Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 120) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-5.17891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.0735 | 1.78580 | 0.892899 | − | 0.450257i | \(-0.148667\pi\) | ||||
0.892899 | + | 0.450257i | \(0.148667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.3578 | −1.32549 | −0.662747 | − | 0.748844i | \(-0.730609\pi\) | ||||
−0.662747 | + | 0.748844i | \(0.730609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.3578 | −1.28771 | −0.643856 | − | 0.765147i | \(-0.722666\pi\) | ||||
−0.643856 | + | 0.765147i | \(0.722666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.7891 | −0.253793 | −0.126897 | − | 0.991916i | \(-0.540502\pi\) | ||||
−0.126897 | + | 0.991916i | \(0.540502\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 130.863 | 1.58010 | 0.790051 | − | 0.613042i | \(-0.210054\pi\) | ||||
0.790051 | + | 0.613042i | \(0.210054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 99.2204 | 1.03103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −70.8625 | −0.642429 | −0.321214 | − | 0.947007i | \(-0.604091\pi\) | ||||
−0.321214 | + | 0.947007i | \(0.604091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 104.505 | 0.669174 | 0.334587 | − | 0.942365i | \(-0.391403\pi\) | ||||
0.334587 | + | 0.942365i | \(0.391403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 210.441 | 1.21923 | 0.609617 | − | 0.792696i | \(-0.291323\pi\) | ||||
0.609617 | + | 0.792696i | \(0.291323\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −145.073 | −0.765274 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 300.945 | 1.33717 | 0.668583 | − | 0.743638i | \(-0.266901\pi\) | ||||
0.668583 | + | 0.743638i | \(0.266901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −181.073 | −0.743460 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.147 | 0.914747 | 0.457374 | − | 0.889275i | \(-0.348790\pi\) | ||||
0.457374 | + | 0.889275i | \(0.348790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 108.000 | 0.383020 | 0.191510 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 278.991 | 0.865850 | 0.432925 | − | 0.901430i | \(-0.357481\pi\) | ||||
0.432925 | + | 0.901430i | \(0.357481\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 750.853 | 2.18908 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −53.3673 | −0.146528 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 328.358 | 0.851008 | 0.425504 | − | 0.904957i | \(-0.360097\pi\) | ||||
0.425504 | + | 0.904957i | \(0.360097\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 392.588 | 0.912272 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −889.533 | −1.96284 | −0.981418 | − | 0.191882i | \(-0.938541\pi\) | ||||
−0.981418 | + | 0.191882i | \(0.938541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −241.450 | −0.506795 | −0.253398 | − | 0.967362i | \(-0.581548\pi\) | ||||
−0.253398 | + | 0.967362i | \(0.581548\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 297.661 | 0.595266 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −103.834 | −0.189334 | −0.0946669 | − | 0.995509i | \(-0.530179\pi\) | ||||
−0.0946669 | + | 0.995509i | \(0.530179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −212.588 | −0.370906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 277.597 | 0.464010 | 0.232005 | − | 0.972715i | \(-0.425471\pi\) | ||||
0.232005 | + | 0.972715i | \(0.425471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 274.403 | 0.439951 | 0.219976 | − | 0.975505i | \(-0.429402\pi\) | ||||
0.219976 | + | 0.975505i | \(0.429402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1599.36 | −2.36706 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −366.991 | −0.522654 | −0.261327 | − | 0.965250i | \(-0.584160\pi\) | ||||
−0.261327 | + | 0.965250i | \(0.584160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −57.7251 | −0.0763391 | −0.0381696 | − | 0.999271i | \(-0.512153\pi\) | ||||
−0.0381696 | + | 0.999271i | \(0.512153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 313.514 | 0.386348 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −203.175 | −0.241983 | −0.120992 | − | 0.992654i | \(-0.538607\pi\) | ||||
−0.120992 | + | 0.992654i | \(0.538607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1996.24 | −2.29959 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 631.322 | 0.703925 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1283.45 | 1.34345 | 0.671725 | − | 0.740801i | \(-0.265554\pi\) | ||||
0.671725 | + | 0.740801i | \(0.265554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −435.220 | −0.441831 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 886.908 | 0.873768 | 0.436884 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436884 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 783.055 | 0.749094 | 0.374547 | − | 0.927208i | \(-0.377798\pi\) | ||||
0.374547 | + | 0.927208i | \(0.377798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1301.51 | −1.17590 | −0.587950 | − | 0.808897i | \(-0.700065\pi\) | ||||
−0.587950 | + | 0.808897i | \(0.700065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1161.91 | 1.02102 | 0.510508 | − | 0.859873i | \(-0.329457\pi\) | ||||
0.510508 | + | 0.859873i | \(0.329457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 902.836 | 0.772013 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 507.808 | 0.422748 | 0.211374 | − | 0.977405i | \(-0.432206\pi\) | ||||
