Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,4,Mod(1,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, 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("1600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(94.4030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 200) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1600.1 |
$q$-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 | ||||||||
\(3\) | −5.00000 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.107990 | 0.0539949 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539949 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.0000 | 1.06899 | 0.534497 | − | 0.845170i | \(-0.320501\pi\) | ||||
0.534497 | + | 0.845170i | \(0.320501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 84.0000 | 1.79211 | 0.896054 | − | 0.443945i | \(-0.146421\pi\) | ||||
0.896054 | + | 0.443945i | \(0.146421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 61.0000 | 0.870275 | 0.435137 | − | 0.900364i | \(-0.356700\pi\) | ||||
0.435137 | + | 0.900364i | \(0.356700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 151.000 | 1.82325 | 0.911626 | − | 0.411021i | \(-0.134828\pi\) | ||||
0.911626 | + | 0.411021i | \(0.134828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.0000 | −0.103913 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −58.0000 | −0.525819 | −0.262909 | − | 0.964821i | \(-0.584682\pi\) | ||||
−0.262909 | + | 0.964821i | \(0.584682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −192.000 | −1.22943 | −0.614716 | − | 0.788749i | \(-0.710729\pi\) | ||||
−0.614716 | + | 0.788749i | \(0.710729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | 0.104287 | 0.0521435 | − | 0.998640i | \(-0.483395\pi\) | ||||
0.0521435 | + | 0.998640i | \(0.483395\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −195.000 | −1.02864 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −138.000 | −0.613164 | −0.306582 | − | 0.951844i | \(-0.599185\pi\) | ||||
−0.306582 | + | 0.951844i | \(0.599185\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −420.000 | −1.72446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 229.000 | 0.872288 | 0.436144 | − | 0.899877i | \(-0.356344\pi\) | ||||
0.436144 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −212.000 | −0.657944 | −0.328972 | − | 0.944340i | \(-0.606702\pi\) | ||||
−0.328972 | + | 0.944340i | \(0.606702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −305.000 | −0.837422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 578.000 | 1.49801 | 0.749004 | − | 0.662566i | \(-0.230532\pi\) | ||||
0.749004 | + | 0.662566i | \(0.230532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −755.000 | −1.75442 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −336.000 | −0.741415 | −0.370707 | − | 0.928750i | \(-0.620885\pi\) | ||||
−0.370707 | + | 0.928750i | \(0.620885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −858.000 | −1.80091 | −0.900456 | − | 0.434947i | \(-0.856767\pi\) | ||||
−0.900456 | + | 0.434947i | \(0.856767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.00799925 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 209.000 | 0.381096 | 0.190548 | − | 0.981678i | \(-0.438974\pi\) | ||||
0.190548 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 290.000 | 0.505970 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 780.000 | 1.30379 | 0.651894 | − | 0.758310i | \(-0.273975\pi\) | ||||
0.651894 | + | 0.758310i | \(0.273975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 403.000 | 0.646131 | 0.323066 | − | 0.946377i | \(-0.395287\pi\) | ||||
0.323066 | + | 0.946377i | \(0.395287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 78.0000 | 0.115441 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 230.000 | 0.327557 | 0.163779 | − | 0.986497i | \(-0.447632\pi\) | ||||
0.163779 | + | 0.986497i | \(0.447632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1293.00 | 1.70994 | 0.854971 | − | 0.518676i | \(-0.173575\pi\) | ||||
0.854971 | + | 0.518676i | \(0.173575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 960.000 | 1.18302 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1369.00 | −1.63049 | −0.815246 | − | 0.579115i | \(-0.803398\pi\) | ||||
−0.815246 | + | 0.579115i | \(0.803398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 168.000 | 0.193530 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −90.0000 | −0.100350 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −382.000 | −0.399858 | −0.199929 | − | 0.979810i | \(-0.564071\pi\) | ||||
−0.199929 | + | 0.979810i | \(0.564071\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −78.0000 | −0.0791848 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 794.000 | 0.782237 | 0.391119 | − | 0.920340i | \(-0.372088\pi\) | ||||
0.391119 | + | 0.920340i | \(0.372088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1348.00 | −1.28954 | −0.644769 | − | 0.764378i | \(-0.723046\pi\) | ||||
−0.644769 | + | 0.764378i | \(0.723046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 775.000 | 0.700206 | 0.350103 | − | 0.936711i | \(-0.386147\pi\) | ||||
0.350103 | + | 0.936711i | \(0.386147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −446.000 | −0.391918 | −0.195959 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195959 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 690.000 | 0.590017 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 231.000 | 0.192307 | 0.0961533 | − | 0.995367i | \(-0.469346\pi\) | ||||
