Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.7220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.47977.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 60x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.749725\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.3916 | −1.31702 | −0.658510 | − | 0.752572i | \(-0.728813\pi\) | ||||
−0.658510 | + | 0.752572i | \(0.728813\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.8932 | −0.737146 | −0.368573 | − | 0.929599i | \(-0.620154\pi\) | ||||
−0.368573 | + | 0.929599i | \(0.620154\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −68.2815 | −1.45676 | −0.728380 | − | 0.685174i | \(-0.759726\pi\) | ||||
−0.728380 | + | 0.685174i | \(0.759726\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.8899 | −0.882971 | −0.441485 | − | 0.897268i | \(-0.645548\pi\) | ||||
−0.441485 | + | 0.897268i | \(0.645548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −75.1747 | −0.907697 | −0.453849 | − | 0.891079i | \(-0.649949\pi\) | ||||
−0.453849 | + | 0.891079i | \(0.649949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −43.3916 | −0.393381 | −0.196691 | − | 0.980466i | \(-0.563019\pi\) | ||||
−0.196691 | + | 0.980466i | \(0.563019\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 174.951 | 1.12026 | 0.560131 | − | 0.828404i | \(-0.310751\pi\) | ||||
0.560131 | + | 0.828404i | \(0.310751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 222.666 | 1.29007 | 0.645033 | − | 0.764154i | \(-0.276843\pi\) | ||||
0.645033 | + | 0.764154i | \(0.276843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 121.958 | 0.588989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 67.1813 | 0.298501 | 0.149250 | − | 0.988799i | \(-0.452314\pi\) | ||||
0.149250 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.2070 | −0.0845890 | −0.0422945 | − | 0.999105i | \(-0.513467\pi\) | ||||
−0.0422945 | + | 0.999105i | \(0.513467\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −84.7442 | −0.300543 | −0.150272 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150272 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −585.650 | −1.81757 | −0.908785 | − | 0.417264i | \(-0.862989\pi\) | ||||
−0.908785 | + | 0.417264i | \(0.862989\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 251.948 | 0.734542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 38.3625 | 0.0994245 | 0.0497122 | − | 0.998764i | \(-0.484170\pi\) | ||||
0.0497122 | + | 0.998764i | \(0.484170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 134.466 | 0.329662 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.0000 | 0.203006 | 0.101503 | − | 0.994835i | \(-0.467635\pi\) | ||||
0.101503 | + | 0.994835i | \(0.467635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −226.300 | −0.474997 | −0.237498 | − | 0.971388i | \(-0.576327\pi\) | ||||
−0.237498 | + | 0.971388i | \(0.576327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 341.407 | 0.651482 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 858.035 | 1.56456 | 0.782281 | − | 0.622925i | \(-0.214056\pi\) | ||||
0.782281 | + | 0.622925i | \(0.214056\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 116.912 | 0.195422 | 0.0977108 | − | 0.995215i | \(-0.468848\pi\) | ||||
0.0977108 | + | 0.995215i | \(0.468848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 911.769 | 1.46184 | 0.730921 | − | 0.682462i | \(-0.239091\pi\) | ||||
0.730921 | + | 0.682462i | \(0.239091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 655.967 | 0.970836 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −285.129 | −0.406070 | −0.203035 | − | 0.979171i | \(-0.565081\pi\) | ||||
−0.203035 | + | 0.979171i | \(0.565081\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −999.099 | −1.32127 | −0.660635 | − | 0.750707i | \(-0.729713\pi\) | ||||
−0.660635 | + | 0.750707i | \(0.729713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 309.450 | 0.394877 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −374.848 | −0.446447 | −0.223223 | − | 0.974767i | \(-0.571658\pi\) | ||||
−0.223223 | + | 0.974767i | \(0.571658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1665.49 | 1.91858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 375.873 | 0.405935 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −227.413 | −0.238044 | −0.119022 | − | 0.992892i | \(-0.537976\pi\) | ||||
−0.119022 | + | 0.992892i | \(0.537976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1857.75 | 1.83023 | 0.915115 | − | 0.403193i | \(-0.132100\pi\) | ||||
0.915115 | + | 0.403193i | \(0.132100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 172.787 | 0.165294 | 0.0826468 | − | 0.996579i | \(-0.473663\pi\) | ||||
0.0826468 | + | 0.996579i | \(0.473663\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1806.79 | −1.63242 | −0.816209 | − | 0.577756i | \(-0.803928\pi\) | ||||
