Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("384.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(22.6567334422\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(5\) | −4.00000 | −0.357771 | −0.178885 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178885 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0000 | −0.539949 | −0.269975 | − | 0.962867i | \(-0.587015\pi\) | ||||
−0.269975 | + | 0.962867i | \(0.587015\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 0.109640 | 0.0548202 | − | 0.998496i | \(-0.482541\pi\) | ||||
0.0548202 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.0000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.00000 | −0.0965961 | −0.0482980 | − | 0.998833i | \(-0.515380\pi\) | ||||
−0.0482980 | + | 0.998833i | \(0.515380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −30.0000 | −0.311740 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −148.000 | −1.34174 | −0.670872 | − | 0.741573i | \(-0.734080\pi\) | ||||
−0.670872 | + | 0.741573i | \(0.734080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −72.0000 | −0.461037 | −0.230518 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230518 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.0000 | −0.104287 | −0.0521435 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521435 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | 0.0633010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 40.0000 | 0.193178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −262.000 | −1.16412 | −0.582061 | − | 0.813145i | \(-0.697754\pi\) | ||||
−0.582061 | + | 0.813145i | \(0.697754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −78.0000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −1.43985 | −0.719923 | − | 0.694054i | \(-0.755823\pi\) | ||||
−0.719923 | + | 0.694054i | \(0.755823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 432.000 | 1.53208 | 0.766039 | − | 0.642794i | \(-0.222225\pi\) | ||||
0.766039 | + | 0.642794i | \(0.222225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36.0000 | −0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −148.000 | −0.459320 | −0.229660 | − | 0.973271i | \(-0.573761\pi\) | ||||
−0.229660 | + | 0.973271i | \(0.573761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −243.000 | −0.708455 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.0000 | 0.115317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −360.000 | −0.933015 | −0.466508 | − | 0.884517i | \(-0.654488\pi\) | ||||
−0.466508 | + | 0.884517i | \(0.654488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.0000 | −0.0392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.0000 | −0.0557698 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 428.000 | 0.944421 | 0.472211 | − | 0.881486i | \(-0.343456\pi\) | ||||
0.472211 | + | 0.881486i | \(0.343456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 442.000 | 0.927743 | 0.463871 | − | 0.885903i | \(-0.346460\pi\) | ||||
0.463871 | + | 0.885903i | \(0.346460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −90.0000 | −0.179983 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 104.000 | 0.198456 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 692.000 | 1.26181 | 0.630905 | − | 0.775860i | \(-0.282684\pi\) | ||||
0.630905 | + | 0.775860i | \(0.282684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −444.000 | −0.774657 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −540.000 | −0.902623 | −0.451311 | − | 0.892367i | \(-0.649044\pi\) | ||||
−0.451311 | + | 0.892367i | \(0.649044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1018.00 | −1.63216 | −0.816081 | − | 0.577937i | \(-0.803858\pi\) | ||||
−0.816081 | + | 0.577937i | \(0.803858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −327.000 | −0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −40.0000 | −0.0592003 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −386.000 | −0.549726 | −0.274863 | − | 0.961483i | \(-0.588633\pi\) | ||||
−0.274863 | + | 0.961483i | \(0.588633\pi\) | |||||||
\(80\) | 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 | ||||||||
\(85\) | −56.0000 | −0.0714594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −216.000 | −0.266180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −382.000 | −0.454965 | −0.227483 | − | 0.973782i | \(-0.573050\pi\) | ||||
−0.227483 | + | 0.973782i | \(0.573050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 260.000 | 0.299510 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −54.0000 | −0.0602101 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.0000 | 0.0345593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 298.000 | 0.311931 | 0.155966 | − | 0.987762i | \(-0.450151\pi\) | ||||
0.155966 | + | 0.987762i | \(0.450151\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 36.0000 | 0.0365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1800.00 | −1.77333 | −0.886667 | − | 0.462409i | \(-0.846985\pi\) | ||||
−0.886667 | + | 0.462409i | \(0.846985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 818.000 | 0.782524 | 0.391262 | − | 0.920279i | \(-0.372039\pi\) | ||||
0.391262 | + | 0.920279i | \(0.372039\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 120.000 | 0.111531 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −716.000 | −0.646900 | −0.323450 | − | 0.946245i | \(-0.604843\pi\) | ||||
−0.323450 | + | 0.946245i | \(0.604843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1134.00 | 0.996491 | 0.498245 | − | 0.867036i | \(-0.333978\pi\) | ||||
0.498245 | + | 0.867036i | \(0.333978\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −786.000 | −0.672106 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1858.00 | 1.54678 | 0.773389 | − | 0.633932i | \(-0.218560\pi\) | ||||
0.773389 | + | 0.633932i | \(0.218560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 592.000 | 0.480037 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −234.000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −140.000 | −0.107847 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1134.00 | −0.831295 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 936.000 | 0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1402.00 | 0.979586 | 0.489793 | − | 0.871839i | \(-0.337072\pi\) | ||||
