Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(2591,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("5184.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.f (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: | \(41.3944484078\) |
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: | \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.1 | ||
Root | \(1.11871 + 0.645885i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2591 |
Dual form | 5184.2.f.e.2591.2 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −4.04682 | −1.80979 | −0.904896 | − | 0.425632i | \(-0.860052\pi\) | ||||
−0.904896 | + | 0.425632i | \(0.860052\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.89623i | − 1.47264i | −0.676636 | − | 0.736318i | \(-0.736563\pi\) | ||||
0.676636 | − | 0.736318i | \(-0.263437\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.468572i | − 0.141280i | −0.997502 | − | 0.0706400i | \(-0.977496\pi\) | ||||
0.997502 | − | 0.0706400i | \(-0.0225041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89623i | 1.35797i | 0.734152 | + | 0.678985i | \(0.237580\pi\) | ||||
−0.734152 | + | 0.678985i | \(0.762420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.57825i | − 0.867852i | −0.900948 | − | 0.433926i | \(-0.857128\pi\) | ||||
0.900948 | − | 0.433926i | \(-0.142872\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.89623 | −0.435024 | −0.217512 | − | 0.976058i | \(-0.569794\pi\) | ||||
−0.217512 | + | 0.976058i | \(0.569794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.56221 | −1.78534 | −0.892672 | − | 0.450707i | \(-0.851172\pi\) | ||||
−0.892672 | + | 0.450707i | \(0.851172\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3767 | 2.27535 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.36451 | 0.439078 | 0.219539 | − | 0.975604i | \(-0.429545\pi\) | ||||
0.219539 | + | 0.975604i | \(0.429545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.18059i | 1.28967i | 0.764321 | + | 0.644836i | \(0.223074\pi\) | ||||
−0.764321 | + | 0.644836i | \(0.776926\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.7673i | 2.66516i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.16418i | 1.01338i | 0.862127 | + | 0.506692i | \(0.169132\pi\) | ||||
−0.862127 | + | 0.506692i | \(0.830868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 5.13116i | − 0.801353i | −0.916220 | − | 0.400676i | \(-0.868775\pi\) | ||||
0.916220 | − | 0.400676i | \(-0.131225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5409 | −1.60748 | −0.803738 | − | 0.594984i | \(-0.797158\pi\) | ||||
−0.803738 | + | 0.594984i | \(0.797158\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.37380 | −1.36731 | −0.683655 | − | 0.729806i | \(-0.739611\pi\) | ||||
−0.683655 | + | 0.729806i | \(0.739611\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.18059 | −1.16866 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.52280 | −0.758616 | −0.379308 | − | 0.925271i | \(-0.623838\pi\) | ||||
−0.379308 | + | 0.925271i | \(0.623838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89623i | 0.255687i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.26797i | − 0.816021i | −0.912977 | − | 0.408010i | \(-0.866223\pi\) | ||||
0.912977 | − | 0.408010i | \(-0.133777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.983586i | 0.125935i | 0.998016 | + | 0.0629677i | \(0.0200565\pi\) | ||||
−0.998016 | + | 0.0629677i | \(0.979943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 19.8141i | − 2.45764i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7485 | 1.55747 | 0.778736 | − | 0.627351i | \(-0.215861\pi\) | ||||
0.778736 | + | 0.627351i | \(0.215861\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.02890 | 0.359464 | 0.179732 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179732 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.58429 | 0.536550 | 0.268275 | − | 0.963342i | \(-0.413546\pi\) | ||||
0.268275 | + | 0.963342i | \(0.413546\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.82566 | −0.208054 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.6767i | − 1.31373i | −0.754009 | − | 0.656864i | \(-0.771883\pi\) | ||||
0.754009 | − | 0.656864i | \(-0.228117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.66616i | − 0.621941i | −0.950419 | − | 0.310971i | \(-0.899346\pi\) | ||||
0.950419 | − | 0.310971i | \(-0.100654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4805i | 1.57063i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.17610i | 0.336666i | 0.985730 | + | 0.168333i | \(0.0538383\pi\) | ||||
−0.985730 | + | 0.168333i | \(0.946162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.0768 | 1.99979 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.67369 | 0.787304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.611865 | 0.0621255 | 0.0310627 | − | 0.999517i | \(-0.490111\pi\) | ||||
0.0310627 | + | 0.999517i | \(0.490111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.28561 | 0.824449 | 0.412225 | − | 0.911082i | \(-0.364752\pi\) | ||||
