Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.9 | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.g.2239.10 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.86733i | − | 1.07810i | −0.842273 | − | 0.539051i | \(-0.818783\pi\) | ||
0.842273 | − | 0.539051i | \(-0.181217\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.07366 | + | 0.836614i | −0.927370 | + | 0.374145i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64040 | + | 0.168201i | −0.997977 | + | 0.0635738i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.486908 | −0.162303 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.26303i | − | 1.28535i | −0.766138 | − | 0.642676i | \(-0.777824\pi\) | ||
0.766138 | − | 0.642676i | \(-0.222176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.57238 | 1.54550 | 0.772750 | − | 0.634710i | \(-0.218881\pi\) | ||||
0.772750 | + | 0.634710i | \(0.218881\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56223 | + | 3.87221i | 0.403366 | + | 0.999799i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.01761 | −0.731878 | −0.365939 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365939 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0464832 | −0.0106640 | −0.00533198 | − | 0.999986i | \(-0.501697\pi\) | ||||
−0.00533198 | + | 0.999986i | \(0.501697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.314085 | + | 4.93049i | 0.0685390 | + | 1.07592i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.58465 | −1.16448 | −0.582240 | − | 0.813017i | \(-0.697824\pi\) | ||||
−0.582240 | + | 0.813017i | \(0.697824\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.60015 | − | 3.46971i | 0.720031 | − | 0.693942i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.69276i | − | 0.903123i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.21067 | −0.224817 | −0.112408 | − | 0.993662i | \(-0.535856\pi\) | ||||
−0.112408 | + | 0.993662i | \(0.535856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.62124 | −0.829999 | −0.414999 | − | 0.909822i | \(-0.636218\pi\) | ||||
−0.414999 | + | 0.909822i | \(0.636218\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.96047 | −1.38574 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.33458 | − | 2.55779i | 0.901708 | − | 0.432345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.87892i | − | 1.62408i | −0.583599 | − | 0.812042i | \(-0.698356\pi\) | ||
0.583599 | − | 0.812042i | \(-0.301644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 10.4055i | − | 1.66621i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5213i | 1.64316i | 0.570096 | + | 0.821578i | \(0.306906\pi\) | ||||
−0.570096 | + | 0.821578i | \(0.693094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.4259 | −1.89493 | −0.947467 | − | 0.319854i | \(-0.896366\pi\) | ||||
−0.947467 | + | 0.319854i | \(0.896366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00968 | − | 0.407354i | 0.150515 | − | 0.0607247i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.78840i | 0.990190i | 0.868839 | + | 0.495095i | \(0.164867\pi\) | ||||
−0.868839 | + | 0.495095i | \(0.835133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.94342 | − | 0.888233i | 0.991917 | − | 0.126890i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.63486i | 0.789038i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.99936i | 0.686715i | 0.939205 | + | 0.343358i | \(0.111564\pi\) | ||||
−0.939205 | + | 0.343358i | \(0.888436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.56651 | + | 8.84009i | 0.480908 | + | 1.19200i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0867992i | 0.0114968i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.06269 | 0.919484 | 0.459742 | − | 0.888053i | \(-0.347942\pi\) | ||||
0.459742 | + | 0.888053i | \(0.347942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5761i | 1.48216i | 0.671415 | + | 0.741081i | \(0.265687\pi\) | ||||
−0.671415 | + | 0.741081i | \(0.734313\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.28563 | − | 0.0818982i | 0.161974 | − | 0.0103182i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.5552 | + | 4.66193i | −1.43325 | + | 0.578241i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.65798 | 0.813402 | 0.406701 | − | 0.913561i | \(-0.366679\pi\) | ||||
0.406701 | + | 0.913561i | \(0.366679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.4284i | 1.25543i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.11624i | 0.607186i | 0.952802 | + | 0.303593i | \(0.0981863\pi\) | ||||
−0.952802 | + | 0.303593i | \(0.901814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.67546 | −1.13243 | −0.566214 | − | 0.824258i | \(-0.691592\pi\) | ||||
−0.566214 | + | 0.824258i | \(0.691592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.47908 | − | 6.72266i | −0.748140 | − | 0.776266i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.717044 | + | 11.2561i | 0.0817148 | + | 1.28275i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.90273i | − | 0.664109i | −0.943260 | − | 0.332054i | \(-0.892258\pi\) | ||
0.943260 | − | 0.332054i | \(-0.107742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.2236 | −1.13596 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1201i | 1.22059i | 0.792175 | + | 0.610294i | \(0.208949\pi\) | ||||
−0.792175 | + | 0.610294i | \(0.791051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25750 | − | 2.52457i | 0.678721 | − | 0.273828i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.26072i | 0.242375i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.51888i | 0.161001i | 0.996755 | + | 0.0805005i | \(0.0256519\pi\) | ||||
−0.996755 | + | 0.0805005i | \(0.974348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7133 | + | 0.937278i | −1.54237 | + | 0.0982534i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.62936i | 0.894823i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0963904 | − | 0.0388885i | 0.00988945 | − | 0.00398987i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.01761 | −0.306392 | −0.153196 | − | 0.988196i | \(-0.548957\pi\) | ||||
−0.153196 | + | 0.988196i | \(0.548957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.07570i | 0.208616i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.464155i | 0.0461852i | 0.999733 | + | 0.0230926i | \(0.00735125\pi\) | ||||
−0.999733 | + | 0.0230926i | \(0.992649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.67886i | 0.165423i | 0.996574 | + | 0.0827113i | \(0.0263579\pi\) | ||||
−0.996574 | + | 0.0827113i | \(0.973642\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.77622 | − | 9.96140i | −0.466111 | − | 0.972133i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.65798 | −0.643651 | −0.321826 | − | 0.946799i | \(-0.604297\pi\) | ||||
−0.321826 | + | 0.946799i | \(0.604297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0975 | −1.25451 | −0.627257 | − | 0.778812i | \(-0.715822\pi\) | ||||
−0.627257 | + | 0.778812i | \(0.715822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.4472 | −1.75093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1608i | 1.52028i | 0.649757 | + | 0.760142i | \(0.274871\pi\) | ||||
