Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(17,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.cp (of order \(6\), 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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.28 | ||
Character | \(\chi\) | \(=\) | 2016.593 |
Dual form | 2016.2.cp.b.17.28 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.18706 | + | 1.84005i | 1.42530 | + | 0.822896i | 0.996745 | − | 0.0806207i | \(-0.0256903\pi\) |
0.428553 | + | 0.903517i | \(0.359024\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.998380 | − | 2.45015i | 0.377352 | − | 0.926070i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.568599 | − | 0.984843i | −0.171439 | − | 0.296941i | 0.767484 | − | 0.641068i | \(-0.221508\pi\) |
−0.938923 | + | 0.344127i | \(0.888175\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.62005 | 1.00402 | 0.502011 | − | 0.864861i | \(-0.332594\pi\) | ||||
0.502011 | + | 0.864861i | \(0.332594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.84947 | − | 4.93542i | −0.691097 | − | 1.19702i | −0.971479 | − | 0.237127i | \(-0.923794\pi\) |
0.280381 | − | 0.959889i | \(-0.409539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.63386 | − | 4.56198i | 0.604250 | − | 1.04659i | −0.387920 | − | 0.921693i | \(-0.626806\pi\) |
0.992170 | − | 0.124898i | \(-0.0398603\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.19122 | − | 1.84245i | −0.665416 | − | 0.384178i | 0.128922 | − | 0.991655i | \(-0.458848\pi\) |
−0.794337 | + | 0.607477i | \(0.792182\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.27158 | + | 7.39859i | 0.854316 | + | 1.47972i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82838 | 0.339522 | 0.169761 | − | 0.985485i | \(-0.445700\pi\) | ||||
0.169761 | + | 0.985485i | \(0.445700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.52097 | − | 3.18753i | 0.991595 | − | 0.572498i | 0.0858442 | − | 0.996309i | \(-0.472641\pi\) |
0.905751 | + | 0.423811i | \(0.139308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.69030 | − | 5.97171i | 1.29990 | − | 1.00940i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.63700 | − | 4.98657i | −1.41991 | − | 0.819788i | −0.423623 | − | 0.905839i | \(-0.639242\pi\) |
−0.996291 | + | 0.0860510i | \(0.972575\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46900 | 0.541767 | 0.270884 | − | 0.962612i | \(-0.412684\pi\) | ||||
0.270884 | + | 0.962612i | \(0.412684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.00429i | − | 1.06814i | −0.845439 | − | 0.534072i | \(-0.820661\pi\) | ||
0.845439 | − | 0.534072i | \(-0.179339\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.98886 | + | 6.90891i | −0.581835 | + | 1.00777i | 0.413427 | + | 0.910537i | \(0.364332\pi\) |
−0.995262 | + | 0.0972305i | \(0.969002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00648 | − | 4.89236i | −0.715211 | − | 0.698909i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.84057 | + | 4.92001i | 0.390182 | + | 0.675815i | 0.992473 | − | 0.122461i | \(-0.0390787\pi\) |
−0.602291 | + | 0.798276i | \(0.705745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.18501i | − | 0.564306i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.813177 | − | 0.469488i | 0.105867 | − | 0.0611221i | −0.446132 | − | 0.894967i | \(-0.647199\pi\) |
0.551998 | + | 0.833845i | \(0.313865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.98482 | + | 3.43782i | −0.254131 | + | 0.440167i | −0.964659 | − | 0.263501i | \(-0.915123\pi\) |
0.710528 | + | 0.703669i | \(0.248456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.5373 | + | 6.66109i | 1.43103 | + | 0.826206i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.18293 | + | 1.26031i | −0.266687 | + | 0.153972i | −0.627381 | − | 0.778712i | \(-0.715873\pi\) |
0.360694 | + | 0.932684i | \(0.382540\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0093i | 1.66260i | 0.555821 | + | 0.831302i | \(0.312404\pi\) | ||||
−0.555821 | + | 0.831302i | \(0.687596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.72069 | − | 3.88019i | 0.786597 | − | 0.454142i | −0.0521661 | − | 0.998638i | \(-0.516613\pi\) |
0.838763 | + | 0.544496i | \(0.183279\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.98069 | + | 0.409906i | −0.339681 | + | 0.0467132i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.68289 | + | 13.3072i | −0.864393 | + | 1.49717i | 0.00325650 | + | 0.999995i | \(0.498963\pi\) |
−0.867649 | + | 0.497177i | \(0.834370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.89078i | 0.317304i | 0.987335 | + | 0.158652i | \(0.0507148\pi\) | ||||
−0.987335 | + | 0.158652i | \(0.949285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 20.9727i | − | 2.27480i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.04281 | + | 1.80621i | −0.110538 | + | 0.191458i | −0.915987 | − | 0.401207i | \(-0.868591\pi\) |
0.805449 | + | 0.592665i | \(0.201924\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.61419 | − | 8.86968i | 0.378870 | − | 0.929795i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.7886 | − | 9.69289i | 1.72247 | − | 0.994469i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3900i | 1.05494i | 0.849573 | + | 0.527471i | \(0.176860\pi\) | ||||
−0.849573 | + | 0.527471i | \(0.823140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.0193 | − | 9.82609i | 1.69348 | − | 0.977732i | 0.741813 | − | 0.670606i | \(-0.233966\pi\) |
0.951669 | − | 0.307126i | \(-0.0993674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.80827 | − | 4.50811i | −0.769372 | − | 0.444197i | 0.0632787 | − | 0.997996i | \(-0.479844\pi\) |
−0.832650 | + | 0.553799i | \(0.813178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.22682 | + | 5.58902i | −0.311949 | + | 0.540311i | −0.978784 | − | 0.204894i | \(-0.934315\pi\) |
0.666836 | + | 0.745205i | \(0.267648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00494 | − | 3.46695i | 0.575169 | − | 0.332074i | −0.184042 | − | 0.982918i | \(-0.558918\pi\) |