0.489793 | + | 0.871839i | \(0.337072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1296.00 | 0.884546 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1188.00 | −0.792336 | −0.396168 | − | 0.918178i | \(-0.629660\pi\) | ||||
−0.396168 | + | 0.918178i | \(0.629660\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.0000 | 0.0521570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −108.000 | −0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 734.000 | 0.457736 | 0.228868 | − | 0.973457i | \(-0.426498\pi\) | ||||
0.228868 | + | 0.973457i | \(0.426498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −404.000 | −0.246524 | −0.123262 | − | 0.992374i | \(-0.539336\pi\) | ||||
−0.123262 | + | 0.992374i | \(0.539336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −444.000 | −0.265188 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −104.000 | −0.0608176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 288.000 | 0.164946 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −729.000 | −0.409027 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 684.000 | 0.376077 | 0.188038 | − | 0.982162i | \(-0.439787\pi\) | ||||
0.188038 | + | 0.982162i | \(0.439787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3502.00 | 1.88734 | 0.943671 | − | 0.330885i | \(-0.107347\pi\) | ||||
0.943671 | + | 0.330885i | \(0.107347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 126.000 | 0.0665784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 72.0000 | 0.0373108 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3258.00 | 1.65616 | 0.828079 | − | 0.560612i | \(-0.189434\pi\) | ||||
0.828079 | + | 0.560612i | \(0.189434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1080.00 | −0.538677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1480.00 | 0.724474 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 856.000 | 0.411332 | 0.205666 | − | 0.978622i | \(-0.434064\pi\) | ||||
0.205666 | + | 0.978622i | \(0.434064\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48.0000 | −0.0226472 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1552.00 | −0.719146 | −0.359573 | − | 0.933117i | \(-0.617078\pi\) | ||||
−0.359573 | + | 0.933117i | \(0.617078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −72.0000 | −0.0321987 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1548.00 | 0.680302 | 0.340151 | − | 0.940371i | \(-0.389522\pi\) | ||||
0.340151 | + | 0.940371i | \(0.389522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1090.00 | 0.470836 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1284.00 | 0.545262 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3420.00 | −1.42806 | −0.714030 | − | 0.700115i | \(-0.753132\pi\) | ||||
−0.714030 | + | 0.700115i | \(0.753132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3502.00 | 1.43813 | 0.719065 | − | 0.694943i | \(-0.244570\pi\) | ||||
0.719065 | + | 0.694943i | \(0.244570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1326.00 | 0.535632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1048.00 | 0.416489 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 56.0000 | 0.0218991 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −270.000 | −0.103913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4792.00 | 1.81538 | 0.907688 | − | 0.419645i | \(-0.137845\pi\) | ||||
0.907688 | + | 0.419645i | \(0.137845\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −98.0000 | −0.0365502 | −0.0182751 | − | 0.999833i | \(-0.505817\pi\) | ||||
−0.0182751 | + | 0.999833i | \(0.505817\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 312.000 | 0.114578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1184.00 | −0.428206 | −0.214103 | − | 0.976811i | \(-0.568683\pi\) | ||||
−0.214103 | + | 0.976811i | \(0.568683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1466.00 | 0.522221 | 0.261111 | − | 0.965309i | \(-0.415911\pi\) | ||||
0.261111 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2076.00 | 0.728506 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 720.000 | 0.248936 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1512.00 | 0.515135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1332.00 | −0.447248 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.0000 | −0.0105908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2692.00 | 0.878317 | 0.439159 | − | 0.898410i | \(-0.355277\pi\) | ||||
0.439159 | + | 0.898410i | \(0.355277\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1620.00 | −0.521129 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1728.00 | −0.548133 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 180.000 | 0.0563097 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3054.00 | −0.942330 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −364.000 | −0.110793 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4554.00 | 1.36753 | 0.683763 | − | 0.729704i | \(-0.260342\pi\) | ||||
0.683763 | + | 0.729704i | \(0.260342\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5580.00 | −1.63153 | −0.815766 | − | 0.578383i | \(-0.803684\pi\) | ||||
−0.815766 | + | 0.578383i | \(0.803684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 902.000 | 0.260288 | 0.130144 | − | 0.991495i | \(-0.458456\pi\) | ||||
0.130144 | + | 0.991495i | \(0.458456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −120.000 | −0.0341793 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1962.00 | 0.551652 | 0.275826 | − | 0.961208i | \(-0.411049\pi\) | ||||
0.275826 | + | 0.961208i | \(0.411049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 592.000 | 0.164331 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1158.00 | −0.317385 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2016.00 | −0.545624 | −0.272812 | − | 0.962067i | \(-0.587954\pi\) | ||||
−0.272812 | + | 0.962067i | \(0.587954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1826.00 | −0.488062 | −0.244031 | − | 0.969767i | \(-0.578470\pi\) | ||||
−0.244031 | + | 0.969767i | \(0.578470\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 972.000 | 0.253464 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 208.000 | 0.0535819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −324.000 | −0.0824605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3060.00 | 0.769504 | 0.384752 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384752 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −592.000 | −0.147110 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −168.000 | −0.0412571 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −558.000 | −0.135436 | −0.0677181 | − | 0.997704i | \(-0.521572\pi\) | ||||
