Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(1,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, 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("1152.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.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: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 128) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1152.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.0000 | 1.07990 | 0.539949 | − | 0.841698i | \(-0.318443\pi\) | ||||
0.539949 | + | 0.841698i | \(0.318443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.0000 | −0.383742 | −0.191871 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191871 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0000 | 1.15207 | 0.576035 | − | 0.817425i | \(-0.304599\pi\) | ||||
0.576035 | + | 0.817425i | \(0.304599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.0000 | 0.941609 | 0.470804 | − | 0.882238i | \(-0.343964\pi\) | ||||
0.470804 | + | 0.882238i | \(0.343964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 162.000 | 1.95607 | 0.978035 | − | 0.208438i | \(-0.0668381\pi\) | ||||
0.978035 | + | 0.208438i | \(0.0668381\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −172.000 | −1.55933 | −0.779663 | − | 0.626200i | \(-0.784609\pi\) | ||||
−0.779663 | + | 0.626200i | \(0.784609\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.0128066 | 0.00640329 | − | 0.999979i | \(-0.497962\pi\) | ||||
0.00640329 | + | 0.999979i | \(0.497962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.000 | −0.741596 | −0.370798 | − | 0.928714i | \(-0.620916\pi\) | ||||
−0.370798 | + | 0.928714i | \(0.620916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −120.000 | −0.579534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 158.000 | 0.702028 | 0.351014 | − | 0.936370i | \(-0.385837\pi\) | ||||
0.351014 | + | 0.936370i | \(0.385837\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −202.000 | −0.769441 | −0.384721 | − | 0.923033i | \(-0.625702\pi\) | ||||
−0.384721 | + | 0.923033i | \(0.625702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −298.000 | −1.05685 | −0.528425 | − | 0.848980i | \(-0.677217\pi\) | ||||
−0.528425 | + | 0.848980i | \(0.677217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 408.000 | 1.26623 | 0.633116 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633116 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 690.000 | 1.78828 | 0.894140 | − | 0.447788i | \(-0.147788\pi\) | ||||
0.894140 | + | 0.447788i | \(0.147788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 84.0000 | 0.205937 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 322.000 | 0.710523 | 0.355261 | − | 0.934767i | \(-0.384392\pi\) | ||||
0.355261 | + | 0.934767i | \(0.384392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −298.000 | −0.625492 | −0.312746 | − | 0.949837i | \(-0.601249\pi\) | ||||
−0.312746 | + | 0.949837i | \(0.601249\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −324.000 | −0.618265 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 202.000 | 0.368332 | 0.184166 | − | 0.982895i | \(-0.441042\pi\) | ||||
0.184166 | + | 0.982895i | \(0.441042\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 700.000 | 1.17007 | 0.585033 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585033 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −418.000 | −0.670181 | −0.335090 | − | 0.942186i | \(-0.608767\pi\) | ||||
−0.335090 | + | 0.942186i | \(0.608767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −280.000 | −0.414402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 744.000 | 1.05958 | 0.529788 | − | 0.848130i | \(-0.322271\pi\) | ||||
0.529788 | + | 0.848130i | \(0.322271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 678.000 | 0.896629 | 0.448314 | − | 0.893876i | \(-0.352025\pi\) | ||||
0.448314 | + | 0.893876i | \(0.352025\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −396.000 | −0.505320 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 82.0000 | 0.0976627 | 0.0488314 | − | 0.998807i | \(-0.484450\pi\) | ||||
0.0488314 | + | 0.998807i | \(0.484450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1080.00 | 1.24412 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −972.000 | −1.04974 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1122.00 | −1.17445 | −0.587226 | − | 0.809423i | \(-0.699780\pi\) | ||||
−0.587226 | + | 0.809423i | \(0.699780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1390.00 | −1.36941 | −0.684704 | − | 0.728821i | \(-0.740068\pi\) | ||||
−0.684704 | + | 0.728821i | \(0.740068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 788.000 | 0.753825 | 0.376912 | − | 0.926249i | \(-0.376986\pi\) | ||||
0.376912 | + | 0.926249i | \(0.376986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1614.00 | −1.45824 | −0.729118 | − | 0.684388i | \(-0.760070\pi\) | ||||
