Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1839,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1839");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.m (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1839.1 | ||
Character | \(\chi\) | \(=\) | 1840.1839 |
Dual form | 1840.2.m.g.1839.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.28652 | −1.89747 | −0.948737 | − | 0.316068i | \(-0.897637\pi\) | ||||
−0.948737 | + | 0.316068i | \(0.897637\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.54120 | + | 1.62009i | 0.689246 | + | 0.724527i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.73174i | 1.03250i | 0.856438 | + | 0.516250i | \(0.172672\pi\) | ||||
−0.856438 | + | 0.516250i | \(0.827328\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.80121 | 2.60040 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.28639 | −0.689372 | −0.344686 | − | 0.938718i | \(-0.612015\pi\) | ||||
−0.344686 | + | 0.938718i | \(0.612015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.92586i | − | 1.36619i | −0.730331 | − | 0.683094i | \(-0.760634\pi\) | ||
0.730331 | − | 0.683094i | \(-0.239366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.06519 | − | 5.32446i | −1.30783 | − | 1.37477i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.97341 | −1.44876 | −0.724382 | − | 0.689398i | \(-0.757875\pi\) | ||||
−0.724382 | + | 0.689398i | \(0.757875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.377877 | 0.0866910 | 0.0433455 | − | 0.999060i | \(-0.486198\pi\) | ||||
0.0433455 | + | 0.999060i | \(0.486198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 8.97791i | − | 1.95914i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.582385 | − | 4.76034i | −0.121436 | − | 0.992599i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.249397 | + | 4.99378i | −0.0498794 | + | 0.998755i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.7793 | −3.03672 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70400 | 0.687815 | 0.343907 | − | 0.939004i | \(-0.388249\pi\) | ||||
0.343907 | + | 0.939004i | \(0.388249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.89324i | 0.519641i | 0.965657 | + | 0.259820i | \(0.0836634\pi\) | ||||
−0.965657 | + | 0.259820i | \(0.916337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.51426 | 1.30806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.42567 | + | 4.21016i | −0.748074 | + | 0.711647i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.23320 | −1.18913 | −0.594566 | − | 0.804047i | \(-0.702676\pi\) | ||||
−0.594566 | + | 0.804047i | \(0.702676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.1889i | 2.59230i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.451624 | 0.0705318 | 0.0352659 | − | 0.999378i | \(-0.488772\pi\) | ||||
0.0352659 | + | 0.999378i | \(0.488772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.359476i | − | 0.0548196i | −0.999624 | − | 0.0274098i | \(-0.991274\pi\) | ||
0.999624 | − | 0.0274098i | \(-0.00872591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.0232 | + | 12.6387i | 1.79232 | + | 1.88406i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1733 | 1.77565 | 0.887826 | − | 0.460179i | \(-0.152215\pi\) | ||||
0.887826 | + | 0.460179i | \(0.152215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.462395 | −0.0660565 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.6317 | 2.74899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.69298 | −1.33143 | −0.665716 | − | 0.746205i | \(-0.731874\pi\) | ||||
−0.665716 | + | 0.746205i | \(0.731874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.52378 | − | 3.70416i | −0.475147 | − | 0.499468i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.24190 | −0.164494 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 10.7427i | − | 1.39858i | −0.714838 | − | 0.699290i | \(-0.753500\pi\) | ||
0.714838 | − | 0.699290i | \(-0.246500\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.73249i | − | 0.862007i | −0.902350 | − | 0.431003i | \(-0.858160\pi\) | ||
0.902350 | − | 0.431003i | \(-0.141840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 21.3109i | 2.68492i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.98034 | − | 7.59174i | 0.989840 | − | 0.941639i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.06480i | 0.863103i | 0.902088 | + | 0.431551i | \(0.142034\pi\) | ||||
−0.902088 | + | 0.431551i | \(0.857966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.91402 | + | 15.6449i | 0.230421 | + | 1.88343i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.34667i | − | 0.871889i | −0.899974 | − | 0.435945i | \(-0.856414\pi\) | ||
0.899974 | − | 0.435945i | \(-0.143586\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.24543i | 0.145767i | 0.997340 | + | 0.0728834i | \(0.0232201\pi\) | ||||
−0.997340 | + | 0.0728834i | \(0.976780\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.819647 | − | 16.4121i | 0.0946447 | − | 1.89511i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 6.24581i | − | 0.711776i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6417 | −1.53481 | −0.767405 | − | 0.641163i | \(-0.778452\pi\) | ||||
−0.767405 | + | 0.641163i | \(0.778452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.4553 | 3.16170 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.1841i | − | 1.66667i | −0.552768 | − | 0.833335i | \(-0.686429\pi\) | ||
0.552768 | − | 0.833335i | \(-0.313571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.20623 | − | 9.67748i | −0.998556 | − | 1.04967i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.1733 | −1.30511 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1526i | 1.28818i | 0.764951 | + | 0.644089i | \(0.222763\pi\) | ||||
−0.764951 | + | 0.644089i | \(0.777237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.4562 | 1.41059 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.50868i | − | 0.986004i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.582385 | + | 0.612196i | 0.0597514 | + | 0.0628100i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.34220 | 0.440883 | 0.220442 | − | 0.975400i | \(-0.429250\pi\) | ||||
0.220442 | + | 0.975400i | \(0.429250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.8366 | −1.79264 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.11922 | 0.310374 | 0.155187 | − | 0.987885i | \(-0.450402\pi\) | ||||
0.155187 | + | 0.987885i | \(0.450402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.38893i | − | 0.333921i | −0.985964 | − | 0.166960i | \(-0.946605\pi\) | ||
0.985964 | − | 0.166960i | \(-0.0533952\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.5450 | − | 13.8368i | 1.41945 | − | 1.35033i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.94818i | − | 0.768380i | −0.923254 | − | 0.384190i | \(-0.874481\pi\) | ||
0.923254 | − | 0.384190i | \(-0.125519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.1195i | − | 1.35240i | −0.736718 | − | 0.676200i | \(-0.763625\pi\) | ||