0.759211 | + | 0.650844i | \(0.225585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9073i | 1.68458i | 0.539028 | + | 0.842288i | \(0.318792\pi\) | ||||
−0.539028 | + | 0.842288i | \(0.681208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.78042 | − | 11.7440i | −0.632277 | − | 1.09514i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.9374 | + | 2.05420i | −1.36931 | + | 0.188308i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.85339 | − | 8.40632i | 0.441217 | − | 0.764211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.0392i | 1.16626i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.16038 | 0.102967 | 0.0514837 | − | 0.998674i | \(-0.483605\pi\) | ||||
0.0514837 | + | 0.998674i | \(0.483605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2555 | − | 5.92101i | −0.896026 | − | 0.517321i | −0.0201174 | − | 0.999798i | \(-0.506404\pi\) |
−0.875909 | + | 0.482477i | \(0.839737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54795 | − | 11.0080i | −0.741201 | − | 0.954511i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.36092 | − | 1.94043i | 0.287143 | − | 0.165782i | −0.349510 | − | 0.936933i | \(-0.613652\pi\) |
0.636653 | + | 0.771151i | \(0.280319\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.63508 | 0.647599 | 0.323799 | − | 0.946126i | \(-0.395040\pi\) | ||||
0.323799 | + | 0.946126i | \(0.395040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.05836 | − | 3.56518i | −0.172129 | − | 0.298136i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.82716 | + | 3.36432i | 0.483920 | + | 0.279391i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.50369 | − | 6.06857i | 0.287034 | − | 0.497157i | −0.686067 | − | 0.727539i | \(-0.740664\pi\) |
0.973100 | + | 0.230382i | \(0.0739975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.11816 | + | 15.7931i | 0.742025 | + | 1.28523i | 0.951572 | + | 0.307427i | \(0.0994679\pi\) |
−0.209547 | + | 0.977799i | \(0.567199\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.4609 | 1.88442 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.98079 | + | 12.0911i | 0.557128 | + | 0.964974i | 0.997735 | + | 0.0672736i | \(0.0214300\pi\) |
−0.440607 | + | 0.897700i | \(0.645237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.70034 | + | 5.97951i | −0.606872 | + | 0.471251i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.75280 | + | 5.05343i | 0.685572 | + | 0.395815i | 0.801951 | − | 0.597390i | \(-0.203795\pi\) |
−0.116379 | + | 0.993205i | \(0.537129\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.21398 | −0.403470 | −0.201735 | − | 0.979440i | \(-0.564658\pi\) | ||||
−0.201735 | + | 0.979440i | \(0.564658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.104796 | 0.00806124 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.22284 | − | 1.86071i | −0.245028 | − | 0.141467i | 0.372457 | − | 0.928049i | \(-0.378515\pi\) |
−0.617486 | + | 0.786582i | \(0.711849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.3923 | − | 3.07941i | 1.69270 | − | 0.232781i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1792 | + | 22.8270i | 0.985057 | + | 1.70617i | 0.641681 | + | 0.766972i | \(0.278237\pi\) |
0.343377 | + | 0.939198i | \(0.388429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.91329 | 0.365202 | 0.182601 | − | 0.983187i | \(-0.441548\pi\) | ||||
0.182601 | + | 0.983187i | \(0.441548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.3511 | − | 31.7850i | −1.34920 | − | 2.33688i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.24041 | + | 5.61255i | −0.236962 | + | 0.410431i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.29844 | + | 3.05906i | 0.383382 | + | 0.221345i | 0.679289 | − | 0.733871i | \(-0.262288\pi\) |
−0.295907 | + | 0.955217i | \(0.595622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.25188 | − | 16.0247i | −0.665965 | − | 1.15349i | −0.979023 | − | 0.203751i | \(-0.934687\pi\) |
0.313058 | − | 0.949734i | \(-0.398647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.99827 | 0.213618 | 0.106809 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106809 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.27718 | − | 0.737381i | 0.0905370 | − | 0.0522715i | −0.454048 | − | 0.890977i | \(-0.650021\pi\) |
0.544585 | + | 0.838706i | \(0.316687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.82542 | − | 4.47981i | 0.128119 | − | 0.314421i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0559 | + | 6.38315i | 0.772180 | + | 0.445818i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.99045 | −0.414368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.8952i | − | 1.23196i | −0.787764 | − | 0.615978i | \(-0.788761\pi\) | ||
0.787764 | − | 0.615978i | \(-0.211239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.8882 | − | 22.3231i | 0.878971 | − | 1.52242i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.29791 | − | 16.7096i | −0.155992 | − | 1.13432i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.3152 | − | 17.8665i | −0.693877 | − | 1.20183i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.26160i | 0.0844828i | 0.999107 | + | 0.0422414i | \(0.0134499\pi\) | ||||
−0.999107 | + | 0.0422414i | \(0.986550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.642193 | + | 0.370770i | −0.0426238 | + | 0.0246089i | −0.521160 | − | 0.853459i | \(-0.674501\pi\) |
0.478537 | + | 0.878068i | \(0.341167\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.62136 | − | 8.00442i | 0.305388 | − | 0.528947i | −0.671960 | − | 0.740588i | \(-0.734547\pi\) |
0.977348 | + | 0.211640i | \(0.0678806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.423385 | − | 0.244441i | −0.0277369 | − | 0.0160139i | 0.486067 | − | 0.873921i | \(-0.338431\pi\) |
