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 | 2591.13 | ||
Root | \(-0.367543 - 0.212201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2591 |
Dual form | 5184.2.f.e.2591.14 |
$q$-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 | ||||||||
\(5\) | 2.24254 | 1.00289 | 0.501446 | − | 0.865189i | \(-0.332802\pi\) | ||||
0.501446 | + | 0.865189i | \(0.332802\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.77162i | − 1.42554i | −0.701399 | − | 0.712769i | \(-0.747441\pi\) | ||||
0.701399 | − | 0.712769i | \(-0.252559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.57370i | 0.776001i | 0.921659 | + | 0.388000i | \(0.126834\pi\) | ||||
−0.921659 | + | 0.388000i | \(0.873166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77162i | 0.768709i | 0.923186 | + | 0.384355i | \(0.125576\pi\) | ||||
−0.923186 | + | 0.384355i | \(0.874424\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.81624i | − 1.16811i | −0.811714 | − | 0.584055i | \(-0.801465\pi\) | ||||
0.811714 | − | 0.584055i | \(-0.198535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.77162 | 1.32410 | 0.662050 | − | 0.749459i | \(-0.269687\pi\) | ||||
0.662050 | + | 0.749459i | \(0.269687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.91137 | 0.398548 | 0.199274 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199274 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0289668 | 0.00579337 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2533 | −1.90400 | −0.951999 | − | 0.306102i | \(-0.900975\pi\) | ||||
−0.951999 | + | 0.306102i | \(0.900975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.22512i | − 1.11806i | −0.829146 | − | 0.559032i | \(-0.811173\pi\) | ||||
0.829146 | − | 0.559032i | \(-0.188827\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 8.45799i | − 1.42966i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.96043i | − 0.322293i | −0.986931 | − | 0.161146i | \(-0.948481\pi\) | ||||
0.986931 | − | 0.161146i | \(-0.0515191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 10.6118i | − 1.65728i | −0.559779 | − | 0.828642i | \(-0.689114\pi\) | ||||
0.559779 | − | 0.828642i | \(-0.310886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01060 | 0.764110 | 0.382055 | − | 0.924140i | \(-0.375217\pi\) | ||||
0.382055 | + | 0.924140i | \(0.375217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.36915 | 0.929036 | 0.464518 | − | 0.885564i | \(-0.346228\pi\) | ||||
0.464518 | + | 0.885564i | \(0.346228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.22512 | −1.03216 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.35856 | −0.323973 | −0.161987 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161987 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.77162i | 0.778245i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.22196i | 0.679841i | 0.940454 | + | 0.339920i | \(0.110400\pi\) | ||||
−0.940454 | + | 0.339920i | \(0.889600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26469i | 0.289964i | 0.989434 | + | 0.144982i | \(0.0463124\pi\) | ||||
−0.989434 | + | 0.144982i | \(0.953688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.21546i | 0.770933i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.5326 | 1.53111 | 0.765553 | − | 0.643373i | \(-0.222466\pi\) | ||||
0.765553 | + | 0.643373i | \(0.222466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.19446 | −0.141756 | −0.0708781 | − | 0.997485i | \(-0.522580\pi\) | ||||
−0.0708781 | + | 0.997485i | \(0.522580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.57221 | 1.00330 | 0.501650 | − | 0.865070i | \(-0.332726\pi\) | ||||
0.501650 | + | 0.865070i | \(0.332726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.70703 | 1.10622 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 2.39557i | − 0.269522i | −0.990878 | − | 0.134761i | \(-0.956973\pi\) | ||||
0.990878 | − | 0.134761i | \(-0.0430267\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 15.3593i | − 1.68590i | −0.537993 | − | 0.842950i | \(-0.680817\pi\) | ||||
0.537993 | − | 0.842950i | \(-0.319183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 10.8006i | − 1.17149i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7111i | 1.55938i | 0.626168 | + | 0.779688i | \(0.284622\pi\) | ||||
−0.626168 | + | 0.779688i | \(0.715378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4535 | 1.09582 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9431 | 1.32793 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.7684 | −1.39797 | −0.698983 | − | 0.715139i | \(-0.746364\pi\) | ||||
−0.698983 | + | 0.715139i | \(0.746364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.20106 | −0.219014 | −0.109507 | − | 0.993986i | \(-0.534927\pi\) | ||||
−0.109507 | + | 0.993986i | \(0.534927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.00000i | − 0.197066i | −0.995134 | − | 0.0985329i | \(-0.968585\pi\) | ||||
0.995134 | − | 0.0985329i | \(-0.0314150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.16717i | 0.112835i | 0.998407 | + | 0.0564174i | \(0.0179677\pi\) | ||||
