Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.986764 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.0000 | −1.32275 | −0.661373 | − | 0.750057i | \(-0.730026\pi\) | ||||
−0.661373 | + | 0.750057i | \(0.730026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 18.0000 | 0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 114.000 | 1.62642 | 0.813208 | − | 0.581974i | \(-0.197719\pi\) | ||||
0.813208 | + | 0.581974i | \(0.197719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.0000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.0000 | 0.217580 | 0.108790 | − | 0.994065i | \(-0.465302\pi\) | ||||
0.108790 | + | 0.994065i | \(0.465302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −54.0000 | −0.345778 | −0.172889 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172889 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 112.000 | 0.648897 | 0.324448 | − | 0.945903i | \(-0.394821\pi\) | ||||
0.324448 | + | 0.945903i | \(0.394821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −108.000 | −0.569709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.0000 | 0.202837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 178.000 | 0.790892 | 0.395446 | − | 0.918489i | \(-0.370590\pi\) | ||||
0.395446 | + | 0.918489i | \(0.370590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 186.000 | 0.763688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 378.000 | 1.43985 | 0.719923 | − | 0.694054i | \(-0.244177\pi\) | ||||
0.719923 | + | 0.694054i | \(0.244177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −172.000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54.0000 | −0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 192.000 | 0.595874 | 0.297937 | − | 0.954586i | \(-0.403701\pi\) | ||||
0.297937 | + | 0.954586i | \(0.403701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −342.000 | −0.939011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 402.000 | 1.04187 | 0.520933 | − | 0.853597i | \(-0.325584\pi\) | ||||
0.520933 | + | 0.853597i | \(0.325584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −216.000 | −0.529553 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 396.000 | 0.873810 | 0.436905 | − | 0.899508i | \(-0.356075\pi\) | ||||
0.436905 | + | 0.899508i | \(0.356075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −254.000 | −0.533137 | −0.266569 | − | 0.963816i | \(-0.585890\pi\) | ||||
−0.266569 | + | 0.963816i | \(0.585890\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 372.000 | 0.709860 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1012.00 | −1.84531 | −0.922653 | − | 0.385632i | \(-0.873984\pi\) | ||||
−0.922653 | + | 0.385632i | \(0.873984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −72.0000 | −0.125620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −840.000 | −1.40408 | −0.702040 | − | 0.712138i | \(-0.747727\pi\) | ||||
−0.702040 | + | 0.712138i | \(0.747727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 890.000 | 1.42694 | 0.713470 | − | 0.700686i | \(-0.247122\pi\) | ||||
0.713470 | + | 0.700686i | \(0.247122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −252.000 | −0.372962 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −80.0000 | −0.113933 | −0.0569665 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569665 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −108.000 | −0.142826 | −0.0714129 | − | 0.997447i | \(-0.522751\pi\) | ||||
−0.0714129 | + | 0.997447i | \(0.522751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −684.000 | −0.872826 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 162.000 | 0.199635 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1638.00 | −1.95087 | −0.975436 | − | 0.220282i | \(-0.929302\pi\) | ||||
−0.975436 | + | 0.220282i | \(0.929302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 434.000 | 0.499951 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −336.000 | −0.374641 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 456.000 | 0.492470 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1010.00 | 1.05722 | 0.528608 | − | 0.848866i | \(-0.322714\pi\) | ||||
0.528608 | + | 0.848866i | \(0.322714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 324.000 | 0.328921 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.00591111 | −0.00295556 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295556 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 472.000 | 0.451530 | 0.225765 | − | 0.974182i | \(-0.427512\pi\) | ||||
0.225765 | + | 0.974182i | \(0.427512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −126.000 | −0.117108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −972.000 | −0.878194 | −0.439097 | − | 0.898440i | \(-0.644702\pi\) | ||||
−0.439097 | + | 0.898440i | \(0.644702\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1786.00 | 1.56943 | 0.784715 | − | 0.619857i | \(-0.212810\pi\) | ||||
0.784715 | + | 0.619857i | \(0.212810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −534.000 | −0.456622 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2286.00 | −1.90309 | −0.951543 | − | 0.307515i | \(-0.900503\pi\) | ||||
−0.951543 | + | 0.307515i | \(0.900503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −144.000 | −0.116766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −558.000 | −0.440916 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −798.000 | −0.614727 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0000 | −0.0262960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1134.00 | −0.831295 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1328.00 | −0.927881 | −0.463941 | − | 0.885866i | \(-0.653565\pi\) | ||||
−0.463941 | + | 0.885866i | \(0.653565\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 516.000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1212.00 | −0.808343 | −0.404171 | − | 0.914683i | \(-0.632440\pi\) | ||||
−0.404171 | + | 0.914683i | \(0.632440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 532.000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 162.000 | 0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1254.00 | −0.782018 | −0.391009 | − | 0.920387i | \(-0.627874\pi\) | ||||
−0.391009 | + | 0.920387i | \(0.627874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −340.000 | −0.207471 | −0.103735 | − | 0.994605i | \(-0.533079\pi\) | ||||
