Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.6 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.6 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.17902 | − | 1.17902i | −0.527275 | − | 0.527275i | 0.392484 | − | 0.919759i | \(-0.371616\pi\) |
−0.919759 | + | 0.392484i | \(0.871616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.54895 | + | 4.54895i | −1.37156 | + | 1.37156i | −0.513428 | + | 0.858133i | \(0.671625\pi\) |
−0.858133 | + | 0.513428i | \(0.828375\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56073 | + | 2.56073i | 0.710218 | + | 0.710218i | 0.966581 | − | 0.256363i | \(-0.0825241\pi\) |
−0.256363 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.05280i | 0.497876i | 0.968519 | + | 0.248938i | \(0.0800815\pi\) | ||||
−0.968519 | + | 0.248938i | \(0.919918\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.64422 | − | 3.64422i | 0.836042 | − | 0.836042i | −0.152293 | − | 0.988335i | \(-0.548666\pi\) |
0.988335 | + | 0.152293i | \(0.0486657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.27140i | − | 0.473620i | −0.971556 | − | 0.236810i | \(-0.923898\pi\) | ||
0.971556 | − | 0.236810i | \(-0.0761019\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.21982i | − | 0.443963i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.544898 | + | 0.544898i | −0.101185 | + | 0.101185i | −0.755887 | − | 0.654702i | \(-0.772794\pi\) |
0.654702 | + | 0.755887i | \(0.272794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1006i | 1.81412i | 0.421004 | + | 0.907059i | \(0.361678\pi\) | ||||
−0.421004 | + | 0.907059i | \(0.638322\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.17902 | + | 1.17902i | 0.199291 | + | 0.199291i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.71698 | − | 4.71698i | 0.775467 | − | 0.775467i | −0.203590 | − | 0.979056i | \(-0.565261\pi\) |
0.979056 | + | 0.203590i | \(0.0652608\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.487549 | 0.0761424 | 0.0380712 | − | 0.999275i | \(-0.487879\pi\) | ||||
0.0380712 | + | 0.999275i | \(0.487879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.56607 | − | 7.56607i | −1.15381 | − | 1.15381i | −0.985781 | − | 0.168033i | \(-0.946258\pi\) |
−0.168033 | − | 0.985781i | \(-0.553742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.768184 | 0.112051 | 0.0560256 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560256 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.269015 | + | 0.269015i | 0.0369520 | + | 0.0369520i | 0.725341 | − | 0.688389i | \(-0.241682\pi\) |
−0.688389 | + | 0.725341i | \(0.741682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7266 | 1.44638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0979540 | + | 0.0979540i | −0.0127525 | + | 0.0127525i | −0.713454 | − | 0.700702i | \(-0.752870\pi\) |
0.700702 | + | 0.713454i | \(0.252870\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.41725 | − | 7.41725i | −0.949682 | − | 0.949682i | 0.0491117 | − | 0.998793i | \(-0.484361\pi\) |
−0.998793 | + | 0.0491117i | \(0.984361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.03831i | − | 0.748960i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.83972 | + | 6.83972i | −0.835604 | + | 0.835604i | −0.988277 | − | 0.152672i | \(-0.951212\pi\) |
0.152672 | + | 0.988277i | \(0.451212\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.66316i | 1.02813i | 0.857752 | + | 0.514064i | \(0.171861\pi\) | ||||
−0.857752 | + | 0.514064i | \(0.828139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.6358i | − | 1.59594i | −0.602694 | − | 0.797972i | \(-0.705906\pi\) | ||
0.602694 | − | 0.797972i | \(-0.294094\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.54895 | − | 4.54895i | 0.518401 | − | 0.518401i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.29142i | − | 1.04537i | −0.852527 | − | 0.522683i | \(-0.824931\pi\) | ||
0.852527 | − | 0.522683i | \(-0.175069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.76640 | − | 9.76640i | −1.07200 | − | 1.07200i | −0.997198 | − | 0.0748037i | \(-0.976167\pi\) |
−0.0748037 | − | 0.997198i | \(-0.523833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.42029 | − | 2.42029i | 0.262517 | − | 0.262517i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.27355 | 0.770995 | 0.385497 | − | 0.922709i | \(-0.374030\pi\) | ||||
0.385497 | + | 0.922709i | \(0.374030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.56073 | − | 2.56073i | −0.268437 | − | 0.268437i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.59324 | −0.881648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4508 | 1.06112 | 0.530561 | − | 0.847647i | \(-0.321981\pi\) | ||||
0.530561 | + | 0.847647i | \(0.321981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.75000 | − | 5.75000i | −0.572147 | − | 0.572147i | 0.360581 | − | 0.932728i | \(-0.382578\pi\) |
−0.932728 | + | 0.360581i | \(0.882578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.11905 | −0.701460 | −0.350730 | − | 0.936477i | \(-0.614067\pi\) | ||||
−0.350730 | + | 0.936477i | \(0.614067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.13593 | + | 6.13593i | −0.593182 | + | 0.593182i | −0.938490 | − | 0.345307i | \(-0.887775\pi\) |
0.345307 | + | 0.938490i | \(0.387775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.54344 | + | 1.54344i | 0.147835 | + | 0.147835i | 0.777150 | − | 0.629315i | \(-0.216665\pi\) |
−0.629315 | + | 0.777150i | \(0.716665\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.0023i | − | 1.31723i | −0.752481 | − | 0.658614i | \(-0.771143\pi\) | ||