−0.998407 | + | 0.0564174i | \(0.982032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 17.6118i | − 1.68690i | −0.537206 | − | 0.843451i | \(-0.680520\pi\) | ||||
0.537206 | − | 0.843451i | \(-0.319480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.405719i | − 0.0381668i | −0.999818 | − | 0.0190834i | \(-0.993925\pi\) | ||||
0.999818 | − | 0.0190834i | \(-0.00607481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.28631 | 0.399701 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.1650 | −1.66518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.37605 | 0.397823 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1477 | −0.997082 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.1639i | − 1.25685i | −0.777872 | − | 0.628423i | \(-0.783701\pi\) | ||||
0.777872 | − | 0.628423i | \(-0.216299\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2509i | 1.85670i | 0.371710 | + | 0.928349i | \(0.378771\pi\) | ||||
−0.371710 | + | 0.928349i | \(0.621229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 21.7684i | − 1.88756i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 7.62506i | − 0.651453i | −0.945464 | − | 0.325726i | \(-0.894391\pi\) | ||||
0.945464 | − | 0.325726i | \(-0.105609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0726 | −1.36326 | −0.681631 | − | 0.731696i | \(-0.738729\pi\) | ||||
−0.681631 | + | 0.731696i | \(0.738729\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.13333 | −0.596519 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.9935 | −1.90950 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.3596 | 1.74985 | 0.874923 | − | 0.484262i | \(-0.160912\pi\) | ||||
0.874923 | + | 0.484262i | \(0.160912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.54324i | 0.613860i | 0.951732 | + | 0.306930i | \(0.0993018\pi\) | ||||
−0.951732 | + | 0.306930i | \(0.900698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 13.9601i | − 1.12130i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 16.2068i | − 1.29344i | −0.762728 | − | 0.646720i | \(-0.776140\pi\) | ||||
0.762728 | − | 0.646720i | \(-0.223860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.20896i | − 0.568145i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7545 | −1.15566 | −0.577831 | − | 0.816157i | \(-0.696101\pi\) | ||||
−0.577831 | + | 0.816157i | \(0.696101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.5539 | 1.59051 | 0.795256 | − | 0.606274i | \(-0.207337\pi\) | ||||
0.795256 | + | 0.606274i | \(0.207337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.31812 | 0.409086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0732 | 0.841877 | 0.420939 | − | 0.907089i | \(-0.361701\pi\) | ||||
0.420939 | + | 0.907089i | \(0.361701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 0.109252i | − 0.00825867i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 0.232048i | − 0.0173441i | −0.999962 | − | 0.00867203i | \(-0.997240\pi\) | ||||
0.999962 | − | 0.00867203i | \(-0.00276043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.47796i | − 0.332844i | −0.986055 | − | 0.166422i | \(-0.946779\pi\) | ||||
0.986055 | − | 0.166422i | \(-0.0532215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 4.39634i | − 0.323225i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.3956 | 0.906454 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.58521 | −0.693562 | −0.346781 | − | 0.937946i | \(-0.612725\pi\) | ||||
−0.346781 | + | 0.937946i | \(0.612725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0865 | −0.870004 | −0.435002 | − | 0.900430i | \(-0.643252\pi\) | ||||
−0.435002 | + | 0.900430i | \(0.643252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1477 | −0.794242 | −0.397121 | − | 0.917766i | \(-0.629991\pi\) | ||||
−0.397121 | + | 0.917766i | \(0.629991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 13.5432i | − 0.960055i | −0.877253 | − | 0.480027i | \(-0.840627\pi\) | ||||
0.877253 | − | 0.480027i | \(-0.159373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.6717i | 2.71422i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 23.7973i | − 1.66208i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.8544i | 1.02750i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.1639 | 1.93888 | 0.969442 | − | 0.245320i | \(-0.0788929\pi\) | ||||
0.969442 | + | 0.245320i | \(0.0788929\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.2365 | 0.766320 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.4788 | −1.59384 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.3488 | 0.897936 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 21.9902i | − 1.47257i | −0.676669 | − | 0.736287i | \(-0.736577\pi\) | ||||
0.676669 | − | 0.736287i | \(-0.263423\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.7856i | − 0.848608i | −0.905520 | − | 0.424304i | \(-0.860519\pi\) | ||||
0.905520 | − | 0.424304i | \(-0.139481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.02447i | − 0.199862i | −0.994994 | − | 0.0999312i | \(-0.968138\pi\) | ||||