−0.103735 | + | 0.994605i | \(0.533079\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −576.000 | −0.344028 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2232.00 | −1.30524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 324.000 | 0.185564 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1038.00 | −0.570713 | −0.285357 | − | 0.958421i | \(-0.592112\pi\) | ||||
−0.285357 | + | 0.958421i | \(0.592112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2936.00 | −1.58231 | −0.791153 | − | 0.611618i | \(-0.790519\pi\) | ||||
−0.791153 | + | 0.611618i | \(0.790519\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1026.00 | 0.542138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −672.000 | −0.348234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1330.00 | 0.676086 | 0.338043 | − | 0.941131i | \(-0.390235\pi\) | ||||
0.338043 | + | 0.941131i | \(0.390235\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1206.00 | −0.601522 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −168.000 | −0.0822376 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3364.00 | −1.61650 | −0.808248 | − | 0.588842i | \(-0.799584\pi\) | ||||
−0.808248 | + | 0.588842i | \(0.799584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 648.000 | 0.305738 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3048.00 | −1.41234 | −0.706172 | − | 0.708041i | \(-0.749579\pi\) | ||||
−0.706172 | + | 0.708041i | \(0.749579\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −684.000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2706.00 | 1.18921 | 0.594605 | − | 0.804018i | \(-0.297308\pi\) | ||||
0.594605 | + | 0.804018i | \(0.297308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 623.000 | 0.269111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1188.00 | −0.504495 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4716.00 | 1.96922 | 0.984610 | − | 0.174766i | \(-0.0559168\pi\) | ||||
0.984610 | + | 0.174766i | \(0.0559168\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1910.00 | −0.784360 | −0.392180 | − | 0.919888i | \(-0.628279\pi\) | ||||
−0.392180 | + | 0.919888i | \(0.628279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 762.000 | 0.307807 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1068.00 | −0.424437 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4104.00 | 1.60489 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4080.00 | −1.54565 | −0.772823 | − | 0.634621i | \(-0.781156\pi\) | ||||
−0.772823 | + | 0.634621i | \(0.781156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2686.00 | −1.00177 | −0.500887 | − | 0.865512i | \(-0.666993\pi\) | ||||
−0.500887 | + | 0.865512i | \(0.666993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1116.00 | −0.409838 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −510.000 | −0.184447 | −0.0922233 | − | 0.995738i | \(-0.529397\pi\) | ||||
−0.0922233 | + | 0.995738i | \(0.529397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1352.00 | −0.481612 | −0.240806 | − | 0.970573i | \(-0.577412\pi\) | ||||
−0.240806 | + | 0.970573i | \(0.577412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3036.00 | 1.06539 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 378.000 | 0.130692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2268.00 | −0.772702 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 216.000 | 0.0725268 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2736.00 | −0.905517 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3364.00 | −1.09757 | −0.548785 | − | 0.835963i | \(-0.684909\pi\) | ||||
−0.548785 | + | 0.835963i | \(0.684909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2520.00 | 0.810646 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1032.00 | 0.327357 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −784.000 | −0.245260 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2670.00 | −0.823844 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7068.00 | −2.15134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4768.00 | 1.43179 | 0.715894 | − | 0.698209i | \(-0.246019\pi\) | ||||
0.715894 | + | 0.698209i | \(0.246019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 420.000 | 0.122803 | 0.0614017 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614017 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1882.00 | 0.543083 | 0.271542 | − | 0.962427i | \(-0.412467\pi\) | ||||
0.271542 | + | 0.962427i | \(0.412467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 756.000 | 0.215330 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5082.00 | 1.42890 | 0.714448 | − | 0.699688i | \(-0.246678\pi\) | ||||
0.714448 | + | 0.699688i | \(0.246678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1152.00 | −0.319780 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 240.000 | 0.0657792 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5424.00 | 1.46799 | 0.733995 | − | 0.679155i | \(-0.237654\pi\) | ||||
0.733995 | + | 0.679155i | \(0.237654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2590.00 | −0.692268 | −0.346134 | − | 0.938185i | \(-0.612506\pi\) | ||||
−0.346134 | + | 0.938185i | \(0.612506\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −294.000 | −0.0766652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4712.00 | 1.21384 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 324.000 | 0.0824605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4932.00 | −1.24026 | −0.620130 | − | 0.784499i | \(-0.712920\pi\) | ||||
−0.620130 | + | 0.784499i | \(0.712920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 864.000 | 0.214700 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2052.00 | 0.503926 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3438.00 | −0.834461 | −0.417231 | − | 0.908801i | \(-0.636999\pi\) | ||||
−0.417231 | + | 0.908801i | \(0.636999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1246.00 | −0.298929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −486.000 | −0.115259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6120.00 | −1.43489 | −0.717444 | − | 0.696617i | \(-0.754688\pi\) | ||||