0.0961533 | + | 0.995367i | \(0.469346\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −168.000 | −0.132749 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 122.000 | 0.0939809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.000 | 0.142750 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1145.00 | −0.839359 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2386.00 | 1.66711 | 0.833556 | − | 0.552435i | \(-0.186301\pi\) | ||||
0.833556 | + | 0.552435i | \(0.186301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −820.000 | −0.559666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2452.00 | 1.63536 | 0.817680 | − | 0.575673i | \(-0.195260\pi\) | ||||
0.817680 | + | 0.575673i | \(0.195260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 302.000 | 0.196893 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1125.00 | 0.701571 | 0.350786 | − | 0.936456i | \(-0.385915\pi\) | ||||
0.350786 | + | 0.936456i | \(0.385915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1377.00 | −0.840256 | −0.420128 | − | 0.907465i | \(-0.638015\pi\) | ||||
−0.420128 | + | 0.907465i | \(0.638015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1060.00 | 0.633107 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3276.00 | 1.91575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1695.00 | 0.951029 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1920.00 | −1.05565 | −0.527827 | − | 0.849352i | \(-0.676993\pi\) | ||||
−0.527827 | + | 0.849352i | \(0.676993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1854.00 | −0.999181 | −0.499591 | − | 0.866262i | \(-0.666516\pi\) | ||||
−0.499591 | + | 0.866262i | \(0.666516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −122.000 | −0.0644648 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −634.000 | −0.322285 | −0.161142 | − | 0.986931i | \(-0.551518\pi\) | ||||
−0.161142 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2890.00 | −1.44146 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −116.000 | −0.0567831 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −103.000 | −0.0494944 | −0.0247472 | − | 0.999694i | \(-0.507878\pi\) | ||||
−0.0247472 | + | 0.999694i | \(0.507878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 44.0000 | 0.0203882 | 0.0101941 | − | 0.999948i | \(-0.496755\pi\) | ||||
0.0101941 | + | 0.999948i | \(0.496755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4859.00 | 2.21165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −302.000 | −0.135056 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1128.00 | −0.495724 | −0.247862 | − | 0.968795i | \(-0.579728\pi\) | ||||
−0.247862 | + | 0.968795i | \(0.579728\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1680.00 | 0.713427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2245.00 | −0.937426 | −0.468713 | − | 0.883351i | \(-0.655282\pi\) | ||||
−0.468713 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3050.00 | −1.25251 | −0.626256 | − | 0.779617i | \(-0.715414\pi\) | ||||
−0.626256 | + | 0.779617i | \(0.715414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4290.00 | 1.73293 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2379.00 | 0.930319 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 290.000 | 0.111611 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4222.00 | 1.59944 | 0.799720 | − | 0.600373i | \(-0.204981\pi\) | ||||
0.799720 | + | 0.600373i | \(0.204981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3357.00 | 1.25203 | 0.626016 | − | 0.779810i | \(-0.284684\pi\) | ||||
0.626016 | + | 0.779810i | \(0.284684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −166.000 | −0.0600356 | −0.0300178 | − | 0.999549i | \(-0.509556\pi\) | ||||
−0.0300178 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3372.00 | −1.20118 | −0.600590 | − | 0.799557i | \(-0.705068\pi\) | ||||
−0.600590 | + | 0.799557i | \(0.705068\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1045.00 | −0.366710 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −384.000 | −0.132766 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 116.000 | 0.0389496 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5889.00 | 1.94905 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5601.00 | 1.82743 | 0.913717 | − | 0.406350i | \(-0.133199\pi\) | ||||
0.913717 | + | 0.406350i | \(0.133199\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3900.00 | −1.25457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.0000 | 0.0112619 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2015.00 | −0.621740 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5124.00 | 1.55963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 828.000 | 0.248641 | 0.124321 | − | 0.992242i | \(-0.460325\pi\) | ||||
0.124321 | + | 0.992242i | \(0.460325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2388.00 | 0.698225 | 0.349113 | − | 0.937081i | \(-0.386483\pi\) | ||||
0.349113 | + | 0.937081i | \(0.386483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2844.00 | 0.820685 | 0.410342 | − | 0.911932i | \(-0.365409\pi\) | ||||
0.410342 | + | 0.911932i | \(0.365409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −390.000 | −0.111083 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5962.00 | −1.67632 | −0.838162 | − | 0.545421i | \(-0.816370\pi\) | ||||
−0.838162 | + | 0.545421i | \(0.816370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1150.00 | −0.315192 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4320.00 | 1.16919 | 0.584597 | − | 0.811324i | \(-0.301252\pi\) | ||||
0.584597 | + | 0.811324i | \(0.301252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3857.00 | 1.03092 | 0.515459 | − | 0.856914i | \(-0.327621\pi\) | ||||
