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: | 4.4.39528.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 2x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.12265\) 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 | ||||||||
\(5\) | 2.73965 | 1.22521 | 0.612604 | − | 0.790390i | \(-0.290122\pi\) | ||||
0.612604 | + | 0.790390i | \(0.290122\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24531 | −0.676986 | −0.338493 | − | 0.940969i | \(-0.609917\pi\) | ||||
−0.338493 | + | 0.940969i | \(0.609917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.458685 | −0.127216 | −0.0636082 | − | 0.997975i | \(-0.520261\pi\) | ||||
−0.0636082 | + | 0.997975i | \(0.520261\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.44364 | 1.80535 | 0.902674 | − | 0.430325i | \(-0.141601\pi\) | ||||
0.902674 | + | 0.430325i | \(0.141601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24531 | −0.973941 | −0.486970 | − | 0.873418i | \(-0.661898\pi\) | ||||
−0.486970 | + | 0.873418i | \(0.661898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.70399 | −0.980851 | −0.490425 | − | 0.871483i | \(-0.663159\pi\) | ||||
−0.490425 | + | 0.871483i | \(0.663159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50566 | 0.501133 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73965 | 0.323044 | 0.161522 | − | 0.986869i | \(-0.448360\pi\) | ||||
0.161522 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.73965 | 0.312450 | 0.156225 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156225 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73965 | −0.463085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.49434 | 0.410066 | 0.205033 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205033 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73965 | 0.740208 | 0.370104 | − | 0.928990i | \(-0.379322\pi\) | ||||
0.370104 | + | 0.928990i | \(0.379322\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.96435 | 0.299560 | 0.149780 | − | 0.988719i | \(-0.452143\pi\) | ||||
0.149780 | + | 0.988719i | \(0.452143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.90233 | 1.44440 | 0.722201 | − | 0.691683i | \(-0.243130\pi\) | ||||
0.722201 | + | 0.691683i | \(0.243130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.42303 | −0.744911 | −0.372455 | − | 0.928050i | \(-0.621484\pi\) | ||||
−0.372455 | + | 0.928050i | \(0.621484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.15135 | −0.829448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.47929 | 0.843532 | 0.421766 | − | 0.906705i | \(-0.361410\pi\) | ||||
0.421766 | + | 0.906705i | \(0.361410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.23398 | 0.670143 | 0.335071 | − | 0.942193i | \(-0.391240\pi\) | ||||
0.335071 | + | 0.942193i | \(0.391240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.25664 | −0.155866 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.77530 | 0.339057 | 0.169528 | − | 0.985525i | \(-0.445776\pi\) | ||||
0.169528 | + | 0.985525i | \(0.445776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.703994 | 0.0835488 | 0.0417744 | − | 0.999127i | \(-0.486699\pi\) | ||||
0.0417744 | + | 0.999127i | \(0.486699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96991 | −0.932808 | −0.466404 | − | 0.884572i | \(-0.654451\pi\) | ||||
−0.466404 | + | 0.884572i | \(0.654451\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.24531 | 0.255877 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.66834 | 0.750247 | 0.375124 | − | 0.926975i | \(-0.377600\pi\) | ||||
0.375124 | + | 0.926975i | \(0.377600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.50566 | 0.384796 | 0.192398 | − | 0.981317i | \(-0.438373\pi\) | ||||
0.192398 | + | 0.981317i | \(0.438373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.3929 | 2.21193 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.78662 | 0.189382 | 0.0946909 | − | 0.995507i | \(-0.469814\pi\) | ||||
0.0946909 | + | 0.995507i | \(0.469814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.458685 | 0.0480833 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.6306 | −1.19328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1627 | 1.33647 | 0.668234 | − | 0.743951i | \(-0.267051\pi\) | ||||
0.668234 | + | 0.743951i | \(0.267051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.49062 | 0.247826 | 0.123913 | − | 0.992293i | \(-0.460456\pi\) | ||||
0.123913 | + | 0.992293i | \(0.460456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3816 | 1.02293 | 0.511466 | − | 0.859304i | \(-0.329103\pi\) | ||||
0.511466 | + | 0.859304i | \(0.329103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.49434 | 0.813610 | 0.406805 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406805 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.75469 | 0.165067 | 0.0825337 | − | 0.996588i | \(-0.473699\pi\) | ||||