−0.717444 | + | 0.696617i | \(0.754688\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2412.00 | −0.559124 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4914.00 | 1.12634 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000 | 0.00407985 | 0.00203992 | − | 0.999998i | \(-0.499351\pi\) | ||||
0.00203992 | + | 0.999998i | \(0.499351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6896.00 | −1.54576 | −0.772882 | − | 0.634549i | \(-0.781186\pi\) | ||||
−0.772882 | + | 0.634549i | \(0.781186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1302.00 | −0.288647 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3204.00 | −0.702576 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6254.00 | −1.35656 | −0.678279 | − | 0.734805i | \(-0.737274\pi\) | ||||
−0.678279 | + | 0.734805i | \(0.737274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1008.00 | 0.216299 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1194.00 | 0.253481 | 0.126740 | − | 0.991936i | \(-0.459549\pi\) | ||||
0.126740 | + | 0.991936i | \(0.459549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7156.00 | −1.50311 | −0.751555 | − | 0.659671i | \(-0.770696\pi\) | ||||
−0.751555 | + | 0.659671i | \(0.770696\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1368.00 | −0.284327 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2646.00 | −0.544211 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8083.00 | 1.64523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3030.00 | −0.610384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3738.00 | 0.745312 | 0.372656 | − | 0.927970i | \(-0.378447\pi\) | ||||
0.372656 | + | 0.927970i | \(0.378447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2376.00 | −0.468936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −972.000 | −0.189903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1488.00 | −0.287804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1204.00 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.0000 | 0.00341278 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1524.00 | 0.286111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −844.000 | −0.156904 | −0.0784522 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784522 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1416.00 | −0.260691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6312.00 | −1.15087 | −0.575435 | − | 0.817847i | \(-0.695167\pi\) | ||||
−0.575435 | + | 0.817847i | \(0.695167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8282.00 | 1.49561 | 0.747806 | − | 0.663918i | \(-0.231108\pi\) | ||||
0.747806 | + | 0.663918i | \(0.231108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 378.000 | 0.0676123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9318.00 | −1.65095 | −0.825475 | − | 0.564439i | \(-0.809093\pi\) | ||||
−0.825475 | + | 0.564439i | \(0.809093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1944.00 | −0.341201 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2916.00 | 0.507026 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8664.00 | −1.49250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5518.00 | 0.941796 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5358.00 | −0.906110 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1344.00 | −0.225219 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1652.00 | 0.274327 | 0.137163 | − | 0.990548i | \(-0.456201\pi\) | ||||
0.137163 | + | 0.990548i | \(0.456201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1602.00 | 0.263631 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6072.00 | 0.990295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1294.00 | −0.209165 | −0.104583 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104583 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6858.00 | 1.09875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4032.00 | 0.640308 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 432.000 | 0.0674148 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3636.00 | 0.562509 | 0.281255 | − | 0.959633i | \(-0.409249\pi\) | ||||
0.281255 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10478.0 | −1.60709 | −0.803545 | − | 0.595244i | \(-0.797055\pi\) | ||||
−0.803545 | + | 0.595244i | \(0.797055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1674.00 | 0.254563 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7566.00 | −1.14079 | −0.570393 | − | 0.821372i | \(-0.693209\pi\) | ||||
−0.570393 | + | 0.821372i | \(0.693209\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5040.00 | 0.753508 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2394.00 | 0.354913 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8040.00 | 1.18199 | 0.590996 | − | 0.806675i | \(-0.298735\pi\) | ||||
0.590996 | + | 0.806675i | \(0.298735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1083.00 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 105.000 | 0.0151820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5340.00 | −0.765776 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7568.00 | −1.07642 | −0.538210 | − | 0.842811i | \(-0.680899\pi\) | ||||
−0.538210 | + | 0.842811i | \(0.680899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3402.00 | 0.479949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2814.00 | −0.393789 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13522.0 | 1.87706 | 0.938529 | − | 0.345200i | \(-0.112189\pi\) | ||||
0.938529 | + | 0.345200i | \(0.112189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3852.00 | −0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3348.00 | 0.457376 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2468.00 | 0.334492 | 0.167246 | − | 0.985915i | \(-0.446513\pi\) | ||||
0.167246 | + | 0.985915i | \(0.446513\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3984.00 | 0.535713 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12336.0 | 1.64580 | 0.822898 | − | 0.568189i | \(-0.192356\pi\) | ||||
0.822898 | + | 0.568189i | \(0.192356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1512.00 | 0.200152 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1548.00 | −0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3762.00 | 0.490337 | 0.245168 | − | 0.969481i | \(-0.421157\pi\) | ||||