−0.513804 | + | 0.857907i | \(0.671764\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.4255 | + | 14.6794i | −1.65858 | + | 0.957579i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36060i | 0.0880098i | 0.999031 | + | 0.0440049i | \(0.0140117\pi\) | ||||
−0.999031 | + | 0.0440049i | \(0.985988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.282523 | − | 0.163115i | 0.0181989 | − | 0.0105071i | −0.490873 | − | 0.871231i | \(-0.663322\pi\) |
0.509072 | + | 0.860724i | \(0.329989\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.95375 | − | 24.8044i | −0.444259 | − | 1.58470i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.53473 | − | 16.5146i | 0.606680 | − | 1.05080i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.972392i | − | 0.0613768i | −0.999529 | − | 0.0306884i | \(-0.990230\pi\) | ||
0.999529 | − | 0.0306884i | \(-0.00976996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.19047i | 0.263453i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.08066 | + | 12.2641i | −0.441680 | + | 0.765012i | −0.997814 | − | 0.0660806i | \(-0.978951\pi\) |
0.556135 | + | 0.831092i | \(0.312284\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.8409 | + | 16.1835i | −1.29499 | + | 1.00559i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.9754 | − | 9.22341i | 0.985086 | − | 0.568740i | 0.0812844 | − | 0.996691i | \(-0.474098\pi\) |
0.903802 | + | 0.427951i | \(0.140764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.9072i | 1.28432i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.9445 | + | 9.78291i | −1.03312 | + | 0.596475i | −0.917878 | − | 0.396862i | \(-0.870099\pi\) |
−0.115246 | + | 0.993337i | \(0.536766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4255 | − | 10.0606i | −1.05853 | − | 0.611141i | −0.133502 | − | 0.991049i | \(-0.542622\pi\) |
−0.925024 | + | 0.379908i | \(0.875956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.85763 | − | 8.41367i | 0.292926 | − | 0.507363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.82065 | + | 3.93790i | −0.409813 | + | 0.236606i | −0.690709 | − | 0.723132i | \(-0.742702\pi\) |
0.280896 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.6351i | − | 1.17133i | −0.810552 | − | 0.585666i | \(-0.800833\pi\) | ||
0.810552 | − | 0.585666i | \(-0.199167\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0872 | + | 19.2035i | 0.659063 | + | 1.14153i | 0.980859 | + | 0.194721i | \(0.0623803\pi\) |
−0.321796 | + | 0.946809i | \(0.604286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46338 | − | 8.49958i | 0.204437 | − | 0.501715i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.73892 | + | 13.4042i | −0.455231 | + | 0.788483i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.6531i | 1.08973i | 0.838525 | + | 0.544863i | \(0.183418\pi\) | ||||
−0.838525 | + | 0.544863i | \(0.816582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.45553 | 0.201189 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.5524 | − | 6.66978i | −0.668092 | − | 0.385723i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1616 | − | 6.99294i | −0.989176 | − | 0.403066i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.6515 | + | 7.30436i | −0.724424 | + | 0.418246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.7926 | 1.52913 | 0.764566 | − | 0.644546i | \(-0.222953\pi\) | ||||
0.764566 | + | 0.644546i | \(0.222953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8790 | + | 22.3071i | 0.730302 | + | 1.26492i | 0.956754 | + | 0.290898i | \(0.0939540\pi\) |
−0.226452 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2421 | + | 6.49065i | 0.635443 | + | 0.366873i | 0.782857 | − | 0.622202i | \(-0.213762\pi\) |
−0.147414 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5090 | + | 18.2021i | −0.590243 | + | 1.02233i | 0.403956 | + | 0.914778i | \(0.367635\pi\) |
−0.994199 | + | 0.107553i | \(0.965698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.03962 | − | 1.80067i | −0.0582073 | − | 0.100818i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.0204 | −1.67038 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.4633 | + | 26.7833i | 0.857752 | + | 1.48567i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.9455 | + | 16.6710i | 0.713707 | + | 0.919103i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6548 | − | 6.72892i | −0.640607 | − | 0.369855i | 0.144241 | − | 0.989543i | \(-0.453926\pi\) |
−0.784848 | + | 0.619688i | \(0.787259\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.27617 | −0.506811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.1178 | −1.31378 | −0.656891 | − | 0.753985i | \(-0.728129\pi\) | ||||
−0.656891 | + | 0.753985i | \(0.728129\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.27843 | − | 3.62486i | −0.339996 | − | 0.196297i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9854 | + | 7.38218i | −0.917125 | + | 0.398600i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.10821 | − | 3.65153i | −0.113175 | − | 0.196025i | 0.803874 | − | 0.594800i | \(-0.202769\pi\) |
−0.917049 | + | 0.398775i | \(0.869435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.32452 | 0.499130 | 0.249565 | − | 0.968358i | \(-0.419712\pi\) | ||||
0.249565 | + | 0.968358i | \(0.419712\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5650 | + | 18.2992i | 0.562320 | + | 0.973967i | 0.997293 | + | 0.0735234i | \(0.0234244\pi\) |
−0.434974 | + | 0.900443i | \(0.643242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.7779 | + | 44.6487i | −1.36815 | + | 2.36970i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.51917 | − | 5.49590i | −0.502403 | − | 0.290062i | 0.227303 | − | 0.973824i | \(-0.427009\pi\) |
−0.729705 | + | 0.683762i | \(0.760343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.37446 | − | 7.57680i | −0.230235 | − | 0.398779i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.5590 | 1.49485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.8547 | + | 9.73104i | −0.879806 | + | 0.507956i | −0.870594 | − | 0.492002i | \(-0.836265\pi\) |
