Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1765.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.59024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.1841 | −1.03585 | −0.517923 | − | 0.855427i | \(-0.673295\pi\) | ||||
−0.517923 | + | 0.855427i | \(0.673295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.3867 | −0.503980 | −0.251990 | − | 0.967730i | \(-0.581085\pi\) | ||||
−0.251990 | + | 0.967730i | \(0.581085\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.0829 | 0.300453 | 0.150226 | − | 0.988652i | \(-0.452000\pi\) | ||||
0.150226 | + | 0.988652i | \(0.452000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 63.8746 | 0.911286 | 0.455643 | − | 0.890163i | \(-0.349409\pi\) | ||||
0.455643 | + | 0.890163i | \(0.349409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 101.409 | 1.22446 | 0.612230 | − | 0.790680i | \(-0.290273\pi\) | ||||
0.612230 | + | 0.790680i | \(0.290273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 155.528 | 1.40999 | 0.704997 | − | 0.709210i | \(-0.250948\pi\) | ||||
0.704997 | + | 0.709210i | \(0.250948\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.2428 | −0.372946 | −0.186473 | − | 0.982460i | \(-0.559706\pi\) | ||||
−0.186473 | + | 0.982460i | \(0.559706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.467 | 0.790653 | 0.395327 | − | 0.918541i | \(-0.370631\pi\) | ||||
0.395327 | + | 0.918541i | \(0.370631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 95.9207 | 0.463244 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −117.924 | −0.523962 | −0.261981 | − | 0.965073i | \(-0.584376\pi\) | ||||
−0.261981 | + | 0.965073i | \(0.584376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −276.802 | −1.05437 | −0.527186 | − | 0.849750i | \(-0.676753\pi\) | ||||
−0.527186 | + | 0.849750i | \(0.676753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −451.406 | −1.60090 | −0.800451 | − | 0.599398i | \(-0.795407\pi\) | ||||
−0.800451 | + | 0.599398i | \(0.795407\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −15.2922 | −0.0474596 | −0.0237298 | − | 0.999718i | \(-0.507554\pi\) | ||||
−0.0237298 | + | 0.999718i | \(0.507554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.0310 | 0.0729767 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −266.666 | −0.691121 | −0.345561 | − | 0.938396i | \(-0.612311\pi\) | ||||
−0.345561 | + | 0.938396i | \(0.612311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 91.9333 | 0.225387 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 585.668 | 1.29233 | 0.646165 | − | 0.763198i | \(-0.276372\pi\) | ||||
0.646165 | + | 0.763198i | \(0.276372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −392.105 | −0.823015 | −0.411507 | − | 0.911406i | \(-0.634998\pi\) | ||||
−0.411507 | + | 0.911406i | \(0.634998\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −70.4144 | −0.134367 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1031.46 | −1.88079 | −0.940393 | − | 0.340089i | \(-0.889543\pi\) | ||||
−0.940393 | + | 0.340089i | \(0.889543\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −657.723 | −1.09940 | −0.549700 | − | 0.835362i | \(-0.685258\pi\) | ||||
−0.549700 | + | 0.835362i | \(0.685258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 125.680 | 0.201503 | 0.100752 | − | 0.994912i | \(-0.467875\pi\) | ||||
0.100752 | + | 0.994912i | \(0.467875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 352.732 | 0.522046 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −962.698 | −1.37104 | −0.685519 | − | 0.728055i | \(-0.740424\pi\) | ||||
−0.685519 | + | 0.728055i | \(0.740424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 721.338 | 0.953942 | 0.476971 | − | 0.878919i | \(-0.341735\pi\) | ||||
0.476971 | + | 0.878919i | \(0.341735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −319.373 | −0.407539 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 122.234 | 0.145582 | 0.0727910 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727910 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −270.168 | −0.311223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −507.043 | −0.547595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 153.724 | 0.160910 | 0.0804552 | − | 0.996758i | \(-0.474363\pi\) | ||||
0.0804552 | + | 0.996758i | \(0.474363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −254.759 | −0.250985 | −0.125493 | − | 0.992095i | \(-0.540051\pi\) | ||||
−0.125493 | + | 0.992095i | \(0.540051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 729.969 | 0.698311 | 0.349155 | − | 0.937065i | \(-0.386469\pi\) | ||||
0.349155 | + | 0.937065i | \(0.386469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 516.799 | 0.466924 | 0.233462 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233462 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1040.20 | −0.914067 | −0.457034 | − | 0.889449i | \(-0.651088\pi\) | ||||