−0.0677181 | + | 0.997704i | \(0.521572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2620.00 | 0.628567 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −648.000 | −0.153679 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5544.00 | −1.29984 | −0.649920 | − | 0.760003i | \(-0.725197\pi\) | ||||
−0.649920 | + | 0.760003i | \(0.725197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1440.00 | 0.333806 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1146.00 | −0.262674 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4856.00 | −1.10065 | −0.550326 | − | 0.834950i | \(-0.685497\pi\) | ||||
−0.550326 | + | 0.834950i | \(0.685497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7030.00 | −1.57580 | −0.787901 | − | 0.615803i | \(-0.788832\pi\) | ||||
−0.787901 | + | 0.615803i | \(0.788832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 780.000 | 0.172922 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −436.000 | −0.0956065 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −738.000 | −0.160080 | −0.0800399 | − | 0.996792i | \(-0.525505\pi\) | ||||
−0.0800399 | + | 0.996792i | \(0.525505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −162.000 | −0.0347623 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1854.00 | −0.393596 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1404.00 | −0.294909 | −0.147454 | − | 0.989069i | \(-0.547108\pi\) | ||||
−0.147454 | + | 0.989069i | \(0.547108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 96.0000 | 0.0199528 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3780.00 | 0.777444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 894.000 | 0.180093 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2056.00 | 0.409941 | 0.204971 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204971 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1712.00 | −0.337886 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 108.000 | 0.0211003 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3848.00 | 0.744266 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4320.00 | −0.827245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5400.00 | −1.02383 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1768.00 | −0.331919 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2340.00 | 0.435019 | 0.217510 | − | 0.976058i | \(-0.430207\pi\) | ||||
0.217510 | + | 0.976058i | \(0.430207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2454.00 | 0.451790 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1616.00 | −0.294646 | −0.147323 | − | 0.989088i | \(-0.547066\pi\) | ||||
−0.147323 | + | 0.989088i | \(0.547066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3286.00 | 0.593405 | 0.296702 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296702 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 360.000 | 0.0643927 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9936.00 | −1.76045 | −0.880223 | − | 0.474560i | \(-0.842607\pi\) | ||||
−0.880223 | + | 0.474560i | \(0.842607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −288.000 | −0.0505483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2148.00 | −0.373488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −112.000 | −0.0192936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2834.00 | 0.483699 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3402.00 | 0.575324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1480.00 | 0.248009 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2116.00 | 0.351377 | 0.175689 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175689 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2358.00 | −0.388041 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2768.00 | −0.451439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7874.00 | −1.27277 | −0.636386 | − | 0.771371i | \(-0.719571\pi\) | ||||
−0.636386 | + | 0.771371i | \(0.719571\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5574.00 | 0.893033 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −72.0000 | −0.0114341 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5860.00 | 0.922479 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1776.00 | 0.277150 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10476.0 | 1.62069 | 0.810347 | − | 0.585950i | \(-0.199278\pi\) | ||||
0.810347 | + | 0.585950i | \(0.199278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7030.00 | −1.07824 | −0.539122 | − | 0.842228i | \(-0.681244\pi\) | ||||
−0.539122 | + | 0.842228i | \(0.681244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −702.000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5310.00 | −0.800631 | −0.400316 | − | 0.916377i | \(-0.631099\pi\) | ||||
−0.400316 | + | 0.916377i | \(0.631099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2160.00 | 0.322932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −420.000 | −0.0622654 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7628.00 | −1.12142 | −0.560711 | − | 0.828012i | \(-0.689472\pi\) | ||||
−0.560711 | + | 0.828012i | \(0.689472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6795.00 | −0.990669 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3945.00 | −0.570410 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4072.00 | 0.583940 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13778.0 | −1.95969 | −0.979844 | − | 0.199763i | \(-0.935983\pi\) | ||||
−0.979844 | + | 0.199763i | \(0.935983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3402.00 | −0.479949 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3600.00 | 0.503781 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2566.00 | −0.356200 | −0.178100 | − | 0.984012i | \(-0.556995\pi\) | ||||
−0.178100 | + | 0.984012i | \(0.556995\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2808.00 | 0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1872.00 | 0.255737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7120.00 | −0.964986 | −0.482493 | − | 0.875900i | \(-0.660269\pi\) | ||||
−0.482493 | + | 0.875900i | \(0.660269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4206.00 | 0.565564 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14040.0 | 1.87313 | 0.936567 | − | 0.350488i | \(-0.113984\pi\) | ||||