0.0825337 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.8873 | −1.20175 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.44364 | −0.682357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.95859 | −0.541690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.83360 | −0.611216 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.24903 | 0.199569 | 0.0997845 | − | 0.995009i | \(-0.468185\pi\) | ||||
0.0997845 | + | 0.995009i | \(0.468185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.9549 | 1.56872 | 0.784362 | − | 0.620303i | \(-0.212990\pi\) | ||||
0.784362 | + | 0.620303i | \(0.212990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.24531 | 0.368115 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.24531 | 0.704444 | 0.352222 | − | 0.935916i | \(-0.385426\pi\) | ||||
0.352222 | + | 0.935916i | \(0.385426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2865 | 1.04213 | 0.521065 | − | 0.853517i | \(-0.325535\pi\) | ||||
0.521065 | + | 0.853517i | \(0.325535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.02989 | 0.0861237 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.76602 | 0.395796 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.23027 | −0.674250 | −0.337125 | − | 0.941460i | \(-0.609454\pi\) | ||||
−0.337125 | + | 0.941460i | \(0.609454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6269 | −1.10894 | −0.554472 | − | 0.832202i | \(-0.687080\pi\) | ||||
−0.554472 | + | 0.832202i | \(0.687080\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.76602 | 0.382816 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.4173 | 1.54967 | 0.774833 | − | 0.632165i | \(-0.217834\pi\) | ||||
0.774833 | + | 0.632165i | \(0.217834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.70399 | 0.370727 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0056 | −0.940348 | −0.470174 | − | 0.882574i | \(-0.655809\pi\) | ||||
−0.470174 | + | 0.882574i | \(0.655809\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.06759 | −0.469524 | −0.234762 | − | 0.972053i | \(-0.575431\pi\) | ||||
−0.234762 | + | 0.972053i | \(0.575431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7896 | −0.983816 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.98867 | −0.683396 | −0.341698 | − | 0.939810i | \(-0.611002\pi\) | ||||
−0.341698 | + | 0.939810i | \(0.611002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50566 | −0.189410 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.2039 | −1.58485 | −0.792427 | − | 0.609967i | \(-0.791183\pi\) | ||||
−0.792427 | + | 0.609967i | \(0.791183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1833 | 1.35155 | 0.675777 | − | 0.737107i | \(-0.263808\pi\) | ||||
0.675777 | + | 0.737107i | \(0.263808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.83360 | 0.502416 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.7133 | −1.22220 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.9699 | 1.87912 | 0.939558 | − | 0.342389i | \(-0.111236\pi\) | ||||
0.939558 | + | 0.342389i | \(0.111236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9699 | 1.36548 | 0.682742 | − | 0.730659i | \(-0.260787\pi\) | ||||
0.682742 | + | 0.730659i | \(0.260787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.31661 | −0.165052 | −0.0825259 | − | 0.996589i | \(-0.526299\pi\) | ||||
−0.0825259 | + | 0.996589i | \(0.526299\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.3929 | 1.51651 | 0.758253 | − | 0.651961i | \(-0.226053\pi\) | ||||
0.758253 | + | 0.651961i | \(0.226053\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.73965 | −0.122099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.9850 | 0.906909 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.53203 | 0.659344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.1007 | 1.72800 | 0.864000 | − | 0.503491i | \(-0.167951\pi\) | ||||
0.864000 | + | 0.503491i | \(0.167951\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.38162 | 0.367023 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.73965 | −0.118095 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.41429 | −0.229670 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.1025 | −1.68099 | −0.840494 | − | 0.541821i | \(-0.817735\pi\) | ||||
−0.840494 | + | 0.541821i | \(0.817735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.4529 | 1.35751 | 0.678754 | − | 0.734366i | \(-0.262520\pi\) | ||||
0.678754 | + | 0.734366i | \(0.262520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.88728 | −0.190797 | −0.0953985 | − | 0.995439i | \(-0.530413\pi\) | ||||
−0.0953985 | + | 0.995439i | \(0.530413\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6119 | −1.08828 | −0.544140 | − | 0.838994i | \(-0.683144\pi\) | ||||