−0.457034 | + | 0.889449i | \(0.651088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1491.03 | −1.24128 | −0.620639 | − | 0.784096i | \(-0.713127\pi\) | ||||
−0.620639 | + | 0.784096i | \(0.713127\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −777.641 | −0.630569 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1225.38 | −0.943952 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −992.931 | −0.746004 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1272.29 | −0.888954 | −0.444477 | − | 0.895790i | \(-0.646610\pi\) | ||||
−0.444477 | + | 0.895790i | \(0.646610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 490.988 | 0.327464 | 0.163732 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163732 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1945.44 | −1.26835 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2295.08 | 1.43125 | 0.715627 | − | 0.698483i | \(-0.246141\pi\) | ||||
0.715627 | + | 0.698483i | \(0.246141\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1514.52 | 0.924173 | 0.462086 | − | 0.886835i | \(-0.347101\pi\) | ||||
0.462086 | + | 0.886835i | \(0.347101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −258.937 | −0.151422 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 291.214 | 0.166786 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −58.6349 | −0.0322386 | −0.0161193 | − | 0.999870i | \(-0.505131\pi\) | ||||
−0.0161193 | + | 0.999870i | \(0.505131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −354.303 | −0.190945 | −0.0954727 | − | 0.995432i | \(-0.530436\pi\) | ||||
−0.0954727 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −682.336 | −0.353591 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1515.71 | 0.770488 | 0.385244 | − | 0.922815i | \(-0.374117\pi\) | ||||
0.385244 | + | 0.922815i | \(0.374117\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2983.67 | −1.46054 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −998.554 | −0.479833 | −0.239916 | − | 0.970794i | \(-0.577120\pi\) | ||||
−0.239916 | + | 0.970794i | \(0.577120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3085.21 | 1.42958 | 0.714792 | − | 0.699337i | \(-0.246521\pi\) | ||||
0.714792 | + | 0.699337i | \(0.246521\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1998.67 | −0.909728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −911.357 | −0.400516 | −0.200258 | − | 0.979743i | \(-0.564178\pi\) | ||||
−0.200258 | + | 0.979743i | \(0.564178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −479.603 | −0.207169 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2443.08 | 1.02013 | 0.510067 | − | 0.860134i | \(-0.329620\pi\) | ||||
0.510067 | + | 0.860134i | \(0.329620\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3175.54 | −1.30407 | −0.652034 | − | 0.758190i | \(-0.726084\pi\) | ||||
−0.652034 | + | 0.758190i | \(0.726084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 589.620 | 0.234323 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1174.44 | −0.459270 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1335.56 | 0.505956 | 0.252978 | − | 0.967472i | \(-0.418590\pi\) | ||||
0.252978 | + | 0.967472i | \(0.418590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2041.12 | −0.761261 | −0.380630 | − | 0.924727i | \(-0.624293\pi\) | ||||
−0.380630 | + | 0.924727i | \(0.624293\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2565.55 | −0.927858 | −0.463929 | − | 0.885872i | \(-0.653561\pi\) | ||||
−0.463929 | + | 0.885872i | \(0.653561\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2650.29 | −0.944091 | −0.472046 | − | 0.881574i | \(-0.656484\pi\) | ||||
−0.472046 | + | 0.881574i | \(0.656484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1117.34 | 0.386314 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1384.01 | 0.471530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1864.56 | −0.617104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3078.89 | −1.00455 | −0.502274 | − | 0.864708i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864708i | \(0.667503\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2257.03 | 0.715946 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2618.01 | −0.818995 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 899.537 | 0.273798 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3855.41 | −1.15775 | −0.578873 | − | 0.815417i | \(-0.696507\pi\) | ||||
−0.578873 | + | 0.815417i | \(0.696507\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2003.70 | 0.585859 | 0.292929 | − | 0.956134i | \(-0.405370\pi\) | ||||
0.292929 | + | 0.956134i | \(0.405370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1861.72 | −0.537230 | −0.268615 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268615 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5152.83 | 1.44881 | 0.724406 | − | 0.689373i | \(-0.242114\pi\) | ||||
