Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1889,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.k (of order \(2\), degree \(1\), not 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: | \(24.1467615712\) |
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: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} - 45 x^{12} + 306 x^{11} - 378 x^{10} + 1704 x^{9} + 917 x^{8} - 12522 x^{7} + 27090 x^{6} - 35292 x^{5} + 30948 x^{4} - 18000 x^{3} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.16 | ||
Root | \(0.121385 + 0.453016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1889 |
Dual form | 3024.2.k.l.1889.15 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.29876 | 1.92246 | 0.961231 | − | 0.275744i | \(-0.0889243\pi\) | ||||
0.961231 | + | 0.275744i | \(0.0889243\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.832811 | + | 2.51126i | −0.314773 | + | 0.949167i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.51682i | 0.758850i | 0.925223 | + | 0.379425i | \(0.123878\pi\) | ||||
−0.925223 | + | 0.379425i | \(0.876122\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.36755i | 1.48869i | 0.667796 | + | 0.744345i | \(0.267238\pi\) | ||||
−0.667796 | + | 0.744345i | \(0.732762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.29047 | 0.798056 | 0.399028 | − | 0.916939i | \(-0.369348\pi\) | ||||
0.399028 | + | 0.916939i | \(0.369348\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.663261i | 0.152163i | 0.997102 | + | 0.0760813i | \(0.0242408\pi\) | ||||
−0.997102 | + | 0.0760813i | \(0.975759\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.44566i | − | 1.34401i | −0.740545 | − | 0.672007i | \(-0.765433\pi\) | ||
0.740545 | − | 0.672007i | \(-0.234567\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.4793 | 2.69586 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.26322i | − | 0.791661i | −0.918324 | − | 0.395830i | \(-0.870457\pi\) | ||
0.918324 | − | 0.395830i | \(-0.129543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.78838i | 0.860019i | 0.902824 | + | 0.430010i | \(0.141490\pi\) | ||||
−0.902824 | + | 0.430010i | \(0.858510\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.58005 | + | 10.7953i | −0.605139 | + | 1.82474i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.746404 | −0.122708 | −0.0613540 | − | 0.998116i | \(-0.519542\pi\) | ||||
−0.0613540 | + | 0.998116i | \(0.519542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.99475 | −1.24857 | −0.624285 | − | 0.781196i | \(-0.714610\pi\) | ||||
−0.624285 | + | 0.781196i | \(0.714610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.69926 | −1.17413 | −0.587063 | − | 0.809541i | \(-0.699716\pi\) | ||||
−0.587063 | + | 0.809541i | \(0.699716\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.32128 | 1.35965 | 0.679824 | − | 0.733375i | \(-0.262056\pi\) | ||||
0.679824 | + | 0.733375i | \(0.262056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.61285 | − | 4.18281i | −0.801836 | − | 0.597544i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.8137i | 1.62273i | 0.584537 | + | 0.811367i | \(0.301276\pi\) | ||||
−0.584537 | + | 0.811367i | \(0.698724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8192i | 1.45886i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.15289 | 0.150093 | 0.0750467 | − | 0.997180i | \(-0.476089\pi\) | ||||
0.0750467 | + | 0.997180i | \(0.476089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.7083i | − | 1.37106i | −0.728046 | − | 0.685529i | \(-0.759571\pi\) | ||
0.728046 | − | 0.685529i | \(-0.240429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.0738i | 2.86195i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.587975 | −0.0718326 | −0.0359163 | − | 0.999355i | \(-0.511435\pi\) | ||||
−0.0359163 | + | 0.999355i | \(0.511435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.77691i | 1.16031i | 0.814508 | + | 0.580153i | \(0.197007\pi\) | ||||
−0.814508 | + | 0.580153i | \(0.802993\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6408i | 1.47949i | 0.672887 | + | 0.739745i | \(0.265054\pi\) | ||||
−0.672887 | + | 0.739745i | \(0.734946\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.32039 | − | 2.09603i | −0.720275 | − | 0.238865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.1113 | −1.25012 | −0.625059 | − | 0.780578i | \(-0.714925\pi\) | ||||
−0.625059 | + | 0.780578i | \(0.714925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.07281 | 0.776341 | 0.388171 | − | 0.921588i | \(-0.373107\pi\) | ||||
0.388171 | + | 0.921588i | \(0.373107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1449 | 1.53423 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.25676 | −0.345215 | −0.172608 | − | 0.984991i | \(-0.555219\pi\) | ||||
−0.172608 | + | 0.984991i | \(0.555219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.4793 | − | 4.47015i | −1.41301 | − | 0.468599i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.85120i | 0.292527i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8192i | − | 1.09852i | −0.835651 | − | 0.549261i | \(-0.814909\pi\) | ||
0.835651 | − | 0.549261i | \(-0.185091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.16010 | −0.712456 | −0.356228 | − | 0.934399i | \(-0.615937\pi\) | ||||
