Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.a (trivial) |
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: | yes |
Analytic conductor: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.3288334336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} - 8x^{5} + 24x^{4} + 8x^{3} - 16x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 4608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.49930\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | 2.97127 | 1.32879 | 0.664395 | − | 0.747381i | \(-0.268689\pi\) | ||||
0.664395 | + | 0.747381i | \(0.268689\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.27411 | 0.859533 | 0.429766 | − | 0.902940i | \(-0.358596\pi\) | ||||
0.429766 | + | 0.902940i | \(0.358596\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.69552 | −1.11424 | −0.557120 | − | 0.830432i | \(-0.688094\pi\) | ||||
−0.557120 | + | 0.830432i | \(0.688094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | 0.946932 | 0.473466 | − | 0.880812i | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.74053 | 0.422140 | 0.211070 | − | 0.977471i | \(-0.432305\pi\) | ||||
0.211070 | + | 0.977471i | \(0.432305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.76429 | 1.78125 | 0.890626 | − | 0.454737i | \(-0.150267\pi\) | ||||
0.890626 | + | 0.454737i | \(0.150267\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.16478 | −0.451389 | −0.225694 | − | 0.974198i | \(-0.572465\pi\) | ||||
−0.225694 | + | 0.974198i | \(0.572465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.82843 | 0.765685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.43275 | −1.00884 | −0.504418 | − | 0.863460i | \(-0.668293\pi\) | ||||
−0.504418 | + | 0.863460i | \(0.668293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.70626 | 1.56369 | 0.781845 | − | 0.623472i | \(-0.214279\pi\) | ||||
0.781845 | + | 0.623472i | \(0.214279\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.75699 | 1.14214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.585786 | 0.0963027 | 0.0481513 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481513 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1445 | 1.58431 | 0.792155 | − | 0.610319i | \(-0.208959\pi\) | ||||
0.792155 | + | 0.610319i | \(0.208959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.33214 | 0.203150 | 0.101575 | − | 0.994828i | \(-0.467612\pi\) | ||||
0.101575 | + | 0.994828i | \(0.467612\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.6173 | −1.84042 | −0.920210 | − | 0.391424i | \(-0.871982\pi\) | ||||
−0.920210 | + | 0.391424i | \(0.871982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.82843 | −0.261204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.43275 | 0.746245 | 0.373122 | − | 0.927782i | \(-0.378287\pi\) | ||||
0.373122 | + | 0.927782i | \(0.378287\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9804 | −1.48059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.32957 | 0.563662 | 0.281831 | − | 0.959464i | \(-0.409058\pi\) | ||||
0.281831 | + | 0.959464i | \(0.409058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.41421 | 0.949293 | 0.474646 | − | 0.880177i | \(-0.342576\pi\) | ||||
0.474646 | + | 0.880177i | \(0.342576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.1445 | 1.25828 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.43215 | −0.785812 | −0.392906 | − | 0.919579i | \(-0.628530\pi\) | ||||
−0.392906 | + | 0.919579i | \(0.628530\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.12293 | −0.726659 | −0.363329 | − | 0.931661i | \(-0.618360\pi\) | ||||
−0.363329 | + | 0.931661i | \(0.618360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4853 | 1.22721 | 0.613605 | − | 0.789613i | \(-0.289719\pi\) | ||||
0.613605 | + | 0.789613i | \(0.289719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.40401 | −0.957726 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.27411 | −0.255857 | −0.127929 | − | 0.991783i | \(-0.540833\pi\) | ||||
−0.127929 | + | 0.991783i | \(0.540833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.81845 | −1.07772 | −0.538858 | − | 0.842397i | \(-0.681144\pi\) | ||||
−0.538858 | + | 0.842397i | \(0.681144\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.17157 | 0.560936 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8851 | 1.25981 | 0.629907 | − | 0.776670i | \(-0.283093\pi\) | ||||
0.629907 | + | 0.776670i | \(0.283093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.76429 | 0.813919 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.0698 | 2.36691 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3137 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.89422 | 0.785505 | 0.392752 | − | 0.919644i | \(-0.371523\pi\) | ||||
0.392752 | + | 0.919644i | \(0.371523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.70626 | −0.857853 | −0.428927 | − | 0.903339i | \(-0.641108\pi\) | ||||
−0.428927 | + | 0.903339i | \(0.641108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.7206 | −1.13307 | −0.566537 | − | 0.824036i | \(-0.691717\pi\) | ||||