0.412225 | + | 0.911082i | \(0.364752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.25315i | − 0.411167i | −0.978640 | − | 0.205584i | \(-0.934091\pi\) | ||||
0.978640 | − | 0.205584i | \(-0.0659092\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.42011i | 0.902283i | 0.892452 | + | 0.451141i | \(0.148983\pi\) | ||||
−0.892452 | + | 0.451141i | \(0.851017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.84622i | 0.926254i | 0.886292 | + | 0.463127i | \(0.153273\pi\) | ||||
−0.886292 | + | 0.463127i | \(0.846727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 34.6497 | 3.23110 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.9417 | −1.27803 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7804 | 0.980040 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −25.8055 | −2.30812 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.2885i | − 1.26790i | −0.773373 | − | 0.633951i | \(-0.781432\pi\) | ||||
0.773373 | − | 0.633951i | \(-0.218568\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5444i | 1.53286i | 0.642329 | + | 0.766429i | \(0.277968\pi\) | ||||
−0.642329 | + | 0.766429i | \(0.722032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.38814i | 0.640633i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7310i | 1.00225i | 0.865375 | + | 0.501124i | \(0.167080\pi\) | ||||
−0.865375 | + | 0.501124i | \(0.832920\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.75963 | 0.488525 | 0.244263 | − | 0.969709i | \(-0.421454\pi\) | ||||
0.244263 | + | 0.969709i | \(0.421454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.29424 | 0.191854 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.56873 | −0.794639 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.2022 | 1.57311 | 0.786554 | − | 0.617522i | \(-0.211863\pi\) | ||||
0.786554 | + | 0.617522i | \(0.211863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.79246i | 0.634141i | 0.948402 | + | 0.317071i | \(0.102699\pi\) | ||||
−0.948402 | + | 0.317071i | \(0.897301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 29.0585i | − 2.33404i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.73707i | − 0.777103i | −0.921427 | − | 0.388551i | \(-0.872976\pi\) | ||||
0.921427 | − | 0.388551i | \(-0.127024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.3603i | 2.62916i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.21342 | −0.721651 | −0.360825 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360825 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.88386 | 0.610072 | 0.305036 | − | 0.952341i | \(-0.401332\pi\) | ||||
0.305036 | + | 0.952341i | \(0.401332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9730 | −0.844080 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4747 | 1.55666 | 0.778331 | − | 0.627854i | \(-0.216067\pi\) | ||||
0.778331 | + | 0.627854i | \(0.216067\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 44.3264i | − 3.35076i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.1392i | 1.43053i | 0.698851 | + | 0.715267i | \(0.253695\pi\) | ||||
−0.698851 | + | 0.715267i | \(0.746305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 11.2894i | − 0.839133i | −0.907725 | − | 0.419567i | \(-0.862182\pi\) | ||||
0.907725 | − | 0.419567i | \(-0.137818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 24.9453i | − 1.83402i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.67667 | −0.122610 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7694 | 1.43046 | 0.715231 | − | 0.698889i | \(-0.246322\pi\) | ||||
0.715231 | + | 0.698889i | \(0.246322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5849 | 1.33777 | 0.668886 | − | 0.743365i | \(-0.266772\pi\) | ||||
0.668886 | + | 0.743365i | \(0.266772\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.8055 | −1.83857 | −0.919284 | − | 0.393596i | \(-0.871231\pi\) | ||||
−0.919284 | + | 0.393596i | \(0.871231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.79246i | − 0.127064i | −0.997980 | − | 0.0635319i | \(-0.979764\pi\) | ||||
0.997980 | − | 0.0635319i | \(-0.0202365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.21265i | − 0.646601i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.7649i | 1.45028i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.888520i | 0.0614602i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.288533 | −0.0198634 | −0.00993170 | − | 0.999951i | \(-0.503161\pi\) | ||||
−0.00993170 | + | 0.999951i | \(0.503161\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 42.6572 | 2.90920 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.9772 | 1.89922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.5199 | 1.17852 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.85309i | 0.124092i | 0.998073 | + | 0.0620460i | \(0.0197625\pi\) | ||||
−0.998073 | + | 0.0620460i | \(0.980237\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6.13473i | − 0.407176i | −0.979057 | − | 0.203588i | \(-0.934740\pi\) | ||||
0.979057 | − | 0.203588i | \(-0.0652603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 21.3662i | − 1.41192i | −0.708253 | − | 0.705959i | \(-0.750516\pi\) | ||||