−0.356228 | + | 0.934399i | \(0.615937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.22392i | 0.219129i | 0.993980 | + | 0.109565i | \(0.0349457\pi\) | ||||
−0.993980 | + | 0.109565i | \(0.965054\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.860825i | − | 0.0832191i | −0.999134 | − | 0.0416095i | \(-0.986751\pi\) | ||
0.999134 | − | 0.0416095i | \(-0.0132486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.07765 | 0.582133 | 0.291066 | − | 0.956703i | \(-0.405990\pi\) | ||||
0.291066 | + | 0.956703i | \(0.405990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.7425i | − | 1.10464i | −0.833631 | − | 0.552322i | \(-0.813742\pi\) | ||
0.833631 | − | 0.552322i | \(-0.186258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 27.7083i | − | 2.58382i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.74034 | + | 8.26322i | −0.251206 | + | 0.757488i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.66562 | 0.424147 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 36.4504 | 3.26023 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.44566 | 0.660696 | 0.330348 | − | 0.943859i | \(-0.392834\pi\) | ||||
0.330348 | + | 0.943859i | \(0.392834\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.81934 | −0.158957 | −0.0794784 | − | 0.996837i | \(-0.525325\pi\) | ||||
−0.0794784 | + | 0.996837i | \(0.525325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.66562 | − | 0.552371i | −0.144428 | − | 0.0478966i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.51368i | 0.812809i | 0.913693 | + | 0.406404i | \(0.133218\pi\) | ||||
−0.913693 | + | 0.406404i | \(0.866782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.8749i | − | 1.68576i | −0.538099 | − | 0.842882i | \(-0.680857\pi\) | ||
0.538099 | − | 0.842882i | \(-0.319143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.5091 | −1.12969 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 18.3266i | − | 1.52194i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.29373i | 0.679448i | 0.940525 | + | 0.339724i | \(0.110334\pi\) | ||||
−0.940525 | + | 0.339724i | \(0.889666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.0057 | 1.70942 | 0.854712 | − | 0.519103i | \(-0.173734\pi\) | ||||
0.854712 | + | 0.519103i | \(0.173734\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.5841i | 1.65335i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.70616i | − | 0.694827i | −0.937712 | − | 0.347414i | \(-0.887060\pi\) | ||
0.937712 | − | 0.347414i | \(-0.112940\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.1867 | + | 5.36802i | 1.27569 | + | 0.423059i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2593 | −1.66516 | −0.832580 | − | 0.553905i | \(-0.813137\pi\) | ||||
−0.832580 | + | 0.553905i | \(0.813137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.66854 | 0.748174 | 0.374087 | − | 0.927394i | \(-0.377956\pi\) | ||||
0.374087 | + | 0.927394i | \(0.377956\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.8105 | −1.21620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.43741 | 0.109284 | 0.0546422 | − | 0.998506i | \(-0.482598\pi\) | ||||
0.0546422 | + | 0.998506i | \(0.482598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2257 | + | 33.8500i | −0.848584 | + | 2.55882i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2129i | 1.36130i | 0.732609 | + | 0.680650i | \(0.238302\pi\) | ||||
−0.732609 | + | 0.680650i | \(0.761698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.11918i | − | 0.0831878i | −0.999135 | − | 0.0415939i | \(-0.986756\pi\) | ||
0.999135 | − | 0.0415939i | \(-0.0132436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.20861 | −0.235902 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.28152i | 0.605604i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.2976i | − | 0.745108i | −0.928010 | − | 0.372554i | \(-0.878482\pi\) | ||
0.928010 | − | 0.372554i | \(-0.121518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2226 | 0.807818 | 0.403909 | − | 0.914799i | \(-0.367651\pi\) | ||||
0.403909 | + | 0.914799i | \(0.367651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.18558i | 0.226963i | 0.993540 | + | 0.113481i | \(0.0362003\pi\) | ||||
−0.993540 | + | 0.113481i | \(0.963800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.5895i | − | 0.750672i | −0.926889 | − | 0.375336i | \(-0.877527\pi\) | ||
0.926889 | − | 0.375336i | \(-0.122473\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7061 | + | 3.55046i | 0.751418 | + | 0.249193i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34.3675 | −2.40033 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.66931 | −0.115468 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8105 | 1.01960 | 0.509800 | − | 0.860293i | \(-0.329719\pi\) | ||||
0.509800 | + | 0.860293i | \(0.329719\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.0972 | −2.25721 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0249 | − | 3.98782i | −0.816302 | − | 0.270711i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.6617i | 1.18806i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.2934i | − | 0.957157i | −0.878045 | − | 0.478579i | \(-0.841152\pi\) | ||
0.878045 | − | 0.478579i | \(-0.158848\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.5910 | 0.902066 | 0.451033 | − | 0.892507i | \(-0.351056\pi\) | ||||
