Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.15690\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | 0.766021 | 0.342575 | 0.171288 | − | 0.985221i | \(-0.445207\pi\) | ||||
0.171288 | + | 0.985221i | \(0.445207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.54779 | 1.67272 | 0.836360 | − | 0.548180i | \(-0.184679\pi\) | ||||
0.836360 | + | 0.548180i | \(0.184679\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.31381 | 1.75114 | 0.875568 | − | 0.483096i | \(-0.160488\pi\) | ||||
0.875568 | + | 0.483096i | \(0.160488\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.15032 | 1.73421 | 0.867104 | − | 0.498128i | \(-0.165979\pi\) | ||||
0.867104 | + | 0.498128i | \(0.165979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.15032 | 1.41098 | 0.705490 | − | 0.708720i | \(-0.250727\pi\) | ||||
0.705490 | + | 0.708720i | \(0.250727\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.17923 | −1.49697 | −0.748487 | − | 0.663150i | \(-0.769219\pi\) | ||||
−0.748487 | + | 0.663150i | \(0.769219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41321 | −0.882642 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.16349 | 0.587445 | 0.293723 | − | 0.955891i | \(-0.405106\pi\) | ||||
0.293723 | + | 0.955891i | \(0.405106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.163489 | 0.0293635 | 0.0146817 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146817 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.766021 | −0.129481 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.31381 | 0.873585 | 0.436792 | − | 0.899562i | \(-0.356114\pi\) | ||||
0.436792 | + | 0.899562i | \(0.356114\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.865425 | 0.135157 | 0.0675783 | − | 0.997714i | \(-0.478473\pi\) | ||||
0.0675783 | + | 0.997714i | \(0.478473\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.31381 | 1.26784 | 0.633922 | − | 0.773397i | \(-0.281444\pi\) | ||||
0.633922 | + | 0.773397i | \(0.281444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.36855 | −0.345489 | −0.172745 | − | 0.984967i | \(-0.555264\pi\) | ||||
−0.172745 | + | 0.984967i | \(0.555264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24972 | 0.573032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.36855 | −0.308359 | −0.154180 | − | 0.988043i | \(-0.549273\pi\) | ||||
−0.154180 | + | 0.988043i | \(0.549273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5635 | −1.73663 | −0.868316 | − | 0.496011i | \(-0.834797\pi\) | ||||
−0.868316 | + | 0.496011i | \(0.834797\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.83651 | 0.599895 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.05092 | −0.861406 | −0.430703 | − | 0.902494i | \(-0.641734\pi\) | ||||
−0.430703 | + | 0.902494i | \(0.641734\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.86159 | −0.933000 | −0.466500 | − | 0.884521i | \(-0.654485\pi\) | ||||
−0.466500 | + | 0.884521i | \(0.654485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.98683 | −0.232541 | −0.116270 | − | 0.993218i | \(-0.537094\pi\) | ||||
−0.116270 | + | 0.993218i | \(0.537094\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.54779 | −0.632229 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.24972 | −0.590640 | −0.295320 | − | 0.955398i | \(-0.595426\pi\) | ||||
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5282 | 1.37515 | 0.687575 | − | 0.726113i | \(-0.258675\pi\) | ||||
0.687575 | + | 0.726113i | \(0.258675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.47730 | 0.594096 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.86542 | 0.515734 | 0.257867 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257867 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.31381 | −0.661867 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.71128 | 0.483367 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.26289 | 0.331297 | 0.165648 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165648 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1503 | 1.50751 | 0.753757 | − | 0.657154i | \(-0.228240\pi\) | ||||
0.753757 | + | 0.657154i | \(0.228240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.42638 | −0.140546 | −0.0702728 | − | 0.997528i | \(-0.522387\pi\) | ||||
−0.0702728 | + | 0.997528i | \(0.522387\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.2459 | −1.37720 | −0.688601 | − | 0.725140i | \(-0.741775\pi\) | ||||
−0.688601 | + | 0.725140i | \(0.741775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.7270 | −1.69794 | −0.848970 | − | 0.528441i | \(-0.822777\pi\) | ||||
−0.848970 | + | 0.528441i | \(0.822777\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.09557 | −0.667495 | −0.333748 | − | 0.942662i | \(-0.608313\pi\) | ||||