0.245168 | + | 0.969481i | \(0.421157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2736.00 | 0.353876 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3636.00 | 0.466697 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 480.000 | 0.0611428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8770.00 | 1.10870 | 0.554350 | − | 0.832284i | \(-0.312967\pi\) | ||||
0.554350 | + | 0.832284i | \(0.312967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1596.00 | −0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6642.00 | 0.827146 | 0.413573 | − | 0.910471i | \(-0.364281\pi\) | ||||
0.413573 | + | 0.910471i | \(0.364281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6944.00 | −0.858326 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −486.000 | −0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6408.00 | 0.780424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1510.00 | −0.182554 | −0.0912771 | − | 0.995826i | \(-0.529095\pi\) | ||||
−0.0912771 | + | 0.995826i | \(0.529095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3762.00 | 0.451498 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2772.00 | −0.330269 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 648.000 | 0.0766484 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1020.00 | 0.119783 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1260.00 | −0.146909 | −0.0734547 | − | 0.997299i | \(-0.523402\pi\) | ||||
−0.0734547 | + | 0.997299i | \(0.523402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3998.00 | −0.462828 | −0.231414 | − | 0.972855i | \(-0.574335\pi\) | ||||
−0.231414 | + | 0.972855i | \(0.574335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1728.00 | 0.198625 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10146.0 | −1.15801 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1778.00 | 0.201507 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6696.00 | 0.753580 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2736.00 | 0.305774 | 0.152887 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152887 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2690.00 | 0.298552 | 0.149276 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149276 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −972.000 | −0.107135 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1824.00 | −0.199665 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1240.00 | 0.134811 | 0.0674054 | − | 0.997726i | \(-0.478528\pi\) | ||||
0.0674054 | + | 0.997726i | \(0.478528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3900.00 | −0.418272 | −0.209136 | − | 0.977887i | \(-0.567065\pi\) | ||||
−0.209136 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9828.00 | 1.04695 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3114.00 | 0.329501 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10878.0 | −1.14335 | −0.571675 | − | 0.820480i | \(-0.693706\pi\) | ||||
−0.571675 | + | 0.820480i | \(0.693706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13608.0 | 1.42079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8808.00 | 0.913545 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2604.00 | −0.268302 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2330.00 | 0.238496 | 0.119248 | − | 0.992864i | \(-0.461952\pi\) | ||||
0.119248 | + | 0.992864i | \(0.461952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3078.00 | −0.313004 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15150.0 | −1.53060 | −0.765299 | − | 0.643675i | \(-0.777409\pi\) | ||||
−0.765299 | + | 0.643675i | \(0.777409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2992.00 | 0.300324 | 0.150162 | − | 0.988661i | \(-0.452020\pi\) | ||||
0.150162 | + | 0.988661i | \(0.452020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2016.00 | 0.201053 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8724.00 | 0.864451 | 0.432225 | − | 0.901766i | \(-0.357728\pi\) | ||||
0.432225 | + | 0.901766i | \(0.357728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7084.00 | 0.697460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3990.00 | −0.390339 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6192.00 | −0.601921 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6764.00 | 0.653376 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3618.00 | 0.347289 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9744.00 | −0.929467 | −0.464734 | − | 0.885451i | \(-0.653850\pi\) | ||||
−0.464734 | + | 0.885451i | \(0.653850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11036.0 | −1.04615 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 504.000 | 0.0474799 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6060.00 | −0.567362 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4136.00 | −0.384846 | −0.192423 | − | 0.981312i | \(-0.561635\pi\) | ||||
−0.192423 | + | 0.981312i | \(0.561635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10092.0 | 0.933284 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16212.0 | 1.49010 | 0.745048 | − | 0.667011i | \(-0.232426\pi\) | ||||
0.745048 | + | 0.667011i | \(0.232426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6156.00 | −0.562378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1944.00 | −0.176518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5880.00 | 0.530692 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2396.00 | 0.214949 | 0.107475 | − | 0.994208i | \(-0.465724\pi\) | ||||
0.107475 | + | 0.994208i | \(0.465724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9144.00 | 0.815417 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13128.0 | −1.16371 | −0.581857 | − | 0.813291i | \(-0.697674\pi\) | ||||
−0.581857 | + | 0.813291i | \(0.697674\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 0.00317224 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4941.00 | −0.432816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12798.0 | −1.11446 | −0.557231 | − | 0.830357i | \(-0.688136\pi\) | ||||
−0.557231 | + | 0.830357i | \(0.688136\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6230.00 | −0.539333 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2052.00 | 0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2832.00 | −0.242316 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6912.00 | 0.587987 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8118.00 | −0.686591 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7386.00 | 0.621087 | 0.310544 | − | 0.950559i | \(-0.399489\pi\) | ||||