0.752481 | − | 0.658614i | \(-0.228857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.67803 | + | 2.67803i | −0.249728 | + | 0.249728i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.05280i | − | 0.188179i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 30.3859i | − | 2.76236i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.51232 | + | 8.51232i | −0.761365 | + | 0.761365i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.32939i | 0.472906i | 0.971643 | + | 0.236453i | \(0.0759850\pi\) | ||||
−0.971643 | + | 0.236453i | \(0.924015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4364 | − | 13.4364i | −1.17395 | − | 1.17395i | −0.981261 | − | 0.192685i | \(-0.938280\pi\) |
−0.192685 | − | 0.981261i | \(-0.561720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.64422 | + | 3.64422i | −0.315994 | + | 0.315994i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1704 | −0.868914 | −0.434457 | − | 0.900693i | \(-0.643060\pi\) | ||||
−0.434457 | + | 0.900693i | \(0.643060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.90089 | + | 6.90089i | 0.585326 | + | 0.585326i | 0.936362 | − | 0.351036i | \(-0.114171\pi\) |
−0.351036 | + | 0.936362i | \(0.614171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.2973 | −1.94821 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.28489 | 0.106705 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.134093 | + | 0.134093i | 0.0109853 | + | 0.0109853i | 0.712578 | − | 0.701593i | \(-0.247527\pi\) |
−0.701593 | + | 0.712578i | \(0.747527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7321 | 1.11750 | 0.558750 | − | 0.829336i | \(-0.311281\pi\) | ||||
0.558750 | + | 0.829336i | \(0.311281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.9088 | − | 11.9088i | 0.956538 | − | 0.956538i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.49258 | − | 2.49258i | −0.198929 | − | 0.198929i | 0.600612 | − | 0.799541i | \(-0.294924\pi\) |
−0.799541 | + | 0.600612i | \(0.794924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.27140i | 0.179012i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.43203 | + | 6.43203i | −0.503796 | + | 0.503796i | −0.912615 | − | 0.408820i | \(-0.865941\pi\) |
0.408820 | + | 0.912615i | \(0.365941\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.38595i | 0.339395i | 0.985496 | + | 0.169697i | \(0.0542790\pi\) | ||||
−0.985496 | + | 0.169697i | \(0.945721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.114651i | 0.00881930i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2846 | + | 18.2846i | −1.39015 | + | 1.39015i | −0.565191 | + | 0.824960i | \(0.691197\pi\) |
−0.824960 | + | 0.565191i | \(0.808803\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.21982i | 0.167802i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.18124 | + | 3.18124i | 0.237777 | + | 0.237777i | 0.815929 | − | 0.578152i | \(-0.196226\pi\) |
−0.578152 | + | 0.815929i | \(0.696226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4064 | + | 18.4064i | −1.36813 | + | 1.36813i | −0.505036 | + | 0.863098i | \(0.668521\pi\) |
−0.863098 | + | 0.505036i | \(0.831479\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.1228 | −0.817768 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.33807 | − | 9.33807i | −0.682867 | − | 0.682867i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1964 | −1.60607 | −0.803037 | − | 0.595929i | \(-0.796784\pi\) | ||||
−0.803037 | + | 0.595929i | \(0.796784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.93243 | −0.499007 | −0.249503 | − | 0.968374i | \(-0.580267\pi\) | ||||
−0.249503 | + | 0.968374i | \(0.580267\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.07895 | − | 6.07895i | −0.433107 | − | 0.433107i | 0.456577 | − | 0.889684i | \(-0.349075\pi\) |
−0.889684 | + | 0.456577i | \(0.849075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.9223 | 0.774265 | 0.387132 | − | 0.922024i | \(-0.373466\pi\) | ||||
0.387132 | + | 0.922024i | \(0.373466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.544898 | − | 0.544898i | 0.0382444 | − | 0.0382444i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.574831 | − | 0.574831i | −0.0401480 | − | 0.0401480i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.1548i | 2.29337i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.67612 | − | 9.67612i | 0.666131 | − | 0.666131i | −0.290687 | − | 0.956818i | \(-0.593884\pi\) |
0.956818 | + | 0.290687i | \(0.0938838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.8411i | 1.21675i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.1006i | − | 0.685672i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.25665 | + | 5.25665i | −0.353601 | + | 0.353601i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.17535i | − | 0.279602i | −0.990180 | − | 0.139801i | \(-0.955354\pi\) | ||
0.990180 | − | 0.139801i | \(-0.0446463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2251 | − | 21.2251i | −1.40876 | − | 1.40876i | −0.766413 | − | 0.642348i | \(-0.777961\pi\) |
−0.642348 | − | 0.766413i | \(-0.722039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.46169 | + | 6.46169i | −0.427000 | + | 0.427000i | −0.887605 | − | 0.460605i | \(-0.847633\pi\) |
0.460605 | + | 0.887605i | \(0.347633\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6456 | 0.697413 | 0.348707 | − | 0.937232i | \(-0.386621\pi\) | ||||
0.348707 | + | 0.937232i | \(0.386621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.905705 | − | 0.905705i | −0.0590817 | − | 0.0590817i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2774 | 0.664792 | 0.332396 | − | 0.943140i | \(-0.392143\pi\) | ||||