−0.333748 | + | 0.942662i | \(0.608313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.49945 | −0.512826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.15032 | −0.655469 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7779 | 1.79799 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.21072 | −0.644946 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.37789 | −0.477211 | −0.238605 | − | 0.971117i | \(-0.576690\pi\) | ||||
−0.238605 | + | 0.971117i | \(0.576690\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.69553 | −0.759732 | −0.379866 | − | 0.925042i | \(-0.624030\pi\) | ||||
−0.379866 | + | 0.925042i | \(0.624030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.15032 | −0.533300 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0917 | −1.54568 | −0.772841 | − | 0.634600i | \(-0.781165\pi\) | ||||
−0.772841 | + | 0.634600i | \(0.781165\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8905 | −1.00854 | −0.504270 | − | 0.863546i | \(-0.668238\pi\) | ||||
−0.504270 | + | 0.863546i | \(0.668238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.0277 | 2.92916 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.42330 | 0.201244 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.8327 | 1.62476 | 0.812378 | − | 0.583131i | \(-0.198173\pi\) | ||||
0.812378 | + | 0.583131i | \(0.198173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5635 | −1.26654 | −0.633271 | − | 0.773930i | \(-0.718288\pi\) | ||||
−0.633271 | + | 0.773930i | \(0.718288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.125236 | 0.0100592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6408 | −1.00884 | −0.504422 | − | 0.863457i | \(-0.668294\pi\) | ||||
−0.504422 | + | 0.863457i | \(0.668294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.17923 | 0.565803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.6144 | −1.92795 | −0.963976 | − | 0.265989i | \(-0.914302\pi\) | ||||
−0.963976 | + | 0.265989i | \(0.914302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.09557 | 0.239543 | 0.119771 | − | 0.992802i | \(-0.461784\pi\) | ||||
0.119771 | + | 0.992802i | \(0.461784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.8642 | 2.06647 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9163 | 1.21010 | 0.605048 | − | 0.796189i | \(-0.293154\pi\) | ||||
0.605048 | + | 0.796189i | \(0.293154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.41321 | 0.333607 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6824 | 1.24690 | 0.623449 | − | 0.781864i | \(-0.285731\pi\) | ||||
0.623449 | + | 0.781864i | \(0.285731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8642 | 1.32783 | 0.663917 | − | 0.747807i | \(-0.268893\pi\) | ||||
0.663917 | + | 0.747807i | \(0.268893\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.07049 | 0.299268 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 39.6684 | 2.90084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.58936 | 0.115002 | 0.0575011 | − | 0.998345i | \(-0.481687\pi\) | ||||
0.0575011 | + | 0.998345i | \(0.481687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.36472 | −0.530124 | −0.265062 | − | 0.964231i | \(-0.585392\pi\) | ||||
−0.265062 | + | 0.964231i | \(0.585392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.73085 | 0.693294 | 0.346647 | − | 0.937996i | \(-0.387320\pi\) | ||||
0.346647 | + | 0.937996i | \(0.387320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.37789 | 0.593893 | 0.296947 | − | 0.954894i | \(-0.404032\pi\) | ||||
0.296947 | + | 0.954894i | \(0.404032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.16349 | −0.222033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.662934 | 0.0463013 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 34.1207 | 2.36018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.23655 | 0.360499 | 0.180250 | − | 0.983621i | \(-0.442309\pi\) | ||||
0.180250 | + | 0.983621i | \(0.442309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.36855 | 0.434332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.163489 | −0.0110983 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 45.1457 | 3.03683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.31381 | 0.489769 | 0.244884 | − | 0.969552i | \(-0.421250\pi\) | ||||
0.244884 | + | 0.969552i | \(0.421250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.76860 | −0.581992 | −0.290996 | − | 0.956724i | \(-0.593987\pi\) | ||||
−0.290996 | + | 0.956724i | \(0.593987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6917 | −1.30126 | −0.650632 | − | 0.759393i | \(-0.725496\pi\) | ||||
−0.650632 | + | 0.759393i | \(0.725496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3585 | 1.20270 | 0.601352 | − | 0.798985i | \(-0.294629\pi\) | ||||
