Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.58 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.24697 | 1.85509 | 0.927543 | − | 0.373718i | \(-0.121917\pi\) | ||||
0.927543 | + | 0.373718i | \(0.121917\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 19.5307 | 2.44134 | ||||||||
\(5\) | −10.0958 | −0.903000 | −0.451500 | − | 0.892271i | \(-0.649111\pi\) | ||||
−0.451500 | + | 0.892271i | \(0.649111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.804440 | 0.0434357 | 0.0217178 | − | 0.999764i | \(-0.493086\pi\) | ||||
0.0217178 | + | 0.999764i | \(0.493086\pi\) | |||||||
\(8\) | 60.5014 | 2.67381 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −52.9726 | −1.67514 | ||||||||
\(11\) | −0.829353 | −0.0227327 | −0.0113663 | − | 0.999935i | \(-0.503618\pi\) | ||||
−0.0113663 | + | 0.999935i | \(0.503618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −86.7323 | −1.85040 | −0.925201 | − | 0.379478i | \(-0.876104\pi\) | ||||
−0.925201 | + | 0.379478i | \(0.876104\pi\) | |||||||
\(14\) | 4.22087 | 0.0805768 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 161.203 | 2.51880 | ||||||||
\(17\) | −50.2442 | −0.716824 | −0.358412 | − | 0.933563i | \(-0.616682\pi\) | ||||
−0.358412 | + | 0.933563i | \(0.616682\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 121.120 | 1.46246 | 0.731230 | − | 0.682131i | \(-0.238947\pi\) | ||||
0.731230 | + | 0.682131i | \(0.238947\pi\) | |||||||
\(20\) | −197.179 | −2.20453 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.35159 | −0.0421711 | ||||||||
\(23\) | 76.0475 | 0.689435 | 0.344717 | − | 0.938707i | \(-0.387975\pi\) | ||||
0.344717 | + | 0.938707i | \(0.387975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.0740 | −0.184592 | ||||||||
\(26\) | −455.082 | −3.43265 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.7113 | 0.106041 | ||||||||
\(29\) | −40.2936 | −0.258011 | −0.129006 | − | 0.991644i | \(-0.541179\pi\) | ||||
−0.129006 | + | 0.991644i | \(0.541179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −81.0073 | −0.469334 | −0.234667 | − | 0.972076i | \(-0.575400\pi\) | ||||
−0.234667 | + | 0.972076i | \(0.575400\pi\) | |||||||
\(32\) | 361.819 | 1.99879 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −263.630 | −1.32977 | ||||||||
\(35\) | −8.12150 | −0.0392224 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −321.670 | −1.42925 | −0.714624 | − | 0.699509i | \(-0.753402\pi\) | ||||
−0.714624 | + | 0.699509i | \(0.753402\pi\) | |||||||
\(38\) | 635.511 | 2.71299 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −610.813 | −2.41445 | ||||||||
\(41\) | 147.774 | 0.562887 | 0.281444 | − | 0.959578i | \(-0.409187\pi\) | ||||
0.281444 | + | 0.959578i | \(0.409187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.4253 | 0.114996 | 0.0574978 | − | 0.998346i | \(-0.481688\pi\) | ||||
0.0574978 | + | 0.998346i | \(0.481688\pi\) | |||||||
\(44\) | −16.1979 | −0.0554982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 399.019 | 1.27896 | ||||||||
\(47\) | −271.172 | −0.841585 | −0.420792 | − | 0.907157i | \(-0.638248\pi\) | ||||
−0.420792 | + | 0.907157i | \(0.638248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.353 | −0.998113 | ||||||||
\(50\) | −121.068 | −0.342433 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1693.95 | −4.51746 | ||||||||
\(53\) | 110.872 | 0.287347 | 0.143674 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143674 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.37302 | 0.0205276 | ||||||||
\(56\) | 48.6697 | 0.116139 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −211.419 | −0.478633 | ||||||||
\(59\) | −817.455 | −1.80379 | −0.901894 | − | 0.431957i | \(-0.857823\pi\) | ||||
−0.901894 | + | 0.431957i | \(0.857823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −492.812 | −1.03440 | −0.517198 | − | 0.855866i | \(-0.673025\pi\) | ||||
−0.517198 | + | 0.855866i | \(0.673025\pi\) | |||||||
\(62\) | −425.043 | −0.870654 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 608.826 | 1.18911 | ||||||||
\(65\) | 875.636 | 1.67091 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 862.135 | 1.57204 | 0.786019 | − | 0.618202i | \(-0.212139\pi\) | ||||
0.786019 | + | 0.618202i | \(0.212139\pi\) | |||||||
\(68\) | −981.306 | −1.75001 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −42.6133 | −0.0727609 | ||||||||
\(71\) | −395.164 | −0.660526 | −0.330263 | − | 0.943889i | \(-0.607137\pi\) | ||||
−0.330263 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1025.61 | −1.64436 | −0.822181 | − | 0.569227i | \(-0.807243\pi\) | ||||
−0.822181 | + | 0.569227i | \(0.807243\pi\) | |||||||
\(74\) | −1687.79 | −2.65138 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2365.55 | 3.57036 | ||||||||
\(77\) | −0.667165 | −0.000987409 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 210.661 | 0.300015 | 0.150007 | − | 0.988685i | \(-0.452070\pi\) | ||||
0.150007 | + | 0.988685i | \(0.452070\pi\) | |||||||
\(80\) | −1627.48 | −2.27448 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 775.365 | 1.04420 | ||||||||
\(83\) | −879.930 | −1.16367 | −0.581836 | − | 0.813306i | \(-0.697666\pi\) | ||||
−0.581836 | + | 0.813306i | \(0.697666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 507.258 | 0.647292 | ||||||||
\(86\) | 170.135 | 0.213327 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −50.1770 | −0.0607828 | ||||||||
\(89\) | 461.975 | 0.550216 | 0.275108 | − | 0.961413i | \(-0.411286\pi\) | ||||
0.275108 | + | 0.961413i | \(0.411286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −69.7709 | −0.0803734 | ||||||||
\(92\) | 1485.26 | 1.68314 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1422.83 | −1.56121 | ||||||||
\(95\) | −1222.80 | −1.32060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −372.791 | −0.390218 | −0.195109 | − | 0.980782i | \(-0.562506\pi\) | ||||
−0.195109 | + | 0.980782i | \(0.562506\pi\) | |||||||
\(98\) | −1796.32 | −1.85159 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −450.651 | −0.450651 | ||||||||
\(101\) | −982.265 | −0.967713 | −0.483856 | − | 0.875147i | \(-0.660764\pi\) | ||||
−0.483856 | + | 0.875147i | \(0.660764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1237.81 | 1.18413 | 0.592065 | − | 0.805890i | \(-0.298313\pi\) | ||||
0.592065 | + | 0.805890i | \(0.298313\pi\) | |||||||