−0.729118 | + | 0.684388i | \(0.760070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2014.00 | 1.76978 | 0.884891 | − | 0.465798i | \(-0.154233\pi\) | ||||
0.884891 | + | 0.465798i | \(0.154233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 542.000 | 0.451213 | 0.225607 | − | 0.974219i | \(-0.427564\pi\) | ||||
0.225607 | + | 0.974219i | \(0.427564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1032.00 | 0.836822 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1320.00 | 1.01684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1135.00 | −0.852742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1712.00 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2118.00 | 1.41260 | 0.706300 | − | 0.707913i | \(-0.250363\pi\) | ||||
0.706300 | + | 0.707913i | \(0.250363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3240.00 | 2.11236 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 486.000 | 0.303079 | 0.151539 | − | 0.988451i | \(-0.451577\pi\) | ||||
0.151539 | + | 0.988451i | \(0.451577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1286.00 | 0.784727 | 0.392364 | − | 0.919810i | \(-0.371657\pi\) | ||||
0.392364 | + | 0.919810i | \(0.371657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −756.000 | −0.442097 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.00687273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2666.00 | 1.46582 | 0.732910 | − | 0.680325i | \(-0.238162\pi\) | ||||
0.732910 | + | 0.680325i | \(0.238162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 172.000 | 0.0926964 | 0.0463482 | − | 0.998925i | \(-0.485242\pi\) | ||||
0.0463482 | + | 0.998925i | \(0.485242\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 768.000 | 0.397982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 838.000 | 0.425985 | 0.212993 | − | 0.977054i | \(-0.431679\pi\) | ||||
0.212993 | + | 0.977054i | \(0.431679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3440.00 | −1.68391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1346.00 | 0.646791 | 0.323395 | − | 0.946264i | \(-0.395176\pi\) | ||||
0.323395 | + | 0.946264i | \(0.395176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1052.00 | 0.487462 | 0.243731 | − | 0.969843i | \(-0.421629\pi\) | ||||
0.243731 | + | 0.969843i | \(0.421629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −38.0000 | −0.0166999 | −0.00834996 | − | 0.999965i | \(-0.502658\pi\) | ||||
−0.00834996 | + | 0.999965i | \(0.502658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1780.00 | −0.768888 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2790.00 | 1.16500 | 0.582498 | − | 0.812832i | \(-0.302075\pi\) | ||||
0.582498 | + | 0.812832i | \(0.302075\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3418.00 | −1.40364 | −0.701818 | − | 0.712357i | \(-0.747628\pi\) | ||||
−0.701818 | + | 0.712357i | \(0.747628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −948.000 | −0.376748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −924.000 | −0.361335 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1968.00 | 0.745547 | 0.372774 | − | 0.927922i | \(-0.378407\pi\) | ||||
0.372774 | + | 0.927922i | \(0.378407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1058.00 | −0.394593 | −0.197297 | − | 0.980344i | \(-0.563216\pi\) | ||||
−0.197297 | + | 0.980344i | \(0.563216\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −726.000 | −0.262565 | −0.131283 | − | 0.991345i | \(-0.541910\pi\) | ||||
−0.131283 | + | 0.991345i | \(0.541910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4116.00 | 1.46621 | 0.733104 | − | 0.680116i | \(-0.238071\pi\) | ||||
0.733104 | + | 0.680116i | \(0.238071\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40.0000 | 0.0138298 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1212.00 | 0.412926 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2268.00 | −0.750626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1482.00 | 0.483531 | 0.241766 | − | 0.970335i | \(-0.422273\pi\) | ||||
0.241766 | + | 0.970335i | \(0.422273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1788.00 | 0.567166 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2560.00 | −0.800848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3564.00 | 1.08480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −896.000 | −0.269061 | −0.134530 | − | 0.990909i | \(-0.542953\pi\) | ||||
−0.134530 | + | 0.990909i | \(0.542953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3410.00 | −0.997047 | −0.498523 | − | 0.866876i | \(-0.666124\pi\) | ||||
−0.498523 | + | 0.866876i | \(0.666124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4502.00 | 1.29913 | 0.649564 | − | 0.760307i | \(-0.274951\pi\) | ||||
0.649564 | + | 0.760307i | \(0.274951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2302.00 | −0.647249 | −0.323625 | − | 0.946186i | \(-0.604901\pi\) | ||||
−0.323625 | + | 0.946186i | \(0.604901\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2448.00 | −0.679532 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4024.00 | −1.08908 | −0.544542 | − | 0.838734i | \(-0.683296\pi\) | ||||