0.451033 | + | 0.892507i | \(0.351056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.7102i | 0.972076i | 0.873938 | + | 0.486038i | \(0.161558\pi\) | ||||
−0.873938 | + | 0.486038i | \(0.838442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.553594i | 0.0362671i | 0.999836 | + | 0.0181336i | \(0.00577241\pi\) | ||||
−0.999836 | + | 0.0181336i | \(0.994228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 40.0699 | 2.61387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.2161i | − | 0.984246i | −0.870526 | − | 0.492123i | \(-0.836221\pi\) | ||
0.870526 | − | 0.492123i | \(-0.163779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.80115i | 0.373685i | 0.982390 | + | 0.186842i | \(0.0598254\pi\) | ||||
−0.982390 | + | 0.186842i | \(0.940175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.1283 | − | 17.9809i | −1.54150 | − | 1.14876i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.56008 | −0.226523 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5884 | 1.42577 | 0.712884 | − | 0.701282i | \(-0.247389\pi\) | ||||
0.712884 | + | 0.701282i | \(0.247389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.2226 | 1.01990 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.48068 | 0.341875 | 0.170938 | − | 0.985282i | \(-0.445320\pi\) | ||||
0.170938 | + | 0.985282i | \(0.445320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.621613 | − | 1.87441i | 0.0386252 | − | 0.116470i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 26.6954i | − | 1.64611i | −0.567963 | − | 0.823054i | \(-0.692268\pi\) | ||
0.567963 | − | 0.823054i | \(-0.307732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 50.7841i | 3.11964i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0113 | −0.610401 | −0.305201 | − | 0.952288i | \(-0.598724\pi\) | ||||
−0.305201 | + | 0.952288i | \(0.598724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5216i | 0.699887i | 0.936771 | + | 0.349944i | \(0.113799\pi\) | ||||
−0.936771 | + | 0.349944i | \(0.886201\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.9250i | 2.04575i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.91608 | −0.235295 | −0.117647 | − | 0.993055i | \(-0.537535\pi\) | ||||
−0.117647 | + | 0.993055i | \(0.537535\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.3235i | 1.39136i | 0.718351 | + | 0.695681i | \(0.244897\pi\) | ||||
−0.718351 | + | 0.695681i | \(0.755103\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.67536i | 0.159033i | 0.996834 | + | 0.0795167i | \(0.0253377\pi\) | ||||
−0.996834 | + | 0.0795167i | \(0.974662\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.65812 | − | 20.0769i | 0.393016 | − | 1.18510i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.17281 | −0.363107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.67271 | 0.389824 | 0.194912 | − | 0.980821i | \(-0.437558\pi\) | ||||
0.194912 | + | 0.980821i | \(0.437558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.95599 | 0.288549 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 34.5974 | 2.00082 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.41203 | − | 19.3348i | 0.369583 | − | 1.11444i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 46.0324i | − | 2.63581i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.6036i | 1.51835i | 0.650888 | + | 0.759174i | \(0.274397\pi\) | ||||
−0.650888 | + | 0.759174i | \(0.725603\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.18756 | 0.0673401 | 0.0336701 | − | 0.999433i | \(-0.489280\pi\) | ||||
0.0336701 | + | 0.999433i | \(0.489280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.70048i | − | 0.209163i | −0.994516 | − | 0.104582i | \(-0.966650\pi\) | ||
0.994516 | − | 0.104582i | \(-0.0333504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.1170i | − | 0.568229i | −0.958790 | − | 0.284115i | \(-0.908300\pi\) | ||
0.958790 | − | 0.284115i | \(-0.0916996\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7298 | 0.600751 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.18244i | 0.121434i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 72.3508i | 4.01330i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.76286 | + | 23.4081i | −0.427980 | + | 1.29053i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.03677 | 0.276846 | 0.138423 | − | 0.990373i | \(-0.455797\pi\) | ||||
0.138423 | + | 0.990373i | \(0.455797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52756 | −0.138095 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.2930 | −1.43227 | −0.716135 | − | 0.697962i | \(-0.754091\pi\) | ||||
−0.716135 | + | 0.697962i | \(0.754091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0515 | −0.652625 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1786 | − | 10.6118i | 0.819565 | − | 0.572986i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.8817i | 0.798892i | 0.916757 | + | 0.399446i | \(0.130797\pi\) | ||||
−0.916757 | + | 0.399446i | \(0.869203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.1413i | − | 1.18520i | −0.805498 | − | 0.592599i | \(-0.798102\pi\) | ||