0.994994 | − | 0.0999312i | \(-0.0318623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.7558i | 1.55630i | 0.628081 | + | 0.778148i | \(0.283840\pi\) | ||||
−0.628081 | + | 0.778148i | \(0.716160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.2831 | 0.931724 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.4222 | −1.90317 | −0.951583 | − | 0.307391i | \(-0.900544\pi\) | ||||
−0.951583 | + | 0.307391i | \(0.900544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.87803 | −0.378637 | −0.189319 | − | 0.981916i | \(-0.560628\pi\) | ||||
−0.189319 | + | 0.981916i | \(0.560628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.2026 | −1.03515 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.9967i | 1.01785i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.06886i | − 0.130586i | −0.997866 | − | 0.0652928i | \(-0.979202\pi\) | ||||
0.997866 | − | 0.0652928i | \(-0.0207981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.91930i | 0.309273i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.19477i | − 0.448798i | −0.974497 | − | 0.224399i | \(-0.927958\pi\) | ||||
0.974497 | − | 0.224399i | \(-0.0720418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.39400 | −0.459441 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1625 | −1.67491 | −0.837454 | − | 0.546507i | \(-0.815957\pi\) | ||||
−0.837454 | + | 0.546507i | \(0.815957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.28915 | −0.324910 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7078 | −0.652869 | −0.326434 | − | 0.945220i | \(-0.605847\pi\) | ||||
−0.326434 | + | 0.945220i | \(0.605847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 3.24463i | − 0.197097i | −0.995132 | − | 0.0985486i | \(-0.968580\pi\) | ||||
0.995132 | − | 0.0985486i | \(-0.0314200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0745520i | 0.00449566i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0008i | 1.38199i | 0.722862 | + | 0.690993i | \(0.242826\pi\) | ||||
−0.722862 | + | 0.690993i | \(0.757174\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1757i | 1.44220i | 0.692830 | + | 0.721101i | \(0.256364\pi\) | ||||
−0.692830 | + | 0.721101i | \(0.743636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2236 | 1.38050 | 0.690248 | − | 0.723572i | \(-0.257501\pi\) | ||||
0.690248 | + | 0.723572i | \(0.257501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −40.0237 | −2.36252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.19615 | −0.364480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7723 | 0.921428 | 0.460714 | − | 0.887549i | \(-0.347593\pi\) | ||||
0.460714 | + | 0.887549i | \(0.347593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7104i | 0.681807i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.29759i | 0.306367i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 18.8981i | − 1.08927i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.07865i | 0.290802i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7104 | 1.01079 | 0.505394 | − | 0.862889i | \(-0.331347\pi\) | ||||
0.505394 | + | 0.862889i | \(0.331347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4336 | 0.648341 | 0.324170 | − | 0.945999i | \(-0.394915\pi\) | ||||
0.324170 | + | 0.945999i | \(0.394915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.376055 | 0.0212559 | 0.0106279 | − | 0.999944i | \(-0.496617\pi\) | ||||
0.0106279 | + | 0.999944i | \(0.496617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.7492 | −1.27772 | −0.638862 | − | 0.769322i | \(-0.720594\pi\) | ||||
−0.638862 | + | 0.769322i | \(0.720594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 26.3890i | − 1.47750i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 27.7975i | − 1.54669i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0802851i | 0.00445341i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 24.0220i | − 1.32438i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0670 | 1.54270 | 0.771350 | − | 0.636411i | \(-0.219582\pi\) | ||||
0.771350 | + | 0.636411i | \(0.219582\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.1049 | 1.53553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9193 | 0.703759 | 0.351879 | − | 0.936045i | \(-0.385543\pi\) | ||||
0.351879 | + | 0.936045i | \(0.385543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0216 | 0.867619 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.849064i | 0.0458452i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6800i | 0.734378i | 0.930146 | + | 0.367189i | \(0.119680\pi\) | ||||
−0.930146 | + | 0.367189i | \(0.880320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.1533i | − 0.918196i | −0.888386 | − | 0.459098i | \(-0.848173\pi\) | ||||
0.888386 | − | 0.459098i | \(-0.151827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 6.63156i | − 0.352962i | −0.984304 | − | 0.176481i | \(-0.943529\pi\) | ||||
0.984304 | − | 0.176481i | \(-0.0564715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.67862 | −0.142166 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.921669 | 0.0486438 | 0.0243219 | − | 0.999704i | \(-0.492257\pi\) | ||||