0.332396 | + | 0.943140i | \(0.392143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.195675 | −0.0126045 | −0.00630227 | − | 0.999980i | \(-0.502006\pi\) | ||||
−0.00630227 | + | 0.999980i | \(0.502006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.17902 | − | 1.17902i | −0.0753249 | − | 0.0753249i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.6637 | 1.18754 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.95377 | − | 8.95377i | 0.565157 | − | 0.565157i | −0.365611 | − | 0.930768i | \(-0.619140\pi\) |
0.930768 | + | 0.365611i | \(0.119140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.3325 | + | 10.3325i | 0.649599 | + | 0.649599i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.3928i | − | 1.33445i | −0.744858 | − | 0.667223i | \(-0.767483\pi\) | ||
0.744858 | − | 0.667223i | \(-0.232517\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.71698 | + | 4.71698i | −0.293099 | + | 0.293099i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 31.7659i | − | 1.95877i | −0.202006 | − | 0.979384i | \(-0.564746\pi\) | ||
0.202006 | − | 0.979384i | \(-0.435254\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.634348i | − | 0.0389677i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1414 | − | 11.1414i | 0.679301 | − | 0.679301i | −0.280541 | − | 0.959842i | \(-0.590514\pi\) |
0.959842 | + | 0.280541i | \(0.0905140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.1289i | − | 1.16200i | −0.813904 | − | 0.580999i | \(-0.802662\pi\) | ||
0.813904 | − | 0.580999i | \(-0.197338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0978 | + | 10.0978i | 0.608922 | + | 0.608922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.64734 | + | 1.64734i | −0.0989791 | + | 0.0989791i | −0.754862 | − | 0.655883i | \(-0.772296\pi\) |
0.655883 | + | 0.754862i | \(0.272296\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.73918 | 0.282716 | 0.141358 | − | 0.989959i | \(-0.454853\pi\) | ||||
0.141358 | + | 0.989959i | \(0.454853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.70607 | − | 9.70607i | −0.576966 | − | 0.576966i | 0.357100 | − | 0.934066i | \(-0.383766\pi\) |
−0.934066 | + | 0.357100i | \(0.883766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.487549 | −0.0287791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7860 | 0.752119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.58419 | − | 4.58419i | −0.267811 | − | 0.267811i | 0.560406 | − | 0.828218i | \(-0.310645\pi\) |
−0.828218 | + | 0.560406i | \(0.810645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.230980 | 0.0134482 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.81644 | − | 5.81644i | 0.336373 | − | 0.336373i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.56607 | + | 7.56607i | 0.436101 | + | 0.436101i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.4902i | 1.00149i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3272 | − | 12.3272i | 0.703552 | − | 0.703552i | −0.261619 | − | 0.965171i | \(-0.584256\pi\) |
0.965171 | + | 0.261619i | \(0.0842565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24831i | 0.0707852i | 0.999373 | + | 0.0353926i | \(0.0112682\pi\) | ||||
−0.999373 | + | 0.0353926i | \(0.988732\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.1106i | 1.30629i | 0.757234 | + | 0.653144i | \(0.226550\pi\) | ||||
−0.757234 | + | 0.653144i | \(0.773450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.92113 | − | 6.92113i | 0.388729 | − | 0.388729i | −0.485505 | − | 0.874234i | \(-0.661364\pi\) |
0.874234 | + | 0.485505i | \(0.161364\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.95743i | − | 0.277563i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.48085 | + | 7.48085i | 0.416245 | + | 0.416245i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.68434 | − | 5.68434i | 0.315311 | − | 0.315311i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.768184 | −0.0423513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3780 | − | 14.3780i | −0.790288 | − | 0.790288i | 0.191253 | − | 0.981541i | \(-0.438745\pi\) |
−0.981541 | + | 0.191253i | \(0.938745\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.1283 | 0.881186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.99526 | −0.326583 | −0.163291 | − | 0.986578i | \(-0.552211\pi\) | ||||
−0.163291 | + | 0.986578i | \(0.552211\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.9471 | − | 45.9471i | −2.48817 | − | 2.48817i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6602 | − | 11.6602i | 0.625954 | − | 0.625954i | −0.321094 | − | 0.947047i | \(-0.604050\pi\) |
0.947047 | + | 0.321094i | \(0.104050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.7098 | − | 18.7098i | −1.00151 | − | 1.00151i | −0.999999 | − | 0.00151266i | \(-0.999519\pi\) |
−0.00151266 | − | 0.999999i | \(-0.500481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.65833i | 0.247938i | 0.992286 | + | 0.123969i | \(0.0395624\pi\) | ||||
−0.992286 | + | 0.123969i | \(0.960438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2141 | − | 10.2141i | 0.542106 | − | 0.542106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.3794i | 0.706140i | 0.935597 | + | 0.353070i | \(0.114862\pi\) | ||||
−0.935597 | + | 0.353070i | \(0.885138\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 7.56074i | − | 0.397934i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.0769 | + | 16.0769i | −0.841501 | + | 0.841501i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 20.7376i | − | 1.08249i | −0.840864 | − | 0.541247i | \(-0.817953\pi\) | ||