0.736718 | − | 0.676200i | \(-0.236375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.7721 | 2.25634 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.322974 | 0.0303828 | 0.0151914 | − | 0.999885i | \(-0.495164\pi\) | ||||
0.0151914 | + | 0.999885i | \(0.495164\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.81462 | − | 8.28016i | 0.635466 | − | 0.772129i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 38.4277i | − | 3.55264i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.3178i | − | 1.49585i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.77244 | −0.524767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.48427 | −0.133832 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.47475 | + | 7.29237i | −0.758005 | + | 0.652249i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5340 | 0.934738 | 0.467369 | − | 0.884062i | \(-0.345202\pi\) | ||||
0.467369 | + | 0.884062i | \(0.345202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.18143i | 0.104019i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.3581i | − | 0.992362i | −0.868219 | − | 0.496181i | \(-0.834735\pi\) | ||
0.868219 | − | 0.496181i | \(-0.165265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.03226i | 0.0895084i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.3190 | − | 25.5639i | −2.09305 | − | 2.20019i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.0252 | 1.62543 | 0.812716 | − | 0.582660i | \(-0.197988\pi\) | ||||
0.812716 | + | 0.582660i | \(0.197988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.12171i | − | 0.773693i | −0.922144 | − | 0.386847i | \(-0.873564\pi\) | ||
0.922144 | − | 0.386847i | \(-0.126436\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −40.0076 | −3.36925 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2624i | 0.941810i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.70860 | + | 6.00081i | 0.474074 | + | 0.498341i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.51967 | 0.125340 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.95344i | 0.487725i | 0.969810 | + | 0.243863i | \(0.0784146\pi\) | ||||
−0.969810 | + | 0.243863i | \(0.921585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9.94683i | − | 0.809462i | −0.914436 | − | 0.404731i | \(-0.867365\pi\) | ||
0.914436 | − | 0.404731i | \(-0.132635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −46.5998 | −3.76737 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.68731 | + | 4.45906i | −0.376494 | + | 0.358160i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2147 | 1.29407 | 0.647036 | − | 0.762460i | \(-0.276008\pi\) | ||||
0.647036 | + | 0.762460i | \(0.276008\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.8562 | 2.52636 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.0040 | − | 1.59092i | 1.02486 | − | 0.125382i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1754 | 1.11030 | 0.555151 | − | 0.831750i | \(-0.312661\pi\) | ||||
0.555151 | + | 0.831750i | \(0.312661\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.5810 | + | 12.1738i | 0.901578 | + | 0.947728i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.85134 | 0.684937 | 0.342468 | − | 0.939529i | \(-0.388737\pi\) | ||||
0.342468 | + | 0.939529i | \(0.388737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2641 | −0.866467 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.94790 | 0.225432 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 24.2863i | − | 1.84645i | −0.384260 | − | 0.923225i | \(-0.625543\pi\) | ||
0.384260 | − | 0.923225i | \(-0.374457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.6417 | − | 0.681287i | −1.03121 | − | 0.0515004i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35.3061i | 2.65377i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8358i | 1.10888i | 0.832223 | + | 0.554441i | \(0.187068\pi\) | ||||
−0.832223 | + | 0.554441i | \(0.812932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.42685i | − | 0.254716i | −0.991857 | − | 0.127358i | \(-0.959350\pi\) | ||
0.991857 | − | 0.127358i | \(-0.0406497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.1265i | 1.63563i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.1478 | − | 11.7185i | −0.819604 | − | 0.861558i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6575 | 0.998737 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 43.1049i | − | 3.13542i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.37462 | 0.678324 | 0.339162 | − | 0.940728i | \(-0.389857\pi\) | ||||
0.339162 | + | 0.940728i | \(0.389857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.72975i | − | 0.124510i | −0.998060 | − | 0.0622550i | \(-0.980171\pi\) | ||
0.998060 | − | 0.0622550i | \(-0.0198292\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.2276 | + | 24.9504i | −1.87819 | + | 1.78673i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8158i | 1.12683i | 0.826174 | + | 0.563415i | \(0.190513\pi\) | ||||
−0.826174 | + | 0.563415i | \(0.809487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9550 | −1.41458 | −0.707288 | − | 0.706926i | \(-0.750082\pi\) | ||||
−0.707288 | + | 0.706926i | \(0.750082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 23.2186i | − | 1.63771i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1183i | 0.710169i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.696043 | + | 0.731672i | 0.0486138 | + | 0.0511022i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.54331 | − | 37.1364i | −0.315782 | − | 2.58116i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.863973 | −0.0597623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0013i | 1.30810i | 0.756449 | + | 0.654052i | \(0.226932\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.1450i | 1.65439i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.582385 | − | 0.554025i | 0.0397183 | − | 0.0377842i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.90357 | −0.536529 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 4.09314i | − | 0.276588i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.4242i | 1.97928i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.87457 | −0.125531 | −0.0627653 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627653 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.94560 | + | 38.9575i | −0.129706 | + | 2.59717i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.18877i | 0.344391i | 0.985063 | + | 0.172195i | \(0.0550860\pi\) | ||||
−0.985063 | + | 0.172195i | \(0.944914\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.8023i | − | 1.04425i | −0.852870 | − | 0.522124i | \(-0.825140\pi\) | ||
0.852870 | − | 0.522124i | \(-0.174860\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.5270i | 1.35058i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.6477i | − | 0.959603i | −0.877377 | − | 0.479802i | \(-0.840709\pi\) | ||
0.877377 | − | 0.479802i | \(-0.159291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.7614 | + | 19.7218i | 1.22386 | + | 1.28651i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 44.8337 | 2.91226 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.60182i | − | 0.621090i | −0.950559 | − | 0.310545i | \(-0.899488\pi\) | ||