0.708253 | − | 0.705959i | \(-0.249484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.0325i | 0.919303i | 0.888099 | + | 0.459651i | \(0.152026\pi\) | ||||
−0.888099 | + | 0.459651i | \(0.847974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.9341 | 2.47455 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.35219 | 0.410889 | 0.205445 | − | 0.978669i | \(-0.434136\pi\) | ||||
0.205445 | + | 0.978669i | \(0.434136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7769 | −0.758616 | −0.379308 | − | 0.925270i | \(-0.623838\pi\) | ||||
−0.379308 | + | 0.925270i | \(0.623838\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33.1054 | 2.11502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 9.28436i | − 0.590750i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.24621i | 0.331138i | 0.986198 | + | 0.165569i | \(0.0529460\pi\) | ||||
−0.986198 | + | 0.165569i | \(0.947054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.01202i | 0.252233i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8395i | 1.36231i | 0.732140 | + | 0.681155i | \(0.238522\pi\) | ||||
−0.732140 | + | 0.681155i | \(0.761478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0170 | 1.49235 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.52766 | 0.587501 | 0.293750 | − | 0.955882i | \(-0.405097\pi\) | ||||
0.293750 | + | 0.955882i | \(0.405097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.3498 | 1.37294 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4565 | 0.942397 | 0.471198 | − | 0.882027i | \(-0.343822\pi\) | ||||
0.471198 | + | 0.882027i | \(0.343822\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 16.2765i | − 0.988728i | −0.869255 | − | 0.494364i | \(-0.835401\pi\) | ||||
0.869255 | − | 0.494364i | \(-0.164599\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.33083i | − 0.321461i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6878i | 0.762338i | 0.924505 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924505 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 7.33452i | − 0.437541i | −0.975776 | − | 0.218770i | \(-0.929795\pi\) | ||||
0.975776 | − | 0.218770i | \(-0.0702045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.84022 | 0.406609 | 0.203304 | − | 0.979116i | \(-0.434832\pi\) | ||||
0.203304 | + | 0.979116i | \(0.434832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.9922 | −1.18010 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.19615 | 0.246832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.9969 | −1.34349 | −0.671747 | − | 0.740781i | \(-0.734456\pi\) | ||||
−0.671747 | + | 0.740781i | \(0.734456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.3654i | 1.47683i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 41.9225i | − 2.42444i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.0698i | 2.36723i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 3.98040i | − 0.227917i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.3654 | −1.10524 | −0.552619 | − | 0.833434i | \(-0.686372\pi\) | ||||
−0.552619 | + | 0.833434i | \(0.686372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.9142 | −0.959119 | −0.479559 | − | 0.877509i | \(-0.659204\pi\) | ||||
−0.479559 | + | 0.877509i | \(0.659204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.78044 | 0.383253 | 0.191627 | − | 0.981468i | \(-0.438624\pi\) | ||||
0.191627 | + | 0.981468i | \(0.438624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.77583 | 0.492900 | 0.246450 | − | 0.969156i | \(-0.420736\pi\) | ||||
0.246450 | + | 0.969156i | \(0.420736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.10794i | − 0.0620328i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.78517i | 0.377537i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 55.7031i | 3.08985i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.5225i | 2.01355i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8722 | 0.982345 | 0.491172 | − | 0.871062i | \(-0.336569\pi\) | ||||
0.491172 | + | 0.871062i | \(0.336569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −51.5907 | −2.81870 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.98798 | 0.217239 | 0.108620 | − | 0.994083i | \(-0.465357\pi\) | ||||
0.108620 | + | 0.994083i | \(0.465357\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.36463 | 0.182205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.59985i | 0.248369i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 22.0353i | − 1.18292i | −0.806335 | − | 0.591458i | \(-0.798552\pi\) | ||||
0.806335 | − | 0.591458i | \(-0.201448\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.25239i | 0.227625i | 0.993502 | + | 0.113813i | \(0.0363063\pi\) | ||||
−0.993502 | + | 0.113813i | \(0.963694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.81516i | − 0.0966112i | −0.998833 | − | 0.0483056i | \(-0.984618\pi\) | ||||