−0.816209 | + | 0.577756i | \(0.803928\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 287.644 | 0.252764 | 0.126382 | − | 0.991982i | \(-0.459663\pi\) | ||||
0.126382 | + | 0.991982i | \(0.459663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −671.875 | −0.559333 | −0.279667 | − | 0.960097i | \(-0.590224\pi\) | ||||
−0.279667 | + | 0.960097i | \(0.590224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 216.958 | 0.175925 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1509.59 | 1.16289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −607.756 | −0.456616 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1818.41 | 1.27053 | 0.635265 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635265 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1768.99 | 1.17983 | 0.589915 | − | 0.807465i | \(-0.299161\pi\) | ||||
0.589915 | + | 0.807465i | \(0.299161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1833.63 | 1.19546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1842.85 | −1.14924 | −0.574618 | − | 0.818422i | \(-0.694849\pi\) | ||||
−0.574618 | + | 0.818422i | \(0.694849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1371.14 | 0.836678 | 0.418339 | − | 0.908291i | \(-0.362612\pi\) | ||||
0.418339 | + | 0.908291i | \(0.362612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1836.31 | 1.07384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −874.756 | −0.500997 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2139.65 | −1.17642 | −0.588212 | − | 0.808707i | \(-0.700168\pi\) | ||||
−0.588212 | + | 0.808707i | \(0.700168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1199.81 | −0.646616 | −0.323308 | − | 0.946294i | \(-0.604795\pi\) | ||||
−0.323308 | + | 0.946294i | \(0.604795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1113.33 | −0.576935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1847.13 | 0.938960 | 0.469480 | − | 0.882943i | \(-0.344441\pi\) | ||||
0.469480 | + | 0.882943i | \(0.344441\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1058.39 | 0.518091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3203.12 | −1.53919 | −0.769595 | − | 0.638532i | \(-0.779542\pi\) | ||||
−0.769595 | + | 0.638532i | \(0.779542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 590.884 | 0.273796 | 0.136898 | − | 0.990585i | \(-0.456287\pi\) | ||||
0.136898 | + | 0.990585i | \(0.456287\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2465.36 | 1.12215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3110.68 | 1.36705 | 0.683527 | − | 0.729925i | \(-0.260445\pi\) | ||||
0.683527 | + | 0.729925i | \(0.260445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −609.789 | −0.263404 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2448.94 | −1.02258 | −0.511291 | − | 0.859408i | \(-0.670832\pi\) | ||||
−0.511291 | + | 0.859408i | \(0.670832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2416.13 | 0.992206 | 0.496103 | − | 0.868264i | \(-0.334764\pi\) | ||||
0.496103 | + | 0.868264i | \(0.334764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −335.906 | −0.133494 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1664.42 | 0.650879 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1652.25 | −0.625929 | −0.312964 | − | 0.949765i | \(-0.601322\pi\) | ||||
−0.312964 | + | 0.949765i | \(0.601322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4736.65 | 1.76659 | 0.883295 | − | 0.468818i | \(-0.155320\pi\) | ||||
0.883295 | + | 0.468818i | \(0.155320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2106.79 | −0.761944 | −0.380972 | − | 0.924587i | \(-0.624411\pi\) | ||||
−0.380972 | + | 0.924587i | \(0.624411\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 891.149 | 0.317447 | 0.158723 | − | 0.987323i | \(-0.449262\pi\) | ||||
0.158723 | + | 0.987323i | \(0.449262\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4267.33 | −1.47541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 111.035 | 0.0378294 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2021.69 | 0.669105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3607.11 | 1.17689 | 0.588444 | − | 0.808538i | \(-0.299741\pi\) | ||||
0.588444 | + | 0.808538i | \(0.299741\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 423.721 | 0.134407 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5431.18 | −1.69904 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4225.93 | 1.28628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2507.12 | 0.752865 | 0.376432 | − | 0.926444i | \(-0.377151\pi\) | ||||
0.376432 | + | 0.926444i | \(0.377151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3970.82 | −1.16102 | −0.580512 | − | 0.814252i | \(-0.697147\pi\) | ||||
−0.580512 | + | 0.814252i | \(0.697147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5494.88 | 1.58564 | 0.792820 | − | 0.609455i | \(-0.208612\pi\) | ||||
0.792820 | + | 0.609455i | \(0.208612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6895.27 | 1.93873 | 0.969365 | − | 0.245625i | \(-0.0789931\pi\) | ||||