0.936567 | + | 0.350488i | \(0.113984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 160.000 | 0.0211801 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3888.00 | 0.510693 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4972.00 | 0.648047 | 0.324024 | − | 0.946049i | \(-0.394964\pi\) | ||||
0.324024 | + | 0.946049i | \(0.394964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2072.00 | −0.267994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3564.00 | −0.457456 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1544.00 | 0.196676 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8766.00 | −1.10819 | −0.554097 | − | 0.832452i | \(-0.686936\pi\) | ||||
−0.554097 | + | 0.832452i | \(0.686936\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 240.000 | 0.0301129 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12042.0 | −1.49962 | −0.749811 | − | 0.661652i | \(-0.769856\pi\) | ||||
−0.749811 | + | 0.661652i | \(0.769856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 468.000 | 0.0578480 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −324.000 | −0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1048.00 | −0.127635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8002.00 | 0.967417 | 0.483708 | − | 0.875229i | \(-0.339290\pi\) | ||||
0.483708 | + | 0.875229i | \(0.339290\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2202.00 | 0.264274 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4280.00 | −0.509940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 432.000 | 0.0510989 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1212.00 | −0.142331 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −364.000 | −0.0424405 | −0.0212202 | − | 0.999775i | \(-0.506755\pi\) | ||||
−0.0212202 | + | 0.999775i | \(0.506755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1502.00 | 0.173879 | 0.0869394 | − | 0.996214i | \(-0.472291\pi\) | ||||
0.0869394 | + | 0.996214i | \(0.472291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1332.00 | −0.153107 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1526.00 | −0.174169 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4420.00 | −0.500934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −312.000 | −0.0351131 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3532.00 | −0.394734 | −0.197367 | − | 0.980330i | \(-0.563239\pi\) | ||||
−0.197367 | + | 0.980330i | \(0.563239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8946.00 | 0.992881 | 0.496440 | − | 0.868071i | \(-0.334640\pi\) | ||||
0.496440 | + | 0.868071i | \(0.334640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 864.000 | 0.0952313 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1184.00 | 0.129607 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1602.00 | 0.174167 | 0.0870835 | − | 0.996201i | \(-0.472245\pi\) | ||||
0.0870835 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2187.00 | −0.236152 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4356.00 | −0.467178 | −0.233589 | − | 0.972335i | \(-0.575047\pi\) | ||||
−0.233589 | + | 0.972335i | \(0.575047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1528.00 | 0.162773 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2052.00 | 0.217128 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2110.00 | 0.221775 | 0.110888 | − | 0.993833i | \(-0.464631\pi\) | ||||
0.110888 | + | 0.993833i | \(0.464631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1512.00 | −0.157865 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10506.0 | 1.08966 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1040.00 | −0.107156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13698.0 | 1.40211 | 0.701056 | − | 0.713106i | \(-0.252712\pi\) | ||||
0.701056 | + | 0.713106i | \(0.252712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 378.000 | 0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12028.0 | 1.21518 | 0.607592 | − | 0.794249i | \(-0.292136\pi\) | ||||
0.607592 | + | 0.794249i | \(0.292136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10286.0 | −1.03246 | −0.516232 | − | 0.856449i | \(-0.672666\pi\) | ||||
−0.516232 | + | 0.856449i | \(0.672666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 216.000 | 0.0215414 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11516.0 | −1.14111 | −0.570553 | − | 0.821260i | \(-0.693271\pi\) | ||||
−0.570553 | + | 0.821260i | \(0.693271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6920.00 | −0.681313 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9774.00 | 0.956183 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1728.00 | 0.167978 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 872.000 | 0.0842318 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3240.00 | −0.311005 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13932.0 | 1.32895 | 0.664477 | − | 0.747308i | \(-0.268654\pi\) | ||||
0.664477 | + | 0.747308i | \(0.268654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6812.00 | 0.645739 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4440.00 | 0.418275 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1192.00 | −0.111600 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10682.0 | −0.993938 | −0.496969 | − | 0.867768i | \(-0.665554\pi\) | ||||
−0.496969 | + | 0.867768i | \(0.665554\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2568.00 | 0.237483 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11660.0 | 1.07171 | 0.535854 | − | 0.844311i | \(-0.319990\pi\) | ||||
0.535854 | + | 0.844311i | \(0.319990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1008.00 | −0.0920853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −144.000 | −0.0130754 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5400.00 | 0.487370 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12404.0 | −1.11278 | −0.556392 | − | 0.830920i | \(-0.687815\pi\) | ||||
−0.556392 | + | 0.830920i | \(0.687815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4656.00 | −0.415199 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2308.00 | 0.204590 | 0.102295 | − | 0.994754i | \(-0.467381\pi\) | ||||