−0.544140 | + | 0.838994i | \(0.683144\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.1289 | 1.76969 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.7658 | −1.01981 | −0.509903 | − | 0.860232i | \(-0.670319\pi\) | ||||
−0.509903 | + | 0.860232i | \(0.670319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.82599 | 0.117623 | 0.0588113 | − | 0.998269i | \(-0.481269\pi\) | ||||
0.0588113 | + | 0.998269i | \(0.481269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.73965 | 0.175030 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.94726 | 0.123901 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.4529 | −1.22786 | −0.613929 | − | 0.789361i | \(-0.710412\pi\) | ||||
−0.613929 | + | 0.789361i | \(0.710412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5619 | 0.664022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.43808 | 0.463975 | 0.231987 | − | 0.972719i | \(-0.425477\pi\) | ||||
0.231987 | + | 0.972719i | \(0.425477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.49434 | −0.154991 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.90789 | −0.487621 | −0.243811 | − | 0.969823i | \(-0.578398\pi\) | ||||
−0.243811 | + | 0.969823i | \(0.578398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.8572 | −0.912670 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.7096 | −1.75045 | −0.875226 | − | 0.483714i | \(-0.839288\pi\) | ||||
−0.875226 | + | 0.483714i | \(0.839288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3929 | −1.29953 | −0.649764 | − | 0.760136i | \(-0.725132\pi\) | ||||
−0.649764 | + | 0.760136i | \(0.725132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.62599 | −0.339260 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.47557 | −0.0886587 | −0.0443293 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443293 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.96991 | −0.475445 | −0.237723 | − | 0.971333i | \(-0.576401\pi\) | ||||
−0.237723 | + | 0.971333i | \(0.576401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.3166 | 0.732147 | 0.366073 | − | 0.930586i | \(-0.380702\pi\) | ||||
0.366073 | + | 0.930586i | \(0.380702\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.73965 | −0.279772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.4078 | 2.25928 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.0349 | −1.92992 | −0.964960 | − | 0.262396i | \(-0.915487\pi\) | ||||
−0.964960 | + | 0.262396i | \(0.915487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.7510 | 1.03350 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.15765 | 0.124780 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.96435 | −0.113223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3393 | 0.821064 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9285 | 0.623722 | 0.311861 | − | 0.950128i | \(-0.399048\pi\) | ||||
0.311861 | + | 0.950128i | \(0.399048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.4342 | 1.15871 | 0.579357 | − | 0.815074i | \(-0.303304\pi\) | ||||
0.579357 | + | 0.815074i | \(0.303304\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3066 | 1.88260 | 0.941300 | − | 0.337571i | \(-0.109605\pi\) | ||||
0.941300 | + | 0.337571i | \(0.109605\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.9699 | −1.34628 | −0.673142 | − | 0.739513i | \(-0.735056\pi\) | ||||
−0.673142 | + | 0.739513i | \(0.735056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.90604 | −0.218697 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.6006 | −1.75830 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.14931 | −0.0637523 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.90233 | −0.545933 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9530 | −1.04175 | −0.520876 | − | 0.853632i | \(-0.674395\pi\) | ||||
−0.520876 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.60334 | 0.415415 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7933 | 1.29611 | 0.648053 | − | 0.761596i | \(-0.275584\pi\) | ||||
0.648053 | + | 0.761596i | \(0.275584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.90604 | −0.211524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.58943 | 0.300056 | 0.150028 | − | 0.988682i | \(-0.452064\pi\) | ||||
0.150028 | + | 0.988682i | \(0.452064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.2772 | 0.657186 | 0.328593 | − | 0.944472i | \(-0.393426\pi\) | ||||
0.328593 | + | 0.944472i | \(0.393426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.92293 | −0.474920 | −0.237460 | − | 0.971397i | \(-0.576315\pi\) | ||||
−0.237460 | + | 0.971397i | \(0.576315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.92870 | 0.102365 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.81651 | 0.359762 | 0.179881 | − | 0.983688i | \(-0.442429\pi\) | ||||