0.969365 | + | 0.245625i | \(0.0789931\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2928.25 | 0.812842 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4308.62 | −1.16612 | −0.583058 | − | 0.812431i | \(-0.698144\pi\) | ||||
−0.583058 | + | 0.812431i | \(0.698144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3448.92 | 0.921843 | 0.460922 | − | 0.887441i | \(-0.347519\pi\) | ||||
0.460922 | + | 0.887441i | \(0.347519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1259.74 | −0.328497 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5133.04 | 1.32230 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6184.80 | −1.55530 | −0.777652 | − | 0.628695i | \(-0.783589\pi\) | ||||
−0.777652 | + | 0.628695i | \(0.783589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1166.94 | 0.289979 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4616.98 | 1.12062 | 0.560310 | − | 0.828283i | \(-0.310682\pi\) | ||||
0.560310 | + | 0.828283i | \(0.310682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1638.66 | −0.393132 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −728.557 | −0.170816 | −0.0854082 | − | 0.996346i | \(-0.527219\pi\) | ||||
−0.0854082 | + | 0.996346i | \(0.527219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −191.813 | −0.0444640 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6718.17 | 1.52273 | 0.761364 | − | 0.648325i | \(-0.224530\pi\) | ||||
0.761364 | + | 0.648325i | \(0.224530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2435.89 | −0.546015 | −0.273007 | − | 0.962012i | \(-0.588018\pi\) | ||||
−0.273007 | + | 0.962012i | \(0.588018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −672.330 | −0.147429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4808.18 | −1.04295 | −0.521473 | − | 0.853268i | \(-0.674617\pi\) | ||||
−0.521473 | + | 0.853268i | \(0.674617\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3535.67 | −0.750606 | −0.375303 | − | 0.926902i | \(-0.622461\pi\) | ||||
−0.375303 | + | 0.926902i | \(0.622461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3070.64 | 0.644984 | 0.322492 | − | 0.946572i | \(-0.395479\pi\) | ||||
0.322492 | + | 0.946572i | \(0.395479\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 541.663 | 0.111405 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1082.64 | −0.220362 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1245.18 | 0.248273 | 0.124136 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124136 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −460.000 | −0.0907872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2962.84 | 0.573061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2067.04 | 0.395822 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1131.50 | 0.212425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4269.79 | −0.793778 | −0.396889 | − | 0.917867i | \(-0.629910\pi\) | ||||
−0.396889 | + | 0.917867i | \(0.629910\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2584.39 | −0.471213 | −0.235607 | − | 0.971849i | \(-0.575708\pi\) | ||||
−0.235607 | + | 0.971849i | \(0.575708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8899.44 | −1.60711 | −0.803556 | − | 0.595229i | \(-0.797061\pi\) | ||||
−0.803556 | + | 0.595229i | \(0.797061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6168.58 | 1.09294 | 0.546470 | − | 0.837479i | \(-0.315971\pi\) | ||||
0.546470 | + | 0.837479i | \(0.315971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4705.00 | −0.825797 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4652.55 | 0.801470 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1707.04 | −0.291352 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14284.9 | 2.39378 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9996.33 | −1.65996 | −0.829982 | − | 0.557791i | \(-0.811649\pi\) | ||||
−0.829982 | + | 0.557791i | \(0.811649\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4290.18 | −0.699694 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2497.40 | −0.403685 | −0.201843 | − | 0.979418i | \(-0.564693\pi\) | ||||
−0.201843 | + | 0.979418i | \(0.564693\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5988.21 | −0.950967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2220.90 | 0.349614 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9001.22 | −1.39254 | −0.696269 | − | 0.717780i | \(-0.745158\pi\) | ||||
−0.696269 | + | 0.717780i | \(0.745158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10707.4 | −1.64227 | −0.821135 | − | 0.570733i | \(-0.806659\pi\) | ||||
−0.821135 | + | 0.570733i | \(0.806659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2843.35 | −0.428714 | −0.214357 | − | 0.976755i | \(-0.568766\pi\) | ||||
−0.214357 | + | 0.976755i | \(0.568766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −584.561 | −0.0873952 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9328.89 | 1.37148 | 0.685738 | − | 0.727849i | \(-0.259480\pi\) | ||||