0.102295 | + | 0.994754i | \(0.467381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7200.00 | 0.634447 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4563.00 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1984.00 | 0.172769 | 0.0863843 | − | 0.996262i | \(-0.472469\pi\) | ||||
0.0863843 | + | 0.996262i | \(0.472469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10180.0 | 0.881285 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −216.000 | −0.0185899 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3272.00 | −0.279964 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −592.000 | −0.0503600 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4644.00 | 0.392773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3982.00 | 0.334846 | 0.167423 | − | 0.985885i | \(-0.446455\pi\) | ||||
0.167423 | + | 0.985885i | \(0.446455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18368.0 | −1.53571 | −0.767855 | − | 0.640623i | \(-0.778676\pi\) | ||||
−0.767855 | + | 0.640623i | \(0.778676\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3270.00 | 0.271837 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −252.000 | −0.0208298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9737.00 | 0.800279 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3852.00 | 0.314807 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9828.00 | 0.798683 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2864.00 | 0.231442 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10260.0 | −0.824491 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −972.000 | −0.0776753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2870.00 | 0.228079 | 0.114040 | − | 0.993476i | \(-0.463621\pi\) | ||||
0.114040 | + | 0.993476i | \(0.463621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10506.0 | 0.830305 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4536.00 | −0.356515 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14176.0 | −1.10808 | −0.554042 | − | 0.832489i | \(-0.686915\pi\) | ||||
−0.554042 | + | 0.832489i | \(0.686915\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3978.00 | 0.309248 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 576.000 | 0.0445343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3860.00 | 0.296824 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3144.00 | 0.240460 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12884.0 | 0.980094 | 0.490047 | − | 0.871696i | \(-0.336980\pi\) | ||||
0.490047 | + | 0.871696i | \(0.336980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11232.0 | −0.849844 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 168.000 | 0.0126434 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15588.0 | −1.16688 | −0.583442 | − | 0.812155i | \(-0.698295\pi\) | ||||
−0.583442 | + | 0.812155i | \(0.698295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7432.00 | −0.553392 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −810.000 | −0.0599944 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4730.00 | −0.348492 | −0.174246 | − | 0.984702i | \(-0.555749\pi\) | ||||
−0.174246 | + | 0.984702i | \(0.555749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4724.00 | −0.346223 | −0.173111 | − | 0.984902i | \(-0.555382\pi\) | ||||
−0.173111 | + | 0.984902i | \(0.555382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14376.0 | 1.04811 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16132.0 | 1.17000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16838.0 | 1.21486 | 0.607431 | − | 0.794373i | \(-0.292200\pi\) | ||||
0.607431 | + | 0.794373i | \(0.292200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −294.000 | −0.0211023 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1080.00 | 0.0771187 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1440.00 | −0.102296 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 936.000 | 0.0661519 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9932.00 | 0.698360 | 0.349180 | − | 0.937056i | \(-0.386460\pi\) | ||||
0.349180 | + | 0.937056i | \(0.386460\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 144.000 | 0.0100737 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3552.00 | −0.247225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15714.0 | 1.08819 | 0.544095 | − | 0.839024i | \(-0.316873\pi\) | ||||
0.544095 | + | 0.839024i | \(0.316873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 560.000 | 0.0385845 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4398.00 | 0.301504 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20340.0 | 1.38743 | 0.693714 | − | 0.720250i | \(-0.255973\pi\) | ||||
0.693714 | + | 0.720250i | \(0.255973\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16434.0 | −1.11540 | −0.557701 | − | 0.830042i | \(-0.688316\pi\) | ||||
−0.557701 | + | 0.830042i | \(0.688316\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6228.00 | 0.420603 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5260.00 | 0.353470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8234.00 | 0.550589 | 0.275295 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275295 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2160.00 | 0.143724 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3848.00 | 0.254785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6506.00 | 0.428670 | 0.214335 | − | 0.976760i | \(-0.431242\pi\) | ||||
0.214335 | + | 0.976760i | \(0.431242\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4536.00 | 0.297413 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20542.0 | −1.34034 | −0.670170 | − | 0.742208i | \(-0.733779\pi\) | ||||
−0.670170 | + | 0.742208i | \(0.733779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11116.0 | −0.721793 | −0.360896 | − | 0.932606i | \(-0.617529\pi\) | ||||
−0.360896 | + | 0.932606i | \(0.617529\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3996.00 | −0.258219 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3820.00 | 0.245658 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −96.0000 | −0.00611463 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3668.00 | −0.232516 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3574.00 | 0.225481 | 0.112741 | − | 0.993624i | \(-0.464037\pi\) | ||||
