.954840 | + | 0.297122i | \(0.903973\pi\) | |||||||
\(44\) | −19.8527 | + | 75.5286i | −0.451197 | + | 1.71656i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 24.2345 | − | 18.6877i | 0.526837 | − | 0.406254i | ||||
\(47\) | 6.62863 | 0.141035 | 0.0705174 | − | 0.997511i | \(-0.477535\pi\) | ||||
0.0705174 | + | 0.997511i | \(0.477535\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45.0997 | 0.920402 | ||||||||
\(50\) | 77.0017 | − | 59.3774i | 1.54003 | − | 1.18755i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −71.2892 | − | 18.7384i | −1.37095 | − | 0.360353i | ||||
\(53\) | −68.3031 | −1.28874 | −0.644369 | − | 0.764715i | \(-0.722880\pi\) | ||||
−0.644369 | + | 0.764715i | \(0.722880\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 167.514i | − | 3.04571i | ||||||
\(56\) | −14.5531 | + | 6.15029i | −0.259877 | + | 0.109827i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −61.1761 | + | 47.1740i | −1.05476 | + | 0.813345i | ||||
\(59\) | − | 83.5099i | − | 1.41542i | −0.706502 | − | 0.707711i | \(-0.749728\pi\) | ||
0.706502 | − | 0.707711i | \(-0.250272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.9786 | 0.245551 | 0.122776 | − | 0.992434i | \(-0.460820\pi\) | ||||
0.122776 | + | 0.992434i | \(0.460820\pi\) | |||||||
\(62\) | 71.7286 | − | 55.3112i | 1.15691 | − | 0.892117i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.6035 | + | 45.8969i | −0.696930 | + | 0.717140i | ||||
\(65\) | 158.112 | 2.43249 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 92.3068 | 1.37771 | 0.688857 | − | 0.724897i | \(-0.258113\pi\) | ||||
0.688857 | + | 0.724897i | \(0.258113\pi\) | |||||||
\(68\) | −85.9724 | − | 22.5978i | −1.26430 | − | 0.332321i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 26.8375 | − | 20.6949i | 0.383393 | − | 0.295642i | ||||
\(71\) | − | 43.3087i | − | 0.609981i | −0.952355 | − | 0.304991i | \(-0.901347\pi\) | ||
0.952355 | − | 0.304991i | \(-0.0986533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.8594 | 0.628210 | 0.314105 | − | 0.949388i | \(-0.398296\pi\) | ||||
0.314105 | + | 0.949388i | \(0.398296\pi\) | |||||||
\(74\) | 12.1161 | + | 15.7123i | 0.163730 | + | 0.212329i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.1582 | − | 75.3181i | 0.133661 | − | 0.991027i | ||||
\(77\) | − | 38.5573i | − | 0.500745i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −84.8589 | −1.07416 | −0.537082 | − | 0.843530i | \(-0.680473\pi\) | ||||
−0.537082 | + | 0.843530i | \(0.680473\pi\) | |||||||
\(80\) | 67.5051 | − | 119.538i | 0.843813 | − | 1.49423i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −57.9226 | + | 44.6652i | −0.706373 | + | 0.544697i | ||||
\(83\) | −11.0536 | −0.133176 | −0.0665882 | − | 0.997781i | \(-0.521211\pi\) | ||||
−0.0665882 | + | 0.997781i | \(0.521211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 190.677 | 2.24326 | ||||||||
\(86\) | −31.2072 | − | 40.4701i | −0.362874 | − | 0.470582i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −60.8002 | − | 143.868i | −0.690912 | − | 1.63487i | ||||
\(89\) | −58.4355 | −0.656579 | −0.328289 | − | 0.944577i | \(-0.606472\pi\) | ||||
−0.328289 | + | 0.944577i | \(0.606472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 36.3931 | 0.399925 | ||||||||
\(92\) | −15.5594 | + | 59.1951i | −0.169124 | + | 0.643425i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.4984 | + | 8.09554i | −0.111686 | + | 0.0861228i | ||||
\(95\) | 19.9969 | + | 161.791i | 0.210494 | + | 1.70306i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 30.6354i | − | 0.315829i | −0.987453 | − | 0.157914i | \(-0.949523\pi\) | ||
0.987453 | − | 0.157914i | \(-0.0504770\pi\) | |||||||
\(98\) | −71.4290 | + | 55.0802i | −0.728867 | + | 0.562043i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −49.4379 | + | 188.084i | −0.494379 | + | 1.88084i | ||||
\(101\) | 124.757i | 1.23522i | 0.786485 | + | 0.617609i | \(0.211899\pi\) | ||||
−0.786485 | + | 0.617609i | \(0.788101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −105.988 | −1.02901 | −0.514503 | − | 0.857488i | \(-0.672024\pi\) | ||||
−0.514503 | + | 0.857488i | \(0.672024\pi\) | |||||||
\(104\) | 135.793 | − | 57.3876i | 1.30570 | − | 0.551803i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 108.179 | − | 83.4185i | 1.02055 | − | 0.786967i | ||||
\(107\) | − | 41.3861i | − | 0.386786i | −0.981121 | − | 0.193393i | \(-0.938051\pi\) | ||
0.981121 | − | 0.193393i | \(-0.0619492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 202.416i | − | 1.85703i | −0.371294 | − | 0.928516i | \(-0.621086\pi\) | ||
0.371294 | − | 0.928516i | \(-0.378914\pi\) | |||||||
\(110\) | 204.585 | + | 265.309i | 1.85986 | + | 2.41190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15.5379 | − | 27.5145i | 0.138731 | − | 0.245665i | ||||
\(113\) | 27.0070 | 0.239000 | 0.119500 | − | 0.992834i | \(-0.461871\pi\) | ||||
0.119500 | + | 0.992834i | \(0.461871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 131.288i | − | 1.14164i | ||||||
\(116\) | 39.2773 | − | 149.429i | 0.338597 | − | 1.28818i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 101.991 | + | 132.263i | 0.864326 | + | 1.12087i | ||||
\(119\) | 43.8889 | 0.368815 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 260.168 | 2.15015 | ||||||||
\(122\) | −23.7232 | + | 18.2934i | −0.194452 | + | 0.149946i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −46.0524 | + | 175.204i | −0.371390 | + | 1.41294i | ||||
\(125\) | − | 202.647i | − | 1.62118i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 159.466 | 1.25564 | 0.627821 | − | 0.778358i | \(-0.283947\pi\) | ||||
0.627821 | + | 0.778358i | \(0.283947\pi\) | |||||||
\(128\) | 14.5892 | − | 127.166i | 0.113978 | − | 0.993483i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −250.417 | + | 193.101i | −1.92629 | + | 1.48540i | ||||
\(131\) | −190.126 | −1.45134 | −0.725672 | − | 0.688040i | \(-0.758471\pi\) | ||||
−0.725672 | + | 0.688040i | \(0.758471\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.60276 | + | 37.2400i | 0.0346072 | + | 0.280000i | ||||
\(134\) | −146.196 | + | 112.734i | −1.09101 | + | 0.841300i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 163.762 | − | 69.2075i | 1.20413 | − | 0.508879i | ||||
\(137\) | − | 57.9607i | − | 0.423071i | −0.977370 | − | 0.211535i | \(-0.932154\pi\) | ||
0.977370 | − | 0.211535i | \(-0.0678464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 141.678i | − | 1.01927i | −0.860392 | − | 0.509633i | \(-0.829781\pi\) | ||
0.860392 | − | 0.509633i | \(-0.170219\pi\) | |||||||
\(140\) | −17.2307 | + | 65.5533i | −0.123076 | + | 0.468238i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 52.8928 | + | 68.5924i | 0.372485 | + | 0.483045i | ||||
\(143\) | 359.774i | 2.51590i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 331.416i | 2.28563i | ||||||||
\(146\) | −72.6322 | + | 56.0080i | −0.497480 | + | 0.383616i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.3789 | − | 10.0879i | −0.259317 | − | 0.0681614i | ||||
\(149\) | − | 212.670i | − | 1.42732i | −0.700494 | − | 0.713658i | \(-0.747037\pi\) | ||
0.700494 | − | 0.713658i | \(-0.252963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30.4374 | 0.201572 | 0.100786 | − | 0.994908i | \(-0.467864\pi\) | ||||
0.100786 | + | 0.994908i | \(0.467864\pi\) | |||||||
\(152\) | 75.8972 | + | 131.695i | 0.499324 | + | 0.866415i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 47.0900 | + | 61.0672i | 0.305779 | + | 0.396540i | ||||
\(155\) | − | 388.583i | − | 2.50699i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −137.773 | −0.877536 | −0.438768 | − | 0.898600i | \(-0.644585\pi\) | ||||
−0.438768 | + | 0.898600i | \(0.644585\pi\) | |||||||