0.685738 | + | 0.727849i | \(0.259480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1207.77 | −0.176086 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4558.85 | −0.653756 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 46.7367 | 0.00664751 | 0.00332376 | − | 0.999994i | \(-0.498942\pi\) | ||||
0.00332376 | + | 0.999994i | \(0.498942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −935.721 | −0.130944 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3791.98 | −0.526384 | −0.263192 | − | 0.964743i | \(-0.584775\pi\) | ||||
−0.263192 | + | 0.964743i | \(0.584775\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11945.9 | −1.63195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1881.74 | 0.255035 | 0.127518 | − | 0.991836i | \(-0.459299\pi\) | ||||
0.127518 | + | 0.991836i | \(0.459299\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12011.9 | −1.60256 | −0.801280 | − | 0.598289i | \(-0.795847\pi\) | ||||
−0.801280 | + | 0.598289i | \(0.795847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3279.83 | −0.434171 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7758.91 | 1.01129 | 0.505645 | − | 0.862741i | \(-0.331254\pi\) | ||||
0.505645 | + | 0.862741i | \(0.331254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2685.50 | 0.347344 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1425.65 | 0.181600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14841.9 | 1.87630 | 0.938152 | − | 0.346223i | \(-0.112536\pi\) | ||||
0.938152 | + | 0.346223i | \(0.112536\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −435.446 | −0.0542273 | −0.0271136 | − | 0.999632i | \(-0.508632\pi\) | ||||
−0.0271136 | + | 0.999632i | \(0.508632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15204.0 | −1.87932 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1806.72 | −0.220039 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10550.6 | 1.27554 | 0.637770 | − | 0.770227i | \(-0.279857\pi\) | ||||
0.637770 | + | 0.770227i | \(0.279857\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2244.02 | −0.267364 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4995.50 | 0.590890 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4161.11 | 0.485164 | 0.242582 | − | 0.970131i | \(-0.422006\pi\) | ||||
0.242582 | + | 0.970131i | \(0.422006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 154.745 | 0.0179140 | 0.00895701 | − | 0.999960i | \(-0.497149\pi\) | ||||
0.00895701 | + | 0.999960i | \(0.497149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1547.25 | −0.176594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5519.82 | 0.625580 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4393.72 | −0.491040 | −0.245520 | − | 0.969392i | \(-0.578959\pi\) | ||||
−0.245520 | + | 0.969392i | \(0.578959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4437.08 | 0.492454 | 0.246227 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246227 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3261.95 | 0.357071 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7046.68 | −0.766104 | −0.383052 | − | 0.923727i | \(-0.625127\pi\) | ||||
−0.383052 | + | 0.923727i | \(0.625127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7335.09 | 0.786683 | 0.393341 | − | 0.919392i | \(-0.371319\pi\) | ||||
0.393341 | + | 0.919392i | \(0.371319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1874.24 | 0.199657 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 731.914 | 0.0769290 | 0.0384645 | − | 0.999260i | \(-0.487753\pi\) | ||||
0.0384645 | + | 0.999260i | \(0.487753\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 597.217 | 0.0623545 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8327.45 | −0.858016 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12611.7 | −1.29092 | −0.645462 | − | 0.763792i | \(-0.723335\pi\) | ||||
−0.645462 | + | 0.763792i | \(0.723335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12971.9 | 1.31055 | 0.655275 | − | 0.755391i | \(-0.272553\pi\) | ||||
0.655275 | + | 0.755391i | \(0.272553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9899.48 | 0.993667 | 0.496833 | − | 0.867846i | \(-0.334496\pi\) | ||||
0.496833 | + | 0.867846i | \(0.334496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2180.60 | −0.216073 | −0.108037 | − | 0.994147i | \(-0.534456\pi\) | ||||
−0.108037 | + | 0.994147i | \(0.534456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20928.8 | −2.06056 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2279.04 | 0.221544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1879.37 | −0.181539 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4132.54 | −0.394197 | −0.197099 | − | 0.980384i | \(-0.563152\pi\) | ||||