−0.00921137 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.8907 | − | 2.04778i | 0.773088 | − | 0.106316i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.130569 | + | 0.0753842i | 0.00676062 | + | 0.00390325i | 0.503377 | − | 0.864067i | \(-0.332091\pi\) |
−0.496616 | + | 0.867970i | \(0.665424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.61884 | 0.340888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 32.9127i | − | 1.69061i | −0.534283 | − | 0.845306i | \(-0.679418\pi\) | ||
0.534283 | − | 0.845306i | \(-0.320582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.38834 | + | 14.5290i | −0.428624 | + | 0.742398i | −0.996751 | − | 0.0805423i | \(-0.974335\pi\) |
0.568127 | + | 0.822941i | \(0.307668\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2539 | − | 4.17823i | −0.522587 | − | 0.212942i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6509 | − | 21.9121i | −0.641428 | − | 1.11099i | −0.985114 | − | 0.171902i | \(-0.945009\pi\) |
0.343686 | − | 0.939085i | \(-0.388324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0000i | 1.06202i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −48.9717 | + | 28.2738i | −2.46403 | + | 1.42261i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7452 | + | 30.7356i | −0.890606 | + | 1.54257i | −0.0514552 | + | 0.998675i | \(0.516386\pi\) |
−0.839151 | + | 0.543899i | \(0.816947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.98000 | − | 1.72050i | −0.148814 | − | 0.0859179i | 0.423744 | − | 0.905782i | \(-0.360716\pi\) |
−0.572558 | + | 0.819864i | \(0.694049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.9862 | − | 11.5390i | 0.995584 | − | 0.574800i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3414i | 0.562175i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.30301 | + | 3.06169i | −0.262217 | + | 0.151391i | −0.625345 | − | 0.780348i | \(-0.715042\pi\) |
0.363129 | + | 0.931739i | \(0.381709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.338457 | − | 2.46113i | −0.0166544 | − | 0.121104i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.31918 | + | 9.21309i | −0.261108 | + | 0.452253i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.9546i | 0.584022i | 0.956415 | + | 0.292011i | \(0.0943244\pi\) | ||||
−0.956415 | + | 0.292011i | \(0.905676\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1616i | 0.592720i | 0.955076 | + | 0.296360i | \(0.0957728\pi\) | ||||
−0.955076 | + | 0.296360i | \(0.904227\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.3434 | − | 42.1641i | 1.18083 | − | 2.04526i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.44156 | + | 8.29536i | 0.311729 | + | 0.401441i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.6396 | + | 11.3389i | −0.946006 | + | 0.546177i | −0.891838 | − | 0.452355i | \(-0.850584\pi\) |
−0.0541683 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.754762i | − | 0.0362716i | −0.999836 | − | 0.0181358i | \(-0.994227\pi\) | ||
0.999836 | − | 0.0181358i | \(-0.00577312\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.8105 | + | 9.70554i | −0.804154 | + | 0.464279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2969 | − | 9.40902i | −0.777809 | − | 0.449068i | 0.0578444 | − | 0.998326i | \(-0.481577\pi\) |
−0.835653 | + | 0.549258i | \(0.814911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.46180 | − | 5.99600i | 0.164475 | − | 0.284879i | −0.771994 | − | 0.635630i | \(-0.780740\pi\) |
0.936469 | + | 0.350751i | \(0.114074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.64703 | + | 3.83766i | −0.315099 | + | 0.181923i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.270365i | − | 0.0127593i | −0.999980 | − | 0.00637965i | \(-0.997969\pi\) | ||
0.999980 | − | 0.00637965i | \(-0.00203072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.97247 | − | 3.41642i | −0.0928801 | − | 0.160873i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.8393 | − | 21.6179i | 1.30513 | − | 1.01346i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.91551 | + | 3.31776i | −0.0896037 | + | 0.155198i | −0.907344 | − | 0.420390i | \(-0.861893\pi\) |
0.817740 | + | 0.575588i | \(0.195227\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4863i | 0.721267i | 0.932708 | + | 0.360634i | \(0.117439\pi\) | ||||
−0.932708 | + | 0.360634i | \(0.882561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.51872 | 0.302950 | 0.151475 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151475 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.1086 | − | 11.0323i | −0.884240 | − | 0.510516i | −0.0121856 | − | 0.999926i | \(-0.503879\pi\) |
−0.872054 | + | 0.489410i | \(0.837212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.908568 | + | 6.60677i | 0.0419538 | + | 0.305072i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.89812 | + | 3.98263i | −0.317176 | + | 0.183122i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 45.0030 | 2.06488 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.97672 | + | 10.3520i | 0.273083 | + | 0.472994i | 0.969650 | − | 0.244498i | \(-0.0786233\pi\) |
−0.696567 | + | 0.717492i | \(0.745290\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.2664 | − | 18.0517i | −1.42563 | − | 0.823085i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.1181 | + | 33.1135i | −0.868107 | + | 1.50361i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.13421 | − | 1.96451i | −0.0513959 | − | 0.0890203i | 0.839183 | − | 0.543849i | \(-0.183034\pi\) |
−0.890579 | + | 0.454829i | \(0.849700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1155 | 0.682153 | 0.341077 | − | 0.940036i | \(-0.389208\pi\) | ||||
0.341077 | + | 0.940036i | \(0.389208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.20991 | − | 9.02383i | −0.234643 | − | 0.406413i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.3250 | + | 13.9867i | 1.53969 | + | 0.627387i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.1204 | + | 21.4315i | 1.66174 | + | 0.959404i | 0.971886 | + | 0.235452i | \(0.0756571\pi\) |