0.950559 | − | 0.310545i | \(-0.100512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.8553i | − | 1.21458i | −0.794481 | − | 0.607289i | \(-0.792257\pi\) | ||
0.794481 | − | 0.607289i | \(-0.207743\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −46.1810 | −2.96251 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.712644 | − | 0.749123i | −0.0455292 | − | 0.0478597i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.86137i | − | 0.118436i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 49.9028i | 3.16246i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9057 | 1.57203 | 0.786017 | − | 0.618205i | \(-0.212140\pi\) | ||||
0.786017 | + | 0.618205i | \(0.212140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.33156 | + | 10.8840i | 0.0837143 | + | 0.684270i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 30.2565 | + | 31.8052i | 1.89473 | + | 1.99172i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.5764i | − | 1.03401i | −0.855983 | − | 0.517004i | \(-0.827047\pi\) | ||
0.855983 | − | 0.517004i | \(-0.172953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.7592i | − | 1.22778i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.8957 | 1.78860 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7754i | 1.09608i | 0.836453 | + | 0.548039i | \(0.184626\pi\) | ||||
−0.836453 | + | 0.548039i | \(0.815374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9388 | − | 15.7035i | −0.917685 | − | 0.964659i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 39.9399i | − | 2.44428i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.2884 | −1.11506 | −0.557532 | − | 0.830155i | \(-0.688252\pi\) | ||||
−0.557532 | + | 0.830155i | \(0.688252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.44481i | − | 0.512986i | −0.966546 | − | 0.256493i | \(-0.917433\pi\) | ||
0.966546 | − | 0.256493i | \(-0.0825670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −44.2239 | −2.67655 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.570218 | − | 11.4177i | 0.0343854 | − | 0.688513i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.9612i | 1.68003i | 0.542565 | + | 0.840014i | \(0.317453\pi\) | ||||
−0.542565 | + | 0.840014i | \(0.682547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.5708i | 1.35128i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.3900i | − | 1.69360i | −0.531909 | − | 0.846802i | \(-0.678525\pi\) | ||
0.531909 | − | 0.846802i | \(-0.321475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.11525i | − | 0.541845i | −0.962601 | − | 0.270923i | \(-0.912671\pi\) | ||
0.962601 | − | 0.270923i | \(-0.0873288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.91402 | − | 2.01199i | −0.113377 | − | 0.119180i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.23372i | 0.0728241i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.6816 | 1.09892 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2707 | −0.836564 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.14021 | −0.300294 | −0.150147 | − | 0.988664i | \(-0.547975\pi\) | ||||
−0.150147 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4042 | − | 16.5567i | 1.01331 | − | 0.963966i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 36.0775 | 2.09343 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.4488 | + | 2.86874i | −1.35608 | + | 0.165904i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.981995 | 0.0566013 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.2514 | −0.588927 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9072 | − | 10.3761i | 0.624547 | − | 0.594135i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0988 | −0.918806 | −0.459403 | − | 0.888228i | \(-0.651937\pi\) | ||||
−0.459403 | + | 0.888228i | \(0.651937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1378i | 0.633606i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 13.6114i | − | 0.771834i | −0.922534 | − | 0.385917i | \(-0.873885\pi\) | ||
0.922534 | − | 0.385917i | \(-0.126115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7024 | 0.944073 | 0.472037 | − | 0.881579i | \(-0.343519\pi\) | ||||
0.472037 | + | 0.881579i | \(0.343519\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.5256 | + | 32.8443i | −1.94530 | + | 1.85057i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.1290i | − | 1.35522i | −0.735423 | − | 0.677609i | \(-0.763016\pi\) | ||
0.735423 | − | 0.677609i | \(-0.236984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.46877 | −0.474160 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1219i | 1.45798i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.25722 | −0.125595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.5986 | + | 1.22849i | 1.36449 | + | 0.0681445i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.4039i | 2.56614i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.2542i | 1.83336i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.49579i | 0.521936i | 0.965348 | + | 0.260968i | \(0.0840416\pi\) | ||||
−0.965348 | + | 0.260968i | \(0.915958\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −56.4278 | −3.09222 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.4456 | + | 10.8883i | −0.625341 | + | 0.594890i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.95485 | −0.542275 | −0.271138 | − | 0.962541i | \(-0.587400\pi\) | ||||
−0.271138 | + | 0.962541i | \(0.587400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.06146 | −0.0576506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.61506i | − | 0.358226i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8590i | 0.964297i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.3964 | + | 27.2129i | −1.20578 | + | 1.46509i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.5546 | −1.53289 | −0.766446 | − | 0.642309i | \(-0.777977\pi\) | ||||
−0.766446 | + | 0.642309i | \(0.777977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7060 | 0.626610 | 0.313305 | − | 0.949652i | \(-0.398564\pi\) | ||||
0.313305 | + | 0.949652i | \(0.398564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 77.7265i | 4.14873i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6128i | 0.564864i | 0.959287 | + | 0.282432i | \(0.0911411\pi\) | ||||
−0.959287 | + | 0.282432i | \(0.908859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9023 | − | 11.3227i | 0.631707 | − | 0.600946i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 53.6288i | 2.83833i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.7030 | 0.881548 | 0.440774 | − | 0.897618i | \(-0.354704\pi\) | ||||
0.440774 | + | 0.897618i | \(0.354704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8572 | −0.992485 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.9712 | 0.995731 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.01771 | + | 1.91946i | −0.105612 | + | 0.100469i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.96080i | 0.102353i | 0.998690 | + | 0.0511764i | \(0.0162971\pi\) | ||||
