Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(1889,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{25} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.14 | ||
Root | \(-2.13875i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.1889 |
Dual form | 2016.2.k.a.1889.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.61313 | 1.16863 | 0.584313 | − | 0.811529i | \(-0.301364\pi\) | ||||
0.584313 | + | 0.811529i | \(0.301364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25928 | + | 2.32685i | −0.475963 | + | 0.879465i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29945i | 1.29633i | 0.761499 | + | 0.648167i | \(0.224464\pi\) | ||||
−0.761499 | + | 0.648167i | \(0.775536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.53073i | − | 0.424549i | −0.977210 | − | 0.212275i | \(-0.931913\pi\) | ||
0.977210 | − | 0.212275i | \(-0.0680871\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.448342 | −0.108739 | −0.0543694 | − | 0.998521i | \(-0.517315\pi\) | ||||
−0.0543694 | + | 0.998521i | \(0.517315\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92762i | 0.442227i | 0.975248 | + | 0.221113i | \(0.0709691\pi\) | ||||
−0.975248 | + | 0.221113i | \(0.929031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.737669i | 0.153815i | 0.997038 | + | 0.0769073i | \(0.0245046\pi\) | ||||
−0.997038 | + | 0.0769073i | \(0.975495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82843 | 0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.58132i | 1.18204i | 0.806657 | + | 0.591020i | \(0.201274\pi\) | ||||
−0.806657 | + | 0.591020i | \(0.798726\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.29066 | + | 6.08034i | −0.556223 | + | 1.02777i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.82843 | −0.464991 | −0.232495 | − | 0.972598i | \(-0.574689\pi\) | ||||
−0.232495 | + | 0.972598i | \(0.574689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.94269 | −1.08427 | −0.542133 | − | 0.840292i | \(-0.682383\pi\) | ||||
−0.542133 | + | 0.840292i | \(0.682383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.64212 | 1.47041 | 0.735205 | − | 0.677845i | \(-0.237086\pi\) | ||||
0.735205 | + | 0.677845i | \(0.237086\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.72607 | −0.397638 | −0.198819 | − | 0.980036i | \(-0.563711\pi\) | ||||
−0.198819 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.82843 | − | 5.86030i | −0.546918 | − | 0.837186i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.58579i | 0.355185i | 0.984104 | + | 0.177593i | \(0.0568309\pi\) | ||||
−0.984104 | + | 0.177593i | \(0.943169\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.2350i | 1.51493i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.30739 | −1.21172 | −0.605859 | − | 0.795572i | \(-0.707171\pi\) | ||||
−0.605859 | + | 0.795572i | \(0.707171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.28772i | 1.06113i | 0.847643 | + | 0.530567i | \(0.178021\pi\) | ||||
−0.847643 | + | 0.530567i | \(0.821979\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.00000i | − | 0.496139i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.47534 | −0.180241 | −0.0901206 | − | 0.995931i | \(-0.528725\pi\) | ||||
−0.0901206 | + | 0.995931i | \(0.528725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.4230i | − | 1.35566i | −0.735218 | − | 0.677831i | \(-0.762920\pi\) | ||
0.735218 | − | 0.677831i | \(-0.237080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0866i | 1.29758i | 0.760966 | + | 0.648792i | \(0.224725\pi\) | ||||
−0.760966 | + | 0.648792i | \(0.775275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0042 | − | 5.41421i | −1.14008 | − | 0.617007i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.7225 | 1.76892 | 0.884458 | − | 0.466620i | \(-0.154528\pi\) | ||||
0.884458 | + | 0.466620i | \(0.154528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8887 | −1.74401 | −0.872006 | − | 0.489496i | \(-0.837181\pi\) | ||||
−0.872006 | + | 0.489496i | \(0.837181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | −0.127075 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3952 | 1.84389 | 0.921944 | − | 0.387324i | \(-0.126601\pi\) | ||||
0.921944 | + | 0.387324i | \(0.126601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56178 | + | 1.92762i | 0.373376 | + | 0.202070i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.03712i | 0.516798i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.75699i | − | 0.686068i | −0.939323 | − | 0.343034i | \(-0.888545\pi\) | ||
0.939323 | − | 0.343034i | \(-0.111455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.83938 | 0.780047 | 0.390024 | − | 0.920805i | \(-0.372467\pi\) | ||||
0.390024 | + | 0.920805i | \(0.372467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8887i | 1.56556i | 0.622298 | + | 0.782780i | \(0.286199\pi\) | ||||
−0.622298 | + | 0.782780i | \(0.713801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.737669i | − | 0.0713132i | −0.999364 | − | 0.0356566i | \(-0.988648\pi\) | ||
0.999364 | − | 0.0356566i | \(-0.0113523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3137 | 1.46679 | 0.733394 | − | 0.679804i | \(-0.237935\pi\) | ||||