0.515459 | + | 0.856914i | \(0.327621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −560.000 | −0.147835 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12684.0 | 3.26746 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6465.00 | −1.64539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −287.000 | −0.0721724 | −0.0360862 | − | 0.999349i | \(-0.511489\pi\) | ||||
−0.0360862 | + | 0.999349i | \(0.511489\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2262.00 | −0.562098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2130.00 | −0.516987 | −0.258494 | − | 0.966013i | \(-0.583226\pi\) | ||||
−0.258494 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −276.000 | −0.0662155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 384.000 | 0.0910690 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3066.00 | −0.718850 | −0.359425 | − | 0.933174i | \(-0.617027\pi\) | ||||
−0.359425 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6845.00 | 1.56894 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3744.00 | 0.848609 | 0.424304 | − | 0.905520i | \(-0.360519\pi\) | ||||
0.424304 | + | 0.905520i | \(0.360519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3346.00 | 0.750019 | 0.375009 | − | 0.927021i | \(-0.377640\pi\) | ||||
0.375009 | + | 0.927021i | \(0.377640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −840.000 | −0.186224 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7040.00 | 1.52705 | 0.763525 | − | 0.645779i | \(-0.223467\pi\) | ||||
0.763525 | + | 0.645779i | \(0.223467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −36.0000 | −0.00772496 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3010.00 | −0.639009 | −0.319505 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319505 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6001.00 | 1.26050 | 0.630252 | − | 0.776391i | \(-0.282952\pi\) | ||||
0.630252 | + | 0.776391i | \(0.282952\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 458.000 | 0.0941982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1192.00 | −0.242622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1910.00 | 0.384764 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4802.00 | 0.957460 | 0.478730 | − | 0.877962i | \(-0.341097\pi\) | ||||
0.478730 | + | 0.877962i | \(0.341097\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5655.00 | 1.10484 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4872.00 | −0.942325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 328.000 | 0.0628093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3970.00 | −0.752708 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6149.00 | −1.14313 | −0.571567 | − | 0.820556i | \(-0.693664\pi\) | ||||
−0.571567 | + | 0.820556i | \(0.693664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6740.00 | 1.24086 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 878.000 | 0.160086 | 0.0800431 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800431 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4042.00 | 0.729928 | 0.364964 | − | 0.931022i | \(-0.381081\pi\) | ||||
0.364964 | + | 0.931022i | \(0.381081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3844.00 | 0.681074 | 0.340537 | − | 0.940231i | \(-0.389391\pi\) | ||||
0.340537 | + | 0.940231i | \(0.389391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7488.00 | −1.31426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3875.00 | −0.673774 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9211.00 | 1.58673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2230.00 | 0.377123 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −424.000 | −0.0710513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2717.00 | −0.451178 | −0.225589 | − | 0.974223i | \(-0.572431\pi\) | ||||
−0.225589 | + | 0.974223i | \(0.572431\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 276.000 | 0.0454195 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1603.00 | 0.259113 | 0.129556 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129556 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1155.00 | −0.185047 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 702.000 | 0.111482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1364.00 | −0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11607.0 | 1.79567 | 0.897833 | − | 0.440335i | \(-0.145140\pi\) | ||||
0.897833 | + | 0.440335i | \(0.145140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4030.00 | −0.618112 | −0.309056 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309056 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12180.0 | 1.85219 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2106.00 | −0.317538 | −0.158769 | − | 0.987316i | \(-0.550753\pi\) | ||||
−0.158769 | + | 0.987316i | \(0.550753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −610.000 | −0.0904331 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7394.00 | −1.08702 | −0.543510 | − | 0.839402i | \(-0.682905\pi\) | ||||
−0.543510 | + | 0.839402i | \(0.682905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15942.0 | 2.32425 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −950.000 | −0.137361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6940.00 | −0.987098 | −0.493549 | − | 0.869718i | \(-0.664301\pi\) | ||||
−0.493549 | + | 0.869718i | \(0.664301\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −458.000 | −0.0646139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1156.00 | 0.161770 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7486.00 | 1.03917 | 0.519585 | − | 0.854419i | \(-0.326087\pi\) | ||||