0.310544 | + | 0.950559i | \(0.399489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5180.00 | 0.433089 | 0.216545 | − | 0.976273i | \(-0.430521\pi\) | ||||
0.216545 | + | 0.976273i | \(0.430521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1869.00 | −0.155371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12768.0 | 1.05538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11591.0 | −0.952659 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3564.00 | 0.291270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23436.0 | −1.90455 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5832.00 | 0.471288 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14148.0 | −1.13693 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1764.00 | 0.140966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4070.00 | −0.323444 | −0.161722 | − | 0.986836i | \(-0.551705\pi\) | ||||
−0.161722 | + | 0.986836i | \(0.551705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5730.00 | 0.452851 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10716.0 | −0.842244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14780.0 | 1.15530 | 0.577648 | − | 0.816286i | \(-0.303971\pi\) | ||||
0.577648 | + | 0.816286i | \(0.303971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2286.00 | −0.177712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4104.00 | 0.317307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 560.000 | 0.0430626 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3204.00 | 0.245049 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6858.00 | 0.521693 | 0.260846 | − | 0.965380i | \(-0.415998\pi\) | ||||
0.260846 | + | 0.965380i | \(0.415998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10664.0 | 0.806868 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12312.0 | −0.926583 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6660.00 | 0.498553 | 0.249277 | − | 0.968432i | \(-0.419807\pi\) | ||||
0.249277 | + | 0.968432i | \(0.419807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13716.0 | 1.02130 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −150.000 | −0.0110515 | −0.00552577 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552577 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8188.00 | −0.600100 | −0.300050 | − | 0.953923i | \(-0.597003\pi\) | ||||
−0.300050 | + | 0.953923i | \(0.597003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12240.0 | 0.892379 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2136.00 | −0.154917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5854.00 | −0.422366 | −0.211183 | − | 0.977447i | \(-0.567732\pi\) | ||||
−0.211183 | + | 0.977447i | \(0.567732\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8058.00 | 0.578375 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 756.000 | 0.0539831 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14472.0 | 1.02808 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3348.00 | 0.236620 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17580.0 | 1.23612 | 0.618062 | − | 0.786130i | \(-0.287918\pi\) | ||||
0.618062 | + | 0.786130i | \(0.287918\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8512.00 | −0.595468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1530.00 | 0.106490 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17154.0 | 1.18791 | 0.593955 | − | 0.804498i | \(-0.297566\pi\) | ||||
0.593955 | + | 0.804498i | \(0.297566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4788.00 | 0.329897 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4056.00 | 0.278059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18120.0 | 1.23600 | 0.617999 | − | 0.786179i | \(-0.287943\pi\) | ||||
0.617999 | + | 0.786179i | \(0.287943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17546.0 | 1.19088 | 0.595438 | − | 0.803401i | \(-0.296979\pi\) | ||||
0.595438 | + | 0.803401i | \(0.296979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9108.00 | −0.615102 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 210.000 | 0.0141119 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14560.0 | 0.973595 | 0.486798 | − | 0.873515i | \(-0.338165\pi\) | ||||
0.486798 | + | 0.873515i | \(0.338165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1134.00 | −0.0754548 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11904.0 | −0.788190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4498.00 | 0.296366 | 0.148183 | − | 0.988960i | \(-0.452657\pi\) | ||||
0.148183 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6804.00 | 0.446120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5478.00 | −0.357433 | −0.178716 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178716 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6044.00 | 0.392454 | 0.196227 | − | 0.980559i | \(-0.437131\pi\) | ||||
0.196227 | + | 0.980559i | \(0.437131\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −648.000 | −0.0418733 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11466.0 | 0.737360 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8208.00 | 0.522801 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20292.0 | 1.28632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15352.0 | 0.968547 | 0.484274 | − | 0.874917i | \(-0.339084\pi\) | ||||
0.484274 | + | 0.874917i | \(0.339084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10092.0 | 0.633682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7968.00 | 0.497953 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3038.00 | −0.188964 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7560.00 | −0.468027 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22398.0 | −1.38014 | −0.690068 | − | 0.723744i | \(-0.742420\pi\) | ||||
−0.690068 | + | 0.723744i | \(0.742420\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3764.00 | 0.230852 | 0.115426 | − | 0.993316i | \(-0.463177\pi\) | ||||
0.115426 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3096.00 | −0.189000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17688.0 | 1.07479 | 0.537393 | − | 0.843332i | \(-0.319409\pi\) | ||||