\(158\) | 134.400 | − | 103.638i | 0.850631 | − | 0.655937i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 39.0770 | + | 271.768i | 0.244231 | + | 1.69855i | ||||
\(161\) | − | 30.2191i | − | 0.187696i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 233.944i | − | 1.43524i | −0.696436 | − | 0.717619i | \(-0.745232\pi\) | ||
0.696436 | − | 0.717619i | \(-0.254768\pi\) | |||||||
\(164\) | 37.1884 | − | 141.482i | 0.226759 | − | 0.862692i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.5068 | − | 13.4998i | 0.105462 | − | 0.0813240i | ||||
\(167\) | − | 78.2491i | − | 0.468558i | −0.972169 | − | 0.234279i | \(-0.924727\pi\) | ||
0.972169 | − | 0.234279i | \(-0.0752729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −170.580 | −1.00935 | ||||||||
\(170\) | −301.995 | + | 232.874i | −1.77644 | + | 1.36985i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 98.8521 | + | 25.9833i | 0.574721 | + | 0.151065i | ||||
\(173\) | 8.60024 | 0.0497124 | 0.0248562 | − | 0.999691i | \(-0.492087\pi\) | ||||
0.0248562 | + | 0.999691i | \(0.492087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 96.0170i | − | 0.548669i | ||||||
\(176\) | 272.002 | + | 153.604i | 1.54546 | + | 0.872749i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 92.5503 | − | 71.3672i | 0.519945 | − | 0.400939i | ||||
\(179\) | − | 124.700i | − | 0.696649i | −0.937374 | − | 0.348325i | \(-0.886751\pi\) | ||
0.937374 | − | 0.348325i | \(-0.113249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 29.6930i | 0.164050i | 0.996630 | + | 0.0820249i | \(0.0261387\pi\) | ||||
−0.996630 | + | 0.0820249i | \(0.973861\pi\) | |||||||
\(182\) | −57.6395 | + | 44.4469i | −0.316701 | + | 0.244214i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −47.6519 | − | 112.756i | −0.258978 | − | 0.612805i | ||||
\(185\) | 85.1201 | 0.460109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 433.875i | 2.32019i | ||||||||
\(188\) | 6.74038 | − | 25.6435i | 0.0358531 | − | 0.136401i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −229.266 | − | 231.823i | −1.20666 | − | 1.22012i | ||||
\(191\) | −341.405 | −1.78746 | −0.893731 | − | 0.448604i | \(-0.851922\pi\) | ||||
−0.893731 | + | 0.448604i | \(0.851922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70.7259i | 0.366455i | 0.983070 | + | 0.183228i | \(0.0586546\pi\) | ||||
−0.983070 | + | 0.183228i | \(0.941345\pi\) | |||||||
\(194\) | 37.4150 | + | 48.5204i | 0.192861 | + | 0.250105i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 45.8600 | − | 174.472i | 0.233980 | − | 0.890165i | ||||
\(197\) | − | 62.6710i | − | 0.318127i | −0.987268 | − | 0.159063i | \(-0.949153\pi\) | ||
0.987268 | − | 0.159063i | \(-0.0508474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 163.761i | 0.822917i | 0.911428 | + | 0.411459i | \(0.134981\pi\) | ||||
−0.911428 | + | 0.411459i | \(0.865019\pi\) | |||||||
\(200\) | −151.407 | − | 358.267i | −0.757036 | − | 1.79133i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −152.366 | − | 197.591i | −0.754286 | − | 0.978171i | ||||
\(203\) | 76.2833i | 0.375780i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 313.790i | 1.53069i | ||||||||
\(206\) | 167.864 | − | 129.443i | 0.814872 | − | 0.628362i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −144.982 | + | 256.734i | −0.697029 | + | 1.23430i | ||||
\(209\) | −368.146 | + | 45.5018i | −1.76146 | + | 0.217712i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 165.887 | 0.786195 | 0.393097 | − | 0.919497i | \(-0.371404\pi\) | ||||
0.393097 | + | 0.919497i | \(0.371404\pi\) | |||||||
\(212\) | −69.4546 | + | 264.237i | −0.327616 | + | 1.24640i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 50.5448 | + | 65.5474i | 0.236191 | + | 0.306296i | ||||
\(215\) | −219.243 | −1.01974 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 89.4417i | − | 0.412174i | ||||||
\(218\) | 247.211 | + | 320.588i | 1.13399 | + | 1.47058i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −648.043 | − | 170.338i | −2.94565 | − | 0.774264i | ||||
\(221\) | −409.522 | −1.85304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −330.103 | −1.48028 | −0.740140 | − | 0.672453i | \(-0.765241\pi\) | ||||
−0.740140 | + | 0.672453i | \(0.765241\pi\) | |||||||
\(224\) | 8.99450 | + | 62.5540i | 0.0401540 | + | 0.279259i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −42.7738 | + | 32.9837i | −0.189265 | + | 0.145945i | ||||
\(227\) | 173.113i | 0.762610i | 0.924449 | + | 0.381305i | \(0.124525\pi\) | ||||
−0.924449 | + | 0.381305i | \(0.875475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −128.530 | −0.561264 | −0.280632 | − | 0.959815i | \(-0.590544\pi\) | ||||
−0.280632 | + | 0.959815i | \(0.590544\pi\) | |||||||
\(230\) | 160.342 | + | 207.935i | 0.697140 | + | 0.904064i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 120.290 | + | 284.635i | 0.518489 | + | 1.22687i | ||||
\(233\) | − | 43.7130i | − | 0.187609i | −0.995591 | − | 0.0938046i | \(-0.970097\pi\) | ||
0.995591 | − | 0.0938046i | \(-0.0299029\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 56.8744i | 0.242019i | ||||||||
\(236\) | −323.066 | − | 84.9178i | −1.36892 | − | 0.359821i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −69.5114 | + | 53.6015i | −0.292065 | + | 0.225216i | ||||
\(239\) | −296.201 | −1.23934 | −0.619668 | − | 0.784864i | \(-0.712733\pi\) | ||||
−0.619668 | + | 0.784864i | \(0.712733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 40.6438i | − | 0.168646i | −0.996438 | − | 0.0843232i | \(-0.973127\pi\) | ||
0.996438 | − | 0.0843232i | \(-0.0268728\pi\) | |||||||
\(242\) | −412.055 | + | 317.743i | −1.70271 | + | 1.31299i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.2312 | − | 57.9462i | 0.0624228 | − | 0.237484i | ||||
\(245\) | 386.960i | 1.57943i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.9478 | − | 347.482i | −0.173878 | − | 1.40681i | ||||
\(248\) | −141.039 | − | 333.732i | −0.568704 | − | 1.34569i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 247.493 | + | 320.953i | 0.989972 | + | 1.28381i | ||||
\(251\) | −230.349 | −0.917726 | −0.458863 | − | 0.888507i | \(-0.651743\pi\) | ||||
−0.458863 | + | 0.888507i | \(0.651743\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 298.739 | 1.18079 | ||||||||
\(254\) | −252.563 | + | 194.756i | −0.994344 | + | 0.766757i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 132.201 | + | 219.223i | 0.516410 | + | 0.856341i | ||||
\(257\) | 209.168 | 0.813885 | 0.406942 | − | 0.913454i | \(-0.366595\pi\) | ||||
0.406942 | + | 0.913454i | \(0.366595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.5924 | 0.0756464 | ||||||||
\(260\) | 160.777 | − | 611.669i | 0.618374 | − | 2.35257i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 301.122 | − | 232.201i | 1.14932 | − | 0.886263i | ||||
\(263\) | 321.884 | 1.22389 | 0.611947 | − | 0.790899i | \(-0.290387\pi\) | ||||
0.611947 | + | 0.790899i | \(0.290387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 586.048i | − | 2.21150i | ||||||
\(266\) | −52.7711 | − | 53.3595i | −0.198388 | − | 0.200600i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 93.8630 | − | 357.097i | 0.350235 | − | 1.33245i | ||||
\(269\) | −267.268 | −0.993563 | −0.496782 | − | 0.867876i | \(-0.665485\pi\) | ||||
−0.496782 | + | 0.867876i | \(0.665485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 153.314i | 0.565734i | 0.959159 | + | 0.282867i | \(0.0912855\pi\) | ||||
−0.959159 | + | 0.282867i | \(0.908715\pi\) | |||||||
\(272\) | −174.844 | + | 309.613i | −0.642808 | + | 1.13828i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 70.7873 | + | 91.7983i | 0.258348 | + | 0.335030i | ||||