0.805498 | − | 0.592599i | \(-0.201898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.2024 | −0.596244 | −0.298122 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298122 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.0285i | 2.23064i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.90483i | 0.469979i | 0.971998 | + | 0.234990i | \(0.0755056\pi\) | ||||
−0.971998 | + | 0.234990i | \(0.924494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5601 | 0.976847 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 54.3396i | 2.84426i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 38.2979i | − | 1.99913i | −0.0294506 | − | 0.999566i | \(-0.509376\pi\) | ||
0.0294506 | − | 0.999566i | \(-0.490624\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.6672 | − | 9.83856i | −1.54025 | − | 0.510793i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.5963 | −1.79133 | −0.895665 | − | 0.444729i | \(-0.853300\pi\) | ||||
−0.895665 | + | 0.444729i | \(0.853300\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.8830 | 1.17854 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6185 | 0.699534 | 0.349767 | − | 0.936837i | \(-0.386261\pi\) | ||||
0.349767 | + | 0.936837i | \(0.386261\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.0832 | 1.89486 | 0.947431 | − | 0.319959i | \(-0.103669\pi\) | ||||
0.947431 | + | 0.319959i | \(0.103669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.1698 | − | 9.01034i | −1.38470 | − | 0.459209i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 12.9490i | − | 0.656539i | −0.944584 | − | 0.328270i | \(-0.893535\pi\) | ||
0.944584 | − | 0.328270i | \(-0.106465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 21.2093i | − | 1.07260i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −47.7647 | −2.40330 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.9614i | − | 0.550134i | −0.961425 | − | 0.275067i | \(-0.911300\pi\) | ||
0.961425 | − | 0.275067i | \(-0.0887001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 37.2562i | − | 1.86049i | −0.366944 | − | 0.930243i | \(-0.619596\pi\) | ||
0.366944 | − | 0.930243i | \(-0.380404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.7019 | −1.28030 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.87856i | − | 0.0931169i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.2173i | 1.29636i | 0.761485 | + | 0.648182i | \(0.224470\pi\) | ||||
−0.761485 | + | 0.648182i | \(0.775530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.960139 | + | 2.89521i | −0.0472453 | + | 0.142464i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.4043 | 1.49249 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.87161 | −0.286847 | −0.143423 | − | 0.989661i | \(-0.545811\pi\) | ||||
−0.143423 | + | 0.989661i | \(0.545811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1874 | 1.61746 | 0.808729 | − | 0.588182i | \(-0.200156\pi\) | ||||
0.808729 | + | 0.588182i | \(0.200156\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 44.3532 | 2.15145 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.8913 | + | 8.91799i | 1.30136 | + | 0.431572i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.3985i | − | 0.838057i | −0.907973 | − | 0.419029i | \(-0.862371\pi\) | ||
0.907973 | − | 0.419029i | \(-0.137629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.8045i | − | 1.43231i | −0.697939 | − | 0.716157i | \(-0.745899\pi\) | ||
0.697939 | − | 0.716157i | \(-0.254101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.27516 | 0.204509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.950228i | − | 0.0453519i | −0.999743 | − | 0.0226759i | \(-0.992781\pi\) | ||
0.999743 | − | 0.0226759i | \(-0.00721860\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 0.926232i | − | 0.0440066i | −0.999758 | − | 0.0220033i | \(-0.992996\pi\) | ||
0.999758 | − | 0.0220033i | \(-0.00700444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | −0.663664 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.31037i | 0.0618401i | 0.999522 | + | 0.0309200i | \(0.00984372\pi\) | ||||
−0.999522 | + | 0.0309200i | \(0.990156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.1213i | − | 0.947477i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −57.9442 | − | 19.2161i | −2.71647 | − | 0.900864i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.5963 | 1.75868 | 0.879341 | − | 0.476192i | \(-0.157983\pi\) | ||||
0.879341 | + | 0.476192i | \(0.157983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.6103 | −1.00649 | −0.503246 | − | 0.864143i | \(-0.667861\pi\) | ||||
−0.503246 | + | 0.864143i | \(0.667861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.29037 | −0.245864 | −0.122932 | − | 0.992415i | \(-0.539230\pi\) | ||||
−0.122932 | + | 0.992415i | \(0.539230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.9242 | −1.15335 | −0.576676 | − | 0.816973i | \(-0.695651\pi\) | ||||
−0.576676 | + | 0.816973i | \(0.695651\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.489672 | − | 1.47656i | 0.0226109 | − | 0.0681811i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 19.3776i | − | 0.890985i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.94030i | 0.410209i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.4503 | −0.980090 | −0.490045 | − | 0.871697i | \(-0.663020\pi\) | ||||