0.724406 | + | 0.689373i | \(0.242114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 76.4611 | 0.0212246 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2866.90 | −0.775919 | −0.387959 | − | 0.921676i | \(-0.626820\pi\) | ||||
−0.387959 | + | 0.921676i | \(0.626820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −336.196 | −0.0898600 | −0.0449300 | − | 0.998990i | \(-0.514306\pi\) | ||||
−0.0449300 | + | 0.998990i | \(0.514306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −125.155 | −0.0326362 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1428.12 | 0.367892 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1897.62 | 0.477198 | 0.238599 | − | 0.971118i | \(-0.423312\pi\) | ||||
0.238599 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2859.64 | −0.710610 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5125.56 | −1.24406 | −0.622030 | − | 0.782993i | \(-0.713692\pi\) | ||||
−0.622030 | + | 0.782993i | \(0.713692\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2262.27 | 0.542743 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −724.470 | −0.169858 | −0.0849291 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849291 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1333.33 | 0.309079 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8315.15 | −1.88470 | −0.942349 | − | 0.334632i | \(-0.891388\pi\) | ||||
−0.942349 | + | 0.334632i | \(0.891388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4207.73 | 0.943178 | 0.471589 | − | 0.881819i | \(-0.343681\pi\) | ||||
0.471589 | + | 0.881819i | \(0.343681\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −459.666 | −0.100796 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4105.54 | −0.890534 | −0.445267 | − | 0.895398i | \(-0.646891\pi\) | ||||
−0.445267 | + | 0.895398i | \(0.646891\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5166.52 | −1.09683 | −0.548414 | − | 0.836207i | \(-0.684768\pi\) | ||||
−0.548414 | + | 0.836207i | \(0.684768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5575.42 | 1.17111 | 0.585556 | − | 0.810632i | \(-0.300876\pi\) | ||||
0.585556 | + | 0.810632i | \(0.300876\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5310.21 | 1.09217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −833.039 | −0.169558 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8071.59 | −1.60938 | −0.804689 | − | 0.593697i | \(-0.797668\pi\) | ||||
−0.804689 | + | 0.593697i | \(0.797668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2928.34 | −0.577947 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2190.28 | 0.423637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8659.84 | 1.65829 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1960.53 | 0.368063 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3972.33 | −0.738478 | −0.369239 | − | 0.929335i | \(-0.620382\pi\) | ||||
−0.369239 | + | 0.929335i | \(0.620382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4668.82 | 0.851269 | 0.425634 | − | 0.904895i | \(-0.360051\pi\) | ||||
0.425634 | + | 0.904895i | \(0.360051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3161.61 | 0.570941 | 0.285470 | − | 0.958388i | \(-0.407850\pi\) | ||||
0.285470 | + | 0.958388i | \(0.407850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 91.1973 | 0.0161582 | 0.00807910 | − | 0.999967i | \(-0.497428\pi\) | ||||
0.00807910 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1070.89 | 0.187957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6477.43 | 1.11583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 352.072 | 0.0600906 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 293.368 | 0.0491608 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7496.53 | −1.24485 | −0.622426 | − | 0.782678i | \(-0.713853\pi\) | ||||
−0.622426 | + | 0.782678i | \(0.713853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5157.29 | 0.841113 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11689.4 | 1.88949 | 0.944747 | − | 0.327799i | \(-0.106307\pi\) | ||||
0.944747 | + | 0.327799i | \(0.106307\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2509.18 | −0.398474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6099.96 | 0.960253 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3958.51 | 0.612403 | 0.306202 | − | 0.951967i | \(-0.400942\pi\) | ||||
0.306202 | + | 0.951967i | \(0.400942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5997.04 | −0.919811 | −0.459906 | − | 0.887968i | \(-0.652117\pi\) | ||||
−0.459906 | + | 0.887968i | \(0.652117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8029.56 | −1.21068 | −0.605340 | − | 0.795967i | \(-0.706963\pi\) | ||||
−0.605340 | + | 0.795967i | \(0.706963\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3288.62 | 0.491667 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5454.65 | −0.801909 | −0.400955 | − | 0.916098i | \(-0.631322\pi\) | ||||