0.211374 | + | 0.977405i | \(0.432206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −543.220 | −0.429237 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −588.346 | −0.453224 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1007.48 | 0.756933 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 720.441 | 0.528130 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −796.064 | −0.556215 | −0.278107 | − | 0.960550i | \(-0.589707\pi\) | ||||
−0.278107 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 324.000 | 0.221137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.4764 | 0.0610102 | 0.0305051 | − | 0.999535i | \(-0.490288\pi\) | ||||
0.0305051 | + | 0.999535i | \(0.490288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4328.08 | 2.82174 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2273.28 | 1.41766 | 0.708829 | − | 0.705380i | \(-0.249224\pi\) | ||||
0.708829 | + | 0.705380i | \(0.249224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 738.735 | 0.450782 | 0.225391 | − | 0.974268i | \(-0.427634\pi\) | ||||
0.225391 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 836.972 | 0.499899 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2918.77 | 1.70685 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2252.56 | 1.26386 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1507.15 | 0.828661 | 0.414330 | − | 0.910127i | \(-0.364016\pi\) | ||||
0.414330 | + | 0.910127i | \(0.364016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −154.365 | −0.0831925 | −0.0415962 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415962 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −160.102 | −0.0845978 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −315.514 | −0.160387 | −0.0801935 | − | 0.996779i | \(-0.525554\pi\) | ||||
−0.0801935 | + | 0.996779i | \(0.525554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 985.073 | 0.491330 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2343.67 | −1.14725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1457.85 | 0.700539 | 0.350270 | − | 0.936649i | \(-0.386090\pi\) | ||||
0.350270 | + | 0.936649i | \(0.386090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2198.61 | 1.01876 | 0.509381 | − | 0.860541i | \(-0.329874\pi\) | ||||
0.509381 | + | 0.860541i | \(0.329874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1446.07 | 0.658200 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1177.76 | 0.526700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2030.49 | −0.892343 | −0.446171 | − | 0.894948i | \(-0.647213\pi\) | ||||
−0.446171 | + | 0.894948i | \(0.647213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2668.60 | −1.13324 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −427.220 | −0.178391 | −0.0891954 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891954 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3779.97 | −1.55228 | −0.776140 | − | 0.630561i | \(-0.782825\pi\) | ||||
−0.776140 | + | 0.630561i | \(0.782825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −724.350 | −0.292598 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 860.241 | 0.336401 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 892.983 | 0.343677 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1565.60 | −0.593103 | −0.296551 | − | 0.955017i | \(-0.595837\pi\) | ||||
−0.296551 | + | 0.955017i | \(0.595837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2642.63 | −0.985599 | −0.492800 | − | 0.870143i | \(-0.664026\pi\) | ||||
−0.492800 | + | 0.870143i | \(0.664026\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 98.4522 | 0.0356062 | 0.0178031 | − | 0.999842i | \(-0.494333\pi\) | ||||
0.0178031 | + | 0.999842i | \(0.494333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1131.62 | −0.403106 | −0.201553 | − | 0.979478i | \(-0.564599\pi\) | ||||
−0.201553 | + | 0.979478i | \(0.564599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −311.503 | −0.109312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3456.33 | 1.19501 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −637.763 | −0.214143 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6328.23 | −2.09441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1902.85 | 0.620841 | 0.310420 | − | 0.950599i | \(-0.399530\pi\) | ||||
0.310420 | + | 0.950599i | \(0.399530\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 832.791 | 0.267896 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6960.00 | 2.17731 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 823.209 | 0.254006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1073.71 | 0.326813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4855.59 | −1.45809 | −0.729046 | − | 0.684465i | \(-0.760036\pi\) | ||||
−0.729046 | + | 0.684465i | \(0.760036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6536.19 | 1.91111 | 0.955555 | − | 0.294812i | \(-0.0952571\pi\) | ||||
0.955555 | + | 0.294812i | \(0.0952571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5510.35 | −1.59011 | −0.795053 | − | 0.606539i | \(-0.792557\pi\) | ||||
−0.795053 | + | 0.606539i | \(0.792557\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4798.08 | −1.36663 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5915.65 | 1.66329 | 0.831646 | − | 0.555306i | \(-0.187399\pi\) | ||||
0.831646 | + | 0.555306i | \(0.187399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1100.97 | −0.301754 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2263.25 | −0.612543 | −0.306272 | − | 0.951944i | \(-0.599082\pi\) | ||||
−0.306272 | + | 0.951944i | \(0.599082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 772.493 | 0.206476 | 0.103238 | − | 0.994657i | \(-0.467080\pi\) | ||||