−0.998690 | + | 0.0511764i | \(0.983703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52321 | 0.183411 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 26.4787i | − | 1.37470i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.3228 | −1.62183 | −0.810916 | − | 0.585163i | \(-0.801031\pi\) | ||||
−0.810916 | + | 0.585163i | \(0.801031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.8524 | − | 23.9665i | 1.43829 | − | 1.23763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 18.2454i | − | 0.939684i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.853853 | −0.0438595 | −0.0219297 | − | 0.999760i | \(-0.506981\pi\) | ||||
−0.0219297 | + | 0.999760i | \(0.506981\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.6201 | −1.77364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.33128i | 0.119123i | 0.998225 | + | 0.0595614i | \(0.0189702\pi\) | ||||
−0.998225 | + | 0.0595614i | \(0.981030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1188 | − | 9.62605i | 0.515701 | − | 0.490589i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.80435i | − | 0.142553i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10.4152i | − | 0.528074i | −0.964513 | − | 0.264037i | \(-0.914946\pi\) | ||
0.964513 | − | 0.264037i | \(-0.0850541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.47882 | + | 28.4355i | 0.175932 | + | 1.43804i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.3286i | 1.88298i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.0246 | − | 22.1008i | −1.05786 | − | 1.11201i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.63854i | 0.483745i | 0.970308 | + | 0.241872i | \(0.0777615\pi\) | ||||
−0.970308 | + | 0.241872i | \(0.922238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 3.39255i | − | 0.169840i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 18.4820i | − | 0.922947i | −0.887154 | − | 0.461473i | \(-0.847321\pi\) | ||
0.887154 | − | 0.461473i | \(-0.152679\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.2517 | 0.709927 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 43.8553 | + | 46.1002i | 2.17919 | + | 2.29074i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.5379 | 0.819753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0001 | −1.28562 | −0.642811 | − | 0.766025i | \(-0.722232\pi\) | ||||
−0.642811 | + | 0.766025i | \(0.722232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −62.5267 | −3.08421 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3462 | 1.44403 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.5996 | − | 23.4017i | 1.20755 | − | 1.14875i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.9787i | 1.46806i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0811 | −0.785614 | −0.392807 | − | 0.919621i | \(-0.628496\pi\) | ||||
−0.392807 | + | 0.919621i | \(0.628496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5031i | 1.14547i | 0.819740 | + | 0.572735i | \(0.194118\pi\) | ||||
−0.819740 | + | 0.572735i | \(0.805882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 94.9662 | 4.61741 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.48975 | − | 29.8299i | 0.0722635 | − | 1.44696i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.3914 | 0.890022 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 37.0141i | − | 1.78706i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.61906 | −0.318829 | −0.159415 | − | 0.987212i | \(-0.550961\pi\) | ||||
−0.159415 | + | 0.987212i | \(0.550961\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.3334 | 0.977163 | 0.488581 | − | 0.872518i | \(-0.337515\pi\) | ||||
0.488581 | + | 0.872518i | \(0.337515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.7614 | − | 19.7218i | −0.899542 | − | 0.945588i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.220070 | − | 1.79882i | −0.0105274 | − | 0.0860494i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.1971i | 0.725317i | 0.931922 | + | 0.362659i | \(0.118131\pi\) | ||||
−0.931922 | + | 0.362659i | \(0.881869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.60724 | −0.171774 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.20593 | −0.389875 | −0.194938 | − | 0.980816i | \(-0.562450\pi\) | ||||
−0.194938 | + | 0.980816i | \(0.562450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6884 | + | 18.7297i | −0.933320 | + | 0.887872i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 19.5661i | − | 0.925445i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.0265 | −1.08669 | −0.543343 | − | 0.839511i | \(-0.682842\pi\) | ||||
−0.543343 | + | 0.839511i | \(0.682842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.03259 | −0.0486226 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.6905i | 1.53593i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.7386 | + | 21.8002i | 0.972243 | + | 1.02201i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.0523 | −1.78001 | −0.890005 | − | 0.455951i | \(-0.849299\pi\) | ||||
−0.890005 | + | 0.455951i | \(0.849299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 94.2561 | 4.39950 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.7920 | 1.34098 | 0.670489 | − | 0.741919i | \(-0.266084\pi\) | ||||
0.670489 | + | 0.741919i | \(0.266084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.34881 | 0.0626843 | 0.0313421 | − | 0.999509i | \(-0.490022\pi\) | ||||
0.0313421 | + | 0.999509i | \(0.490022\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.4049 | − | 14.6548i | 0.714387 | − | 0.679600i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.23187i | 0.380926i | 0.981694 | + | 0.190463i | \(0.0609988\pi\) | ||||
−0.981694 | + | 0.190463i | \(0.939001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.2992 | −0.891154 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.2898 | −2.45547 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.821902i | 0.0377911i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0942413 | + | 1.88703i | −0.00432409 | + | 0.0865831i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −75.6170 | −3.46226 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.78805 | −0.127389 | −0.0636946 | − | 0.997969i | \(-0.520288\pi\) | ||||
−0.0636946 | + | 0.997969i | \(0.520288\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.6297i | 1.62458i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −42.7379 | + | 5.22860i | −1.94464 | + | 0.237910i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.69220 | + | 7.03476i | 0.303877 | + | 0.319432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.35672 | −0.0614787 | −0.0307394 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307394 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.5877 | −2.10677 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.539939i | − | 0.0243671i | −0.999926 | − | 0.0121835i | \(-0.996122\pi\) | ||