−0.400955 | + | 0.916098i | \(0.631322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3424.70 | 0.499300 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −628.401 | −0.0901151 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3946.72 | −0.561354 | −0.280677 | − | 0.959802i | \(-0.590559\pi\) | ||||
−0.280677 | + | 0.959802i | \(0.590559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5115.76 | 0.715895 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2114.12 | 0.293472 | 0.146736 | − | 0.989176i | \(-0.453123\pi\) | ||||
0.146736 | + | 0.989176i | \(0.453123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −820.227 | −0.112053 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 426.559 | 0.0578123 | 0.0289062 | − | 0.999582i | \(-0.490798\pi\) | ||||
0.0289062 | + | 0.999582i | \(0.490798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10172.3 | −1.35713 | −0.678565 | − | 0.734541i | \(-0.737398\pi\) | ||||
−0.678565 | + | 0.734541i | \(0.737398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1763.66 | −0.233466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3696.72 | −0.481828 | −0.240914 | − | 0.970546i | \(-0.577447\pi\) | ||||
−0.240914 | + | 0.970546i | \(0.577447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9934.30 | 1.28491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4813.49 | 0.613146 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10586.5 | 1.33834 | 0.669169 | − | 0.743110i | \(-0.266650\pi\) | ||||
0.669169 | + | 0.743110i | \(0.266650\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14940.5 | 1.86058 | 0.930292 | − | 0.366821i | \(-0.119554\pi\) | ||||
0.930292 | + | 0.366821i | \(0.119554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1921.85 | 0.237554 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2168.23 | 0.264066 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14189.2 | 1.71544 | 0.857718 | − | 0.514121i | \(-0.171882\pi\) | ||||
0.857718 | + | 0.514121i | \(0.171882\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11235.5 | −1.33865 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3606.69 | −0.426616 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5880.89 | −0.685681 | −0.342840 | − | 0.939394i | \(-0.611389\pi\) | ||||
−0.342840 | + | 0.939394i | \(0.611389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7490.46 | −0.867133 | −0.433566 | − | 0.901122i | \(-0.642745\pi\) | ||||
−0.433566 | + | 0.901122i | \(0.642745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1596.86 | 0.182257 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7522.20 | 0.852517 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4049.42 | 0.452561 | 0.226281 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226281 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6088.93 | −0.675785 | −0.337893 | − | 0.941185i | \(-0.609714\pi\) | ||||
−0.337893 | + | 0.941185i | \(0.609714\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15771.9 | 1.72648 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3087.19 | −0.335634 | −0.167817 | − | 0.985818i | \(-0.553672\pi\) | ||||
−0.167817 | + | 0.985818i | \(0.553672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2650.74 | −0.284290 | −0.142145 | − | 0.989846i | \(-0.545400\pi\) | ||||
−0.142145 | + | 0.989846i | \(0.545400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −611.171 | −0.0651062 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10985.3 | −1.15463 | −0.577316 | − | 0.816521i | \(-0.695900\pi\) | ||||
−0.577316 | + | 0.816521i | \(0.695900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5089.47 | 0.531383 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1350.84 | 0.139183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12928.5 | −1.32335 | −0.661674 | − | 0.749792i | \(-0.730154\pi\) | ||||
−0.661674 | + | 0.749792i | \(0.730154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 664.298 | 0.0671138 | 0.0335569 | − | 0.999437i | \(-0.489317\pi\) | ||||
0.0335569 | + | 0.999437i | \(0.489317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8395.26 | 0.842680 | 0.421340 | − | 0.906903i | \(-0.361560\pi\) | ||||
0.421340 | + | 0.906903i | \(0.361560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3022.18 | 0.299464 | 0.149732 | − | 0.988727i | \(-0.452159\pi\) | ||||
0.149732 | + | 0.988727i | \(0.452159\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19787.6 | 1.94820 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8299.85 | 0.806824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2535.21 | 0.244892 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5507.36 | 0.525339 | 0.262670 | − | 0.964886i | \(-0.415397\pi\) | ||||
0.262670 | + | 0.964886i | \(0.415397\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1660.71 | −0.157426 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −768.620 | −0.0719613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2170.87 | 0.201995 | 0.100998 | − | 0.994887i | \(-0.467797\pi\) | ||||