0.0243219 | + | 0.999704i | \(0.492257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3116 | 0.753242 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.2235 | 1.00620 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 13.0162i | − 0.679443i | −0.940526 | − | 0.339721i | \(-0.889667\pi\) | ||||
0.940526 | − | 0.339721i | \(-0.110333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.89559i | 0.461836i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.21282i | − 0.114576i | −0.998358 | − | 0.0572878i | \(-0.981755\pi\) | ||||
0.998358 | − | 0.0572878i | \(-0.0182453\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 28.4184i | − 1.46362i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.15332 | −0.264708 | −0.132354 | − | 0.991202i | \(-0.542254\pi\) | ||||
−0.132354 | + | 0.991202i | \(0.542254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.0478 | 1.68866 | 0.844332 | − | 0.535820i | \(-0.179997\pi\) | ||||
0.844332 | + | 0.535820i | \(0.179997\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.7684 | 1.10942 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.5790 | −1.55042 | −0.775209 | − | 0.631705i | \(-0.782356\pi\) | ||||
−0.775209 | + | 0.631705i | \(0.782356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.20561i | − 0.465548i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 5.37214i | − 0.270302i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.10485i | 0.256205i | 0.991761 | + | 0.128102i | \(0.0408886\pi\) | ||||
−0.991761 | + | 0.128102i | \(0.959111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.825622i | 0.0412296i | 0.999787 | + | 0.0206148i | \(0.00656235\pi\) | ||||
−0.999787 | + | 0.0206148i | \(0.993438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2537 | 0.859466 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.04557 | 0.250099 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.10315 | −0.202888 | −0.101444 | − | 0.994841i | \(-0.532346\pi\) | ||||
−0.101444 | + | 0.994841i | \(0.532346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6952 | 0.969139 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 34.4437i | − 1.69078i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 24.9172i | − 1.21728i | −0.793445 | − | 0.608642i | \(-0.791714\pi\) | ||||
0.793445 | − | 0.608642i | \(-0.208286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 16.9176i | − 0.824513i | −0.911068 | − | 0.412257i | \(-0.864741\pi\) | ||||
0.911068 | − | 0.412257i | \(-0.135259\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 0.139511i | − 0.00676729i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.54155 | 0.413354 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.33455 | 0.305125 | 0.152562 | − | 0.988294i | \(-0.451248\pi\) | ||||
0.152562 | + | 0.988294i | \(0.451248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3695 | 1.55558 | 0.777790 | − | 0.628524i | \(-0.216341\pi\) | ||||
0.777790 | + | 0.628524i | \(0.216341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.0317 | 0.527718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1321i | 0.531307i | 0.964069 | + | 0.265653i | \(0.0855877\pi\) | ||||
−0.964069 | + | 0.265653i | \(0.914412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.80297i | 0.370730i | 0.982670 | + | 0.185365i | \(0.0593468\pi\) | ||||
−0.982670 | + | 0.185365i | \(0.940653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.9902i | 1.56389i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3258i | 1.05362i | 0.849983 | + | 0.526810i | \(0.176612\pi\) | ||||
−0.849983 | + | 0.526810i | \(0.823388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3116 | 1.28605 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.4423 | 1.09899 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.9768 | −1.44903 | −0.724517 | − | 0.689257i | \(-0.757937\pi\) | ||||
−0.724517 | + | 0.689257i | \(0.757937\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.18130 | −0.287892 | −0.143946 | − | 0.989586i | \(-0.545979\pi\) | ||||
−0.143946 | + | 0.989586i | \(0.545979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.53094i | − 0.0711490i | −0.999367 | − | 0.0355745i | \(-0.988674\pi\) | ||||
0.999367 | − | 0.0355745i | \(-0.0113261\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.97014i | 0.415089i | 0.978226 | + | 0.207544i | \(0.0665471\pi\) | ||||
−0.978226 | + | 0.207544i | \(0.933453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 47.2684i | − 2.18265i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.8958i | 0.592950i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.167186 | 0.00767100 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.1253 | 1.65061 | 0.825303 | − | 0.564690i | \(-0.191004\pi\) | ||||
0.825303 | + | 0.564690i | \(0.191004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.43357 | 0.247749 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.8760 | −1.40201 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.1027i | 1.90786i | 0.300034 | + | 0.953928i | \(0.403002\pi\) | ||||