0.179881 | + | 0.983688i | \(0.442429\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.977349 | −0.0514394 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.8347 | −1.14288 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4230 | 0.909475 | 0.454737 | − | 0.890626i | \(-0.349733\pi\) | ||||
0.454737 | + | 0.890626i | \(0.349733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.42303 | 0.281550 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.3214 | −1.41465 | −0.707325 | − | 0.706888i | \(-0.750098\pi\) | ||||
−0.707325 | + | 0.706888i | \(0.750098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.797950 | −0.0410965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5968 | −0.698423 | −0.349211 | − | 0.937044i | \(-0.613550\pi\) | ||||
−0.349211 | + | 0.937044i | \(0.613550\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5582 | −0.743889 | −0.371945 | − | 0.928255i | \(-0.621309\pi\) | ||||
−0.371945 | + | 0.928255i | \(0.621309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.15135 | 0.313502 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.79591 | −0.395268 | −0.197634 | − | 0.980276i | \(-0.563326\pi\) | ||||
−0.197634 | + | 0.980276i | \(0.563326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.0148 | −1.77078 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.2689 | 0.919208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.53183 | −0.327823 | −0.163912 | − | 0.986475i | \(-0.552411\pi\) | ||||
−0.163912 | + | 0.986475i | \(0.552411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.3254 | 1.41450 | 0.707250 | − | 0.706963i | \(-0.249935\pi\) | ||||
0.707250 | + | 0.706963i | \(0.249935\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.797950 | −0.0397487 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.60056 | −0.277609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.8572 | 1.82247 | 0.911235 | − | 0.411886i | \(-0.135130\pi\) | ||||
0.911235 | + | 0.411886i | \(0.135130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.47929 | −0.318825 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.60428 | 0.471455 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.3254 | −1.04181 | −0.520906 | − | 0.853614i | \(-0.674406\pi\) | ||||
−0.520906 | + | 0.853614i | \(0.674406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0111 | −0.975283 | −0.487641 | − | 0.873044i | \(-0.662143\pi\) | ||||
−0.487641 | + | 0.873044i | \(0.662143\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.6513 | 0.904719 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.23398 | −0.253290 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.50938 | −0.361714 | −0.180857 | − | 0.983509i | \(-0.557887\pi\) | ||||
−0.180857 | + | 0.983509i | \(0.557887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2752 | 0.541852 | 0.270926 | − | 0.962600i | \(-0.412670\pi\) | ||||
0.270926 | + | 0.962600i | \(0.412670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.9699 | 0.955290 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8421 | 1.18565 | 0.592826 | − | 0.805331i | \(-0.298012\pi\) | ||||
0.592826 | + | 0.805331i | \(0.298012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.1851 | 1.52916 | 0.764581 | − | 0.644528i | \(-0.222946\pi\) | ||||
0.764581 | + | 0.644528i | \(0.222946\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89472 | 0.232032 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.2340 | 0.907708 | 0.453854 | − | 0.891076i | \(-0.350049\pi\) | ||||
0.453854 | + | 0.891076i | \(0.350049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6420 | −0.501111 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.25664 | 0.0589120 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8197 | 0.833570 | 0.416785 | − | 0.909005i | \(-0.363157\pi\) | ||||
0.416785 | + | 0.909005i | \(0.363157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.69843 | −0.218828 | −0.109414 | − | 0.993996i | \(-0.534897\pi\) | ||||
−0.109414 | + | 0.993996i | \(0.534897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2902 | 0.571176 | 0.285588 | − | 0.958352i | \(-0.407811\pi\) | ||||
0.285588 | + | 0.958352i | \(0.407811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.2839 | −1.35510 | −0.677550 | − | 0.735477i | \(-0.736958\pi\) | ||||
−0.677550 | + | 0.735477i | \(0.736958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.77530 | −0.128151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.41057 | −0.202798 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6373 | −0.488073 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.3289 | 1.70560 | 0.852800 | − | 0.522238i | \(-0.174903\pi\) | ||||
0.852800 | + | 0.522238i | \(0.174903\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.14412 | −0.0521672 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.0611 | 1.63745 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.9285 | −0.857732 | −0.428866 | − | 0.903368i | \(-0.641087\pi\) | ||||