0.537393 | + | 0.843332i | \(0.319409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14256.0 | 0.862245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2352.00 | 0.141601 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19878.0 | −1.19125 | −0.595625 | − | 0.803263i | \(-0.703096\pi\) | ||||
−0.595625 | + | 0.803263i | \(0.703096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7272.00 | 0.433802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8010.00 | 0.475647 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20004.0 | −1.18247 | −0.591233 | − | 0.806501i | \(-0.701359\pi\) | ||||
−0.591233 | + | 0.806501i | \(0.701359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1306.00 | 0.0768495 | 0.0384247 | − | 0.999261i | \(-0.487766\pi\) | ||||
0.0384247 | + | 0.999261i | \(0.487766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21204.0 | 1.24207 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3192.00 | −0.186136 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1296.00 | −0.0752344 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14304.0 | −0.826644 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9144.00 | −0.526081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13054.0 | −0.747689 | −0.373845 | − | 0.927491i | \(-0.621961\pi\) | ||||
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5046.00 | −0.286460 | −0.143230 | − | 0.989689i | \(-0.545749\pi\) | ||||
−0.143230 | + | 0.989689i | \(0.545749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7070.00 | −0.399590 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1260.00 | −0.0709006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12468.0 | 0.698499 | 0.349249 | − | 0.937030i | \(-0.386437\pi\) | ||||
0.349249 | + | 0.937030i | \(0.386437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7524.00 | 0.419675 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5646.00 | −0.313549 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24924.0 | −1.37813 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23212.0 | −1.27790 | −0.638948 | − | 0.769250i | \(-0.720630\pi\) | ||||
−0.638948 | + | 0.769250i | \(0.720630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2268.00 | −0.124321 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2040.00 | 0.111340 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43092.0 | 2.34179 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15246.0 | −0.824974 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35958.0 | −1.93740 | −0.968698 | − | 0.248241i | \(-0.920147\pi\) | ||||
−0.968698 | + | 0.248241i | \(0.920147\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13528.0 | −0.725773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3456.00 | 0.184625 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 42.0000 | 0.00223419 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6446.00 | −0.341445 | −0.170723 | − | 0.985319i | \(-0.554610\pi\) | ||||
−0.170723 | + | 0.985319i | \(0.554610\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −720.000 | −0.0379777 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2688.00 | 0.141187 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13392.0 | 0.700465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16272.0 | −0.847544 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4704.00 | 0.243991 | 0.121996 | − | 0.992531i | \(-0.461071\pi\) | ||||
0.121996 | + | 0.992531i | \(0.461071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3304.00 | −0.170662 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7770.00 | 0.399681 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4806.00 | 0.246194 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10600.0 | 0.540760 | 0.270380 | − | 0.962754i | \(-0.412851\pi\) | ||||
0.270380 | + | 0.962754i | \(0.412851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19608.0 | −0.992104 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12542.0 | −0.631991 | −0.315995 | − | 0.948761i | \(-0.602338\pi\) | ||||
−0.315995 | + | 0.948761i | \(0.602338\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 882.000 | 0.0442627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36432.0 | −1.82088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23324.0 | 1.16101 | 0.580506 | − | 0.814256i | \(-0.302855\pi\) | ||||
0.580506 | + | 0.814256i | \(0.302855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14136.0 | −0.700808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6312.00 | 0.311662 | 0.155831 | − | 0.987784i | \(-0.450194\pi\) | ||||
0.155831 | + | 0.987784i | \(0.450194\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6228.00 | 0.306277 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −972.000 | −0.0476086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6804.00 | 0.331926 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35840.0 | −1.74144 | −0.870719 | − | 0.491781i | \(-0.836346\pi\) | ||||
−0.870719 | + | 0.491781i | \(0.836346\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14796.0 | 0.716064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17616.0 | 0.849155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34594.0 | 1.66095 | 0.830476 | − | 0.557055i | \(-0.188069\pi\) | ||||
0.830476 | + | 0.557055i | \(0.188069\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2592.00 | −0.123957 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23946.0 | 1.14066 | 0.570330 | − | 0.821416i | \(-0.306815\pi\) | ||||
0.570330 | + | 0.821416i | \(0.306815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12502.0 | −0.593188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6156.00 | −0.290942 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24552.0 | −1.15583 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18770.0 | 0.880187 | 0.440093 | − | 0.897952i | \(-0.354945\pi\) | ||||
0.440093 | + | 0.897952i | \(0.354945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10314.0 | 0.481776 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30342.0 | −1.41181 | −0.705903 | − | 0.708309i | \(-0.749459\pi\) | ||||