0.100998 | + | 0.994887i | \(0.467797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14007.5 | −1.28747 | −0.643735 | − | 0.765248i | \(-0.722616\pi\) | ||||
−0.643735 | + | 0.765248i | \(0.722616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3720.24 | −0.339860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12617.9 | 1.13881 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9227.59 | 0.827823 | 0.413911 | − | 0.910317i | \(-0.364162\pi\) | ||||
0.413911 | + | 0.910317i | \(0.364162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17747.2 | 1.57318 | 0.786591 | − | 0.617475i | \(-0.211844\pi\) | ||||
0.786591 | + | 0.617475i | \(0.211844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1273.80 | 0.112244 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15368.2 | −1.33828 | −0.669140 | − | 0.743137i | \(-0.733337\pi\) | ||||
−0.669140 | + | 0.743137i | \(0.733337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2411.07 | −0.208727 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3649.85 | −0.312294 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 281.173 | 0.0239187 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3932.31 | −0.330667 | −0.165333 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165333 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2709.21 | −0.226511 | −0.113256 | − | 0.993566i | \(-0.536128\pi\) | ||||
−0.113256 | + | 0.993566i | \(0.536128\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8716.79 | 0.720511 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12022.0 | 0.988085 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3898.17 | −0.316789 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2584.00 | −0.208815 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −460.236 | −0.0367788 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14223.8 | −1.13036 | −0.565182 | − | 0.824966i | \(-0.691194\pi\) | ||||
−0.565182 | + | 0.824966i | \(0.691194\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5201.01 | 0.408783 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11158.6 | 0.872222 | 0.436111 | − | 0.899893i | \(-0.356356\pi\) | ||||
0.436111 | + | 0.899893i | \(0.356356\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5906.32 | −0.456657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18468.5 | 1.42018 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11127.4 | −0.846472 | −0.423236 | − | 0.906019i | \(-0.639106\pi\) | ||||
−0.423236 | + | 0.906019i | \(0.639106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6357.10 | −0.480996 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15868.5 | −1.18788 | −0.593941 | − | 0.804508i | \(-0.702429\pi\) | ||||
−0.593941 | + | 0.804508i | \(0.702429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7455.16 | 0.555117 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12406.3 | −0.914061 | −0.457030 | − | 0.889451i | \(-0.651087\pi\) | ||||
−0.457030 | + | 0.889451i | \(0.651087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21374.3 | 1.56652 | 0.783262 | − | 0.621692i | \(-0.213554\pi\) | ||||
0.783262 | + | 0.621692i | \(0.213554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3888.21 | 0.281999 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8980.90 | 0.647972 | 0.323986 | − | 0.946062i | \(-0.394977\pi\) | ||||
0.323986 | + | 0.946062i | \(0.394977\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13838.3 | −0.988137 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4903.10 | 0.348312 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18682.7 | 1.31366 | 0.656829 | − | 0.754039i | \(-0.271897\pi\) | ||||
0.656829 | + | 0.754039i | \(0.271897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13839.0 | 0.968123 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1890.65 | −0.130927 | −0.0654634 | − | 0.997855i | \(-0.520853\pi\) | ||||
−0.0654634 | + | 0.997855i | \(0.520853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6126.89 | 0.422148 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −482.005 | −0.0328784 | −0.0164392 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164392 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16119.3 | 1.09404 | 0.547020 | − | 0.837120i | \(-0.315762\pi\) | ||||
0.547020 | + | 0.837120i | \(0.315762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4964.65 | 0.333623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10459.0 | 0.699368 | 0.349684 | − | 0.936868i | \(-0.386289\pi\) | ||||
0.349684 | + | 0.936868i | \(0.386289\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −215.358 | −0.0142594 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10833.9 | 0.713826 | 0.356913 | − | 0.934138i | \(-0.383829\pi\) | ||||