0.733394 | + | 0.679804i | \(0.237935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.07107i | − | 0.288902i | −0.989512 | − | 0.144451i | \(-0.953858\pi\) | ||
0.989512 | − | 0.144451i | \(-0.0461416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92762i | 0.179752i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.564588 | − | 1.04322i | 0.0517557 | − | 0.0956320i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.48528 | −0.680480 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.28772 | −0.741276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.59890 | 0.763029 | 0.381515 | − | 0.924363i | \(-0.375403\pi\) | ||||
0.381515 | + | 0.924363i | \(0.375403\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.7439 | −1.72504 | −0.862518 | − | 0.506026i | \(-0.831114\pi\) | ||||
−0.862518 | + | 0.506026i | \(0.831114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.48528 | − | 2.42742i | −0.388923 | − | 0.210484i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.0711i | 1.62935i | 0.579917 | + | 0.814676i | \(0.303085\pi\) | ||||
−0.579917 | + | 0.814676i | \(0.696915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.85525i | 0.326998i | 0.986544 | + | 0.163499i | \(0.0522780\pi\) | ||||
−0.986544 | + | 0.163499i | \(0.947722\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.58132 | 0.550357 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.69552i | 0.306896i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.58579i | − | 0.539529i | −0.962926 | − | 0.269764i | \(-0.913054\pi\) | ||
0.962926 | − | 0.269764i | \(-0.0869458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6792 | 1.19458 | 0.597290 | − | 0.802025i | \(-0.296244\pi\) | ||||
0.597290 | + | 0.802025i | \(0.296244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.1978i | 1.38136i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.0083i | − | 1.59684i | −0.602102 | − | 0.798419i | \(-0.705670\pi\) | ||
0.602102 | − | 0.798419i | \(-0.294330\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.71644 | − | 0.928932i | −0.135275 | − | 0.0732101i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.6731 | −1.46259 | −0.731297 | − | 0.682059i | \(-0.761085\pi\) | ||||
−0.731297 | + | 0.682059i | \(0.761085\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4366 | 0.807605 | 0.403803 | − | 0.914846i | \(-0.367688\pi\) | ||||
0.403803 | + | 0.914846i | \(0.367688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6569 | 0.819758 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.10748 | 0.692429 | 0.346214 | − | 0.938155i | \(-0.387467\pi\) | ||||
0.346214 | + | 0.938155i | \(0.387467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.30250 | + | 4.25447i | −0.174053 | + | 0.321608i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.82411i | 0.211084i | 0.994415 | + | 0.105542i | \(0.0336578\pi\) | ||||
−0.994415 | + | 0.105542i | \(0.966342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.1899i | − | 0.757407i | −0.925518 | − | 0.378704i | \(-0.876370\pi\) | ||
0.925518 | − | 0.378704i | \(-0.123630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.39104 | −0.543400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.92762i | − | 0.140962i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.33657i | 0.675571i | 0.941223 | + | 0.337785i | \(0.109678\pi\) | ||||
−0.941223 | + | 0.337785i | \(0.890322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.7990 | 1.13724 | 0.568618 | − | 0.822602i | \(-0.307478\pi\) | ||||
0.568618 | + | 0.822602i | \(0.307478\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7279i | 1.19182i | 0.803053 | + | 0.595908i | \(0.203208\pi\) | ||||
−0.803053 | + | 0.595908i | \(0.796792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9611i | 0.989675i | 0.868986 | + | 0.494837i | \(0.164772\pi\) | ||||
−0.868986 | + | 0.494837i | \(0.835228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.29066 | − | 1.78089i | −0.230959 | − | 0.124994i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.1421 | −1.26710 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.28772 | −0.573274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7164 | −1.35733 | −0.678665 | − | 0.734448i | \(-0.737441\pi\) | ||||
−0.678665 | + | 0.734448i | \(0.737441\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.1961 | 1.71836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.3137 | − | 8.28772i | −1.03956 | − | 0.562607i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.686292i | 0.0461650i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.65369i | − | 0.311634i | −0.987786 | − | 0.155817i | \(-0.950199\pi\) | ||
0.987786 | − | 0.155817i | \(-0.0498011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.0179 | −1.12952 | −0.564758 | − | 0.825257i | \(-0.691031\pi\) | ||||
−0.564758 | + | 0.825257i | \(0.691031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.0334i | 1.85250i | 0.376910 | + | 0.926250i | \(0.376987\pi\) | ||||
−0.376910 | + | 0.926250i | \(0.623013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.0711i | − | 0.987338i | −0.869650 | − | 0.493669i | \(-0.835655\pi\) | ||
0.869650 | − | 0.493669i | \(-0.164345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.12356 | −0.464690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.4601i | 1.06472i | 0.846519 | + | 0.532359i | \(0.178694\pi\) | ||||