0.519585 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16128.0 | −2.20327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1285.00 | 0.174158 | 0.0870792 | − | 0.996201i | \(-0.472247\pi\) | ||||
0.0870792 | + | 0.996201i | \(0.472247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11930.0 | −1.60418 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9622.00 | 1.28371 | 0.641855 | − | 0.766826i | \(-0.278165\pi\) | ||||
0.641855 | + | 0.766826i | \(0.278165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −328.000 | −0.0430831 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1974.00 | −0.257290 | −0.128645 | − | 0.991691i | \(-0.541063\pi\) | ||||
−0.128645 | + | 0.991691i | \(0.541063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3538.00 | −0.457607 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12260.0 | −1.57363 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8084.00 | −1.02198 | −0.510988 | − | 0.859588i | \(-0.670720\pi\) | ||||
−0.510988 | + | 0.859588i | \(0.670720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1510.00 | −0.189460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5667.00 | −0.705727 | −0.352863 | − | 0.935675i | \(-0.614792\pi\) | ||||
−0.352863 | + | 0.935675i | \(0.614792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1512.00 | 0.186894 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5382.00 | −0.655469 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4835.00 | −0.584536 | −0.292268 | − | 0.956336i | \(-0.594410\pi\) | ||||
−0.292268 | + | 0.956336i | \(0.594410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5625.00 | −0.675087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −672.000 | −0.0800653 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6885.00 | 0.808537 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4619.00 | 0.538551 | 0.269276 | − | 0.963063i | \(-0.413216\pi\) | ||||
0.269276 | + | 0.963063i | \(0.413216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7476.00 | −0.865458 | −0.432729 | − | 0.901524i | \(-0.642449\pi\) | ||||
−0.432729 | + | 0.901524i | \(0.642449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 424.000 | 0.0487366 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1716.00 | −0.194480 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16380.0 | −1.84344 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7810.00 | −0.872841 | −0.436420 | − | 0.899743i | \(-0.643754\pi\) | ||||
−0.436420 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2029.00 | 0.225191 | 0.112595 | − | 0.993641i | \(-0.464084\pi\) | ||||
0.112595 | + | 0.993641i | \(0.464084\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8758.00 | −0.958700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3208.00 | −0.348769 | −0.174384 | − | 0.984678i | \(-0.555794\pi\) | ||||
−0.174384 | + | 0.984678i | \(0.555794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 678.000 | 0.0732102 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13227.0 | −1.41859 | −0.709293 | − | 0.704914i | \(-0.750986\pi\) | ||||
−0.709293 | + | 0.704914i | \(0.750986\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9600.00 | 1.01580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3617.00 | 0.380171 | 0.190086 | − | 0.981768i | \(-0.439123\pi\) | ||||
0.190086 | + | 0.981768i | \(0.439123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8931.00 | 0.932471 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9270.00 | 0.961463 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6215.00 | −0.636161 | −0.318080 | − | 0.948064i | \(-0.603038\pi\) | ||||
−0.318080 | + | 0.948064i | \(0.603038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8845.00 | 0.899454 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7108.00 | 0.718118 | 0.359059 | − | 0.933315i | \(-0.383098\pi\) | ||||
0.359059 | + | 0.933315i | \(0.383098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3364.00 | −0.337664 | −0.168832 | − | 0.985645i | \(-0.554000\pi\) | ||||
−0.168832 | + | 0.985645i | \(0.554000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18964.0 | 1.87912 | 0.939560 | − | 0.342384i | \(-0.111234\pi\) | ||||
0.939560 | + | 0.342384i | \(0.111234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 418.000 | 0.0411545 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3170.00 | 0.310119 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6396.00 | 0.621751 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1156.00 | −0.110964 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10926.0 | 1.04222 | 0.521108 | − | 0.853491i | \(-0.325519\pi\) | ||||
0.521108 | + | 0.853491i | \(0.325519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11592.0 | −1.09886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 580.000 | 0.0546396 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4350.00 | −0.404758 | −0.202379 | − | 0.979307i | \(-0.564867\pi\) | ||||
−0.202379 | + | 0.979307i | \(0.564867\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 515.000 | 0.0476260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1324.00 | −0.121693 | −0.0608465 | − | 0.998147i | \(-0.519380\pi\) | ||||
−0.0608465 | + | 0.998147i | \(0.519380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11712.0 | −1.06994 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1560.00 | 0.140796 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9068.00 | 0.813506 | 0.406753 | − | 0.913538i | \(-0.366661\pi\) | ||||