−0.649757 | + | 0.760142i | \(0.725129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.5807 | − | 4.67220i | 1.07990 | − | 0.435685i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.71324 | −0.250839 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.96769 | − | 0.507563i | 0.730397 | − | 0.0465283i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.17343 | −0.652130 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.6468 | 1.77149 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.56270 | + | 10.2069i | −0.408100 | + | 0.912937i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.40526 | 0.745846 | 0.372923 | − | 0.927862i | \(-0.378356\pi\) | ||||
0.372923 | + | 0.927862i | \(0.378356\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.2032i | 2.04293i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.12073 | −0.0979187 | −0.0489594 | − | 0.998801i | \(-0.515590\pi\) | ||||
−0.0489594 | + | 0.998801i | \(0.515590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.122734 | − | 0.00781849i | 0.0106424 | − | 0.000677949i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.92603 | + | 9.73121i | 0.337899 | + | 0.837529i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4.27185i | − | 0.364969i | −0.983209 | − | 0.182484i | \(-0.941586\pi\) | ||
0.983209 | − | 0.182484i | \(-0.0584139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.369778 | 0.0313641 | 0.0156821 | − | 0.999877i | \(-0.495008\pi\) | ||||
0.0156821 | + | 0.999877i | \(0.495008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6762 | 1.06753 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 23.7552i | − | 1.98651i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.51053 | − | 1.01287i | 0.208488 | − | 0.0841140i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.65862 | − | 12.9656i | −0.136801 | − | 1.06939i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5383 | −1.35487 | −0.677437 | − | 0.735581i | \(-0.736909\pi\) | ||||
−0.677437 | + | 0.735581i | \(0.736909\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.84168i | − | 0.149874i | −0.997188 | − | 0.0749370i | \(-0.976124\pi\) | ||
0.997188 | − | 0.0749370i | \(-0.0238756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.46930 | 0.118786 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.58289 | − | 3.86619i | 0.769716 | − | 0.310540i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.88403 | −0.549405 | −0.274703 | − | 0.961529i | \(-0.588579\pi\) | ||||
−0.274703 | + | 0.961529i | \(0.588579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.33544 | 0.740348 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.7457 | − | 0.939342i | 1.16212 | − | 0.0740305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.94845 | 0.309266 | 0.154633 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154633 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.5073 | − | 6.65984i | 1.28509 | − | 0.518468i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.87928i | − | 0.609717i | −0.952398 | − | 0.304858i | \(-0.901391\pi\) | ||
0.952398 | − | 0.304858i | \(-0.0986091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.0514 | 1.38857 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0226330 | 0.00173079 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.9532 | −0.984814 | −0.492407 | − | 0.870365i | \(-0.663883\pi\) | ||||
−0.492407 | + | 0.870365i | \(0.663883\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92224 | + | 9.76697i | −0.674458 | + | 0.738313i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 13.1883i | − | 0.991297i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.98609i | 0.522165i | 0.965316 | + | 0.261083i | \(0.0840795\pi\) | ||||
−0.965316 | + | 0.261083i | \(0.915920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.1459i | − | 1.57176i | −0.618377 | − | 0.785882i | \(-0.712210\pi\) | ||
0.618377 | − | 0.785882i | \(-0.287790\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.6163 | 1.59792 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.26484 | + | 20.4855i | 0.607643 | + | 1.50613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8642i | 0.940720i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.789325 | + | 12.3908i | 0.0574150 | + | 0.901296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7773i | 1.14160i | 0.821088 | + | 0.570802i | \(0.193368\pi\) | ||||
−0.821088 | + | 0.570802i | \(0.806632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.96235i | 0.357198i | 0.983922 | + | 0.178599i | \(0.0571564\pi\) | ||||
−0.983922 | + | 0.178599i | \(0.942844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.70535 | + | 21.5774i | 0.623403 | + | 1.54519i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.5088i | − | 1.24745i | −0.781643 | − | 0.623726i | \(-0.785618\pi\) | ||
0.781643 | − | 0.623726i | \(-0.214382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.43247 | −0.526874 | −0.263437 | − | 0.964677i | \(-0.584856\pi\) | ||||
−0.263437 | + | 0.964677i | \(0.584856\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 12.4326i | − | 0.876930i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.19666 | − | 0.203636i | 0.224362 | − | 0.0142925i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.80230 | − | 21.8177i | −0.614779 | − | 1.52381i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.71921 | 0.188998 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.198159i | 0.0137070i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21.8042i | − | 1.50106i | −0.660834 | − | 0.750532i | \(-0.729797\pi\) | ||
0.660834 | − | 0.750532i | \(-0.270203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.55369 | 0.654608 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.7671 | − | 10.3957i | 1.75730 | − | 0.708980i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.2019 | − | 0.777295i | 0.828320 | − | 0.0527662i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.0673i | 1.22087i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.8153 | −1.13112 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6451i | 1.24857i | 0.781197 | + | 0.624284i | \(0.214609\pi\) | ||||
−0.781197 | + | 0.624284i | \(0.785391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.75294 | + | 1.68943i | −0.116863 | + | 0.112629i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4234i | 0.824571i | 0.911055 | + | 0.412285i | \(0.135269\pi\) | ||||
−0.911055 | + | 0.412285i | \(0.864731\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.06384i | 0.598955i | 0.954103 | + | 0.299478i | \(0.0968124\pi\) | ||||
−0.954103 | + | 0.299478i | \(0.903188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.0188 | − | 1.33896i | 1.38294 | − | 0.0880968i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.36535i | 0.0894473i | 0.998999 | + | 0.0447236i | \(0.0142407\pi\) | ||||
−0.998999 | + | 0.0447236i | \(0.985759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.67927 | − | 14.0769i | −0.370475 | − | 0.918273i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0223 | −0.715977 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.1208i | − | 1.30151i | −0.759288 | − | 0.650754i | \(-0.774453\pi\) | ||
0.759288 | − | 0.650754i | \(-0.225547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.60404i | 0.232157i | 0.993240 | + | 0.116078i | \(0.0370324\pi\) | ||||