−0.428866 | + | 0.903368i | \(0.641087\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.0273 | −1.44537 | −0.722686 | − | 0.691176i | \(-0.757093\pi\) | ||||
−0.722686 | + | 0.691176i | \(0.757093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9493 | 0.583207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.703994 | −0.0315785 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.5554 | −1.63645 | −0.818223 | − | 0.574901i | \(-0.805040\pi\) | ||||
−0.818223 | + | 0.574901i | \(0.805040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.57697 | −0.427016 | −0.213508 | − | 0.976941i | \(-0.568489\pi\) | ||||
−0.213508 | + | 0.976941i | \(0.568489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.82341 | 0.303638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.54430 | 0.201422 | 0.100711 | − | 0.994916i | \(-0.467888\pi\) | ||||
0.100711 | + | 0.994916i | \(0.467888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.96991 | 0.352568 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.4420 | 1.25330 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.2338 | −0.977841 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2370 | 1.41233 | 0.706164 | − | 0.708049i | \(-0.250424\pi\) | ||||
0.706164 | + | 0.708049i | \(0.250424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.5707 | −1.07440 | −0.537200 | − | 0.843455i | \(-0.680518\pi\) | ||||
−0.537200 | + | 0.843455i | \(0.680518\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9493 | 0.564081 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.872436 | −0.0379320 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.17401 | −0.0941666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9586 | −0.473781 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.24531 | −0.0967123 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.8007 | 1.66817 | 0.834087 | − | 0.551633i | \(-0.185995\pi\) | ||||
0.834087 | + | 0.551633i | \(0.185995\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.2715 | 0.996841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.8035 | 1.06052 | 0.530261 | − | 0.847835i | \(-0.322094\pi\) | ||||
0.530261 | + | 0.847835i | \(0.322094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.38534 | −0.314626 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.66834 | −0.283567 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.29919 | −0.0974197 | −0.0487099 | − | 0.998813i | \(-0.515511\pi\) | ||||
−0.0487099 | + | 0.998813i | \(0.515511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.901017 | −0.0381090 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.9021 | 1.51309 | 0.756547 | − | 0.653939i | \(-0.226885\pi\) | ||||
0.756547 | + | 0.653939i | \(0.226885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.80723 | 0.202242 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3591 | 1.10503 | 0.552516 | − | 0.833502i | \(-0.313668\pi\) | ||||
0.552516 | + | 0.833502i | \(0.313668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8591 | 0.705530 | 0.352765 | − | 0.935712i | \(-0.385242\pi\) | ||||
0.352765 | + | 0.935712i | \(0.385242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.7866 | −0.491536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.43808 | 0.143129 | 0.0715645 | − | 0.997436i | \(-0.477201\pi\) | ||||
0.0715645 | + | 0.997436i | \(0.477201\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50566 | −0.145439 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.1764 | 0.504294 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.3291 | 0.962894 | 0.481447 | − | 0.876475i | \(-0.340111\pi\) | ||||
0.481447 | + | 0.876475i | \(0.340111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.38534 | −0.304308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2604 | 0.626668 | 0.313334 | − | 0.949643i | \(-0.398554\pi\) | ||||
0.313334 | + | 0.949643i | \(0.398554\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.3929 | −0.836029 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8366 | 0.483630 | 0.241815 | − | 0.970322i | \(-0.422257\pi\) | ||||
0.241815 | + | 0.970322i | \(0.422257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.7473 | −0.560762 | −0.280381 | − | 0.959889i | \(-0.590461\pi\) | ||||
−0.280381 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.3244 | −0.663682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.5330 | −1.80754 | −0.903769 | − | 0.428021i | \(-0.859211\pi\) | ||||
−0.903769 | + | 0.428021i | \(0.859211\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.54205 | −0.183752 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.2951 | −1.66789 | −0.833946 | − | 0.551846i | \(-0.813924\pi\) | ||||
−0.833946 | + | 0.551846i | \(0.813924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.46053 | 0.340608 | 0.170304 | − | 0.985392i | \(-0.445525\pi\) | ||||