0.103238 | + | 0.994657i | \(0.467080\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7898.58 | −2.03471 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −173.175 | −0.0440744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −596.192 | −0.149926 | −0.0749628 | − | 0.997186i | \(-0.523884\pi\) | ||||
−0.0749628 | + | 0.997186i | \(0.523884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3426.76 | 0.851535 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4139.19 | 1.00465 | 0.502326 | − | 0.864678i | \(-0.332478\pi\) | ||||
0.502326 | + | 0.864678i | \(0.332478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9953.30 | 2.38791 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 940.542 | 0.223058 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1611.34 | 0.377792 | 0.188896 | − | 0.981997i | \(-0.439509\pi\) | ||||
0.188896 | + | 0.981997i | \(0.439509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −609.526 | −0.139709 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7031.33 | −1.59371 | −0.796855 | − | 0.604171i | \(-0.793504\pi\) | ||||
−0.796855 | + | 0.604171i | \(0.793504\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5441.27 | 1.21968 | 0.609840 | − | 0.792524i | \(-0.291234\pi\) | ||||
0.609840 | + | 0.792524i | \(0.291234\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5988.72 | −1.32767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1080.43 | 0.234355 | 0.117178 | − | 0.993111i | \(-0.462615\pi\) | ||||
0.117178 | + | 0.993111i | \(0.462615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1893.97 | 0.406411 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1602.99 | −0.340308 | −0.170154 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170154 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −334.810 | −0.0703265 | −0.0351632 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351632 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7942.49 | 1.63355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4596.55 | −0.935589 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3850.35 | 0.775641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 539.250 | 0.107520 | 0.0537599 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537599 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1305.66 | −0.255091 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4277.11 | 0.827263 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3571.93 | 0.683996 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2660.72 | 0.504470 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8477.58 | −1.57603 | −0.788015 | − | 0.615656i | \(-0.788891\pi\) | ||||
−0.788015 | + | 0.615656i | \(0.788891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2349.16 | 0.432490 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3646.92 | −0.664945 | −0.332473 | − | 0.943113i | \(-0.607883\pi\) | ||||
−0.332473 | + | 0.943113i | \(0.607883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7537.05 | 1.36108 | 0.680542 | − | 0.732709i | \(-0.261745\pi\) | ||||
0.680542 | + | 0.732709i | \(0.261745\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10721.2 | −1.89956 | −0.949781 | − | 0.312916i | \(-0.898694\pi\) | ||||
−0.949781 | + | 0.312916i | \(0.898694\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5053.62 | −0.886986 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3904.52 | −0.678907 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2327.92 | −0.401019 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3485.73 | 0.589484 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9227.18 | 1.54623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4405.14 | 0.731505 | 0.365753 | − | 0.930712i | \(-0.380812\pi\) | ||||
0.365753 | + | 0.930712i | \(0.380812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2708.51 | 0.445722 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −186.117 | −0.0300844 | −0.0150422 | − | 0.999887i | \(-0.504788\pi\) | ||||
−0.0150422 | + | 0.999887i | \(0.504788\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1523.42 | 0.244074 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10176.5 | −1.61609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13489.1 | 2.12345 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5547.38 | −0.858211 | −0.429105 | − | 0.903254i | \(-0.641171\pi\) | ||||
−0.429105 | + | 0.903254i | \(0.641171\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9078.82 | 1.39249 | 0.696244 | − | 0.717805i | \(-0.254853\pi\) | ||||
0.696244 | + | 0.717805i | \(0.254853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1629.66 | −0.247820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10678.1 | 1.61002 | 0.805009 | − | 0.593262i | \(-0.202160\pi\) | ||||
0.805009 | + | 0.593262i | \(0.202160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1765.04 | −0.261669 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 265.733 | 0.0390665 | 0.0195332 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195332 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10266.0 | 1.49672 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3022.44 | 0.437016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5854.21 | 0.832663 | 0.416332 | − | 0.909213i | \(-0.363316\pi\) | ||||
0.416332 | + | 0.909213i | \(0.363316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2161.32 | 0.304916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10859.9 | 1.51973 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10134.5 | −1.40682 | −0.703408 | − | 0.710787i | \(-0.748339\pi\) | ||||