0.840864 | − | 0.541247i | \(-0.182047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.269015 | − | 0.269015i | −0.0139665 | − | 0.0139665i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.84888 | − | 6.84888i | 0.354622 | − | 0.354622i | −0.507204 | − | 0.861826i | \(-0.669321\pi\) |
0.861826 | + | 0.507204i | \(0.169321\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.79067 | −0.143727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1046 | − | 17.1046i | −0.878602 | − | 0.878602i | 0.114788 | − | 0.993390i | \(-0.463381\pi\) |
−0.993390 | + | 0.114788i | \(0.963381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.7106 | 0.751678 | 0.375839 | − | 0.926685i | \(-0.377355\pi\) | ||||
0.375839 | + | 0.926685i | \(0.377355\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.7266 | −0.546680 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.86662 | + | 4.86662i | 0.246747 | + | 0.246747i | 0.819634 | − | 0.572887i | \(-0.194177\pi\) |
−0.572887 | + | 0.819634i | \(0.694177\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66272 | 0.235804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.9548 | + | 10.9548i | −0.551195 | + | 0.551195i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4535 | + | 25.4535i | 1.27747 | + | 1.27747i | 0.942077 | + | 0.335396i | \(0.108870\pi\) |
0.335396 | + | 0.942077i | \(0.391130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0632i | 1.05184i | 0.850533 | + | 0.525922i | \(0.176280\pi\) | ||||
−0.850533 | + | 0.525922i | \(0.823720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.8648 | + | 25.8648i | −1.28842 | + | 1.28842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.9146i | 2.12720i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 36.0796i | − | 1.78402i | −0.452016 | − | 0.892010i | \(-0.649295\pi\) | ||
0.452016 | − | 0.892010i | \(-0.350705\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0979540 | − | 0.0979540i | 0.00482000 | − | 0.00482000i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.0296i | 1.13048i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.95680 | − | 4.95680i | −0.242155 | − | 0.242155i | 0.575586 | − | 0.817741i | \(-0.304774\pi\) |
−0.817741 | + | 0.575586i | \(0.804774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.80250 | + | 7.80250i | −0.380271 | + | 0.380271i | −0.871200 | − | 0.490929i | \(-0.836657\pi\) |
0.490929 | + | 0.871200i | \(0.336657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.55683 | 0.221039 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.41725 | + | 7.41725i | 0.358946 | + | 0.358946i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.41852 | 0.212832 | 0.106416 | − | 0.994322i | \(-0.466062\pi\) | ||||
0.106416 | + | 0.994322i | \(0.466062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.06712 | −0.147396 | −0.0736981 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736981 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.27750 | − | 8.27750i | −0.395966 | − | 0.395966i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.24215 | 0.202467 | 0.101233 | − | 0.994863i | \(-0.467721\pi\) | ||||
0.101233 | + | 0.994863i | \(0.467721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.34161 | + | 2.34161i | −0.111253 | + | 0.111253i | −0.760542 | − | 0.649289i | \(-0.775067\pi\) |
0.649289 | + | 0.760542i | \(0.275067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.57567 | − | 8.57567i | −0.406526 | − | 0.406526i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.86849i | 0.418530i | 0.977859 | + | 0.209265i | \(0.0671071\pi\) | ||||
−0.977859 | + | 0.209265i | \(0.932893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.21784 | + | 2.21784i | −0.104434 | + | 0.104434i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.03831i | 0.283080i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.14847i | 0.334392i | 0.985924 | + | 0.167196i | \(0.0534712\pi\) | ||||
−0.985924 | + | 0.167196i | \(0.946529\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8346 | − | 17.8346i | 0.830638 | − | 0.830638i | −0.156966 | − | 0.987604i | \(-0.550171\pi\) |
0.987604 | + | 0.156966i | \(0.0501714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1618i | 0.751102i | 0.926802 | + | 0.375551i | \(0.122547\pi\) | ||||
−0.926802 | + | 0.375551i | \(0.877453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5356 | + | 13.5356i | 0.626352 | + | 0.626352i | 0.947148 | − | 0.320797i | \(-0.103951\pi\) |
−0.320797 | + | 0.947148i | \(0.603951\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.83972 | − | 6.83972i | 0.315829 | − | 0.315829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 68.8354 | 3.16505 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.08951 | − | 8.08951i | −0.371172 | − | 0.371172i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.85872 | −0.450456 | −0.225228 | − | 0.974306i | \(-0.572313\pi\) | ||||
−0.225228 | + | 0.974306i | \(0.572313\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1578 | 1.10150 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.3218 | − | 12.3218i | −0.559503 | − | 0.559503i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4055 | 1.33249 | 0.666245 | − | 0.745733i | \(-0.267900\pi\) | ||||
0.666245 | + | 0.745733i | \(0.267900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.21529 | − | 5.21529i | 0.235363 | − | 0.235363i | −0.579564 | − | 0.814927i | \(-0.696777\pi\) |