0.998833 | − | 0.0483056i | \(-0.0153821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.2574 | −0.650556 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.8880 | 1.10243 | 0.551213 | − | 0.834365i | \(-0.314165\pi\) | ||||
0.551213 | + | 0.834365i | \(0.314165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4043 | −0.810754 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.5518 | −0.971045 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 14.1727i | − 0.739811i | −0.929069 | − | 0.369906i | \(-0.879390\pi\) | ||||
0.929069 | − | 0.369906i | \(-0.120610\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.5181i | 1.11716i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3462i | 1.51949i | 0.650221 | + | 0.759745i | \(0.274676\pi\) | ||||
−0.650221 | + | 0.759745i | \(0.725324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.5772i | 0.596254i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.74761 | 0.397968 | 0.198984 | − | 0.980003i | \(-0.436236\pi\) | ||||
0.198984 | + | 0.980003i | \(0.436236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.0948 | 1.84436 | 0.922180 | − | 0.386762i | \(-0.126406\pi\) | ||||
0.922180 | + | 0.386762i | \(0.126406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.38814 | 0.376534 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.3765 | −1.48945 | −0.744723 | − | 0.667373i | \(-0.767419\pi\) | ||||
−0.744723 | + | 0.667373i | \(0.767419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6377i | 1.54941i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.2534i | 2.37757i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.33275i | − 0.0668889i | −0.999441 | − | 0.0334444i | \(-0.989352\pi\) | ||||
0.999441 | − | 0.0334444i | \(-0.0106477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 31.2133i | − 1.55872i | −0.626578 | − | 0.779358i | \(-0.715545\pi\) | ||||
0.626578 | − | 0.779358i | \(-0.284455\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.1578 | −1.75134 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.88836 | 0.143171 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9575 | −0.541813 | −0.270906 | − | 0.962606i | \(-0.587323\pi\) | ||||
−0.270906 | + | 0.962606i | \(0.587323\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.4214 | −1.20170 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.9299i | 1.12558i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 18.1535i | − 0.886855i | −0.896310 | − | 0.443428i | \(-0.853762\pi\) | ||||
0.896310 | − | 0.443428i | \(-0.146238\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6127i | 0.907128i | 0.891224 | + | 0.453564i | \(0.149848\pi\) | ||||
−0.891224 | + | 0.453564i | \(0.850152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 40.7088i | − 1.97467i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.83228 | 0.185457 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.0852 | 1.20831 | 0.604156 | − | 0.796866i | \(-0.293510\pi\) | ||||
0.604156 | + | 0.796866i | \(0.293510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3492 | 1.21820 | 0.609102 | − | 0.793092i | \(-0.291530\pi\) | ||||
0.609102 | + | 0.793092i | \(0.291530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.2359 | 0.776668 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 29.3342i | − 1.40005i | −0.714120 | − | 0.700023i | \(-0.753173\pi\) | ||||
0.714120 | − | 0.700023i | \(-0.246827\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.4404i | 0.971154i | 0.874194 | + | 0.485577i | \(0.161390\pi\) | ||||
−0.874194 | + | 0.485577i | \(0.838610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.8531i | − 0.609295i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 40.0304i | − 1.88915i | −0.328291 | − | 0.944577i | \(-0.606473\pi\) | ||||
0.328291 | − | 0.944577i | \(-0.393527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.40432 | −0.113215 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −77.2004 | −3.61921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9737 | 0.934329 | 0.467164 | − | 0.884170i | \(-0.345276\pi\) | ||||
0.467164 | + | 0.884170i | \(0.345276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6016 | 0.540341 | 0.270171 | − | 0.962812i | \(-0.412920\pi\) | ||||
0.270171 | + | 0.962812i | \(0.412920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.3732i | 0.575031i | 0.957776 | + | 0.287516i | \(0.0928293\pi\) | ||||
−0.957776 | + | 0.287516i | \(0.907171\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.1873i | 0.749058i | 0.927215 | + | 0.374529i | \(0.122196\pi\) | ||||
−0.927215 | + | 0.374529i | \(0.877804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 49.6709i | − 2.29359i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.93918i | 0.227104i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.5729 | −0.989832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.46203 | 0.0668020 | 0.0334010 | − | 0.999442i | \(-0.489366\pi\) | ||||
0.0334010 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.1812 | −1.37614 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.47611 | −0.112434 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7577i | 0.714048i | 0.934095 | + | 0.357024i | \(0.116208\pi\) | ||||