0.406753 | + | 0.913538i | \(0.366661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −220.000 | −0.0196185 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19836.0 | −1.75834 | −0.879169 | − | 0.476511i | \(-0.841901\pi\) | ||||
−0.879169 | + | 0.476511i | \(0.841901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24295.0 | −2.12816 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2682.00 | −0.233551 | −0.116776 | − | 0.993158i | \(-0.537256\pi\) | ||||
−0.116776 | + | 0.993158i | \(0.537256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 806.000 | 0.0697756 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21895.0 | 1.88438 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8268.00 | −0.703339 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5640.00 | 0.477011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3035.00 | −0.255213 | −0.127606 | − | 0.991825i | \(-0.540729\pi\) | ||||
−0.127606 | + | 0.991825i | \(0.540729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7701.00 | −0.643865 | −0.321932 | − | 0.946763i | \(-0.604332\pi\) | ||||
−0.321932 | + | 0.946763i | \(0.604332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1098.00 | 0.0907583 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8803.00 | −0.723514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 672.000 | 0.0549196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19236.0 | 1.56323 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11225.0 | 0.902038 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13221.0 | −1.05653 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18112.0 | 1.43936 | 0.719682 | − | 0.694304i | \(-0.244288\pi\) | ||||
0.719682 | + | 0.694304i | \(0.244288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15250.0 | 1.20523 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19541.0 | −1.52745 | −0.763723 | − | 0.645544i | \(-0.776631\pi\) | ||||
−0.763723 | + | 0.645544i | \(0.776631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1716.00 | 0.133401 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28992.0 | −2.24156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 460.000 | 0.0353729 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13508.0 | 1.02756 | 0.513781 | − | 0.857921i | \(-0.328244\pi\) | ||||
0.513781 | + | 0.857921i | \(0.328244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13776.0 | 1.04233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11895.0 | −0.895200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8712.00 | 0.652162 | 0.326081 | − | 0.945342i | \(-0.394272\pi\) | ||||
0.326081 | + | 0.945342i | \(0.394272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1342.00 | −0.0993981 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9623.00 | −0.708993 | −0.354497 | − | 0.935057i | \(-0.615348\pi\) | ||||
−0.354497 | + | 0.935057i | \(0.615348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 604.000 | 0.0442673 | 0.0221336 | − | 0.999755i | \(-0.492954\pi\) | ||||
0.0221336 | + | 0.999755i | \(0.492954\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21110.0 | −1.53906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3629.00 | −0.261832 | −0.130916 | − | 0.991393i | \(-0.541792\pi\) | ||||
−0.130916 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16785.0 | −1.20477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2586.00 | 0.184656 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22542.0 | 1.60136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9219.00 | −0.648226 | −0.324113 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324113 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2718.00 | 0.190141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 830.000 | 0.0577693 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19111.0 | 1.32343 | 0.661716 | − | 0.749755i | \(-0.269829\pi\) | ||||
0.661716 | + | 0.749755i | \(0.269829\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16860.0 | 1.15584 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17086.0 | 1.16547 | 0.582734 | − | 0.812663i | \(-0.301983\pi\) | ||||
0.582734 | + | 0.812663i | \(0.301983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9035.00 | 0.613220 | 0.306610 | − | 0.951835i | \(-0.400805\pi\) | ||||
0.306610 | + | 0.951835i | \(0.400805\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −418.000 | −0.0282293 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14784.0 | −0.988573 | −0.494287 | − | 0.869299i | \(-0.664571\pi\) | ||||
−0.494287 | + | 0.869299i | \(0.664571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1920.00 | 0.127754 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17808.0 | −1.17911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17846.0 | −1.17585 | −0.587923 | − | 0.808917i | \(-0.700054\pi\) | ||||
−0.587923 | + | 0.808917i | \(0.700054\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11618.0 | −0.758060 | −0.379030 | − | 0.925384i | \(-0.623742\pi\) | ||||
−0.379030 | + | 0.925384i | \(0.623742\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9556.00 | −0.620498 | −0.310249 | − | 0.950655i | \(-0.600412\pi\) | ||||
−0.310249 | + | 0.950655i | \(0.600412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8410.00 | −0.543449 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2738.00 | −0.176076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29445.0 | −1.87547 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8418.00 | −0.533621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19394.0 | 1.22355 | 0.611777 | − | 0.791030i | \(-0.290455\pi\) | ||||