−0.490045 | + | 0.871697i | \(0.663020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.00636i | − | 0.182674i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 46.5091i | − | 2.11187i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6946 | −1.07371 | −0.536853 | − | 0.843676i | \(-0.680387\pi\) | ||||
−0.536853 | + | 0.843676i | \(0.680387\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.91534i | 0.176697i | 0.996090 | + | 0.0883484i | \(0.0281589\pi\) | ||||
−0.996090 | + | 0.0883484i | \(0.971841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.0280i | − | 0.631790i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.5524 | − | 8.14231i | −1.10132 | − | 0.365233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.5098 | 1.27627 | 0.638137 | − | 0.769923i | \(-0.279705\pi\) | ||||
0.638137 | + | 0.769923i | \(0.279705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.6995 | 1.05671 | 0.528355 | − | 0.849024i | \(-0.322809\pi\) | ||||
0.528355 | + | 0.849024i | \(0.322809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.7795 | −1.36967 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.18192 | −0.0523877 | −0.0261938 | − | 0.999657i | \(-0.508339\pi\) | ||||
−0.0261938 | + | 0.999657i | \(0.508339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.7443 | − | 10.5274i | −1.40428 | − | 0.465703i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.56008i | 0.421268i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.4600i | 1.03177i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.0033 | −1.35828 | −0.679139 | − | 0.734009i | \(-0.737647\pi\) | ||||
−0.679139 | + | 0.734009i | \(0.737647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8296i | 0.604727i | 0.953193 | + | 0.302363i | \(0.0977756\pi\) | ||||
−0.953193 | + | 0.302363i | \(0.902224\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.7560i | 0.686343i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5466 | −0.806373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 42.9122i | − | 1.85873i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.70048i | − | 0.159986i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5274 | − | 14.1265i | 0.453446 | − | 0.608473i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.6026 | −1.65966 | −0.829828 | − | 0.558019i | \(-0.811561\pi\) | ||||
−0.829828 | + | 0.558019i | \(0.811561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.1263 | 1.11913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0089 | 0.513463 | 0.256731 | − | 0.966483i | \(-0.417354\pi\) | ||||
0.256731 | + | 0.966483i | \(0.417354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82763 | 0.120461 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.25360 | − | 27.9033i | 0.393503 | − | 1.18657i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.8059i | 1.34766i | 0.738886 | + | 0.673830i | \(0.235352\pi\) | ||||
−0.738886 | + | 0.673830i | \(0.764648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 41.3261i | − | 1.74791i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.38005 | 0.353177 | 0.176589 | − | 0.984285i | \(-0.443494\pi\) | ||||
0.176589 | + | 0.984285i | \(0.443494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 50.4782i | − | 2.12364i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.1087i | 0.633389i | 0.948528 | + | 0.316694i | \(0.102573\pi\) | ||||
−0.948528 | + | 0.316694i | \(0.897427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.3007 | −0.598467 | −0.299234 | − | 0.954180i | \(-0.596731\pi\) | ||||
−0.299234 | + | 0.954180i | \(0.596731\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 86.8830i | − | 3.62327i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11.3671i | − | 0.473218i | −0.971605 | − | 0.236609i | \(-0.923964\pi\) | ||
0.971605 | − | 0.236609i | \(-0.0760360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.89031 | + | 17.7617i | −0.244371 | + | 0.736878i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.7329 | −1.23141 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8647 | 0.613532 | 0.306766 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306766 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.17595 | −0.130863 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.3207 | −0.998730 | −0.499365 | − | 0.866392i | \(-0.666433\pi\) | ||||
−0.499365 | + | 0.866392i | \(0.666433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.7800 | + | 35.5216i | −0.482935 | + | 1.45624i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.8041i | − | 0.564018i | −0.959412 | − | 0.282009i | \(-0.908999\pi\) | ||
0.959412 | − | 0.282009i | \(-0.0910009\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.70621i | 0.0695979i | 0.999394 | + | 0.0347990i | \(0.0110791\pi\) | ||||
−0.999394 | + | 0.0347990i | \(0.988921\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.0564 | 0.815407 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.0595i | − | 1.09831i | −0.835720 | − | 0.549156i | \(-0.814949\pi\) | ||
0.835720 | − | 0.549156i | \(-0.185051\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.0324i | 2.02409i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3456 | 0.498635 | 0.249318 | − | 0.968422i | \(-0.419794\pi\) | ||||
0.249318 | + | 0.968422i | \(0.419794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.5875i | − | 0.506752i | −0.967368 | − | 0.253376i | \(-0.918459\pi\) | ||