−0.197099 | + | 0.980384i | \(0.563152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4587.23 | −0.434844 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1137.07 | 0.106457 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19277.8 | −1.79376 | −0.896880 | − | 0.442275i | \(-0.854172\pi\) | ||||
−0.896880 | + | 0.442275i | \(0.854172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1315.88 | 0.120946 | 0.0604732 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604732 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10827.7 | −0.989159 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2851.67 | −0.257374 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10477.9 | 0.939988 | 0.469994 | − | 0.882670i | \(-0.344256\pi\) | ||||
0.469994 | + | 0.882670i | \(0.344256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9312.29 | 0.825476 | 0.412738 | − | 0.910850i | \(-0.364572\pi\) | ||||
0.412738 | + | 0.910850i | \(0.364572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9288.76 | −0.818504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21595.3 | 1.88054 | 0.940270 | − | 0.340429i | \(-0.110572\pi\) | ||||
0.940270 | + | 0.340429i | \(0.110572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22239.5 | −1.92528 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −863.936 | −0.0739215 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15750.0 | 1.33981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9386.88 | −0.789341 | −0.394670 | − | 0.918823i | \(-0.629141\pi\) | ||||
−0.394670 | + | 0.918823i | \(0.629141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19068.9 | −1.59431 | −0.797156 | − | 0.603773i | \(-0.793663\pi\) | ||||
−0.797156 | + | 0.603773i | \(0.793663\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13780.8 | −1.13909 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10284.2 | −0.845251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1516.33 | 0.123226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9033.94 | 0.730040 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6775.69 | −0.541465 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22209.4 | −1.76499 | −0.882493 | − | 0.470325i | \(-0.844137\pi\) | ||||
−0.882493 | + | 0.470325i | \(0.844137\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1438.22 | −0.113040 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2233.14 | −0.174556 | −0.0872782 | − | 0.996184i | \(-0.527817\pi\) | ||||
−0.0872782 | + | 0.996184i | \(0.527817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13151.9 | −1.01686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6954.74 | 0.534802 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19727.7 | −1.50070 | −0.750351 | − | 0.661039i | \(-0.770116\pi\) | ||||
−0.750351 | + | 0.661039i | \(0.770116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5786.46 | 0.437819 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12025.7 | 0.900216 | 0.450108 | − | 0.892974i | \(-0.351385\pi\) | ||||
0.450108 | + | 0.892974i | \(0.351385\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3359.37 | 0.250142 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19708.8 | −1.45209 | −0.726044 | − | 0.687648i | \(-0.758643\pi\) | ||||
−0.726044 | + | 0.687648i | \(0.758643\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3965.65 | 0.290643 | 0.145322 | − | 0.989384i | \(-0.453578\pi\) | ||||
0.145322 | + | 0.989384i | \(0.453578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1084.79 | −0.0786762 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4134.92 | 0.298334 | 0.149167 | − | 0.988812i | \(-0.452341\pi\) | ||||
0.149167 | + | 0.988812i | \(0.452341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24369.6 | 1.74014 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1031.69 | −0.0732904 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10949.0 | −0.769873 | −0.384937 | − | 0.922943i | \(-0.625777\pi\) | ||||
−0.384937 | + | 0.922943i | \(0.625777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16738.9 | −1.17099 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17834.7 | 1.23505 | 0.617523 | − | 0.786553i | \(-0.288136\pi\) | ||||
0.617523 | + | 0.786553i | \(0.288136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7547.95 | −0.520060 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6052.79 | 0.412872 | 0.206436 | − | 0.978460i | \(-0.433814\pi\) | ||||
0.206436 | + | 0.978460i | \(0.433814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5233.02 | 0.355174 | 0.177587 | − | 0.984105i | \(-0.443171\pi\) | ||||
0.177587 | + | 0.984105i | \(0.443171\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3038.78 | 0.204205 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24209.4 | −1.61883 | −0.809413 | − | 0.587240i | \(-0.800215\pi\) | ||||
−0.809413 | + | 0.587240i | \(0.800215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39989.0 | 2.64776 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7255.45 | 0.478050 | 0.239025 | − | 0.971013i | \(-0.423172\pi\) | ||||