−0.703408 | + | 0.710787i | \(0.748339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6307.68 | −0.861703 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4235.70 | 0.574072 | 0.287036 | − | 0.957920i | \(-0.407330\pi\) | ||||
0.287036 | + | 0.957920i | \(0.407330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2388.19 | −0.321131 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8100.84 | −1.08077 | −0.540383 | − | 0.841419i | \(-0.681721\pi\) | ||||
−0.540383 | + | 0.841419i | \(0.681721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 972.000 | 0.127673 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13820.2 | −1.80131 | −0.900656 | − | 0.434532i | \(-0.856914\pi\) | ||||
−0.900656 | + | 0.434532i | \(0.856914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1260.58 | 0.163044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 274.429 | 0.0352242 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11523.9 | 1.45685 | 0.728425 | − | 0.685125i | \(-0.240252\pi\) | ||||
0.728425 | + | 0.685125i | \(0.240252\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12984.2 | 1.62913 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 700.915 | 0.0872869 | 0.0436434 | − | 0.999047i | \(-0.486103\pi\) | ||||
0.0436434 | + | 0.999047i | \(0.486103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12701.7 | −1.57002 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14553.1 | −1.77240 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6650.69 | 0.804047 | 0.402024 | − | 0.915629i | \(-0.368307\pi\) | ||||
0.402024 | + | 0.915629i | \(0.368307\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6819.83 | 0.818485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −29419.9 | −3.50523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2216.20 | 0.260259 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13844.4 | −1.61418 | −0.807091 | − | 0.590426i | \(-0.798960\pi\) | ||||
−0.807091 | + | 0.590426i | \(0.798960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12576.3 | 1.45590 | 0.727949 | − | 0.685631i | \(-0.240474\pi\) | ||||
0.727949 | + | 0.685631i | \(0.240474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2510.92 | 0.288617 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7985.59 | −0.905035 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8756.32 | 0.985452 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13440.6 | −1.50212 | −0.751059 | − | 0.660236i | \(-0.770456\pi\) | ||||
−0.751059 | + | 0.660236i | \(0.770456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3012.87 | 0.334387 | 0.167193 | − | 0.985924i | \(-0.446530\pi\) | ||||
0.167193 | + | 0.985924i | \(0.446530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9273.25 | −1.01510 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10675.0 | −1.16057 | −0.580283 | − | 0.814415i | \(-0.697058\pi\) | ||||
−0.580283 | + | 0.814415i | \(0.697058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6757.68 | 0.729692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −125.868 | −0.0134992 | −0.00674962 | − | 0.999977i | \(-0.502148\pi\) | ||||
−0.00674962 | + | 0.999977i | \(0.502148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4521.45 | 0.478428 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9707.21 | −1.02029 | −0.510146 | − | 0.860088i | \(-0.670409\pi\) | ||||
−0.510146 | + | 0.860088i | \(0.670409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11613.0 | −1.21249 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −463.096 | −0.0480312 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1279.97 | −0.131016 | −0.0655082 | − | 0.997852i | \(-0.520867\pi\) | ||||
−0.0655082 | + | 0.997852i | \(0.520867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −480.305 | −0.0488425 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3080.48 | 0.311220 | 0.155610 | − | 0.987819i | \(-0.450266\pi\) | ||||
0.155610 | + | 0.987819i | \(0.450266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18017.3 | −1.80850 | −0.904248 | − | 0.427008i | \(-0.859568\pi\) | ||||
−0.904248 | + | 0.427008i | \(0.859568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7236.77 | 0.717083 | 0.358541 | − | 0.933514i | \(-0.383274\pi\) | ||||
0.358541 | + | 0.933514i | \(0.383274\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3434.16 | −0.338112 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −946.542 | −0.0925995 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5222.64 | −0.507690 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2955.22 | 0.283669 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4932.78 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18164.4 | −1.72188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7031.01 | −0.662364 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5937.91 | 0.552510 | 0.276255 | − | 0.961084i | \(-0.410907\pi\) | ||||
0.276255 | + | 0.961084i | \(0.410907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4373.56 | 0.404456 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15703.5 | −1.44336 | −0.721678 | − | 0.692229i | \(-0.756629\pi\) | ||||
−0.721678 | + | 0.692229i | \(0.756629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1859.04 | −0.169832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9181.09 | 0.828628 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5656.77 | 0.507478 | 0.253739 | − | 0.967273i | \(-0.418340\pi\) | ||||
0.253739 | + | 0.967273i | \(0.418340\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6595.82 | 0.588183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −290.441 | −0.0257457 | −0.0128729 | − | 0.999917i | \(-0.504098\pi\) | ||||