\(104\) | −5247.43 | −4.94762 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 581.741 | 0.533054 | ||||||||
\(107\) | −1287.57 | −1.16331 | −0.581657 | − | 0.813434i | \(-0.697595\pi\) | ||||
−0.581657 | + | 0.813434i | \(0.697595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2123.88 | 1.86634 | 0.933169 | − | 0.359438i | \(-0.117032\pi\) | ||||
0.933169 | + | 0.359438i | \(0.117032\pi\) | |||||||
\(110\) | 43.9330 | 0.0380804 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 129.678 | 0.109406 | ||||||||
\(113\) | 633.826 | 0.527658 | 0.263829 | − | 0.964569i | \(-0.415015\pi\) | ||||
0.263829 | + | 0.964569i | \(0.415015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −767.763 | −0.622559 | ||||||||
\(116\) | −786.962 | −0.629893 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4289.16 | −3.34618 | ||||||||
\(119\) | −40.4184 | −0.0311357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.31 | −0.999483 | ||||||||
\(122\) | −2585.77 | −1.91889 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1582.13 | −1.14580 | ||||||||
\(125\) | 1494.93 | 1.06969 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −567.851 | −0.396761 | −0.198380 | − | 0.980125i | \(-0.563568\pi\) | ||||
−0.198380 | + | 0.980125i | \(0.563568\pi\) | |||||||
\(128\) | 299.943 | 0.207121 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4594.44 | 3.09968 | ||||||||
\(131\) | −1255.97 | −0.837671 | −0.418836 | − | 0.908062i | \(-0.637562\pi\) | ||||
−0.418836 | + | 0.908062i | \(0.637562\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 97.4334 | 0.0635229 | ||||||||
\(134\) | 4523.60 | 2.91627 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3039.85 | −1.91665 | ||||||||
\(137\) | 1960.41 | 1.22255 | 0.611273 | − | 0.791420i | \(-0.290658\pi\) | ||||
0.611273 | + | 0.791420i | \(0.290658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 36.7466 | 0.0224231 | 0.0112115 | − | 0.999937i | \(-0.496431\pi\) | ||||
0.0112115 | + | 0.999937i | \(0.496431\pi\) | |||||||
\(140\) | −158.619 | −0.0957552 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2073.41 | −1.22533 | ||||||||
\(143\) | 71.9318 | 0.0420646 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 406.797 | 0.232984 | ||||||||
\(146\) | −5381.34 | −3.05043 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6282.44 | −3.48928 | ||||||||
\(149\) | −1648.67 | −0.906470 | −0.453235 | − | 0.891391i | \(-0.649730\pi\) | ||||
−0.453235 | + | 0.891391i | \(0.649730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 418.856 | 0.225735 | 0.112868 | − | 0.993610i | \(-0.463996\pi\) | ||||
0.112868 | + | 0.993610i | \(0.463996\pi\) | |||||||
\(152\) | 7327.91 | 3.91034 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.50060 | −0.00183173 | ||||||||
\(155\) | 817.837 | 0.423808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1258.72 | 0.639854 | 0.319927 | − | 0.947442i | \(-0.396342\pi\) | ||||
0.319927 | + | 0.947442i | \(0.396342\pi\) | |||||||
\(158\) | 1105.33 | 0.556553 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3652.86 | −1.80490 | ||||||||
\(161\) | 61.1756 | 0.0299460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1096.41 | 0.526855 | 0.263427 | − | 0.964679i | \(-0.415147\pi\) | ||||
0.263427 | + | 0.964679i | \(0.415147\pi\) | |||||||
\(164\) | 2886.13 | 1.37420 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4616.97 | −2.15871 | ||||||||
\(167\) | 2947.26 | 1.36567 | 0.682833 | − | 0.730575i | \(-0.260748\pi\) | ||||
0.682833 | + | 0.730575i | \(0.260748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5325.50 | 2.42399 | ||||||||
\(170\) | 2661.57 | 1.20078 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 633.290 | 0.280744 | ||||||||
\(173\) | −3254.19 | −1.43012 | −0.715062 | − | 0.699061i | \(-0.753602\pi\) | ||||
−0.715062 | + | 0.699061i | \(0.753602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.5616 | −0.00801786 | ||||||||
\(176\) | −133.695 | −0.0572591 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2423.97 | 1.02070 | ||||||||
\(179\) | −690.970 | −0.288523 | −0.144261 | − | 0.989540i | \(-0.546081\pi\) | ||||
−0.144261 | + | 0.989540i | \(0.546081\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4480.00 | 1.83975 | 0.919877 | − | 0.392207i | \(-0.128288\pi\) | ||||
0.919877 | + | 0.392207i | \(0.128288\pi\) | |||||||
\(182\) | −366.086 | −0.149100 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4600.98 | 1.84342 | ||||||||
\(185\) | 3247.53 | 1.29061 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.6702 | 0.0162953 | ||||||||
\(188\) | −5296.18 | −2.05459 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6416.02 | −2.44983 | ||||||||
\(191\) | −3071.51 | −1.16359 | −0.581797 | − | 0.813334i | \(-0.697650\pi\) | ||||
−0.581797 | + | 0.813334i | \(0.697650\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1090.71 | −0.406793 | −0.203397 | − | 0.979096i | \(-0.565198\pi\) | ||||
−0.203397 | + | 0.979096i | \(0.565198\pi\) | |||||||
\(194\) | −1956.02 | −0.723888 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6686.40 | −2.43673 | ||||||||
\(197\) | 4977.93 | 1.80032 | 0.900160 | − | 0.435560i | \(-0.143450\pi\) | ||||
0.900160 | + | 0.435560i | \(0.143450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1050.73 | −0.374294 | −0.187147 | − | 0.982332i | \(-0.559924\pi\) | ||||
−0.187147 | + | 0.982332i | \(0.559924\pi\) | |||||||
\(200\) | −1396.01 | −0.493563 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5153.92 | −1.79519 | ||||||||
\(203\) | −32.4137 | −0.0112069 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1491.90 | −0.508287 | ||||||||
\(206\) | 6494.77 | 2.19666 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13981.5 | −4.66080 | ||||||||
\(209\) | −100.451 | −0.0332456 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −467.437 | −0.152510 | −0.0762551 | − | 0.997088i | \(-0.524296\pi\) | ||||
−0.0762551 | + | 0.997088i | \(0.524296\pi\) | |||||||
\(212\) | 2165.41 | 0.701513 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6755.87 | −2.15804 | ||||||||
\(215\) | −327.361 | −0.103841 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −65.1655 | −0.0203858 | ||||||||
\(218\) | 11143.9 | 3.46222 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 163.531 | 0.0501149 | ||||||||