\(275\) | 949.200 | 3.45164 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −144.036 | −0.519985 | −0.259993 | − | 0.965611i | \(-0.583720\pi\) | ||||
−0.259993 | + | 0.965611i | \(0.583720\pi\) | |||||||
\(278\) | 173.031 | + | 224.390i | 0.622414 | + | 0.807158i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −52.7702 | − | 124.867i | −0.188465 | − | 0.445954i | ||||
\(281\) | −472.868 | −1.68281 | −0.841403 | − | 0.540409i | \(-0.818270\pi\) | ||||
−0.841403 | + | 0.540409i | \(0.818270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 378.854i | − | 1.33871i | −0.742945 | − | 0.669353i | \(-0.766571\pi\) | ||
0.742945 | − | 0.669353i | \(-0.233429\pi\) | |||||||
\(284\) | −167.544 | − | 44.0388i | −0.589942 | − | 0.155066i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −439.391 | − | 569.810i | −1.53633 | − | 1.99234i | ||||
\(287\) | 72.2263i | 0.251660i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −204.870 | −0.708893 | ||||||||
\(290\) | −404.758 | − | 524.898i | −1.39572 | − | 1.80999i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 46.6325 | − | 177.411i | 0.159700 | − | 0.607572i | ||||
\(293\) | 215.739 | 0.736310 | 0.368155 | − | 0.929764i | \(-0.379990\pi\) | ||||
0.368155 | + | 0.929764i | \(0.379990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 716.524 | 2.42889 | ||||||||
\(296\) | 73.1049 | − | 30.8949i | 0.246976 | − | 0.104375i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 259.734 | + | 336.827i | 0.871590 | + | 1.13029i | ||||
\(299\) | 281.971i | 0.943046i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −50.4640 | −0.167654 | ||||||||
\(302\) | −48.2069 | + | 37.1732i | −0.159625 | + | 0.123090i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −281.045 | − | 115.886i | −0.924491 | − | 0.381204i | ||||
\(305\) | 128.518i | 0.421372i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 146.016 | 0.475624 | 0.237812 | − | 0.971311i | \(-0.423570\pi\) | ||||
0.237812 | + | 0.971311i | \(0.423570\pi\) | |||||||
\(308\) | −149.163 | − | 39.2074i | −0.484294 | − | 0.127297i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 474.576 | + | 615.439i | 1.53089 | + | 1.98529i | ||||
\(311\) | 174.557 | 0.561277 | 0.280638 | − | 0.959814i | \(-0.409454\pi\) | ||||
0.280638 | + | 0.959814i | \(0.409454\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −221.912 | −0.708983 | −0.354491 | − | 0.935059i | \(-0.615346\pi\) | ||||
−0.354491 | + | 0.935059i | \(0.615346\pi\) | |||||||
\(314\) | 218.205 | − | 168.262i | 0.694922 | − | 0.535867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −86.2895 | + | 328.284i | −0.273068 | + | 1.03887i | ||||
\(317\) | 228.532 | 0.720922 | 0.360461 | − | 0.932774i | \(-0.382619\pi\) | ||||
0.360461 | + | 0.932774i | \(0.382619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −754.118 | −2.36401 | ||||||||
\(320\) | −393.801 | − | 382.703i | −1.23063 | − | 1.19595i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 36.9066 | + | 47.8611i | 0.114617 | + | 0.148637i | ||||
\(323\) | −51.7936 | − | 419.052i | −0.160352 | − | 1.29737i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 895.923i | 2.75668i | ||||||||
\(326\) | 285.715 | + | 370.521i | 0.876427 | + | 1.13657i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 113.892 | + | 269.497i | 0.347232 | + | 0.821637i | ||||
\(329\) | 13.0910i | 0.0397903i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −70.8876 | −0.214162 | −0.107081 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107081 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(332\) | −11.2400 | + | 42.7620i | −0.0338554 | + | 0.128801i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 95.5656 | + | 123.931i | 0.286124 | + | 0.371051i | ||||
\(335\) | 792.003i | 2.36419i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 343.633i | 1.01968i | 0.860269 | + | 0.509841i | \(0.170296\pi\) | ||||
−0.860269 | + | 0.509841i | \(0.829704\pi\) | |||||||
\(338\) | 270.165 | − | 208.329i | 0.799303 | − | 0.616357i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 193.892 | − | 737.653i | 0.570271 | − | 2.16957i | ||||
\(341\) | 884.198 | 2.59296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 185.839i | 0.541805i | ||||||||
\(344\) | −188.295 | + | 79.5756i | −0.547371 | + | 0.231324i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.6211 | + | 10.5035i | −0.0393673 | + | 0.0303568i | ||||
\(347\) | 258.524 | 0.745025 | 0.372512 | − | 0.928027i | \(-0.378496\pi\) | ||||
0.372512 | + | 0.928027i | \(0.378496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −193.375 | −0.554083 | −0.277041 | − | 0.960858i | \(-0.589354\pi\) | ||||
−0.277041 | + | 0.960858i | \(0.589354\pi\) | |||||||
\(350\) | 117.265 | + | 152.072i | 0.335044 | + | 0.434491i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −618.393 | + | 88.9174i | −1.75680 | + | 0.252606i | ||||
\(353\) | 206.728i | 0.585632i | 0.956169 | + | 0.292816i | \(0.0945923\pi\) | ||||
−0.956169 | + | 0.292816i | \(0.905408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 371.593 | 1.04674 | ||||||||
\(356\) | −59.4207 | + | 226.063i | −0.166912 | + | 0.635009i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 152.296 | + | 197.501i | 0.425409 | + | 0.551678i | ||||
\(359\) | 293.931 | 0.818749 | 0.409374 | − | 0.912367i | \(-0.365747\pi\) | ||||
0.409374 | + | 0.912367i | \(0.365747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 350.136 | − | 87.8945i | 0.969907 | − | 0.243475i | ||||
\(362\) | −36.2640 | − | 47.0279i | −0.100177 | − | 0.129911i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 37.0067 | − | 140.790i | 0.101667 | − | 0.386786i | ||||
\(365\) | 393.478i | 1.07802i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 312.496i | 0.851486i | 0.904844 | + | 0.425743i | \(0.139987\pi\) | ||||
−0.904844 | + | 0.425743i | \(0.860013\pi\) | |||||||
\(368\) | 213.180 | + | 120.386i | 0.579294 | + | 0.327136i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −134.813 | + | 103.957i | −0.364361 | + | 0.280965i | ||||
\(371\) | − | 134.893i | − | 0.363593i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 499.888i | − | 1.34018i | −0.742278 | − | 0.670092i | \(-0.766255\pi\) | ||
0.742278 | − | 0.670092i | \(-0.233745\pi\) | |||||||
\(374\) | −529.891 | − | 687.172i | −1.41682 | − | 1.83736i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.6429 | + | 48.8462i | 0.0549013 | + | 0.129910i | ||||
\(377\) | − | 711.790i | − | 1.88804i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −83.9885 | −0.221605 | −0.110803 | − | 0.993842i | \(-0.535342\pi\) | ||||
−0.110803 | + | 0.993842i | \(0.535342\pi\) | |||||||
\(380\) | 646.237 | + | 87.1587i | 1.70062 | + | 0.229365i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 540.718 | − | 416.958i | 1.41549 | − | 1.09151i | ||||
\(383\) | − | 710.012i | − | 1.85382i | −0.375287 | − | 0.926909i | \(-0.622456\pi\) | ||
0.375287 | − | 0.926909i | \(-0.377544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 330.826 | 0.859289 | ||||||||
\(386\) | −86.3775 | − | 112.016i | −0.223776 | − | 0.290196i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −118.516 | − | 31.1519i | −0.305453 | − | 0.0802884i | ||||
\(389\) | 259.248i | 0.666447i | 0.942848 | + | 0.333224i | \(0.108136\pi\) | ||||
−0.942848 | + | 0.333224i | \(0.891864\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 340.048i | 0.869687i | ||||||||
\(392\) | 140.450 | + | 332.338i | 0.358290 | + | 0.847802i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 76.5400 | + | 99.2585i | 0.194264 | + | 0.251925i | ||||
\(395\) | − | 728.099i | − | 1.84329i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −62.6323 | −0.157764 | −0.0788820 | − | 0.996884i | \(-0.525135\pi\) | ||||
−0.0788820 | + | 0.996884i | \(0.525135\pi\) | |||||||