0.170304 | + | 0.985392i | \(0.445525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9259 | 1.36360 | 0.681799 | − | 0.731540i | \(-0.261198\pi\) | ||||
0.681799 | + | 0.731540i | \(0.261198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.78662 | −0.0715796 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2500 | −1.25000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.5670 | 0.740313 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.6982 | 1.81922 | 0.909609 | − | 0.415465i | \(-0.136381\pi\) | ||||
0.909609 | + | 0.415465i | \(0.136381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.16154 | 0.244513 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.458685 | −0.0181738 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.0685 | 1.89859 | 0.949296 | − | 0.314383i | \(-0.101798\pi\) | ||||
0.949296 | + | 0.314383i | \(0.101798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.2013 | 0.954407 | 0.477203 | − | 0.878793i | \(-0.341651\pi\) | ||||
0.477203 | + | 0.878793i | \(0.341651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.5207 | −0.492240 | −0.246120 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246120 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5480 | −0.571060 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0951 | −0.708116 | −0.354058 | − | 0.935224i | \(-0.615198\pi\) | ||||
−0.354058 | + | 0.935224i | \(0.615198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 49.1900 | 1.92201 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.86483 | 0.306370 | 0.153185 | − | 0.988198i | \(-0.451047\pi\) | ||||
0.153185 | + | 0.988198i | \(0.451047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1738 | 0.667984 | 0.333992 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333992 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.6306 | 0.451017 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.18329 | −0.316858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7519 | −0.453678 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.64083 | 0.101797 | 0.0508983 | − | 0.998704i | \(-0.483792\pi\) | ||||
0.0508983 | + | 0.998704i | \(0.483792\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.5545 | −0.559374 | −0.279687 | − | 0.960091i | \(-0.590231\pi\) | ||||
−0.279687 | + | 0.960091i | \(0.590231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1627 | −0.505137 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.23398 | −0.276801 | −0.138400 | − | 0.990376i | \(-0.544196\pi\) | ||||
−0.138400 | + | 0.990376i | \(0.544196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.5892 | 0.863090 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.48746 | 0.0947649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.79610 | −0.258536 | −0.129268 | − | 0.991610i | \(-0.541263\pi\) | ||||
−0.129268 | + | 0.991610i | \(0.541263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.6607 | 1.27682 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.2802 | 1.33633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.83732 | −0.333781 | −0.166890 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166890 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5892 | −0.399380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.49062 | −0.0936694 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.8195 | −0.969672 | −0.484836 | − | 0.874605i | \(-0.661121\pi\) | ||||
−0.484836 | + | 0.874605i | \(0.661121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.18329 | −0.306467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82153 | 0.105519 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.3216 | −1.72751 | −0.863753 | − | 0.503916i | \(-0.831892\pi\) | ||||
−0.863753 | + | 0.503916i | \(0.831892\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3816 | −0.386632 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.35897 | 0.161888 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.3240 | −1.16174 | −0.580872 | − | 0.813995i | \(-0.697288\pi\) | ||||
−0.580872 | + | 0.813995i | \(0.697288\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.6219 | 0.540811 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.0405 | 1.29425 | 0.647125 | − | 0.762384i | \(-0.275971\pi\) | ||||
0.647125 | + | 0.762384i | \(0.275971\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.23140 | −0.229537 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0824 | 0.591602 | 0.295801 | − | 0.955250i | \(-0.404414\pi\) | ||||
0.295801 | + | 0.955250i | \(0.404414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.39871 | −0.124686 | −0.0623432 | − | 0.998055i | \(-0.519857\pi\) | ||||
−0.0623432 | + | 0.998055i | \(0.519857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5480 | −0.826095 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4041 | −0.525613 | −0.262807 | − | 0.964849i | \(-0.584648\pi\) | ||||