0.601352 | + | 0.798985i | \(0.294629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81436 | −0.118356 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.708701 | 0.0458421 | 0.0229210 | − | 0.999737i | \(-0.492703\pi\) | ||||
0.0229210 | + | 0.999737i | \(0.492703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.42330 | 0.284930 | 0.142465 | − | 0.989800i | \(-0.454497\pi\) | ||||
0.142465 | + | 0.989800i | \(0.454497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.766021 | 0.0489393 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.8319 | 2.47082 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.9546 | 1.19640 | 0.598202 | − | 0.801346i | \(-0.295882\pi\) | ||||
0.598202 | + | 0.801346i | \(0.295882\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.8288 | −2.50402 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2849 | 1.14058 | 0.570290 | − | 0.821443i | \(-0.306831\pi\) | ||||
0.570290 | + | 0.821443i | \(0.306831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.31381 | −0.330184 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.5440 | −1.02014 | −0.510072 | − | 0.860132i | \(-0.670381\pi\) | ||||
−0.510072 | + | 0.860132i | \(0.670381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.06409 | 0.188225 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.852255 | −0.0519629 | −0.0259815 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259815 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9283 | −1.14981 | −0.574905 | − | 0.818220i | \(-0.694961\pi\) | ||||
−0.574905 | + | 0.818220i | \(0.694961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.4836 | −1.47641 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8773 | 0.893893 | 0.446946 | − | 0.894561i | \(-0.352511\pi\) | ||||
0.446946 | + | 0.894561i | \(0.352511\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.6692 | 0.755781 | 0.377890 | − | 0.925850i | \(-0.376650\pi\) | ||||
0.377890 | + | 0.925850i | \(0.376650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.06409 | 0.419916 | 0.209958 | − | 0.977710i | \(-0.432667\pi\) | ||||
0.209958 | + | 0.977710i | \(0.432667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.865425 | −0.0510844 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.1271 | 2.00747 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.27849 | −0.0746901 | −0.0373451 | − | 0.999302i | \(-0.511890\pi\) | ||||
−0.0373451 | + | 0.999302i | \(0.511890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.81436 | −0.105636 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −45.3283 | −2.62140 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.31381 | −0.479200 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.3900 | −0.594927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2320 | 1.83958 | 0.919788 | − | 0.392416i | \(-0.128361\pi\) | ||||
0.919788 | + | 0.392416i | \(0.128361\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.36230 | −0.190658 | −0.0953292 | − | 0.995446i | \(-0.530390\pi\) | ||||
−0.0953292 | + | 0.995446i | \(0.530390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.72394 | −0.267013 | −0.133506 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133506 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2327 | −0.574727 | −0.287363 | − | 0.957822i | \(-0.592779\pi\) | ||||
−0.287363 | + | 0.957822i | \(0.592779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5504 | 0.982632 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.9767 | 2.44693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.8642 | −1.54563 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.36855 | 0.130583 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80119 | 0.208932 | 0.104466 | − | 0.994528i | \(-0.466687\pi\) | ||||
0.104466 | + | 0.994528i | \(0.466687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.40115 | −0.295096 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1911 | −0.609621 | −0.304810 | − | 0.952413i | \(-0.598593\pi\) | ||||
−0.304810 | + | 0.952413i | \(0.598593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.907001 | 0.0491169 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.66036 | −0.303864 | −0.151932 | − | 0.988391i | \(-0.548549\pi\) | ||||
−0.151932 | + | 0.988391i | \(0.548549\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.6276 | −1.63946 | −0.819729 | − | 0.572751i | \(-0.805876\pi\) | ||||
−0.819729 | + | 0.572751i | \(0.805876\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.3521 | 1.56225 | 0.781126 | − | 0.624373i | \(-0.214645\pi\) | ||||
0.781126 | + | 0.624373i | \(0.214645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.02215 | −0.319622 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5351 | 0.714357 | 0.357178 | − | 0.934036i | \(-0.383739\pi\) | ||||