\(398\) | −200.001 | − | 259.364i | −0.502514 | − | 0.651669i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 677.350 | + | 382.510i | 1.69337 | + | 0.956276i | ||||
\(401\) | −387.772 | −0.967012 | −0.483506 | − | 0.875341i | \(-0.660637\pi\) | ||||
−0.483506 | + | 0.875341i | \(0.660637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 834.569i | 2.07089i | ||||||||
\(404\) | 482.634 | + | 126.860i | 1.19464 | + | 0.314011i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −93.1647 | − | 120.818i | −0.229470 | − | 0.297581i | ||||
\(407\) | 193.686i | 0.475886i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 579.965i | − | 1.41801i | −0.705205 | − | 0.709003i | \(-0.749145\pi\) | ||
0.705205 | − | 0.709003i | \(-0.250855\pi\) | |||||||
\(410\) | −383.232 | − | 496.982i | −0.934712 | − | 1.21215i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −107.775 | + | 410.023i | −0.261589 | + | 0.995202i | ||||
\(413\) | 164.925 | 0.399334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 94.8414i | − | 0.228534i | ||||||
\(416\) | −83.9265 | − | 583.683i | −0.201746 | − | 1.40308i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 527.499 | − | 521.682i | 1.26196 | − | 1.24804i | ||||
\(419\) | 215.425 | 0.514141 | 0.257071 | − | 0.966393i | \(-0.417243\pi\) | ||||
0.257071 | + | 0.966393i | \(0.417243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 162.626i | 0.386285i | 0.981171 | + | 0.193142i | \(0.0618679\pi\) | ||||
−0.981171 | + | 0.193142i | \(0.938132\pi\) | |||||||
\(422\) | −262.732 | + | 202.598i | −0.622589 | + | 0.480089i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −212.710 | − | 503.324i | −0.501674 | − | 1.18708i | ||||
\(425\) | 1080.45i | 2.54224i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.5815i | 0.0692776i | ||||||||
\(428\) | −160.106 | − | 42.0838i | −0.374079 | − | 0.0983267i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 347.238 | − | 267.761i | 0.807529 | − | 0.622701i | ||||
\(431\) | 447.567i | 1.03844i | 0.854641 | + | 0.519219i | \(0.173777\pi\) | ||||
−0.854641 | + | 0.519219i | \(0.826223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 213.226i | − | 0.492440i | −0.969214 | − | 0.246220i | \(-0.920811\pi\) | ||
0.969214 | − | 0.246220i | \(-0.0791885\pi\) | |||||||
\(434\) | 109.235 | + | 141.658i | 0.251694 | + | 0.326401i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −783.066 | − | 205.829i | −1.79602 | − | 0.472085i | ||||
\(437\) | −288.532 | + | 35.6618i | −0.660257 | + | 0.0816059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 82.9617 | 0.188979 | 0.0944894 | − | 0.995526i | \(-0.469878\pi\) | ||||
0.0944894 | + | 0.995526i | \(0.469878\pi\) | |||||||
\(440\) | 1234.41 | − | 521.673i | 2.80547 | − | 1.18562i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 648.602 | − | 500.149i | 1.46743 | − | 1.13156i | ||||
\(443\) | −93.2293 | −0.210450 | −0.105225 | − | 0.994448i | \(-0.533556\pi\) | ||||
−0.105225 | + | 0.994448i | \(0.533556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 501.383i | − | 1.12670i | ||||||
\(446\) | 522.817 | − | 403.154i | 1.17224 | − | 0.903932i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −90.6426 | − | 88.0882i | −0.202327 | − | 0.196625i | ||||
\(449\) | 393.075 | 0.875445 | 0.437723 | − | 0.899110i | \(-0.355785\pi\) | ||||
0.437723 | + | 0.899110i | \(0.355785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −714.012 | −1.58317 | ||||||||
\(452\) | 27.4624 | − | 104.479i | 0.0607574 | − | 0.231149i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −211.422 | − | 274.176i | −0.465687 | − | 0.603912i | ||||
\(455\) | 312.257i | 0.686280i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −168.784 | −0.369330 | −0.184665 | − | 0.982802i | \(-0.559120\pi\) | ||||
−0.184665 | + | 0.982802i | \(0.559120\pi\) | |||||||
\(458\) | 203.565 | − | 156.973i | 0.444466 | − | 0.342736i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −507.901 | − | 133.502i | −1.10413 | − | 0.290221i | ||||
\(461\) | − | 770.815i | − | 1.67205i | −0.548692 | − | 0.836024i | \(-0.684874\pi\) | ||
0.548692 | − | 0.836024i | \(-0.315126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 731.387i | 1.57967i | 0.613319 | + | 0.789835i | \(0.289834\pi\) | ||||
−0.613319 | + | 0.789835i | \(0.710166\pi\) | |||||||
\(464\) | −538.139 | − | 303.896i | −1.15978 | − | 0.654947i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 53.3866 | + | 69.2327i | 0.114563 | + | 0.148568i | ||||
\(467\) | 185.326 | 0.396843 | 0.198421 | − | 0.980117i | \(-0.436419\pi\) | ||||
0.198421 | + | 0.980117i | \(0.436419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 182.298i | 0.388696i | ||||||||
\(470\) | −69.4606 | − | 90.0778i | −0.147789 | − | 0.191655i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 615.382 | − | 260.067i | 1.30378 | − | 0.550989i | ||||
\(473\) | − | 498.875i | − | 1.05470i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −916.771 | + | 113.310i | −1.93005 | + | 0.238548i | ||||
\(476\) | 44.6289 | − | 169.788i | 0.0937581 | − | 0.356698i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 469.125 | − | 361.751i | 0.981432 | − | 0.756800i | ||||
\(479\) | 287.726 | 0.600680 | 0.300340 | − | 0.953832i | \(-0.402900\pi\) | ||||
0.300340 | + | 0.953832i | \(0.402900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −182.814 | −0.380071 | ||||||||
\(482\) | 49.6382 | + | 64.3717i | 0.102984 | + | 0.133551i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 264.554 | − | 1006.48i | 0.546600 | − | 2.07951i | ||||
\(485\) | 262.855 | 0.541969 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 221.341 | 0.454500 | 0.227250 | − | 0.973836i | \(-0.427027\pi\) | ||||
0.227250 | + | 0.973836i | \(0.427027\pi\) | |||||||
\(488\) | 46.6465 | + | 110.377i | 0.0955871 | + | 0.226183i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −472.594 | − | 612.869i | −0.964478 | − | 1.25075i | ||||
\(491\) | −574.726 | −1.17052 | −0.585260 | − | 0.810845i | \(-0.699008\pi\) | ||||
−0.585260 | + | 0.810845i | \(0.699008\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 858.395i | − | 1.74117i | ||||||
\(494\) | 492.400 | + | 497.891i | 0.996762 | + | 1.00788i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 630.964 | + | 356.316i | 1.27211 | + | 0.718378i | ||||
\(497\) | 85.5310 | 0.172095 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4831i | 0.0430522i | 0.999768 | + | 0.0215261i | \(0.00685250\pi\) | ||||
−0.999768 | + | 0.0215261i | \(0.993147\pi\) | |||||||
\(500\) | −783.960 | − | 206.064i | −1.56792 | − | 0.412128i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 364.828 | − | 281.325i | 0.726748 | − | 0.560409i | ||||
\(503\) | −423.978 | −0.842898 | −0.421449 | − | 0.906852i | \(-0.638478\pi\) | ||||
−0.421449 | + | 0.906852i | \(0.638478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1070.43 | −2.11966 | ||||||||
\(506\) | −473.143 | + | 364.849i | −0.935065 | + | 0.721046i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 162.155 | − | 616.911i | 0.319203 | − | 1.21439i | ||||
\(509\) | −277.215 | −0.544627 | −0.272313 | − | 0.962209i | \(-0.587789\pi\) | ||||
−0.272313 | + | 0.962209i | \(0.587789\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 90.5684i | 0.177238i | ||||||||
\(512\) | −477.118 | − | 185.750i | −0.931870 | − | 0.362792i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −331.281 | + | 255.457i | −0.644516 | + | 0.496998i | ||||
\(515\) | − | 909.386i | − | 1.76580i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −129.414 | −0.250318 | ||||||||
\(518\) | −31.0305 | + | 23.9282i | −0.0599045 | + | 0.0461934i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 492.391 | + | 1165.12i | 0.946907 | + | 2.24062i | ||||