−0.993240 | + | 0.116078i | \(0.962968\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.01259i | 0.321558i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.6552 | + | 7.65086i | −0.872399 | + | 0.488795i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.259022 | −0.0164812 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.7648 | 1.31592 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.8309 | −1.37795 | −0.688976 | − | 0.724784i | \(-0.741939\pi\) | ||||
−0.688976 | + | 0.724784i | \(0.741939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.8075i | 1.49677i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.71420 | − | 11.6848i | −0.295215 | − | 0.731731i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.0520 | 1.31319 | 0.656595 | − | 0.754244i | \(-0.271996\pi\) | ||||
0.656595 | + | 0.754244i | \(0.271996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66164 | + | 26.0843i | 0.103249 | + | 1.62080i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.589487 | 0.0364883 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.71567 | −0.167455 | −0.0837276 | − | 0.996489i | \(-0.526683\pi\) | ||||
−0.0837276 | + | 0.996489i | \(0.526683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.18253 | − | 10.3670i | −0.256931 | − | 0.636839i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.83625 | 0.173575 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 25.9926i | − | 1.58479i | −0.610005 | − | 0.792397i | \(-0.708833\pi\) | ||
0.610005 | − | 0.792397i | \(-0.291167\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.4482 | −1.54587 | −0.772933 | − | 0.634487i | \(-0.781211\pi\) | ||||
−0.772933 | + | 0.634487i | \(0.781211\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.75020 | + | 27.4746i | 0.105927 | + | 1.66284i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.7915 | − | 15.3476i | −0.891960 | − | 0.925493i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50956i | 0.511290i | 0.966771 | + | 0.255645i | \(0.0822878\pi\) | ||||
−0.966771 | + | 0.255645i | \(0.917712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.25012 | 0.134711 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1347 | −0.604588 | −0.302294 | − | 0.953215i | \(-0.597753\pi\) | ||||
−0.302294 | + | 0.953215i | \(0.597753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.5926i | − | 0.807993i | −0.914760 | − | 0.403997i | \(-0.867621\pi\) | ||
0.914760 | − | 0.403997i | \(-0.132379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0726174 | − | 0.179992i | −0.00430149 | − | 0.0106618i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.76969 | − | 27.7805i | −0.104462 | − | 1.63983i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.89404 | −0.464355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.63486i | 0.330321i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0627 | −1.05524 | −0.527619 | − | 0.849481i | \(-0.676915\pi\) | ||||
−0.527619 | + | 0.849481i | \(0.676915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6456 | + | 5.90874i | −0.852702 | + | 0.344020i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.0054 | −1.16083 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.1198 | −1.79971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.8094 | − | 2.09005i | 1.89110 | − | 0.120468i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.866730 | 0.0497923 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.68469 | − | 24.0048i | −0.554544 | − | 1.37451i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5799i | 1.06041i | 0.847869 | + | 0.530205i | \(0.177885\pi\) | ||||
−0.847869 | + | 0.530205i | \(0.822115\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.13497 | 0.178342 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2396 | −0.694046 | −0.347023 | − | 0.937857i | \(-0.612807\pi\) | ||||
−0.347023 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.1509 | 1.30857 | 0.654283 | − | 0.756250i | \(-0.272971\pi\) | ||||
0.654283 | + | 0.756250i | \(0.272971\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.59745 | + | 1.24541i | −0.146350 | + | 0.0701707i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.61492i | − | 0.146868i | −0.997300 | − | 0.0734342i | \(-0.976604\pi\) | ||
0.997300 | − | 0.0734342i | \(-0.0233959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.16114i | 0.288969i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4326i | 0.693922i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.140268 | 0.00780472 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0614 | − | 19.3345i | 1.11281 | − | 1.07249i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.4573i | 1.35249i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.14181 | − | 17.9241i | −0.0629502 | − | 0.988187i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.8342i | − | 0.705434i | −0.935730 | − | 0.352717i | \(-0.885258\pi\) | ||
0.935730 | − | 0.352717i | \(-0.114742\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.81013i | 0.263593i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.8064 | + | 5.57016i | −0.754325 | + | 0.304330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.05930i | − | 0.166651i | −0.996522 | − | 0.0833254i | \(-0.973446\pi\) | ||
0.996522 | − | 0.0833254i | \(-0.0265541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.1776 | 1.63902 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.7005i | 1.06684i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1840 | + | 3.51318i | −0.981843 | + | 0.189694i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.72452 | − | 21.6249i | −0.469712 | − | 1.16425i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.7386 | −0.898574 | −0.449287 | − | 0.893387i | \(-0.648322\pi\) | ||||
−0.449287 | + | 0.893387i | \(0.648322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.8680i | − | 1.75938i | −0.475544 | − | 0.879692i | \(-0.657749\pi\) | ||
0.475544 | − | 0.879692i | \(-0.342251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 26.1499i | − | 1.39578i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.7338 | 1.79547 | 0.897736 | − | 0.440535i | \(-0.145211\pi\) | ||||
0.897736 | + | 0.440535i | \(0.145211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.28032 | − | 10.6094i | −0.227176 | − | 0.563086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.947787 | − | 14.8783i | −0.0501622 | − | 0.787442i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.1542i | − | 0.588698i | −0.955698 | − | 0.294349i | \(-0.904897\pi\) | ||
0.955698 | − | 0.294349i | \(-0.0951028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9978 | −0.999886 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3951i | 0.703063i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0637 | − | 8.09463i | 1.05018 | − | 0.423692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.3476i | − | 1.47973i | −0.672755 | − | 0.739865i | \(-0.734889\pi\) | ||
0.672755 | − | 0.739865i | \(-0.265111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.12292i | − | 0.266689i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.840895 | − | 13.2003i | −0.0436571 | − | 0.685326i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.6333i | 1.48258i | 0.671187 | + | 0.741288i | \(0.265785\pi\) | ||||