0.689851 | + | 0.723952i | \(0.257676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.5210 | −1.80674 | −0.903372 | − | 0.428858i | \(-0.858916\pi\) | ||||
−0.903372 | + | 0.428858i | \(0.858916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 72.3220 | 3.21829 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.81718 | − | 5.66795i | −0.435139 | − | 0.251227i | 0.266395 | − | 0.963864i | \(-0.414168\pi\) |
−0.701533 | + | 0.712637i | \(0.747501\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.79725 | − | 20.3406i | −0.123743 | − | 0.899815i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.5903 | − | 28.7352i | −0.731056 | − | 1.26623i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.07225 | 0.398997 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.86146 | − | 8.42029i | −0.212984 | − | 0.368900i | 0.739663 | − | 0.672978i | \(-0.234985\pi\) |
−0.952647 | + | 0.304078i | \(0.901652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.28564 | + | 16.0832i | −0.406033 | + | 0.703269i | −0.994441 | − | 0.105295i | \(-0.966421\pi\) |
0.588408 | + | 0.808564i | \(0.299755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.4636 | − | 18.1655i | −1.37058 | − | 0.791303i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.71073 | − | 8.15923i | −0.204815 | − | 0.354749i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5580 | 0.543947 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.5682 | + | 11.8750i | −0.889239 | + | 0.513402i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.97153 | + | 7.71238i | −0.0849198 | + | 0.332196i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.795518 | + | 0.459292i | 0.0342020 | + | 0.0197465i | 0.517004 | − | 0.855983i | \(-0.327047\pi\) |
−0.482802 | + | 0.875730i | \(0.660381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.5175 | 1.09305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4217i | 1.21523i | 0.794233 | + | 0.607613i | \(0.207873\pi\) | ||||
−0.794233 | + | 0.607613i | \(0.792127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.81570 | − | 8.34105i | 0.205156 | − | 0.355340i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.9341 | + | 32.1098i | 1.06031 | + | 1.36545i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7308 | − | 22.0504i | −0.539420 | − | 0.934304i | −0.998935 | − | 0.0461335i | \(-0.985310\pi\) |
0.459515 | − | 0.888170i | \(-0.348023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 25.3559i | − | 1.07244i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6292 | − | 9.02355i | 0.658694 | − | 0.380297i | −0.133085 | − | 0.991105i | \(-0.542488\pi\) |
0.791779 | + | 0.610807i | \(0.209155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.9503 | + | 57.0716i | −1.38623 | + | 2.40102i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9348 | − | 15.5508i | −1.12917 | − | 0.651925i | −0.185442 | − | 0.982655i | \(-0.559372\pi\) |
−0.943725 | + | 0.330730i | \(0.892705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0094 | + | 21.9447i | −1.59064 | + | 0.918359i | −0.597447 | + | 0.801908i | \(0.703818\pi\) |
−0.993197 | + | 0.116450i | \(0.962848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 31.4807i | − | 1.31284i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7081 | + | 14.8426i | −1.07024 | + | 0.617906i | −0.928248 | − | 0.371962i | \(-0.878685\pi\) |
−0.141996 | + | 0.989867i | \(0.545352\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.08284 | + | 2.88610i | 0.293846 | + | 0.119735i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.23029 | − | 5.59503i | 0.133785 | − | 0.231722i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 39.8767i | − | 1.64589i | −0.568122 | − | 0.822944i | \(-0.692330\pi\) | ||
0.568122 | − | 0.822944i | \(-0.307670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 33.5821i | − | 1.38373i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.90705 | − | 5.03515i | 0.119378 | − | 0.206769i | −0.800143 | − | 0.599809i | \(-0.795243\pi\) |
0.919521 | + | 0.393040i | \(0.128577\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −51.3862 | − | 20.9387i | −2.10663 | − | 0.858402i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.85117 | + | 4.53288i | −0.320790 | + | 0.185208i | −0.651745 | − | 0.758438i | \(-0.725963\pi\) |
0.330955 | + | 0.943647i | \(0.392629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.2715i | − | 0.990056i | −0.868877 | − | 0.495028i | \(-0.835158\pi\) | ||
0.868877 | − | 0.495028i | \(-0.164842\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.9361 | − | 17.8610i | 1.25773 | − | 0.726152i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.9254 | + | 12.6586i | 0.889923 | + | 0.513797i | 0.873917 | − | 0.486074i | \(-0.161572\pi\) |
0.0160059 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.4399 | + | 25.0106i | −0.584175 | + | 1.01182i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.971418 | + | 0.560849i | −0.0392352 | + | 0.0226525i | −0.519489 | − | 0.854477i | \(-0.673878\pi\) |
0.480254 | + | 0.877129i | \(0.340544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.9684i | − | 1.00519i | −0.864522 | − | 0.502596i | \(-0.832378\pi\) | ||
0.864522 | − | 0.502596i | \(-0.167622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5995 | + | 28.7513i | 0.667192 | + | 1.15561i | 0.978686 | + | 0.205362i | \(0.0658373\pi\) |
−0.311494 | + | 0.950248i | \(0.600829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.38435 | + | 4.35833i | 0.135591 | + | 0.174613i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.63487 | + | 4.56373i | −0.105395 | + | 0.182549i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.8363i | 2.26621i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5394 | 0.618613 | 0.309307 | − | 0.950962i | \(-0.399903\pi\) | ||||