0.611777 | + | 0.791030i | \(0.290455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28005.0 | −1.75845 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28476.0 | −1.77121 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1560.00 | −0.0965769 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12138.0 | 0.747929 | 0.373964 | − | 0.927443i | \(-0.377998\pi\) | ||||
0.373964 | + | 0.927443i | \(0.377998\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27036.0 | −1.65816 | −0.829079 | − | 0.559131i | \(-0.811135\pi\) | ||||
−0.829079 | + | 0.559131i | \(0.811135\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17556.0 | −1.06677 | −0.533383 | − | 0.845874i | \(-0.679080\pi\) | ||||
−0.533383 | + | 0.845874i | \(0.679080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13104.0 | −0.792569 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −180.000 | −0.0108368 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17262.0 | −1.03448 | −0.517239 | − | 0.855841i | \(-0.673040\pi\) | ||||
−0.517239 | + | 0.855841i | \(0.673040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −806.000 | −0.0478616 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10517.0 | 0.621675 | 0.310838 | − | 0.950463i | \(-0.399390\pi\) | ||||
0.310838 | + | 0.950463i | \(0.399390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1408.00 | −0.0828515 | −0.0414258 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414258 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25620.0 | −1.50075 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11136.0 | 0.646458 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4140.00 | −0.239255 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33462.0 | −1.92517 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9626.00 | 0.551345 | 0.275672 | − | 0.961252i | \(-0.411100\pi\) | ||||
0.275672 | + | 0.961252i | \(0.411100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28464.0 | 1.61589 | 0.807947 | − | 0.589255i | \(-0.200579\pi\) | ||||
0.807947 | + | 0.589255i | \(0.200579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −764.000 | −0.0431806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11940.0 | −0.671868 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3963.00 | 0.222020 | 0.111010 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111010 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14220.0 | −0.789704 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 48552.0 | 2.68459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31781.0 | −1.74965 | −0.874824 | − | 0.484442i | \(-0.839023\pi\) | ||||
−0.874824 | + | 0.484442i | \(0.839023\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −156.000 | −0.00855115 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13969.0 | 0.759130 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29810.0 | 1.61304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28004.0 | 1.50884 | 0.754420 | − | 0.656392i | \(-0.227918\pi\) | ||||
0.754420 | + | 0.656392i | \(0.227918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20838.0 | −1.11795 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1588.00 | 0.0844737 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35228.0 | 1.86603 | 0.933015 | − | 0.359837i | \(-0.117168\pi\) | ||||
0.933015 | + | 0.359837i | \(0.117168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −460.000 | −0.0242635 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1044.00 | −0.0548361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21600.0 | −1.12506 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8658.00 | 0.449081 | 0.224540 | − | 0.974465i | \(-0.427912\pi\) | ||||
0.224540 | + | 0.974465i | \(0.427912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2696.00 | −0.139257 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19285.0 | −0.992001 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5728.00 | 0.292214 | 0.146107 | − | 0.989269i | \(-0.453326\pi\) | ||||
0.146107 | + | 0.989269i | \(0.453326\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10004.0 | 0.506171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21460.0 | 1.08137 | 0.540684 | − | 0.841226i | \(-0.318165\pi\) | ||||
0.540684 | + | 0.841226i | \(0.318165\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8151.00 | 0.407389 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29164.0 | 1.45171 | 0.725856 | − | 0.687847i | \(-0.241444\pi\) | ||||
0.725856 | + | 0.687847i | \(0.241444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −63420.0 | −3.14412 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29478.0 | 1.45551 | 0.727754 | − | 0.685838i | \(-0.240564\pi\) | ||||
0.727754 | + | 0.685838i | \(0.240564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2586.00 | −0.126662 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1550.00 | 0.0756152 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −576.000 | −0.0279874 | −0.0139937 | − | 0.999902i | \(-0.504454\pi\) | ||||
−0.0139937 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1435.00 | 0.0694480 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2880.00 | 0.138277 | 0.0691383 | − | 0.997607i | \(-0.477975\pi\) | ||||
0.0691383 | + | 0.997607i | \(0.477975\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11310.0 | 0.540879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20789.0 | 0.990277 | 0.495138 | − | 0.868814i | \(-0.335117\pi\) | ||||
0.495138 | + | 0.868814i | \(0.335117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −892.000 | −0.0423232 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28224.0 | −1.32870 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26421.0 | 1.23897 | 0.619484 | − | 0.785010i | \(-0.287342\pi\) | ||||