0.112741 | + | 0.993624i | \(0.464037\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8076.00 | 0.507097 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5608.00 | −0.350467 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6318.00 | 0.392980 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4860.00 | −0.300874 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7110.00 | 0.438109 | 0.219055 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219055 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1728.00 | 0.105981 | 0.0529904 | − | 0.998595i | \(-0.483125\pi\) | ||||
0.0529904 | + | 0.998595i | \(0.483125\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5184.00 | −0.316465 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14724.0 | −0.894683 | −0.447342 | − | 0.894363i | \(-0.647629\pi\) | ||||
−0.447342 | + | 0.894363i | \(0.647629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1712.00 | 0.103547 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 540.000 | 0.0325104 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23076.0 | 1.38290 | 0.691450 | − | 0.722424i | \(-0.256972\pi\) | ||||
0.691450 | + | 0.722424i | \(0.256972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4752.00 | 0.283475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9162.00 | −0.544054 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27252.0 | 1.61091 | 0.805453 | − | 0.592660i | \(-0.201922\pi\) | ||||
0.805453 | + | 0.592660i | \(0.201922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18910.0 | −1.11273 | −0.556364 | − | 0.830938i | \(-0.687804\pi\) | ||||
−0.556364 | + | 0.830938i | \(0.687804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1092.00 | −0.0639665 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −320.000 | −0.0186603 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10656.0 | 0.618594 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13662.0 | 0.789542 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1768.00 | 0.101718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −350.000 | −0.0200468 | −0.0100234 | − | 0.999950i | \(-0.503191\pi\) | ||||
−0.0100234 | + | 0.999950i | \(0.503191\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2943.00 | −0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13468.0 | −0.764575 | −0.382288 | − | 0.924043i | \(-0.624864\pi\) | ||||
−0.382288 | + | 0.924043i | \(0.624864\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2980.00 | −0.168427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16740.0 | −0.941965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12852.0 | −0.720012 | −0.360006 | − | 0.932950i | \(-0.617225\pi\) | ||||
−0.360006 | + | 0.932950i | \(0.617225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2936.00 | −0.163765 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2706.00 | 0.150277 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9360.00 | 0.517544 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1080.00 | 0.0594575 | 0.0297288 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297288 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −360.000 | −0.0197334 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1616.00 | 0.0881991 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5292.00 | −0.287588 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5886.00 | 0.318496 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22720.0 | −1.22414 | −0.612070 | − | 0.790803i | \(-0.709663\pi\) | ||||
−0.612070 | + | 0.790803i | \(0.709663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2096.00 | 0.112450 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1776.00 | 0.0948766 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18000.0 | 0.957510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22346.0 | −1.18367 | −0.591835 | − | 0.806059i | \(-0.701596\pi\) | ||||
−0.591835 | + | 0.806059i | \(0.701596\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3474.00 | −0.183242 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2664.00 | 0.139926 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 416.000 | 0.0217588 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6048.00 | −0.315016 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35244.0 | −1.82807 | −0.914033 | − | 0.405640i | \(-0.867049\pi\) | ||||
−0.914033 | + | 0.405640i | \(0.867049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8180.00 | −0.422523 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5478.00 | −0.281783 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7848.00 | 0.402024 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25074.0 | −1.27915 | −0.639576 | − | 0.768728i | \(-0.720890\pi\) | ||||
−0.639576 | + | 0.768728i | \(0.720890\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6048.00 | 0.306010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23742.0 | 1.19636 | 0.598179 | − | 0.801362i | \(-0.295891\pi\) | ||||
0.598179 | + | 0.801362i | \(0.295891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2916.00 | 0.146338 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2768.00 | 0.138345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4932.00 | 0.245503 | 0.122751 | − | 0.992437i | \(-0.460828\pi\) | ||||
0.122751 | + | 0.992437i | \(0.460828\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 624.000 | 0.0309355 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26248.0 | 1.29602 | 0.648012 | − | 0.761630i | \(-0.275601\pi\) | ||||
0.648012 | + | 0.761630i | \(0.275601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2736.00 | −0.134549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −972.000 | −0.0476086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7160.00 | 0.349293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26146.0 | −1.27041 | −0.635207 | − | 0.772342i | \(-0.719085\pi\) | ||||
−0.635207 | + | 0.772342i | \(0.719085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9180.00 | 0.444273 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14008.0 | −0.675236 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4202.00 | −0.201749 | −0.100875 | − | 0.994899i | \(-0.532164\pi\) | ||||
−0.100875 | + | 0.994899i | \(0.532164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1776.00 | −0.0849337 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31018.0 | −1.47753 | −0.738766 | − | 0.673962i | \(-0.764591\pi\) | ||||
