Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(223,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.b (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.8 | ||
Root | \(-2.06644i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.223 |
Dual form | 672.2.b.a.223.1 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.33660i | 1.93938i | 0.244329 | + | 0.969692i | \(0.421432\pi\) | ||||
−0.244329 | + | 0.969692i | \(0.578568\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.65222 | − | 2.06644i | −0.624482 | − | 0.781040i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.79628i | 1.14462i | 0.820037 | + | 0.572310i | \(0.193953\pi\) | ||||
−0.820037 | + | 0.572310i | \(0.806047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.82843i | − | 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.33660i | − | 1.11970i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.33660i | 1.05178i | 0.850553 | + | 0.525890i | \(0.176267\pi\) | ||||
−0.850553 | + | 0.525890i | \(0.823733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.54032 | −0.582789 | −0.291395 | − | 0.956603i | \(-0.594119\pi\) | ||||
−0.291395 | + | 0.956603i | \(0.594119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.65222 | + | 2.06644i | 0.360545 | + | 0.450933i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.64104i | − | 1.17624i | −0.808774 | − | 0.588119i | \(-0.799869\pi\) | ||
0.808774 | − | 0.588119i | \(-0.200131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.8061 | −2.76121 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.50162 | −1.76441 | −0.882203 | − | 0.470869i | \(-0.843940\pi\) | ||||
−0.882203 | + | 0.470869i | \(0.843940\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84476 | −0.331330 | −0.165665 | − | 0.986182i | \(-0.552977\pi\) | ||||
−0.165665 | + | 0.986182i | \(0.552977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.79628i | − | 0.660847i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.96130 | − | 7.16502i | 1.51474 | − | 1.21111i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.11654 | 0.841153 | 0.420577 | − | 0.907257i | \(-0.361828\pi\) | ||||
0.420577 | + | 0.907257i | \(0.361828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.82843i | 0.452911i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.32026i | − | 0.206190i | −0.994672 | − | 0.103095i | \(-0.967125\pi\) | ||
0.994672 | − | 0.103095i | \(-0.0328745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47602i | 0.377589i | 0.982017 | + | 0.188795i | \(0.0604581\pi\) | ||||
−0.982017 | + | 0.188795i | \(0.939542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.33660i | 0.646462i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2657 | −1.78914 | −0.894571 | − | 0.446925i | \(-0.852519\pi\) | ||||
−0.894571 | + | 0.446925i | \(0.852519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.54032 | + | 6.82843i | −0.220046 | + | 0.975490i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.33660i | − | 0.607245i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.23587 | 0.169760 | 0.0848801 | − | 0.996391i | \(-0.472949\pi\) | ||||
0.0848801 | + | 0.996391i | \(0.472949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.4629 | −2.21986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.54032 | 0.336473 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.65685 | 0.215704 | 0.107852 | − | 0.994167i | \(-0.465603\pi\) | ||||
0.107852 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.50162i | − | 0.448336i | −0.974550 | − | 0.224168i | \(-0.928034\pi\) | ||
0.974550 | − | 0.224168i | \(-0.0719665\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.65222 | − | 2.06644i | −0.208161 | − | 0.260347i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.2657 | 1.52138 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.1492i | 1.36209i | 0.732240 | + | 0.681046i | \(0.238475\pi\) | ||||
−0.732240 | + | 0.681046i | \(0.761525\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.64104i | 0.679102i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.03215i | 0.359850i | 0.983680 | + | 0.179925i | \(0.0575855\pi\) | ||||
−0.983680 | + | 0.179925i | \(0.942414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.01634i | − | 0.353036i | −0.984297 | − | 0.176518i | \(-0.943517\pi\) | ||
0.984297 | − | 0.176518i | \(-0.0564833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.8061 | 1.59419 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.84476 | − | 6.27230i | 0.893994 | − | 0.714794i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1972i | 1.14727i | 0.819110 | + | 0.573636i | \(0.194468\pi\) | ||||
−0.819110 | + | 0.573636i | \(0.805532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.04796 | −0.334557 | −0.167279 | − | 0.985910i | \(-0.553498\pi\) | ||||
−0.167279 | + | 0.985910i | \(0.553498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.8061 | −2.03980 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.50162 | 1.01868 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.53804i | 0.693031i | 0.938044 | + | 0.346515i | \(0.112635\pi\) | ||||
−0.938044 | + | 0.346515i | \(0.887365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.84476 | + | 4.67319i | −0.612698 | + | 0.489884i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.84476 | 0.191293 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 11.0163i | − | 1.13025i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.33005i | − | 0.642719i | −0.946957 | − | 0.321359i | \(-0.895860\pi\) | ||
0.946957 | − | 0.321359i | \(-0.104140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.79628i | 0.381540i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.97711i | 0.694249i | 0.937819 | + | 0.347124i | \(0.112842\pi\) | ||||
−0.937819 | + | 0.347124i | \(0.887158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.84476 | 0.970034 | 0.485017 | − | 0.874505i | \(-0.338813\pi\) | ||||
0.485017 | + | 0.874505i | \(0.338813\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.96130 | + | 7.16502i | −0.874533 | + | 0.699235i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.46947i | 0.432080i | 0.976385 | + | 0.216040i | \(0.0693141\pi\) | ||||
−0.976385 | + | 0.216040i | \(0.930686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.60889 | 0.441452 | 0.220726 | − | 0.975336i | \(-0.429157\pi\) | ||||
0.220726 | + | 0.975336i | \(0.429157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.11654 | −0.485640 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9553 | 1.68909 | 0.844545 | − | 0.535484i | \(-0.179871\pi\) | ||||