0.814927 | + | 0.579564i | \(0.196777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.11856 | − | 1.11856i | −0.0503776 | − | 0.0503776i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.66316i | − | 0.388596i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.8610 | − | 11.8610i | 0.530973 | − | 0.530973i | −0.389889 | − | 0.920862i | \(-0.627487\pi\) |
0.920862 | + | 0.389889i | \(0.127487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.18051i | 0.409339i | 0.978831 | + | 0.204669i | \(0.0656119\pi\) | ||||
−0.978831 | + | 0.204669i | \(0.934388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5588i | 0.603357i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.7454 | + | 15.7454i | −0.697902 | + | 0.697902i | −0.963958 | − | 0.266056i | \(-0.914279\pi\) |
0.266056 | + | 0.963958i | \(0.414279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6358i | 0.603210i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.39351 | + | 8.39351i | 0.369862 | + | 0.369862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.49443 | + | 3.49443i | −0.153685 | + | 0.153685i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2555 | −1.54457 | −0.772286 | − | 0.635275i | \(-0.780887\pi\) | ||||
−0.772286 | + | 0.635275i | \(0.780887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.3455 | − | 13.3455i | −0.583559 | − | 0.583559i | 0.352320 | − | 0.935880i | \(-0.385393\pi\) |
−0.935880 | + | 0.352320i | \(0.885393\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7344 | −0.903206 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8407 | 0.775684 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24848 | + | 1.24848i | 0.0540777 | + | 0.0540777i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.4688 | 0.625540 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.54895 | + | 4.54895i | −0.195937 | + | 0.195937i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4225 | + | 22.4225i | 0.964020 | + | 0.964020i | 0.999375 | − | 0.0353552i | \(-0.0112563\pi\) |
−0.0353552 | + | 0.999375i | \(0.511256\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.63950i | − | 0.155899i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.02624 | − | 6.02624i | 0.257664 | − | 0.257664i | −0.566440 | − | 0.824103i | \(-0.691680\pi\) |
0.824103 | + | 0.566440i | \(0.191680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.97146i | 0.169190i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.29142i | 0.395111i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.9169 | − | 19.9169i | 0.843905 | − | 0.843905i | −0.145459 | − | 0.989364i | \(-0.546466\pi\) |
0.989364 | + | 0.145459i | \(0.0464658\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 38.7493i | − | 1.63892i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0269 | − | 18.0269i | −0.759743 | − | 0.759743i | 0.216533 | − | 0.976275i | \(-0.430525\pi\) |
−0.976275 | + | 0.216533i | \(0.930525\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.5090 | + | 16.5090i | −0.694541 | + | 0.694541i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.6582 | −1.20142 | −0.600708 | − | 0.799469i | \(-0.705115\pi\) | ||||
−0.600708 | + | 0.799469i | \(0.705115\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74392 | + | 4.74392i | 0.198527 | + | 0.198527i | 0.799368 | − | 0.600841i | \(-0.205168\pi\) |
−0.600841 | + | 0.799368i | \(0.705168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.04209 | −0.210270 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.7361 | −1.15467 | −0.577335 | − | 0.816507i | \(-0.695907\pi\) | ||||
−0.577335 | + | 0.816507i | \(0.695907\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.76640 | + | 9.76640i | 0.405179 | + | 0.405179i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.44747 | −0.101364 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.8086 | − | 19.8086i | 0.817587 | − | 0.817587i | −0.168171 | − | 0.985758i | \(-0.553786\pi\) |
0.985758 | + | 0.168171i | \(0.0537860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.8088 | + | 36.8088i | 1.51668 | + | 1.51668i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.8296i | − | 0.773239i | −0.922239 | − | 0.386620i | \(-0.873643\pi\) | ||
0.922239 | − | 0.386620i | \(-0.126357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.42029 | + | 2.42029i | −0.0992222 | + | 0.0992222i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0141i | 0.981188i | 0.871388 | + | 0.490594i | \(0.163220\pi\) | ||||
−0.871388 | + | 0.490594i | \(0.836780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.3602i | − | 0.585766i | −0.956148 | − | 0.292883i | \(-0.905385\pi\) | ||
0.956148 | − | 0.292883i | \(-0.0946147\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.8257 | + | 35.8257i | −1.45652 | + | 1.45652i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.44642i | 0.261652i | 0.991405 | + | 0.130826i | \(0.0417629\pi\) | ||||
−0.991405 | + | 0.130826i | \(0.958237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.96711 | + | 1.96711i | 0.0795807 | + | 0.0795807i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.4106 | + | 31.4106i | −1.26866 | + | 1.26866i | −0.321884 | + | 0.946779i | \(0.604316\pi\) |
−0.946779 | + | 0.321884i | \(0.895684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.2797 | 1.21902 | 0.609508 | − | 0.792780i | \(-0.291367\pi\) | ||||
0.609508 | + | 0.792780i | \(0.291367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.97556 | − | 6.97556i | −0.280372 | − | 0.280372i | 0.552886 | − | 0.833257i | \(-0.313527\pi\) |