0.357178 | + | 0.934036i | \(0.383739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8264 | 0.990864 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.52195 | −0.0796627 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.74262 | 0.508560 | 0.254280 | − | 0.967131i | \(-0.418161\pi\) | ||||
0.254280 | + | 0.967131i | \(0.418161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3360 | −0.845844 | −0.422922 | − | 0.906166i | \(-0.638996\pi\) | ||||
−0.422922 | + | 0.906166i | \(0.638996\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.9737 | 1.02870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.9414 | −1.69209 | −0.846044 | − | 0.533114i | \(-0.821022\pi\) | ||||
−0.846044 | + | 0.533114i | \(0.821022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.2944 | −1.59907 | −0.799534 | − | 0.600621i | \(-0.794920\pi\) | ||||
−0.799534 | + | 0.600621i | \(0.794920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.24972 | −0.216586 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.39106 | −0.273338 | −0.136669 | − | 0.990617i | \(-0.543640\pi\) | ||||
−0.136669 | + | 0.990617i | \(0.543640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.3338 | −2.59606 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.02140 | −0.202339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0817 | 1.20862 | 0.604312 | − | 0.796748i | \(-0.293448\pi\) | ||||
0.604312 | + | 0.796748i | \(0.293448\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.2642 | −1.51132 | −0.755661 | − | 0.654963i | \(-0.772684\pi\) | ||||
−0.755661 | + | 0.654963i | \(0.772684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.03224 | 0.0514194 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.4799 | 1.46126 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.0055 | −1.18700 | −0.593498 | − | 0.804835i | \(-0.702254\pi\) | ||||
−0.593498 | + | 0.804835i | \(0.702254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.36855 | 0.116549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.59688 | 0.471092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.7308 | −1.06162 | −0.530811 | − | 0.847490i | \(-0.678112\pi\) | ||||
−0.530811 | + | 0.847490i | \(0.678112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0246 | 0.878464 | 0.439232 | − | 0.898374i | \(-0.355251\pi\) | ||||
0.439232 | + | 0.898374i | \(0.355251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.5559 | −1.53068 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.5635 | 0.656385 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.8523 | 1.00442 | 0.502209 | − | 0.864746i | \(-0.332521\pi\) | ||||
0.502209 | + | 0.864746i | \(0.332521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.20432 | −0.105933 | −0.0529663 | − | 0.998596i | \(-0.516868\pi\) | ||||
−0.0529663 | + | 0.998596i | \(0.516868\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −44.1546 | −2.11220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.6013 | −1.74688 | −0.873442 | − | 0.486929i | \(-0.838117\pi\) | ||||
−0.873442 | + | 0.486929i | \(0.838117\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.5075 | 1.35443 | 0.677217 | − | 0.735784i | \(-0.263186\pi\) | ||||
0.677217 | + | 0.735784i | \(0.263186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.72702 | 0.176678 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.7232 | 1.87465 | 0.937327 | − | 0.348452i | \(-0.113293\pi\) | ||||
0.937327 | + | 0.348452i | \(0.113293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.80119 | 0.226079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.83651 | −0.226739 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.6917 | −0.500137 | −0.250068 | − | 0.968228i | \(-0.580453\pi\) | ||||
−0.250068 | + | 0.968228i | \(0.580453\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.7113 | −0.592023 | −0.296012 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296012 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6276 | −0.679803 | −0.339901 | − | 0.940461i | \(-0.610394\pi\) | ||||
−0.339901 | + | 0.940461i | \(0.610394\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.7963 | 1.65645 | 0.828227 | − | 0.560393i | \(-0.189350\pi\) | ||||
0.828227 | + | 0.560393i | \(0.189350\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.05092 | 0.325581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.1232 | 2.12075 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.1427 | −1.24539 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.3193 | −0.928413 | −0.464207 | − | 0.885727i | \(-0.653660\pi\) | ||||
−0.464207 | + | 0.885727i | \(0.653660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.5504 | 1.52976 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.49945 | 0.113494 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.4409 | 1.24346 | 0.621732 | − | 0.783230i | \(-0.286429\pi\) | ||||