0.239025 | + | 0.971013i | \(0.423172\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29694.7 | −1.93754 | −0.968772 | − | 0.247951i | \(-0.920243\pi\) | ||||
−0.968772 | + | 0.247951i | \(0.920243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10775.2 | 0.699665 | 0.349833 | − | 0.936812i | \(-0.386238\pi\) | ||||
0.349833 | + | 0.936812i | \(0.386238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9143.11 | 0.587979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4157.84 | −0.263568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3661.18 | −0.230981 | −0.115491 | − | 0.993309i | \(-0.536844\pi\) | ||||
−0.115491 | + | 0.993309i | \(0.536844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9092.03 | −0.568199 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17203.4 | −1.07005 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5627.43 | −0.346755 | −0.173378 | − | 0.984855i | \(-0.555468\pi\) | ||||
−0.173378 | + | 0.984855i | \(0.555468\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10732.5 | −0.658243 | −0.329122 | − | 0.944288i | \(-0.606753\pi\) | ||||
−0.329122 | + | 0.944288i | \(0.606753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28753.1 | −1.74714 | −0.873571 | − | 0.486697i | \(-0.838202\pi\) | ||||
−0.873571 | + | 0.486697i | \(0.838202\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2474.17 | −0.149645 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27398.6 | 1.64195 | 0.820974 | − | 0.570966i | \(-0.193431\pi\) | ||||
0.820974 | + | 0.570966i | \(0.193431\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8844.97 | −0.527636 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26446.7 | 1.56331 | 0.781653 | − | 0.623714i | \(-0.214377\pi\) | ||||
0.781653 | + | 0.623714i | \(0.214377\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25643.7 | 1.50897 | 0.754483 | − | 0.656320i | \(-0.227888\pi\) | ||||
0.754483 | + | 0.656320i | \(0.227888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9168.13 | −0.534624 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7591.40 | −0.440690 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6085.94 | 0.350142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10796.0 | 0.618357 | 0.309179 | − | 0.951004i | \(-0.399946\pi\) | ||||
0.309179 | + | 0.951004i | \(0.399946\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13183.2 | 0.748406 | 0.374203 | − | 0.927347i | \(-0.377916\pi\) | ||||
0.374203 | + | 0.927347i | \(0.377916\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5546.96 | 0.313509 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1349.06 | 0.0755786 | 0.0377893 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377893 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9214.26 | 0.513954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2619.45 | −0.144838 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25133.8 | 1.38370 | 0.691849 | − | 0.722042i | \(-0.256796\pi\) | ||||
0.691849 | + | 0.722042i | \(0.256796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6855.68 | −0.374174 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1374.39 | 0.0746896 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14808.9 | 0.797895 | 0.398948 | − | 0.916974i | \(-0.369375\pi\) | ||||
0.398948 | + | 0.916974i | \(0.369375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5050.33 | −0.270948 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45313.5 | −2.41045 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13857.2 | −0.734019 | −0.367009 | − | 0.930217i | \(-0.619618\pi\) | ||||
−0.367009 | + | 0.930217i | \(0.619618\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9661.84 | −0.507488 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9181.54 | −0.480238 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21853.5 | 1.13352 | 0.566759 | − | 0.823884i | \(-0.308197\pi\) | ||||
0.566759 | + | 0.823884i | \(0.308197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4214.55 | −0.217695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4373.78 | 0.224053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1442.23 | −0.0735757 | −0.0367878 | − | 0.999323i | \(-0.511713\pi\) | ||||
−0.0367878 | + | 0.999323i | \(0.511713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5244.81 | 0.265371 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2606.50 | 0.131342 | 0.0656708 | − | 0.997841i | \(-0.479081\pi\) | ||||
0.0656708 | + | 0.997841i | \(0.479081\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23075.3 | −1.15331 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9072.37 | 0.451600 | 0.225800 | − | 0.974174i | \(-0.427500\pi\) | ||||
0.225800 | + | 0.974174i | \(0.427500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10093.2 | 0.498364 | 0.249182 | − | 0.968457i | \(-0.419838\pi\) | ||||