−0.300034 | + | 0.953928i | \(0.596998\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.64825i | − 0.119514i | −0.998213 | − | 0.0597570i | \(-0.980967\pi\) | ||||
0.998213 | − | 0.0597570i | \(-0.0190326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 49.3825i | 2.22408i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.50505i | 0.202079i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.0253 | −1.03075 | −0.515377 | − | 0.856964i | \(-0.672348\pi\) | ||||
−0.515377 | + | 0.856964i | \(0.672348\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.0980 | 0.985301 | 0.492650 | − | 0.870227i | \(-0.336028\pi\) | ||||
0.492650 | + | 0.870227i | \(0.336028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.93596 | −0.219648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.9064 | 0.749363 | 0.374681 | − | 0.927154i | \(-0.377752\pi\) | ||||
0.374681 | + | 0.927154i | \(0.377752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 32.3311i | − 1.43024i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.48507i | − 0.197636i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3923i | 0.720933i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 17.5687i | − 0.769700i | −0.922979 | − | 0.384850i | \(-0.874253\pi\) | ||||
0.922979 | − | 0.384850i | \(-0.125747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.6354 | 0.989776 | 0.494888 | − | 0.868957i | \(-0.335209\pi\) | ||||
0.494888 | + | 0.868957i | \(0.335209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.9817 | −1.30602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.3467 | −0.841160 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.4119 | 1.27397 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.61742i | 0.113161i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 18.5953i | − 0.800957i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.86701i | 0.424216i | 0.977246 | + | 0.212108i | \(0.0680328\pi\) | ||||
−0.977246 | + | 0.212108i | \(0.931967\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 39.4950i | − 1.69178i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5383 | −0.536098 | −0.268049 | − | 0.963405i | \(-0.586379\pi\) | ||||
−0.268049 | + | 0.963405i | \(0.586379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.1784 | −2.52108 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.03516 | −0.384214 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.93876 | 0.166891 | 0.0834453 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834453 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8875i | 0.587378i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.2250i | 1.40027i | 0.714012 | + | 0.700134i | \(0.246876\pi\) | ||||
−0.714012 | + | 0.700134i | \(0.753124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 0.909839i | − 0.0382772i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 3.82654i | − 0.160417i | −0.996778 | − | 0.0802084i | \(-0.974441\pi\) | ||||
0.996778 | − | 0.0802084i | \(-0.0255586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.63129 | −0.403057 | −0.201528 | − | 0.979483i | \(-0.564591\pi\) | ||||
−0.201528 | + | 0.979483i | \(0.564591\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0553663 | 0.00230893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6754 | 0.569313 | 0.284656 | − | 0.958630i | \(-0.408121\pi\) | ||||
0.284656 | + | 0.958630i | \(0.408121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.9293 | −2.40331 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 6.07023i | − 0.251403i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 28.4598i | − 1.17466i | −0.809346 | − | 0.587332i | \(-0.800178\pi\) | ||||
0.809346 | − | 0.587332i | \(-0.199822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 35.9290i | − 1.48043i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.70103i | 0.234113i | 0.993125 | + | 0.117057i | \(0.0373459\pi\) | ||||
−0.993125 | + | 0.117057i | \(0.962654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −40.7357 | −1.67000 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5997 | −0.637387 | −0.318693 | − | 0.947858i | \(-0.603244\pi\) | ||||
−0.318693 | + | 0.947858i | \(0.603244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1607 | −0.618416 | −0.309208 | − | 0.950994i | \(-0.600064\pi\) | ||||
−0.309208 | + | 0.950994i | \(0.600064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.81346 | 0.398974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 35.9837i | − 1.46053i | −0.683162 | − | 0.730267i | \(-0.739396\pi\) | ||||
0.683162 | − | 0.730267i | \(-0.260604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.6529i | 0.714159i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.1003i | 0.973404i | 0.873568 | + | 0.486702i | \(0.161800\pi\) | ||||
−0.873568 | + | 0.486702i | \(0.838200\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.1317i | 1.13254i | 0.824219 | + | 0.566271i | \(0.191614\pi\) | ||||