\(221\) | 4357.80 | 1.32641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1929.50 | −0.579411 | −0.289706 | − | 0.957116i | \(-0.593557\pi\) | ||||
−0.289706 | + | 0.957116i | \(0.593557\pi\) | |||||||
\(224\) | 291.061 | 0.0868185 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3325.67 | 0.978851 | ||||||||
\(227\) | 3767.18 | 1.10148 | 0.550741 | − | 0.834676i | \(-0.314345\pi\) | ||||
0.550741 | + | 0.834676i | \(0.314345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3912.29 | 1.12896 | 0.564480 | − | 0.825447i | \(-0.309077\pi\) | ||||
0.564480 | + | 0.825447i | \(0.309077\pi\) | |||||||
\(230\) | −4028.43 | −1.15490 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2437.82 | −0.689873 | ||||||||
\(233\) | −2768.47 | −0.778406 | −0.389203 | − | 0.921152i | \(-0.627250\pi\) | ||||
−0.389203 | + | 0.921152i | \(0.627250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2737.71 | 0.759950 | ||||||||
\(236\) | −15965.5 | −4.40366 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −212.074 | −0.0577594 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 649.271 | 0.173540 | 0.0867701 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867701 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(242\) | −6980.11 | −1.85413 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9624.98 | −2.52531 | ||||||||
\(245\) | 3456.34 | 0.901296 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10505.0 | −2.70614 | ||||||||
\(248\) | −4901.05 | −1.25491 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7843.86 | 1.98436 | ||||||||
\(251\) | 2455.96 | 0.617604 | 0.308802 | − | 0.951126i | \(-0.400072\pi\) | ||||
0.308802 | + | 0.951126i | \(0.400072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −63.0702 | −0.0156727 | ||||||||
\(254\) | −2979.50 | −0.736025 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3296.82 | −0.804887 | ||||||||
\(257\) | 382.561 | 0.0928541 | 0.0464271 | − | 0.998922i | \(-0.485216\pi\) | ||||
0.0464271 | + | 0.998922i | \(0.485216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −258.764 | −0.0620803 | ||||||||
\(260\) | 17101.8 | 4.07927 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6590.06 | −1.55395 | ||||||||
\(263\) | −2500.94 | −0.586367 | −0.293183 | − | 0.956056i | \(-0.594715\pi\) | ||||
−0.293183 | + | 0.956056i | \(0.594715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1119.34 | −0.259474 | ||||||||
\(266\) | 511.231 | 0.117840 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16838.1 | 3.83788 | ||||||||
\(269\) | −7654.24 | −1.73490 | −0.867448 | − | 0.497527i | \(-0.834241\pi\) | ||||
−0.867448 | + | 0.497527i | \(0.834241\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7244.71 | −1.62393 | −0.811964 | − | 0.583707i | \(-0.801602\pi\) | ||||
−0.811964 | + | 0.583707i | \(0.801602\pi\) | |||||||
\(272\) | −8099.54 | −1.80554 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10286.2 | 2.26793 | ||||||||
\(275\) | 19.1365 | 0.00419626 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3761.47 | 0.815901 | 0.407951 | − | 0.913004i | \(-0.366244\pi\) | ||||
0.407951 | + | 0.913004i | \(0.366244\pi\) | |||||||
\(278\) | 192.809 | 0.0415967 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −491.362 | −0.104873 | ||||||||
\(281\) | −1308.50 | −0.277789 | −0.138894 | − | 0.990307i | \(-0.544355\pi\) | ||||
−0.138894 | + | 0.990307i | \(0.544355\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6594.73 | −1.38521 | −0.692607 | − | 0.721315i | \(-0.743538\pi\) | ||||
−0.692607 | + | 0.721315i | \(0.743538\pi\) | |||||||
\(284\) | −7717.84 | −1.61257 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 377.424 | 0.0780334 | ||||||||
\(287\) | 118.875 | 0.0244494 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2388.52 | −0.486163 | ||||||||
\(290\) | 2134.45 | 0.432205 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −20030.9 | −4.01445 | ||||||||
\(293\) | −54.5617 | −0.0108789 | −0.00543947 | − | 0.999985i | \(-0.501731\pi\) | ||||
−0.00543947 | + | 0.999985i | \(0.501731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8252.89 | 1.62882 | ||||||||
\(296\) | −19461.5 | −3.82154 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8650.51 | −1.68158 | ||||||||
\(299\) | −6595.78 | −1.27573 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.0842 | 0.00499491 | ||||||||
\(302\) | 2197.73 | 0.418758 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 19524.9 | 3.68365 | ||||||||
\(305\) | 4975.36 | 0.934059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 401.434 | 0.0746288 | 0.0373144 | − | 0.999304i | \(-0.488120\pi\) | ||||
0.0373144 | + | 0.999304i | \(0.488120\pi\) | |||||||
\(308\) | −13.0302 | −0.00241060 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4291.17 | 0.786200 | ||||||||
\(311\) | 181.977 | 0.0331800 | 0.0165900 | − | 0.999862i | \(-0.494719\pi\) | ||||
0.0165900 | + | 0.999862i | \(0.494719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3794.05 | 0.685151 | 0.342575 | − | 0.939490i | \(-0.388701\pi\) | ||||
0.342575 | + | 0.939490i | \(0.388701\pi\) | |||||||
\(314\) | 6604.49 | 1.18698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4114.35 | 0.732438 | ||||||||
\(317\) | −5855.74 | −1.03751 | −0.518756 | − | 0.854923i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854923i | \(0.673605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.4176 | 0.00586529 | ||||||||
\(320\) | −6146.61 | −1.07377 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 320.987 | 0.0555525 | ||||||||
\(323\) | −6085.56 | −1.04833 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2001.26 | 0.341569 | ||||||||
\(326\) | 5752.82 | 0.977360 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8940.52 | 1.50505 | ||||||||
\(329\) | −218.141 | −0.0365548 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5803.68 | 0.963744 | 0.481872 | − | 0.876242i | \(-0.339957\pi\) | ||||
0.481872 | + | 0.876242i | \(0.339957\pi\) | |||||||
\(332\) | −17185.7 | −2.84092 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15464.2 | 2.53343 | ||||||||
\(335\) | −8703.98 | −1.41955 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9871.07 | −1.59558 | −0.797792 | − | 0.602933i | \(-0.793999\pi\) | ||||
−0.797792 | + | 0.602933i | \(0.793999\pi\) | |||||||