−0.544542 | + | 0.838734i | \(0.683296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3586.00 | −0.958484 | −0.479242 | − | 0.877683i | \(-0.659088\pi\) | ||||
−0.479242 | + | 0.877683i | \(0.659088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −342.000 | −0.0891820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8748.00 | 2.25353 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1250.00 | 0.314340 | 0.157170 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157170 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2408.00 | 0.598378 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6638.00 | 1.61116 | 0.805578 | − | 0.592490i | \(-0.201855\pi\) | ||||
0.805578 | + | 0.592490i | \(0.201855\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3160.00 | 0.758119 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1724.00 | 0.404207 | 0.202103 | − | 0.979364i | \(-0.435222\pi\) | ||||
0.202103 | + | 0.979364i | \(0.435222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4140.00 | −0.959691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4814.00 | −1.09113 | −0.545566 | − | 0.838068i | \(-0.683685\pi\) | ||||
−0.545566 | + | 0.838068i | \(0.683685\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1640.00 | −0.367612 | −0.183806 | − | 0.982963i | \(-0.558842\pi\) | ||||
−0.183806 | + | 0.982963i | \(0.558842\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1246.00 | 0.273224 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3982.00 | 0.863737 | 0.431869 | − | 0.901937i | \(-0.357854\pi\) | ||||
0.431869 | + | 0.901937i | \(0.357854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4126.00 | −0.875931 | −0.437965 | − | 0.898992i | \(-0.644301\pi\) | ||||
−0.437965 | + | 0.898992i | \(0.644301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3446.00 | 0.723828 | 0.361914 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361914 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4040.00 | −0.830919 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1514.00 | 0.301873 | 0.150937 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150937 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1932.00 | −0.381306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9288.00 | −1.79645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5960.00 | −1.14129 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1788.00 | 0.335674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5490.00 | 1.02062 | 0.510311 | − | 0.859990i | \(-0.329530\pi\) | ||||
0.510311 | + | 0.859990i | \(0.329530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5556.00 | 1.01303 | 0.506514 | − | 0.862232i | \(-0.330934\pi\) | ||||
0.506514 | + | 0.862232i | \(0.330934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2054.00 | −0.370923 | −0.185462 | − | 0.982652i | \(-0.559378\pi\) | ||||
−0.185462 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2494.00 | −0.441883 | −0.220942 | − | 0.975287i | \(-0.570913\pi\) | ||||
−0.220942 | + | 0.975287i | \(0.570913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.0000 | −0.00491442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10692.0 | 1.84185 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4806.00 | −0.820274 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8160.00 | 1.36740 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2914.00 | −0.483891 | −0.241946 | − | 0.970290i | \(-0.577786\pi\) | ||||
−0.241946 | + | 0.970290i | \(0.577786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1212.00 | −0.197668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7186.00 | 1.16156 | 0.580781 | − | 0.814060i | \(-0.302747\pi\) | ||||
0.580781 | + | 0.814060i | \(0.302747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1792.00 | 0.284581 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5720.00 | −0.900440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4446.00 | −0.687821 | −0.343910 | − | 0.939002i | \(-0.611752\pi\) | ||||
−0.343910 | + | 0.939002i | \(0.611752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 430.000 | 0.0659524 | 0.0329762 | − | 0.999456i | \(-0.489501\pi\) | ||||
0.0329762 | + | 0.999456i | \(0.489501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −850.000 | −0.128161 | −0.0640806 | − | 0.997945i | \(-0.520411\pi\) | ||||
−0.0640806 | + | 0.997945i | \(0.520411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4200.00 | −0.627924 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10988.0 | 1.61539 | 0.807694 | − | 0.589602i | \(-0.200715\pi\) | ||||
0.807694 | + | 0.589602i | \(0.200715\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19385.0 | 2.82621 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2508.00 | 0.359657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 872.000 | 0.124027 | 0.0620137 | − | 0.998075i | \(-0.480248\pi\) | ||||