0.999926 | − | 0.0121835i | \(-0.00387824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.1255 | −0.996482 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.4898 | − | 28.8969i | −1.23557 | − | 1.29882i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.0692 | 0.900226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 23.4902i | − | 1.05157i | −0.850619 | − | 0.525783i | \(-0.823772\pi\) | ||
0.850619 | − | 0.525783i | \(-0.176228\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.0901 | −1.29965 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 17.7835i | − | 0.792929i | −0.918050 | − | 0.396464i | \(-0.870237\pi\) | ||
0.918050 | − | 0.396464i | \(-0.129763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.80735 | + | 5.05343i | 0.213924 | + | 0.224875i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.0196 | 1.64410 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.3504 | 1.30094 | 0.650468 | − | 0.759534i | \(-0.274573\pi\) | ||||
0.650468 | + | 0.759534i | \(0.274573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.40219 | −0.150504 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.96263 | −0.263256 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.49037 | − | 5.22302i | 0.241935 | − | 0.230154i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.8328 | −1.22408 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 79.8173i | 3.50359i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 15.4545i | − | 0.677074i | −0.940953 | − | 0.338537i | \(-0.890068\pi\) | ||
0.940953 | − | 0.338537i | \(-0.109932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5873i | 1.38122i | 0.723229 | + | 0.690608i | \(0.242657\pi\) | ||||
−0.723229 | + | 0.690608i | \(0.757343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 44.8337 | + | 2.23906i | 1.95670 | + | 0.0977207i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 17.2825i | − | 0.752837i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3217 | + | 5.54470i | −0.970507 | + | 0.241074i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 83.8060i | − | 3.63687i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.22463i | − | 0.0963596i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.8768 | − | 12.2497i | 0.556712 | − | 0.529603i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 48.7582i | − | 2.10407i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.05721 | 0.0455375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7309 | −0.891292 | −0.445646 | − | 0.895209i | \(-0.647026\pi\) | ||||
−0.445646 | + | 0.895209i | \(0.647026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2624i | 0.483316i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.8749 | − | 21.7610i | 0.979851 | − | 0.932137i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.88064 | −0.422466 | −0.211233 | − | 0.977436i | \(-0.567748\pi\) | ||||
−0.211233 | + | 0.977436i | \(0.567748\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 52.5216i | − | 2.24157i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.39966 | 0.0596273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 37.2655i | − | 1.58469i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 36.6375 | + | 38.5129i | 1.55518 | + | 1.63478i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3481 | −0.565576 | −0.282788 | − | 0.959182i | \(-0.591259\pi\) | ||||
−0.282788 | + | 0.959182i | \(0.591259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.77073 | −0.0748939 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.8857 | −1.89508 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.9591i | 1.05190i | 0.850516 | + | 0.525950i | \(0.176290\pi\) | ||||
−0.850516 | + | 0.525950i | \(0.823710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.497768 | + | 0.523247i | 0.0209412 | + | 0.0220132i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 77.7324i | 3.26445i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 33.7602i | − | 1.41530i | −0.706562 | − | 0.707651i | \(-0.749755\pi\) | ||
0.706562 | − | 0.707651i | \(-0.250245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3767 | −1.60602 | −0.803008 | − | 0.595968i | \(-0.796768\pi\) | ||||
−0.803008 | + | 0.595968i | \(0.796768\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.8099 | −1.28710 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.9173 | − | 1.72109i | 0.997421 | − | 0.0717743i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.7420i | − | 1.07166i | −0.844327 | − | 0.535828i | \(-0.820000\pi\) | ||
0.844327 | − | 0.535828i | \(-0.180000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.68485i | 0.236254i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.4790 | 1.72084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.1619 | 0.917852 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 62.2563 | − | 59.2248i | 2.57398 | − | 2.44864i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.8165 | 0.694091 | 0.347045 | − | 0.937848i | \(-0.387185\pi\) | ||||
0.347045 | + | 0.937848i | \(0.387185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.09329i | 0.0450482i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 51.9790i | − | 2.13813i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26.0486i | − | 1.06969i | −0.844951 | − | 0.534843i | \(-0.820371\pi\) | ||
0.844951 | − | 0.534843i | \(-0.179629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.4363 | − | 25.1490i | 1.08378 | − | 1.03101i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 65.5827 | 2.68412 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.6703i | − | 0.844567i | −0.906464 | − | 0.422283i | \(-0.861229\pi\) | ||
0.906464 | − | 0.422283i | \(-0.138771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.32601 | 0.339625 | 0.169813 | − | 0.985476i | \(-0.445684\pi\) | ||||
0.169813 | + | 0.985476i | \(0.445684\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 55.1140i | 2.24442i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.89649 | − | 9.35188i | −0.361694 | − | 0.380208i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9501 | −0.647396 | −0.323698 | − | 0.946160i | \(-0.604926\pi\) | ||||
−0.323698 | + | 0.946160i | \(0.604926\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 33.2542i | − | 1.34753i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 59.9637i | − | 2.42587i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1501 | 0.935023 | 0.467512 | − | 0.883987i | \(-0.345151\pi\) | ||||
0.467512 | + | 0.883987i | \(0.345151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.28756 | − | 2.40465i | −0.0922433 | − | 0.0969650i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.88371 | −0.116094 | −0.0580468 | − | 0.998314i | \(-0.518487\pi\) | ||||
−0.0580468 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.49465 | −0.261042 | −0.130521 | − | 0.991446i | \(-0.541665\pi\) | ||||