−0.262807 | + | 0.964849i | \(0.584648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.3330 | −1.35869 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2691 | −0.554965 | −0.277482 | − | 0.960731i | \(-0.589500\pi\) | ||||
−0.277482 | + | 0.960731i | \(0.589500\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.7276 | −1.18637 | −0.593187 | − | 0.805065i | \(-0.702131\pi\) | ||||
−0.593187 | + | 0.805065i | \(0.702131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.49434 | −0.307516 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.97196 | −0.107311 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.40799 | 0.267139 | 0.133569 | − | 0.991039i | \(-0.457356\pi\) | ||||
0.133569 | + | 0.991039i | \(0.457356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.6982 | −0.492691 | −0.246346 | − | 0.969182i | \(-0.579230\pi\) | ||||
−0.246346 | + | 0.969182i | \(0.579230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.35897 | 0.156579 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.1213 | −0.720919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.58069 | −0.0565614 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.1965 | 1.89866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.3367 | 1.25962 | 0.629808 | − | 0.776751i | \(-0.283133\pi\) | ||||
0.629808 | + | 0.776751i | \(0.283133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.75469 | −0.0623896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.40075 | −0.0852531 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.40055 | 0.191297 | 0.0956487 | − | 0.995415i | \(-0.469507\pi\) | ||||
0.0956487 | + | 0.995415i | \(0.469507\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.7094 | 2.60765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.8949 | 0.631498 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8873 | 0.454217 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.7445 | −1.25671 | −0.628354 | − | 0.777927i | \(-0.716271\pi\) | ||||
−0.628354 | + | 0.777927i | \(0.716271\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.34670 | −0.293092 | −0.146546 | − | 0.989204i | \(-0.546816\pi\) | ||||
−0.146546 | + | 0.989204i | \(0.546816\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.8910 | −1.15212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.33926 | −0.291754 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8797 | −0.589105 | −0.294552 | − | 0.955635i | \(-0.595171\pi\) | ||||
−0.294552 | + | 0.955635i | \(0.595171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.3315 | −0.569279 | −0.284639 | − | 0.958635i | \(-0.591874\pi\) | ||||
−0.284639 | + | 0.958635i | \(0.591874\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6533 | −1.23979 | −0.619893 | − | 0.784686i | \(-0.712824\pi\) | ||||
−0.619893 | + | 0.784686i | \(0.712824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.0011 | −1.63242 | −0.816208 | − | 0.577758i | \(-0.803928\pi\) | ||||
−0.816208 | + | 0.577758i | \(0.803928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.44364 | 0.257907 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6230 | −0.575264 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.8724 | 0.582501 | 0.291251 | − | 0.956647i | \(-0.405929\pi\) | ||||
0.291251 | + | 0.956647i | \(0.405929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9736 | −0.895642 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.0390 | −1.20538 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.95859 | 0.204739 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.7333 | −0.402214 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.22470 | −0.247369 | −0.123685 | − | 0.992322i | \(-0.539471\pi\) | ||||
−0.123685 | + | 0.992322i | \(0.539471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.3796 | −1.51598 | −0.757989 | − | 0.652268i | \(-0.773818\pi\) | ||||
−0.757989 | + | 0.652268i | \(0.773818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.2464 | −1.81674 | −0.908372 | − | 0.418163i | \(-0.862674\pi\) | ||||
−0.908372 | + | 0.418163i | \(0.862674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.0594 | 0.580710 | 0.290355 | − | 0.956919i | \(-0.406227\pi\) | ||||
0.290355 | + | 0.956919i | \(0.406227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.6258 | −0.837302 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9725 | −0.507907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.27299 | −0.0431336 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.83360 | 0.231018 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.59553 | −0.256483 | −0.128241 | − | 0.991743i | \(-0.540933\pi\) | ||||
−0.128241 | + | 0.991743i | \(0.540933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.7040 | 0.764917 | 0.382459 | − | 0.923973i | \(-0.375077\pi\) | ||||