0.0620137 | + | 0.998075i | \(0.480248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13800.0 | 1.93116 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3454.00 | 0.479467 | 0.239734 | − | 0.970839i | \(-0.422940\pi\) | ||||
0.239734 | + | 0.970839i | \(0.422940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 108.000 | 0.0147541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1490.00 | −0.201942 | −0.100971 | − | 0.994889i | \(-0.532195\pi\) | ||||
−0.100971 | + | 0.994889i | \(0.532195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10240.0 | −1.36616 | −0.683080 | − | 0.730343i | \(-0.739360\pi\) | ||||
−0.683080 | + | 0.730343i | \(0.739360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1680.00 | 0.222392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7458.00 | 0.972071 | 0.486035 | − | 0.873939i | \(-0.338443\pi\) | ||||
0.486035 | + | 0.873939i | \(0.338443\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11352.0 | −1.46827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4464.00 | −0.568628 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4706.00 | −0.594930 | −0.297465 | − | 0.954733i | \(-0.596141\pi\) | ||||
−0.297465 | + | 0.954733i | \(0.596141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5598.00 | −0.697134 | −0.348567 | − | 0.937284i | \(-0.613332\pi\) | ||||
−0.348567 | + | 0.937284i | \(0.613332\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6912.00 | −0.854370 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2212.00 | −0.269397 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −838.000 | −0.101312 | −0.0506558 | − | 0.998716i | \(-0.516131\pi\) | ||||
−0.0506558 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6440.00 | 0.767292 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4068.00 | −0.481181 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.0000 | −0.00303146 | −0.00151573 | − | 0.999999i | \(-0.500482\pi\) | ||||
−0.00151573 | + | 0.999999i | \(0.500482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15578.0 | −1.80339 | −0.901693 | − | 0.432377i | \(-0.857675\pi\) | ||||
−0.901693 | + | 0.432377i | \(0.857675\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5874.00 | −0.670426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5960.00 | −0.675467 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6792.00 | 0.759070 | 0.379535 | − | 0.925177i | \(-0.376084\pi\) | ||||
0.379535 | + | 0.925177i | \(0.376084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9314.00 | −1.03372 | −0.516862 | − | 0.856069i | \(-0.672900\pi\) | ||||
−0.516862 | + | 0.856069i | \(0.672900\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27864.0 | −3.05015 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3828.00 | −0.416174 | −0.208087 | − | 0.978110i | \(-0.566724\pi\) | ||||
−0.208087 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15414.0 | −1.65314 | −0.826570 | − | 0.562834i | \(-0.809711\pi\) | ||||
−0.826570 | + | 0.562834i | \(0.809711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −492.000 | −0.0524113 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3650.00 | 0.383640 | 0.191820 | − | 0.981430i | \(-0.438561\pi\) | ||||
0.191820 | + | 0.981430i | \(0.438561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2828.00 | 0.295267 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6480.00 | −0.667664 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15862.0 | −1.62362 | −0.811809 | − | 0.583924i | \(-0.801517\pi\) | ||||
−0.811809 | + | 0.583924i | \(0.801517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −78.0000 | −0.00788031 | −0.00394015 | − | 0.999992i | \(-0.501254\pi\) | ||||
−0.00394015 | + | 0.999992i | \(0.501254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4376.00 | −0.439244 | −0.219622 | − | 0.975585i | \(-0.570482\pi\) | ||||
−0.219622 | + | 0.975585i | \(0.570482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13714.0 | −1.35890 | −0.679452 | − | 0.733720i | \(-0.737782\pi\) | ||||
−0.679452 | + | 0.733720i | \(0.737782\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4040.00 | 0.397761 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4172.00 | 0.405558 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14418.0 | −1.39272 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19072.0 | −1.81925 | −0.909626 | − | 0.415428i | \(-0.863632\pi\) | ||||
−0.909626 | + | 0.415428i | \(0.863632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8532.00 | 0.808785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6732.00 | 0.630277 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19428.0 | 1.80773 | 0.903867 | − | 0.427813i | \(-0.140716\pi\) | ||||
0.903867 | + | 0.427813i | \(0.140716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2490.00 | 0.228864 | 0.114432 | − | 0.993431i | \(-0.463495\pi\) | ||||