0.249182 | + | 0.968457i | \(0.419838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10698.3 | 0.526113 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44070.4 | 2.14993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22033.4 | 1.07059 | 0.535294 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535294 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5999.04 | 0.289175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8362.75 | 0.401518 | 0.200759 | − | 0.979641i | \(-0.435659\pi\) | ||||
0.200759 | + | 0.979641i | \(0.435659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11405.1 | 0.543280 | 0.271640 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271640 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7016.09 | −0.332896 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6281.89 | −0.295731 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1447.34 | 0.0678704 | 0.0339352 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339352 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25835.9 | −1.20214 | −0.601070 | − | 0.799196i | \(-0.705259\pi\) | ||||
−0.601070 | + | 0.799196i | \(0.705259\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5566.66 | 0.258013 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1669.40 | 0.0767812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3144.14 | −0.144054 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9235.63 | −0.419916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15859.9 | 0.718355 | 0.359178 | − | 0.933269i | \(-0.383057\pi\) | ||||
0.359178 | + | 0.933269i | \(0.383057\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16388.1 | 0.736653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15452.1 | 0.691956 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32805.2 | −1.45799 | −0.728997 | − | 0.684517i | \(-0.760013\pi\) | ||||
−0.728997 | + | 0.684517i | \(0.760013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36245.8 | 1.60486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24520.4 | −1.07759 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5291.94 | −0.231697 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17068.4 | −0.741772 | −0.370886 | − | 0.928678i | \(-0.620946\pi\) | ||||
−0.370886 | + | 0.928678i | \(0.620946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12079.5 | 0.523018 | 0.261509 | − | 0.965201i | \(-0.415780\pi\) | ||||
0.261509 | + | 0.965201i | \(0.415780\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16015.6 | 0.688347 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6370.61 | 0.272802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34364.3 | −1.46081 | −0.730403 | − | 0.683016i | \(-0.760668\pi\) | ||||
−0.730403 | + | 0.683016i | \(0.760668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12983.0 | 0.549891 | 0.274946 | − | 0.961460i | \(-0.411340\pi\) | ||||
0.274946 | + | 0.961460i | \(0.411340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25503.7 | 1.07237 | 0.536186 | − | 0.844100i | \(-0.319865\pi\) | ||||
0.536186 | + | 0.844100i | \(0.319865\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26016.9 | 1.08999 | 0.544997 | − | 0.838438i | \(-0.316531\pi\) | ||||
0.544997 | + | 0.838438i | \(0.316531\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15593.0 | −0.648579 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2954.42 | −0.122445 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11090.3 | 0.456353 | 0.228177 | − | 0.973620i | \(-0.426724\pi\) | ||||
0.228177 | + | 0.973620i | \(0.426724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6218.91 | 0.254988 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12326.8 | −0.501839 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14824.1 | 0.601372 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2915.10 | −0.117425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41006.8 | 1.64601 | 0.823004 | − | 0.568036i | \(-0.192296\pi\) | ||||
0.823004 | + | 0.568036i | \(0.192296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38890.1 | −1.55013 | −0.775065 | − | 0.631881i | \(-0.782283\pi\) | ||||
−0.775065 | + | 0.631881i | \(0.782283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43062.9 | 1.71046 | 0.855232 | − | 0.518246i | \(-0.173415\pi\) | ||||
0.855232 | + | 0.518246i | \(0.173415\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2294.97 | 0.0905232 | 0.0452616 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452616 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15553.4 | −0.611365 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7668.03 | 0.299333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −58587.9 | −2.27919 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3048.94 | 0.117798 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33278.9 | 1.28136 | 0.640678 | − | 0.767810i | \(-0.278653\pi\) | ||||