0.621732 | + | 0.783230i | \(0.286429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.52564 | −0.204239 | −0.102120 | − | 0.994772i | \(-0.532562\pi\) | ||||
−0.102120 | + | 0.994772i | \(0.532562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.6200 | 1.01875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.86159 | 0.352641 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.87734 | 0.0840412 | 0.0420206 | − | 0.999117i | \(-0.486620\pi\) | ||||
0.0420206 | + | 0.999117i | \(0.486620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.7834 | −1.68468 | −0.842340 | − | 0.538946i | \(-0.818823\pi\) | ||||
−0.842340 | + | 0.538946i | \(0.818823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6055 | 0.516436 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.3678 | 0.947111 | 0.473556 | − | 0.880764i | \(-0.342970\pi\) | ||||
0.473556 | + | 0.880764i | \(0.342970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.98683 | 0.0878922 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.09264 | −0.0481474 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1402 | −0.577907 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.8484 | −1.39530 | −0.697652 | − | 0.716436i | \(-0.745772\pi\) | ||||
−0.697652 | + | 0.716436i | \(0.745772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.2366 | −0.622521 | −0.311260 | − | 0.950325i | \(-0.600751\pi\) | ||||
−0.311260 | + | 0.950325i | \(0.600751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.16900 | 0.0509223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.5414 | 1.24093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.46413 | 0.236678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9127 | −0.471795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.54779 | 0.238960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5767 | −0.798675 | −0.399337 | − | 0.916804i | \(-0.630760\pi\) | ||||
−0.399337 | + | 0.916804i | \(0.630760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5793 | −0.581672 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.10183 | −0.260895 | −0.130448 | − | 0.991455i | \(-0.541641\pi\) | ||||
−0.130448 | + | 0.991455i | \(0.541641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.4565 | 0.828873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.24972 | 0.223241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.5309 | 1.29364 | 0.646819 | − | 0.762644i | \(-0.276099\pi\) | ||||
0.646819 | + | 0.762644i | \(0.276099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.4918 | 2.22017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9899 | 0.673894 | 0.336947 | − | 0.941524i | \(-0.390606\pi\) | ||||
0.336947 | + | 0.941524i | \(0.390606\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.43536 | −0.228667 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.5057 | 0.733877 | 0.366939 | − | 0.930245i | \(-0.380406\pi\) | ||||
0.366939 | + | 0.930245i | \(0.380406\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.4918 | −1.27604 | −0.638021 | − | 0.770019i | \(-0.720247\pi\) | ||||
−0.638021 | + | 0.770019i | \(0.720247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.6835 | 1.32129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9283 | 1.53734 | 0.768672 | − | 0.639644i | \(-0.220918\pi\) | ||||
0.768672 | + | 0.639644i | \(0.220918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5282 | −0.519758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.1911 | 0.919063 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.2867 | −1.86918 | −0.934591 | − | 0.355723i | \(-0.884235\pi\) | ||||
−0.934591 | + | 0.355723i | \(0.884235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.00551 | 0.0414313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.7203 | −0.891944 | −0.445972 | − | 0.895047i | \(-0.647142\pi\) | ||||
−0.445972 | + | 0.895047i | \(0.647142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.47730 | −0.224547 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.5125 | −0.838117 | −0.419058 | − | 0.907959i | \(-0.637640\pi\) | ||||
−0.419058 | + | 0.907959i | \(0.637640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.31381 | −0.0943822 | −0.0471911 | − | 0.998886i | \(-0.515027\pi\) | ||||
−0.0471911 | + | 0.998886i | \(0.515027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.1503 | 0.615948 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.3647 | −0.867167 | −0.433584 | − | 0.901113i | \(-0.642751\pi\) | ||||
−0.433584 | + | 0.901113i | \(0.642751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.9546 | −0.604998 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.163489 | 0.00660325 | 0.00330163 | − | 0.999995i | \(-0.498949\pi\) | ||||
0.00330163 | + | 0.999995i | \(0.498949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5220 | 0.705407 | 0.352704 | − | 0.935735i | \(-0.385262\pi\) | ||||