0.114432 | + | 0.993431i | \(0.463495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 132.000 | 0.0120588 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14000.0 | 1.26355 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2826.00 | 0.253525 | 0.126763 | − | 0.991933i | \(-0.459541\pi\) | ||||
0.126763 | + | 0.991933i | \(0.459541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2268.00 | −0.201044 | −0.100522 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100522 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8340.00 | 0.734901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10534.0 | −0.917311 | −0.458656 | − | 0.888614i | \(-0.651669\pi\) | ||||
−0.458656 | + | 0.888614i | \(0.651669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8360.00 | −0.723727 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4728.00 | −0.404545 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5712.00 | −0.485906 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9478.00 | 0.797003 | 0.398502 | − | 0.917168i | \(-0.369530\pi\) | ||||
0.398502 | + | 0.917168i | \(0.369530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5858.00 | −0.489775 | −0.244888 | − | 0.969551i | \(-0.578751\pi\) | ||||
−0.244888 | + | 0.969551i | \(0.578751\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8448.00 | −0.698293 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17417.0 | 1.43150 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10908.0 | −0.886450 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9684.00 | 0.782572 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −798.000 | −0.0637705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1910.00 | 0.151788 | 0.0758940 | − | 0.997116i | \(-0.475819\pi\) | ||||
0.0758940 | + | 0.997116i | \(0.475819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12084.0 | −0.949765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1754.00 | 0.137104 | 0.0685518 | − | 0.997648i | \(-0.478162\pi\) | ||||
0.0685518 | + | 0.997648i | \(0.478162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 324.000 | 0.0250506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14880.0 | 1.14424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2294.00 | −0.174506 | −0.0872531 | − | 0.996186i | \(-0.527809\pi\) | ||||
−0.0872531 | + | 0.996186i | \(0.527809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16092.0 | −1.21757 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16242.0 | −1.21584 | −0.607921 | − | 0.793998i | \(-0.707996\pi\) | ||||
−0.607921 | + | 0.793998i | \(0.707996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3252.00 | −0.242146 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15990.0 | 1.17809 | 0.589047 | − | 0.808099i | \(-0.299503\pi\) | ||||
0.589047 | + | 0.808099i | \(0.299503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21674.0 | −1.58849 | −0.794246 | − | 0.607597i | \(-0.792134\pi\) | ||||
−0.794246 | + | 0.607597i | \(0.792134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15308.0 | 1.11024 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12542.0 | −0.904905 | −0.452453 | − | 0.891788i | \(-0.649451\pi\) | ||||
−0.452453 | + | 0.891788i | \(0.649451\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13560.0 | 0.968268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9660.00 | −0.686237 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18578.0 | 1.30630 | 0.653148 | − | 0.757230i | \(-0.273448\pi\) | ||||
0.653148 | + | 0.757230i | \(0.273448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20736.0 | −1.45061 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14514.0 | −1.00509 | −0.502545 | − | 0.864551i | \(-0.667603\pi\) | ||||
−0.502545 | + | 0.864551i | \(0.667603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7920.00 | −0.545695 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3460.00 | 0.236013 | 0.118006 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118006 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20686.0 | 1.40399 | 0.701996 | − | 0.712181i | \(-0.252292\pi\) | ||||
0.701996 | + | 0.712181i | \(0.252292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6810.00 | 0.457630 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9776.00 | −0.653700 | −0.326850 | − | 0.945076i | \(-0.605987\pi\) | ||||
−0.326850 | + | 0.945076i | \(0.605987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22032.0 | 1.45879 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8794.00 | −0.579423 | −0.289712 | − | 0.957114i | \(-0.593559\pi\) | ||||
−0.289712 | + | 0.957114i | \(0.593559\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16398.0 | −1.06995 | −0.534975 | − | 0.844868i | \(-0.679679\pi\) | ||||
−0.534975 | + | 0.844868i | \(0.679679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21374.0 | 1.38787 | 0.693937 | − | 0.720036i | \(-0.255875\pi\) | ||||
0.693937 | + | 0.720036i | \(0.255875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1640.00 | 0.105466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10428.0 | 0.661036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18916.0 | −1.19340 | −0.596699 | − | 0.802465i | \(-0.703521\pi\) | ||||