−0.738766 | + | 0.673962i | \(0.764591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11340.0 | −0.538054 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −504.000 | −0.0238198 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11128.0 | −0.523871 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7570.00 | −0.354982 | −0.177491 | − | 0.984122i | \(-0.556798\pi\) | ||||
−0.177491 | + | 0.984122i | \(0.556798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1674.00 | −0.0781941 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31392.0 | −1.46066 | −0.730331 | − | 0.683093i | \(-0.760634\pi\) | ||||
−0.730331 | + | 0.683093i | \(0.760634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1962.00 | 0.0909382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7860.00 | 0.362903 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3024.00 | 0.139083 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2160.00 | −0.0989640 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1944.00 | −0.0887266 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13032.0 | −0.592525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14608.0 | 0.661651 | 0.330825 | − | 0.943692i | \(-0.392673\pi\) | ||||
0.330825 | + | 0.943692i | \(0.392673\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16632.0 | −0.750462 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18580.0 | −0.835182 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11492.0 | −0.514619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4320.00 | 0.192723 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30204.0 | −1.34238 | −0.671192 | − | 0.741283i | \(-0.734218\pi\) | ||||
−0.671192 | + | 0.741283i | \(0.734218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2072.00 | −0.0917423 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3438.00 | −0.151655 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4072.00 | −0.178951 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5920.00 | −0.259196 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14568.0 | −0.635462 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −306.000 | −0.0132984 | −0.00664919 | − | 0.999978i | \(-0.502117\pi\) | ||||
−0.00664919 | + | 0.999978i | \(0.502117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34920.0 | 1.51197 | 0.755985 | − | 0.654589i | \(-0.227158\pi\) | ||||
0.755985 | + | 0.654589i | \(0.227158\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21090.0 | −0.909789 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3424.00 | −0.147163 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3456.00 | −0.147993 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2340.00 | 0.0998367 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14720.0 | −0.625739 | −0.312869 | − | 0.949796i | \(-0.601290\pi\) | ||||
−0.312869 | + | 0.949796i | \(0.601290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14030.0 | 0.594235 | 0.297117 | − | 0.954841i | \(-0.403975\pi\) | ||||
0.297117 | + | 0.954841i | \(0.403975\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1308.00 | −0.0551984 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24764.0 | −1.04127 | −0.520634 | − | 0.853780i | \(-0.674304\pi\) | ||||
−0.520634 | + | 0.853780i | \(0.674304\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1810.00 | −0.0758310 | −0.0379155 | − | 0.999281i | \(-0.512072\pi\) | ||||
−0.0379155 | + | 0.999281i | \(0.512072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2214.00 | −0.0924222 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3402.00 | −0.141503 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6208.00 | 0.257289 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −486.000 | −0.0200700 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4500.00 | −0.185170 | −0.0925848 | − | 0.995705i | \(-0.529513\pi\) | ||||
−0.0925848 | + | 0.995705i | \(0.529513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19205.0 | −0.787445 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5562.00 | −0.227243 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6084.00 | 0.247688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13150.0 | 0.533458 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4212.00 | −0.170266 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38776.0 | 1.56196 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29458.0 | 1.18244 | 0.591221 | − | 0.806510i | \(-0.298646\pi\) | ||||
0.591221 | + | 0.806510i | \(0.298646\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 288.000 | 0.0115198 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15030.0 | 0.599084 | 0.299542 | − | 0.954083i | \(-0.403166\pi\) | ||||
0.299542 | + | 0.954083i | \(0.403166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27368.0 | 1.08706 | 0.543530 | − | 0.839390i | \(-0.317088\pi\) | ||||
0.543530 | + | 0.839390i | \(0.317088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11340.0 | 0.448857 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39352.0 | −1.55221 | −0.776105 | − | 0.630603i | \(-0.782807\pi\) | ||||
−0.776105 | + | 0.630603i | \(0.782807\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6192.00 | −0.243392 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14151.0 | −0.554317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1544.00 | −0.0602723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17992.0 | −0.699926 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2682.00 | 0.103977 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9360.00 | −0.361629 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32246.0 | −1.24159 | −0.620793 | − | 0.783975i | \(-0.713189\pi\) | ||||
−0.620793 | + | 0.783975i | \(0.713189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6168.00 | 0.236680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1714.00 | 0.0655461 | 0.0327731 | − | 0.999463i | \(-0.489566\pi\) | ||||
0.0327731 | + | 0.999463i | \(0.489566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1288.00 | −0.0490879 | −0.0245440 | − | 0.999699i | \(-0.507813\pi\) | ||||
−0.0245440 | + | 0.999699i | \(0.507813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5136.00 | −0.195079 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12888.0 | 0.487865 | 0.243933 | − | 0.969792i | \(-0.421562\pi\) | ||||