0.352704 | + | 0.935735i | \(0.385262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1988 | 0.771665 | 0.385833 | − | 0.922569i | \(-0.373914\pi\) | ||||
0.385833 | + | 0.922569i | \(0.373914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.86542 | −0.194929 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.5425 | 0.661700 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 37.9954 | 1.51498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18675 | 0.0472437 | 0.0236218 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236218 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.11958 | −0.163481 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.31381 | 0.250162 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.6591 | −1.60594 | −0.802969 | − | 0.596021i | \(-0.796748\pi\) | ||||
−0.802969 | + | 0.596021i | \(0.796748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5868 | −0.417502 | −0.208751 | − | 0.977969i | \(-0.566940\pi\) | ||||
−0.208751 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.8303 | 1.01549 | 0.507746 | − | 0.861507i | \(-0.330479\pi\) | ||||
0.507746 | + | 0.861507i | \(0.330479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.1402 | −0.515799 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.2327 | 0.870034 | 0.435017 | − | 0.900422i | \(-0.356742\pi\) | ||||
0.435017 | + | 0.900422i | \(0.356742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.66096 | −0.260265 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.9388 | 1.04939 | 0.524694 | − | 0.851291i | \(-0.324180\pi\) | ||||
0.524694 | + | 0.851291i | \(0.324180\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7301 | 0.650725 | 0.325363 | − | 0.945589i | \(-0.394514\pi\) | ||||
0.325363 | + | 0.945589i | \(0.394514\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.71128 | −0.182695 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.7114 | −0.879390 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −75.2476 | −2.90490 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.36472 | −0.129701 | −0.0648503 | − | 0.997895i | \(-0.520657\pi\) | ||||
−0.0648503 | + | 0.997895i | \(0.520657\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.1307 | −0.389356 | −0.194678 | − | 0.980867i | \(-0.562366\pi\) | ||||
−0.194678 | + | 0.980867i | \(0.562366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.26289 | −0.125218 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7151 | 0.983961 | 0.491981 | − | 0.870606i | \(-0.336273\pi\) | ||||
0.491981 | + | 0.870606i | \(0.336273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8587 | −0.529512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.2552 | 0.962148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.51812 | −0.324045 | −0.162022 | − | 0.986787i | \(-0.551802\pi\) | ||||
−0.162022 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.10838 | −0.345501 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.18806 | 0.234390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.62519 | −0.0991520 | −0.0495760 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495760 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.6816 | 1.23261 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.1503 | −0.569786 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.2577 | −1.36168 | −0.680842 | − | 0.732430i | \(-0.738386\pi\) | ||||
−0.680842 | + | 0.732430i | \(0.738386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.17372 | −0.0439563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.8319 | 1.00346 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.8603 | −1.44925 | −0.724623 | − | 0.689145i | \(-0.757986\pi\) | ||||
−0.724623 | + | 0.689145i | \(0.757986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42638 | 0.0531212 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.9611 | −0.518504 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.7180 | −0.582950 | −0.291475 | − | 0.956578i | \(-0.594146\pi\) | ||||
−0.291475 | + | 0.956578i | \(0.594146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.4464 | 2.19870 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7503 | −0.544814 | −0.272407 | − | 0.962182i | \(-0.587820\pi\) | ||||
−0.272407 | + | 0.962182i | \(0.587820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.1170 | −1.44089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.7935 | 1.16954 | 0.584772 | − | 0.811198i | \(-0.301184\pi\) | ||||
0.584772 | + | 0.811198i | \(0.301184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3673 | 1.51762 | 0.758809 | − | 0.651313i | \(-0.225781\pi\) | ||||
0.758809 | + | 0.651313i | \(0.225781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.1923 | 0.556601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.2459 | 0.520534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.42330 | 0.307371 | 0.153685 | − | 0.988120i | \(-0.450886\pi\) | ||||