−0.596699 | + | 0.802465i | \(0.703521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10272.0 | −0.641940 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3078.00 | 0.191452 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5250.00 | 0.323498 | 0.161749 | − | 0.986832i | \(-0.448286\pi\) | ||||
0.161749 | + | 0.986832i | \(0.448286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4502.00 | −0.276114 | −0.138057 | − | 0.990424i | \(-0.544086\pi\) | ||||
−0.138057 | + | 0.990424i | \(0.544086\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11076.0 | −0.673018 | −0.336509 | − | 0.941680i | \(-0.609246\pi\) | ||||
−0.336509 | + | 0.941680i | \(0.609246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4508.00 | −0.272657 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30766.0 | −1.84375 | −0.921873 | − | 0.387491i | \(-0.873342\pi\) | ||||
−0.921873 | + | 0.387491i | \(0.873342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12708.0 | −0.758080 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20518.0 | 1.21285 | 0.606425 | − | 0.795141i | \(-0.292603\pi\) | ||||
0.606425 | + | 0.795141i | \(0.292603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 70.0000 | 0.00411904 | 0.00205952 | − | 0.999998i | \(-0.499344\pi\) | ||||
0.00205952 | + | 0.999998i | \(0.499344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19440.0 | −1.13361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −344.000 | −0.0199696 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4172.00 | 0.240027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23070.0 | 1.32137 | 0.660686 | − | 0.750663i | \(-0.270266\pi\) | ||||
0.660686 | + | 0.750663i | \(0.270266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2622.00 | −0.148850 | −0.0744251 | − | 0.997227i | \(-0.523712\pi\) | ||||
−0.0744251 | + | 0.997227i | \(0.523712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22440.0 | −1.26829 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14682.0 | 0.822535 | 0.411267 | − | 0.911515i | \(-0.365086\pi\) | ||||
0.411267 | + | 0.911515i | \(0.365086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2916.00 | −0.162649 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37260.0 | 2.06022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23270.0 | −1.28109 | −0.640545 | − | 0.767921i | \(-0.721291\pi\) | ||||
−0.640545 | + | 0.767921i | \(0.721291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7716.00 | −0.421129 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13332.0 | −0.724513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31530.0 | 1.69882 | 0.849409 | − | 0.527735i | \(-0.176959\pi\) | ||||
0.849409 | + | 0.527735i | \(0.176959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25596.0 | 1.37322 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27800.0 | −1.47882 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22014.0 | 1.16608 | 0.583042 | − | 0.812442i | \(-0.301862\pi\) | ||||
0.583042 | + | 0.812442i | \(0.301862\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22016.0 | 1.15639 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4536.00 | 0.237254 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19016.0 | −0.986338 | −0.493169 | − | 0.869933i | \(-0.664162\pi\) | ||||
−0.493169 | + | 0.869933i | \(0.664162\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15760.0 | 0.814054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −178.000 | −0.00911828 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15996.0 | 0.816037 | 0.408018 | − | 0.912974i | \(-0.366220\pi\) | ||||
0.408018 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19668.0 | −0.995140 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10622.0 | 0.535242 | 0.267621 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267621 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2828.00 | −0.141344 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8878.00 | −0.441925 | −0.220962 | − | 0.975282i | \(-0.570920\pi\) | ||||
−0.220962 | + | 0.975282i | \(0.570920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21852.0 | 1.07897 | 0.539483 | − | 0.841996i | \(-0.318620\pi\) | ||||
0.539483 | + | 0.841996i | \(0.318620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15996.0 | −0.786642 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32280.0 | −1.57475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32024.0 | 1.55602 | 0.778011 | − | 0.628251i | \(-0.216229\pi\) | ||||
0.778011 | + | 0.628251i | \(0.216229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1032.00 | −0.0497461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26602.0 | −1.27723 | −0.638617 | − | 0.769525i | \(-0.720493\pi\) | ||||