−0.846519 | + | 0.532359i | \(0.821306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.2095i | 1.10856i | 0.832330 | + | 0.554280i | \(0.187006\pi\) | ||||
−0.832330 | + | 0.554280i | \(0.812994\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0042 | − | 15.3137i | −0.639142 | − | 0.978357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.95068 | 0.187747 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0335 | 0.759545 | 0.379772 | − | 0.925080i | \(-0.376002\pi\) | ||||
0.379772 | + | 0.925080i | \(0.376002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.17157 | −0.199395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.61313 | 0.163002 | 0.0815012 | − | 0.996673i | \(-0.474029\pi\) | ||||
0.0815012 | + | 0.996673i | \(0.474029\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.56178 | − | 6.58132i | 0.221318 | − | 0.408943i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.5466i | − | 1.14363i | −0.820382 | − | 0.571816i | \(-0.806239\pi\) | ||
0.820382 | − | 0.571816i | \(-0.193761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.75699i | 0.415078i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0238 | 1.03796 | 0.518979 | − | 0.854787i | \(-0.326312\pi\) | ||||
0.518979 | + | 0.854787i | \(0.326312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.58132i | − | 0.399786i | −0.979818 | − | 0.199893i | \(-0.935940\pi\) | ||
0.979818 | − | 0.199893i | \(-0.0640595\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.86123i | 0.474050i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.4558 | 1.64966 | 0.824831 | − | 0.565380i | \(-0.191270\pi\) | ||||
0.824831 | + | 0.565380i | \(0.191270\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.7279i | − | 0.997904i | −0.866630 | − | 0.498952i | \(-0.833718\pi\) | ||
0.866630 | − | 0.498952i | \(-0.166282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 11.2350i | − | 0.667852i | −0.942599 | − | 0.333926i | \(-0.891626\pi\) | ||
0.942599 | − | 0.333926i | \(-0.108374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.74280 | − | 16.1546i | 0.516071 | − | 0.953575i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7990 | −0.988176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.7975 | 0.689219 | 0.344609 | − | 0.938746i | \(-0.388011\pi\) | ||||
0.344609 | + | 0.938746i | \(0.388011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.3214 | −1.41604 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.12918 | 0.0653019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.1421 | + | 22.4357i | −0.699861 | + | 1.29317i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.6569i | 1.24007i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.3976i | − | 1.39245i | −0.717825 | − | 0.696223i | \(-0.754862\pi\) | ||
0.717825 | − | 0.696223i | \(-0.245138\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.0179 | 0.964995 | 0.482498 | − | 0.875897i | \(-0.339730\pi\) | ||||
0.482498 | + | 0.875897i | \(0.339730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.4412i | − | 1.32498i | −0.749073 | − | 0.662488i | \(-0.769501\pi\) | ||
0.749073 | − | 0.662488i | \(-0.230499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.10051i | − | 0.342639i | −0.985216 | − | 0.171319i | \(-0.945197\pi\) | ||
0.985216 | − | 0.171319i | \(-0.0548030\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.08034 | −0.340434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.864233i | − | 0.0480872i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.79884i | − | 0.155251i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.43289 | − | 6.34315i | 0.189261 | − | 0.349709i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5928 | 0.692163 | 0.346081 | − | 0.938204i | \(-0.387512\pi\) | ||||
0.346081 | + | 0.938204i | \(0.387512\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.85525 | −0.210635 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6569 | 1.17972 | 0.589862 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589862 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.2960 | −1.53232 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4571 | − | 1.52840i | 0.996589 | − | 0.0825258i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.4973i | − | 1.15403i | −0.816732 | − | 0.577017i | \(-0.804217\pi\) | ||
0.816732 | − | 0.577017i | \(-0.195783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.43289i | 0.183758i | 0.995770 | + | 0.0918791i | \(0.0292873\pi\) | ||||
−0.995770 | + | 0.0918791i | \(0.970713\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.83938 | −0.417248 | −0.208624 | − | 0.977996i | \(-0.566898\pi\) | ||||
−0.208624 | + | 0.977996i | \(0.566898\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 29.8498i | − | 1.58426i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 30.0962i | − | 1.58841i | −0.607647 | − | 0.794207i | \(-0.707886\pi\) | ||
0.607647 | − | 0.794207i | \(-0.292114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2843 | 0.804435 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.9706i | 1.51639i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.9790i | − | 1.61709i | −0.588436 | − | 0.808544i | \(-0.700256\pi\) | ||