0.967368 | − | 0.253376i | \(-0.0815409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.5031i | − | 0.502542i | −0.967917 | − | 0.251271i | \(-0.919152\pi\) | ||
0.967917 | − | 0.251271i | \(-0.0808485\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.71226 | − | 8.17856i | 0.108664 | − | 0.327667i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.2951 | 3.57180 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.45602 | −0.0979279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.4715 | −1.85000 | −0.925001 | − | 0.379964i | \(-0.875937\pi\) | ||||
−0.925001 | + | 0.379964i | \(0.875937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.0071 | 1.27016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.4514 | − | 30.1272i | 0.889557 | − | 1.19368i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.81129i | − | 0.150537i | −0.997163 | − | 0.0752684i | \(-0.976019\pi\) | ||
0.997163 | − | 0.0752684i | \(-0.0239814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.84837i | − | 0.0728927i | −0.999336 | − | 0.0364464i | \(-0.988396\pi\) | ||
0.999336 | − | 0.0364464i | \(-0.0116038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.9174 | 0.783034 | 0.391517 | − | 0.920171i | \(-0.371950\pi\) | ||||
0.391517 | + | 0.920171i | \(0.371950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.90162i | 0.113898i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 36.2937i | − | 1.42028i | −0.704059 | − | 0.710142i | \(-0.748631\pi\) | ||
0.704059 | − | 0.710142i | \(-0.251369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.82091 | −0.305588 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.43678i | 0.367605i | 0.982963 | + | 0.183802i | \(0.0588406\pi\) | ||||
−0.982963 | + | 0.183802i | \(0.941159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5015i | 0.836310i | 0.908376 | + | 0.418155i | \(0.137323\pi\) | ||||
−0.908376 | + | 0.418155i | \(0.862677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.16010 | − | 2.37451i | −0.277657 | − | 0.0920795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.4793 | −1.06400 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.9509 | 1.04043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.30649 | −0.281644 | −0.140822 | − | 0.990035i | \(-0.544975\pi\) | ||||
−0.140822 | + | 0.990035i | \(0.544975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.03284 | 0.0396952 | 0.0198476 | − | 0.999803i | \(-0.493682\pi\) | ||||
0.0198476 | + | 0.999803i | \(0.493682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1698 | + | 9.01034i | 1.04268 | + | 0.345785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.7363i | − | 0.984770i | −0.870377 | − | 0.492385i | \(-0.836125\pi\) | ||
0.870377 | − | 0.492385i | \(-0.163875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.8970i | 1.56259i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.4105 | −2.41575 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.4970i | − | 0.817783i | −0.912583 | − | 0.408892i | \(-0.865915\pi\) | ||
0.912583 | − | 0.408892i | \(-0.134085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 85.4372i | − | 3.24082i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.3065 | −0.996429 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.27211i | − | 0.350203i | −0.984550 | − | 0.175101i | \(-0.943975\pi\) | ||
0.984550 | − | 0.175101i | \(-0.0560253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.495061i | − | 0.0186716i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.96301 | − | 17.9809i | 0.224262 | − | 0.676240i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.67285 | −0.175493 | −0.0877464 | − | 0.996143i | \(-0.527967\pi\) | ||||
−0.0877464 | + | 0.996143i | \(0.527967\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.8643 | 1.15588 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58.0725 | −2.17179 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.6248 | −1.32858 | −0.664290 | − | 0.747475i | \(-0.731266\pi\) | ||||
−0.664290 | + | 0.747475i | \(0.731266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.58484 | − | 1.85210i | −0.207990 | − | 0.0689759i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 57.4653i | − | 2.13421i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.8768i | − | 1.25642i | −0.778043 | − | 0.628211i | \(-0.783788\pi\) | ||
0.778043 | − | 0.628211i | \(-0.216212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3342 | −0.937018 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.0002i | − | 1.07115i | −0.844489 | − | 0.535573i | \(-0.820096\pi\) | ||
0.844489 | − | 0.535573i | \(-0.179904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.47983i | − | 0.0545101i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.22257 | −0.0817585 | −0.0408793 | − | 0.999164i | \(-0.513016\pi\) | ||||
−0.0408793 | + | 0.999164i | \(0.513016\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 37.5002i | − | 1.37575i | −0.725830 | − | 0.687874i | \(-0.758544\pi\) | ||
0.725830 | − | 0.687874i | \(-0.241456\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.6527i | 1.30621i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.16176 | + | 0.716904i | 0.0789888 | + | 0.0261951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0912 | 0.404722 | 0.202361 | − | 0.979311i | \(-0.435139\pi\) | ||||