−0.824219 | + | 0.566271i | \(0.808386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0849 | −1.45038 | −0.725188 | − | 0.688551i | \(-0.758247\pi\) | ||||
−0.725188 | + | 0.688551i | \(0.758247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.4848 | 2.22295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1440 | −1.00576 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.44190 | −0.376473 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5302i | 1.41443i | 0.706996 | + | 0.707217i | \(0.250050\pi\) | ||||
−0.706996 | + | 0.707217i | \(0.749950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 31.7631i | − 1.26048i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 20.0253i | − 0.793431i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 30.4054i | − 1.20094i | −0.799647 | − | 0.600470i | \(-0.794980\pi\) | ||||
0.799647 | − | 0.600470i | \(-0.205020\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.38578 | 0.251831 | 0.125915 | − | 0.992041i | \(-0.459813\pi\) | ||||
0.125915 | + | 0.992041i | \(0.459813\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.4730 | 1.19802 | 0.599009 | − | 0.800742i | \(-0.295561\pi\) | ||||
0.599009 | + | 0.800742i | \(0.295561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4398 | −0.527557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.7411 | −1.39866 | −0.699328 | − | 0.714801i | \(-0.746517\pi\) | ||||
−0.699328 | + | 0.714801i | \(0.746517\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 47.6558i | 1.86207i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0672402i | 0.00261931i | 0.999999 | + | 0.00130965i | \(0.000416876\pi\) | ||||
−0.999999 | + | 0.00130965i | \(0.999583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 9.61954i | − 0.374157i | −0.982345 | − | 0.187078i | \(-0.940098\pi\) | ||||
0.982345 | − | 0.187078i | \(-0.0599018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 48.8163i | − 1.89302i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5979 | −0.758834 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.82864 | −0.225012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0800 | 0.774026 | 0.387013 | − | 0.922074i | \(-0.373507\pi\) | ||||
0.387013 | + | 0.922074i | \(0.373507\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6332 | 0.869864 | 0.434932 | − | 0.900463i | \(-0.356772\pi\) | ||||
0.434932 | + | 0.900463i | \(0.356772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 51.9290i | 1.99285i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.38622i | 0.129570i | 0.997899 | + | 0.0647851i | \(0.0206362\pi\) | ||||
−0.997899 | + | 0.0647851i | \(0.979364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 17.0995i | − 0.653337i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 6.53703i | − 0.249041i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.59057 | −0.174634 | −0.0873168 | − | 0.996181i | \(-0.527829\pi\) | ||||
−0.0873168 | + | 0.996181i | \(0.527829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.0434 | −1.36720 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.1089 | −1.93589 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.8717 | −0.561696 | −0.280848 | − | 0.959752i | \(-0.590616\pi\) | ||||
−0.280848 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.3149i | − 0.426748i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.30158i | 0.312213i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 14.3851i | − 0.540243i | −0.962826 | − | 0.270122i | \(-0.912936\pi\) | ||||
0.962826 | − | 0.270122i | \(-0.0870639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 11.8985i | − 0.445602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.9967 | −0.598244 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.35549 | −0.0878449 | −0.0439224 | − | 0.999035i | \(-0.513985\pi\) | ||||
−0.0439224 | + | 0.999035i | \(0.513985\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.54324 | −0.280925 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.297007 | −0.0110306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.41182i | 0.0523613i | 0.999657 | + | 0.0261807i | \(0.00833452\pi\) | ||||
−0.999657 | + | 0.0261807i | \(0.991665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 24.1323i | − 0.892564i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.3784i | 1.23286i | 0.787409 | + | 0.616430i | \(0.211422\pi\) | ||||
−0.787409 | + | 0.616430i | \(0.788578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.2553i | 1.18814i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.74220 | 0.248016 | 0.124008 | − | 0.992281i | \(-0.460425\pi\) | ||||
0.124008 | + | 0.992281i | \(0.460425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.5581 | 1.01101 | 0.505505 | − | 0.862824i | \(-0.331306\pi\) | ||||
0.505505 | + | 0.862824i | \(0.331306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47.8996 | 1.75491 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.40213 | 0.160850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 9.01951i | − 0.329127i | −0.986367 | − | 0.164563i | \(-0.947379\pi\) | ||||