−0.671187 | + | 0.741288i | \(0.734215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0597 | + | 8.52005i | 0.984239 | + | 0.439973i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.74634 | −0.347454 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9281i | 1.02364i | 0.859093 | + | 0.511820i | \(0.171029\pi\) | ||||
−0.859093 | + | 0.511820i | \(0.828971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 15.6954i | − | 0.804098i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.22155i | 0.266809i | 0.991062 | + | 0.133404i | \(0.0425909\pi\) | ||||
−0.991062 | + | 0.133404i | \(0.957409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.9039 | − | 22.7415i | −0.555715 | − | 1.15901i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.05027 | 0.307553 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.9831 | 0.556866 | 0.278433 | − | 0.960456i | \(-0.410185\pi\) | ||||
0.278433 | + | 0.960456i | \(0.410185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8523 | 0.852257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.09277i | 0.105566i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.93830 | + | 12.2403i | 0.248473 | + | 0.615875i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4503 | 1.67882 | 0.839412 | − | 0.543495i | \(-0.182899\pi\) | ||||
0.839412 | + | 0.543495i | \(0.182899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0145997 | − | 0.229185i | −0.000730898 | − | 0.0114736i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.51024 | 0.175293 | 0.0876466 | − | 0.996152i | \(-0.472065\pi\) | ||||
0.0876466 | + | 0.996152i | \(0.472065\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.7513 | −1.28276 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.2004 | − | 8.55324i | 1.05346 | − | 0.425014i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.1141 | −2.08752 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.4267i | − | 1.10893i | −0.832207 | − | 0.554465i | \(-0.812923\pi\) | ||
0.832207 | − | 0.554465i | \(-0.187077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.97694 | −0.393474 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.6483 | + | 1.18795i | −0.917624 | + | 0.0584551i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.30322 | − | 23.0593i | −0.456677 | − | 1.13194i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.690495i | − | 0.0338137i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.797437 | −0.0389573 | −0.0194787 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194787 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.1666 | −0.544227 | −0.272114 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272114 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.30533i | − | 0.160710i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8639 | + | 10.4702i | −0.526974 | + | 0.507881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.94710 | − | 30.5654i | −0.0942268 | − | 1.47916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −44.3588 | −2.14166 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.8568i | 0.522954i | 0.965210 | + | 0.261477i | \(0.0842096\pi\) | ||||
−0.965210 | + | 0.261477i | \(0.915790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5291 | −0.505996 | −0.252998 | − | 0.967467i | \(-0.581417\pi\) | ||||
−0.252998 | + | 0.967467i | \(0.581417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.89135 | − | 4.68798i | −0.0906835 | − | 0.224771i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.259592 | 0.0124180 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.9523 | 1.66818 | 0.834092 | − | 0.551626i | \(-0.185992\pi\) | ||||
0.834092 | + | 0.551626i | \(0.185992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.38081 | + | 0.432488i | −0.160991 | + | 0.0205947i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0336 | −0.619246 | −0.309623 | − | 0.950859i | \(-0.600203\pi\) | ||||
−0.309623 | + | 0.950859i | \(0.600203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.27072 | − | 3.14965i | −0.0602377 | − | 0.149308i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.8825i | 1.46069i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.9459 | 0.658147 | 0.329073 | − | 0.944304i | \(-0.393264\pi\) | ||||
0.329073 | + | 0.944304i | \(0.393264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.8528 | 2.11203 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.43902 | −0.161579 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.7263 | − | 14.2530i | 1.39359 | − | 0.668189i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4758i | 0.817485i | 0.912650 | + | 0.408743i | \(0.134033\pi\) | ||||
−0.912650 | + | 0.408743i | \(0.865967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.1609i | 0.660975i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0195231i | 0.000909280i | 1.00000 | 0.000454640i | \(0.000144716\pi\) | |||||
−1.00000 | 0.000454640i | \(0.999855\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.582327 | −0.0270630 | −0.0135315 | − | 0.999908i | \(-0.504307\pi\) | ||||
−0.0135315 | + | 0.999908i | \(0.504307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.21944 | − | 17.8944i | −0.334793 | − | 0.829832i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.3130i | 0.754878i | 0.926034 | + | 0.377439i | \(0.123195\pi\) | ||||
−0.926034 | + | 0.377439i | \(0.876805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5797 | + | 1.11988i | −0.811757 | + | 0.0517111i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8547i | 0.592315i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.9720i | 2.43566i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.167347 | + | 0.161283i | −0.00767839 | + | 0.00740018i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.43423i | − | 0.111456i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.1467 | −0.554995 | −0.277498 | − | 0.960726i | \(-0.589505\pi\) | ||||
−0.277498 | + | 0.960726i | \(0.589505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 55.0491i | − | 2.51002i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.75406 | − | 27.5351i | −0.0798124 | − | 1.25289i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.25750 | − | 2.52457i | 0.284139 | − | 0.114635i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.964581 | 0.0437093 | 0.0218547 | − | 0.999761i | \(-0.493043\pi\) | ||||
0.0218547 | + | 0.999761i | \(0.493043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.37304i | − | 0.333420i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1152i | 1.31395i | 0.753912 | + | 0.656976i | \(0.228165\pi\) | ||||
−0.753912 | + | 0.656976i | \(0.771835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.65334 | 0.164538 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73656 | − | 4.30431i | −0.0780527 | − | 0.193464i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.860554 | − | 13.5089i | −0.0386011 | − | 0.605958i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.4725i | − | 1.09554i | −0.836630 | − | 0.547769i | \(-0.815477\pi\) | ||