0.356913 | + | 0.934138i | \(0.383829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27174.2 | 1.77308 | 0.886540 | − | 0.462652i | \(-0.153102\pi\) | ||||
0.886540 | + | 0.462652i | \(0.153102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27200.7 | −1.76622 | −0.883109 | − | 0.469169i | \(-0.844554\pi\) | ||||
−0.883109 | + | 0.469169i | \(0.844554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2344.96 | −0.150800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7532.34 | −0.477479 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15341.6 | 0.967890 | 0.483945 | − | 0.875098i | \(-0.339204\pi\) | ||||
0.483945 | + | 0.875098i | \(0.339204\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6361.43 | 0.397552 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 352.508 | 0.0219260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22072.0 | −1.36005 | −0.680024 | − | 0.733190i | \(-0.738030\pi\) | ||||
−0.680024 | + | 0.733190i | \(0.738030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14931.1 | 0.915746 | 0.457873 | − | 0.889018i | \(-0.348611\pi\) | ||||
0.457873 | + | 0.889018i | \(0.348611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22095.3 | 1.34259 | 0.671297 | − | 0.741189i | \(-0.265738\pi\) | ||||
0.671297 | + | 0.741189i | \(0.265738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10768.5 | −0.651309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3457.94 | 0.207228 | 0.103614 | − | 0.994618i | \(-0.466959\pi\) | ||||
0.103614 | + | 0.994618i | \(0.466959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2454.94 | −0.146446 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16748.0 | −0.990001 | −0.495001 | − | 0.868893i | \(-0.664832\pi\) | ||||
−0.495001 | + | 0.868893i | \(0.664832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12355.4 | 0.727031 | 0.363516 | − | 0.931588i | \(-0.381576\pi\) | ||||
0.363516 | + | 0.931588i | \(0.381576\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9727.18 | 0.567224 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9058.41 | −0.525851 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7209.50 | 0.414783 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33472.3 | −1.91718 | −0.958589 | − | 0.284793i | \(-0.908075\pi\) | ||||
−0.958589 | + | 0.284793i | \(0.908075\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27977.0 | 1.58825 | 0.794124 | − | 0.607756i | \(-0.207930\pi\) | ||||
0.794124 | + | 0.607756i | \(0.207930\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2949.06 | −0.166678 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17231.4 | −0.965361 | −0.482681 | − | 0.875796i | \(-0.660337\pi\) | ||||
−0.482681 | + | 0.875796i | \(0.660337\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11475.4 | −0.640076 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3755.43 | −0.207649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15600.0 | −0.858832 | −0.429416 | − | 0.903107i | \(-0.641281\pi\) | ||||
−0.429416 | + | 0.903107i | \(0.641281\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7572.61 | −0.413303 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17680.6 | −0.960834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27816.5 | −1.49874 | −0.749369 | − | 0.662153i | \(-0.769643\pi\) | ||||
−0.749369 | + | 0.662153i | \(0.769643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11958.5 | −0.641570 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4887.34 | 0.259982 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12257.3 | −0.649269 | −0.324634 | − | 0.945840i | \(-0.605241\pi\) | ||||
−0.324634 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21224.5 | 1.11482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1294.68 | 0.0677181 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21906.3 | −1.13625 | −0.568127 | − | 0.822941i | \(-0.692332\pi\) | ||||
−0.568127 | + | 0.822941i | \(0.692332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14003.8 | −0.723342 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1456.07 | −0.0745891 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33924.8 | 1.73067 | 0.865337 | − | 0.501190i | \(-0.167104\pi\) | ||||
0.865337 | + | 0.501190i | \(0.167104\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28833.4 | −1.45888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2784.84 | −0.140328 | −0.0701639 | − | 0.997535i | \(-0.522352\pi\) | ||||
−0.0701639 | + | 0.997535i | \(0.522352\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18965.1 | 0.947880 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27327.4 | −1.36029 | −0.680144 | − | 0.733078i | \(-0.738083\pi\) | ||||
−0.680144 | + | 0.733078i | \(0.738083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4088.32 | −0.201865 | −0.100933 | − | 0.994893i | \(-0.532183\pi\) | ||||