0.153685 | + | 0.988120i | \(0.450886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.9220 | −0.433886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.8828 | −1.01342 | −0.506710 | − | 0.862117i | \(-0.669138\pi\) | ||||
−0.506710 | + | 0.862117i | \(0.669138\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.3415 | 0.628628 | 0.314314 | − | 0.949319i | \(-0.398226\pi\) | ||||
0.314314 | + | 0.949319i | \(0.398226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7270 | 0.641761 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.9546 | −0.539979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.8960 | 1.51081 | 0.755404 | − | 0.655259i | \(-0.227440\pi\) | ||||
0.755404 | + | 0.655259i | \(0.227440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.0289 | −0.864260 | −0.432130 | − | 0.901811i | \(-0.642238\pi\) | ||||
−0.432130 | + | 0.901811i | \(0.642238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.721511 | −0.0259174 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.32264 | 0.190703 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.6144 | −1.56065 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.68311 | −0.345605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9923 | 1.35428 | 0.677140 | − | 0.735854i | \(-0.263219\pi\) | ||||
0.677140 | + | 0.735854i | \(0.263219\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.09557 | 0.252290 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −85.6375 | −3.04108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.5470 | −0.727813 | −0.363907 | − | 0.931435i | \(-0.618557\pi\) | ||||
−0.363907 | + | 0.931435i | \(0.618557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.9359 | −0.599150 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0225 | −0.388976 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.49945 | 0.193830 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.13715 | −0.250929 | −0.125464 | − | 0.992098i | \(-0.540042\pi\) | ||||
−0.125464 | + | 0.992098i | \(0.540042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6276 | −1.32128 | −0.660642 | − | 0.750701i | \(-0.729716\pi\) | ||||
−0.660642 | + | 0.750701i | \(0.729716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.8552 | −0.660468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.1326 | 1.78890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.78485 | 0.166992 | 0.0834961 | − | 0.996508i | \(-0.473391\pi\) | ||||
0.0834961 | + | 0.996508i | \(0.473391\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.65396 | −0.0925111 | −0.0462555 | − | 0.998930i | \(-0.514729\pi\) | ||||
−0.0462555 | + | 0.998930i | \(0.514729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.2239 | 1.64214 | 0.821068 | − | 0.570831i | \(-0.193379\pi\) | ||||
0.821068 | + | 0.570831i | \(0.193379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3401 | −0.428591 | −0.214296 | − | 0.976769i | \(-0.568746\pi\) | ||||
−0.214296 | + | 0.976769i | \(0.568746\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.15032 | 0.247744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.37127 | 0.0820613 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.18983 | −0.248220 | −0.124110 | − | 0.992268i | \(-0.539608\pi\) | ||||
−0.124110 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9923 | −0.654908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.5785 | 0.707923 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.7779 | −0.679578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.1491 | −1.30773 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.9923 | −1.02692 | −0.513459 | − | 0.858114i | \(-0.671636\pi\) | ||||
−0.513459 | + | 0.858114i | \(0.671636\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.97492 | 0.306577 | 0.153289 | − | 0.988181i | \(-0.451014\pi\) | ||||
0.153289 | + | 0.988181i | \(0.451014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.5403 | 1.51969 | 0.759847 | − | 0.650102i | \(-0.225274\pi\) | ||||
0.759847 | + | 0.650102i | \(0.225274\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7842 | 1.32023 | 0.660115 | − | 0.751165i | \(-0.270508\pi\) | ||||
0.660115 | + | 0.751165i | \(0.270508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.1923 | 0.414549 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.1243 | −0.987976 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.5181 | −1.50844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.21072 | 0.243767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.66051 | −0.191142 | −0.0955709 | − | 0.995423i | \(-0.530468\pi\) | ||||