0.588436 | − | 0.808544i | \(-0.299744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.01673 | − | 3.25623i | −0.312373 | − | 0.169055i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9706 | −0.775146 | −0.387573 | − | 0.921839i | \(-0.626687\pi\) | ||||
−0.387573 | + | 0.921839i | \(0.626687\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.16478 | 0.111492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.55568 | 0.388109 | 0.194055 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194055 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.58132 | −0.336289 | −0.168145 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168145 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.1421 | − | 14.1480i | −1.33233 | − | 0.721050i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9289i | 1.06114i | 0.847641 | + | 0.530569i | \(0.178022\pi\) | ||||
−0.847641 | + | 0.530569i | \(0.821978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.330728i | − | 0.0167256i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.0848 | 2.06720 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 24.8632i | − | 1.24785i | −0.781486 | − | 0.623923i | \(-0.785538\pi\) | ||
0.781486 | − | 0.623923i | \(-0.214462\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.5858i | − | 0.528629i | −0.964437 | − | 0.264314i | \(-0.914854\pi\) | ||
0.964437 | − | 0.264314i | \(-0.0851457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0742 | 0.501834 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.1607i | − | 0.602783i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.9414i | − | 0.788251i | −0.919057 | − | 0.394125i | \(-0.871048\pi\) | ||
0.919057 | − | 0.394125i | \(-0.128952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7206 | − | 21.6569i | 0.576733 | − | 1.06566i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.5192 | −2.03810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1626 | −0.643037 | −0.321518 | − | 0.946903i | \(-0.604193\pi\) | ||||
−0.321518 | + | 0.946903i | \(0.604193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.51472 | −0.463719 | −0.231860 | − | 0.972749i | \(-0.574481\pi\) | ||||
−0.231860 | + | 0.972749i | \(0.574481\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.819760 | −0.0397642 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.2842 | − | 10.4366i | −0.933230 | − | 0.505061i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.8862i | − | 1.00605i | −0.864272 | − | 0.503025i | \(-0.832220\pi\) | ||
0.864272 | − | 0.503025i | \(-0.167780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7206i | 0.563256i | 0.959524 | + | 0.281628i | \(0.0908745\pi\) | ||||
−0.959524 | + | 0.281628i | \(0.909126\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.42195 | −0.0680210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.9611i | − | 0.666326i | −0.942869 | − | 0.333163i | \(-0.891884\pi\) | ||
0.942869 | − | 0.333163i | \(-0.108116\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.737669i | 0.0350477i | 0.999846 | + | 0.0175239i | \(0.00557830\pi\) | ||||
−0.999846 | + | 0.0175239i | \(0.994422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.4558 | 2.15481 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0416i | − | 0.568280i | −0.958783 | − | 0.284140i | \(-0.908292\pi\) | ||
0.958783 | − | 0.284140i | \(-0.0917080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29.8498i | − | 1.40557i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.30739 | + | 5.03712i | 0.436337 | + | 0.236144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.97056 | −0.419625 | −0.209813 | − | 0.977742i | \(-0.567285\pi\) | ||||
−0.209813 | + | 0.977742i | \(0.567285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.50981 | 0.163468 | 0.0817341 | − | 0.996654i | \(-0.473954\pi\) | ||||
0.0817341 | + | 0.996654i | \(0.473954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.59890 | 0.399625 | 0.199812 | − | 0.979834i | \(-0.435967\pi\) | ||||
0.199812 | + | 0.979834i | \(0.435967\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6482 | 1.41823 | 0.709115 | − | 0.705092i | \(-0.249095\pi\) | ||||
0.709115 | + | 0.705092i | \(0.249095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.85786 | − | 3.43289i | 0.0857882 | − | 0.158516i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 41.4558i | 1.90614i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.52452i | 0.161716i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.3253 | −1.20283 | −0.601416 | − | 0.798936i | \(-0.705397\pi\) | ||||
−0.601416 | + | 0.798936i | \(0.705397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.32957i | 0.197411i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 17.6569i | − | 0.801756i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.7286 | −0.531472 | −0.265736 | − | 0.964046i | \(-0.585615\pi\) | ||||
−0.265736 | + | 0.964046i | \(0.585615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.1084i | − | 0.997736i | −0.866678 | − | 0.498868i | \(-0.833749\pi\) | ||
0.866678 | − | 0.498868i | \(-0.166251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.634051i | − | 0.0285562i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.5796 | + | 14.3848i | 1.19226 | + | 0.645245i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6792 | 0.657133 | 0.328567 | − | 0.944481i | \(-0.393434\pi\) | ||||