0.243933 | + | 0.969792i | \(0.421562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14020.0 | −0.528927 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 324.000 | 0.0121823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1184.00 | 0.0443685 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13680.0 | 0.510918 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11544.0 | 0.429702 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1296.00 | 0.0480801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5040.00 | −0.186356 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12960.0 | −0.477610 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14008.0 | −0.514521 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44920.0 | 1.64448 | 0.822240 | − | 0.569140i | \(-0.192724\pi\) | ||||
0.822240 | + | 0.569140i | \(0.192724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16200.0 | −0.591111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12384.0 | −0.450384 | −0.225192 | − | 0.974314i | \(-0.572301\pi\) | ||||
−0.225192 | + | 0.974314i | \(0.572301\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −432.000 | −0.0156595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5304.00 | −0.191634 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11880.0 | 0.427821 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8190.00 | 0.293975 | 0.146988 | − | 0.989138i | \(-0.453042\pi\) | ||||
0.146988 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7020.00 | 0.251158 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14040.0 | 0.500685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28558.0 | 1.01511 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7362.00 | 0.260841 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4698.00 | −0.165916 | −0.0829582 | − | 0.996553i | \(-0.526437\pi\) | ||||
−0.0829582 | + | 0.996553i | \(0.526437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1944.00 | 0.0684340 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4848.00 | −0.170114 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −224.000 | −0.00783485 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10646.0 | −0.371174 | −0.185587 | − | 0.982628i | \(-0.559419\pi\) | ||||
−0.185587 | + | 0.982628i | \(0.559419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9858.00 | 0.342602 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25852.0 | 0.895591 | 0.447795 | − | 0.894136i | \(-0.352209\pi\) | ||||
0.447795 | + | 0.894136i | \(0.352209\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55944.0 | 1.93191 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1080.00 | 0.0371771 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3172.00 | 0.108845 | 0.0544225 | − | 0.998518i | \(-0.482668\pi\) | ||||
0.0544225 | + | 0.998518i | \(0.482668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26468.0 | 0.905361 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29808.0 | −1.01639 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53150.0 | 1.80661 | 0.903304 | − | 0.429001i | \(-0.141134\pi\) | ||||
0.903304 | + | 0.429001i | \(0.141134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19168.0 | −0.649489 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −864.000 | −0.0291841 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7340.00 | −0.247154 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29467.0 | −0.989124 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6444.00 | −0.215633 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 392.000 | 0.0130766 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9802.00 | 0.325968 | 0.162984 | − | 0.986629i | \(-0.447888\pi\) | ||||
0.162984 | + | 0.986629i | \(0.447888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −336.000 | −0.0111392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46660.0 | −1.54211 | −0.771056 | − | 0.636767i | \(-0.780271\pi\) | ||||
−0.771056 | + | 0.636767i | \(0.780271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4040.00 | 0.133110 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8502.00 | 0.279264 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41994.0 | −1.37514 | −0.687568 | − | 0.726120i | \(-0.741322\pi\) | ||||
−0.687568 | + | 0.726120i | \(0.741322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1528.00 | −0.0498826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10206.0 | 0.332164 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11848.0 | 0.384428 | 0.192214 | − | 0.981353i | \(-0.438433\pi\) | ||||
0.192214 | + | 0.981353i | \(0.438433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4736.00 | 0.153200 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4440.00 | 0.143188 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −63936.0 | −2.05566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7390.00 | 0.236883 | 0.118442 | − | 0.992961i | \(-0.462210\pi\) | ||||
0.118442 | + | 0.992961i | \(0.462210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6348.00 | 0.202868 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5864.00 | −0.186835 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47682.0 | 1.51465 | 0.757324 | − | 0.653039i | \(-0.226506\pi\) | ||||
0.757324 | + | 0.653039i | \(0.226506\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7074.00 | −0.224035 |
(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 | 384.4.a.f.1.1 | yes | 1 | |
3.2 | odd | 2 | 1152.4.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 384.4.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 384.4.a.g.1.1 | yes | 1 | ||
8.5 | even | 2 | 384.4.a.c.1.1 | yes | 1 | ||
12.11 | even | 2 | 1152.4.a.h.1.1 | 1 | |||
16.3 | odd | 4 | 768.4.d.f.385.1 | 2 | |||
16.5 | even | 4 | 768.4.d.k.385.1 | 2 | |||
16.11 | odd | 4 | 768.4.d.f.385.2 | 2 | |||
16.13 | even | 4 | 768.4.d.k.385.2 | 2 | |||
24.5 | odd | 2 | 1152.4.a.e.1.1 | 1 | |||
24.11 | even | 2 | 1152.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
384.4.a.c.1.1 | yes | 1 | 8.5 | even | 2 | ||
384.4.a.f.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
384.4.a.g.1.1 | yes | 1 | 8.3 | odd | 2 | ||
768.4.d.f.385.1 | 2 | 16.3 | odd | 4 | |||
768.4.d.f.385.2 | 2 | 16.11 | odd | 4 | |||
768.4.d.k.385.1 | 2 | 16.5 | even | 4 | |||
768.4.d.k.385.2 | 2 | 16.13 | even | 4 | |||
1152.4.a.e.1.1 | 1 | 24.5 | odd | 2 | |||
1152.4.a.f.1.1 | 1 | 24.11 | even | 2 | |||
1152.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
1152.4.a.h.1.1 | 1 | 12.11 | even | 2 |