0.309307 | + | 0.950962i | \(0.399903\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.69821 | + | 2.13516i | 0.146759 | + | 0.0847314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1237 | − | 17.7106i | −0.718088 | − | 0.701720i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.1136 | + | 19.1182i | −1.30791 | + | 0.755122i | −0.981747 | − | 0.190191i | \(-0.939089\pi\) |
−0.326163 | + | 0.945314i | \(0.605756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.17969 | 0.125395 | 0.0626974 | − | 0.998033i | \(-0.480030\pi\) | ||||
0.0626974 | + | 0.998033i | \(0.480030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.13828 | − | 15.8280i | −0.359263 | − | 0.622262i | 0.628575 | − | 0.777749i | \(-0.283639\pi\) |
−0.987838 | + | 0.155487i | \(0.950305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.924744 | − | 0.533901i | −0.0362994 | − | 0.0209574i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.2442 | − | 38.5282i | 0.870485 | − | 1.50772i | 0.00898848 | − | 0.999960i | \(-0.497139\pi\) |
0.861496 | − | 0.507764i | \(-0.169528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.7899 | − | 37.7413i | −0.851403 | − | 1.47467i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7165 | 0.962818 | 0.481409 | − | 0.876496i | \(-0.340125\pi\) | ||||
0.481409 | + | 0.876496i | \(0.340125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.39973 | + | 16.2808i | 0.365607 | + | 0.633250i | 0.988873 | − | 0.148760i | \(-0.0475281\pi\) |
−0.623266 | + | 0.782010i | \(0.714195\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.98766 | − | 50.8117i | −0.270970 | − | 1.97039i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.83477 | − | 3.36871i | −0.225923 | − | 0.130437i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.51428 | 0.174272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7132 | 0.875531 | 0.437766 | − | 0.899089i | \(-0.355770\pi\) | ||||
0.437766 | + | 0.899089i | \(0.355770\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.0283 | − | 17.9142i | −1.19251 | − | 0.688498i | −0.233638 | − | 0.972324i | \(-0.575063\pi\) |
−0.958876 | + | 0.283825i | \(0.908396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.4570 | + | 10.3731i | 0.976950 | + | 0.398084i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.91001 | − | 10.2364i | −0.226140 | − | 0.391686i | 0.730521 | − | 0.682891i | \(-0.239277\pi\) |
−0.956661 | + | 0.291204i | \(0.905944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.2820 | 0.545686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2830 | + | 17.8107i | 0.391752 | + | 0.678534i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.8555 | − | 29.1945i | 0.641213 | − | 1.11061i | −0.343950 | − | 0.938988i | \(-0.611765\pi\) |
0.985162 | − | 0.171625i | \(-0.0549016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.3335 | + | 14.0489i | 0.923021 | + | 0.532906i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.88481 | − | 17.1210i | −0.374414 | − | 0.648504i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.35428 | 0.277767 | 0.138884 | − | 0.990309i | \(-0.455649\pi\) | ||||
0.138884 | + | 0.990309i | \(0.455649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.4973 | + | 26.2679i | −1.71596 | + | 0.990713i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.08368 | − | 51.5100i | −0.266409 | − | 1.93723i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.1899 | + | 18.5848i | 1.20892 | + | 0.697968i | 0.962523 | − | 0.271202i | \(-0.0874210\pi\) |
0.246394 | + | 0.969170i | \(0.420754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23.4915 | −0.879764 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 15.1500i | − | 0.566576i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.83186 | + | 17.0293i | −0.366667 | + | 0.635085i | −0.989042 | − | 0.147634i | \(-0.952834\pi\) |
0.622376 | + | 0.782719i | \(0.286168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.8412 | + | 14.6306i | −0.701682 | + | 0.544873i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.81007 | + | 13.5274i | 0.290059 | + | 0.502397i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.1400i | − | 0.895302i | −0.894208 | − | 0.447651i | \(-0.852261\pi\) | ||
0.894208 | − | 0.447651i | \(-0.147739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.5691 | + | 19.9585i | −1.27858 | + | 0.738191i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.741275 | + | 1.28393i | −0.0273796 | + | 0.0474229i | −0.879391 | − | 0.476101i | \(-0.842050\pi\) |
0.852011 | + | 0.523524i | \(0.175383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.48242 | + | 1.43323i | 0.0914412 | + | 0.0527936i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3252 | − | 11.7348i | 0.747676 | − | 0.431671i | −0.0771774 | − | 0.997017i | \(-0.524591\pi\) |
0.824854 | + | 0.565346i | \(0.191257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.90858i | − | 0.216765i | −0.994109 | − | 0.108382i | \(-0.965433\pi\) | ||
0.994109 | − | 0.108382i | \(-0.0345671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.3330 | − | 12.8939i | 0.818217 | − | 0.472398i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.4723 | + | 13.4862i | 0.382651 | + | 0.492774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1457 | − | 27.9652i | 0.589166 | − | 1.02047i | −0.405175 | − | 0.914239i | \(-0.632790\pi\) |
0.994342 | − | 0.106227i | \(-0.0338771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 67.1115i | 2.44244i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7.01154i | − | 0.254839i | −0.991849 | − | 0.127419i | \(-0.959331\pi\) | ||
0.991849 | − | 0.127419i | \(-0.0406694\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.4606 | − | 30.2426i | 0.632945 | − | 1.09629i | −0.354001 | − | 0.935245i | \(-0.615179\pi\) |
0.986946 | − | 0.161049i | \(-0.0514876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.49935 | − | 18.1743i | −0.0904824 | − | 0.657955i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.94375 | − | 1.69957i | 0.106292 | − | 0.0613680i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6649i | 1.46642i | 0.680005 | + | 0.733208i | \(0.261978\pi\) | ||||