0.328567 | + | 0.944481i | \(0.393434\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.5035 | 1.53843 | 0.769217 | − | 0.638988i | \(-0.220647\pi\) | ||||
0.769217 | + | 0.638988i | \(0.220647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.4853 | 0.911583 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.04601 | −0.267985 | −0.133992 | − | 0.990982i | \(-0.542780\pi\) | ||||
−0.133992 | + | 0.990982i | \(0.542780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.7967 | − | 13.9611i | −1.14118 | − | 0.617602i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 41.5192i | 1.82955i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.7206i | − | 0.515472i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.4567 | −0.896223 | −0.448111 | − | 0.893978i | \(-0.647903\pi\) | ||||
−0.448111 | + | 0.893978i | \(0.647903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.45214i | 0.238405i | 0.992870 | + | 0.119203i | \(0.0380338\pi\) | ||||
−0.992870 | + | 0.119203i | \(0.961966\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.95068i | − | 0.128534i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4558 | 0.976341 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.6274i | 0.460325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.92762i | − | 0.0833384i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.1961 | − | 16.4601i | 1.08527 | − | 0.708988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.7990 | −1.45313 | −0.726566 | − | 0.687097i | \(-0.758885\pi\) | ||||
−0.726566 | + | 0.687097i | \(0.758885\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.0166 | 1.71412 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.9696 | −1.28141 | −0.640704 | − | 0.767788i | \(-0.721357\pi\) | ||||
−0.640704 | + | 0.767788i | \(0.721357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.72607 | −0.116134 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.7990 | + | 36.5838i | −0.841939 | + | 1.55570i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 10.8701i | − | 0.460579i | −0.973122 | − | 0.230290i | \(-0.926033\pi\) | ||
0.973122 | − | 0.230290i | \(-0.0739673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.7595i | − | 0.624261i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.72607 | −0.114890 | −0.0574451 | − | 0.998349i | \(-0.518295\pi\) | ||||
−0.0574451 | + | 0.998349i | \(0.518295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.02509i | − | 0.337618i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 36.7279i | − | 1.53971i | −0.638216 | − | 0.769857i | \(-0.720327\pi\) | ||
0.638216 | − | 0.769857i | \(-0.279673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.59890 | −0.359853 | −0.179926 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179926 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.34877i | 0.0562478i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.2960i | 1.17798i | 0.808140 | + | 0.588990i | \(0.200474\pi\) | ||||
−0.808140 | + | 0.588990i | \(0.799526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.0083 | − | 36.9706i | 0.830085 | − | 1.53380i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.1175 | −0.460438 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.5992 | 0.974043 | 0.487021 | − | 0.873390i | \(-0.338083\pi\) | ||||
0.487021 | + | 0.873390i | \(0.338083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.6863 | −0.522730 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.3421 | −1.41026 | −0.705130 | − | 0.709078i | \(-0.749111\pi\) | ||||
−0.705130 | + | 0.709078i | \(0.749111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.47534 | − | 2.72607i | 0.0604830 | − | 0.111758i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.8186i | 1.87210i | 0.351869 | + | 0.936049i | \(0.385546\pi\) | ||||
−0.351869 | + | 0.936049i | \(0.614454\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2960i | 1.15422i | 0.816667 | + | 0.577110i | \(0.195820\pi\) | ||||
−0.816667 | + | 0.577110i | \(0.804180\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.5600 | −0.795226 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.6716i | − | 0.879622i | −0.898090 | − | 0.439811i | \(-0.855045\pi\) | ||
0.898090 | − | 0.439811i | \(-0.144955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.17289i | 0.168817i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.2843 | 1.38473 | 0.692364 | − | 0.721548i | \(-0.256569\pi\) | ||||
0.692364 | + | 0.721548i | \(0.256569\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.04163i | − | 0.162710i | −0.996685 | − | 0.0813550i | \(-0.974075\pi\) | ||
0.996685 | − | 0.0813550i | \(-0.0259247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.5369i | 1.87048i | 0.354018 | + | 0.935238i | \(0.384815\pi\) | ||||
−0.354018 | + | 0.935238i | \(0.615185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.9054 | + | 40.4760i | −0.877622 | + | 1.62163i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.26810 | 0.0505625 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8709 | 1.42800 | 0.714000 | − | 0.700146i | \(-0.246882\pi\) | ||||