−0.638617 | + | 0.769525i | \(0.720493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13958.0 | 0.664885 | 0.332442 | − | 0.943124i | \(-0.392127\pi\) | ||||
0.332442 | + | 0.943124i | \(0.392127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40280.0 | 1.91118 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17388.0 | 0.818571 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11970.0 | −0.561312 | −0.280656 | − | 0.959808i | \(-0.590552\pi\) | ||||
−0.280656 | + | 0.959808i | \(0.590552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12318.0 | −0.573154 | −0.286577 | − | 0.958057i | \(-0.592517\pi\) | ||||
−0.286577 | + | 0.958057i | \(0.592517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11392.0 | 0.528016 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32724.0 | −1.50508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9800.00 | −0.449003 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5028.00 | −0.228608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26698.0 | 1.20925 | 0.604626 | − | 0.796510i | \(-0.293323\pi\) | ||||
0.604626 | + | 0.796510i | \(0.293323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10840.0 | 0.487264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16092.0 | −0.720610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4794.00 | 0.213064 | 0.106532 | − | 0.994309i | \(-0.466025\pi\) | ||||
0.106532 | + | 0.994309i | \(0.466025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26928.0 | 1.19230 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5852.00 | 0.257176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20640.0 | 0.903683 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39114.0 | −1.69985 | −0.849923 | − | 0.526907i | \(-0.823351\pi\) | ||||
−0.849923 | + | 0.526907i | \(0.823351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1090.00 | −0.0471949 | −0.0235975 | − | 0.999722i | \(-0.507512\pi\) | ||||
−0.0235975 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8076.00 | −0.347104 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48276.0 | −2.06727 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9730.00 | 0.413617 | 0.206808 | − | 0.978381i | \(-0.433692\pi\) | ||||
0.206808 | + | 0.978381i | \(0.433692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1100.00 | 0.0465900 | 0.0232950 | − | 0.999729i | \(-0.492584\pi\) | ||||
0.0232950 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38074.0 | 1.60092 | 0.800461 | − | 0.599385i | \(-0.204588\pi\) | ||||
0.800461 | + | 0.599385i | \(0.204588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24230.0 | 1.01513 | 0.507565 | − | 0.861613i | \(-0.330546\pi\) | ||||
0.507565 | + | 0.861613i | \(0.330546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3762.00 | 0.156477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6312.00 | −0.261600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16820.0 | −0.692123 | −0.346061 | − | 0.938212i | \(-0.612481\pi\) | ||||
−0.346061 | + | 0.938212i | \(0.612481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24385.0 | −0.999836 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4314.00 | −0.175629 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22700.0 | −0.920875 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27176.0 | −1.09469 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22162.0 | −0.889581 | −0.444790 | − | 0.895635i | \(-0.646722\pi\) | ||||
−0.444790 | + | 0.895635i | \(0.646722\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8790.00 | 0.350363 | 0.175181 | − | 0.984536i | \(-0.443949\pi\) | ||||
0.175181 | + | 0.984536i | \(0.443949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10558.0 | 0.419365 | 0.209682 | − | 0.977770i | \(-0.432757\pi\) | ||||
0.209682 | + | 0.977770i | \(0.432757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7392.00 | 0.291572 | 0.145786 | − | 0.989316i | \(-0.453429\pi\) | ||||
0.145786 | + | 0.989316i | \(0.453429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 228.000 | 0.00896212 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10416.0 | −0.406604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10908.0 | 0.424344 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25680.0 | 0.992163 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6574.00 | 0.253122 | 0.126561 | − | 0.991959i | \(-0.459606\pi\) | ||||
0.126561 | + | 0.991959i | \(0.459606\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47154.0 | −1.80324 | −0.901622 | − | 0.432524i | \(-0.857623\pi\) | ||||
−0.901622 | + | 0.432524i | \(0.857623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 642.000 | 0.0244677 | 0.0122339 | − | 0.999925i | \(-0.496106\pi\) | ||||
0.0122339 | + | 0.999925i | \(0.496106\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23308.0 | −0.882307 | −0.441153 | − | 0.897432i | \(-0.645431\pi\) | ||||