\(521\) | −120.819 | −0.231899 | −0.115949 | − | 0.993255i | \(-0.536991\pi\) | ||||
−0.115949 | + | 0.993255i | \(0.536991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −441.034 | −0.843277 | −0.421639 | − | 0.906764i | \(-0.638545\pi\) | ||||
−0.421639 | + | 0.906764i | \(0.638545\pi\) | |||||||
\(524\) | −193.331 | + | 735.520i | −0.368953 | + | 1.40366i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −509.801 | + | 393.117i | −0.969203 | + | 0.747370i | ||||
\(527\) | 1006.46i | 1.90980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −294.865 | −0.557401 | ||||||||
\(530\) | 715.740 | + | 928.184i | 1.35045 | + | 1.75129i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 148.747 | + | 20.0617i | 0.279599 | + | 0.0377099i | ||||
\(533\) | − | 673.935i | − | 1.26442i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 355.097 | 0.663733 | ||||||||
\(536\) | 287.462 | + | 680.206i | 0.536310 | + | 1.26904i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 423.300 | − | 326.415i | 0.786804 | − | 0.606719i | ||||
\(539\) | −880.505 | −1.63359 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 208.239 | 0.384915 | 0.192458 | − | 0.981305i | \(-0.438354\pi\) | ||||
0.192458 | + | 0.981305i | \(0.438354\pi\) | |||||||
\(542\) | −187.242 | − | 242.819i | −0.345465 | − | 0.448005i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −101.213 | − | 703.903i | −0.186053 | − | 1.29394i | ||||
\(545\) | 1736.75 | 3.18671 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −127.787 | −0.233615 | −0.116808 | − | 0.993155i | \(-0.537266\pi\) | ||||
−0.116808 | + | 0.993155i | \(0.537266\pi\) | |||||||
\(548\) | −224.226 | − | 58.9378i | −0.409172 | − | 0.107551i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1503.35 | + | 1159.26i | −2.73336 | + | 2.10774i | ||||
\(551\) | 728.354 | − | 90.0225i | 1.32188 | − | 0.163380i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 167.589i | − | 0.303055i | ||||||
\(554\) | 228.124 | − | 175.911i | 0.411777 | − | 0.317529i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −548.094 | − | 144.066i | −0.985781 | − | 0.259112i | ||||
\(557\) | 473.636i | 0.850334i | 0.905115 | + | 0.425167i | \(0.139785\pi\) | ||||
−0.905115 | + | 0.425167i | \(0.860215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 470.873 | 0.842349 | ||||||||
\(560\) | 236.078 | + | 133.317i | 0.421567 | + | 0.238066i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 748.930 | − | 577.513i | 1.33262 | − | 1.02760i | ||||
\(563\) | − | 582.932i | − | 1.03540i | −0.855561 | − | 0.517701i | \(-0.826788\pi\) | ||
0.855561 | − | 0.517701i | \(-0.173212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 231.723i | 0.410130i | ||||||||
\(566\) | 462.694 | + | 600.029i | 0.817480 | + | 1.06012i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 319.140 | − | 134.872i | 0.561867 | − | 0.237451i | ||||
\(569\) | 2.03986 | 0.00358499 | 0.00179250 | − | 0.999998i | \(-0.499429\pi\) | ||||
0.00179250 | + | 0.999998i | \(0.499429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 538.359i | 0.942836i | 0.881910 | + | 0.471418i | \(0.156258\pi\) | ||||
−0.881910 | + | 0.471418i | \(0.843742\pi\) | |||||||
\(572\) | 1391.82 | + | 365.839i | 2.43325 | + | 0.639579i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −88.2099 | − | 114.392i | −0.153676 | − | 0.199290i | ||||
\(575\) | 743.931 | 1.29379 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3506 | 0.0214049 | 0.0107024 | − | 0.999943i | \(-0.496593\pi\) | ||||
0.0107024 | + | 0.999943i | \(0.496593\pi\) | |||||||
\(578\) | 324.474 | − | 250.208i | 0.561373 | − | 0.432885i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1282.11 | + | 337.004i | 2.21054 | + | 0.581041i | ||||
\(581\) | − | 21.8300i | − | 0.0375732i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1333.52 | 2.28734 | ||||||||
\(584\) | 142.815 | + | 337.936i | 0.244547 | + | 0.578658i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −341.688 | + | 263.482i | −0.583085 | + | 0.449627i | ||||
\(587\) | 783.659 | 1.33502 | 0.667512 | − | 0.744599i | \(-0.267359\pi\) | ||||
0.667512 | + | 0.744599i | \(0.267359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −853.990 | + | 105.551i | −1.44990 | + | 0.179203i | ||||
\(590\) | −1134.83 | + | 875.090i | −1.92344 | + | 1.48320i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −78.0518 | + | 138.214i | −0.131844 | + | 0.233470i | ||||
\(593\) | − | 49.3469i | − | 0.0832157i | −0.999134 | − | 0.0416078i | \(-0.986752\pi\) | ||
0.999134 | − | 0.0416078i | \(-0.0132480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 376.572i | 0.632894i | ||||||||
\(596\) | −822.734 | − | 216.256i | −1.38043 | − | 0.362845i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −344.371 | − | 446.586i | −0.575871 | − | 0.746799i | ||||
\(599\) | − | 204.239i | − | 0.340966i | −0.985361 | − | 0.170483i | \(-0.945467\pi\) | ||
0.985361 | − | 0.170483i | \(-0.0545328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 766.529i | 1.27542i | 0.770276 | + | 0.637711i | \(0.220119\pi\) | ||||
−0.770276 | + | 0.637711i | \(0.779881\pi\) | |||||||
\(602\) | 79.9250 | − | 61.6316i | 0.132766 | − | 0.102378i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30.9506 | − | 117.750i | 0.0512427 | − | 0.194950i | ||||
\(605\) | 2232.27i | 3.68971i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 471.612 | 0.776956 | 0.388478 | − | 0.921458i | \(-0.373001\pi\) | ||||
0.388478 | + | 0.921458i | \(0.373001\pi\) | |||||||
\(608\) | 586.651 | − | 159.700i | 0.964887 | − | 0.262664i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −156.959 | − | 203.548i | −0.257310 | − | 0.333685i | ||||
\(611\) | − | 122.150i | − | 0.199919i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −549.108 | −0.895771 | −0.447885 | − | 0.894091i | \(-0.647823\pi\) | ||||
−0.447885 | + | 0.894091i | \(0.647823\pi\) | |||||||
\(614\) | −231.261 | + | 178.330i | −0.376647 | + | 0.290439i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 284.128 | − | 120.075i | 0.461247 | − | 0.194928i | ||||
\(617\) | 95.8758i | 0.155390i | 0.996977 | + | 0.0776951i | \(0.0247561\pi\) | ||||
−0.996977 | + | 0.0776951i | \(0.975244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 329.998i | − | 0.533115i | −0.963819 | − | 0.266557i | \(-0.914114\pi\) | ||
0.963819 | − | 0.266557i | \(-0.0858862\pi\) | |||||||
\(620\) | −1503.27 | − | 395.134i | −2.42463 | − | 0.637314i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −276.464 | + | 213.186i | −0.444476 | + | 0.342743i | ||||
\(623\) | − | 115.405i | − | 0.185241i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 523.280 | 0.837248 | ||||||||
\(626\) | 351.464 | − | 271.020i | 0.561444 | − | 0.432940i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −140.096 | + | 532.988i | −0.223082 | + | 0.848707i | ||||
\(629\) | −220.468 | −0.350506 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 177.755i | 0.281704i | 0.990031 | + | 0.140852i | \(0.0449842\pi\) | ||||
−0.990031 | + | 0.140852i | \(0.955016\pi\) | |||||||
\(632\) | −264.268 | − | 625.323i | −0.418145 | − | 0.989435i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −361.950 | + | 279.106i | −0.570899 | + | 0.440230i | ||||
\(635\) | 1368.24i | 2.15471i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 831.083i | − | 1.30468i | ||||||
\(638\) | 1194.37 | − | 921.003i | 1.87206 | − | 1.44358i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1091.10 | + | 125.177i | 1.70484 | + | 0.195589i | ||||
\(641\) | −754.164 | −1.17654 | −0.588271 | − | 0.808664i | \(-0.700191\pi\) | ||||