0.844545 | + | 0.535484i | \(0.179871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.4629 | 2.28118 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.82843i | − | 0.261488i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.96130 | − | 7.16502i | 0.821481 | − | 0.656817i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.41172 | −0.310156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.32026i | 0.119044i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 38.1883i | − | 3.41567i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.11654i | − | 0.808962i | −0.914546 | − | 0.404481i | \(-0.867452\pi\) | ||
0.914546 | − | 0.404481i | \(-0.132548\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 2.47602i | − | 0.218001i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.57622 | −0.399826 | −0.199913 | − | 0.979814i | \(-0.564066\pi\) | ||||
−0.199913 | + | 0.979814i | \(0.564066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.19717 | + | 5.24941i | 0.363941 | + | 0.455181i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 4.33660i | − | 0.373235i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9226 | 1.01862 | 0.509308 | − | 0.860584i | \(-0.329901\pi\) | ||||
0.509308 | + | 0.860584i | \(0.329901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.31371 | −0.620341 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.2657 | 1.03296 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.7375 | 0.897914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 41.2047i | − | 3.42186i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.54032 | − | 6.82843i | 0.127043 | − | 0.563199i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.6867 | −1.36703 | −0.683515 | − | 0.729937i | \(-0.739550\pi\) | ||||
−0.683515 | + | 0.729937i | \(0.739550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.10020i | − | 0.496427i | −0.968705 | − | 0.248214i | \(-0.920157\pi\) | ||
0.968705 | − | 0.248214i | \(-0.0798435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.33660i | 0.350593i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.81209i | 0.623473i | 0.950169 | + | 0.311736i | \(0.100911\pi\) | ||||
−0.950169 | + | 0.311736i | \(0.899089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.23587 | −0.0980111 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.6569 | + | 9.32026i | −0.918689 | + | 0.734539i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4629i | 1.13282i | 0.824122 | + | 0.566412i | \(0.191669\pi\) | ||||
−0.824122 | + | 0.566412i | \(0.808331\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.4629 | 1.28164 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.2984 | 1.41597 | 0.707987 | − | 0.706225i | \(-0.249603\pi\) | ||||
0.707987 | + | 0.706225i | \(0.249603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.54032 | −0.194263 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3203i | 1.31683i | 0.752653 | + | 0.658417i | \(0.228774\pi\) | ||||
−0.752653 | + | 0.658417i | \(0.771226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.8107 | + | 28.5294i | 1.72433 | + | 2.15662i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.65685 | −0.124537 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.2680i | 0.767468i | 0.923444 | + | 0.383734i | \(0.125362\pi\) | ||||
−0.923444 | + | 0.383734i | \(0.874638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.9570i | − | 1.11175i | −0.831267 | − | 0.555874i | \(-0.812384\pi\) | ||
0.831267 | − | 0.555874i | \(-0.187616\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.50162i | 0.258847i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.1883i | 1.63132i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.4629 | −1.20389 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.65222 | + | 2.06644i | 0.120182 | + | 0.150311i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9231i | 1.80337i | 0.432389 | + | 0.901687i | \(0.357671\pi\) | ||||
−0.432389 | + | 0.901687i | \(0.642329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.49236 | 0.107422 | 0.0537111 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537111 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.2657 | −0.878368 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.89273 | 0.491087 | 0.245543 | − | 0.969386i | \(-0.421034\pi\) | ||||
0.245543 | + | 0.969386i | \(0.421034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.9940 | −1.63000 | −0.815000 | − | 0.579461i | \(-0.803263\pi\) | ||||
−0.815000 | + | 0.579461i | \(0.803263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.1492i | − | 0.786405i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.6988 | + | 19.6345i | 1.10184 | + | 1.37807i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.72543 | 0.399881 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.64104i | − | 0.392080i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.64375i | − | 0.667072i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.60462i | 0.454681i | 0.973815 | + | 0.227340i | \(0.0730030\pi\) | ||||
−0.973815 | + | 0.227340i | \(0.926997\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.03215i | − | 0.207760i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7375 | −0.732291 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.04796 | + | 3.81209i | 0.206909 | + | 0.258781i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.01634i | 0.203825i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.2657 | 0.825083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0093 | −1.07206 | −0.536030 | − | 0.844199i | \(-0.680077\pi\) | ||||
−0.536030 | + | 0.844199i | \(0.680077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.8061 | −0.920404 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.310470 | 0.0206066 | 0.0103033 | − | 0.999947i | \(-0.496720\pi\) | ||||
0.0103033 | + | 0.999947i | \(0.496720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5180i | 1.48803i | 0.668164 | + | 0.744014i | \(0.267081\pi\) | ||||
−0.668164 | + | 0.744014i | \(0.732919\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.84476 | + | 6.27230i | −0.516148 | + | 0.412687i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.6569 | −0.763666 | −0.381833 | − | 0.924231i | \(-0.624707\pi\) | ||||
−0.381833 | + | 0.924231i | \(0.624707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 53.1916i | − | 3.46984i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.1972i | − | 0.662378i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.88721i | 0.251443i | 0.992066 | + | 0.125721i | \(0.0401245\pi\) | ||||
−0.992066 | + | 0.125721i | \(0.959875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.54459i | − | 0.292743i | −0.989230 | − | 0.146371i | \(-0.953241\pi\) | ||