−0.0128729 | + | 0.999917i | \(0.504098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4338.20 | 0.380012 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17330.6 | 1.50916 | 0.754582 | − | 0.656206i | \(-0.227840\pi\) | ||||
0.754582 | + | 0.656206i | \(0.227840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9075.45 | 0.785664 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3533.29 | 0.304091 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13491.4 | −1.14768 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6091.47 | −0.515194 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6174.36 | 0.519201 | 0.259601 | − | 0.965716i | \(-0.416409\pi\) | ||||
0.259601 | + | 0.965716i | \(0.416409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13389.4 | 1.11946 | 0.559730 | − | 0.828675i | \(-0.310905\pi\) | ||||
0.559730 | + | 0.828675i | \(0.310905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3743.55 | −0.309434 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7145.50 | −0.587285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8005.80 | −0.654279 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14494.7 | −1.17793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1281.66 | −0.102994 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36309.6 | −2.90161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14355.5 | −1.14084 | −0.570418 | − | 0.821354i | \(-0.693219\pi\) | ||||
−0.570418 | + | 0.821354i | \(0.693219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11339.9 | −0.896209 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21133.9 | 1.65195 | 0.825977 | − | 0.563704i | \(-0.190624\pi\) | ||||
0.825977 | + | 0.563704i | \(0.190624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2173.05 | −0.168932 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13675.8 | 1.05736 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12137.6 | −0.933355 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3098.60 | 0.235713 | 0.117856 | − | 0.993031i | \(-0.462398\pi\) | ||||
0.117856 | + | 0.993031i | \(0.462398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6518.64 | −0.493219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2580.72 | 0.194221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7908.77 | −0.592033 | −0.296017 | − | 0.955183i | \(-0.595658\pi\) | ||||
−0.296017 | + | 0.955183i | \(0.595658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2678.95 | 0.198422 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10740.7 | −0.791345 | −0.395673 | − | 0.918392i | \(-0.629488\pi\) | ||||
−0.395673 | + | 0.918392i | \(0.629488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14701.2 | −1.07745 | −0.538725 | − | 0.842482i | \(-0.681094\pi\) | ||||
−0.538725 | + | 0.842482i | \(0.681094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4696.79 | −0.342428 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15788.1 | 1.13911 | 0.569554 | − | 0.821954i | \(-0.307116\pi\) | ||||
0.569554 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7927.89 | −0.569036 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1909.17 | −0.136326 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15878.7 | −1.12801 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14778.5 | −1.03913 | −0.519567 | − | 0.854430i | \(-0.673907\pi\) | ||||
−0.519567 | + | 0.854430i | \(0.673907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27538.8 | 1.92651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 295.356 | 0.0205573 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11143.9 | 0.771713 | 0.385857 | − | 0.922559i | \(-0.373906\pi\) | ||||
0.385857 | + | 0.922559i | \(0.373906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3394.85 | −0.232733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7707.87 | 0.525768 | 0.262884 | − | 0.964827i | \(-0.415326\pi\) | ||||
0.262884 | + | 0.964827i | \(0.415326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13681.4 | −0.928580 | −0.464290 | − | 0.885683i | \(-0.653691\pi\) | ||||
−0.464290 | + | 0.885683i | \(0.653691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −934.508 | −0.0631113 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11552.4 | −0.772481 | −0.386241 | − | 0.922398i | \(-0.626227\pi\) | ||||
−0.386241 | + | 0.922398i | \(0.626227\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10369.0 | 0.689939 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16839.3 | −1.11496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9904.66 | −0.652603 | −0.326301 | − | 0.945266i | \(-0.605802\pi\) | ||||
−0.326301 | + | 0.945266i | \(0.605802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20323.5 | 1.32608 | 0.663042 | − | 0.748582i | \(-0.269265\pi\) | ||||
0.663042 | + | 0.748582i | \(0.269265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9223.99 | 0.598940 | 0.299470 | − | 0.954106i | \(-0.403190\pi\) | ||||
0.299470 | + | 0.954106i | \(0.403190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1913.29 | −0.123635 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6719.70 | −0.432134 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18984.7 | −1.20921 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5353.54 | −0.339364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16916.0 | 1.06722 | 0.533610 | − | 0.845730i | \(-0.320835\pi\) | ||||
0.533610 | + | 0.845730i | \(0.320835\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5708.54 | 0.358443 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −45319.9 | −2.81890 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2498.37 | 0.154670 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5811.35 | −0.358088 | −0.179044 | − | 0.983841i | \(-0.557300\pi\) | ||||