0.714000 | + | 0.700146i | \(0.246882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.4700 | 0.891695 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.97056 | + | 5.86030i | −0.355427 | + | 0.232194i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.2426i | 1.43150i | 0.698357 | + | 0.715749i | \(0.253915\pi\) | ||||
−0.698357 | + | 0.715749i | \(0.746085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.8319i | − | 0.506041i | −0.967461 | − | 0.253020i | \(-0.918576\pi\) | ||
0.967461 | − | 0.253020i | \(-0.0814240\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.3743 | 1.31208 | 0.656039 | − | 0.754727i | \(-0.272230\pi\) | ||||
0.656039 | + | 0.754727i | \(0.272230\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 40.0166i | − | 1.57079i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.72792i | 0.341550i | 0.985310 | + | 0.170775i | \(0.0546271\pi\) | ||||
−0.985310 | + | 0.170775i | \(0.945373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51.5934 | −2.01592 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20.6330i | − | 0.803748i | −0.915695 | − | 0.401874i | \(-0.868359\pi\) | ||
0.915695 | − | 0.401874i | \(-0.131641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13.1426i | − | 0.511186i | −0.966784 | − | 0.255593i | \(-0.917729\pi\) | ||
0.966784 | − | 0.255593i | \(-0.0822707\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.7206 | − | 6.34315i | −0.454506 | − | 0.245977i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.04322 | −0.0403937 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.6326 | −1.37558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8284 | 0.879971 | 0.439986 | − | 0.898005i | \(-0.354984\pi\) | ||||
0.439986 | + | 0.898005i | \(0.354984\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.3421 | −1.31987 | −0.659936 | − | 0.751322i | \(-0.729417\pi\) | ||||
−0.659936 | + | 0.751322i | \(0.729417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7225 | + | 8.50894i | 0.603373 | + | 0.326543i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 39.3062i | − | 1.50401i | −0.659158 | − | 0.752004i | \(-0.729087\pi\) | ||
0.659158 | − | 0.752004i | \(-0.270913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 49.8351i | 1.90410i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.95815 | 0.150794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.9222i | 1.06221i | 0.847306 | + | 0.531104i | \(0.178223\pi\) | ||||
−0.847306 | + | 0.531104i | \(0.821777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0742i | 0.382138i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.11270 | 0.117902 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0416i | 1.21020i | 0.796151 | + | 0.605098i | \(0.206866\pi\) | ||||
−0.796151 | + | 0.605098i | \(0.793134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.45214i | − | 0.205631i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.87197 | + | 18.2410i | −0.371274 | + | 0.686024i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.2843 | −0.912015 | −0.456007 | − | 0.889976i | \(-0.650721\pi\) | ||||
−0.456007 | + | 0.889976i | \(0.650721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.85483 | −0.181815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.1978 | 0.643161 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.8731 | −0.778436 | −0.389218 | − | 0.921146i | \(-0.627255\pi\) | ||||
−0.389218 | + | 0.921146i | \(0.627255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.9706 | − | 20.0083i | −1.37686 | − | 0.745149i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.58579i | 0.0960337i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.7930i | − | 0.993697i | −0.867837 | − | 0.496848i | \(-0.834491\pi\) | ||
0.867837 | − | 0.496848i | \(-0.165509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.32296 | −0.159891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.1786i | − | 0.856120i | −0.903750 | − | 0.428060i | \(-0.859197\pi\) | ||
0.903750 | − | 0.428060i | \(-0.140803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 6.34315i | − | 0.233653i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.42602 | −0.162814 | −0.0814068 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814068 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.86123i | − | 0.288401i | −0.989549 | − | 0.144200i | \(-0.953939\pi\) | ||
0.989549 | − | 0.144200i | \(-0.0460610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 17.2095i | − | 0.630507i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.71644 | + | 0.928932i | 0.0627175 | + | 0.0339424i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.7657 | 0.611789 | 0.305894 | − | 0.952065i | \(-0.401045\pi\) | ||||
0.305894 | + | 0.952065i | \(0.401045\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.3587 | 1.39602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.34315 | −0.230546 | −0.115273 | − | 0.993334i | \(-0.536774\pi\) | ||||
−0.115273 | + | 0.993334i | \(0.536774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.46796 | −0.270713 | −0.135357 | − | 0.990797i | \(-0.543218\pi\) | ||||