0.989230 | − | 0.146371i | \(-0.0467595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.6121 | − | 6.67974i | −1.89185 | − | 0.426753i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.18511i | 0.457177i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.04796 | 0.193157 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.92260 | −0.373831 | −0.186916 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186916 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4150 | 1.34635 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.8061 | 1.17768 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.0261258i | 0.00162968i | 1.00000 | 0.000814840i | \(0.000259372\pi\) | |||||
−1.00000 | 0.000814840i | \(0.999741\pi\) | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.45366 | − | 10.5730i | −0.525285 | − | 0.656974i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.50162 | −0.588135 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3785i | 0.763293i | 0.924308 | + | 0.381647i | \(0.124643\pi\) | ||||
−0.924308 | + | 0.381647i | \(0.875357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.35948i | 0.329230i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.53804i | − | 0.400122i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.13515i | 0.130182i | 0.997879 | + | 0.0650912i | \(0.0207338\pi\) | ||||
−0.997879 | + | 0.0650912i | \(0.979266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.3763 | 1.60224 | 0.801122 | − | 0.598501i | \(-0.204237\pi\) | ||||
0.801122 | + | 0.598501i | \(0.204237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.84476 | − | 4.67319i | 0.353741 | − | 0.282834i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 52.4116i | − | 3.16054i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.1198 | −1.44922 | −0.724608 | − | 0.689161i | \(-0.757979\pi\) | ||||
−0.724608 | + | 0.689161i | \(0.757979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.84476 | −0.110443 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6416 | −0.634823 | −0.317411 | − | 0.948288i | \(-0.602814\pi\) | ||||
−0.317411 | + | 0.948288i | \(0.602814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.5436 | 1.04286 | 0.521428 | − | 0.853295i | \(-0.325399\pi\) | ||||
0.521428 | + | 0.853295i | \(0.325399\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.0163i | 0.652552i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.72823 | + | 2.18136i | −0.161042 | + | 0.128762i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.80606 | −0.106239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.33005i | 0.371074i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.64707i | − | 0.505167i | −0.967575 | − | 0.252584i | \(-0.918720\pi\) | ||
0.967575 | − | 0.252584i | \(-0.0812802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.18511i | 0.418333i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.79628i | − | 0.220282i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.9553 | −0.922717 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.11654 | − | 4.09093i | 0.294912 | − | 0.235798i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6.97711i | − | 0.400825i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.1851 | 0.869497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.3823 | −1.33450 | −0.667249 | − | 0.744835i | \(-0.732528\pi\) | ||||
−0.667249 | + | 0.744835i | \(0.732528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.84476 | −0.560049 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1883 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283427\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.8779i | 1.01052i | 0.862968 | + | 0.505259i | \(0.168603\pi\) | ||||
−0.862968 | + | 0.505259i | \(0.831397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.96130 | − | 7.16502i | 0.504912 | − | 0.403703i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1585 | −0.851385 | −0.425692 | − | 0.904868i | \(-0.639969\pi\) | ||||
−0.425692 | + | 0.904868i | \(0.639969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.0708i | − | 2.01958i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 4.46947i | − | 0.249461i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.0163i | − | 0.612965i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 39.0494i | 2.16607i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.60889 | −0.254872 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.2657 | + | 25.3464i | 1.11729 | + | 1.39739i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.57194i | 0.471157i | 0.971855 | + | 0.235578i | \(0.0756984\pi\) | ||||
−0.971855 | + | 0.235578i | \(0.924302\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.11654 | 0.280384 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −48.3496 | −2.64162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3943 | −1.21990 | −0.609949 | − | 0.792441i | \(-0.708810\pi\) | ||||
−0.609949 | + | 0.792441i | \(0.708810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.9553 | −0.975197 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.00324i | − | 0.379247i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6555 | − | 8.09911i | 0.899310 | − | 0.437311i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.4629 | −1.31704 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.4205i | 0.613082i | 0.951857 | + | 0.306541i | \(0.0991717\pi\) | ||||
−0.951857 | + | 0.306541i | \(0.900828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.65081i | − | 0.302481i | −0.988497 | − | 0.151241i | \(-0.951673\pi\) | ||
0.988497 | − | 0.151241i | \(-0.0483268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82843i | 0.150970i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 27.3398i | − | 1.45515i | −0.686027 | − | 0.727576i | \(-0.740647\pi\) | ||
0.686027 | − | 0.727576i | \(-0.259353\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.1492 | −0.697888 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.96130 | + | 7.16502i | −0.474282 | + | 0.379213i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.2848i | − | 1.22892i | −0.788946 | − | 0.614462i | \(-0.789373\pi\) | ||
0.788946 | − | 0.614462i | \(-0.210627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5468 | −0.660357 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.41172 | 0.179069 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.0806 | 0.684672 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1464 | 0.842836 | 0.421418 | − | 0.906867i | \(-0.361533\pi\) | ||||
0.421418 | + | 0.906867i | \(0.361533\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.32026i | − | 0.0687299i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.04194 | − | 2.55385i | −0.106012 | − | 0.132589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.4750 | 1.42260 | 0.711300 | − | 0.702888i | \(-0.248107\pi\) | ||||