0.619484 | + | 0.785010i | \(0.287342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10650.0 | 0.497471 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32504.0 | 1.51240 | 0.756202 | − | 0.654339i | \(-0.227053\pi\) | ||||
0.756202 | + | 0.654339i | \(0.227053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1380.00 | 0.0637159 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34579.0 | 1.59040 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30420.0 | 1.39374 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27840.0 | −1.27065 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −996.000 | −0.0451125 | −0.0225563 | − | 0.999746i | \(-0.507180\pi\) | ||||
−0.0225563 | + | 0.999746i | \(0.507180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15330.0 | 0.691714 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 462.000 | 0.0207672 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −72072.0 | −3.22743 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15134.0 | 0.672615 | 0.336307 | − | 0.941752i | \(-0.390822\pi\) | ||||
0.336307 | + | 0.941752i | \(0.390822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12932.0 | −0.572592 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2738.00 | 0.120777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15717.0 | 0.690711 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18720.0 | −0.816574 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36942.0 | −1.60545 | −0.802727 | − | 0.596347i | \(-0.796618\pi\) | ||||
−0.802727 | + | 0.596347i | \(0.796618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11748.0 | −0.508666 | −0.254333 | − | 0.967117i | \(-0.581856\pi\) | ||||
−0.254333 | + | 0.967117i | \(0.581856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16730.0 | −0.721706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24764.0 | 1.06044 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −336.000 | −0.0143355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1198.00 | 0.0509263 | 0.0254631 | − | 0.999676i | \(-0.491894\pi\) | ||||
0.0254631 | + | 0.999676i | \(0.491894\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6788.00 | −0.287503 | −0.143751 | − | 0.989614i | \(-0.545917\pi\) | ||||
−0.143751 | + | 0.989614i | \(0.545917\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33011.0 | −1.38803 | −0.694017 | − | 0.719958i | \(-0.744161\pi\) | ||||
−0.694017 | + | 0.719958i | \(0.744161\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17732.0 | −0.742892 | −0.371446 | − | 0.928454i | \(-0.621138\pi\) | ||||
−0.371446 | + | 0.928454i | \(0.621138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35200.0 | −1.46940 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20679.0 | −0.860126 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2610.00 | 0.107784 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8480.00 | −0.348942 | −0.174471 | − | 0.984662i | \(-0.555821\pi\) | ||||
−0.174471 | + | 0.984662i | \(0.555821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12475.0 | 0.511501 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15050.0 | 0.614887 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 380.000 | 0.0154155 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30005.0 | −1.21292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8004.00 | 0.322413 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30014.0 | 1.20476 | 0.602380 | − | 0.798210i | \(-0.294219\pi\) | ||||
0.602380 | + | 0.798210i | \(0.294219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21643.0 | −0.862673 | −0.431337 | − | 0.902191i | \(-0.641958\pi\) | ||||
−0.431337 | + | 0.902191i | \(0.641958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2799.00 | 0.111177 | 0.0555883 | − | 0.998454i | \(-0.482297\pi\) | ||||
0.0555883 | + | 0.998454i | \(0.482297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2290.00 | −0.0906423 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19384.0 | −0.764588 | −0.382294 | − | 0.924041i | \(-0.624866\pi\) | ||||
−0.382294 | + | 0.924041i | \(0.624866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5960.00 | 0.233463 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8970.00 | 0.350157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17556.0 | 0.682965 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 764.000 | 0.0296191 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5132.00 | 0.197600 | 0.0988001 | − | 0.995107i | \(-0.468500\pi\) | ||||
0.0988001 | + | 0.995107i | \(0.468500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24010.0 | −0.921316 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4430.00 | 0.169410 | 0.0847052 | − | 0.996406i | \(-0.473005\pi\) | ||||
0.0847052 | + | 0.996406i | \(0.473005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24317.0 | −0.926764 | −0.463382 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463382 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26100.0 | −0.987996 | −0.493998 | − | 0.869463i | \(-0.664465\pi\) | ||||
−0.493998 | + | 0.869463i | \(0.664465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4772.00 | 0.180031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26169.0 | −0.983944 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32012.0 | −1.19960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24360.0 | 0.906752 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3456.00 | −0.128214 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35258.0 | 1.30368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1640.00 | −0.0604383 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24356.0 | −0.891651 | −0.445826 | − | 0.895120i | \(-0.647090\pi\) | ||||