−0.130521 | + | 0.991446i | \(0.541665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.18961 | + | 75.1147i | 0.368766 | + | 3.01425i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.1978 | −1.33004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8756 | − | 2.49086i | −0.995024 | − | 0.0996345i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83947 | 0.113397 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.2069 | 1.72277 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6830 | 1.14185 | 0.570927 | − | 0.821001i | \(-0.306584\pi\) | ||||
0.570927 | + | 0.821001i | \(0.306584\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 62.4482i | − | 2.48209i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.2350 | + | 17.0660i | 0.644265 | + | 0.677243i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.27769i | 0.0902455i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 57.3129i | − | 2.26726i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.5938i | 1.24788i | 0.781473 | + | 0.623939i | \(0.214469\pi\) | ||||
−0.781473 | + | 0.623939i | \(0.785531\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 47.3512i | − | 1.86735i | −0.358120 | − | 0.933675i | \(-0.616582\pi\) | ||
0.358120 | − | 0.933675i | \(-0.383418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.91402 | + | 1.82082i | −0.0753644 | + | 0.0716945i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.8763 | 0.860045 | 0.430022 | − | 0.902818i | \(-0.358506\pi\) | ||||
0.430022 | + | 0.902818i | \(0.358506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.5619i | 0.964141i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.9752 | 1.01805 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.359578i | 0.0140714i | 0.999975 | + | 0.00703568i | \(0.00223954\pi\) | ||||
−0.999975 | + | 0.00703568i | \(0.997760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4012 | − | 17.5051i | 0.718993 | − | 0.683982i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.71588i | 0.379052i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.91275 | −0.0745104 | −0.0372552 | − | 0.999306i | \(-0.511861\pi\) | ||||
−0.0372552 | + | 0.999306i | \(0.511861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.73207i | − | 0.184056i | −0.995756 | − | 0.0920280i | \(-0.970665\pi\) | ||
0.995756 | − | 0.0920280i | \(-0.0293349\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 96.7031i | − | 3.75564i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.67236 | + | 1.59092i | −0.0648513 | + | 0.0616933i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.15715 | − | 17.6323i | −0.0835252 | − | 0.682725i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.16082 | 0.238191 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3931i | 0.594243i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.7608i | 1.64831i | 0.566366 | + | 0.824154i | \(0.308349\pi\) | ||||
−0.566366 | + | 0.824154i | \(0.691651\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.93530 | − | 78.7982i | 0.151470 | − | 3.03294i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.30895 | −0.0503072 | −0.0251536 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251536 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8617i | 0.455212i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 17.0530i | − | 0.653472i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.4311 | 0.628718 | 0.314359 | − | 0.949304i | \(-0.398210\pi\) | ||||
0.314359 | + | 0.949304i | \(0.398210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.3217 | + | 30.8226i | 1.12032 | + | 1.17767i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.9347i | 1.98143i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47.7462i | 1.81899i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.1615i | 1.90823i | 0.299433 | + | 0.954117i | \(0.403203\pi\) | ||||
−0.299433 | + | 0.954117i | \(0.596797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 48.7249i | − | 1.85091i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.7780 | − | 14.0584i | 0.560562 | − | 0.533265i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.69773 | −0.102184 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.1400i | 1.82082i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.199633i | − | 0.00754004i | −0.999993 | − | 0.00377002i | \(-0.998800\pi\) | ||
0.999993 | − | 0.00377002i | \(-0.00120004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.73326 | −0.103087 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −61.6598 | − | 64.8161i | −2.32224 | − | 2.44111i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.52090i | 0.320461i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.1194i | 1.50671i | 0.657611 | + | 0.753357i | \(0.271567\pi\) | ||||
−0.657611 | + | 0.753357i | \(0.728433\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −106.422 | −3.99113 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.7728 | − | 1.68498i | 0.515795 | − | 0.0631029i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.2461 | + | 17.3576i | −0.682367 | + | 0.649139i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.5566i | 1.17850i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.40670i | − | 0.0524610i | −0.999656 | − | 0.0262305i | \(-0.991650\pi\) | ||
0.999656 | − | 0.0262305i | \(-0.00835039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.25766 | 0.344773 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.9684i | 2.30463i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.923765 | + | 18.4969i | −0.0343078 | + | 0.686959i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.3686i | 1.34884i | 0.738349 | + | 0.674419i | \(0.235606\pi\) | ||||
−0.738349 | + | 0.674419i | \(0.764394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 66.4089 | 2.45959 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.14730i | 0.0794208i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.2005 | 1.30016 | 0.650081 | − | 0.759865i | \(-0.274735\pi\) | ||||
0.650081 | + | 0.759865i | \(0.274735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.34212 | + | 2.46201i | 0.0863904 | + | 0.0908125i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 16.1529i | − | 0.594998i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.59702i | 0.242675i | 0.992611 | + | 0.121338i | \(0.0387184\pi\) | ||||
−0.992611 | + | 0.121338i | \(0.961282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.11743i | 0.224729i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.9968i | − | 0.806985i | −0.914983 | − | 0.403493i | \(-0.867796\pi\) | ||
0.914983 | − | 0.403493i | \(-0.132204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.64513 | + | 9.17546i | −0.353370 | + | 0.336163i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 118.454i | − | 4.33402i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.7124 | 0.793352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8072 | −0.394359 | −0.197179 | − | 0.980367i | \(-0.563178\pi\) | ||||