−0.179044 | + | 0.983841i | \(0.557300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27931.7 | −1.71309 | −0.856547 | − | 0.516069i | \(-0.827395\pi\) | ||||
−0.856547 | + | 0.516069i | \(0.827395\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25437.8 | −1.54569 | −0.772845 | − | 0.634595i | \(-0.781167\pi\) | ||||
−0.772845 | + | 0.634595i | \(0.781167\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43015.9 | 2.60173 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20880.0 | 1.25707 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22647.7 | 1.35723 | 0.678617 | − | 0.734493i | \(-0.262580\pi\) | ||||
0.678617 | + | 0.734493i | \(0.262580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2469.63 | 0.146650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25158.5 | −1.48716 | −0.743579 | − | 0.668649i | \(-0.766873\pi\) | ||||
−0.743579 | + | 0.668649i | \(0.766873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23441.0 | 1.37935 | 0.689675 | − | 0.724119i | \(-0.257753\pi\) | ||||
0.689675 | + | 0.724119i | \(0.257753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3221.13 | 0.188685 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7405.47 | −0.429896 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14566.8 | −0.841829 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11676.0 | 0.671754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3145.33 | −0.180154 | −0.0900770 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900770 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10606.2 | −0.602109 | −0.301054 | − | 0.953607i | \(-0.597339\pi\) | ||||
−0.301054 | + | 0.953607i | \(0.597339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42448.1 | 2.39913 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19608.6 | 1.10338 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7825.06 | 0.438386 | 0.219193 | − | 0.975682i | \(-0.429658\pi\) | ||||
0.219193 | + | 0.975682i | \(0.429658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16531.1 | −0.918049 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19819.0 | −1.09585 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22750.9 | −1.25251 | −0.626256 | − | 0.779618i | \(-0.715413\pi\) | ||||
−0.626256 | + | 0.779618i | \(0.715413\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14394.2 | −0.789022 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4271.99 | −0.232157 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17747.0 | 0.960302 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −133.598 | −0.00719817 | −0.00359908 | − | 0.999994i | \(-0.501146\pi\) | ||||
−0.00359908 | + | 0.999994i | \(0.501146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39382.5 | 2.11286 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29333.1 | 1.56037 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6886.26 | 0.364766 | 0.182383 | − | 0.983228i | \(-0.441619\pi\) | ||||
0.182383 | + | 0.983228i | \(0.441619\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3302.92 | −0.174218 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14912.4 | −0.783271 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6789.76 | −0.353652 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1570.18 | 0.0814436 | 0.0407218 | − | 0.999171i | \(-0.487034\pi\) | ||||
0.0407218 | + | 0.999171i | \(0.487034\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25898.3 | 1.33773 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2317.48 | 0.119209 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3399.18 | 0.173409 | 0.0867047 | − | 0.996234i | \(-0.472366\pi\) | ||||
0.0867047 | + | 0.996234i | \(0.472366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1921.22 | −0.0972078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14152.1 | −0.713125 | −0.356562 | − | 0.934272i | \(-0.616051\pi\) | ||||
−0.356562 | + | 0.934272i | \(0.616051\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5021.20 | 0.250961 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14919.5 | 0.742655 | 0.371328 | − | 0.928502i | \(-0.378903\pi\) | ||||
0.371328 | + | 0.928502i | \(0.378903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23695.7 | −1.17474 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7287.29 | −0.359818 | −0.179909 | − | 0.983683i | \(-0.557580\pi\) | ||||
−0.179909 | + | 0.983683i | \(0.557580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −519.526 | −0.0254464 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43045.3 | −2.09992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18783.4 | −0.912670 | −0.456335 | − | 0.889808i | \(-0.650838\pi\) | ||||
−0.456335 | + | 0.889808i | \(0.650838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1788.58 | −0.0865595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30614.3 | −1.46988 | −0.734939 | − | 0.678134i | \(-0.762789\pi\) | ||||
−0.734939 | + | 0.678134i | \(0.762789\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10280.3 | 0.491634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15277.2 | −0.727723 | −0.363861 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363861 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38428.4 | 1.82333 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53690.3 | 2.52757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17700.1 | −0.830016 | −0.415008 | − | 0.909818i | \(-0.636221\pi\) | ||||