0.711300 | + | 0.702888i | \(0.248107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.1883i | 1.97204i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.8746i | 1.38411i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.90304i | − | 0.251852i | −0.992040 | − | 0.125926i | \(-0.959810\pi\) | ||
0.992040 | − | 0.125926i | \(-0.0401902\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.11654i | 0.467054i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.73749 | 0.139879 | 0.0699397 | − | 0.997551i | \(-0.477719\pi\) | ||||
0.0699397 | + | 0.997551i | \(0.477719\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.2004 | + | 34.0196i | 1.38626 | + | 1.73380i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.47602i | 0.125863i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.4896 | −1.59658 | −0.798292 | − | 0.602270i | \(-0.794263\pi\) | ||||
−0.798292 | + | 0.602270i | \(0.794263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4629 | 1.23714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.57622 | 0.230840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −44.2210 | −2.22500 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.15847i | − | 0.0581421i | −0.999577 | − | 0.0290711i | \(-0.990745\pi\) | ||
0.999577 | − | 0.0290711i | \(-0.00925491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.19717 | − | 5.24941i | −0.210121 | − | 0.262799i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.70482 | −0.135072 | −0.0675361 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675361 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.21778i | 0.259916i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.33660i | 0.215487i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4238i | 0.962801i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.8942i | 1.42873i | 0.699775 | + | 0.714363i | \(0.253284\pi\) | ||||
−0.699775 | + | 0.714363i | \(0.746716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9226 | −0.588098 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.73749 | − | 3.42378i | −0.134703 | − | 0.168473i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 13.2178i | − | 0.648835i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.31371 | 0.358154 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.3464 | −1.43366 | −0.716832 | − | 0.697246i | \(-0.754409\pi\) | ||||
−0.716832 | + | 0.697246i | \(0.754409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8867 | 1.06669 | 0.533346 | − | 0.845897i | \(-0.320934\pi\) | ||||
0.533346 | + | 0.845897i | \(0.320934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.2657 | −0.596381 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 59.8713i | − | 2.90419i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.23587 | + | 5.78546i | −0.350168 | + | 0.279978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.7375 | −0.518411 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.76640i | − | 0.133253i | −0.997778 | − | 0.0666265i | \(-0.978776\pi\) | ||
0.997778 | − | 0.0666265i | \(-0.0212236\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8181i | 1.14463i | 0.820035 | + | 0.572313i | \(0.193954\pi\) | ||||
−0.820035 | + | 0.572313i | \(0.806046\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.2047i | 1.97561i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.3300i | 0.685499i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.8327 | −0.612471 | −0.306236 | − | 0.951956i | \(-0.599070\pi\) | ||||
−0.306236 | + | 0.951956i | \(0.599070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.54032 | + | 6.82843i | −0.0733485 | + | 0.325163i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1917i | 1.05436i | 0.849754 | + | 0.527179i | \(0.176750\pi\) | ||||
−0.849754 | + | 0.527179i | \(0.823250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.3528 | −1.34405 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.6867 | 0.789255 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.11331 | −0.430084 | −0.215042 | − | 0.976605i | \(-0.568989\pi\) | ||||
−0.215042 | + | 0.976605i | \(0.568989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.01207 | 0.236009 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.10020i | 0.286612i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.2657 | − | 25.3464i | −0.950073 | − | 1.18826i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4509 | 0.629204 | 0.314602 | − | 0.949224i | \(-0.398129\pi\) | ||||
0.314602 | + | 0.949224i | \(0.398129\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 4.33660i | − | 0.202415i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.17532i | 0.101315i | 0.998716 | + | 0.0506574i | \(0.0161316\pi\) | ||||
−0.998716 | + | 0.0506574i | \(0.983868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.3343i | − | 1.40976i | −0.709329 | − | 0.704878i | \(-0.751002\pi\) | ||
0.709329 | − | 0.704878i | \(-0.248998\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000i | 0.370991i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.1404 | 1.62610 | 0.813051 | − | 0.582192i | \(-0.197805\pi\) | ||||
0.813051 | + | 0.582192i | \(0.197805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.0391 | − | 18.4210i | 1.06385 | − | 0.850602i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.81209i | − | 0.359962i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.39965 | −0.432196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.0718 | 1.60921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.23587 | 0.0565868 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.9673 | 0.820948 | 0.410474 | − | 0.911872i | \(-0.365363\pi\) | ||||
0.410474 | + | 0.911872i | \(0.365363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.4717i | − | 0.659855i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.6569 | − | 9.32026i | 0.530405 | − | 0.424086i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.4509 | 1.24648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.4313i | 1.56023i | 0.625636 | + | 0.780115i | \(0.284840\pi\) | ||||
−0.625636 | + | 0.780115i | \(0.715160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 14.4629i | − | 0.654036i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.8737i | − | 0.626110i | −0.949735 | − | 0.313055i | \(-0.898648\pi\) | ||
0.949735 | − | 0.313055i | \(-0.101352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 41.2047i | − | 1.85577i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.4629 | −0.739953 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.26575 | − | 5.00979i | 0.281057 | − | 0.224720i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.2494i | − | 1.71228i | −0.516744 | − | 0.856140i | \(-0.672856\pi\) | ||
0.516744 | − | 0.856140i | \(-0.327144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.2984 | −0.817513 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.420546 | 0.0187512 | 0.00937560 | − | 0.999956i | \(-0.497016\pi\) | ||||