−0.197179 | + | 0.980367i | \(0.563178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −81.8531 | −2.98289 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.1148 | − | 15.3301i | 0.586477 | − | 0.557919i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.47219 | 0.344273 | 0.172136 | − | 0.985073i | \(-0.444933\pi\) | ||||
0.172136 | + | 0.985073i | \(0.444933\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.37619 | − | 35.7704i | −0.158846 | − | 1.29838i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.3960 | −1.75436 | −0.877178 | − | 0.480166i | \(-0.840576\pi\) | ||||
−0.877178 | + | 0.480166i | \(0.840576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.5707 | 1.39635 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −71.8197 | − | 75.4960i | −2.59665 | − | 2.72956i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.9170 | −1.91072 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.14793i | 0.185639i | 0.995683 | + | 0.0928195i | \(0.0295880\pi\) | ||||
−0.995683 | + | 0.0928195i | \(0.970412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.4786i | 1.96200i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.7974 | −1.28754 | −0.643771 | − | 0.765218i | \(-0.722631\pi\) | ||||
−0.643771 | + | 0.765218i | \(0.722631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.4482 | − | 0.721564i | −0.518994 | − | 0.0259193i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 64.9391i | 2.32968i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.170658 | 0.00611447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.7973i | 0.601056i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −58.4464 | −2.08870 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9901 | + | 26.2693i | 0.891934 | + | 0.937590i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.7273i | − | 1.05966i | −0.848103 | − | 0.529832i | \(-0.822255\pi\) | ||
0.848103 | − | 0.529832i | \(-0.177745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 58.4192i | − | 2.07978i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.882280i | 0.0313703i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.1633 | −1.17766 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 49.0967 | + | 51.6099i | 1.74128 | + | 1.83041i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.5547 | 0.798927 | 0.399464 | − | 0.916749i | \(-0.369196\pi\) | ||||
0.399464 | + | 0.916749i | \(0.369196\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.7159 | −2.57250 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 94.8054i | 3.34978i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.84754i | − | 0.100487i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.6192 | + | 18.6157i | 0.797223 | + | 0.656119i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 60.1052 | 2.11580 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.2281 | 0.886972 | 0.443486 | − | 0.896281i | \(-0.353742\pi\) | ||||
0.443486 | + | 0.896281i | \(0.353742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6698i | 0.796043i | 0.917376 | + | 0.398022i | \(0.130303\pi\) | ||||
−0.917376 | + | 0.398022i | \(0.869697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7540i | 0.973377i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8471 | + | 22.9654i | 0.765271 | + | 0.804444i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.135838i | − | 0.00475237i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 104.974 | 3.66810 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.09527 | −0.212726 | −0.106363 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106363 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.0738 | −1.88490 | −0.942448 | − | 0.334354i | \(-0.891482\pi\) | ||||
−0.942448 | + | 0.334354i | \(0.891482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.87403 | + | 37.5245i | −0.0652454 | + | 1.30644i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.7729i | − | 0.548476i | −0.961662 | − | 0.274238i | \(-0.911574\pi\) | ||
0.961662 | − | 0.274238i | \(-0.0884256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.7096 | −1.65702 | −0.828511 | − | 0.559972i | \(-0.810812\pi\) | ||||
−0.828511 | + | 0.559972i | \(0.810812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 91.8951i | − | 3.18781i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.76208 | 0.0957003 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.6417 | + | 14.3400i | 0.472090 | + | 0.496255i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 45.6532i | − | 1.57801i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.8696 | −1.16931 | −0.584654 | − | 0.811283i | \(-0.698770\pi\) | ||||
−0.584654 | + | 0.811283i | \(0.698770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.2804 | −0.526911 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 93.3042i | 3.21357i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.3602 | − | 18.2488i | −0.597209 | − | 0.627779i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.7688i | − | 0.541822i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.9575i | 1.02814i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.21251 | + | 34.4325i | 0.144403 | + | 1.18033i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.1776i | 1.13598i | 0.823036 | + | 0.567990i | \(0.192279\pi\) | ||||
−0.823036 | + | 0.567990i | \(0.807721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.54331 | + | 4.77587i | 0.155378 | + | 0.163331i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 38.9386i | − | 1.33012i | −0.746792 | − | 0.665058i | \(-0.768407\pi\) | ||
0.746792 | − | 0.665058i | \(-0.231593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.5373i | 0.803081i | 0.915841 | + | 0.401540i | \(0.131525\pi\) | ||||
−0.915841 | + | 0.401540i | \(0.868475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4.05464i | − | 0.138182i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.47024 | 0.0840881 | 0.0420440 | − | 0.999116i | \(-0.486613\pi\) | ||||
0.0420440 | + | 0.999116i | \(0.486613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.3460 | − | 37.4300i | 1.33780 | − | 1.27266i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −61.3976 | −2.08517 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.1902 | 1.05805 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.8002 | 1.17916 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.8744 | 1.14647 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.9208 | − | 23.1508i | −0.673447 | − | 0.782640i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 41.1951i | − | 1.39106i | −0.718497 | − | 0.695530i | \(-0.755170\pi\) | ||
0.718497 | − | 0.695530i | \(-0.244830\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.8934 | 0.569800 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.8457i | − | 0.837073i | −0.908200 | − | 0.418536i | \(-0.862543\pi\) | ||
0.908200 | − | 0.418536i | \(-0.137457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.8271 | −1.30664 | −0.653318 | − | 0.757084i | \(-0.726623\pi\) | ||||