−0.415008 | + | 0.909818i | \(0.636221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12417.6 | 0.580036 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29362.5 | 1.36623 | 0.683116 | − | 0.730310i | \(-0.260625\pi\) | ||||
0.683116 | + | 0.730310i | \(0.260625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29859.9 | 1.37866 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31426.2 | 1.44539 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13424.0 | −0.615042 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2821.63 | 0.128783 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2816.92 | 0.127589 | 0.0637943 | − | 0.997963i | \(-0.479680\pi\) | ||||
0.0637943 | + | 0.997963i | \(0.479680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4834.01 | 0.218118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16795.0 | 0.754943 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14573.4 | 0.652606 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18433.9 | −0.819276 | −0.409638 | − | 0.912248i | \(-0.634345\pi\) | ||||
−0.409638 | + | 0.912248i | \(0.634345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4962.99 | −0.219747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1828.58 | −0.0806612 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13269.5 | −0.583153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21094.0 | −0.920128 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13276.6 | −0.576983 | −0.288492 | − | 0.957482i | \(-0.593154\pi\) | ||||
−0.288492 | + | 0.957482i | \(0.593154\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18842.5 | 0.815845 | 0.407923 | − | 0.913016i | \(-0.366253\pi\) | ||||
0.407923 | + | 0.913016i | \(0.366253\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16323.8 | 0.704183 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14133.2 | 0.605210 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17966.2 | −0.766531 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5863.62 | 0.249259 | 0.124629 | − | 0.992203i | \(-0.460226\pi\) | ||||
0.124629 | + | 0.992203i | \(0.460226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5018.31 | −0.212548 | −0.106274 | − | 0.994337i | \(-0.533892\pi\) | ||||
−0.106274 | + | 0.994337i | \(0.533892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20303.9 | −0.853730 | −0.426865 | − | 0.904315i | \(-0.640382\pi\) | ||||
−0.426865 | + | 0.904315i | \(0.640382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38156.2 | −1.59857 | −0.799287 | − | 0.600949i | \(-0.794789\pi\) | ||||
−0.799287 | + | 0.600949i | \(0.794789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3241.28 | 0.135305 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13357.0 | −0.555573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5681.90 | 0.234642 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41004.6 | −1.68729 | −0.843645 | − | 0.536901i | \(-0.819595\pi\) | ||||
−0.843645 | + | 0.536901i | \(0.819595\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13467.8 | −0.552206 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4808.98 | −0.196477 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33320.8 | 1.35173 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1004.43 | −0.0406030 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21325.8 | −0.859033 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22451.8 | −0.901214 | −0.450607 | − | 0.892722i | \(-0.648792\pi\) | ||||
−0.450607 | + | 0.892722i | \(0.648792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39858.0 | 1.58871 | 0.794354 | − | 0.607455i | \(-0.207809\pi\) | ||||
0.794354 | + | 0.607455i | \(0.207809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32585.0 | −1.29428 | −0.647139 | − | 0.762372i | \(-0.724035\pi\) | ||||
−0.647139 | + | 0.762372i | \(0.724035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23827.5 | 0.943133 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15593.6 | 0.615078 | 0.307539 | − | 0.951535i | \(-0.400495\pi\) | ||||
0.307539 | + | 0.951535i | \(0.400495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13789.6 | −0.540163 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17746.9 | 0.692775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6267.21 | 0.243807 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11551.1 | 0.447817 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1804.75 | −0.0694892 | −0.0347446 | − | 0.999396i | \(-0.511062\pi\) | ||||
−0.0347446 | + | 0.999396i | \(0.511062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1617.75 | 0.0620766 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14788.0 | −0.565515 | −0.282758 | − | 0.959191i | \(-0.591249\pi\) | ||||
−0.282758 | + | 0.959191i | \(0.591249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1999.24 | −0.0761947 | −0.0380973 | − | 0.999274i | \(-0.512130\pi\) | ||||
−0.0380973 | + | 0.999274i | \(0.512130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32474.4 | −1.22929 | −0.614647 | − | 0.788802i | \(-0.710701\pi\) | ||||
−0.614647 | + | 0.788802i | \(0.710701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26328.6 | −0.993287 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3916.98 | −0.147277 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36509.4 | 1.36813 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12831.3 | 0.477620 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21992.0 | 0.815880 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5841.18 | −0.215980 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10715.8 | 0.394905 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27597.9 | 1.01033 | 0.505167 | − | 0.863022i | \(-0.331431\pi\) | ||||