\(338\) | 27942.8 | 4.49670 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9907.11 | 1.58026 | ||||||||
\(341\) | 67.1837 | 0.0106692 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −551.325 | −0.0867894 | ||||||||
\(344\) | 1961.78 | 0.307477 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17074.7 | −2.65300 | ||||||||
\(347\) | 1360.44 | 0.210468 | 0.105234 | − | 0.994447i | \(-0.466441\pi\) | ||||
0.105234 | + | 0.994447i | \(0.466441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7884.72 | 1.20934 | 0.604670 | − | 0.796476i | \(-0.293305\pi\) | ||||
0.604670 | + | 0.796476i | \(0.293305\pi\) | |||||||
\(350\) | −97.3923 | −0.0148738 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −300.076 | −0.0454377 | ||||||||
\(353\) | 3655.13 | 0.551113 | 0.275557 | − | 0.961285i | \(-0.411138\pi\) | ||||
0.275557 | + | 0.961285i | \(0.411138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3989.51 | 0.596454 | ||||||||
\(356\) | 9022.70 | 1.34326 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3625.50 | −0.535234 | ||||||||
\(359\) | 10645.2 | 1.56499 | 0.782497 | − | 0.622654i | \(-0.213946\pi\) | ||||
0.782497 | + | 0.622654i | \(0.213946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7810.96 | 1.13879 | ||||||||
\(362\) | 23506.4 | 3.41290 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1362.68 | −0.196219 | ||||||||
\(365\) | 10354.4 | 1.48486 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5002.35 | 0.711500 | 0.355750 | − | 0.934581i | \(-0.384225\pi\) | ||||
0.355750 | + | 0.934581i | \(0.384225\pi\) | |||||||
\(368\) | 12259.1 | 1.73655 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17039.7 | 2.39419 | ||||||||
\(371\) | 89.1896 | 0.0124811 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9773.39 | 1.35669 | 0.678347 | − | 0.734741i | \(-0.262697\pi\) | ||||
0.678347 | + | 0.734741i | \(0.262697\pi\) | |||||||
\(374\) | 218.642 | 0.0302292 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16406.3 | −2.25024 | ||||||||
\(377\) | 3494.75 | 0.477424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 565.733 | 0.0766748 | 0.0383374 | − | 0.999265i | \(-0.487794\pi\) | ||||
0.0383374 | + | 0.999265i | \(0.487794\pi\) | |||||||
\(380\) | −23882.3 | −3.22404 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16116.1 | −2.15857 | ||||||||
\(383\) | −7907.81 | −1.05501 | −0.527507 | − | 0.849551i | \(-0.676873\pi\) | ||||
−0.527507 | + | 0.849551i | \(0.676873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.73559 | 0.000891630 0 | ||||||||
\(386\) | −5722.93 | −0.754636 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7280.88 | −0.952656 | ||||||||
\(389\) | 2665.09 | 0.347367 | 0.173683 | − | 0.984802i | \(-0.444433\pi\) | ||||
0.173683 | + | 0.984802i | \(0.444433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3820.95 | −0.494204 | ||||||||
\(392\) | −20712.8 | −2.66876 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26119.1 | 3.33975 | ||||||||
\(395\) | −2126.80 | −0.270913 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1845.78 | 0.233343 | 0.116671 | − | 0.993171i | \(-0.462778\pi\) | ||||
0.116671 | + | 0.993171i | \(0.462778\pi\) | |||||||
\(398\) | −5513.17 | −0.694347 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3719.60 | −0.464950 | ||||||||
\(401\) | 8399.16 | 1.04597 | 0.522985 | − | 0.852342i | \(-0.324818\pi\) | ||||
0.522985 | + | 0.852342i | \(0.324818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7025.95 | 0.868456 | ||||||||
\(404\) | −19184.3 | −2.36252 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −170.074 | −0.0207897 | ||||||||
\(407\) | 266.778 | 0.0324906 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 103.382 | 0.0124986 | 0.00624929 | − | 0.999980i | \(-0.498011\pi\) | ||||
0.00624929 | + | 0.999980i | \(0.498011\pi\) | |||||||
\(410\) | −7827.96 | −0.942916 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24175.4 | 2.89086 | ||||||||
\(413\) | −657.593 | −0.0783487 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8883.63 | 1.05080 | ||||||||
\(416\) | −31381.4 | −3.69856 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −527.063 | −0.0616735 | ||||||||
\(419\) | −10313.4 | −1.20249 | −0.601247 | − | 0.799063i | \(-0.705329\pi\) | ||||
−0.601247 | + | 0.799063i | \(0.705329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4651.67 | 0.538500 | 0.269250 | − | 0.963070i | \(-0.413224\pi\) | ||||
0.269250 | + | 0.963070i | \(0.413224\pi\) | |||||||
\(422\) | −2452.63 | −0.282919 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6707.90 | 0.768312 | ||||||||
\(425\) | 1159.33 | 0.132320 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −396.438 | −0.0449297 | ||||||||
\(428\) | −25147.3 | −2.84004 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1717.65 | −0.192634 | ||||||||
\(431\) | 17304.9 | 1.93398 | 0.966991 | − | 0.254811i | \(-0.0820131\pi\) | ||||
0.966991 | + | 0.254811i | \(0.0820131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4053.60 | 0.449893 | 0.224947 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224947 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(434\) | −341.922 | −0.0378174 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 41480.9 | 4.55637 | ||||||||
\(437\) | 9210.84 | 1.00827 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11949.7 | 1.29916 | 0.649578 | − | 0.760295i | \(-0.274946\pi\) | ||||
0.649578 | + | 0.760295i | \(0.274946\pi\) | |||||||
\(440\) | 506.579 | 0.0548869 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22865.3 | 2.46061 | ||||||||
\(443\) | −9196.35 | −0.986302 | −0.493151 | − | 0.869944i | \(-0.664155\pi\) | ||||
−0.493151 | + | 0.869944i | \(0.664155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4664.02 | −0.496845 | ||||||||
\(446\) | −10124.0 | −1.07486 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 489.764 | 0.0516499 | ||||||||
\(449\) | −14223.8 | −1.49501 | −0.747506 | − | 0.664255i | \(-0.768749\pi\) | ||||
−0.747506 | + | 0.664255i | \(0.768749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −122.557 | −0.0127959 | ||||||||
\(452\) | 12379.1 | 1.28819 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19766.3 | 2.04334 | ||||||||
\(455\) | 704.396 | 0.0725772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8717.68 | 0.892333 | 0.446166 | − | 0.894950i | \(-0.352789\pi\) | ||||