−0.566537 | + | 0.824036i | \(0.691717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.07107 | −0.102590 | −0.0512948 | − | 0.998684i | \(-0.516335\pi\) | ||||
−0.0512948 | + | 0.998684i | \(0.516335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8080 | 1.58117 | 0.790583 | − | 0.612355i | \(-0.209778\pi\) | ||||
0.790583 | + | 0.612355i | \(0.209778\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.43215 | −0.599801 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.95815 | 0.362843 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65685 | 0.241532 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.48106 | −0.311355 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2545 | −1.17614 | −0.588072 | − | 0.808808i | \(-0.700113\pi\) | ||||
−0.588072 | + | 0.808808i | \(0.700113\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5140 | 1.18072 | 0.590361 | − | 0.807140i | \(-0.298986\pi\) | ||||
0.590361 | + | 0.807140i | \(0.298986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.6569 | 1.53104 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0675 | −1.28730 | −0.643652 | − | 0.765319i | \(-0.722581\pi\) | ||||
−0.643652 | + | 0.765319i | \(0.722581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8643 | 1.09114 | 0.545568 | − | 0.838067i | \(-0.316314\pi\) | ||||
0.545568 | + | 0.838067i | \(0.316314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6173 | −1.05511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.1421 | −1.34053 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.91380 | 0.730247 | 0.365124 | − | 0.930959i | \(-0.381027\pi\) | ||||
0.365124 | + | 0.930959i | \(0.381027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2545 | 1.07863 | 0.539317 | − | 0.842103i | \(-0.318682\pi\) | ||||
0.539317 | + | 0.842103i | \(0.318682\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.8686 | 2.07782 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.75736 | 0.459487 | 0.229744 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229744 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.92296 | −0.387983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.6286 | 1.61576 | 0.807878 | − | 0.589349i | \(-0.200616\pi\) | ||||
0.807878 | + | 0.589349i | \(0.200616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.2764 | 1.64642 | 0.823210 | − | 0.567738i | \(-0.192181\pi\) | ||||
0.823210 | + | 0.567738i | \(0.192181\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3753 | −0.864846 | −0.432423 | − | 0.901671i | \(-0.642341\pi\) | ||||
−0.432423 | + | 0.901671i | \(0.642341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.70626 | 0.658132 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.9665 | −1.79134 | −0.895669 | − | 0.444721i | \(-0.853303\pi\) | ||||
−0.895669 | + | 0.444721i | \(0.853303\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.7279 | 1.98667 | 0.993335 | − | 0.115260i | \(-0.0367700\pi\) | ||||
0.993335 | + | 0.115260i | \(0.0367700\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.74053 | 0.127966 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.43215 | −0.470366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9469 | 1.22623 | 0.613116 | − | 0.789993i | \(-0.289916\pi\) | ||||
0.613116 | + | 0.789993i | \(0.289916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.48528 | −0.322858 | −0.161429 | − | 0.986884i | \(-0.551610\pi\) | ||||
−0.161429 | + | 0.986884i | \(0.551610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.3753 | −0.810455 | −0.405228 | − | 0.914216i | \(-0.632808\pi\) | ||||
−0.405228 | + | 0.914216i | \(0.632808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.390175 | −0.0276588 | −0.0138294 | − | 0.999904i | \(-0.504402\pi\) | ||||
−0.0138294 | + | 0.999904i | \(0.504402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3547 | −0.867127 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.1421 | 2.10522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −28.6931 | −1.98474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1929 | −1.25245 | −0.626225 | − | 0.779643i | \(-0.715401\pi\) | ||||
−0.626225 | + | 0.779643i | \(0.715401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.95815 | 0.269944 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.7990 | 1.34404 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.94253 | 0.399738 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5902 | −0.709172 | −0.354586 | − | 0.935023i | \(-0.615378\pi\) | ||||
−0.354586 | + | 0.935023i | \(0.615378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.42742 | 0.161113 | 0.0805567 | − | 0.996750i | \(-0.474330\pi\) | ||||
0.0805567 | + | 0.996750i | \(0.474330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9289 | 0.722204 | 0.361102 | − | 0.932526i | \(-0.382401\pi\) | ||||
0.361102 | + | 0.932526i | \(0.382401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.7310 | 1.42364 | 0.711822 | − | 0.702360i | \(-0.247870\pi\) | ||||
0.711822 | + | 0.702360i | \(0.247870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.4893 | −2.44553 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.7402 | −1.21220 | −0.606102 | − | 0.795387i | \(-0.707268\pi\) | ||||