−0.934095 | + | 0.357024i | \(0.883792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.79940i | 0.261723i | 0.991401 | + | 0.130862i | \(0.0417744\pi\) | ||||
−0.991401 | + | 0.130862i | \(0.958226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8.46078i | − 0.381055i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 11.8013i | − 0.529360i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0540 | 1.65877 | 0.829383 | − | 0.558680i | \(-0.188692\pi\) | ||||
0.829383 | + | 0.558680i | \(0.188692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.98721 | −0.0886055 | −0.0443027 | − | 0.999018i | \(-0.514107\pi\) | ||||
−0.0443027 | + | 0.999018i | \(0.514107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.5304 | −1.49208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8358 | −0.879206 | −0.439603 | − | 0.898192i | \(-0.644881\pi\) | ||||
−0.439603 | + | 0.898192i | \(0.644881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 17.8614i | − 0.790143i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8.09364i | − 0.356648i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.39230i | 0.193173i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 10.8050i | − 0.473376i | −0.971586 | − | 0.236688i | \(-0.923938\pi\) | ||||
0.971586 | − | 0.236688i | \(-0.0760619\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.0092 | −1.53085 | −0.765423 | − | 0.643528i | \(-0.777470\pi\) | ||||
−0.765423 | + | 0.643528i | \(0.777470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.6939 | 1.11924 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.3114 | 2.18745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.1233 | 1.08821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.2117i | 0.744127i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.83320i | 0.165108i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.3973i | 1.43586i | 0.696114 | + | 0.717932i | \(0.254911\pi\) | ||||
−0.696114 | + | 0.717932i | \(0.745089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 38.1215i | − 1.63294i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.11664 | −0.0477441 | −0.0238720 | − | 0.999715i | \(-0.507599\pi\) | ||||
−0.0238720 | + | 0.999715i | \(0.507599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.48364 | −0.191010 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.4950 | −1.93464 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.55480 | −0.320107 | −0.160054 | − | 0.987108i | \(-0.551167\pi\) | ||||
−0.160054 | + | 0.987108i | \(0.551167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 51.6107i | − 2.18290i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.3715i | 1.82789i | 0.405836 | + | 0.913946i | \(0.366981\pi\) | ||||
−0.405836 | + | 0.913946i | \(0.633019\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 39.8459i | − 1.67633i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.8719i | 1.08461i | 0.840182 | + | 0.542304i | \(0.182448\pi\) | ||||
−0.840182 | + | 0.542304i | \(0.817552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.0370 | 0.796674 | 0.398337 | − | 0.917239i | \(-0.369588\pi\) | ||||
0.398337 | + | 0.917239i | \(0.369588\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −97.4101 | −4.06228 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5418 | 0.688643 | 0.344321 | − | 0.938852i | \(-0.388109\pi\) | ||||
0.344321 | + | 0.938852i | \(0.388109\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.0766 | −0.915893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.58783i | 0.107177i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.8160i | 0.652794i | 0.945233 | + | 0.326397i | \(0.105835\pi\) | ||||
−0.945233 | + | 0.326397i | \(0.894165\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 13.6160i | − 0.561039i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.7787i | 1.09967i | 0.835274 | + | 0.549834i | \(0.185309\pi\) | ||||
−0.835274 | + | 0.549834i | \(0.814691\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 56.4194 | 2.31297 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.6199 | −0.679069 | −0.339534 | − | 0.940594i | \(-0.610269\pi\) | ||||
−0.339534 | + | 0.940594i | \(0.610269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0042 | 0.815987 | 0.407994 | − | 0.912985i | \(-0.366229\pi\) | ||||
0.407994 | + | 0.912985i | \(0.366229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.6265 | −1.77367 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.42181i | 0.0982984i | 0.998791 | + | 0.0491492i | \(0.0156510\pi\) | ||||
−0.998791 | + | 0.0491492i | \(0.984349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 45.8963i | − 1.85676i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4102i | 0.622412i | 0.950343 | + | 0.311206i | \(0.100733\pi\) | ||||
−0.950343 | + | 0.311206i | \(0.899267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 7.00200i | − 0.281890i | −0.990017 | − | 0.140945i | \(-0.954986\pi\) | ||||