0.446166 | + | 0.894950i | \(0.352789\pi\) | |||||||
\(458\) | 20527.7 | 2.09432 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14995.0 | −1.51988 | ||||||||
\(461\) | −627.326 | −0.0633785 | −0.0316893 | − | 0.999498i | \(-0.510089\pi\) | ||||
−0.0316893 | + | 0.999498i | \(0.510089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2601.88 | −0.261165 | −0.130583 | − | 0.991437i | \(-0.541685\pi\) | ||||
−0.130583 | + | 0.991437i | \(0.541685\pi\) | |||||||
\(464\) | −6495.46 | −0.649880 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14526.1 | −1.44401 | ||||||||
\(467\) | −12141.3 | −1.20307 | −0.601533 | − | 0.798848i | \(-0.705443\pi\) | ||||
−0.601533 | + | 0.798848i | \(0.705443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 693.536 | 0.0682825 | ||||||||
\(470\) | 14364.7 | 1.40977 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −49457.1 | −4.82299 | ||||||||
\(473\) | −26.8920 | −0.00261416 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2794.71 | −0.269958 | ||||||||
\(476\) | −789.402 | −0.0760129 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1254.03 | 0.119995 | ||||||||
\(479\) | −7262.80 | −0.692789 | −0.346394 | − | 0.938089i | \(-0.612594\pi\) | ||||
−0.346394 | + | 0.938089i | \(0.612594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27899.2 | 2.64468 | ||||||||
\(482\) | 3406.71 | 0.321932 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25982.0 | −2.44008 | ||||||||
\(485\) | 3763.64 | 0.352367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6346.92 | 0.590568 | 0.295284 | − | 0.955410i | \(-0.404586\pi\) | ||||
0.295284 | + | 0.955410i | \(0.404586\pi\) | |||||||
\(488\) | −29815.8 | −2.76578 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18135.3 | 1.67198 | ||||||||
\(491\) | −4676.73 | −0.429853 | −0.214926 | − | 0.976630i | \(-0.568951\pi\) | ||||
−0.214926 | + | 0.976630i | \(0.568951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2024.52 | 0.184949 | ||||||||
\(494\) | −55119.4 | −5.02012 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13058.7 | −1.18216 | ||||||||
\(497\) | −317.885 | −0.0286904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4655.75 | −0.417676 | −0.208838 | − | 0.977950i | \(-0.566968\pi\) | ||||
−0.208838 | + | 0.977950i | \(0.566968\pi\) | |||||||
\(500\) | 29197.1 | 2.61147 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12886.3 | 1.14571 | ||||||||
\(503\) | 2338.40 | 0.207285 | 0.103642 | − | 0.994615i | \(-0.466950\pi\) | ||||
0.103642 | + | 0.994615i | \(0.466950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9916.79 | 0.873844 | ||||||||
\(506\) | −330.928 | −0.0290742 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11090.5 | −0.968628 | ||||||||
\(509\) | 7899.22 | 0.687872 | 0.343936 | − | 0.938993i | \(-0.388240\pi\) | ||||
0.343936 | + | 0.938993i | \(0.388240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −825.040 | −0.0714239 | ||||||||
\(512\) | −19697.8 | −1.70025 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2007.29 | 0.172252 | ||||||||
\(515\) | −12496.8 | −1.06927 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 224.897 | 0.0191315 | ||||||||
\(518\) | −1357.73 | −0.115164 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 52977.2 | 4.46770 | ||||||||
\(521\) | 7815.67 | 0.657219 | 0.328609 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328609 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19469.3 | 1.62779 | 0.813895 | − | 0.581012i | \(-0.197343\pi\) | ||||
0.813895 | + | 0.581012i | \(0.197343\pi\) | |||||||
\(524\) | −24530.1 | −2.04504 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13122.4 | −1.08776 | ||||||||
\(527\) | 4070.15 | 0.336430 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6383.78 | −0.524680 | ||||||||
\(530\) | −5873.17 | −0.481347 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1902.95 | 0.155081 | ||||||||
\(533\) | −12816.8 | −1.04157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12999.1 | 1.05047 | ||||||||
\(536\) | 52160.4 | 4.20333 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −40161.6 | −3.21838 | ||||||||
\(539\) | 283.932 | 0.0226898 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8167.14 | −0.649044 | −0.324522 | − | 0.945878i | \(-0.605203\pi\) | ||||
−0.324522 | + | 0.945878i | \(0.605203\pi\) | |||||||
\(542\) | −38012.8 | −3.01253 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18179.3 | −1.43278 | ||||||||
\(545\) | −21442.4 | −1.68530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −300.206 | −0.0234660 | −0.0117330 | − | 0.999931i | \(-0.503735\pi\) | ||||
−0.0117330 | + | 0.999931i | \(0.503735\pi\) | |||||||
\(548\) | 38288.2 | 2.98465 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 100.409 | 0.00778443 | ||||||||
\(551\) | −4880.34 | −0.377331 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 169.464 | 0.0130313 | ||||||||
\(554\) | 19736.3 | 1.51357 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 717.688 | 0.0547424 | ||||||||
\(557\) | 21047.1 | 1.60106 | 0.800532 | − | 0.599289i | \(-0.204550\pi\) | ||||
0.800532 | + | 0.599289i | \(0.204550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2812.32 | −0.212788 | ||||||||
\(560\) | −1309.21 | −0.0987935 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6865.67 | −0.515322 | ||||||||
\(563\) | −337.232 | −0.0252445 | −0.0126222 | − | 0.999920i | \(-0.504018\pi\) | ||||
−0.0126222 | + | 0.999920i | \(0.504018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6399.01 | −0.476475 | ||||||||
\(566\) | −34602.3 | −2.56969 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23908.0 | −1.76612 | ||||||||
\(569\) | −16539.0 | −1.21854 | −0.609270 | − | 0.792963i | \(-0.708538\pi\) | ||||
−0.609270 | + | 0.792963i | \(0.708538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9813.91 | −0.719263 | −0.359632 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359632 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(572\) | 1404.88 | 0.102694 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 623.734 | 0.0453557 | ||||||||
\(575\) | −1754.72 | −0.127264 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9201.66 | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(578\) | −12532.5 | −0.901873 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7945.05 | 0.568793 | ||||||||