−0.653318 | + | 0.757084i | \(0.726623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −57.1991 | + | 54.4138i | −1.92273 | + | 1.82910i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.0801 | −0.842107 | −0.421053 | − | 0.907036i | \(-0.638340\pi\) | ||||
−0.421053 | + | 0.907036i | \(0.638340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.7760i | 0.965117i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −65.0598 | −2.17958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.60000 | 0.153933 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0354 | + | 22.8650i | −0.803415 | + | 0.764293i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 77.0648 | − | 9.42818i | 2.57312 | − | 0.314798i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.7165i | 0.357417i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.9001 | 1.92893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.22735 | −0.107399 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.55181 | − | 5.28147i | 0.184549 | − | 0.175562i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5720i | 1.08154i | 0.841171 | + | 0.540769i | \(0.181867\pi\) | ||||
−0.841171 | + | 0.540769i | \(0.818133\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.3337 | 0.807098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.27302 | −0.0753085 | −0.0376543 | − | 0.999291i | \(-0.511989\pi\) | ||||
−0.0376543 | + | 0.999291i | \(0.511989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.7167i | 1.14895i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −35.8469 | + | 34.1013i | −1.18506 | + | 1.12735i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.0274 | 1.02461 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.7571 | 1.37744 | 0.688719 | − | 0.725028i | \(-0.258173\pi\) | ||||
0.688719 | + | 0.725028i | \(0.258173\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 52.9090 | 1.74341 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.1886 | −1.19116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.80394 | − | 36.1210i | 0.0593131 | − | 1.18765i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 26.4377i | − | 0.868329i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.6236 | 1.36563 | 0.682813 | − | 0.730593i | \(-0.260756\pi\) | ||||
0.682813 | + | 0.730593i | \(0.260756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.174729 | −0.00572650 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.7343i | 1.46453i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.0490 | + | 22.1265i | 0.688376 | + | 0.723612i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.9992 | −0.457334 | −0.228667 | − | 0.973505i | \(-0.573437\pi\) | ||||
−0.228667 | + | 0.973505i | \(0.573437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.8926 | −1.79135 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.7963i | 1.16693i | 0.812139 | + | 0.583463i | \(0.198303\pi\) | ||||
−0.812139 | + | 0.583463i | \(0.801697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.263019 | − | 2.14988i | −0.00856507 | − | 0.0700098i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 69.8338 | − | 66.4333i | 2.27170 | − | 2.16107i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.8042 | −1.03350 | −0.516749 | − | 0.856137i | \(-0.672858\pi\) | ||||
−0.516749 | + | 0.856137i | \(0.672858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.13482 | 0.199145 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.3003i | 2.57149i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.67822 | −0.151542 | −0.0757712 | − | 0.997125i | \(-0.524142\pi\) | ||||
−0.0757712 | + | 0.997125i | \(0.524142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.4482 | + | 15.1878i | 0.467532 | + | 0.491464i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.8328 | 0.899706 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.9719i | 1.67826i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6292 | 0.729973 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 62.0055i | − | 1.99810i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.80235 | − | 2.66589i | 0.0902109 | − | 0.0858180i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3182 | 0.331812 | 0.165906 | − | 0.986142i | \(-0.446945\pi\) | ||||
0.165906 | + | 0.986142i | \(0.446945\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.41838 | 0.238313 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.2995 | −1.93510 | −0.967551 | − | 0.252675i | \(-0.918690\pi\) | ||||
−0.967551 | + | 0.252675i | \(0.918690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.9181 | 0.798838 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −80.8439 | − | 4.03747i | −2.58908 | − | 0.129302i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.82697 | 0.218414 | 0.109207 | − | 0.994019i | \(-0.465169\pi\) | ||||
0.109207 | + | 0.994019i | \(0.465169\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.7856i | − | 0.888033i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 110.149i | − | 3.51679i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42.5123i | − | 1.35593i | −0.735093 | − | 0.677966i | \(-0.762862\pi\) | ||
0.735093 | − | 0.677966i | \(-0.237138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.6231 | + | 24.3753i | −0.816419 | + | 0.776663i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 109.290i | − | 3.47875i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.71123 | + | 0.209354i | −0.0544139 | + | 0.00665706i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.2777i | − | 0.453545i | −0.973948 | − | 0.226772i | \(-0.927183\pi\) | ||
0.973948 | − | 0.226772i | \(-0.0728173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 31.2081i | − | 0.990359i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.7547 | − | 32.3290i | −0.974991 | − | 1.02490i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4129i | 0.614814i | 0.951578 | + | 0.307407i | \(0.0994612\pi\) | ||||
−0.951578 | + | 0.307407i | \(0.900539\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 114.135 | 3.61106 |
(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 | 1840.2.m.g.1839.1 | ✓ | 40 | |
4.3 | odd | 2 | inner | 1840.2.m.g.1839.40 | yes | 40 | |
5.4 | even | 2 | inner | 1840.2.m.g.1839.39 | yes | 40 | |
20.19 | odd | 2 | inner | 1840.2.m.g.1839.2 | yes | 40 | |
23.22 | odd | 2 | inner | 1840.2.m.g.1839.3 | yes | 40 | |
92.91 | even | 2 | inner | 1840.2.m.g.1839.38 | yes | 40 | |
115.114 | odd | 2 | inner | 1840.2.m.g.1839.37 | yes | 40 | |
460.459 | even | 2 | inner | 1840.2.m.g.1839.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.m.g.1839.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1840.2.m.g.1839.2 | yes | 40 | 20.19 | odd | 2 | inner | |
1840.2.m.g.1839.3 | yes | 40 | 23.22 | odd | 2 | inner | |
1840.2.m.g.1839.4 | yes | 40 | 460.459 | even | 2 | inner | |
1840.2.m.g.1839.37 | yes | 40 | 115.114 | odd | 2 | inner | |
1840.2.m.g.1839.38 | yes | 40 | 92.91 | even | 2 | inner | |
1840.2.m.g.1839.39 | yes | 40 | 5.4 | even | 2 | inner | |
1840.2.m.g.1839.40 | yes | 40 | 4.3 | odd | 2 | inner |