−0.588271 | + | 0.808664i | \(0.700191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 290.869i | − | 0.452362i | −0.974085 | − | 0.226181i | \(-0.927376\pi\) | ||
0.974085 | − | 0.226181i | \(-0.0726241\pi\) | |||||||
\(644\) | −116.905 | − | 30.7286i | −0.181530 | − | 0.0477152i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 593.818 | + | 600.440i | 0.919224 | + | 0.929474i | ||||
\(647\) | −611.368 | −0.944927 | −0.472463 | − | 0.881350i | \(-0.656635\pi\) | ||||
−0.472463 | + | 0.881350i | \(0.656635\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1630.41i | 2.51218i | ||||||||
\(650\) | −1094.19 | − | 1418.96i | −1.68337 | − | 2.18302i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −905.033 | − | 237.888i | −1.38809 | − | 0.364859i | ||||
\(653\) | − | 476.483i | − | 0.729683i | −0.931070 | − | 0.364841i | \(-0.881123\pi\) | ||
0.931070 | − | 0.364841i | \(-0.118877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1631.30i | − | 2.49054i | ||||||
\(656\) | −509.519 | − | 287.733i | −0.776706 | − | 0.438618i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.9880 | − | 20.7335i | −0.0242979 | − | 0.0315099i | ||||
\(659\) | − | 690.235i | − | 1.04740i | −0.851903 | − | 0.523699i | \(-0.824552\pi\) | ||
0.851903 | − | 0.523699i | \(-0.175448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 856.826i | − | 1.29626i | −0.761531 | − | 0.648129i | \(-0.775552\pi\) | ||
0.761531 | − | 0.648129i | \(-0.224448\pi\) | |||||||
\(662\) | 112.272 | − | 86.5749i | 0.169595 | − | 0.130778i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.4233 | − | 81.4539i | −0.0518423 | − | 0.122672i | ||||
\(665\) | −319.524 | + | 39.4922i | −0.480487 | + | 0.0593868i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −591.036 | −0.886111 | ||||||||
\(668\) | −302.714 | − | 79.5683i | −0.453165 | − | 0.119114i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −967.272 | − | 1254.38i | −1.44369 | − | 1.87220i | ||||
\(671\) | −292.436 | −0.435821 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 880.796i | 1.30876i | 0.756166 | + | 0.654380i | \(0.227070\pi\) | ||||
−0.756166 | + | 0.654380i | \(0.772930\pi\) | |||||||
\(674\) | −419.678 | − | 544.246i | −0.622668 | − | 0.807487i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −173.456 | + | 659.903i | −0.256591 | + | 0.976188i | ||||
\(677\) | 662.559 | 0.978669 | 0.489335 | − | 0.872096i | \(-0.337240\pi\) | ||||
0.489335 | + | 0.872096i | \(0.337240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 60.5024 | 0.0891051 | ||||||||
\(680\) | 593.808 | + | 1405.10i | 0.873247 | + | 2.06632i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1400.40 | + | 1079.87i | −2.05337 | + | 1.58339i | ||||
\(683\) | 1076.21i | 1.57571i | 0.615858 | + | 0.787857i | \(0.288810\pi\) | ||||
−0.615858 | + | 0.787857i | \(0.711190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 497.309 | 0.725999 | ||||||||
\(686\) | −226.965 | − | 294.332i | −0.330853 | − | 0.429056i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 201.037 | − | 355.997i | 0.292205 | − | 0.517437i | ||||
\(689\) | 1258.67i | 1.82680i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 736.032i | − | 1.06517i | −0.846377 | − | 0.532585i | \(-0.821221\pi\) | ||
0.846377 | − | 0.532585i | \(-0.178779\pi\) | |||||||
\(692\) | 8.74523 | − | 33.2708i | 0.0126376 | − | 0.0480792i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −409.450 | + | 315.734i | −0.589986 | + | 0.454949i | ||||
\(695\) | 1215.61 | 1.74908 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 812.743i | − | 1.16606i | ||||||
\(698\) | 306.268 | − | 236.168i | 0.438779 | − | 0.338350i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −371.451 | − | 97.6358i | −0.530644 | − | 0.139480i | ||||
\(701\) | − | 723.274i | − | 1.03177i | −0.856657 | − | 0.515887i | \(-0.827462\pi\) | ||
0.856657 | − | 0.515887i | \(-0.172538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.1211 | − | 187.069i | −0.0328893 | − | 0.266100i | ||||
\(704\) | 870.818 | − | 896.070i | 1.23696 | − | 1.27283i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −252.477 | − | 327.416i | −0.357616 | − | 0.463762i | ||||
\(707\) | −246.385 | −0.348493 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 246.068 | 0.347063 | 0.173531 | − | 0.984828i | \(-0.444482\pi\) | ||||
0.173531 | + | 0.984828i | \(0.444482\pi\) | |||||||
\(710\) | −588.530 | + | 453.826i | −0.828916 | + | 0.639192i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −181.980 | − | 430.610i | −0.255590 | − | 0.604789i | ||||
\(713\) | 692.986 | 0.971930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3086.90 | −4.31734 | ||||||||
\(716\) | −482.414 | − | 126.803i | −0.673763 | − | 0.177099i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −465.528 | + | 358.977i | −0.648368 | + | 0.499968i | ||||
\(719\) | −1045.36 | −1.45391 | −0.726957 | − | 0.686683i | \(-0.759066\pi\) | ||||
−0.726957 | + | 0.686683i | \(0.759066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 209.317i | − | 0.290315i | ||||||
\(722\) | −447.202 | + | 566.829i | −0.619393 | + | 0.785081i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 114.870 | + | 30.1936i | 0.158660 | + | 0.0417039i | ||||
\(725\) | −1877.93 | −2.59025 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 427.300i | − | 0.587757i | −0.955843 | − | 0.293879i | \(-0.905054\pi\) | ||
0.955843 | − | 0.293879i | \(-0.0949462\pi\) | |||||||
\(728\) | 113.336 | + | 268.180i | 0.155681 | + | 0.368379i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −480.555 | − | 623.192i | −0.658294 | − | 0.853687i | ||||
\(731\) | 567.857 | 0.776823 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1310.42 | 1.78775 | 0.893876 | − | 0.448314i | \(-0.147975\pi\) | ||||
0.893876 | + | 0.448314i | \(0.147975\pi\) | |||||||
\(734\) | −381.650 | − | 494.931i | −0.519960 | − | 0.674293i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −484.663 | + | 69.6886i | −0.658509 | + | 0.0946856i | ||||
\(737\) | −1802.15 | −2.44526 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 121.660i | 0.164628i | 0.996606 | + | 0.0823138i | \(0.0262310\pi\) | ||||
−0.996606 | + | 0.0823138i | \(0.973769\pi\) | |||||||
\(740\) | 86.5551 | − | 329.295i | 0.116966 | − | 0.444993i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 164.744 | + | 213.644i | 0.222028 | + | 0.287929i | ||||
\(743\) | − | 968.498i | − | 1.30350i | −0.758435 | − | 0.651748i | \(-0.774036\pi\) | ||
0.758435 | − | 0.651748i | \(-0.225964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1824.73 | 2.44931 | ||||||||
\(746\) | 610.513 | + | 791.724i | 0.818382 | + | 1.06129i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1678.49 | + | 441.190i | 2.24396 | + | 0.589826i | ||||
\(749\) | 81.7341 | 0.109124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 870.550 | 1.15919 | 0.579594 | − | 0.814905i | \(-0.303211\pi\) | ||||
0.579594 | + | 0.814905i | \(0.303211\pi\) | |||||||
\(752\) | −92.3501 | − | 52.1516i | −0.122806 | − | 0.0693505i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 869.308 | + | 1127.33i | 1.15293 | + | 1.49514i | ||||
\(755\) | 261.156i | 0.345903i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −402.440 | −0.531624 | −0.265812 | − | 0.964025i | \(-0.585640\pi\) | ||||
−0.265812 | + | 0.964025i | \(0.585640\pi\) | |||||||
\(758\) | 133.021 | − | 102.575i | 0.175490 | − | 0.135323i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1129.96 | + | 651.206i | −1.48679 | + | 0.856851i | ||||
\(761\) | 981.995i | 1.29040i | 0.764013 | + | 0.645201i | \(0.223226\pi\) | ||||
−0.764013 | + | 0.645201i | \(0.776774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 399.755 | 0.523926 | ||||||||