−0.680005 | + | 0.733208i | \(0.738022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.3357 | + | 20.4011i | −1.27094 | + | 0.733777i | −0.975165 | − | 0.221481i | \(-0.928911\pi\) |
−0.295774 | + | 0.955258i | \(0.595577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.1665 | + | 27.2316i | 1.69427 | + | 0.978187i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.13688 | − | 15.8255i | 0.327363 | − | 0.567009i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.7970 | − | 7.96570i | 0.493696 | − | 0.285035i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.3801i | 1.83383i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.9930 | − | 27.7007i | −0.570089 | − | 0.987423i | −0.996556 | − | 0.0829199i | \(-0.973575\pi\) |
0.426467 | − | 0.904503i | \(-0.359758\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.8755 | + | 17.8783i | 1.56003 | + | 0.635678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.18517 | + | 12.4451i | −0.255153 | + | 0.441938i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 27.1417i | − | 0.961410i | −0.876883 | − | 0.480705i | \(-0.840381\pi\) | ||
0.876883 | − | 0.480705i | \(-0.159619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.4645 | 1.60842 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.64276 | − | 4.41255i | −0.269707 | − | 0.155715i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.5441 | + | 4.88804i | −1.25276 | + | 0.172281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.8693 | − | 6.27540i | 0.382144 | − | 0.220631i | −0.296606 | − | 0.955000i | \(-0.595855\pi\) |
0.678751 | + | 0.734369i | \(0.262522\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0857 | 0.424388 | 0.212194 | − | 0.977228i | \(-0.431939\pi\) | ||||
0.212194 | + | 0.977228i | \(0.431939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.5971 | + | 32.2112i | 0.651430 | + | 1.12831i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.9534 | − | 18.4483i | −1.11791 | − | 0.645425i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2725 | − | 26.4527i | 0.533012 | − | 0.923204i | −0.466245 | − | 0.884656i | \(-0.654393\pi\) |
0.999257 | − | 0.0385483i | \(-0.0122734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4306 | − | 18.0664i | −0.363589 | − | 0.629754i | 0.624960 | − | 0.780657i | \(-0.285115\pi\) |
−0.988549 | + | 0.150903i | \(0.951782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.1969 | 1.74552 | 0.872759 | − | 0.488151i | \(-0.162328\pi\) | ||||
0.872759 | + | 0.488151i | \(0.162328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.59915 | − | 16.6262i | −0.333392 | − | 0.577453i | 0.649782 | − | 0.760120i | \(-0.274860\pi\) |
−0.983175 | + | 0.182668i | \(0.941527\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.88008 | + | 38.6497i | −0.342325 | + | 1.33913i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6173 | − | 9.59400i | −0.575065 | − | 0.332014i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.77418 | 0.337442 | 0.168721 | − | 0.985664i | \(-0.446036\pi\) | ||||
0.168721 | + | 0.985664i | \(0.446036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6570 | −0.884725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.333992 | + | 0.192830i | 0.0114897 | + | 0.00663357i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.7512 | − | 20.2842i | −0.541218 | − | 0.696975i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.3751 | + | 31.8265i | 0.629889 | + | 1.09100i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.3052 | 1.79090 | 0.895449 | − | 0.445165i | \(-0.146855\pi\) | ||||
0.895449 | + | 0.445165i | \(0.146855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5757 | + | 33.9062i | 0.668695 | + | 1.15821i | 0.978269 | + | 0.207338i | \(0.0664800\pi\) |
−0.309575 | + | 0.950875i | \(0.600187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.9471 | − | 41.4775i | 0.817063 | − | 1.41520i | −0.0907734 | − | 0.995872i | \(-0.528934\pi\) |
0.907837 | − | 0.419324i | \(-0.137733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.8433 | + | 11.4565i | 0.675473 | + | 0.389985i | 0.798147 | − | 0.602462i | \(-0.205814\pi\) |
−0.122674 | + | 0.992447i | \(0.539147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.84760 | − | 11.8604i | −0.232825 | − | 0.403265i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.4739 | 0.592763 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.90232 | + | 4.56241i | −0.267760 | + | 0.154591i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.9480 | + | 13.0181i | 1.08004 | + | 0.440091i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9012 | − | 12.0673i | −0.705783 | − | 0.407484i | 0.103715 | − | 0.994607i | \(-0.466927\pi\) |
−0.809498 | + | 0.587123i | \(0.800260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.8730 | −1.68026 | −0.840131 | − | 0.542383i | \(-0.817522\pi\) | ||||
−0.840131 | + | 0.542383i | \(0.817522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.1798i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547932\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.2756 | + | 17.7979i | −0.345022 | + | 0.597596i | −0.985358 | − | 0.170499i | \(-0.945462\pi\) |
0.640336 | + | 0.768095i | \(0.278795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.15850 | − | 2.84311i | 0.0388549 | − | 0.0953549i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0122 | + | 36.3942i | 0.703147 | + | 1.21789i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 97.0014i | 3.24240i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0944 | − | 5.82802i | 0.336668 | − | 0.194375i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.1882 | − | 28.0388i | 0.539307 | − | 0.934108i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.6589 | + | 9.04070i | 0.520521 | + | 0.300523i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.1180 | + | 18.5433i | −1.06646 | + | 0.615721i | −0.927212 | − | 0.374537i | \(-0.877802\pi\) |