0.986367 | − | 0.164563i | \(-0.0526215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.9160i | 0.615636i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.8213i | 0.756764i | 0.925649 | + | 0.378382i | \(0.123519\pi\) | ||||
−0.925649 | + | 0.378382i | \(0.876481\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1602i | 1.52831i | 0.645035 | + | 0.764153i | \(0.276843\pi\) | ||||
−0.645035 | + | 0.764153i | \(0.723157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −66.4249 | −2.40474 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.4733 | −0.522600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.3279 | 1.34608 | 0.673038 | − | 0.739608i | \(-0.264989\pi\) | ||||
0.673038 | + | 0.739608i | \(0.264989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.26180 | −0.117319 | −0.0586595 | − | 0.998278i | \(-0.518683\pi\) | ||||
−0.0586595 | + | 0.998278i | \(0.518683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 0.180322i | − 0.00647736i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 61.2472i | − 2.19441i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 3.07418i | − 0.110003i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 36.3442i | − 1.29718i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.3172 | −1.40151 | −0.700754 | − | 0.713403i | \(-0.747153\pi\) | ||||
−0.700754 | + | 0.713403i | \(0.747153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.53022 | −0.0544083 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.27686 | −0.222898 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.9204 | −1.20152 | −0.600761 | − | 0.799428i | \(-0.705136\pi\) | ||||
−0.600761 | + | 0.799428i | \(0.705136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 30.6754i | − 1.08522i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0623i | 0.778562i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 16.1663i | − 0.569789i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.7361i | 0.975148i | 0.873082 | + | 0.487574i | \(0.162118\pi\) | ||||
−0.873082 | + | 0.487574i | \(0.837882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.1345 | −1.44443 | −0.722214 | − | 0.691670i | \(-0.756875\pi\) | ||||
−0.722214 | + | 0.691670i | \(0.756875\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0875 | −1.15900 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.9193 | 1.01176 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.3502 | 1.37333 | 0.686666 | − | 0.726973i | \(-0.259074\pi\) | ||||
0.686666 | + | 0.726973i | \(0.259074\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.3213i | 1.47523i | 0.675222 | + | 0.737614i | \(0.264048\pi\) | ||||
−0.675222 | + | 0.737614i | \(0.735952\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.7777i | 1.10502i | 0.833506 | + | 0.552510i | \(0.186330\pi\) | ||||
−0.833506 | + | 0.552510i | \(0.813670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 8.68766i | − 0.301735i | −0.988554 | − | 0.150867i | \(-0.951793\pi\) | ||||
0.988554 | − | 0.150867i | \(-0.0482066\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.7979i | 1.20568i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.0929 | 1.59511 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9147 | −0.445865 | −0.222932 | − | 0.974834i | \(-0.571563\pi\) | ||||
−0.222932 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.1310 | 2.62521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9261 | 0.410270 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 16.5048i | − 0.567112i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.74711i | − 0.128449i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.5644i | 1.56010i | 0.625719 | + | 0.780048i | \(0.284806\pi\) | ||||
−0.625719 | + | 0.780048i | \(0.715194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.19747i | 0.211702i | 0.994382 | + | 0.105851i | \(0.0337566\pi\) | ||||
−0.994382 | + | 0.105851i | \(0.966243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3368 | 0.762120 | 0.381060 | − | 0.924550i | \(-0.375559\pi\) | ||||
0.381060 | + | 0.924550i | \(0.375559\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.2947 | −1.74609 | −0.873046 | − | 0.487638i | \(-0.837859\pi\) | ||||
−0.873046 | + | 0.487638i | \(0.837859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.8320 | 0.844312 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.16547 | 0.209149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.7357i | 1.17697i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.0450i | 1.42138i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0681i | 0.778955i | 0.921036 | + | 0.389477i | \(0.127344\pi\) | ||||
−0.921036 | + | 0.389477i | \(0.872656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1.79075i | − 0.0603320i | −0.999545 | − | 0.0301660i | \(-0.990396\pi\) | ||||
0.999545 | − | 0.0301660i | \(-0.00960360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.85559 | −0.0960981 | −0.0480490 | − | 0.998845i | \(-0.515300\pi\) | ||||