−0.606102 | + | 0.795387i | \(0.707268\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1421 | −1.16864 | −0.584319 | − | 0.811524i | \(-0.698638\pi\) | ||||
−0.584319 | + | 0.811524i | \(0.698638\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.43275 | −0.347085 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5090 | 1.68672 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4776 | 1.16630 | 0.583148 | − | 0.812366i | \(-0.301821\pi\) | ||||
0.583148 | + | 0.812366i | \(0.301821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.92296 | 0.307086 | 0.153543 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153543 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.33214 | 0.0827753 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.5754 | −1.02209 | −0.511043 | − | 0.859555i | \(-0.670741\pi\) | ||||
−0.511043 | + | 0.859555i | \(0.670741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1421 | 0.991604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7218 | 1.56829 | 0.784144 | − | 0.620579i | \(-0.213103\pi\) | ||||
0.784144 | + | 0.620579i | \(0.213103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.3705 | 0.690711 | 0.345356 | − | 0.938472i | \(-0.387758\pi\) | ||||
0.345356 | + | 0.938472i | \(0.387758\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.1480 | −0.853158 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.38478 | −0.503792 | −0.251896 | − | 0.967754i | \(-0.581054\pi\) | ||||
−0.251896 | + | 0.967754i | \(0.581054\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8472 | −1.12433 | −0.562164 | − | 0.827026i | \(-0.690031\pi\) | ||||
−0.562164 | + | 0.827026i | \(0.690031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6250 | −1.46381 | −0.731903 | − | 0.681409i | \(-0.761368\pi\) | ||||
−0.731903 | + | 0.681409i | \(0.761368\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.0698 | 1.36177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9706 | −0.821798 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.41317 | −0.257820 | −0.128910 | − | 0.991656i | \(-0.541148\pi\) | ||||
−0.128910 | + | 0.991656i | \(0.541148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8643 | 0.748989 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.39104 | −0.427435 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.02944 | 0.174614 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.0296 | 1.26141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.43215 | −0.367102 | −0.183551 | − | 0.983010i | \(-0.558759\pi\) | ||||
−0.183551 | + | 0.983010i | \(0.558759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.32957 | −0.245507 | −0.122754 | − | 0.992437i | \(-0.539173\pi\) | ||||
−0.122754 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.1421 | 1.02545 | 0.512727 | − | 0.858552i | \(-0.328635\pi\) | ||||
0.512727 | + | 0.858552i | \(0.328635\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.93338 | 0.557914 | 0.278957 | − | 0.960304i | \(-0.410011\pi\) | ||||
0.278957 | + | 0.960304i | \(0.410011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0768 | 1.12409 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5140 | 0.751937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0711 | 0.725052 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.6931 | −1.58190 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8643 | 0.707086 | 0.353543 | − | 0.935418i | \(-0.384977\pi\) | ||||
0.353543 | + | 0.935418i | \(0.384977\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.1116 | −1.04418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.48528 | −0.135382 | −0.0676910 | − | 0.997706i | \(-0.521563\pi\) | ||||
−0.0676910 | + | 0.997706i | \(0.521563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.1741 | −1.74233 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0768 | −1.08405 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3324 | −1.25255 | −0.626275 | − | 0.779602i | \(-0.715421\pi\) | ||||
−0.626275 | + | 0.779602i | \(0.715421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.2426 | 1.61885 | 0.809426 | − | 0.587222i | \(-0.199779\pi\) | ||||
0.809426 | + | 0.587222i | \(0.199779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.6552 | −1.89773 | −0.948867 | − | 0.315675i | \(-0.897769\pi\) | ||||
−0.948867 | + | 0.315675i | \(0.897769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.1929 | −0.965577 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4525 | −0.551662 | −0.275831 | − | 0.961206i | \(-0.588953\pi\) | ||||
−0.275831 | + | 0.961206i | \(0.588953\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.2843 | 2.17286 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.1546 | 1.63070 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.1188 | −1.36339 | −0.681695 | − | 0.731637i | \(-0.738757\pi\) | ||||
−0.681695 | + | 0.731637i | \(0.738757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.3547 | 0.641422 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.7279 | 1.59103 | 0.795516 | − | 0.605933i | \(-0.207200\pi\) | ||||