\(581\) | −707.851 | −0.0505449 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −91.9519 | −0.00653217 | ||||||||
\(584\) | −62050.7 | −4.39671 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −286.284 | −0.0201813 | ||||||||
\(587\) | −22231.6 | −1.56320 | −0.781599 | − | 0.623782i | \(-0.785595\pi\) | ||||
−0.781599 | + | 0.623782i | \(0.785595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9811.57 | −0.686382 | ||||||||
\(590\) | 43302.7 | 3.02160 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −51854.3 | −3.60000 | ||||||||
\(593\) | 11178.1 | 0.774081 | 0.387040 | − | 0.922063i | \(-0.373497\pi\) | ||||
0.387040 | + | 0.922063i | \(0.373497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 408.058 | 0.0281156 | ||||||||
\(596\) | −32199.6 | −2.21300 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −34607.9 | −2.36659 | ||||||||
\(599\) | 3692.27 | 0.251856 | 0.125928 | − | 0.992039i | \(-0.459809\pi\) | ||||
0.125928 | + | 0.992039i | \(0.459809\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14403.8 | −0.977608 | −0.488804 | − | 0.872394i | \(-0.662567\pi\) | ||||
−0.488804 | + | 0.872394i | \(0.662567\pi\) | |||||||
\(602\) | 136.863 | 0.00926599 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8180.57 | 0.551097 | ||||||||
\(605\) | 13430.6 | 0.902533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17874.2 | 1.19521 | 0.597604 | − | 0.801792i | \(-0.296120\pi\) | ||||
0.597604 | + | 0.801792i | \(0.296120\pi\) | |||||||
\(608\) | 43823.3 | 2.92314 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26105.6 | 1.73276 | ||||||||
\(611\) | 23519.4 | 1.55727 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 315.861 | 0.0208116 | 0.0104058 | − | 0.999946i | \(-0.496688\pi\) | ||||
0.0104058 | + | 0.999946i | \(0.496688\pi\) | |||||||
\(614\) | 2106.31 | 0.138443 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −40.3644 | −0.00264014 | ||||||||
\(617\) | −7184.59 | −0.468786 | −0.234393 | − | 0.972142i | \(-0.575310\pi\) | ||||
−0.234393 | + | 0.972142i | \(0.575310\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2840.58 | −0.184447 | −0.0922235 | − | 0.995738i | \(-0.529397\pi\) | ||||
−0.0922235 | + | 0.995738i | \(0.529397\pi\) | |||||||
\(620\) | 15972.9 | 1.03466 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 954.829 | 0.0615517 | ||||||||
\(623\) | 371.631 | 0.0238990 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12208.3 | −0.781334 | ||||||||
\(626\) | 19907.3 | 1.27101 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24583.8 | 1.56210 | ||||||||
\(629\) | 16162.0 | 1.02452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 836.274 | 0.0527599 | 0.0263800 | − | 0.999652i | \(-0.491602\pi\) | ||||
0.0263800 | + | 0.999652i | \(0.491602\pi\) | |||||||
\(632\) | 12745.3 | 0.802183 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30724.9 | −1.92467 | ||||||||
\(635\) | 5732.93 | 0.358275 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29693.1 | 1.84691 | ||||||||
\(638\) | 175.341 | 0.0108806 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3028.17 | −0.187030 | ||||||||
\(641\) | −31860.5 | −1.96320 | −0.981601 | − | 0.190944i | \(-0.938845\pi\) | ||||
−0.981601 | + | 0.190944i | \(0.938845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26267.6 | 1.61103 | 0.805517 | − | 0.592573i | \(-0.201888\pi\) | ||||
0.805517 | + | 0.592573i | \(0.201888\pi\) | |||||||
\(644\) | 1194.80 | 0.0731085 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31930.8 | −1.94474 | ||||||||
\(647\) | 20151.8 | 1.22450 | 0.612248 | − | 0.790666i | \(-0.290265\pi\) | ||||
0.612248 | + | 0.790666i | \(0.290265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 677.959 | 0.0410049 | ||||||||
\(650\) | 10500.6 | 0.633639 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21413.6 | 1.28623 | ||||||||
\(653\) | 26410.1 | 1.58270 | 0.791352 | − | 0.611361i | \(-0.209378\pi\) | ||||
0.791352 | + | 0.611361i | \(0.209378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12680.1 | 0.756417 | ||||||||
\(656\) | 23821.6 | 1.41780 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1144.58 | −0.0678122 | ||||||||
\(659\) | 720.199 | 0.0425721 | 0.0212860 | − | 0.999773i | \(-0.493224\pi\) | ||||
0.0212860 | + | 0.999773i | \(0.493224\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20377.6 | −1.19909 | −0.599544 | − | 0.800342i | \(-0.704651\pi\) | ||||
−0.599544 | + | 0.800342i | \(0.704651\pi\) | |||||||
\(662\) | 30451.8 | 1.78783 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −53237.0 | −3.11144 | ||||||||
\(665\) | −983.672 | −0.0573612 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3064.22 | −0.177882 | ||||||||
\(668\) | 57562.2 | 3.33406 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −45669.6 | −2.63339 | ||||||||
\(671\) | 408.716 | 0.0235146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7590.31 | −0.434747 | −0.217374 | − | 0.976088i | \(-0.569749\pi\) | ||||
−0.217374 | + | 0.976088i | \(0.569749\pi\) | |||||||
\(674\) | −51793.3 | −2.95994 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 104011. | 5.91778 | ||||||||
\(677\) | 27177.2 | 1.54284 | 0.771421 | − | 0.636325i | \(-0.219546\pi\) | ||||
0.771421 | + | 0.636325i | \(0.219546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −299.888 | −0.0169494 | ||||||||
\(680\) | 30689.8 | 1.73074 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 352.511 | 0.0197923 | ||||||||
\(683\) | −23544.6 | −1.31905 | −0.659524 | − | 0.751684i | \(-0.729242\pi\) | ||||
−0.659524 | + | 0.751684i | \(0.729242\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19792.0 | −1.10396 | ||||||||
\(686\) | −2892.79 | −0.161002 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5227.07 | 0.289652 | ||||||||
\(689\) | −9616.17 | −0.531708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5593.57 | −0.307944 | −0.153972 | − | 0.988075i | \(-0.549207\pi\) | ||||
−0.153972 | + | 0.988075i | \(0.549207\pi\) | |||||||
\(692\) | −63556.7 | −3.49142 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7138.22 | 0.390437 | ||||||||
\(695\) | −370.988 | −0.0202480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7424.78 | −0.403491 | ||||||||
\(698\) | 41370.9 | 2.24343 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −362.522 | −0.0195743 | ||||||||