0.640678 | + | 0.767810i | \(0.278653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9821.12 | 0.375575 | 0.187788 | − | 0.982210i | \(-0.439868\pi\) | ||||
0.187788 | + | 0.982210i | \(0.439868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13745.6 | −0.523869 | −0.261934 | − | 0.965086i | \(-0.584360\pi\) | ||||
−0.261934 | + | 0.965086i | \(0.584360\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24565.8 | 0.929922 | 0.464961 | − | 0.885331i | \(-0.346068\pi\) | ||||
0.464961 | + | 0.885331i | \(0.346068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44353.7 | −1.67331 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44026.0 | 1.64980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12244.7 | 0.457312 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38955.7 | 1.44521 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2374.25 | −0.0877889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12080.6 | −0.443728 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20218.5 | 0.740181 | 0.370091 | − | 0.928996i | \(-0.379327\pi\) | ||||
0.370091 | + | 0.928996i | \(0.379327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4552.96 | 0.165583 | 0.0827915 | − | 0.996567i | \(-0.473616\pi\) | ||||
0.0827915 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26869.0 | 0.973969 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43148.5 | −1.55386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19814.0 | 0.711211 | 0.355605 | − | 0.934636i | \(-0.384275\pi\) | ||||
0.355605 | + | 0.934636i | \(0.384275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7982.94 | −0.284682 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1679.53 | 0.0597002 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40202.9 | 1.41982 | 0.709911 | − | 0.704291i | \(-0.248735\pi\) | ||||
0.709911 | + | 0.704291i | \(0.248735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18940.1 | −0.666742 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8322.09 | −0.291082 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24587.9 | 0.857260 | 0.428630 | − | 0.903480i | \(-0.358996\pi\) | ||||
0.428630 | + | 0.903480i | \(0.358996\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33462.1 | −1.15923 | −0.579614 | − | 0.814891i | \(-0.696797\pi\) | ||||
−0.579614 | + | 0.814891i | \(0.696797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 963.596 | 0.0332757 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8385.17 | −0.287731 | −0.143866 | − | 0.989597i | \(-0.545953\pi\) | ||||
−0.143866 | + | 0.989597i | \(0.545953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62256.9 | −2.12955 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55532.0 | −1.88758 | −0.943788 | − | 0.330552i | \(-0.892765\pi\) | ||||
−0.943788 | + | 0.330552i | \(0.892765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8261.23 | 0.279924 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44950.0 | 1.51357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19789.3 | 0.664272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23683.3 | −0.790043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44080.8 | −1.46592 | −0.732960 | − | 0.680272i | \(-0.761862\pi\) | ||||
−0.732960 | + | 0.680272i | \(0.761862\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29721.4 | 0.982291 | 0.491146 | − | 0.871077i | \(-0.336578\pi\) | ||||
0.491146 | + | 0.871077i | \(0.336578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33444.2 | −1.10192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −462.881 | −0.0151575 | −0.00757876 | − | 0.999971i | \(-0.502412\pi\) | ||||
−0.00757876 | + | 0.999971i | \(0.502412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10080.9 | 0.329096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27389.7 | 0.888703 | 0.444351 | − | 0.895853i | \(-0.353434\pi\) | ||||
0.444351 | + | 0.895853i | \(0.353434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10534.0 | 0.340752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3677.18 | 0.118228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32596.6 | 1.04487 | 0.522435 | − | 0.852679i | \(-0.325024\pi\) | ||||
0.522435 | + | 0.852679i | \(0.325024\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4455.75 | −0.141966 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26630.6 | −0.845936 | −0.422968 | − | 0.906145i | \(-0.639012\pi\) | ||||
−0.422968 | + | 0.906145i | \(0.639012\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1080.4.a.h.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.n.1.1 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bf.1.3 | 3 | |||
12.11 | even | 2 | 2160.4.a.bn.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.h.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.n.1.1 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bf.1.3 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bn.1.3 | 3 | 12.11 | even | 2 |