0.795516 | + | 0.605933i | \(0.207200\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.5486 | −0.955299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1964 | 0.729222 | 0.364611 | − | 0.931160i | \(-0.381202\pi\) | ||||
0.364611 | + | 0.931160i | \(0.381202\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.95815 | 0.202252 | 0.101126 | − | 0.994874i | \(-0.467755\pi\) | ||||
0.101126 | + | 0.994874i | \(0.467755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.9706 | −1.27262 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.3178 | 0.878048 | 0.439024 | − | 0.898475i | \(-0.355324\pi\) | ||||
0.439024 | + | 0.898475i | \(0.355324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.76787 | −0.190549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.75699 | −0.339981 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3848 | 1.02308 | 0.511541 | − | 0.859259i | \(-0.329075\pi\) | ||||
0.511541 | + | 0.859259i | \(0.329075\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.3566 | −1.76562 | −0.882812 | − | 0.469727i | \(-0.844352\pi\) | ||||
−0.882812 | + | 0.469727i | \(0.844352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.7250 | 1.48071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.16478 | −0.107304 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.65685 | 0.477501 | 0.238750 | − | 0.971081i | \(-0.423262\pi\) | ||||
0.238750 | + | 0.971081i | \(0.423262\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.84591 | 0.484486 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.1732 | −1.43206 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.2597 | 1.62484 | 0.812420 | − | 0.583072i | \(-0.198149\pi\) | ||||
0.812420 | + | 0.583072i | \(0.198149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.38478 | −0.408649 | −0.204324 | − | 0.978903i | \(-0.565500\pi\) | ||||
−0.204324 | + | 0.978903i | \(0.565500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.66348 | 0.323226 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.8607 | 0.815948 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.49435 | −0.312822 | −0.156411 | − | 0.987692i | \(-0.549992\pi\) | ||||
−0.156411 | + | 0.987692i | \(0.549992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.97056 | −0.238870 | −0.119435 | − | 0.992842i | \(-0.538108\pi\) | ||||
−0.119435 | + | 0.992842i | \(0.538108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.8080 | −0.804037 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.48661 | −0.452771 | −0.226386 | − | 0.974038i | \(-0.572691\pi\) | ||||
−0.226386 | + | 0.974038i | \(0.572691\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.81845 | 0.466489 | 0.233244 | − | 0.972418i | \(-0.425066\pi\) | ||||
0.233244 | + | 0.972418i | \(0.425066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.3137 | 1.67403 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.66348 | 0.314469 | 0.157235 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157235 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.4893 | −1.76530 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.0698 | 1.08153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.31371 | 0.342121 | 0.171060 | − | 0.985261i | \(-0.445281\pi\) | ||||
0.171060 | + | 0.985261i | \(0.445281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2799 | −1.13083 | −0.565414 | − | 0.824807i | \(-0.691284\pi\) | ||||
−0.565414 | + | 0.824807i | \(0.691284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.4474 | −1.46148 | −0.730741 | − | 0.682655i | \(-0.760825\pi\) | ||||
−0.730741 | + | 0.682655i | \(0.760825\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.2095 | 0.796360 | 0.398180 | − | 0.917307i | \(-0.369642\pi\) | ||||
0.398180 | + | 0.917307i | \(0.369642\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6274 | −0.675431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.92296 | −0.226358 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.7250 | 1.36388 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.3575 | −1.43276 | −0.716381 | − | 0.697710i | \(-0.754203\pi\) | ||||
−0.716381 | + | 0.697710i | \(0.754203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.5011 | −2.06610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7831 | 1.30429 | 0.652143 | − | 0.758096i | \(-0.273870\pi\) | ||||
0.652143 | + | 0.758096i | \(0.273870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.39104 | −0.333553 | −0.166776 | − | 0.985995i | \(-0.553336\pi\) | ||||
−0.166776 | + | 0.985995i | \(0.553336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.45584 | −0.425870 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.9242 | −0.624587 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.43215 | 0.287943 | 0.143971 | − | 0.989582i | \(-0.454013\pi\) | ||||
0.143971 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4525 | −0.466054 | −0.233027 | − | 0.972470i | \(-0.574863\pi\) | ||||