0.836630 | − | 0.547769i | \(-0.184523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.7132 | −0.657336 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.7444i | 1.10330i | 0.834077 | + | 0.551649i | \(0.186001\pi\) | ||||
−0.834077 | + | 0.551649i | \(0.813999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.388319 | − | 0.962502i | −0.0172800 | − | 0.0428308i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 33.7079i | − | 1.49702i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14.2465i | − | 0.631466i | −0.948848 | − | 0.315733i | \(-0.897750\pi\) | ||
0.948848 | − | 0.315733i | \(-0.102250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.5471 | − | 1.62742i | 1.13014 | − | 0.0719928i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.218134i | 0.00963087i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.40455 | − | 3.48138i | −0.0618920 | − | 0.153408i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.9392 | 1.27274 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.1879i | 1.06173i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1921i | 1.05987i | 0.848037 | + | 0.529937i | \(0.177784\pi\) | ||||
−0.848037 | + | 0.529937i | \(0.822216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.4422i | − | 1.59351i | −0.604306 | − | 0.796753i | \(-0.706549\pi\) | ||
0.604306 | − | 0.796753i | \(-0.293451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.2381 | + | 16.6607i | 0.795977 | + | 0.727134i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.9451 | 0.607457 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.18834 | 0.356015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.43888 | −0.149235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 58.6289i | 2.53950i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.8064 | − | 5.57016i | 0.596903 | − | 0.240819i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.0453 | 0.562947 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.78657 | − | 29.6000i | −0.163099 | − | 1.27496i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0685 | 0.733831 | 0.366916 | − | 0.930254i | \(-0.380414\pi\) | ||||
0.366916 | + | 0.930254i | \(0.380414\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.4863 | −1.69452 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.1598 | − | 10.9576i | 1.16340 | − | 0.469370i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.9460 | 1.36591 | 0.682955 | − | 0.730460i | \(-0.260694\pi\) | ||||
0.682955 | + | 0.730460i | \(0.260694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5.63648i | − | 0.240559i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0562760 | 0.00239744 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.992842 | + | 15.5856i | 0.0422200 | + | 0.662765i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.2532 | − | 15.4332i | 1.62376 | − | 0.655101i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 40.8312i | − | 1.73008i | −0.501707 | − | 0.865038i | \(-0.667294\pi\) | ||
0.501707 | − | 0.865038i | \(-0.332706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −69.2419 | −2.92862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0216 | 1.01419 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 19.7917i | − | 0.834120i | −0.908879 | − | 0.417060i | \(-0.863061\pi\) | ||
0.908879 | − | 0.417060i | \(-0.136939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5204 | − | 33.5121i | −0.568807 | − | 1.40987i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9945 | − | 1.71962i | 1.13366 | − | 0.0722174i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.8023 | 0.452856 | 0.226428 | − | 0.974028i | \(-0.427295\pi\) | ||||
0.226428 | + | 0.974028i | \(0.427295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.2186i | − | 0.720575i | −0.932841 | − | 0.360287i | \(-0.882679\pi\) | ||
0.932841 | − | 0.360287i | \(-0.117321\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.4613 | 1.23077 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.1056 | + | 19.3771i | −0.838462 | + | 0.808082i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.2572 | −1.30126 | −0.650628 | − | 0.759397i | \(-0.725494\pi\) | ||||
−0.650628 | + | 0.759397i | \(0.725494\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.26632 | 0.385095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.87041 | − | 29.3615i | −0.0775975 | − | 1.21812i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.3124 | 0.882671 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.62634 | − | 2.26993i | 0.232620 | − | 0.0938501i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.9549i | 1.15382i | 0.816808 | + | 0.576910i | \(0.195742\pi\) | ||||
−0.816808 | + | 0.576910i | \(0.804258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.214810 | 0.00885108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.6947 | −1.34488 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.6892 | −0.972800 | −0.486400 | − | 0.873736i | \(-0.661690\pi\) | ||||
−0.486400 | + | 0.873736i | \(0.661690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0977 | + | 7.71840i | −0.659940 | + | 0.316423i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.8788i | 0.568023i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9.76391i | − | 0.398942i | −0.979904 | − | 0.199471i | \(-0.936078\pi\) | ||
0.979904 | − | 0.199471i | \(-0.0639224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.3030i | − | 0.624221i | −0.950046 | − | 0.312110i | \(-0.898964\pi\) | ||
0.950046 | − | 0.312110i | \(-0.101036\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.24182 | −0.132017 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.8753 | − | 6.00139i | 0.604766 | − | 0.243991i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4718i | 0.627982i | 0.949426 | + | 0.313991i | \(0.101666\pi\) | ||||
−0.949426 | + | 0.313991i | \(0.898334\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.380255 | − | 5.96922i | −0.0154087 | − | 0.241885i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.8276i | 1.53034i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.87239i | − | 0.358352i | −0.983817 | − | 0.179176i | \(-0.942657\pi\) | ||
0.983817 | − | 0.179176i | \(-0.0573432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −40.7408 | + | 16.4368i | −1.64283 | + | 0.662794i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16.9225i | − | 0.681274i | −0.940195 | − | 0.340637i | \(-0.889357\pi\) | ||
0.940195 | − | 0.340637i | \(-0.110643\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.3878 | −0.899841 | −0.449921 | − | 0.893069i | \(-0.648548\pi\) | ||||
−0.449921 | + | 0.893069i | \(0.648548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.2075i | 1.05167i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.255477 | − | 4.01045i | −0.0102355 | − | 0.160675i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.922223 | − | 24.9830i | 0.0368889 | − | 0.999319i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.370028 | 0.0147775 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.8107i | 1.18863i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5691i | 0.818844i | 0.912345 | + | 0.409422i | \(0.134270\pi\) | ||||