\(764\) | −347.161 | + | 1320.76i | −0.454399 | + | 1.72874i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 867.137 | + | 1124.52i | 1.13203 | + | 1.46804i | ||||
\(767\) | −1538.89 | −2.00638 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1362.14 | −1.77132 | −0.885658 | − | 0.464339i | \(-0.846292\pi\) | ||||
−0.885658 | + | 0.464339i | \(0.846292\pi\) | |||||||
\(770\) | −523.963 | + | 404.038i | −0.680472 | + | 0.524724i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 273.610 | + | 71.9183i | 0.354417 | + | 0.0931584i | ||||
\(773\) | −129.403 | −0.167404 | −0.0837019 | − | 0.996491i | \(-0.526674\pi\) | ||||
−0.0837019 | + | 0.996491i | \(0.526674\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2201.87 | 2.84112 | ||||||||
\(776\) | 225.751 | − | 95.4049i | 0.290917 | − | 0.122944i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −316.619 | − | 410.597i | −0.406965 | − | 0.527760i | ||||
\(779\) | 689.618 | − | 85.2348i | 0.885260 | − | 0.109416i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 845.538i | 1.08264i | ||||||||
\(782\) | −415.300 | − | 538.568i | −0.531074 | − | 0.688706i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −628.329 | − | 354.827i | −0.801440 | − | 0.452586i | ||||
\(785\) | − | 1182.11i | − | 1.50587i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0757 | −0.0255091 | −0.0127546 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127546 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(788\) | −242.448 | − | 63.7276i | −0.307676 | − | 0.0808725i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 889.226 | + | 1153.16i | 1.12560 | + | 1.45970i | ||||
\(791\) | 53.3367i | 0.0674294i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 276.022i | − | 0.348073i | ||||||
\(794\) | 99.1972 | − | 76.4928i | 0.124934 | − | 0.0963385i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 633.523 | + | 166.521i | 0.795883 | + | 0.209198i | ||||
\(797\) | −1450.17 | −1.81954 | −0.909768 | − | 0.415118i | \(-0.863740\pi\) | ||||
−0.909768 | + | 0.415118i | \(0.863740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 147.309i | − | 0.184367i | ||||||
\(800\) | −1539.95 | + | 221.426i | −1.92493 | + | 0.276782i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 614.154 | − | 473.585i | 0.765778 | − | 0.590505i | ||||
\(803\) | −895.336 | −1.11499 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 259.283 | 0.322091 | ||||||||
\(806\) | −1019.26 | − | 1321.79i | −1.26459 | − | 1.63994i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −919.332 | + | 388.519i | −1.13779 | + | 0.480840i | ||||
\(809\) | − | 452.472i | − | 0.559298i | −0.960102 | − | 0.279649i | \(-0.909782\pi\) | ||
0.960102 | − | 0.279649i | \(-0.0902181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −849.897 | −1.04796 | −0.523981 | − | 0.851730i | \(-0.675554\pi\) | ||||
−0.523981 | + | 0.851730i | \(0.675554\pi\) | |||||||
\(812\) | 295.109 | + | 77.5694i | 0.363435 | + | 0.0955288i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −236.548 | − | 306.760i | −0.290600 | − | 0.376855i | ||||
\(815\) | 2007.26 | 2.46290 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.5529 | + | 481.831i | 0.0728922 | + | 0.589756i | ||||
\(818\) | 708.310 | + | 918.549i | 0.865905 | + | 1.12292i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1213.93 | + | 319.081i | 1.48040 | + | 0.389123i | ||||
\(821\) | − | 1222.86i | − | 1.48948i | −0.667356 | − | 0.744739i | \(-0.732574\pi\) | ||
0.667356 | − | 0.744739i | \(-0.267426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1490.19i | 1.81069i | 0.424682 | + | 0.905343i | \(0.360386\pi\) | ||||
−0.424682 | + | 0.905343i | \(0.639614\pi\) | |||||||
\(824\) | −330.067 | − | 781.020i | −0.400567 | − | 0.947840i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −261.209 | + | 201.423i | −0.316233 | + | 0.243853i | ||||
\(827\) | − | 963.746i | − | 1.16535i | −0.812705 | − | 0.582676i | \(-0.802006\pi\) | ||
0.812705 | − | 0.582676i | \(-0.197994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 190.778i | 0.230130i | 0.993358 | + | 0.115065i | \(0.0367076\pi\) | ||||
−0.993358 | + | 0.115065i | \(0.963292\pi\) | |||||||
\(830\) | 115.830 | + | 150.210i | 0.139554 | + | 0.180976i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 845.774 | + | 821.939i | 1.01656 | + | 0.987908i | ||||
\(833\) | − | 1002.26i | − | 1.20319i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 671.386 | 0.804055 | ||||||||
\(836\) | −198.325 | + | 1470.47i | −0.237230 | + | 1.75894i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −341.191 | + | 263.099i | −0.407149 | + | 0.313960i | ||||
\(839\) | 203.066i | 0.242034i | 0.992650 | + | 0.121017i | \(0.0386155\pi\) | ||||
−0.992650 | + | 0.121017i | \(0.961384\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 650.976 | 0.774050 | ||||||||
\(842\) | −198.615 | − | 257.567i | −0.235884 | − | 0.305899i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 168.684 | − | 641.749i | 0.199862 | − | 0.760367i | ||||
\(845\) | − | 1463.59i | − | 1.73206i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 513.810i | 0.606624i | ||||||||
\(848\) | 951.598 | + | 537.383i | 1.12217 | + | 0.633706i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1319.56 | − | 1711.22i | −1.55242 | − | 2.01320i | ||||
\(851\) | 151.800i | 0.178379i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 150.584 | 0.176534 | 0.0882672 | − | 0.996097i | \(-0.471867\pi\) | ||||
0.0882672 | + | 0.996097i | \(0.471867\pi\) | |||||||
\(854\) | −36.1279 | − | 46.8513i | −0.0423043 | − | 0.0548610i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 304.973 | − | 128.885i | 0.356277 | − | 0.150566i | ||||
\(857\) | 721.190 | 0.841529 | 0.420765 | − | 0.907170i | \(-0.361762\pi\) | ||||
0.420765 | + | 0.907170i | \(0.361762\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 405.469i | − | 0.472024i | −0.971750 | − | 0.236012i | \(-0.924159\pi\) | ||
0.971750 | − | 0.236012i | \(-0.0758405\pi\) | |||||||
\(860\) | −222.939 | + | 848.162i | −0.259232 | + | 0.986235i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −546.613 | − | 708.858i | −0.634122 | − | 0.822341i | ||||
\(863\) | 475.353i | 0.550814i | 0.961328 | + | 0.275407i | \(0.0888127\pi\) | ||||
−0.961328 | + | 0.275407i | \(0.911187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.7910i | 0.0853075i | ||||||||
\(866\) | 260.413 | + | 337.708i | 0.300708 | + | 0.389964i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −346.013 | − | 90.9496i | −0.398633 | − | 0.104781i | ||||
\(869\) | 1656.74 | 1.90650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1701.00i | − | 1.95293i | ||||||
\(872\) | 1491.60 | − | 630.366i | 1.71055 | − | 0.722896i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 413.425 | − | 408.866i | 0.473026 | − | 0.467810i | ||||
\(875\) | 400.212 | 0.457385 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 665.132i | 0.758418i | 0.925311 | + | 0.379209i | \(0.123804\pi\) | ||||
−0.925311 | + | 0.379209i | \(0.876196\pi\) | |||||||
\(878\) | −131.395 | + | 101.321i | −0.149652 | + | 0.115400i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1317.94 | + | 2333.80i | −1.49766 | + | 2.65205i | ||||
\(881\) | − | 899.387i | − | 1.02087i | −0.859916 | − | 0.510435i | \(-0.829484\pi\) | ||
0.859916 | − | 0.510435i | \(-0.170516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 931.451i | − | 1.05487i | −0.849595 | − | 0.527435i | \(-0.823154\pi\) | ||
0.849595 | − | 0.527435i | \(-0.176846\pi\) | |||||||
\(884\) | −416.426 | + | 1584.27i | −0.471070 | + | 1.79216i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 147.657 | − | 113.861i | 0.166656 | − | 0.128511i | ||||
\(887\) | − | 229.602i | − | 0.258853i | −0.991589 | − | 0.129426i | \(-0.958686\pi\) | ||