0.00937560 | + | 0.999956i | \(0.497016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.2569 | −1.34642 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | −0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8247i | 0.612768i | 0.951908 | + | 0.306384i | \(0.0991192\pi\) | ||||
−0.951908 | + | 0.306384i | \(0.900881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.23307 | + | 4.98366i | −0.275735 | + | 0.220464i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.54032 | 0.112158 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.6928i | 1.88127i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 46.5642i | − | 2.04789i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.3203i | − | 0.760275i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.55438i | − | 0.418585i | −0.977853 | − | 0.209292i | \(-0.932884\pi\) | ||
0.977853 | − | 0.209292i | \(-0.0671161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.2210 | 1.40893 | 0.704463 | − | 0.709740i | \(-0.251188\pi\) | ||||
0.704463 | + | 0.709740i | \(0.251188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.8107 | − | 28.5294i | −0.995540 | − | 1.24512i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.00000i | − | 0.348485i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.82135 | −0.383537 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.65685 | 0.0719014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.73425 | −0.161749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3823 | −0.837969 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10.2680i | − | 0.443098i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.9226 | − | 5.84748i | −1.11657 | − | 0.251869i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.20041 | 0.395557 | 0.197778 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197778 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.9570i | 0.641868i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.9869i | 0.856145i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.5109i | − | 1.09077i | −0.838187 | − | 0.545383i | \(-0.816384\pi\) | ||
0.838187 | − | 0.545383i | \(-0.183616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.50162i | − | 0.149445i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.1371 | 1.02828 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.0718 | − | 16.8480i | 0.896065 | − | 0.716450i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 22.1883i | − | 0.941843i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.3730 | −1.24457 | −0.622287 | − | 0.782789i | \(-0.713796\pi\) | ||||
−0.622287 | + | 0.782789i | \(0.713796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.00324 | 0.296205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.4629 | 0.695065 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.8626 | 1.89073 | 0.945366 | − | 0.326010i | \(-0.105704\pi\) | ||||
0.945366 | + | 0.326010i | \(0.105704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 77.8648i | 3.27580i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.65222 | − | 2.06644i | −0.0693868 | − | 0.0867822i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.5642 | −1.19747 | −0.598736 | − | 0.800946i | \(-0.704330\pi\) | ||||
−0.598736 | + | 0.800946i | \(0.704330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.1645i | − | 1.01125i | −0.862753 | − | 0.505626i | \(-0.831261\pi\) | ||
0.862753 | − | 0.505626i | \(-0.168739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 24.9231i | − | 1.04118i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 77.8806i | 3.24785i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.84196i | 0.201574i | 0.994908 | + | 0.100787i | \(0.0321360\pi\) | ||||
−0.994908 | + | 0.100787i | \(0.967864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.49236 | −0.0620202 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.03591 | + | 6.29842i | 0.208925 | + | 0.261303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.69172i | 0.194311i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.2657 | 0.507126 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1766 | 0.626404 | 0.313202 | − | 0.949687i | \(-0.398598\pi\) | ||||
0.313202 | + | 0.949687i | \(0.398598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.68629 | 0.193095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.89273 | −0.283529 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.9139i | − | 0.940960i | −0.882411 | − | 0.470480i | \(-0.844081\pi\) | ||
0.882411 | − | 0.470480i | \(-0.155919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31.0718 | + | 38.8615i | 1.27382 | + | 1.59317i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.9940 | 0.941081 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.31318i | 0.339667i | 0.985473 | + | 0.169834i | \(0.0543231\pi\) | ||||
−0.985473 | + | 0.169834i | \(0.945677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.8508i | − | 0.891313i | −0.895204 | − | 0.445656i | \(-0.852970\pi\) | ||
0.895204 | − | 0.445656i | \(-0.147030\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.1492i | 0.454031i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 14.7952i | − | 0.601512i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.5408 | −1.64550 | −0.822749 | − | 0.568405i | \(-0.807561\pi\) | ||||
−0.822749 | + | 0.568405i | \(0.807561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.6988 | − | 19.6345i | −0.636147 | − | 0.795630i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6928i | 1.40352i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.0153 | −0.444903 | −0.222452 | − | 0.974944i | \(-0.571406\pi\) | ||||
−0.222452 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.72543 | −0.230871 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.32900 | −0.0937618 | −0.0468809 | − | 0.998900i | \(-0.514928\pi\) | ||||
−0.0468809 | + | 0.998900i | \(0.514928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.7493 | 1.03495 | 0.517475 | − | 0.855698i | \(-0.326872\pi\) | ||||
0.517475 | + | 0.855698i | \(0.326872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.64104i | 0.226367i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5104 | − | 10.8023i | 0.541285 | − | 0.432785i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 96.5771 | 3.86308 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.64375i | 0.385134i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.1883i | 0.884707i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.93143i | − | 0.395364i | −0.980266 | − | 0.197682i | \(-0.936659\pi\) | ||