−0.912345 | + | 0.409422i | \(0.865730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −40.7156 | −1.61830 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.4297 | + | 7.03196i | −0.691676 | + | 0.279055i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.6914 | − | 4.94957i | 1.53301 | − | 0.196109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2.49114i | − | 0.0985479i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.4936 | −0.453969 | −0.226985 | − | 0.973898i | \(-0.572887\pi\) | ||||
−0.226985 | + | 0.973898i | \(0.572887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7105i | 0.935051i | 0.883980 | + | 0.467525i | \(0.154854\pi\) | ||||
−0.883980 | + | 0.467525i | \(0.845146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.4121 | − | 48.1157i | −0.764352 | − | 1.89455i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 22.3311i | − | 0.877926i | −0.898505 | − | 0.438963i | \(-0.855346\pi\) | ||
0.898505 | − | 0.438963i | \(-0.144654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.1085i | − | 1.18186i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.45146 | − | 22.7849i | −0.0568873 | − | 0.893012i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.8441i | − | 0.580896i | −0.956891 | − | 0.290448i | \(-0.906196\pi\) | ||
0.956891 | − | 0.290448i | \(-0.0938043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.32402 | − | 0.937619i | 0.0908069 | − | 0.0366358i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.71106 | 0.183796 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.04938i | 0.352514i | 0.984344 | + | 0.176257i | \(0.0563990\pi\) | ||||
−0.984344 | + | 0.176257i | \(0.943601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 26.4095i | − | 1.02721i | −0.858027 | − | 0.513605i | \(-0.828310\pi\) | ||
0.858027 | − | 0.513605i | \(-0.171690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 31.3996i | 1.21946i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.247968 | + | 0.118894i | −0.00961579 | + | 0.00461051i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.76120 | 0.261795 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.8165 | 1.34608 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.3491 | 1.90510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 46.7468i | − | 1.80196i | −0.433865 | − | 0.900978i | \(-0.642851\pi\) | ||
0.433865 | − | 0.900978i | \(-0.357149\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.2825 | − | 16.8947i | −0.626715 | − | 0.650276i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1268 | −0.504504 | −0.252252 | − | 0.967662i | \(-0.581171\pi\) | ||||
−0.252252 | + | 0.967662i | \(0.581171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.96769 | − | 0.507563i | 0.305772 | − | 0.0194785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.1986 | 0.888971 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.9102 | 0.953162 | 0.476581 | − | 0.879130i | \(-0.341876\pi\) | ||||
0.476581 | + | 0.879130i | \(0.341876\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.57389 | + | 8.85838i | 0.136551 | + | 0.338461i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9251 | 0.645734 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.8583i | 1.06132i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.2251 | 1.41611 | 0.708054 | − | 0.706158i | \(-0.249573\pi\) | ||||
0.708054 | + | 0.706158i | \(0.249573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.349135 | − | 5.48069i | −0.0132625 | − | 0.208194i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.766794 | + | 0.309361i | −0.0290861 | + | 0.0117347i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 31.7493i | − | 1.20259i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.54956 | 0.0964333 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1857 | −0.384709 | −0.192355 | − | 0.981326i | \(-0.561612\pi\) | ||||
−0.192355 | + | 0.981326i | \(0.561612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.459203i | 0.0173192i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.2861 | + | 10.6051i | −0.989991 | + | 0.399409i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.0780712 | − | 1.22556i | −0.00293617 | − | 0.0460918i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.7016 | 1.86658 | 0.933291 | − | 0.359121i | \(-0.116924\pi\) | ||||
0.933291 | + | 0.359121i | \(0.116924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.87409i | 0.107787i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.8080 | 0.966517 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.8740 | + | 49.2603i | 0.743244 | + | 1.84223i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.5722 | −1.40316 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2407 | −0.680263 | −0.340131 | − | 0.940378i | \(-0.610472\pi\) | ||||
−0.340131 | + | 0.940378i | \(0.610472\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.282384 | − | 4.43285i | −0.0105165 | − | 0.165088i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.72992 | 0.250289 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.35862 | + | 4.20069i | −0.161875 | + | 0.156010i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.5072i | 1.46524i | 0.680637 | + | 0.732621i | \(0.261703\pi\) | ||||
−0.680637 | + | 0.732621i | \(0.738297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.3108 | −0.789288 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.4965 | 1.38686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6704 | 0.726545 | 0.363272 | − | 0.931683i | \(-0.381659\pi\) | ||||
0.363272 | + | 0.931683i | \(0.381659\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.2866 | + | 25.4987i | 0.526971 | + | 0.940534i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 28.3832i | − | 1.04551i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 3.40360i | − | 0.125204i | −0.998039 | − | 0.0626018i | \(-0.980060\pi\) | ||
0.998039 | − | 0.0626018i | \(-0.0199398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.483678i | 0.0177684i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.21886 | 0.191462 | 0.0957308 | − | 0.995407i | \(-0.469481\pi\) | ||||
0.0957308 | + | 0.995407i | \(0.469481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.2949 | − | 13.8362i | 1.25647 | − | 0.506919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 5.41446i | − | 0.198105i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.5797 | − | 1.11988i | 0.642349 | − | 0.0409194i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.17145i | − | 0.115728i | −0.998324 | − | 0.0578640i | \(-0.981571\pi\) | ||
0.998324 | − | 0.0578640i | \(-0.0184290\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 40.7653i | 1.48557i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.54078 | + | 3.81903i | 0.0560746 | + | 0.138989i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3380i | 0.993615i | 0.867861 | + | 0.496808i | \(0.165495\pi\) | ||||
−0.867861 | + | 0.496808i | \(0.834505\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44.4565 | 1.61367 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.9547i | − | 0.723356i | −0.932303 | − | 0.361678i | \(-0.882204\pi\) | ||