−0.441153 | + | 0.897432i | \(0.645431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34240.0 | 1.29176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 66096.0 | 2.47684 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16740.0 | −0.625203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −256.000 | −0.00949731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45540.0 | 1.68386 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20508.0 | 0.753270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21450.0 | −0.785265 | −0.392633 | − | 0.919695i | \(-0.628436\pi\) | ||||
−0.392633 | + | 0.919695i | \(0.628436\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40904.0 | 1.48761 | 0.743804 | − | 0.668398i | \(-0.233020\pi\) | ||||
0.743804 | + | 0.668398i | \(0.233020\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9492.00 | −0.344074 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42360.0 | 1.52546 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27380.0 | −0.982789 | −0.491394 | − | 0.870937i | \(-0.663513\pi\) | ||||
−0.491394 | + | 0.870937i | \(0.663513\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37800.0 | 1.34800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14062.0 | −0.499844 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10302.0 | −0.363830 | −0.181915 | − | 0.983314i | \(-0.558230\pi\) | ||||
−0.181915 | + | 0.983314i | \(0.558230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9234.00 | 0.325061 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5544.00 | 0.193912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5054.00 | 0.176208 | 0.0881040 | − | 0.996111i | \(-0.471919\pi\) | ||||
0.0881040 | + | 0.996111i | \(0.471919\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30462.0 | −1.05530 | −0.527648 | − | 0.849463i | \(-0.676926\pi\) | ||||
−0.527648 | + | 0.849463i | \(0.676926\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34744.0 | 1.19981 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32082.0 | −1.10087 | −0.550436 | − | 0.834878i | \(-0.685538\pi\) | ||||
−0.550436 | + | 0.834878i | \(0.685538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22572.0 | −0.772095 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12970.0 | −0.440860 | −0.220430 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220430 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11808.0 | −0.400103 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9720.00 | 0.327294 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13407.0 | −0.450035 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6348.00 | 0.211761 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1652.00 | 0.0549377 | 0.0274688 | − | 0.999623i | \(-0.491255\pi\) | ||||
0.0274688 | + | 0.999623i | \(0.491255\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24650.0 | 0.814682 | 0.407341 | − | 0.913276i | \(-0.366456\pi\) | ||||
0.407341 | + | 0.913276i | \(0.366456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25720.0 | 0.847426 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23646.0 | −0.774312 | −0.387156 | − | 0.922014i | \(-0.626542\pi\) | ||||
−0.387156 | + | 0.922014i | \(0.626542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1148.00 | −0.0374773 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38108.0 | −1.23648 | −0.618238 | − | 0.785991i | \(-0.712153\pi\) | ||||
−0.618238 | + | 0.785991i | \(0.712153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4356.00 | 0.140907 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51256.0 | 1.64797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18640.0 | −0.597497 | −0.298748 | − | 0.954332i | \(-0.596569\pi\) | ||||
−0.298748 | + | 0.954332i | \(0.596569\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24696.0 | −0.786850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29022.0 | 0.921902 | 0.460951 | − | 0.887426i | \(-0.347508\pi\) | ||||
0.460951 | + | 0.887426i | \(0.347508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 128.4.a.d.1.1 | yes | 1 | ||
4.3 | odd | 2 | 1152.4.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 1152.4.a.i.1.1 | 1 | |||
8.5 | even | 2 | 1152.4.a.j.1.1 | 1 | |||
12.11 | even | 2 | 128.4.a.b.1.1 | yes | 1 | ||
24.5 | odd | 2 | 128.4.a.a.1.1 | ✓ | 1 | ||
24.11 | even | 2 | 128.4.a.c.1.1 | yes | 1 | ||
48.5 | odd | 4 | 256.4.b.b.129.1 | 2 | |||
48.11 | even | 4 | 256.4.b.f.129.2 | 2 | |||
48.29 | odd | 4 | 256.4.b.b.129.2 | 2 | |||
48.35 | even | 4 | 256.4.b.f.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.a.a.1.1 | ✓ | 1 | 24.5 | odd | 2 | ||
128.4.a.b.1.1 | yes | 1 | 12.11 | even | 2 | ||
128.4.a.c.1.1 | yes | 1 | 24.11 | even | 2 | ||
128.4.a.d.1.1 | yes | 1 | 3.2 | odd | 2 | ||
256.4.b.b.129.1 | 2 | 48.5 | odd | 4 | |||
256.4.b.b.129.2 | 2 | 48.29 | odd | 4 | |||
256.4.b.f.129.1 | 2 | 48.35 | even | 4 | |||
256.4.b.f.129.2 | 2 | 48.11 | even | 4 | |||
1152.4.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
1152.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1152.4.a.i.1.1 | 1 | 8.3 | odd | 2 | |||
1152.4.a.j.1.1 | 1 | 8.5 | even | 2 |