−0.135357 | + | 0.990797i | \(0.543218\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.2842 | + | 35.6326i | −0.698137 | + | 1.28999i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.2471i | 0.514434i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.1618i | − | 1.26797i | −0.773346 | − | 0.633984i | \(-0.781419\pi\) | ||
0.773346 | − | 0.633984i | \(-0.218581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.30318 | 0.190742 | 0.0953710 | − | 0.995442i | \(-0.469596\pi\) | ||||
0.0953710 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0335i | 0.432254i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 13.3829i | − | 0.479492i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.1127 | 1.75739 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 52.2843i | − | 1.86611i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.71049i | − | 0.274849i | −0.990512 | − | 0.137425i | \(-0.956118\pi\) | ||
0.990512 | − | 0.137425i | \(-0.0438825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.14590 | + | 3.86733i | 0.254079 | + | 0.137507i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6863 | 0.450503 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.21080 | 0.290841 | 0.145421 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145421 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.22221 | 0.0432387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47.6661 | −1.68210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.48528 | − | 2.42742i | −0.158085 | − | 0.0855552i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.3553i | 1.52429i | 0.647405 | + | 0.762146i | \(0.275854\pi\) | ||||
−0.647405 | + | 0.762146i | \(0.724146\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.2295i | 1.30731i | 0.756794 | + | 0.653653i | \(0.226764\pi\) | ||||
−0.756794 | + | 0.653653i | \(0.773236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −48.7953 | −1.70922 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5864i | 0.650255i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.5858i | − | 0.369446i | −0.982791 | − | 0.184723i | \(-0.940861\pi\) | ||
0.982791 | − | 0.184723i | \(-0.0591389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.1181 | 1.74701 | 0.873503 | − | 0.486818i | \(-0.161843\pi\) | ||||
0.873503 | + | 0.486818i | \(0.161843\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.6951i | − | 1.34556i | −0.739843 | − | 0.672780i | \(-0.765100\pi\) | ||
0.739843 | − | 0.672780i | \(-0.234900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.0949i | 1.07997i | 0.841675 | + | 0.539985i | \(0.181570\pi\) | ||||
−0.841675 | + | 0.539985i | \(0.818430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.71644 | + | 2.62742i | 0.0594712 | + | 0.0910346i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.2720 | 0.943788 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.2630 | −1.70075 | −0.850374 | − | 0.526179i | \(-0.823624\pi\) | ||||
−0.850374 | + | 0.526179i | \(0.823624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.8477 | 0.957990 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.42607 | − | 17.4171i | 0.323883 | − | 0.598459i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.08644i | − | 0.0715224i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.28772i | − | 0.283766i | −0.989883 | − | 0.141883i | \(-0.954684\pi\) | ||
0.989883 | − | 0.141883i | \(-0.0453157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.1354 | 1.23436 | 0.617181 | − | 0.786821i | \(-0.288275\pi\) | ||||
0.617181 | + | 0.786821i | \(0.288275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.5603i | 1.28154i | 0.767733 | + | 0.640770i | \(0.221385\pi\) | ||||
−0.767733 | + | 0.640770i | \(0.778615\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.91056i | 0.167157i | 0.996501 | + | 0.0835786i | \(0.0266350\pi\) | ||||
−0.996501 | + | 0.0835786i | \(0.973365\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7990 | 0.809190 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67.5980i | 2.29310i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.25835i | 0.0765213i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4366 | − | 19.2842i | 0.352820 | − | 0.651927i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.31371 | −0.314502 | −0.157251 | − | 0.987559i | \(-0.550263\pi\) | ||||
−0.157251 | + | 0.987559i | \(0.550263\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.3533 | 0.719413 | 0.359706 | − | 0.933066i | \(-0.382877\pi\) | ||||
0.359706 | + | 0.933066i | \(0.382877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0128 | 1.04366 | 0.521832 | − | 0.853048i | \(-0.325249\pi\) | ||||
0.521832 | + | 0.853048i | \(0.325249\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.17821 | −0.274597 | −0.137299 | − | 0.990530i | \(-0.543842\pi\) | ||||
−0.137299 | + | 0.990530i | \(0.543842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8284 | + | 20.0083i | −0.363174 | + | 0.671058i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.25483i | − | 0.175846i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.37976i | 0.246678i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.30739 | −0.310419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.15932i | − | 0.0386224i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 26.6274i | − | 0.885125i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6670 | 0.752647 | 0.376323 | − | 0.926488i | \(-0.377188\pi\) | ||||