0.202361 | + | 0.979311i | \(0.435139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 90.2986 | 3.28630 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0714 | 0.947580 | 0.473790 | − | 0.880638i | \(-0.342886\pi\) | ||||
0.473790 | + | 0.880638i | \(0.342886\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.3809 | 0.956305 | 0.478153 | − | 0.878277i | \(-0.341307\pi\) | ||||
0.478153 | + | 0.878277i | \(0.341307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.06153 | + | 15.2626i | −0.183240 | + | 0.552541i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.18819i | 0.223443i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 43.9095i | − | 1.58342i | −0.610899 | − | 0.791709i | \(-0.709192\pi\) | ||
0.610899 | − | 0.791709i | \(-0.290808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.5616 | 0.667616 | 0.333808 | − | 0.942641i | \(-0.391666\pi\) | ||||
0.333808 | + | 0.942641i | \(0.391666\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 64.5441i | 2.31849i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.30261i | − | 0.189986i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.6067 | −0.880497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 37.4257i | − | 1.33578i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42679i | 0.0865056i | 0.999064 | + | 0.0432528i | \(0.0137721\pi\) | ||||
−0.999064 | + | 0.0432528i | \(0.986228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.4885 | + | 9.77930i | 1.04849 | + | 0.347712i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.4773 | 2.04108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.6530 | 0.766988 | 0.383494 | − | 0.923543i | \(-0.374721\pi\) | ||||
0.383494 | + | 0.923543i | \(0.374721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.6714 | 1.08508 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.8145 | −1.12271 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.5828 | + | 23.0758i | 2.45247 | + | 0.813315i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.3442i | 0.891055i | 0.895268 | + | 0.445528i | \(0.146984\pi\) | ||||
−0.895268 | + | 0.445528i | \(0.853016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.0486i | 1.37118i | 0.727987 | + | 0.685591i | \(0.240456\pi\) | ||||
−0.727987 | + | 0.685591i | \(0.759544\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −91.3887 | −3.20121 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.10662i | − | 0.178658i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.6745i | 1.41955i | 0.704428 | + | 0.709775i | \(0.251203\pi\) | ||||
−0.704428 | + | 0.709775i | \(0.748797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.6153 | −1.27633 | −0.638165 | − | 0.769899i | \(-0.720306\pi\) | ||||
−0.638165 | + | 0.769899i | \(0.720306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.6002i | 0.820660i | 0.911937 | + | 0.410330i | \(0.134586\pi\) | ||||
−0.911937 | + | 0.410330i | \(0.865414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.1455i | − | 0.838609i | −0.907846 | − | 0.419305i | \(-0.862274\pi\) | ||
0.907846 | − | 0.419305i | \(-0.137726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.4689 | − | 13.7634i | −0.639910 | − | 0.476874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.5627 | 1.43834 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.0720 | −1.17630 | −0.588148 | − | 0.808753i | \(-0.700143\pi\) | ||||
−0.588148 | + | 0.808753i | \(0.700143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8249 | 0.373273 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −67.9657 | −2.33809 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.88558 | + | 11.7166i | −0.133510 | + | 0.402587i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.81107i | 0.164921i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.31584i | − | 0.318968i | −0.987200 | − | 0.159484i | \(-0.949017\pi\) | ||
0.987200 | − | 0.159484i | \(-0.0509831\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.7920 | −1.42759 | −0.713793 | − | 0.700357i | \(-0.753024\pi\) | ||||
−0.713793 | + | 0.700357i | \(0.753024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.5649i | 1.28170i | 0.767666 | + | 0.640850i | \(0.221418\pi\) | ||||
−0.767666 | + | 0.640850i | \(0.778582\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.8043i | − | 0.435862i | −0.975964 | − | 0.217931i | \(-0.930069\pi\) | ||
0.975964 | − | 0.217931i | \(-0.0699309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.17909 | 0.210095 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 27.9651i | − | 0.948651i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.15598i | − | 0.106936i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.3563 | + | 91.5366i | −1.02623 | + | 3.09450i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.5497 | 1.33550 | 0.667749 | − | 0.744386i | \(-0.267258\pi\) | ||||
0.667749 | + | 0.744386i | \(0.267258\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.6284 | 1.63833 | 0.819166 | − | 0.573557i | \(-0.194437\pi\) | ||||
0.819166 | + | 0.573557i | \(0.194437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.35363 | 0.314775 | 0.157387 | − | 0.987537i | \(-0.449693\pi\) | ||||