0.932303 | − | 0.361678i | \(-0.117796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.5827 | − | 2.20301i | 1.25198 | − | 0.0797543i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.04683 | + | 1.22923i | −0.110158 | + | 0.0444431i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.3560 | 1.42106 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8811i | 0.392384i | 0.980566 | + | 0.196192i | \(0.0628576\pi\) | ||||
−0.980566 | + | 0.196192i | \(0.937142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 39.3110i | − | 1.41575i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.5968 | 1.64000 | 0.820002 | − | 0.572360i | \(-0.193972\pi\) | ||||
0.820002 | + | 0.572360i | \(0.193972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.6372 | + | 16.0343i | −0.597625 | + | 0.575971i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 48.7079 | − | 3.10282i | 1.74739 | − | 0.111313i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 0.489065i | − | 0.0175226i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.8107 | 0.780448 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.68141i | 0.203037i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2752 | − | 5.75927i | 0.509502 | − | 0.205557i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.0781i | − | 0.893937i | −0.894550 | − | 0.446969i | \(-0.852504\pi\) | ||
0.894550 | − | 0.446969i | \(-0.147496\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.07104i | 0.180534i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.71826 | − | 42.6711i | −0.0966503 | − | 1.51721i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.5062i | 2.29068i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.3586 | + | 7.81016i | −0.686577 | + | 0.276998i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.1965 | −0.963350 | −0.481675 | − | 0.876350i | \(-0.659971\pi\) | ||||
−0.481675 | + | 0.876350i | \(0.659971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20.4847i | − | 0.724698i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 0.739555i | − | 0.0261309i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.2468i | 1.45557i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.7918 | + | 14.2843i | −1.05002 | + | 0.503457i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.5366 | −1.70857 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.4489 | −1.28148 | −0.640738 | − | 0.767760i | \(-0.721371\pi\) | ||||
−0.640738 | + | 0.767760i | \(0.721371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.2471 | −0.886546 | −0.443273 | − | 0.896387i | \(-0.646183\pi\) | ||||
−0.443273 | + | 0.896387i | \(0.646183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.5201i | 1.66660i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.18775 | + | 3.30333i | −0.286804 | + | 0.115710i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.577596 | 0.0202075 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.16403 | − | 0.456368i | 0.250331 | − | 0.0159468i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2810 | 0.463510 | 0.231755 | − | 0.972774i | \(-0.425553\pi\) | ||||
0.231755 | + | 0.972774i | \(0.425553\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.7856 | 0.654824 | 0.327412 | − | 0.944882i | \(-0.393823\pi\) | ||||
0.327412 | + | 0.944882i | \(0.393823\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.6589 | + | 27.6205i | −0.997776 | + | 0.961623i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0550 | −1.56672 | −0.783358 | − | 0.621571i | \(-0.786495\pi\) | ||||
−0.783358 | + | 0.621571i | \(0.786495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.20136i | − | 0.111188i | −0.998453 | − | 0.0555939i | \(-0.982295\pi\) | ||
0.998453 | − | 0.0555939i | \(-0.0177052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.8901 | 0.551222 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.9525 | + | 2.68034i | −0.725962 | + | 0.0928683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.59191 | + | 16.3390i | 0.228123 | + | 0.565433i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.6864i | 0.749590i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.11067 | 0.107392 | 0.0536962 | − | 0.998557i | \(-0.482900\pi\) | ||||
0.0536962 | + | 0.998557i | \(0.482900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5343 | −0.949457 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.9249i | 0.651808i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37.4326 | + | 15.1021i | −1.28772 | + | 0.519527i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9407 | − | 1.20658i | 0.650811 | − | 0.0414584i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.3817 | −0.871099 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.1703i | 1.89121i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1854 | −0.588416 | −0.294208 | − | 0.955741i | \(-0.595056\pi\) | ||||
−0.294208 | + | 0.955741i | \(0.595056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0469333 | + | 0.0189351i | −0.00160508 | + | 0.000647567i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.3754 | −1.10592 | −0.552961 | − | 0.833207i | \(-0.686502\pi\) | ||||
−0.552961 | + | 0.833207i | \(0.686502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.4040 | −1.00325 | −0.501626 | − | 0.865085i | \(-0.667264\pi\) | ||||
−0.501626 | + | 0.865085i | \(0.667264\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −51.8753 | + | 3.30460i | −1.76791 | + | 0.112620i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.0664 | 1.02347 | 0.511736 | − | 0.859143i | \(-0.329003\pi\) | ||||
0.511736 | + | 0.859143i | \(0.329003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.8606 | − | 10.8368i | 0.913287 | − | 0.368463i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7407i | 0.500622i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.1635 | −0.853614 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.1008 | 1.25711 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.46930 | 0.0497282 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.3305 | − | 27.7179i | 0.349236 | − | 0.937035i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.9614i | − | 1.14679i | −0.819278 | − | 0.573397i | \(-0.805625\pi\) | ||
0.819278 | − | 0.573397i | \(-0.194375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.7290i | 1.13765i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.07536i | 0.0362299i | 0.999836 | + | 0.0181149i | \(0.00576648\pi\) | ||||
−0.999836 | + | 0.0181149i | \(0.994234\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0500 | −0.876653 | −0.438327 | − | 0.898816i | \(-0.644429\pi\) | ||||
−0.438327 | + | 0.898816i | \(0.644429\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.0336 | + | 27.3482i | 0.370889 | + | 0.919299i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 28.1243i | − | 0.944320i | −0.881513 | − | 0.472160i | \(-0.843474\pi\) | ||
0.881513 | − | 0.472160i | \(-0.156526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.1932 | + | 1.41377i | −0.744338 | + | 0.0474163i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.5837i | 1.46011i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 0.315546i | − | 0.0105594i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.84466 | − | 14.4868i | −0.195366 | − | 0.484240i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 58.1108i | 1.94026i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.59481 | 0.186597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.0861i | − | 0.502591i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.90280 | − | 61.2658i | −0.129877 | − | 2.03880i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.6910 | + | 43.8495i | 0.588067 | + | 1.45761i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.9347 | −1.12678 | −0.563391 | − | 0.826190i | \(-0.690504\pi\) | ||||