0.376323 | + | 0.926488i | \(0.377188\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.2197i | 1.23314i | 0.787298 | + | 0.616572i | \(0.211479\pi\) | ||||
−0.787298 | + | 0.616572i | \(0.788521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 68.3127i | − | 2.26082i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.8632 | − | 45.9411i | 0.821054 | − | 1.51711i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7657 | 0.553049 | 0.276525 | − | 0.961007i | \(-0.410817\pi\) | ||||
0.276525 | + | 0.961007i | \(0.410817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.4856 | −0.575545 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.17157 | −0.170040 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.5378 | −1.00191 | −0.500956 | − | 0.865473i | \(-0.667018\pi\) | ||||
−0.500956 | + | 0.865473i | \(0.667018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.2965 | − | 7.37976i | 0.370226 | − | 0.241862i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.03712i | − | 0.164731i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.4567 | −0.666868 | −0.333434 | − | 0.942773i | \(-0.608207\pi\) | ||||
−0.333434 | + | 0.942773i | \(0.608207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.12141i | − | 0.166776i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 17.0712i | − | 0.554741i | −0.960763 | − | 0.277370i | \(-0.910537\pi\) | ||
0.960763 | − | 0.277370i | \(-0.0894629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9706 | 0.550888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.8701i | − | 0.481688i | −0.970564 | − | 0.240844i | \(-0.922576\pi\) | ||
0.970564 | − | 0.240844i | \(-0.0774243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.3976i | 0.789489i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.3754 | − | 24.0158i | −1.43296 | − | 0.775511i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3137 | −0.397216 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.2848 | 1.32900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.7225 | −0.505600 | −0.252800 | − | 0.967518i | \(-0.581352\pi\) | ||||
−0.252800 | + | 0.967518i | \(0.581352\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.6326 | 1.14351 | 0.571753 | − | 0.820426i | \(-0.306264\pi\) | ||||
0.571753 | + | 0.820426i | \(0.306264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.97056 | − | 4.85483i | −0.287583 | − | 0.155639i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.58579i | 0.0827266i | 0.999144 | + | 0.0413633i | \(0.0131701\pi\) | ||||
−0.999144 | + | 0.0413633i | \(0.986830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 74.7898i | 2.39029i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.7930 | −0.854563 | −0.427282 | − | 0.904119i | \(-0.640529\pi\) | ||||
−0.427282 | + | 0.904119i | \(0.640529\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.7122i | 1.39279i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.11270i | 0.226171i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.9757 | 0.825145 | 0.412573 | − | 0.910925i | \(-0.364630\pi\) | ||||
0.412573 | + | 0.910925i | \(0.364630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.4821i | 1.15656i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.4386i | 1.31237i | 0.754599 | + | 0.656187i | \(0.227832\pi\) | ||||
−0.754599 | + | 0.656187i | \(0.772168\pi\) | |||||||
\(998\) | 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.k.a.1889.14 | yes | 16 | |
3.2 | odd | 2 | inner | 2016.2.k.a.1889.2 | yes | 16 | |
4.3 | odd | 2 | inner | 2016.2.k.a.1889.15 | yes | 16 | |
7.6 | odd | 2 | inner | 2016.2.k.a.1889.1 | ✓ | 16 | |
8.3 | odd | 2 | 4032.2.k.g.3905.3 | 16 | |||
8.5 | even | 2 | 4032.2.k.g.3905.2 | 16 | |||
12.11 | even | 2 | inner | 2016.2.k.a.1889.3 | yes | 16 | |
21.20 | even | 2 | inner | 2016.2.k.a.1889.13 | yes | 16 | |
24.5 | odd | 2 | 4032.2.k.g.3905.14 | 16 | |||
24.11 | even | 2 | 4032.2.k.g.3905.15 | 16 | |||
28.27 | even | 2 | inner | 2016.2.k.a.1889.4 | yes | 16 | |
56.13 | odd | 2 | 4032.2.k.g.3905.13 | 16 | |||
56.27 | even | 2 | 4032.2.k.g.3905.16 | 16 | |||
84.83 | odd | 2 | inner | 2016.2.k.a.1889.16 | yes | 16 | |
168.83 | odd | 2 | 4032.2.k.g.3905.4 | 16 | |||
168.125 | even | 2 | 4032.2.k.g.3905.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.k.a.1889.1 | ✓ | 16 | 7.6 | odd | 2 | inner | |
2016.2.k.a.1889.2 | yes | 16 | 3.2 | odd | 2 | inner | |
2016.2.k.a.1889.3 | yes | 16 | 12.11 | even | 2 | inner | |
2016.2.k.a.1889.4 | yes | 16 | 28.27 | even | 2 | inner | |
2016.2.k.a.1889.13 | yes | 16 | 21.20 | even | 2 | inner | |
2016.2.k.a.1889.14 | yes | 16 | 1.1 | even | 1 | trivial | |
2016.2.k.a.1889.15 | yes | 16 | 4.3 | odd | 2 | inner | |
2016.2.k.a.1889.16 | yes | 16 | 84.83 | odd | 2 | inner | |
4032.2.k.g.3905.1 | 16 | 168.125 | even | 2 | |||
4032.2.k.g.3905.2 | 16 | 8.5 | even | 2 | |||
4032.2.k.g.3905.3 | 16 | 8.3 | odd | 2 | |||
4032.2.k.g.3905.4 | 16 | 168.83 | odd | 2 | |||
4032.2.k.g.3905.13 | 16 | 56.13 | odd | 2 | |||
4032.2.k.g.3905.14 | 16 | 24.5 | odd | 2 | |||
4032.2.k.g.3905.15 | 16 | 24.11 | even | 2 | |||
4032.2.k.g.3905.16 | 16 | 56.27 | even | 2 |