−0.705903 | + | 0.708309i | \(0.749459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9968.00 | −0.462014 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3738.00 | 0.172587 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28728.0 | −1.32129 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30240.0 | −1.38550 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1458.00 | 0.0665449 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7980.00 | −0.362826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26188.0 | −1.18615 | −0.593076 | − | 0.805147i | \(-0.702087\pi\) | ||||
−0.593076 | + | 0.805147i | \(0.702087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18360.0 | 0.828433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16002.0 | 0.719299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15748.0 | 0.705205 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7236.00 | 0.322811 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34818.0 | 1.54745 | 0.773724 | − | 0.633522i | \(-0.218391\pi\) | ||||
0.773724 | + | 0.633522i | \(0.218391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21888.0 | 0.969139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14742.0 | −0.650291 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32040.0 | 1.40805 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1008.00 | 0.0441333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −54.0000 | −0.00235550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21702.0 | −0.943142 | −0.471571 | − | 0.881828i | \(-0.656313\pi\) | ||||
−0.471571 | + | 0.881828i | \(0.656313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20356.0 | −0.881376 | −0.440688 | − | 0.897660i | \(-0.645265\pi\) | ||||
−0.440688 | + | 0.897660i | \(0.645265\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20688.0 | 0.892448 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20184.0 | 0.867503 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13072.0 | 0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3906.00 | 0.166650 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19890.0 | 0.845513 | 0.422756 | − | 0.906243i | \(-0.361063\pi\) | ||||
0.422756 | + | 0.906243i | \(0.361063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4232.00 | −0.179245 | −0.0896223 | − | 0.995976i | \(-0.528566\pi\) | ||||
−0.0896223 | + | 0.995976i | \(0.528566\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9612.00 | 0.405633 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9636.00 | 0.405171 | 0.202586 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202586 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35294.0 | −1.47866 | −0.739331 | − | 0.673342i | \(-0.764858\pi\) | ||||
−0.739331 | + | 0.673342i | \(0.764858\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18762.0 | 0.783209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5586.00 | 0.232345 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18288.0 | 0.757943 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3024.00 | −0.124880 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3768.00 | 0.155049 | 0.0775243 | − | 0.996990i | \(-0.475298\pi\) | ||||
0.0775243 | + | 0.996990i | \(0.475298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3582.00 | −0.146347 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9882.00 | −0.402309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 245.000 | 0.00993896 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21468.0 | 0.867821 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4272.00 | 0.172083 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39466.0 | 1.58416 | 0.792081 | − | 0.610416i | \(-0.208998\pi\) | ||||
0.792081 | + | 0.610416i | \(0.208998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4104.00 | 0.164157 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34038.0 | −1.35673 | −0.678364 | − | 0.734726i | \(-0.737311\pi\) | ||||
−0.678364 | + | 0.734726i | \(0.737311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3364.00 | −0.133618 | −0.0668092 | − | 0.997766i | \(-0.521282\pi\) | ||||
−0.0668092 | + | 0.997766i | \(0.521282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7938.00 | 0.314200 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13104.0 | −0.516878 | −0.258439 | − | 0.966028i | \(-0.583208\pi\) | ||||
−0.258439 | + | 0.966028i | \(0.583208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16236.0 | −0.638197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24249.0 | −0.949872 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2880.00 | −0.112425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62744.0 | 2.44087 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9090.00 | 0.352405 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8988.00 | −0.347257 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40858.0 | 1.57318 | 0.786589 | − | 0.617477i | \(-0.211845\pi\) | ||||
0.786589 | + | 0.617477i | \(0.211845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11214.0 | −0.430306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37374.0 | −1.42924 | −0.714621 | − | 0.699512i | \(-0.753401\pi\) | ||||
−0.714621 | + | 0.699512i | \(0.753401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9788.00 | 0.373038 | 0.186519 | − | 0.982451i | \(-0.440279\pi\) | ||||
0.186519 | + | 0.982451i | \(0.440279\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7128.00 | 0.270740 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50424.0 | −1.90876 | −0.954381 | − | 0.298591i | \(-0.903483\pi\) | ||||
−0.954381 | + | 0.298591i | \(0.903483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9296.00 | 0.350706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2916.00 | 0.109640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14592.0 | −0.546811 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28296.0 | −1.05679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4464.00 | 0.166163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6048.00 | −0.224374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45828.0 | 1.69451 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3612.00 | −0.133112 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11460.0 | 0.420932 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12412.0 | −0.454392 | −0.227196 | − | 0.973849i | \(-0.572956\pi\) | ||||