−0.0480490 | + | 0.998845i | \(0.515300\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.8305 | −0.397228 | −0.198614 | − | 0.980078i | \(-0.563644\pi\) | ||||
−0.198614 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.4209 | −1.79168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.7603 | 1.23014 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 0.520375i | − 0.0173942i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.8283i | 2.12879i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3594i | 0.378436i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 10.0420i | − 0.333807i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.8198 | 0.525287 | 0.262643 | − | 0.964893i | \(-0.415406\pi\) | ||||
0.262643 | + | 0.964893i | \(0.415406\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5047 | 1.37511 | 0.687557 | − | 0.726131i | \(-0.258683\pi\) | ||||
0.687557 | + | 0.726131i | \(0.258683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.5302 | 1.30826 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 80.1502 | 2.64679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.7014i | 0.649889i | 0.945733 | + | 0.324944i | \(0.105346\pi\) | ||||
−0.945733 | + | 0.324944i | \(0.894654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.31059i | − 0.108969i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 0.0567875i | − 0.00186716i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.3128i | 0.535206i | 0.963529 | + | 0.267603i | \(0.0862316\pi\) | ||||
−0.963529 | + | 0.267603i | \(0.913768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.7006 | −1.36668 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.7975 | 0.909075 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.92325 | 0.0954983 | 0.0477492 | − | 0.998859i | \(-0.484795\pi\) | ||||
0.0477492 | + | 0.998859i | \(0.484795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.0248 | −0.815786 | −0.407893 | − | 0.913030i | \(-0.633736\pi\) | ||||
−0.407893 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 20.2831i | − 0.660507i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.9033i | 1.45916i | 0.683894 | + | 0.729581i | \(0.260285\pi\) | ||||
−0.683894 | + | 0.729581i | \(0.739715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.7589i | 0.771247i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 30.6498i | − 0.992844i | −0.868081 | − | 0.496422i | \(-0.834647\pi\) | ||||
0.868081 | − | 0.496422i | \(-0.165353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.4952 | −0.695568 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.7588 | −0.928671 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.75211 | −0.250068 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.1044 | −0.872520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.63693i | 0.0526403i | 0.999654 | + | 0.0263201i | \(0.00837893\pi\) | ||||
−0.999654 | + | 0.0263201i | \(0.991621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.7448i | 0.409001i | 0.978866 | + | 0.204500i | \(0.0655570\pi\) | ||||
−0.978866 | + | 0.204500i | \(0.934443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 60.6198i | 1.94338i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.1764i | 0.901442i | 0.892665 | + | 0.450721i | \(0.148833\pi\) | ||||
−0.892665 | + | 0.450721i | \(0.851167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.8621 | −1.21008 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.53342 | 0.144593 | 0.0722967 | − | 0.997383i | \(-0.476967\pi\) | ||||
0.0722967 | + | 0.997383i | \(0.476967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.9992 | −0.796539 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.57711 | 0.304534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 32.4984i | − 1.03235i | −0.856485 | − | 0.516173i | \(-0.827356\pi\) | ||||
0.856485 | − | 0.516173i | \(-0.172644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 30.3712i | − 0.962832i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 6.02966i | − 0.190961i | −0.995431 | − | 0.0954806i | \(-0.969561\pi\) | ||||
0.995431 | − | 0.0954806i | \(-0.0304388\pi\) | |||||||
\(998\) | 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.2591.13 | yes | 16 | |
3.2 | odd | 2 | inner | 5184.2.f.e.2591.3 | yes | 16 | |
4.3 | odd | 2 | 5184.2.f.b.2591.14 | yes | 16 | ||
8.3 | odd | 2 | inner | 5184.2.f.e.2591.4 | yes | 16 | |
8.5 | even | 2 | 5184.2.f.b.2591.3 | ✓ | 16 | ||
12.11 | even | 2 | 5184.2.f.b.2591.4 | yes | 16 | ||
24.5 | odd | 2 | 5184.2.f.b.2591.13 | yes | 16 | ||
24.11 | even | 2 | inner | 5184.2.f.e.2591.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5184.2.f.b.2591.3 | ✓ | 16 | 8.5 | even | 2 | ||
5184.2.f.b.2591.4 | yes | 16 | 12.11 | even | 2 | ||
5184.2.f.b.2591.13 | yes | 16 | 24.5 | odd | 2 | ||
5184.2.f.b.2591.14 | yes | 16 | 4.3 | odd | 2 | ||
5184.2.f.e.2591.3 | yes | 16 | 3.2 | odd | 2 | inner | |
5184.2.f.e.2591.4 | yes | 16 | 8.3 | odd | 2 | inner | |
5184.2.f.e.2591.13 | yes | 16 | 1.1 | even | 1 | trivial | |
5184.2.f.e.2591.14 | yes | 16 | 24.11 | even | 2 | inner |