−0.233027 | + | 0.972470i | \(0.574863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.4558 | 1.04377 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.45232 | −0.285994 | −0.142997 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142997 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.8447 | 1.05483 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.8686 | −1.13991 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.6274 | 2.05067 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.4715 | −1.02831 | −0.514153 | − | 0.857699i | \(-0.671894\pi\) | ||||
−0.514153 | + | 0.857699i | \(0.671894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.10001 | −0.223008 | −0.111504 | − | 0.993764i | \(-0.535567\pi\) | ||||
−0.111504 | + | 0.993764i | \(0.535567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.1535 | 0.660096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3137 | −0.796248 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.6356 | 1.50024 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.8250 | −1.50562 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.75699 | 0.291044 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7279 | −0.805176 | −0.402588 | − | 0.915381i | \(-0.631889\pi\) | ||||
−0.402588 | + | 0.915381i | \(0.631889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.18243 | −0.136320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.99643 | 0.170875 | 0.0854374 | − | 0.996344i | \(-0.472771\pi\) | ||||
0.0854374 | + | 0.996344i | \(0.472771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.1814 | −1.79699 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.17157 | −0.219918 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.97127 | −0.125897 | −0.0629483 | − | 0.998017i | \(-0.520050\pi\) | ||||
−0.0629483 | + | 0.998017i | \(0.520050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.54822 | 0.192369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6228 | −0.574131 | −0.287065 | − | 0.957911i | \(-0.592680\pi\) | ||||
−0.287065 | + | 0.957911i | \(0.592680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.9411 | 2.10104 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.6256 | −0.571215 | −0.285607 | − | 0.958347i | \(-0.592195\pi\) | ||||
−0.285607 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.6250 | −1.03053 | −0.515263 | − | 0.857032i | \(-0.672306\pi\) | ||||
−0.515263 | + | 0.857032i | \(0.672306\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.28772 | −0.345622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1127 | −1.04546 | −0.522728 | − | 0.852500i | \(-0.675086\pi\) | ||||
−0.522728 | + | 0.852500i | \(0.675086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3282 | −0.926331 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.0768 | −0.831496 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.12293 | −0.252721 | −0.126360 | − | 0.991984i | \(-0.540330\pi\) | ||||
−0.126360 | + | 0.991984i | \(0.540330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 67.5980 | 2.78533 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.8080 | 0.690223 | 0.345111 | − | 0.938562i | \(-0.387841\pi\) | ||||
0.345111 | + | 0.938562i | \(0.387841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.7607 | 0.482143 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7402 | −0.765705 | −0.382852 | − | 0.923810i | \(-0.625058\pi\) | ||||
−0.382852 | + | 0.923810i | \(0.625058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.1716 | −0.618861 | −0.309431 | − | 0.950922i | \(-0.600138\pi\) | ||||
−0.309431 | + | 0.950922i | \(0.600138\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.89422 | 0.320946 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.7634 | 1.61395 | 0.806974 | − | 0.590587i | \(-0.201104\pi\) | ||||
0.806974 | + | 0.590587i | \(0.201104\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.0781 | −1.74275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.100505 | 0.00405936 | 0.00202968 | − | 0.999998i | \(-0.499354\pi\) | ||||
0.00202968 | + | 0.999998i | \(0.499354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.1929 | 0.731233 | 0.365617 | − | 0.930766i | \(-0.380858\pi\) | ||||
0.365617 | + | 0.930766i | \(0.380858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.0279 | 1.08285 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4853 | −1.17941 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.01958 | 0.0406532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.05446 | 0.121596 | 0.0607981 | − | 0.998150i | \(-0.480635\pi\) | ||||
0.0607981 | + | 0.998150i | \(0.480635\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −39.3826 | −1.56285 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.24264 | −0.247342 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.74053 | 0.0687467 | 0.0343734 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343734 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2929 | 0.918582 | 0.459291 | − | 0.888286i | \(-0.348104\pi\) | ||||
0.459291 | + | 0.888286i | \(0.348104\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.3157 | 1.38840 | 0.694201 | − | 0.719781i | \(-0.255758\pi\) | ||||