0.980266 | − | 0.197682i | \(-0.0633413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.60462i | − | 0.262510i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.5347 | 1.56889 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.3137 | + | 4.35668i | 0.765237 | + | 0.172618i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.03215i | 0.119950i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.7855 | 0.781478 | 0.390739 | − | 0.920501i | \(-0.372219\pi\) | ||||
0.390739 | + | 0.920501i | \(0.372219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.07181 | 0.121140 | 0.0605702 | − | 0.998164i | \(-0.480708\pi\) | ||||
0.0605702 | + | 0.998164i | \(0.480708\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.7375 | 0.422788 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.6242 | −0.614250 | −0.307125 | − | 0.951669i | \(-0.599367\pi\) | ||||
−0.307125 | + | 0.951669i | \(0.599367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.28988i | 0.246899i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.04796 | − | 3.81209i | −0.119459 | − | 0.149408i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.1432 | 0.396934 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19.8452i | − | 0.775416i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.01634i | − | 0.117679i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.68296i | − | 0.182422i | −0.995832 | − | 0.0912112i | \(-0.970926\pi\) | ||
0.995832 | − | 0.0912112i | \(-0.0290738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 7.37302i | − | 0.286777i | −0.989666 | − | 0.143389i | \(-0.954200\pi\) | ||
0.989666 | − | 0.143389i | \(-0.0457999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2657 | −0.476362 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.7646 | + | 18.2014i | −0.882772 | + | 0.705822i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.5990i | 2.07536i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0093 | 0.618954 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2931 | 0.513175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.96734 | 0.268571 | 0.134286 | − | 0.990943i | \(-0.457126\pi\) | ||||
0.134286 | + | 0.990943i | \(0.457126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.8061 | 0.531396 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 20.0130i | − | 0.769163i | −0.923091 | − | 0.384582i | \(-0.874346\pi\) | ||
0.923091 | − | 0.384582i | \(-0.125654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0806 | + | 10.4586i | −0.501989 | + | 0.401366i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.310470 | −0.0118972 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.2155i | 0.735261i | 0.929972 | + | 0.367630i | \(0.119831\pi\) | ||||
−0.929972 | + | 0.367630i | \(0.880169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.7035i | 1.97549i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.5180i | − | 0.859114i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3.49558i | − | 0.133171i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.3735 | −1.87825 | −0.939127 | − | 0.343569i | \(-0.888364\pi\) | ||||
−0.939127 | + | 0.343569i | \(0.888364\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.84476 | − | 6.27230i | 0.297998 | − | 0.238265i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 31.7166i | − | 1.20308i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.72543 | 0.216866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.6569 | 0.440903 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0004 | 0.604328 | 0.302164 | − | 0.953256i | \(-0.402291\pi\) | ||||
0.302164 | + | 0.953256i | \(0.402291\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.9976 | −0.490215 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 53.1916i | 2.00331i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.4178 | − | 11.5277i | 0.542236 | − | 0.433545i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.2210 | −0.834528 | −0.417264 | − | 0.908785i | \(-0.637011\pi\) | ||||
−0.417264 | + | 0.908785i | \(0.637011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.1972i | 0.382424i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.4064i | 0.389723i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.5642i | 1.74140i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 3.88721i | − | 0.145171i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.96732 | 0.0733688 | 0.0366844 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366844 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2657 | − | 20.3436i | −0.605768 | − | 0.757635i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.54459i | 0.169015i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 131.180 | 4.87190 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.4689 | 1.24129 | 0.620647 | − | 0.784090i | \(-0.286870\pi\) | ||||
0.620647 | + | 0.784090i | \(0.286870\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.7375 | −0.397141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.4253i | − | 1.45621i | −0.685468 | − | 0.728103i | \(-0.740402\pi\) | ||
0.685468 | − | 0.728103i | \(-0.259598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.6121 | + | 6.67974i | 1.09226 | + | 0.246386i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.3255 | −1.55908 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 33.5109i | − | 1.23272i | −0.787465 | − | 0.616359i | \(-0.788607\pi\) | ||
0.787465 | − | 0.616359i | \(-0.211393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 7.18511i | − | 0.263952i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.7040i | − | 1.12642i | −0.826313 | − | 0.563211i | \(-0.809566\pi\) | ||
0.826313 | − | 0.563211i | \(-0.190434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 72.3636i | − | 2.65120i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.04796 | −0.111519 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.23587 | − | 7.38456i | 0.337471 | − | 0.269826i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7123i | 0.865275i | 0.901568 | + | 0.432638i | \(0.142417\pi\) | ||||
−0.901568 | + | 0.432638i | \(0.857583\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.92260 | 0.215832 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.4541 | 0.962763 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4717 | −0.598676 | −0.299338 | − | 0.954147i | \(-0.596766\pi\) | ||||
−0.299338 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.4150 | −0.777314 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.8812i | − | 1.19194i | −0.803006 | − | 0.595971i | \(-0.796767\pi\) | ||
0.803006 | − | 0.595971i | \(-0.203233\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.61492 | − | 9.52398i | −0.275678 | − | 0.344791i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.8061 | −0.679935 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 4.68629i | − | 0.169212i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8779i | 1.51015i | 0.655636 | + | 0.755077i | \(0.272401\pi\) | ||||