0.990017 | − | 0.140945i | \(-0.0450141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.9253 | 0.479317 | 0.239659 | − | 0.970857i | \(-0.422964\pi\) | ||||
0.239659 | + | 0.970857i | \(0.422964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.3748 | 0.495786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.5466 | 1.90186 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0569 | 0.879468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.65500i | 0.264932i | 0.991188 | + | 0.132466i | \(0.0422895\pi\) | ||||
−0.991188 | + | 0.132466i | \(0.957711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 57.8231i | 2.29464i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 40.0540i | − 1.58700i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.6695i | 1.52735i | 0.645599 | + | 0.763677i | \(0.276608\pi\) | ||||
−0.645599 | + | 0.763677i | \(0.723392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.8236 | −1.09725 | −0.548627 | − | 0.836067i | \(-0.684849\pi\) | ||||
−0.548627 | + | 0.836067i | \(0.684849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.30252 | 0.208464 | 0.104232 | − | 0.994553i | \(-0.466762\pi\) | ||||
0.104232 | + | 0.994553i | \(0.466762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.93700 | −0.115287 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.0403 | 0.940770 | 0.470385 | − | 0.882461i | \(-0.344115\pi\) | ||||
0.470385 | + | 0.882461i | \(0.344115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 70.9989i | − 2.77416i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 32.5078i | − 1.26632i | −0.774019 | − | 0.633162i | \(-0.781757\pi\) | ||||
0.774019 | − | 0.633162i | \(-0.218243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.8787i | 1.70668i | 0.521352 | + | 0.853342i | \(0.325428\pi\) | ||||
−0.521352 | + | 0.853342i | \(0.674572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 29.8984i | − 1.15941i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.2454 | −0.783905 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.460881 | 0.0177921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0162 | −0.925756 | −0.462878 | − | 0.886422i | \(-0.653183\pi\) | ||||
−0.462878 | + | 0.886422i | \(0.653183\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3455 | −0.705073 | −0.352537 | − | 0.935798i | \(-0.614681\pi\) | ||||
−0.352537 | + | 0.935798i | \(0.614681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 2.38397i | − 0.0914882i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 50.4847i | − 1.93174i | −0.259018 | − | 0.965872i | \(-0.583399\pi\) | ||||
0.259018 | − | 0.965872i | \(-0.416601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 47.4733i | − 1.81386i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 27.0409i | − 1.03018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.5020 | −1.04622 | −0.523112 | − | 0.852264i | \(-0.675229\pi\) | ||||
−0.523112 | + | 0.852264i | \(0.675229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.3082 | −0.884129 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.3606 | −0.695456 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.33376 | −0.239223 | −0.119611 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119611 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.6887i | − 0.440847i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32.2826i | − 1.21411i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 12.1008i | − 0.454457i | −0.973841 | − | 0.227228i | \(-0.927034\pi\) | ||||
0.973841 | − | 0.227228i | \(-0.0729664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 61.4817i | − 2.30251i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.28436 | −0.347215 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.82136 | −0.366275 | −0.183137 | − | 0.983087i | \(-0.558625\pi\) | ||||
−0.183137 | + | 0.983087i | \(0.558625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.79246 | 0.290206 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.9004 | 0.999055 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8494i | 1.47793i | 0.673742 | + | 0.738966i | \(0.264686\pi\) | ||||
−0.673742 | + | 0.738966i | \(0.735314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.7180i | 1.39505i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21.4330i | − 0.791645i | −0.918327 | − | 0.395823i | \(-0.870460\pi\) | ||||
0.918327 | − | 0.395823i | \(-0.129540\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 5.97358i | − 0.220040i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3791 | 1.00716 | 0.503578 | − | 0.863950i | \(-0.332017\pi\) | ||||
0.503578 | + | 0.863950i | \(0.332017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.8229 | 0.543799 | 0.271900 | − | 0.962326i | \(-0.412348\pi\) | ||||
0.271900 | + | 0.962326i | \(0.412348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −77.7079 | −2.84700 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.5712 | −0.605499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 11.4571i | − 0.418076i | −0.977908 | − | 0.209038i | \(-0.932967\pi\) | ||||