−0.833257 | + | 0.552886i | \(0.813527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.27355 | −0.291409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.97334 | 0.358934 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.68300 | + | 9.68300i | 0.386086 | + | 0.386086i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.0268 | −0.558398 | −0.279199 | − | 0.960233i | \(-0.590069\pi\) | ||||
−0.279199 | + | 0.960233i | \(0.590069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.28346 | − | 6.28346i | 0.249352 | − | 0.249352i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.56073 | + | 2.56073i | 0.101460 | + | 0.101460i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.9884i | − | 0.828992i | −0.910051 | − | 0.414496i | \(-0.863958\pi\) | ||
0.910051 | − | 0.414496i | \(-0.136042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.1818 | + | 32.1818i | −1.26913 | + | 1.26913i | −0.322589 | + | 0.946539i | \(0.604553\pi\) |
−0.946539 | + | 0.322589i | \(0.895447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.647703i | − | 0.0254638i | −0.999919 | − | 0.0127319i | \(-0.995947\pi\) | ||
0.999919 | − | 0.0127319i | \(-0.00405280\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.891176i | − | 0.0349817i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.7373 | + | 25.7373i | −1.00718 | + | 1.00718i | −0.00720262 | + | 0.999974i | \(0.502293\pi\) |
−0.999974 | + | 0.00720262i | \(0.997707\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31.6837i | 1.23798i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0862 | + | 17.0862i | 0.665583 | + | 0.665583i | 0.956690 | − | 0.291108i | \(-0.0940238\pi\) |
−0.291108 | + | 0.956690i | \(0.594024\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.34196 | + | 8.34196i | −0.324465 | + | 0.324465i | −0.850477 | − | 0.526012i | \(-0.823687\pi\) |
0.526012 | + | 0.850477i | \(0.323687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.59324 | 0.333232 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.23768 | + | 1.23768i | 0.0479233 | + | 0.0479233i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.4814 | 2.60509 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.69237 | −0.0652361 | −0.0326180 | − | 0.999468i | \(-0.510384\pi\) | ||||
−0.0326180 | + | 0.999468i | \(0.510384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.3935 | + | 36.3935i | 1.39872 | + | 1.39872i | 0.803749 | + | 0.594968i | \(0.202835\pi\) |
0.594968 | + | 0.803749i | \(0.297165\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.4508 | −0.401066 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.6522 | − | 13.6522i | 0.522388 | − | 0.522388i | −0.395904 | − | 0.918292i | \(-0.629569\pi\) |
0.918292 | + | 0.395904i | \(0.129569\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.9911 | + | 11.9911i | 0.458156 | + | 0.458156i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.37775i | 0.0524880i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.36989 | − | 2.36989i | 0.0901550 | − | 0.0901550i | −0.660591 | − | 0.750746i | \(-0.729694\pi\) |
0.750746 | + | 0.660591i | \(0.229694\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 16.2726i | − | 0.617254i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.00084i | 0.0379095i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.6655 | − | 27.6655i | 1.04491 | − | 1.04491i | 0.0459668 | − | 0.998943i | \(-0.485363\pi\) |
0.998943 | − | 0.0459668i | \(-0.0146369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 34.3795i | − | 1.29665i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.75000 | + | 5.75000i | 0.216251 | + | 0.216251i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.38704 | − | 4.38704i | 0.164759 | − | 0.164759i | −0.619912 | − | 0.784671i | \(-0.712832\pi\) |
0.784671 | + | 0.619912i | \(0.212832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.9425 | 0.859202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.4680 | + | 27.4680i | 1.02724 | + | 1.02724i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2313 | −0.679915 | −0.339957 | − | 0.940441i | \(-0.610413\pi\) | ||||
−0.339957 | + | 0.940441i | \(0.610413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.11905 | 0.265127 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.20957 | + | 1.20957i | 0.0449224 | + | 0.0449224i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.1985 | −0.637857 | −0.318928 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318928 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5316 | − | 15.5316i | 0.574457 | − | 0.574457i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.76630 | + | 1.76630i | 0.0652396 | + | 0.0652396i | 0.738974 | − | 0.673734i | \(-0.235311\pi\) |
−0.673734 | + | 0.738974i | \(0.735311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 62.2271i | − | 2.29216i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8217 | + | 20.8217i | −0.765939 | + | 0.765939i | −0.977389 | − | 0.211450i | \(-0.932182\pi\) |
0.211450 | + | 0.977389i | \(0.432182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 39.1460i | − | 1.43613i | −0.695977 | − | 0.718064i | \(-0.745029\pi\) | ||
0.695977 | − | 0.718064i | \(-0.254971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.316196i | − | 0.0115845i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.13593 | − | 6.13593i | 0.224202 | − | 0.224202i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.9147i | 1.63896i | 0.573106 | + | 0.819481i | \(0.305738\pi\) | ||||
−0.573106 | + | 0.819481i | \(0.694262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1904 | − | 16.1904i | −0.589229 | − | 0.589229i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.8730 | + | 35.8730i | −1.30383 | + | 1.30383i | −0.378036 | + | 0.925791i | \(0.623400\pi\) |