−0.655636 | + | 0.755077i | \(0.727599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 0.0261258i | − | 0.000940896i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 20.4521i | − | 0.735611i | −0.929903 | − | 0.367805i | \(-0.880109\pi\) | ||
0.929903 | − | 0.367805i | \(-0.119891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.4689 | 0.914871 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.45366 | + | 10.5730i | 0.303273 | + | 0.379304i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.35388i | 0.120165i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.5109 | −0.411892 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.50162 | 0.339560 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.8779 | −1.20915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.6960 | −1.34372 | −0.671859 | − | 0.740679i | \(-0.734504\pi\) | ||||
−0.671859 | + | 0.740679i | \(0.734504\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 12.3785i | − | 0.440687i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.6661 | − | 37.1034i | −1.05481 | − | 1.31925i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.90407 | −0.351704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 5.35948i | − | 0.190081i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.8713i | 0.987253i | 0.869674 | + | 0.493627i | \(0.164329\pi\) | ||||
−0.869674 | + | 0.493627i | \(0.835671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 53.1916i | − | 1.88178i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.53804i | 0.231010i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.4509 | 0.404092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.4182 | − | 50.5511i | −1.42455 | − | 1.78169i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.13515i | − | 0.0751609i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.2899 | −0.432089 | −0.216045 | − | 0.976384i | \(-0.569316\pi\) | ||||
−0.216045 | + | 0.976384i | \(0.569316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.1557 | 1.83143 | 0.915717 | − | 0.401825i | \(-0.131624\pi\) | ||||
0.915717 | + | 0.401825i | \(0.131624\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.3763 | −0.925056 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −62.7198 | −2.19698 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.28988i | − | 0.220055i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.84476 | + | 4.67319i | −0.204233 | + | 0.163295i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.9254 | −0.869903 | −0.434951 | − | 0.900454i | \(-0.643234\pi\) | ||||
−0.434951 | + | 0.900454i | \(0.643234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.8331i | − | 1.14449i | −0.820082 | − | 0.572246i | \(-0.806072\pi\) | ||
0.820082 | − | 0.572246i | \(-0.193928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 52.4116i | 1.82474i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.5469i | − | 0.784031i | −0.919959 | − | 0.392016i | \(-0.871778\pi\) | ||
0.919959 | − | 0.392016i | \(-0.128222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.6104i | 1.89670i | 0.317231 | + | 0.948348i | \(0.397247\pi\) | ||||
−0.317231 | + | 0.948348i | \(0.602753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.1198 | 0.836706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.6121 | − | 6.67974i | −1.02600 | − | 0.231439i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 79.3529i | 2.74612i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.84476 | 0.0637644 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.1492 | −0.557533 | −0.278767 | − | 0.960359i | \(-0.589926\pi\) | ||||
−0.278767 | + | 0.960359i | \(0.589926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.2808 | 2.11313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.6416 | 0.366515 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.6830i | 0.745917i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.63692 | + | 7.05010i | 0.193687 | + | 0.242244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.5436 | −0.602093 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 28.8626i | − | 0.989397i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.2803i | − | 0.831343i | −0.909515 | − | 0.415671i | \(-0.863547\pi\) | ||
0.909515 | − | 0.415671i | \(-0.136453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 11.0163i | − | 0.376751i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.1949i | − | 0.963119i | −0.876413 | − | 0.481560i | \(-0.840070\pi\) | ||
0.876413 | − | 0.481560i | \(-0.159930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.0871 | 0.958319 | 0.479160 | − | 0.877728i | \(-0.340941\pi\) | ||||
0.479160 | + | 0.877728i | \(0.340941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.72823 | − | 2.18136i | 0.0929778 | − | 0.0743406i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.2042i | 1.02816i | 0.857742 | + | 0.514081i | \(0.171867\pi\) | ||||
−0.857742 | + | 0.514081i | \(0.828133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −75.1110 | −2.55385 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.80606 | 0.0613372 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.7113 | −1.31319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5347 | 1.06851 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.33005i | − | 0.214240i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −78.9138 | + | 63.0957i | −2.66777 | + | 2.13302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7340 | −1.30795 | −0.653977 | − | 0.756515i | \(-0.726901\pi\) | ||||
−0.653977 | + | 0.756515i | \(0.726901\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.64707i | 0.291658i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 14.2407i | − | 0.479780i | −0.970800 | − | 0.239890i | \(-0.922889\pi\) | ||
0.970800 | − | 0.239890i | \(-0.0771114\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.8551i | 1.13931i | 0.821883 | + | 0.569657i | \(0.192924\pi\) | ||||
−0.821883 | + | 0.569657i | \(0.807076\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 7.18511i | − | 0.241525i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.3049 | 1.62192 | 0.810960 | − | 0.585102i | \(-0.198945\pi\) | ||||