0.977908 | − | 0.209038i | \(-0.0670332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 31.5347i | − 1.14766i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33.0507i | − 1.20125i | −0.799531 | − | 0.600624i | \(-0.794919\pi\) | ||||
0.799531 | − | 0.600624i | \(-0.205081\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.12860i | 0.294662i | 0.989087 | + | 0.147331i | \(0.0470682\pi\) | ||||
−0.989087 | + | 0.147331i | \(0.952932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.7029 | 1.32873 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.6894 | 1.10813 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5771 | −0.705967 | −0.352984 | − | 0.935630i | \(-0.614833\pi\) | ||||
−0.352984 | + | 0.935630i | \(0.614833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.7684 | −1.35843 | −0.679217 | − | 0.733938i | \(-0.737680\pi\) | ||||
−0.679217 | + | 0.733938i | \(0.737680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 81.6917i | 2.93445i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.72985i | 0.348608i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.41926i | − 0.0507851i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.4042i | 1.40640i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.03615 | 0.0725807 | 0.0362904 | − | 0.999341i | \(-0.488446\pi\) | ||||
0.0362904 | + | 0.999341i | \(0.488446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.3631 | 1.36404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.81586 | −0.171016 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.2487 | 1.17773 | 0.588865 | − | 0.808231i | \(-0.299575\pi\) | ||||
0.588865 | + | 0.808231i | \(0.299575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.5418i | 1.18662i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.14807i | − 0.0758038i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 135.003i | − 4.75824i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.3485i | 0.609942i | 0.952362 | + | 0.304971i | \(0.0986468\pi\) | ||||
−0.952362 | + | 0.304971i | \(0.901353\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9868 | −1.43924 | −0.719620 | − | 0.694368i | \(-0.755684\pi\) | ||||
−0.719620 | + | 0.694368i | \(0.755684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.2850 | 1.30604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.9880 | 0.699291 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.85801 | −0.169546 | −0.0847729 | − | 0.996400i | \(-0.527016\pi\) | ||||
−0.0847729 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0083i | 0.976309i | 0.872757 | + | 0.488155i | \(0.162330\pi\) | ||||
−0.872757 | + | 0.488155i | \(0.837670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.46917i | − 0.120635i | −0.998179 | − | 0.0603174i | \(-0.980789\pi\) | ||||
0.998179 | − | 0.0603174i | \(-0.0192113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 14.6239i | − 0.507908i | −0.967216 | − | 0.253954i | \(-0.918269\pi\) | ||||
0.967216 | − | 0.253954i | \(-0.0817312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.2722i | 1.01422i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.9046 | −1.10410 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.3680 | 0.530562 | 0.265281 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265281 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4091 | −0.807211 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 44.4059 | 1.52761 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 42.0030i | − 1.44324i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 52.7790i | − 1.80924i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.874295i | 0.0299353i | 0.999888 | + | 0.0149676i | \(0.00476453\pi\) | ||||
−0.999888 | + | 0.0149676i | \(0.995235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.7031i | 1.18543i | 0.805411 | + | 0.592717i | \(0.201945\pi\) | ||||
−0.805411 | + | 0.592717i | \(0.798055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.4933 | −1.34749 | −0.673746 | − | 0.738963i | \(-0.735316\pi\) | ||||
−0.673746 | + | 0.738963i | \(0.735316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.1903 | −0.959611 | −0.479805 | − | 0.877375i | \(-0.659293\pi\) | ||||
−0.479805 | + | 0.877375i | \(0.659293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −82.8574 | −2.81724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.47136 | −0.185603 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62.4194i | 2.11500i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 100.544i | 3.39901i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.5026i | 1.16507i | 0.812806 | + | 0.582535i | \(0.197939\pi\) | ||||
−0.812806 | + | 0.582535i | \(0.802061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.7178i | 0.731690i | 0.930676 | + | 0.365845i | \(0.119220\pi\) | ||||
−0.930676 | + | 0.365845i | \(0.880780\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8314 | −0.364506 | −0.182253 | − | 0.983252i | \(-0.558339\pi\) | ||||