−0.445826 | + | 0.895120i | \(0.647090\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1588.00 | −0.0579435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29900.0 | 1.08741 | 0.543705 | − | 0.839276i | \(-0.317021\pi\) | ||||
0.543705 | + | 0.839276i | \(0.317021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50427.0 | 1.82792 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4904.00 | 0.176602 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34838.0 | 1.25049 | 0.625245 | − | 0.780429i | \(-0.284999\pi\) | ||||
0.625245 | + | 0.780429i | \(0.284999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30745.0 | 1.09998 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 65520.0 | 2.33653 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2696.00 | 0.0955213 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26334.0 | 0.930022 | 0.465011 | − | 0.885305i | \(-0.346050\pi\) | ||||
0.465011 | + | 0.885305i | \(0.346050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51189.0 | −1.80199 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4390.00 | −0.154043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30949.0 | −1.07904 | −0.539520 | − | 0.841973i | \(-0.681394\pi\) | ||||
−0.539520 | + | 0.841973i | \(0.681394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20210.0 | −0.702373 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25276.0 | −0.875637 | −0.437818 | − | 0.899063i | \(-0.644249\pi\) | ||||
−0.437818 | + | 0.899063i | \(0.644249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13282.0 | −0.458665 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1216.00 | 0.0417262 | 0.0208631 | − | 0.999782i | \(-0.493359\pi\) | ||||
0.0208631 | + | 0.999782i | \(0.493359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33852.0 | 1.15794 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19220.0 | −0.655364 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6033.00 | 0.205066 | 0.102533 | − | 0.994730i | \(-0.467305\pi\) | ||||
0.102533 | + | 0.994730i | \(0.467305\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37440.0 | 1.26464 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2250.00 | 0.0757626 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29467.0 | −0.989124 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1550.00 | −0.0518671 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41792.0 | −1.38980 | −0.694902 | − | 0.719105i | \(-0.744552\pi\) | ||||
−0.694902 | + | 0.719105i | \(0.744552\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46055.0 | −1.52683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2105.00 | −0.0695702 | −0.0347851 | − | 0.999395i | \(-0.511075\pi\) | ||||
−0.0347851 | + | 0.999395i | \(0.511075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2754.00 | −0.0907391 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30119.0 | −0.986277 | −0.493138 | − | 0.869951i | \(-0.664150\pi\) | ||||
−0.493138 | + | 0.869951i | \(0.664150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53391.0 | −1.74299 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 892.000 | 0.0290310 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18438.0 | 0.598251 | 0.299126 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299126 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2120.00 | 0.0683691 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9512.00 | −0.305828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2230.00 | 0.0714816 | 0.0357408 | − | 0.999361i | \(-0.488621\pi\) | ||||
0.0357408 | + | 0.999361i | \(0.488621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13585.0 | 0.434146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6804.00 | −0.216133 | −0.108067 | − | 0.994144i | \(-0.534466\pi\) | ||||
−0.108067 | + | 0.994144i | \(0.534466\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20010.0 | −0.633722 |
(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 | 1600.4.a.n.1.1 | 1 | ||
4.3 | odd | 2 | 1600.4.a.bn.1.1 | 1 | |||
5.4 | even | 2 | 1600.4.a.bo.1.1 | 1 | |||
8.3 | odd | 2 | 200.4.a.c.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 400.4.a.q.1.1 | 1 | |||
20.19 | odd | 2 | 1600.4.a.m.1.1 | 1 | |||
24.11 | even | 2 | 1800.4.a.p.1.1 | 1 | |||
40.3 | even | 4 | 200.4.c.d.49.1 | 2 | |||
40.13 | odd | 4 | 400.4.c.g.49.2 | 2 | |||
40.19 | odd | 2 | 200.4.a.h.1.1 | yes | 1 | ||
40.27 | even | 4 | 200.4.c.d.49.2 | 2 | |||
40.29 | even | 2 | 400.4.a.f.1.1 | 1 | |||
40.37 | odd | 4 | 400.4.c.g.49.1 | 2 | |||
120.59 | even | 2 | 1800.4.a.t.1.1 | 1 | |||
120.83 | odd | 4 | 1800.4.f.c.649.2 | 2 | |||
120.107 | odd | 4 | 1800.4.f.c.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.c.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
200.4.a.h.1.1 | yes | 1 | 40.19 | odd | 2 | ||
200.4.c.d.49.1 | 2 | 40.3 | even | 4 | |||
200.4.c.d.49.2 | 2 | 40.27 | even | 4 | |||
400.4.a.f.1.1 | 1 | 40.29 | even | 2 | |||
400.4.a.q.1.1 | 1 | 8.5 | even | 2 | |||
400.4.c.g.49.1 | 2 | 40.37 | odd | 4 | |||
400.4.c.g.49.2 | 2 | 40.13 | odd | 4 | |||
1600.4.a.m.1.1 | 1 | 20.19 | odd | 2 | |||
1600.4.a.n.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1600.4.a.bn.1.1 | 1 | 4.3 | odd | 2 | |||
1600.4.a.bo.1.1 | 1 | 5.4 | even | 2 | |||
1800.4.a.p.1.1 | 1 | 24.11 | even | 2 | |||
1800.4.a.t.1.1 | 1 | 120.59 | even | 2 | |||
1800.4.f.c.649.1 | 2 | 120.107 | odd | 4 | |||
1800.4.f.c.649.2 | 2 | 120.83 | odd | 4 |