0.694201 | + | 0.719781i | \(0.255758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.4144 | 0.524947 | 0.262474 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262474 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.1536 | 1.56893 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.39104 | 0.287914 | 0.143957 | − | 0.989584i | \(-0.454017\pi\) | ||||
0.143957 | + | 0.989584i | \(0.454017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.61522 | 0.140616 | 0.0703080 | − | 0.997525i | \(-0.477602\pi\) | ||||
0.0703080 | + | 0.997525i | \(0.477602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 52.4632 | 2.03444 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7607 | 0.455377 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.3994 | −1.05774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6569 | 0.680622 | 0.340311 | − | 0.940313i | \(-0.389468\pi\) | ||||
0.340311 | + | 0.940313i | \(0.389468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.5298 | 1.63455 | 0.817277 | − | 0.576244i | \(-0.195482\pi\) | ||||
0.817277 | + | 0.576244i | \(0.195482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −34.8250 | −1.33646 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.6507 | 1.55546 | 0.777728 | − | 0.628601i | \(-0.216372\pi\) | ||||
0.777728 | + | 0.628601i | \(0.216372\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.7696 | −1.71056 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.5486 | 0.706644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.76429 | 0.295368 | 0.147684 | − | 0.989035i | \(-0.452818\pi\) | ||||
0.147684 | + | 0.989035i | \(0.452818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.2233 | 1.44989 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.6569 | 0.668801 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.6839 | 1.23446 | 0.617228 | − | 0.786785i | \(-0.288256\pi\) | ||||
0.617228 | + | 0.786785i | \(0.288256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.54822 | 0.171539 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.9523 | 0.675167 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7279 | 0.703342 | 0.351671 | − | 0.936124i | \(-0.385614\pi\) | ||||
0.351671 | + | 0.936124i | \(0.385614\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.8472 | −0.705832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.4893 | −1.40202 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.7821 | 0.551278 | 0.275639 | − | 0.961261i | \(-0.411111\pi\) | ||||
0.275639 | + | 0.961261i | \(0.411111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.7990 | −0.737353 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.7989 | −0.772451 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.6670 | 1.13738 | 0.568688 | − | 0.822553i | \(-0.307451\pi\) | ||||
0.568688 | + | 0.822553i | \(0.307451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.31863 | 0.0857577 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.55635 | −0.0574851 | −0.0287425 | − | 0.999587i | \(-0.509150\pi\) | ||||
−0.0287425 | + | 0.999587i | \(0.509150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7701 | 0.875584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.6250 | 0.905846 | 0.452923 | − | 0.891550i | \(-0.350381\pi\) | ||||
0.452923 | + | 0.891550i | \(0.350381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.7402 | 0.687512 | 0.343756 | − | 0.939059i | \(-0.388301\pi\) | ||||
0.343756 | + | 0.939059i | \(0.388301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.4853 | 0.970346 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.6539 | −0.973914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8670 | 1.49126 | 0.745629 | − | 0.666361i | \(-0.232149\pi\) | ||||
0.745629 | + | 0.666361i | \(0.232149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.3826 | 1.43328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.95837 | −0.0711781 | −0.0355891 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355891 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.4715 | 0.850842 | 0.425421 | − | 0.904996i | \(-0.360126\pi\) | ||||
0.425421 | + | 0.904996i | \(0.360126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.43573 | −0.0881792 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.7821 | 0.533750 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.8284 | −1.11170 | −0.555851 | − | 0.831282i | \(-0.687607\pi\) | ||||
−0.555851 | + | 0.831282i | \(0.687607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.8184 | 0.784755 | 0.392377 | − | 0.919804i | \(-0.371653\pi\) | ||||
0.392377 | + | 0.919804i | \(0.371653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.3313 | 1.19730 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 78.7652 | 2.82206 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6274 | 0.809673 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.1067 | 0.610563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.1964 | −0.506049 | −0.253024 | − | 0.967460i | \(-0.581425\pi\) | ||||