−0.563391 | + | 0.826190i | \(0.690504\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 0.226001i | − | 0.00749598i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.8703i | − | 0.691465i | −0.938333 | − | 0.345732i | \(-0.887631\pi\) | ||
0.938333 | − | 0.345732i | \(-0.112369\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.4053 | 1.56889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −44.8249 | + | 18.0845i | −1.48186 | + | 0.597855i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.95918 | − | 0.188508i | 0.0977207 | − | 0.00622507i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.6755i | − | 1.17682i | −0.808561 | − | 0.588412i | \(-0.799753\pi\) | ||
0.808561 | − | 0.588412i | \(-0.200247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.6947 | 1.14323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.5096i | 0.938406i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.2770 | − | 35.5656i | −1.12702 | − | 1.16939i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.817448i | − | 0.0268485i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.6649i | 1.62945i | 0.579847 | + | 0.814726i | \(0.303112\pi\) | ||||
−0.579847 | + | 0.814726i | \(0.696888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.322752 | + | 0.0412879i | −0.0105778 | + | 0.00135316i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.8554i | 0.748252i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.7623 | − | 26.6759i | −0.351966 | − | 0.872396i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.12715 | −0.265503 | −0.132751 | − | 0.991149i | \(-0.542381\pi\) | ||||
−0.132751 | + | 0.991149i | \(0.542381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 43.2303i | − | 1.41077i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.1049i | 0.753198i | 0.926376 | + | 0.376599i | \(0.122907\pi\) | ||||
−0.926376 | + | 0.376599i | \(0.877093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 58.7580i | − | 1.91342i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.0031 | − | 25.0339i | −0.390460 | − | 0.814353i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.2578 | 1.56817 | 0.784084 | − | 0.620655i | \(-0.213133\pi\) | ||||
0.784084 | + | 0.620655i | \(0.213133\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.9154 | −1.75017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.88291 | −0.158339 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.9217i | − | 1.71430i | −0.515066 | − | 0.857151i | \(-0.672233\pi\) | ||
0.515066 | − | 0.857151i | \(-0.327767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.1995 | − | 32.7168i | −0.427126 | − | 1.05869i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.63754 | 0.311537 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.718528 | + | 11.2794i | 0.0232025 | + | 0.364231i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.64418 | −0.311102 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.24182 | 0.104466 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.15157 | − | 10.2902i | −0.133644 | − | 0.331254i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.36043 | −0.268853 | −0.134427 | − | 0.990924i | \(-0.542919\pi\) | ||||
−0.134427 | + | 0.990924i | \(0.542919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 0.261926i | − | 0.00841428i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.4955 | 1.42793 | 0.713964 | − | 0.700183i | \(-0.246898\pi\) | ||||
0.713964 | + | 0.700183i | \(0.246898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.976360 | + | 0.0621968i | −0.0313007 | + | 0.00199394i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36.1039 | − | 37.4612i | −1.15625 | − | 1.19972i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 15.9555i | − | 0.510461i | −0.966880 | − | 0.255231i | \(-0.917849\pi\) | ||
0.966880 | − | 0.255231i | \(-0.0821514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.47503 | 0.206943 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.37728 | 0.203611 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 48.5017i | − | 1.54696i | −0.633818 | − | 0.773482i | \(-0.718513\pi\) | ||
0.633818 | − | 0.773482i | \(-0.281487\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6481 | + | 36.3074i | 0.466728 | + | 1.15685i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.4701 | + | 2.13214i | −1.06537 | + | 0.0678667i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69.3944 | 2.20661 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4999i | 1.60418i | 0.597202 | + | 0.802091i | \(0.296279\pi\) | ||||
−0.597202 | + | 0.802091i | \(0.703721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.9657 | −0.760529 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4124 | − | 6.21810i | 0.488607 | − | 0.197127i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.0833 | −1.14277 | −0.571384 | − | 0.820683i | \(-0.693593\pi\) | ||||
−0.571384 | + | 0.820683i | \(0.693593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −46.3594 | −1.46675 |
(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 | 2240.2.e.g.2239.9 | 48 | ||
4.3 | odd | 2 | inner | 2240.2.e.g.2239.40 | 48 | ||
5.4 | even | 2 | inner | 2240.2.e.g.2239.6 | 48 | ||
7.6 | odd | 2 | inner | 2240.2.e.g.2239.44 | 48 | ||
8.3 | odd | 2 | 1120.2.e.a.1119.43 | yes | 48 | ||
8.5 | even | 2 | 1120.2.e.a.1119.6 | yes | 48 | ||
20.19 | odd | 2 | inner | 2240.2.e.g.2239.43 | 48 | ||
28.27 | even | 2 | inner | 2240.2.e.g.2239.5 | 48 | ||
35.34 | odd | 2 | inner | 2240.2.e.g.2239.39 | 48 | ||
40.19 | odd | 2 | 1120.2.e.a.1119.40 | yes | 48 | ||
40.29 | even | 2 | 1120.2.e.a.1119.9 | yes | 48 | ||
56.13 | odd | 2 | 1120.2.e.a.1119.39 | yes | 48 | ||
56.27 | even | 2 | 1120.2.e.a.1119.10 | yes | 48 | ||
140.139 | even | 2 | inner | 2240.2.e.g.2239.10 | 48 | ||
280.69 | odd | 2 | 1120.2.e.a.1119.44 | yes | 48 | ||
280.139 | even | 2 | 1120.2.e.a.1119.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.e.a.1119.5 | ✓ | 48 | 280.139 | even | 2 | ||
1120.2.e.a.1119.6 | yes | 48 | 8.5 | even | 2 | ||
1120.2.e.a.1119.9 | yes | 48 | 40.29 | even | 2 | ||
1120.2.e.a.1119.10 | yes | 48 | 56.27 | even | 2 | ||
1120.2.e.a.1119.39 | yes | 48 | 56.13 | odd | 2 | ||
1120.2.e.a.1119.40 | yes | 48 | 40.19 | odd | 2 | ||
1120.2.e.a.1119.43 | yes | 48 | 8.3 | odd | 2 | ||
1120.2.e.a.1119.44 | yes | 48 | 280.69 | odd | 2 | ||
2240.2.e.g.2239.5 | 48 | 28.27 | even | 2 | inner | ||
2240.2.e.g.2239.6 | 48 | 5.4 | even | 2 | inner | ||
2240.2.e.g.2239.9 | 48 | 1.1 | even | 1 | trivial | ||
2240.2.e.g.2239.10 | 48 | 140.139 | even | 2 | inner | ||
2240.2.e.g.2239.39 | 48 | 35.34 | odd | 2 | inner | ||
2240.2.e.g.2239.40 | 48 | 4.3 | odd | 2 | inner | ||
2240.2.e.g.2239.43 | 48 | 20.19 | odd | 2 | inner | ||
2240.2.e.g.2239.44 | 48 | 7.6 | odd | 2 | inner |