\(701\) | −29596.7 | −1.59465 | −0.797327 | − | 0.603548i | \(-0.793753\pi\) | ||||
−0.797327 | + | 0.603548i | \(0.793753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38960.5 | −2.09022 | ||||||||
\(704\) | −504.932 | −0.0270317 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19178.4 | 1.02236 | ||||||||
\(707\) | −790.173 | −0.0420333 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11431.8 | 0.605542 | 0.302771 | − | 0.953063i | \(-0.402088\pi\) | ||||
0.302771 | + | 0.953063i | \(0.402088\pi\) | |||||||
\(710\) | 20932.9 | 1.10647 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27950.1 | 1.47117 | ||||||||
\(713\) | −6160.40 | −0.323575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −726.212 | −0.0379843 | ||||||||
\(716\) | −13495.1 | −0.704382 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 55855.2 | 2.90320 | ||||||||
\(719\) | 14447.3 | 0.749364 | 0.374682 | − | 0.927153i | \(-0.377752\pi\) | ||||
0.374682 | + | 0.927153i | \(0.377752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 995.746 | 0.0514335 | ||||||||
\(722\) | 40983.9 | 2.11255 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 87497.6 | 4.49147 | ||||||||
\(725\) | 929.732 | 0.0476267 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30498.2 | −1.55587 | −0.777935 | − | 0.628345i | \(-0.783733\pi\) | ||||
−0.777935 | + | 0.628345i | \(0.783733\pi\) | |||||||
\(728\) | −4221.24 | −0.214903 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 54329.2 | 2.75454 | ||||||||
\(731\) | −1629.18 | −0.0824317 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3580.60 | −0.180426 | −0.0902132 | − | 0.995922i | \(-0.528755\pi\) | ||||
−0.0902132 | + | 0.995922i | \(0.528755\pi\) | |||||||
\(734\) | 26247.2 | 1.31989 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27515.4 | 1.37803 | ||||||||
\(737\) | −715.015 | −0.0357366 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25098.0 | 1.24932 | 0.624658 | − | 0.780899i | \(-0.285238\pi\) | ||||
0.624658 | + | 0.780899i | \(0.285238\pi\) | |||||||
\(740\) | 63426.6 | 3.15082 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 467.976 | 0.0231535 | ||||||||
\(743\) | −15887.1 | −0.784443 | −0.392221 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392221 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16644.7 | 0.818542 | ||||||||
\(746\) | 51280.7 | 2.51678 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 813.850 | 0.0397825 | ||||||||
\(749\) | −1035.78 | −0.0505293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5066.16 | −0.246161 | −0.123080 | − | 0.992397i | \(-0.539277\pi\) | ||||
−0.123080 | + | 0.992397i | \(0.539277\pi\) | |||||||
\(752\) | −43713.8 | −2.11979 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18336.9 | 0.885663 | ||||||||
\(755\) | −4228.71 | −0.203839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29118.9 | 1.39808 | 0.699039 | − | 0.715084i | \(-0.253612\pi\) | ||||
0.699039 | + | 0.715084i | \(0.253612\pi\) | |||||||
\(758\) | 2968.39 | 0.142238 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −73981.4 | −3.53104 | ||||||||
\(761\) | −39582.7 | −1.88551 | −0.942755 | − | 0.333487i | \(-0.891775\pi\) | ||||
−0.942755 | + | 0.333487i | \(0.891775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1708.53 | 0.0810656 | ||||||||
\(764\) | −59988.7 | −2.84073 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41492.1 | −1.95714 | ||||||||
\(767\) | 70899.8 | 3.33773 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3581.25 | 0.167936 | 0.0839682 | − | 0.996468i | \(-0.473241\pi\) | ||||
0.0839682 | + | 0.996468i | \(0.473241\pi\) | |||||||
\(770\) | 35.3415 | 0.00165405 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21302.4 | −0.993121 | ||||||||
\(773\) | −1820.20 | −0.0846935 | −0.0423468 | − | 0.999103i | \(-0.513483\pi\) | ||||
−0.0423468 | + | 0.999103i | \(0.513483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1869.16 | 0.0866351 | ||||||||
\(776\) | −22554.4 | −1.04337 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13983.7 | 0.644395 | ||||||||
\(779\) | 17898.3 | 0.823200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 327.730 | 0.0150155 | ||||||||
\(782\) | −20048.4 | −0.916790 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −55188.5 | −2.51405 | ||||||||
\(785\) | −12707.9 | −0.577788 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38042.7 | −1.72310 | −0.861548 | − | 0.507676i | \(-0.830505\pi\) | ||||
−0.861548 | + | 0.507676i | \(0.830505\pi\) | |||||||
\(788\) | 97222.6 | 4.39519 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11159.2 | −0.502567 | ||||||||
\(791\) | 509.875 | 0.0229192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42742.8 | 1.91405 | ||||||||
\(794\) | 9684.76 | 0.432871 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20521.6 | −0.913779 | ||||||||
\(797\) | −34264.4 | −1.52285 | −0.761423 | − | 0.648255i | \(-0.775499\pi\) | ||||
−0.761423 | + | 0.648255i | \(0.775499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13624.8 | 0.603268 | ||||||||
\(800\) | −8348.59 | −0.368959 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 44070.1 | 1.94036 | ||||||||
\(803\) | 850.592 | 0.0373807 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −617.619 | −0.0270413 | ||||||||
\(806\) | 36865.0 | 1.61106 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −59428.4 | −2.58748 | ||||||||
\(809\) | −8842.40 | −0.384280 | −0.192140 | − | 0.981368i | \(-0.561543\pi\) | ||||
−0.192140 | + | 0.981368i | \(0.561543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16775.4 | 0.726341 | 0.363170 | − | 0.931723i | \(-0.381694\pi\) | ||||
0.363170 | + | 0.931723i | \(0.381694\pi\) | |||||||
\(812\) | −633.064 | −0.0273598 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1399.78 | 0.0602729 | ||||||||
\(815\) | −11069.2 | −0.475749 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3927.34 | 0.168177 | ||||||||
\(818\) | 542.444 | 0.0231859 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29137.9 | −1.24090 | ||||||||
\(821\) | 16529.4 | 0.702657 | 0.351328 | − | 0.936252i | \(-0.385730\pi\) | ||||
0.351328 | + | 0.936252i | \(0.385730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17811.2 | 0.754386 | 0.377193 | − | 0.926135i | \(-0.376889\pi\) | ||||