−0.182253 | + | 0.983252i | \(0.558339\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.1435 | 0.374164 | 0.187082 | − | 0.982344i | \(-0.440097\pi\) | ||||
0.187082 | + | 0.982344i | \(0.440097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55.6714 | −1.86716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.7749 | 0.594813 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 77.4531i | − 2.58897i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.9785i | 0.566266i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7620i | 0.658366i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.6861i | 1.51866i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7103 | 0.355631 | 0.177816 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177816 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5384 | 0.713600 | 0.356800 | − | 0.934181i | \(-0.383868\pi\) | ||||
0.356800 | + | 0.934181i | \(0.383868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.65500 | −0.0878678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 68.3569 | 2.25734 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 15.5159i | − 0.511824i | −0.966700 | − | 0.255912i | \(-0.917624\pi\) | ||||
0.966700 | − | 0.255912i | \(-0.0823757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8302i | 0.488141i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 70.1283i | 2.30580i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9098i | 1.04693i | 0.852048 | + | 0.523464i | \(0.175360\pi\) | ||||
−0.852048 | + | 0.523464i | \(0.824640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5123 | 0.508394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.78517 | 0.221899 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.01911 | −0.229304 | −0.114652 | − | 0.993406i | \(-0.536575\pi\) | ||||
−0.114652 | + | 0.993406i | \(0.536575\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7306 | 0.382407 | 0.191204 | − | 0.981550i | \(-0.438761\pi\) | ||||
0.191204 | + | 0.981550i | \(0.438761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.9341i | 1.43069i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 5.92535i | − 0.192548i | −0.995355 | − | 0.0962741i | \(-0.969307\pi\) | ||||
0.995355 | − | 0.0962741i | \(-0.0306925\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.4457i | 0.728619i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 8.28906i | − 0.268509i | −0.990947 | − | 0.134255i | \(-0.957136\pi\) | ||||
0.990947 | − | 0.134255i | \(-0.0428640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −80.0030 | −2.58884 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.7067 | 1.47595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5609 | −0.663254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −75.2098 | −2.42109 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.6688i | 1.24351i | 0.783214 | + | 0.621753i | \(0.213579\pi\) | ||||
−0.783214 | + | 0.621753i | \(0.786421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 36.9214i | − 1.18486i | −0.805620 | − | 0.592432i | \(-0.798168\pi\) | ||||
0.805620 | − | 0.592432i | \(-0.201832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 22.4408i | − 0.719420i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.9613i | 1.34246i | 0.741248 | + | 0.671231i | \(0.234234\pi\) | ||||
−0.741248 | + | 0.671231i | \(0.765766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.48823 | 0.0475641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.8430 | 1.11132 | 0.555659 | − | 0.831410i | \(-0.312466\pi\) | ||||
0.555659 | + | 0.831410i | \(0.312466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 104.430 | 3.32743 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 90.2536 | 2.86990 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.9678i | 1.17432i | 0.809471 | + | 0.587160i | \(0.199754\pi\) | ||||
−0.809471 | + | 0.587160i | \(0.800246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.25374i | 0.229959i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.65401i | 0.305746i | 0.988246 | + | 0.152873i | \(0.0488525\pi\) | ||||
−0.988246 | + | 0.152873i | \(0.951148\pi\) | |||||||
\(998\) | 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 | 5184.2.f.e.2591.1 | yes | 16 | |
3.2 | odd | 2 | inner | 5184.2.f.e.2591.15 | yes | 16 | |
4.3 | odd | 2 | 5184.2.f.b.2591.2 | yes | 16 | ||
8.3 | odd | 2 | inner | 5184.2.f.e.2591.16 | yes | 16 | |
8.5 | even | 2 | 5184.2.f.b.2591.15 | yes | 16 | ||
12.11 | even | 2 | 5184.2.f.b.2591.16 | yes | 16 | ||
24.5 | odd | 2 | 5184.2.f.b.2591.1 | ✓ | 16 | ||
24.11 | even | 2 | inner | 5184.2.f.e.2591.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5184.2.f.b.2591.1 | ✓ | 16 | 24.5 | odd | 2 | ||
5184.2.f.b.2591.2 | yes | 16 | 4.3 | odd | 2 | ||
5184.2.f.b.2591.15 | yes | 16 | 8.5 | even | 2 | ||
5184.2.f.b.2591.16 | yes | 16 | 12.11 | even | 2 | ||
5184.2.f.e.2591.1 | yes | 16 | 1.1 | even | 1 | trivial | |
5184.2.f.e.2591.2 | yes | 16 | 24.11 | even | 2 | inner | |
5184.2.f.e.2591.15 | yes | 16 | 3.2 | odd | 2 | inner | |
5184.2.f.e.2591.16 | yes | 16 | 8.3 | odd | 2 | inner |