−0.100933 | + | 0.994893i | \(0.532183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 293.175 | 0.0144176 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9914.34 | −0.483661 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3058.73 | 0.148622 | 0.0743108 | − | 0.997235i | \(-0.476324\pi\) | ||||
0.0743108 | + | 0.997235i | \(0.476324\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1771.51 | 0.0853934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19443.0 | −0.933510 | −0.466755 | − | 0.884387i | \(-0.654577\pi\) | ||||
−0.466755 | + | 0.884387i | \(0.654577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20461.5 | 0.974677 | 0.487338 | − | 0.873213i | \(-0.337968\pi\) | ||||
0.487338 | + | 0.873213i | \(0.337968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19955.4 | 0.946833 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8247.89 | 0.388284 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6375.33 | 0.298960 | 0.149480 | − | 0.988765i | \(-0.452240\pi\) | ||||
0.149480 | + | 0.988765i | \(0.452240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40557.7 | −1.88714 | −0.943569 | − | 0.331177i | \(-0.892554\pi\) | ||||
−0.943569 | + | 0.331177i | \(0.892554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3411.68 | 0.158131 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28070.1 | −1.29104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12093.3 | 0.554076 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7578.53 | −0.344573 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12638.6 | −0.572449 | −0.286225 | − | 0.958163i | \(-0.592400\pi\) | ||||
−0.286225 | + | 0.958163i | \(0.592400\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28604.2 | 1.28577 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5521.97 | −0.247277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6002.79 | 0.266787 | 0.133394 | − | 0.991063i | \(-0.457413\pi\) | ||||
0.133394 | + | 0.991063i | \(0.457413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −976.784 | −0.0432492 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2310.84 | −0.101554 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14918.4 | 0.653172 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22138.8 | 0.962123 | 0.481061 | − | 0.876687i | \(-0.340251\pi\) | ||||
0.481061 | + | 0.876687i | \(0.340251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36472.9 | −1.57921 | −0.789604 | − | 0.613617i | \(-0.789714\pi\) | ||||
−0.789604 | + | 0.613617i | \(0.789714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4992.77 | 0.214588 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45776.5 | −1.96024 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28561.5 | 1.21413 | 0.607065 | − | 0.794652i | \(-0.292347\pi\) | ||||
0.607065 | + | 0.794652i | \(0.292347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40572.2 | −1.71842 | −0.859209 | − | 0.511624i | \(-0.829044\pi\) | ||||
−0.859209 | + | 0.511624i | \(0.829044\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45659.5 | 1.91987 | 0.959937 | − | 0.280215i | \(-0.0904057\pi\) | ||||
0.959937 | + | 0.280215i | \(0.0904057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29623.2 | 1.24108 | 0.620540 | − | 0.784175i | \(-0.286913\pi\) | ||||
0.620540 | + | 0.784175i | \(0.286913\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1598.84 | 0.0665026 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15426.0 | −0.639329 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17564.0 | −0.722738 | −0.361369 | − | 0.932423i | \(-0.617691\pi\) | ||||
−0.361369 | + | 0.932423i | \(0.617691\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20996.8 | −0.860912 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9993.36 | 0.406843 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19048.5 | 0.772745 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18340.5 | −0.738783 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15867.2 | −0.636910 | −0.318455 | − | 0.947938i | \(-0.603164\pi\) | ||||
−0.318455 | + | 0.947938i | \(0.603164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46932.9 | 1.87071 | 0.935354 | − | 0.353714i | \(-0.115081\pi\) | ||||
0.935354 | + | 0.353714i | \(0.115081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24569.7 | −0.975910 | −0.487955 | − | 0.872869i | \(-0.662257\pi\) | ||||
−0.487955 | + | 0.872869i | \(0.662257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24918.5 | −0.982891 | −0.491445 | − | 0.870908i | \(-0.663531\pi\) | ||||
−0.491445 | + | 0.870908i | \(0.663531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4556.79 | 0.179116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17700.8 | 0.690976 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14525.9 | −0.565088 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2398.02 | 0.0926489 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17022.5 | 0.655426 | 0.327713 | − | 0.944777i | \(-0.393722\pi\) | ||||