−0.925791 | + | 0.378036i | \(0.876600\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.4451 | −1.71988 | −0.859941 | − | 0.510393i | \(-0.829500\pi\) | ||||
−0.859941 | + | 0.510393i | \(0.829500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.54344 | − | 1.54344i | −0.0558764 | − | 0.0558764i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.501667 | −0.0181141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.59306 | 0.165630 | 0.0828150 | − | 0.996565i | \(-0.473609\pi\) | ||||
0.0828150 | + | 0.996565i | \(0.473609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.66000 | − | 1.66000i | −0.0597062 | − | 0.0597062i | 0.676623 | − | 0.736329i | \(-0.263443\pi\) |
−0.736329 | + | 0.676623i | \(0.763443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.4214 | 0.805401 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.77674 | − | 1.77674i | 0.0636583 | − | 0.0636583i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.4083 | − | 39.4083i | −1.41014 | − | 1.41014i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.87761i | 0.209781i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7673 | − | 16.7673i | 0.597688 | − | 0.597688i | −0.342009 | − | 0.939697i | \(-0.611107\pi\) |
0.939697 | + | 0.342009i | \(0.111107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0023i | 0.497865i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 37.9871i | − | 1.34896i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.6258 | − | 24.6258i | 0.872290 | − | 0.872290i | −0.120431 | − | 0.992722i | \(-0.538428\pi\) |
0.992722 | + | 0.120431i | \(0.0384277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.57692i | 0.0557876i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62.0284 | + | 62.0284i | 2.18894 | + | 2.18894i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.67803 | − | 2.67803i | 0.0943882 | − | 0.0943882i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.1357 | 1.44626 | 0.723128 | − | 0.690714i | \(-0.242704\pi\) | ||||
0.723128 | + | 0.690714i | \(0.242704\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.55287 | + | 3.55287i | 0.124758 | + | 0.124758i | 0.766729 | − | 0.641971i | \(-0.221883\pi\) |
−0.641971 | + | 0.766729i | \(0.721883\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.1670 | 0.531277 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −55.1449 | −1.92928 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.376144 | − | 0.376144i | −0.0131275 | − | 0.0131275i | 0.700513 | − | 0.713640i | \(-0.252955\pi\) |
−0.713640 | + | 0.700513i | \(0.752955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.94476 | −0.242079 | −0.121039 | − | 0.992648i | \(-0.538623\pi\) | ||||
−0.121039 | + | 0.992648i | \(0.538623\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.45823 | + | 7.45823i | −0.259348 | + | 0.259348i | −0.824789 | − | 0.565441i | \(-0.808706\pi\) |
0.565441 | + | 0.824789i | \(0.308706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4119 | − | 15.4119i | −0.535279 | − | 0.535279i | 0.386860 | − | 0.922139i | \(-0.373560\pi\) |
−0.922139 | + | 0.386860i | \(0.873560\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.05280i | 0.0711251i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.17113 | − | 5.17113i | 0.178954 | − | 0.178954i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.2950i | 0.597091i | 0.954395 | + | 0.298545i | \(0.0965014\pi\) | ||||
−0.954395 | + | 0.298545i | \(0.903499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.4062i | 0.979523i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.135176 | − | 0.135176i | 0.00465019 | − | 0.00465019i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.3859i | 1.04407i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7142 | − | 10.7142i | −0.367277 | − | 0.367277i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.7845 | + | 17.7845i | −0.608930 | + | 0.608930i | −0.942666 | − | 0.333736i | \(-0.891690\pi\) |
0.333736 | + | 0.942666i | \(0.391690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.25624 | 0.145390 | 0.0726952 | − | 0.997354i | \(-0.476840\pi\) | ||||
0.0726952 | + | 0.997354i | \(0.476840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.8297 | − | 27.8297i | −0.949539 | − | 0.949539i | 0.0492479 | − | 0.998787i | \(-0.484318\pi\) |
−0.998787 | + | 0.0492479i | \(0.984318\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.41542 | −0.286464 | −0.143232 | − | 0.989689i | \(-0.545750\pi\) | ||||
−0.143232 | + | 0.989689i | \(0.545750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.1158 | 1.46598 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.2662 | + | 42.2662i | 1.43378 | + | 1.43378i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.0293 | −1.18692 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.51232 | − | 8.51232i | 0.287769 | − | 0.287769i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9657 | − | 14.9657i | −0.505356 | − | 0.505356i | 0.407742 | − | 0.913097i | \(-0.366316\pi\) |
−0.913097 | + | 0.407742i | \(0.866316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.9109i | 0.569743i | 0.958566 | + | 0.284871i | \(0.0919509\pi\) | ||||
−0.958566 | + | 0.284871i | \(0.908049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.0835 | + | 21.0835i | −0.709518 | + | 0.709518i | −0.966434 | − | 0.256916i | \(-0.917294\pi\) |
0.256916 | + | 0.966434i | \(0.417294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 41.4937i | − | 1.39322i | −0.717450 | − | 0.696610i | \(-0.754691\pi\) | ||