0.382459 | + | 0.923973i | \(0.375077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8704 | 1.07252 | 0.536262 | − | 0.844052i | \(-0.319836\pi\) | ||||
0.536262 | + | 0.844052i | \(0.319836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.3029 | −1.18535 | −0.592677 | − | 0.805440i | \(-0.701929\pi\) | ||||
−0.592677 | + | 0.805440i | \(0.701929\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.24903 | −0.0754300 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.0384 | −1.40676 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.0912 | −1.94177 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.02637 | 0.100935 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.3671 | −1.34482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49.8158 | 1.65593 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.1890 | −0.504344 | −0.252172 | − | 0.967682i | \(-0.581145\pi\) | ||||
−0.252172 | + | 0.967682i | \(0.581145\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.1138 | 1.46156 | 0.730778 | − | 0.682615i | \(-0.239157\pi\) | ||||
0.730778 | + | 0.682615i | \(0.239157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.87130 | −0.260502 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.9549 | −0.592922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1590 | −0.368100 | −0.184050 | − | 0.982917i | \(-0.558921\pi\) | ||||
−0.184050 | + | 0.982917i | \(0.558921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.322912 | −0.0106288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.24997 | 0.205498 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.0536799 | −0.00176118 | −0.000880591 | − | 1.00000i | \(-0.500280\pi\) | ||||
−0.000880591 | 1.00000i | \(0.500280\pi\) | ||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.24531 | −0.139134 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.7885 | −1.49744 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.275398 | −0.00899685 | −0.00449843 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449843 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.301768 | 0.00983734 | 0.00491867 | − | 0.999988i | \(-0.498434\pi\) | ||||
0.00491867 | + | 0.999988i | \(0.498434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.2953 | −0.726034 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.7859 | −1.26037 | −0.630186 | − | 0.776444i | \(-0.717021\pi\) | ||||
−0.630186 | + | 0.776444i | \(0.717021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.65568 | 0.118668 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.09396 | −0.262189 | −0.131094 | − | 0.991370i | \(-0.541849\pi\) | ||||
−0.131094 | + | 0.991370i | \(0.541849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 71.1484 | 2.30231 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.24531 | −0.266255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9736 | −0.902375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.9709 | 1.67300 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9475 | 0.416362 | 0.208181 | − | 0.978090i | \(-0.433246\pi\) | ||||
0.208181 | + | 0.978090i | \(0.433246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0886 | 1.41487 | 0.707435 | − | 0.706778i | \(-0.249852\pi\) | ||||
0.707435 | + | 0.706778i | \(0.249852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2865 | −0.393888 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.3365 | −0.970550 | −0.485275 | − | 0.874362i | \(-0.661281\pi\) | ||||
−0.485275 | + | 0.874362i | \(0.661281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.01152 | −0.128209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.95507 | 0.126147 | 0.0630735 | − | 0.998009i | \(-0.479910\pi\) | ||||
0.0630735 | + | 0.998009i | \(0.479910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.34670 | −0.202223 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.24028 | −0.293824 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0650 | 0.351491 | 0.175746 | − | 0.984436i | \(-0.443766\pi\) | ||||
0.175746 | + | 0.984436i | \(0.443766\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 58.6091 | 1.85803 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.1146 | −0.352002 | −0.176001 | − | 0.984390i | \(-0.556316\pi\) | ||||
−0.176001 | + | 0.984390i | \(0.556316\pi\) | |||||||
\(998\) | 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.bk.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 6048.2.a.bs.1.1 | yes | 4 | ||
4.3 | odd | 2 | 6048.2.a.bp.1.4 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bt.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bk.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bp.1.4 | yes | 4 | 4.3 | odd | 2 | ||
6048.2.a.bs.1.1 | yes | 4 | 3.2 | odd | 2 | ||
6048.2.a.bt.1.1 | yes | 4 | 12.11 | even | 2 |