0.810960 | + | 0.585102i | \(0.198945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8387 | + | 15.0625i | −0.631831 | + | 0.505182i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79628i | 0.127180i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.1589 | 1.04269 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.5283 | −1.48842 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9553 | 0.532731 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.5283 | 0.584600 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.35948i | 0.178550i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.11654 | + | 4.09093i | −0.170268 | + | 0.136138i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 64.8626 | 2.15611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.5543i | − | 1.34658i | −0.739377 | − | 0.673292i | \(-0.764880\pi\) | ||
0.739377 | − | 0.673292i | \(-0.235120\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.97711i | 0.231416i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2499i | 1.06849i | 0.845330 | + | 0.534244i | \(0.179404\pi\) | ||||
−0.845330 | + | 0.534244i | \(0.820596\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.5709i | − | 0.382941i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.1851 | −0.502004 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.56093 | + | 9.45646i | 0.249684 | + | 0.312280i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3659i | 1.00168i | 0.865540 | + | 0.500840i | \(0.166976\pi\) | ||||
−0.865540 | + | 0.500840i | \(0.833024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3823 | 0.770472 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.57622 | 0.282290 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.6392 | −2.32260 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.84476 | 0.323345 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.2112i | 1.02401i | 0.858983 | + | 0.512004i | \(0.171097\pi\) | ||||
−0.858983 | + | 0.512004i | \(0.828903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.91290 | − | 17.3464i | 0.128240 | − | 0.568505i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.1883 | −0.726414 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 71.3930i | − | 2.33480i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.43557i | − | 0.0795665i | −0.999208 | − | 0.0397832i | \(-0.987333\pi\) | ||
0.999208 | − | 0.0397832i | \(-0.0126667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 17.8779i | − | 0.583422i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5903i | 0.736422i | 0.929742 | + | 0.368211i | \(0.120030\pi\) | ||||
−0.929742 | + | 0.368211i | \(0.879970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.44763 | −0.242528 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.96130 | + | 7.16502i | −0.291511 | + | 0.233078i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 53.0848i | − | 1.72503i | −0.506035 | − | 0.862513i | \(-0.668889\pi\) | ||
0.506035 | − | 0.862513i | \(-0.331111\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.53149 | −0.276944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.1585 | 0.491547 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.7113 | 1.96663 | 0.983316 | − | 0.181906i | \(-0.0582268\pi\) | ||||
0.983316 | + | 0.181906i | \(0.0582268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −108.082 | −3.49744 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.0708i | 1.16600i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.6988 | − | 24.6373i | −0.636107 | − | 0.795580i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5968 | −0.890221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.46947i | 0.144027i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.47175i | 0.208333i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.4476i | 0.689709i | 0.938656 | + | 0.344855i | \(0.112072\pi\) | ||||
−0.938656 | + | 0.344855i | \(0.887928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.0163i | 0.353896i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.2775 | −1.13211 | −0.566055 | − | 0.824368i | \(-0.691531\pi\) | ||||
−0.566055 | + | 0.824368i | \(0.691531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0839 | + | 15.1133i | 0.387391 | + | 0.484511i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 39.0494i | − | 1.25058i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.2092 | 0.870501 | 0.435250 | − | 0.900309i | \(-0.356660\pi\) | ||||
0.435250 | + | 0.900309i | \(0.356660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.8202 | −0.793258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.60889 | 0.147151 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.0218 | −1.24460 | −0.622300 | − | 0.782778i | \(-0.713802\pi\) | ||||
−0.622300 | + | 0.782778i | \(0.713802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.8910i | 0.952406i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.2657 | − | 25.3464i | −0.645066 | − | 0.806784i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9673 | 0.444135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.1176i | 0.988483i | 0.869325 | + | 0.494241i | \(0.164554\pi\) | ||||
−0.869325 | + | 0.494241i | \(0.835446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.57194i | − | 0.272022i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 99.7156i | − | 3.16120i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 59.5678i | − | 1.88653i | −0.332037 | − | 0.943266i | \(-0.607736\pi\) | ||
0.332037 | − | 0.943266i | \(-0.392264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.11654 | −0.161880 |
(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 | 672.2.b.a.223.8 | yes | 8 | |
3.2 | odd | 2 | 2016.2.b.a.1567.1 | 8 | |||
4.3 | odd | 2 | 672.2.b.b.223.8 | yes | 8 | ||
7.6 | odd | 2 | 672.2.b.b.223.1 | yes | 8 | ||
8.3 | odd | 2 | 1344.2.b.g.895.1 | 8 | |||
8.5 | even | 2 | 1344.2.b.h.895.1 | 8 | |||
12.11 | even | 2 | 2016.2.b.c.1567.1 | 8 | |||
21.20 | even | 2 | 2016.2.b.c.1567.8 | 8 | |||
24.5 | odd | 2 | 4032.2.b.o.3583.8 | 8 | |||
24.11 | even | 2 | 4032.2.b.q.3583.8 | 8 | |||
28.27 | even | 2 | inner | 672.2.b.a.223.1 | ✓ | 8 | |
56.13 | odd | 2 | 1344.2.b.g.895.8 | 8 | |||
56.27 | even | 2 | 1344.2.b.h.895.8 | 8 | |||
84.83 | odd | 2 | 2016.2.b.a.1567.8 | 8 | |||
168.83 | odd | 2 | 4032.2.b.o.3583.1 | 8 | |||
168.125 | even | 2 | 4032.2.b.q.3583.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.b.a.223.1 | ✓ | 8 | 28.27 | even | 2 | inner | |
672.2.b.a.223.8 | yes | 8 | 1.1 | even | 1 | trivial | |
672.2.b.b.223.1 | yes | 8 | 7.6 | odd | 2 | ||
672.2.b.b.223.8 | yes | 8 | 4.3 | odd | 2 | ||
1344.2.b.g.895.1 | 8 | 8.3 | odd | 2 | |||
1344.2.b.g.895.8 | 8 | 56.13 | odd | 2 | |||
1344.2.b.h.895.1 | 8 | 8.5 | even | 2 | |||
1344.2.b.h.895.8 | 8 | 56.27 | even | 2 | |||
2016.2.b.a.1567.1 | 8 | 3.2 | odd | 2 | |||
2016.2.b.a.1567.8 | 8 | 84.83 | odd | 2 | |||
2016.2.b.c.1567.1 | 8 | 12.11 | even | 2 | |||
2016.2.b.c.1567.8 | 8 | 21.20 | even | 2 | |||
4032.2.b.o.3583.1 | 8 | 168.83 | odd | 2 | |||
4032.2.b.o.3583.8 | 8 | 24.5 | odd | 2 | |||
4032.2.b.q.3583.1 | 8 | 168.125 | even | 2 | |||
4032.2.b.q.3583.8 | 8 | 24.11 | even | 2 |