0.717450 | − | 0.696610i | \(-0.245309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.32939i | − | 0.178742i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.79943 | − | 2.79943i | 0.0936795 | − | 0.0936795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.50150i | − | 0.250748i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.50379 | − | 5.50379i | −0.183562 | − | 0.183562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.552232 | + | 0.552232i | −0.0183975 | + | 0.0183975i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.4030 | 1.44276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.24476 | + | 3.24476i | 0.107740 | + | 0.107740i | 0.758922 | − | 0.651182i | \(-0.225726\pi\) |
−0.651182 | + | 0.758922i | \(0.725726\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.2047 | 1.56396 | 0.781980 | − | 0.623303i | \(-0.214210\pi\) | ||||
0.781980 | + | 0.623303i | \(0.214210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 88.8538 | 2.94063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.4364 | + | 13.4364i | 0.443710 | + | 0.443710i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.1617 | −0.698061 | −0.349030 | − | 0.937111i | \(-0.613489\pi\) | ||||
−0.349030 | + | 0.937111i | \(0.613489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.1840 | + | 22.1840i | −0.730195 | + | 0.730195i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4708 | − | 10.4708i | −0.344279 | − | 0.344279i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.4109i | 1.78516i | 0.450886 | + | 0.892581i | \(0.351108\pi\) | ||||
−0.450886 | + | 0.892581i | \(0.648892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.64422 | − | 3.64422i | 0.119435 | − | 0.119435i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.0196i | 0.720117i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.2919i | 1.31628i | 0.752895 | + | 0.658140i | \(0.228657\pi\) | ||||
−0.752895 | + | 0.658140i | \(0.771343\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2053 | − | 21.2053i | 0.691272 | − | 0.691272i | −0.271239 | − | 0.962512i | \(-0.587434\pi\) |
0.962512 | + | 0.271239i | \(0.0874335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.10742i | − | 0.0360626i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.6027 | − | 37.6027i | −1.22192 | − | 1.22192i | −0.966947 | − | 0.254977i | \(-0.917932\pi\) |
−0.254977 | − | 0.966947i | \(-0.582068\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.9175 | − | 34.9175i | 1.13347 | − | 1.13347i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9135 | −0.645062 | −0.322531 | − | 0.946559i | \(-0.604534\pi\) | ||||
−0.322531 | + | 0.946559i | \(0.604534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.1700 | + | 26.1700i | 0.846842 | + | 0.846842i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.1704 | 0.328418 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −71.0217 | −2.29102 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.17348 | + | 8.17348i | 0.263114 | + | 0.263114i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.5899 | 0.790759 | 0.395380 | − | 0.918518i | \(-0.370613\pi\) | ||||
0.395380 | + | 0.918518i | \(0.370613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.9255 | − | 19.9255i | 0.639438 | − | 0.639438i | −0.310979 | − | 0.950417i | \(-0.600657\pi\) |
0.950417 | + | 0.310979i | \(0.100657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.90089 | − | 6.90089i | −0.221232 | − | 0.221232i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.0455i | 1.60110i | 0.599267 | + | 0.800549i | \(0.295459\pi\) | ||||
−0.599267 | + | 0.800549i | \(0.704541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.0870 | + | 33.0870i | −1.05747 | + | 1.05747i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 17.3760i | − | 0.554207i | −0.960840 | − | 0.277104i | \(-0.910625\pi\) | ||
0.960840 | − | 0.277104i | \(-0.0893746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3344i | 0.456733i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.1856 | + | 17.1856i | −0.546470 | + | 0.546470i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.1839i | 1.40355i | 0.712399 | + | 0.701774i | \(0.247609\pi\) | ||||
−0.712399 | + | 0.701774i | \(0.752391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.8777 | − | 12.8777i | −0.408250 | − | 0.408250i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.76515 | − | 1.76515i | 0.0559030 | − | 0.0559030i | −0.678603 | − | 0.734506i | \(-0.737414\pi\) |
0.734506 | + | 0.678603i | \(0.237414\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.e.1583.6 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.15 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.1 | ✓ | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.20 | yes | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.20 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.15 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.1 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.6 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.1 | ✓ | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.323.20 | yes | 40 | 12.11 | even | 2 | ||
1008.2.v.e.827.1 | yes | 40 | 48.5 | odd | 4 | ||
1008.2.v.e.827.20 | yes | 40 | 16.5 | even | 4 | ||
4032.2.v.e.1583.6 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.1583.15 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.6 | 40 | 48.11 | even | 4 | inner | ||
4032.2.v.e.3599.15 | 40 | 16.11 | odd | 4 | inner |