0.991589 | − | 0.129426i | \(-0.0413136\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 314.933i | 0.354255i | ||||||||
\(890\) | 612.338 | + | 794.091i | 0.688021 | + | 0.892238i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −335.668 | + | 1277.03i | −0.376309 | + | 1.43165i | ||||
\(893\) | 124.993 | − | 15.4488i | 0.139970 | − | 0.0172999i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1069.94 | 1.19547 | ||||||||
\(896\) | 251.142 | + | 28.8125i | 0.280292 | + | 0.0321568i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −622.553 | + | 480.062i | −0.693266 | + | 0.534590i | ||||
\(899\) | −1749.33 | −1.94586 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1517.91i | 1.68470i | ||||||||
\(902\) | 1130.85 | − | 872.021i | 1.25372 | − | 0.966764i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 84.1054 | + | 199.014i | 0.0930370 | + | 0.220148i | ||||
\(905\) | −254.769 | −0.281513 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1297.66 | −1.43072 | −0.715361 | − | 0.698755i | \(-0.753738\pi\) | ||||
−0.715361 | + | 0.698755i | \(0.753738\pi\) | |||||||
\(908\) | 669.702 | + | 176.031i | 0.737557 | + | 0.193867i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −381.359 | − | 494.554i | −0.419076 | − | 0.543465i | ||||
\(911\) | 1073.40i | 1.17827i | 0.808034 | + | 0.589136i | \(0.200532\pi\) | ||||
−0.808034 | + | 0.589136i | \(0.799468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 215.806 | 0.236370 | ||||||||
\(914\) | 267.320 | − | 206.135i | 0.292473 | − | 0.225531i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −130.696 | + | 497.228i | −0.142682 | + | 0.542826i | ||||
\(917\) | − | 375.483i | − | 0.409469i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1277.37i | 1.38996i | 0.719031 | + | 0.694978i | \(0.244586\pi\) | ||||
−0.719031 | + | 0.694978i | \(0.755414\pi\) | |||||||
\(920\) | 967.460 | − | 408.858i | 1.05159 | − | 0.444411i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 941.395 | + | 1220.82i | 1.02104 | + | 1.32410i | ||||
\(923\) | −798.079 | −0.864657 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 482.324i | 0.521431i | ||||||||
\(926\) | −893.242 | − | 1158.37i | −0.964624 | − | 1.25094i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1223.45 | − | 175.918i | 1.31838 | − | 0.189566i | ||||
\(929\) | − | 432.225i | − | 0.465258i | −0.972565 | − | 0.232629i | \(-0.925267\pi\) | ||
0.972565 | − | 0.232629i | \(-0.0747329\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 850.423 | − | 105.110i | 0.913452 | − | 0.112900i | ||||
\(932\) | −169.108 | − | 44.4499i | −0.181446 | − | 0.0476930i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −293.519 | + | 226.338i | −0.314260 | + | 0.242332i | ||||
\(935\) | −3722.70 | −3.98149 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.1174 | −0.0492181 | −0.0246091 | − | 0.999697i | \(-0.507834\pi\) | ||||
−0.0246091 | + | 0.999697i | \(0.507834\pi\) | |||||||
\(938\) | −222.641 | − | 288.724i | −0.237357 | − | 0.307808i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 220.024 | + | 57.8332i | 0.234068 | + | 0.0615247i | ||||
\(941\) | −28.6436 | −0.0304395 | −0.0152197 | − | 0.999884i | \(-0.504845\pi\) | ||||
−0.0152197 | + | 0.999884i | \(0.504845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −559.603 | −0.593429 | ||||||||
\(944\) | −657.024 | + | 1163.46i | −0.696000 | + | 1.23248i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 609.275 | + | 790.119i | 0.644054 | + | 0.835220i | ||||
\(947\) | 1518.22 | 1.60319 | 0.801596 | − | 0.597866i | \(-0.203984\pi\) | ||||
0.801596 | + | 0.597866i | \(0.203984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 845.082i | − | 0.890497i | ||||||
\(950\) | 1313.60 | − | 1299.11i | 1.38274 | − | 1.36749i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 136.679 | + | 323.416i | 0.143570 | + | 0.339723i | ||||
\(953\) | 1257.68 | 1.31971 | 0.659855 | − | 0.751393i | \(-0.270618\pi\) | ||||
0.659855 | + | 0.751393i | \(0.270618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2929.29i | − | 3.06732i | ||||||
\(956\) | −301.195 | + | 1145.88i | −0.315058 | + | 1.19862i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −455.701 | + | 351.399i | −0.475680 | + | 0.366805i | ||||
\(959\) | 114.468 | 0.119361 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1090.08 | 1.13432 | ||||||||
\(962\) | 289.542 | − | 223.271i | 0.300979 | − | 0.232090i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −157.234 | − | 41.3290i | −0.163106 | − | 0.0428724i | ||||
\(965\) | −606.836 | −0.628846 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1531.44i | 1.58370i | 0.610716 | + | 0.791849i | \(0.290882\pi\) | ||||
−0.610716 | + | 0.791849i | \(0.709118\pi\) | |||||||
\(968\) | 810.216 | + | 1917.17i | 0.837000 | + | 1.98055i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −416.311 | + | 321.025i | −0.429186 | + | 0.330953i | ||||
\(971\) | − | 134.461i | − | 0.138477i | −0.997600 | − | 0.0692385i | \(-0.977943\pi\) | ||
0.997600 | − | 0.0692385i | \(-0.0220569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 279.802 | 0.287566 | ||||||||
\(974\) | −350.561 | + | 270.324i | −0.359919 | + | 0.277540i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −208.682 | − | 117.846i | −0.213814 | − | 0.120744i | ||||
\(977\) | 1071.76 | 1.09699 | 0.548497 | − | 0.836153i | \(-0.315200\pi\) | ||||
0.548497 | + | 0.836153i | \(0.315200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1140.87 | 1.16534 | ||||||||
\(980\) | 1496.99 | + | 393.484i | 1.52754 | + | 0.401514i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 910.252 | − | 701.912i | 0.926937 | − | 0.714778i | ||||
\(983\) | 393.810i | 0.400620i | 0.979733 | + | 0.200310i | \(0.0641950\pi\) | ||||
−0.979733 | + | 0.200310i | \(0.935805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 537.724 | 0.545913 | ||||||||
\(986\) | 1048.36 | + | 1359.53i | 1.06324 | + | 1.37883i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1387.94 | − | 187.193i | −1.40480 | − | 0.189466i | ||||
\(989\) | − | 390.991i | − | 0.395339i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 937.161 | 0.945673 | 0.472836 | − | 0.881150i | \(-0.343230\pi\) | ||||
0.472836 | + | 0.881150i | \(0.343230\pi\) | |||||||
\(992\) | −1434.49 | + | 206.262i | −1.44606 | + | 0.207926i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −135.464 | + | 104.459i | −0.136282 | + | 0.105089i | ||||
\(995\) | −1405.08 | −1.41214 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1258.54 | 1.26232 | 0.631162 | − | 0.775651i | \(-0.282578\pi\) | ||||
0.631162 | + | 0.775651i | \(0.282578\pi\) | |||||||
\(998\) | −26.2372 | − | 34.0249i | −0.0262898 | − | 0.0340931i | ||||
\(999\) | 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 | 684.3.b.a.683.15 | yes | 80 | |
3.2 | odd | 2 | inner | 684.3.b.a.683.65 | yes | 80 | |
4.3 | odd | 2 | inner | 684.3.b.a.683.14 | yes | 80 | |
12.11 | even | 2 | inner | 684.3.b.a.683.68 | yes | 80 | |
19.18 | odd | 2 | inner | 684.3.b.a.683.66 | yes | 80 | |
57.56 | even | 2 | inner | 684.3.b.a.683.16 | yes | 80 | |
76.75 | even | 2 | inner | 684.3.b.a.683.67 | yes | 80 | |
228.227 | odd | 2 | inner | 684.3.b.a.683.13 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.b.a.683.13 | ✓ | 80 | 228.227 | odd | 2 | inner | |
684.3.b.a.683.14 | yes | 80 | 4.3 | odd | 2 | inner | |
684.3.b.a.683.15 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.b.a.683.16 | yes | 80 | 57.56 | even | 2 | inner | |
684.3.b.a.683.65 | yes | 80 | 3.2 | odd | 2 | inner | |
684.3.b.a.683.66 | yes | 80 | 19.18 | odd | 2 | inner | |
684.3.b.a.683.67 | yes | 80 | 76.75 | even | 2 | inner | |
684.3.b.a.683.68 | yes | 80 | 12.11 | even | 2 | inner |