0.327713 | + | 0.944777i | \(0.393722\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41291.8 | 1.57906 | 0.789532 | − | 0.613710i | \(-0.210323\pi\) | ||||
0.789532 | + | 0.613710i | \(0.210323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42280.0 | 1.61136 | 0.805682 | − | 0.592348i | \(-0.201799\pi\) | ||||
0.805682 | + | 0.592348i | \(0.201799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39376.4 | −1.49056 | −0.745282 | − | 0.666750i | \(-0.767685\pi\) | ||||
−0.745282 | + | 0.666750i | \(0.767685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24407.7 | 0.920819 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1550.76 | −0.0581123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12215.4 | −0.456218 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7948.24 | −0.294871 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17033.2 | −0.629809 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15877.7 | 0.583197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20198.4 | −0.739445 | −0.369722 | − | 0.929142i | \(-0.620547\pi\) | ||||
−0.369722 | + | 0.929142i | \(0.620547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51503.4 | −1.87309 | −0.936544 | − | 0.350551i | \(-0.885994\pi\) | ||||
−0.936544 | + | 0.350551i | \(0.885994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13263.0 | −0.480768 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9419.17 | −0.339202 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15219.5 | −0.546295 | −0.273147 | − | 0.961972i | \(-0.588065\pi\) | ||||
−0.273147 | + | 0.961972i | \(0.588065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9262.63 | −0.330318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2948.10 | −0.104792 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34214.8 | 1.20834 | 0.604172 | − | 0.796854i | \(-0.293504\pi\) | ||||
0.604172 | + | 0.796854i | \(0.293504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2538.36 | 0.0893569 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5872.20 | 0.205392 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9712.23 | 0.338618 | 0.169309 | − | 0.985563i | \(-0.445846\pi\) | ||||
0.169309 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36714.3 | −1.27189 | −0.635947 | − | 0.771733i | \(-0.719390\pi\) | ||||
−0.635947 | + | 0.771733i | \(0.719390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43050.6 | −1.48666 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43936.5 | 1.50765 | 0.753825 | − | 0.657076i | \(-0.228207\pi\) | ||||
0.753825 | + | 0.657076i | \(0.228207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1769.94 | 0.0605423 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15138.8 | −0.514579 | −0.257290 | − | 0.966334i | \(-0.582829\pi\) | ||||
−0.257290 | + | 0.966334i | \(0.582829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6677.79 | −0.226270 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44029.1 | −1.48256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11167.7 | −0.374868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10205.6 | 0.340446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8364.88 | −0.278176 | −0.139088 | − | 0.990280i | \(-0.544417\pi\) | ||||
−0.139088 | + | 0.990280i | \(0.544417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27702.4 | 0.915562 | 0.457781 | − | 0.889065i | \(-0.348644\pi\) | ||||
0.457781 | + | 0.889065i | \(0.348644\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29054.8 | −0.957301 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45969.7 | 1.50532 | 0.752662 | − | 0.658408i | \(-0.228770\pi\) | ||||
0.752662 | + | 0.658408i | \(0.228770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2247.48 | −0.0733705 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34555.2 | −1.12120 | −0.560601 | − | 0.828086i | \(-0.689430\pi\) | ||||
−0.560601 | + | 0.828086i | \(0.689430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12827.8 | 0.414951 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70206.4 | −2.25726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28800.3 | 0.923181 | 0.461591 | − | 0.887093i | \(-0.347279\pi\) | ||||
0.461591 | + | 0.887093i | \(0.347279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13251.5 | 0.422210 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3103.42 | 0.0985819 | 0.0492910 | − | 0.998784i | \(-0.484304\pi\) | ||||
0.0492910 | + | 0.998784i | \(0.484304\pi\) | |||||||
\(998\) | 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 | 1080.4.a.f.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.l.1.1 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bh.1.3 | 3 | |||
12.11 | even | 2 | 2160.4.a.bp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.l.1.1 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bh.1.3 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bp.1.3 | 3 | 12.11 | even | 2 |