0.505167 | + | 0.863022i | \(0.331431\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7982.17 | 0.291256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19861.4 | 0.722325 | 0.361163 | − | 0.932503i | \(-0.382380\pi\) | ||||
0.361163 | + | 0.932503i | \(0.382380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2791.46 | 0.101187 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3025.44 | 0.108952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20886.0 | 0.749691 | 0.374845 | − | 0.927087i | \(-0.377696\pi\) | ||||
0.374845 | + | 0.927087i | \(0.377696\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25432.7 | −0.909921 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16755.2 | −0.597511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7047.49 | 0.249698 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37461.2 | 1.32299 | 0.661497 | − | 0.749948i | \(-0.269922\pi\) | ||||
0.661497 | + | 0.749948i | \(0.269922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 98258.5 | 3.45896 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10940.8 | −0.383906 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27149.0 | 0.946552 | 0.473276 | − | 0.880914i | \(-0.343071\pi\) | ||||
0.473276 | + | 0.880914i | \(0.343071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22611.1 | 0.785822 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43068.3 | −1.49202 | −0.746008 | − | 0.665937i | \(-0.768032\pi\) | ||||
−0.746008 | + | 0.665937i | \(0.768032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17017.4 | −0.587660 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30021.1 | −1.03015 | −0.515076 | − | 0.857145i | \(-0.672236\pi\) | ||||
−0.515076 | + | 0.857145i | \(0.672236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16562.4 | −0.566530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32163.5 | −1.09671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53820.4 | −1.82939 | −0.914697 | − | 0.404140i | \(-0.867571\pi\) | ||||
−0.914697 | + | 0.404140i | \(0.867571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15160.9 | −0.512101 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 75185.1 | 2.53165 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14494.3 | 0.486532 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11713.6 | −0.391967 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32210.2 | 1.07116 | 0.535580 | − | 0.844485i | \(-0.320093\pi\) | ||||
0.535580 | + | 0.844485i | \(0.320093\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6983.77 | −0.231529 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21616.1 | 0.714411 | 0.357206 | − | 0.934026i | \(-0.383730\pi\) | ||||
0.357206 | + | 0.934026i | \(0.383730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24432.5 | 0.805005 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46002.8 | 1.50641 | 0.753204 | − | 0.657787i | \(-0.228507\pi\) | ||||
0.753204 | + | 0.657787i | \(0.228507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9825.11 | 0.320748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10457.2 | 0.340339 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3926.43 | −0.127400 | −0.0636998 | − | 0.997969i | \(-0.520290\pi\) | ||||
−0.0636998 | + | 0.997969i | \(0.520290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27681.5 | 0.892719 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7653.15 | −0.246063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55802.3 | −1.78872 | −0.894359 | − | 0.447351i | \(-0.852368\pi\) | ||||
−0.894359 | + | 0.447351i | \(0.852368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13215.4 | 0.422335 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43880.8 | −1.39390 | −0.696951 | − | 0.717119i | \(-0.745460\pi\) | ||||
−0.696951 | + | 0.717119i | \(0.745460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8125.53 | 0.257338 |
(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 | 1200.4.a.bq.1.2 | 2 | ||
4.3 | odd | 2 | 600.4.a.t.1.1 | 2 | |||
5.2 | odd | 4 | 240.4.f.g.49.2 | 4 | |||
5.3 | odd | 4 | 240.4.f.g.49.4 | 4 | |||
5.4 | even | 2 | 1200.4.a.bo.1.1 | 2 | |||
12.11 | even | 2 | 1800.4.a.bn.1.1 | 2 | |||
15.2 | even | 4 | 720.4.f.i.289.1 | 4 | |||
15.8 | even | 4 | 720.4.f.i.289.2 | 4 | |||
20.3 | even | 4 | 120.4.f.d.49.2 | ✓ | 4 | ||
20.7 | even | 4 | 120.4.f.d.49.4 | yes | 4 | ||
20.19 | odd | 2 | 600.4.a.v.1.2 | 2 | |||
40.3 | even | 4 | 960.4.f.n.769.3 | 4 | |||
40.13 | odd | 4 | 960.4.f.o.769.1 | 4 | |||
40.27 | even | 4 | 960.4.f.n.769.1 | 4 | |||
40.37 | odd | 4 | 960.4.f.o.769.3 | 4 | |||
60.23 | odd | 4 | 360.4.f.d.289.2 | 4 | |||
60.47 | odd | 4 | 360.4.f.d.289.1 | 4 | |||
60.59 | even | 2 | 1800.4.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.f.d.49.2 | ✓ | 4 | 20.3 | even | 4 | ||
120.4.f.d.49.4 | yes | 4 | 20.7 | even | 4 | ||
240.4.f.g.49.2 | 4 | 5.2 | odd | 4 | |||
240.4.f.g.49.4 | 4 | 5.3 | odd | 4 | |||
360.4.f.d.289.1 | 4 | 60.47 | odd | 4 | |||
360.4.f.d.289.2 | 4 | 60.23 | odd | 4 | |||
600.4.a.t.1.1 | 2 | 4.3 | odd | 2 | |||
600.4.a.v.1.2 | 2 | 20.19 | odd | 2 | |||
720.4.f.i.289.1 | 4 | 15.2 | even | 4 | |||
720.4.f.i.289.2 | 4 | 15.8 | even | 4 | |||
960.4.f.n.769.1 | 4 | 40.27 | even | 4 | |||
960.4.f.n.769.3 | 4 | 40.3 | even | 4 | |||
960.4.f.o.769.1 | 4 | 40.13 | odd | 4 | |||
960.4.f.o.769.3 | 4 | 40.37 | odd | 4 | |||
1200.4.a.bo.1.1 | 2 | 5.4 | even | 2 | |||
1200.4.a.bq.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.bl.1.2 | 2 | 60.59 | even | 2 | |||
1800.4.a.bn.1.1 | 2 | 12.11 | even | 2 |