−0.253024 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.2233 | 1.35906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.3137 | 0.898916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.7597 | −0.664503 | −0.332252 | − | 0.943191i | \(-0.607808\pi\) | ||||
−0.332252 | + | 0.943191i | \(0.607808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.9607 | −0.776915 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.7485 | −1.36741 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.6274 | −0.515549 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.3957 | 1.31476 | 0.657382 | − | 0.753558i | \(-0.271664\pi\) | ||||
0.657382 | + | 0.753558i | \(0.271664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3965 | 0.856676 | 0.428338 | − | 0.903619i | \(-0.359099\pi\) | ||||
0.428338 | + | 0.903619i | \(0.359099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 61.2931 | 2.14700 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3431 | 0.361861 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.6448 | 1.06951 | 0.534755 | − | 0.845007i | \(-0.320404\pi\) | ||||
0.534755 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.27411 | −0.0792705 | −0.0396352 | − | 0.999214i | \(-0.512620\pi\) | ||||
−0.0396352 | + | 0.999214i | \(0.512620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.2346 | −0.877492 | −0.438746 | − | 0.898611i | \(-0.644577\pi\) | ||||
−0.438746 | + | 0.898611i | \(0.644577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.5563 | 0.748683 | 0.374341 | − | 0.927291i | \(-0.377869\pi\) | ||||
0.374341 | + | 0.927291i | \(0.377869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.18243 | −0.110265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.2179 | 2.18775 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9887 | −0.448420 | −0.224210 | − | 0.974541i | \(-0.571980\pi\) | ||||
−0.224210 | + | 0.974541i | \(0.571980\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.514719 | 0.0177489 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.99084 | −0.137289 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.04198 | 0.207605 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.26810 | −0.0434700 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.5269 | −0.497392 | −0.248696 | − | 0.968582i | \(-0.580002\pi\) | ||||
−0.248696 | + | 0.968582i | \(0.580002\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.5486 | −0.633606 | −0.316803 | − | 0.948491i | \(-0.602609\pi\) | ||||
−0.316803 | + | 0.948491i | \(0.602609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6286 | −0.703839 | −0.351919 | − | 0.936030i | \(-0.614471\pi\) | ||||
−0.351919 | + | 0.936030i | \(0.614471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.5223 | −1.14111 | −0.570556 | − | 0.821259i | \(-0.693272\pi\) | ||||
−0.570556 | + | 0.821259i | \(0.693272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.7990 | −1.14920 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.40401 | 0.285087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.9607 | −0.744111 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.91630 | −0.267620 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8406 | −1.54793 | −0.773964 | − | 0.633230i | \(-0.781729\pi\) | ||||
−0.773964 | + | 0.633230i | \(0.781729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.7689 | −0.497576 | −0.248788 | − | 0.968558i | \(-0.580032\pi\) | ||||
−0.248788 | + | 0.968558i | \(0.580032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8607 | −0.567409 | −0.283704 | − | 0.958912i | \(-0.591563\pi\) | ||||
−0.283704 | + | 0.958912i | \(0.591563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.6034 | −1.46406 | −0.732029 | − | 0.681273i | \(-0.761427\pi\) | ||||
−0.732029 | + | 0.681273i | \(0.761427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.1421 | −1.01093 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −97.9643 | −3.27825 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.2108 | −2.38031 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.2989 | −1.57751 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.45584 | 0.315020 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 79.4158 | 2.63987 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4286 | 0.346275 | 0.173138 | − | 0.984898i | \(-0.444609\pi\) | ||||
0.173138 | + | 0.984898i | \(0.444609\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6565 | 0.883170 | 0.441585 | − | 0.897219i | \(-0.354416\pi\) | ||||
0.441585 | + | 0.897219i | \(0.354416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.2843 | 1.20083 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.7322 | 1.01487 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.8402 | 1.97395 | 0.986974 | − | 0.160881i | \(-0.0514335\pi\) | ||||
0.986974 | + | 0.160881i | \(0.0514335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.9050 | −0.688097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24264 | 0.0737376 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.18243 | 0.104412 | 0.0522060 | − | 0.998636i | \(-0.483375\pi\) | ||||