0.157387 | + | 0.987537i | \(0.449693\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.7316 | −1.46836 | −0.734181 | − | 0.678954i | \(-0.762434\pi\) | ||||
−0.734181 | + | 0.678954i | \(0.762434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.20083 | + | 18.6980i | −0.207969 | + | 0.627111i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.18244i | 0.206887i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 78.2930i | 2.61705i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.4140 | 0.680843 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.8726i | 1.29503i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.81107i | − | 0.159925i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.21996 | 0.140121 | 0.0700607 | − | 0.997543i | \(-0.477681\pi\) | ||||
0.0700607 | + | 0.997543i | \(0.477681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.5267i | 1.57463i | 0.616552 | + | 0.787314i | \(0.288529\pi\) | ||||
−0.616552 | + | 0.787314i | \(0.711471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.8010i | 0.589126i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.51517 | − | 4.56884i | 0.0500353 | − | 0.150877i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.28410 | 0.108332 | 0.0541662 | − | 0.998532i | \(-0.482750\pi\) | ||||
0.0541662 | + | 0.998532i | \(0.482750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −52.4780 | −1.72733 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0610 | −0.330804 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.6294 | 0.709637 | 0.354818 | − | 0.934935i | \(-0.384543\pi\) | ||||
0.354818 | + | 0.934935i | \(0.384543\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.77429 | − | 3.72279i | 0.0909238 | − | 0.122009i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.6002i | 1.16425i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.01251i | 0.0984143i | 0.998789 | + | 0.0492071i | \(0.0156694\pi\) | ||||
−0.998789 | + | 0.0492071i | \(0.984331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.9167 | 0.975257 | 0.487628 | − | 0.873051i | \(-0.337862\pi\) | ||||
0.487628 | + | 0.873051i | \(0.337862\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.5315i | 1.67810i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45.8209i | − | 1.48898i | −0.667634 | − | 0.744490i | \(-0.732693\pi\) | ||
0.667634 | − | 0.744490i | \(-0.267307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −67.8499 | −2.20250 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.5009i | 0.469731i | 0.972028 | + | 0.234865i | \(0.0754649\pi\) | ||||
−0.972028 | + | 0.234865i | \(0.924535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 44.2669i | − | 1.43244i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.8913 | − | 7.92310i | −0.771491 | − | 0.255850i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.07137 | 0.260367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.2431 | 1.55300 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4224 | −0.463793 | −0.231896 | − | 0.972740i | \(-0.574493\pi\) | ||||
−0.231896 | + | 0.972740i | \(0.574493\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.4034 | 1.00778 | 0.503891 | − | 0.863767i | \(-0.331901\pi\) | ||||
0.503891 | + | 0.863767i | \(0.331901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.9109 | + | 16.5520i | 1.60007 | + | 0.530633i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.2067i | 1.44629i | 0.690696 | + | 0.723145i | \(0.257304\pi\) | ||||
−0.690696 | + | 0.723145i | \(0.742696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.19667i | − | 0.261967i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1835 | −0.356698 | −0.178349 | − | 0.983967i | \(-0.557076\pi\) | ||||
−0.178349 | + | 0.983967i | \(0.557076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6940i | 0.436328i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.6268i | 1.57804i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.4509 | −1.25320 | −0.626599 | − | 0.779342i | \(-0.715554\pi\) | ||||
−0.626599 | + | 0.779342i | \(0.715554\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 45.5218i | − | 1.44314i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.8764i | 0.502810i | 0.967882 | + | 0.251405i | \(0.0808926\pi\) | ||||
−0.967882 | + | 0.251405i | \(0.919107\pi\) | |||||||
\(998\) | 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 | 3024.2.k.l.1889.16 | 16 | ||
3.2 | odd | 2 | inner | 3024.2.k.l.1889.2 | 16 | ||
4.3 | odd | 2 | 1512.2.k.b.377.15 | yes | 16 | ||
7.6 | odd | 2 | inner | 3024.2.k.l.1889.1 | 16 | ||
12.11 | even | 2 | 1512.2.k.b.377.1 | ✓ | 16 | ||
21.20 | even | 2 | inner | 3024.2.k.l.1889.15 | 16 | ||
28.27 | even | 2 | 1512.2.k.b.377.2 | yes | 16 | ||
84.83 | odd | 2 | 1512.2.k.b.377.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.b.377.1 | ✓ | 16 | 12.11 | even | 2 | ||
1512.2.k.b.377.2 | yes | 16 | 28.27 | even | 2 | ||
1512.2.k.b.377.15 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.k.b.377.16 | yes | 16 | 84.83 | odd | 2 | ||
3024.2.k.l.1889.1 | 16 | 7.6 | odd | 2 | inner | ||
3024.2.k.l.1889.2 | 16 | 3.2 | odd | 2 | inner | ||
3024.2.k.l.1889.15 | 16 | 21.20 | even | 2 | inner | ||
3024.2.k.l.1889.16 | 16 | 1.1 | even | 1 | trivial |