−0.227196 | + | 0.973849i | \(0.572956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −54.0000 | −0.00197037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6576.00 | −0.239158 | −0.119579 | − | 0.992825i | \(-0.538154\pi\) | ||||
−0.119579 | + | 0.992825i | \(0.538154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3888.00 | −0.140935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4572.00 | −0.165187 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8484.00 | 0.305525 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8264.00 | −0.296631 | −0.148316 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148316 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2532.00 | 0.0905887 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 52080.0 | 1.85724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15842.0 | −0.563115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4248.00 | 0.150510 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39426.0 | 1.39238 | 0.696192 | − | 0.717855i | \(-0.254876\pi\) | ||||
0.696192 | + | 0.717855i | \(0.254876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3724.00 | −0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18936.0 | 0.664455 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24624.0 | −0.861274 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4678.00 | −0.163099 | −0.0815494 | − | 0.996669i | \(-0.525987\pi\) | ||||
−0.0815494 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24846.0 | −0.863492 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17346.0 | 0.600918 | 0.300459 | − | 0.953795i | \(-0.402860\pi\) | ||||
0.300459 | + | 0.953795i | \(0.402860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9072.00 | 0.313282 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1134.00 | −0.0390360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19452.0 | 0.667482 | 0.333741 | − | 0.942665i | \(-0.391689\pi\) | ||||
0.333741 | + | 0.942665i | \(0.391689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55180.0 | −1.88748 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27954.0 | 0.953176 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4458.00 | 0.151531 | 0.0757654 | − | 0.997126i | \(-0.475860\pi\) | ||||
0.0757654 | + | 0.997126i | \(0.475860\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24480.0 | 0.829481 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5832.00 | 0.196992 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8778.00 | 0.295575 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17247.0 | −0.578933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8748.00 | −0.292731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16116.0 | 0.537609 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52520.0 | −1.74657 | −0.873283 | − | 0.487213i | \(-0.838013\pi\) | ||||
−0.873283 | + | 0.487213i | \(0.838013\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25992.0 | 0.861696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10404.0 | −0.343852 | −0.171926 | − | 0.985110i | \(-0.554999\pi\) | ||||
−0.171926 | + | 0.985110i | \(0.554999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2380.00 | 0.0784165 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16554.0 | −0.543746 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7566.00 | −0.247756 | −0.123878 | − | 0.992297i | \(-0.539533\pi\) | ||||
−0.123878 | + | 0.992297i | \(0.539533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58968.0 | −1.92505 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16074.0 | 0.523143 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44376.0 | −1.43985 | −0.719926 | − | 0.694051i | \(-0.755824\pi\) | ||||
−0.719926 | + | 0.694051i | \(0.755824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3060.00 | 0.0989845 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4032.00 | 0.130030 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4128.00 | −0.132723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27328.0 | 0.875986 | 0.437993 | − | 0.898978i | \(-0.355689\pi\) | ||||
0.437993 | + | 0.898978i | \(0.355689\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4956.00 | −0.158383 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8112.00 | 0.258460 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2774.00 | −0.0881178 | −0.0440589 | − | 0.999029i | \(-0.514029\pi\) | ||||
−0.0440589 | + | 0.999029i | \(0.514029\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4806.00 | −0.152207 |
(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 | 1344.4.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.q.1.1 | 1 | |||
8.3 | odd | 2 | 84.4.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 336.4.a.k.1.1 | 1 | |||
24.5 | odd | 2 | 1008.4.a.h.1.1 | 1 | |||
24.11 | even | 2 | 252.4.a.b.1.1 | 1 | |||
40.3 | even | 4 | 2100.4.k.j.1849.1 | 2 | |||
40.19 | odd | 2 | 2100.4.a.l.1.1 | 1 | |||
40.27 | even | 4 | 2100.4.k.j.1849.2 | 2 | |||
56.3 | even | 6 | 588.4.i.c.373.1 | 2 | |||
56.11 | odd | 6 | 588.4.i.f.373.1 | 2 | |||
56.13 | odd | 2 | 2352.4.a.d.1.1 | 1 | |||
56.19 | even | 6 | 588.4.i.c.361.1 | 2 | |||
56.27 | even | 2 | 588.4.a.d.1.1 | 1 | |||
56.51 | odd | 6 | 588.4.i.f.361.1 | 2 | |||
168.11 | even | 6 | 1764.4.k.l.1549.1 | 2 | |||
168.59 | odd | 6 | 1764.4.k.f.1549.1 | 2 | |||
168.83 | odd | 2 | 1764.4.a.j.1.1 | 1 | |||
168.107 | even | 6 | 1764.4.k.l.361.1 | 2 | |||
168.131 | odd | 6 | 1764.4.k.f.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
252.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
336.4.a.k.1.1 | 1 | 8.5 | even | 2 | |||
588.4.a.d.1.1 | 1 | 56.27 | even | 2 | |||
588.4.i.c.361.1 | 2 | 56.19 | even | 6 | |||
588.4.i.c.373.1 | 2 | 56.3 | even | 6 | |||
588.4.i.f.361.1 | 2 | 56.51 | odd | 6 | |||
588.4.i.f.373.1 | 2 | 56.11 | odd | 6 | |||
1008.4.a.h.1.1 | 1 | 24.5 | odd | 2 | |||
1344.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1344.4.a.q.1.1 | 1 | 4.3 | odd | 2 | |||
1764.4.a.j.1.1 | 1 | 168.83 | odd | 2 | |||
1764.4.k.f.361.1 | 2 | 168.131 | odd | 6 | |||
1764.4.k.f.1549.1 | 2 | 168.59 | odd | 6 | |||
1764.4.k.l.361.1 | 2 | 168.107 | even | 6 | |||
1764.4.k.l.1549.1 | 2 | 168.11 | even | 6 | |||
2100.4.a.l.1.1 | 1 | 40.19 | odd | 2 | |||
2100.4.k.j.1849.1 | 2 | 40.3 | even | 4 | |||
2100.4.k.j.1849.2 | 2 | 40.27 | even | 4 | |||
2352.4.a.d.1.1 | 1 | 56.13 | odd | 2 |