0.0522060 | + | 0.998636i | \(0.483375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1964 | −0.465270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.1116 | −0.625018 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.9411 | 0.520774 | 0.260387 | − | 0.965504i | \(-0.416150\pi\) | ||||
0.260387 | + | 0.965504i | \(0.416150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.2420 | −1.01846 | −0.509231 | − | 0.860630i | \(-0.670070\pi\) | ||||
−0.509231 | + | 0.860630i | \(0.670070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.9607 | −0.715140 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.0894 | 0.977774 | 0.488887 | − | 0.872347i | \(-0.337403\pi\) | ||||
0.488887 | + | 0.872347i | \(0.337403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.7990 | 1.16208 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.298627 | 0.00967349 | 0.00483674 | − | 0.999988i | \(-0.498460\pi\) | ||||
0.00483674 | + | 0.999988i | \(0.498460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.3536 | 1.62941 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.2651 | −1.10648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.7990 | 1.44513 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.3270 | −0.429010 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.1116 | −1.09696 | −0.548478 | − | 0.836165i | \(-0.684793\pi\) | ||||
−0.548478 | + | 0.836165i | \(0.684793\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6733 | −0.470888 | −0.235444 | − | 0.971888i | \(-0.575654\pi\) | ||||
−0.235444 | + | 0.971888i | \(0.575654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.2548 | 0.937867 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.1067 | 0.547290 | 0.273645 | − | 0.961831i | \(-0.411771\pi\) | ||||
0.273645 | + | 0.961831i | \(0.411771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.9215 | −1.40374 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.3183 | 0.552367 | 0.276184 | − | 0.961105i | \(-0.410930\pi\) | ||||
0.276184 | + | 0.961105i | \(0.410930\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.7990 | −1.07693 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.88380 | −0.0916995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4277 | 1.34776 | 0.673881 | − | 0.738840i | \(-0.264626\pi\) | ||||
0.673881 | + | 0.738840i | \(0.264626\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.15932 | −0.0367528 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.0416 | −1.20479 | −0.602395 | − | 0.798198i | \(-0.705787\pi\) | ||||
−0.602395 | + | 0.798198i | \(0.705787\pi\) | |||||||
\(998\) | 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 | 9216.2.a.bs.1.8 | 8 | ||
3.2 | odd | 2 | inner | 9216.2.a.bs.1.2 | 8 | ||
4.3 | odd | 2 | inner | 9216.2.a.bs.1.7 | 8 | ||
8.3 | odd | 2 | 9216.2.a.br.1.1 | 8 | |||
8.5 | even | 2 | 9216.2.a.br.1.2 | 8 | |||
12.11 | even | 2 | inner | 9216.2.a.bs.1.1 | 8 | ||
24.5 | odd | 2 | 9216.2.a.br.1.8 | 8 | |||
24.11 | even | 2 | 9216.2.a.br.1.7 | 8 | |||
32.3 | odd | 8 | 4608.2.k.bk.1153.2 | yes | 16 | ||
32.5 | even | 8 | 4608.2.k.bl.3457.8 | yes | 16 | ||
32.11 | odd | 8 | 4608.2.k.bk.3457.1 | yes | 16 | ||
32.13 | even | 8 | 4608.2.k.bl.1153.7 | yes | 16 | ||
32.19 | odd | 8 | 4608.2.k.bl.1153.8 | yes | 16 | ||
32.21 | even | 8 | 4608.2.k.bk.3457.2 | yes | 16 | ||
32.27 | odd | 8 | 4608.2.k.bl.3457.7 | yes | 16 | ||
32.29 | even | 8 | 4608.2.k.bk.1153.1 | ✓ | 16 | ||
96.5 | odd | 8 | 4608.2.k.bl.3457.2 | yes | 16 | ||
96.11 | even | 8 | 4608.2.k.bk.3457.7 | yes | 16 | ||
96.29 | odd | 8 | 4608.2.k.bk.1153.7 | yes | 16 | ||
96.35 | even | 8 | 4608.2.k.bk.1153.8 | yes | 16 | ||
96.53 | odd | 8 | 4608.2.k.bk.3457.8 | yes | 16 | ||
96.59 | even | 8 | 4608.2.k.bl.3457.1 | yes | 16 | ||
96.77 | odd | 8 | 4608.2.k.bl.1153.1 | yes | 16 | ||
96.83 | even | 8 | 4608.2.k.bl.1153.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4608.2.k.bk.1153.1 | ✓ | 16 | 32.29 | even | 8 | ||
4608.2.k.bk.1153.2 | yes | 16 | 32.3 | odd | 8 | ||
4608.2.k.bk.1153.7 | yes | 16 | 96.29 | odd | 8 | ||
4608.2.k.bk.1153.8 | yes | 16 | 96.35 | even | 8 | ||
4608.2.k.bk.3457.1 | yes | 16 | 32.11 | odd | 8 | ||
4608.2.k.bk.3457.2 | yes | 16 | 32.21 | even | 8 | ||
4608.2.k.bk.3457.7 | yes | 16 | 96.11 | even | 8 | ||
4608.2.k.bk.3457.8 | yes | 16 | 96.53 | odd | 8 | ||
4608.2.k.bl.1153.1 | yes | 16 | 96.77 | odd | 8 | ||
4608.2.k.bl.1153.2 | yes | 16 | 96.83 | even | 8 | ||
4608.2.k.bl.1153.7 | yes | 16 | 32.13 | even | 8 | ||
4608.2.k.bl.1153.8 | yes | 16 | 32.19 | odd | 8 | ||
4608.2.k.bl.3457.1 | yes | 16 | 96.59 | even | 8 | ||
4608.2.k.bl.3457.2 | yes | 16 | 96.5 | odd | 8 | ||
4608.2.k.bl.3457.7 | yes | 16 | 32.27 | odd | 8 | ||
4608.2.k.bl.3457.8 | yes | 16 | 32.5 | even | 8 | ||
9216.2.a.br.1.1 | 8 | 8.3 | odd | 2 | |||
9216.2.a.br.1.2 | 8 | 8.5 | even | 2 | |||
9216.2.a.br.1.7 | 8 | 24.11 | even | 2 | |||
9216.2.a.br.1.8 | 8 | 24.5 | odd | 2 | |||
9216.2.a.bs.1.1 | 8 | 12.11 | even | 2 | inner | ||
9216.2.a.bs.1.2 | 8 | 3.2 | odd | 2 | inner | ||
9216.2.a.bs.1.7 | 8 | 4.3 | odd | 2 | inner | ||
9216.2.a.bs.1.8 | 8 | 1.1 | even | 1 | trivial |