−0.139248 | + | 0.990258i | \(0.544468\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.53166i | 0.315798i | 0.987455 | + | 0.157899i | \(0.0504720\pi\) | ||||
−0.987455 | + | 0.157899i | \(0.949528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.84696 | − | 1.64369i | 0.0942207 | − | 0.0543984i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.7462 | + | 19.2161i | −0.817193 | + | 0.634571i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.0199 | + | 22.5511i | −0.429487 | + | 0.743894i | −0.996828 | − | 0.0795896i | \(-0.974639\pi\) |
0.567340 | + | 0.823483i | \(0.307972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.7146i | 1.66929i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 85.2022i | − | 2.80143i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.7273 | + | 28.9725i | −0.548804 | + | 0.950556i | 0.449553 | + | 0.893254i | \(0.351583\pi\) |
−0.998357 | + | 0.0573025i | \(0.981750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.5052 | + | 9.95365i | −1.16364 | + | 0.326218i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6548 | + | 11.9250i | −0.675483 | + | 0.389991i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9751i | 0.619890i | 0.950754 | + | 0.309945i | \(0.100311\pi\) | ||||
−0.950754 | + | 0.309945i | \(0.899689\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.97034 | + | 2.29228i | −0.129429 | + | 0.0747261i | −0.563317 | − | 0.826241i | \(-0.690475\pi\) |
0.433887 | + | 0.900967i | \(0.357142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0704 | − | 6.39148i | −0.360501 | − | 0.208135i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.53547 | − | 13.0518i | 0.244870 | − | 0.424127i | −0.717225 | − | 0.696842i | \(-0.754588\pi\) |
0.962095 | + | 0.272714i | \(0.0879214\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.3293 | − | 14.0465i | 0.789761 | − | 0.455969i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.61355i | 0.0522679i | 0.999658 | + | 0.0261339i | \(0.00831964\pi\) | ||||
−0.999658 | + | 0.0261339i | \(0.991680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2576 | + | 19.4988i | 0.364289 | + | 0.630966i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.39887 | − | 10.1720i | −0.0451718 | − | 0.328473i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.82071 | − | 8.34972i | 0.155507 | − | 0.269346i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 68.0957i | − | 2.19208i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.2361 | −1.61548 | −0.807742 | − | 0.589536i | \(-0.799311\pi\) | ||||
−0.807742 | + | 0.589536i | \(0.799311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2190 | + | 11.0961i | 0.616767 | + | 0.356091i | 0.775609 | − | 0.631213i | \(-0.217443\pi\) |
−0.158842 | + | 0.987304i | \(0.550776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.62271 | − | 18.7071i | 0.244373 | − | 0.599722i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.72372 | − | 0.995188i | 0.0551466 | − | 0.0318389i | −0.472173 | − | 0.881506i | \(-0.656530\pi\) |
0.527320 | + | 0.849667i | \(0.323197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.37177 | 0.0758022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.8788 | − | 50.0195i | −0.921089 | − | 1.59537i | −0.797733 | − | 0.603011i | \(-0.793968\pi\) |
−0.123356 | − | 0.992362i | \(-0.539366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.55568 | + | 5.51698i | 0.304469 | + | 0.175785i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9051 | + | 22.3522i | −0.410357 | + | 0.710760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.6512 | + | 49.6252i | 0.910134 | + | 1.57640i | 0.813874 | + | 0.581042i | \(0.197355\pi\) |
0.0962601 | + | 0.995356i | \(0.469312\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.42727 | 0.172056 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3607 | − | 17.9452i | −0.328125 | − | 0.568330i | 0.654015 | − | 0.756482i | \(-0.273083\pi\) |
−0.982140 | + | 0.188152i | \(0.939750\pi\) | |||||||
\(998\) | 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 | 2016.2.cp.b.593.28 | 56 | ||
3.2 | odd | 2 | inner | 2016.2.cp.b.593.2 | 56 | ||
4.3 | odd | 2 | 504.2.ch.b.341.12 | yes | 56 | ||
7.3 | odd | 6 | inner | 2016.2.cp.b.17.27 | 56 | ||
8.3 | odd | 2 | 504.2.ch.b.341.23 | yes | 56 | ||
8.5 | even | 2 | inner | 2016.2.cp.b.593.1 | 56 | ||
12.11 | even | 2 | 504.2.ch.b.341.17 | yes | 56 | ||
21.17 | even | 6 | inner | 2016.2.cp.b.17.1 | 56 | ||
24.5 | odd | 2 | inner | 2016.2.cp.b.593.27 | 56 | ||
24.11 | even | 2 | 504.2.ch.b.341.6 | yes | 56 | ||
28.3 | even | 6 | 504.2.ch.b.269.6 | ✓ | 56 | ||
56.3 | even | 6 | 504.2.ch.b.269.17 | yes | 56 | ||
56.45 | odd | 6 | inner | 2016.2.cp.b.17.2 | 56 | ||
84.59 | odd | 6 | 504.2.ch.b.269.23 | yes | 56 | ||
168.59 | odd | 6 | 504.2.ch.b.269.12 | yes | 56 | ||
168.101 | even | 6 | inner | 2016.2.cp.b.17.28 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.ch.b.269.6 | ✓ | 56 | 28.3 | even | 6 | ||
504.2.ch.b.269.12 | yes | 56 | 168.59 | odd | 6 | ||
504.2.ch.b.269.17 | yes | 56 | 56.3 | even | 6 | ||
504.2.ch.b.269.23 | yes | 56 | 84.59 | odd | 6 | ||
504.2.ch.b.341.6 | yes | 56 | 24.11 | even | 2 | ||
504.2.ch.b.341.12 | yes | 56 | 4.3 | odd | 2 | ||
504.2.ch.b.341.17 | yes | 56 | 12.11 | even | 2 | ||
504.2.ch.b.341.23 | yes | 56 | 8.3 | odd | 2 | ||
2016.2.cp.b.17.1 | 56 | 21.17 | even | 6 | inner | ||
2016.2.cp.b.17.2 | 56 | 56.45 | odd | 6 | inner | ||
2016.2.cp.b.17.27 | 56 | 7.3 | odd | 6 | inner | ||
2016.2.cp.b.17.28 | 56 | 168.101 | even | 6 | inner | ||
2016.2.cp.b.593.1 | 56 | 8.5 | even | 2 | inner | ||
2016.2.cp.b.593.2 | 56 | 3.2 | odd | 2 | inner | ||
2016.2.cp.b.593.27 | 56 | 24.5 | odd | 2 | inner | ||
2016.2.cp.b.593.28 | 56 | 1.1 | even | 1 | trivial |