−0.0955709 | + | 0.995423i | \(0.530468\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.7684 | −0.901852 | −0.450926 | − | 0.892561i | \(-0.648906\pi\) | ||||
−0.450926 | + | 0.892561i | \(0.648906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0377 | −0.371450 | −0.185725 | − | 0.982602i | \(-0.559463\pi\) | ||||
−0.185725 | + | 0.982602i | \(0.559463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.617527 | 0.0207345 | 0.0103673 | − | 0.999946i | \(-0.496700\pi\) | ||||
0.0103673 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.37789 | 0.180369 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.5674 | −0.487478 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7790 | 0.427156 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.517195 | 0.0172494 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.6013 | 0.952847 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.6843 | 0.454883 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.9283 | 1.75745 | 0.878727 | − | 0.477325i | \(-0.158394\pi\) | ||||
0.878727 | + | 0.477325i | \(0.158394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.2268 | 1.89601 | 0.948005 | − | 0.318256i | \(-0.103097\pi\) | ||||
0.948005 | + | 0.318256i | \(0.103097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.5038 | 2.30024 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.69553 | 0.287152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7887 | 0.586794 | 0.293397 | − | 0.955991i | \(-0.405214\pi\) | ||||
0.293397 | + | 0.955991i | \(0.405214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.6366 | −1.63381 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.4510 | −0.771063 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.62453 | 0.151726 | 0.0758630 | − | 0.997118i | \(-0.475829\pi\) | ||||
0.0758630 | + | 0.997118i | \(0.475829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.15032 | 0.201569 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.3869 | 0.993757 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.43536 | 0.242903 | 0.121451 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121451 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.8238 | −0.939631 | −0.469815 | − | 0.882765i | \(-0.655679\pi\) | ||||
−0.469815 | + | 0.882765i | \(0.655679\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.21309 | −0.202326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.5571 | −1.05796 | −0.528982 | − | 0.848633i | \(-0.677426\pi\) | ||||
−0.528982 | + | 0.848633i | \(0.677426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5445 | −0.407211 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7834 | −1.22393 | −0.611963 | − | 0.790886i | \(-0.709620\pi\) | ||||
−0.611963 | + | 0.790886i | \(0.709620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.21749 | 0.0393969 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0917 | 0.584213 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9733 | −0.999138 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.64153 | −0.181607 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.6074 | 1.75606 | 0.878028 | − | 0.478608i | \(-0.158859\pi\) | ||||
0.878028 | + | 0.478608i | \(0.158859\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.554552 | 0.0177964 | 0.00889820 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889820 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8905 | 0.381192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.4551 | −0.398475 | −0.199238 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199238 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.9923 | 0.862679 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.47694 | −0.110897 | −0.0554485 | − | 0.998462i | \(-0.517659\pi\) | ||||
−0.0554485 | + | 0.998462i | \(0.517659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.45404 | 0.237505 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −59.6868 | −1.89793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.96049 | −0.125809 | −0.0629046 | − | 0.998020i | \(-0.520036\pi\) | ||||
−0.0629046 | + | 0.998020i | \(0.520036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.41764 | 0.203453 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6013 | −0.335746 | −0.167873 | − | 0.985809i | \(-0.553690\pi\) | ||||
−0.167873 | + | 0.985809i | \(0.553690\pi\) | |||||||
\(998\) | 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 | 6048.2.a.br.1.3 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bm.1.2 | ✓ | 4 | ||
4.3 | odd | 2 | 6048.2.a.bv.1.3 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bo.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bm.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
6048.2.a.bo.1.2 | yes | 4 | 12.11 | even | 2 | ||
6048.2.a.br.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bv.1.3 | yes | 4 | 4.3 | odd | 2 |