0.377193 | + | 0.926135i | \(0.376889\pi\) | |||||||
\(824\) | 74889.4 | 3.16614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3450.37 | −0.145344 | ||||||||
\(827\) | 18973.0 | 0.797772 | 0.398886 | − | 0.917001i | \(-0.369397\pi\) | ||||
0.398886 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29108.6 | −1.21952 | −0.609762 | − | 0.792585i | \(-0.708735\pi\) | ||||
−0.609762 | + | 0.792585i | \(0.708735\pi\) | |||||||
\(830\) | 46612.2 | 1.94932 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −52804.9 | −2.20034 | ||||||||
\(833\) | 17201.3 | 0.715472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29755.1 | −1.23320 | ||||||||
\(836\) | −1961.88 | −0.0811639 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54114.4 | −2.23073 | ||||||||
\(839\) | −32777.9 | −1.34877 | −0.674386 | − | 0.738379i | \(-0.735592\pi\) | ||||
−0.674386 | + | 0.738379i | \(0.735592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22765.4 | −0.933430 | ||||||||
\(842\) | 24407.2 | 0.998964 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9129.37 | −0.372329 | ||||||||
\(845\) | −53765.4 | −2.18886 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1070.16 | −0.0434132 | ||||||||
\(848\) | 17872.9 | 0.723771 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6082.99 | 0.245465 | ||||||||
\(851\) | −24462.2 | −0.985373 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11519.2 | 0.462380 | 0.231190 | − | 0.972909i | \(-0.425738\pi\) | ||||
0.231190 | + | 0.972909i | \(0.425738\pi\) | |||||||
\(854\) | −2080.10 | −0.0833484 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −77900.0 | −3.11048 | ||||||||
\(857\) | −21343.7 | −0.850743 | −0.425372 | − | 0.905019i | \(-0.639857\pi\) | ||||
−0.425372 | + | 0.905019i | \(0.639857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21764.2 | 0.864475 | 0.432238 | − | 0.901760i | \(-0.357724\pi\) | ||||
0.432238 | + | 0.901760i | \(0.357724\pi\) | |||||||
\(860\) | −6393.60 | −0.253511 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 90798.2 | 3.58770 | ||||||||
\(863\) | −22120.1 | −0.872510 | −0.436255 | − | 0.899823i | \(-0.643695\pi\) | ||||
−0.436255 | + | 0.899823i | \(0.643695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32853.8 | 1.29140 | ||||||||
\(866\) | 21269.1 | 0.834590 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1272.73 | −0.0497687 | ||||||||
\(869\) | −174.712 | −0.00682014 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74775.0 | −2.90890 | ||||||||
\(872\) | 128498. | 4.99023 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48329.0 | 1.87043 | ||||||||
\(875\) | 1202.58 | 0.0464625 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45552.7 | 1.75394 | 0.876970 | − | 0.480545i | \(-0.159561\pi\) | ||||
0.876970 | + | 0.480545i | \(0.159561\pi\) | |||||||
\(878\) | 62699.9 | 2.41004 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1349.76 | 0.0517050 | ||||||||
\(881\) | 16750.7 | 0.640576 | 0.320288 | − | 0.947320i | \(-0.396220\pi\) | ||||
0.320288 | + | 0.947320i | \(0.396220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7820.30 | −0.298045 | −0.149023 | − | 0.988834i | \(-0.547613\pi\) | ||||
−0.149023 | + | 0.988834i | \(0.547613\pi\) | |||||||
\(884\) | 85111.0 | 3.23823 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48253.0 | −1.82967 | ||||||||
\(887\) | 3307.54 | 0.125205 | 0.0626023 | − | 0.998039i | \(-0.480060\pi\) | ||||
0.0626023 | + | 0.998039i | \(0.480060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −456.802 | −0.0172336 | ||||||||
\(890\) | −24472.0 | −0.921690 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37684.5 | −1.41454 | ||||||||
\(893\) | −32844.2 | −1.23078 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6975.93 | 0.260536 | ||||||||
\(896\) | 241.286 | 0.00899642 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −74631.7 | −2.77337 | ||||||||
\(899\) | 3264.07 | 0.121093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5570.66 | −0.205978 | ||||||||
\(902\) | −643.052 | −0.0237376 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 38347.4 | 1.41086 | ||||||||
\(905\) | −45229.3 | −1.66130 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22776.0 | 0.833807 | 0.416904 | − | 0.908951i | \(-0.363115\pi\) | ||||
0.416904 | + | 0.908951i | \(0.363115\pi\) | |||||||
\(908\) | 73575.7 | 2.68909 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3695.95 | 0.134637 | ||||||||
\(911\) | −19433.9 | −0.706777 | −0.353388 | − | 0.935477i | \(-0.614971\pi\) | ||||
−0.353388 | + | 0.935477i | \(0.614971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 729.773 | 0.0264534 | ||||||||
\(914\) | 45741.5 | 1.65535 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 76409.9 | 2.75617 | ||||||||
\(917\) | −1010.36 | −0.0363848 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3518.51 | 0.126295 | 0.0631473 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631473 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(920\) | −46450.8 | −1.66460 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3291.56 | −0.117573 | ||||||||
\(923\) | 34273.5 | 1.22224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7422.20 | 0.263827 | ||||||||
\(926\) | −13652.0 | −0.484484 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14579.0 | −0.515709 | ||||||||
\(929\) | −29305.0 | −1.03495 | −0.517474 | − | 0.855699i | \(-0.673128\pi\) | ||||
−0.517474 | + | 0.855699i | \(0.673128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41465.6 | −1.45970 | ||||||||
\(932\) | −54070.3 | −1.90035 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −63705.0 | −2.23179 | ||||||||
\(935\) | −420.696 | −0.0147147 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3989.30 | 0.139087 | 0.0695436 | − | 0.997579i | \(-0.477846\pi\) | ||||
0.0695436 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(938\) | 3638.96 | 0.126670 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53469.4 | 1.85530 | ||||||||
\(941\) | 5735.38 | 0.198691 | 0.0993453 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993453 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11237.8 | 0.388074 | ||||||||
\(944\) | −131776. | −4.54339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −141.102 | −0.00484949 | ||||||||
\(947\) | −9209.74 | −0.316026 | −0.158013 | − | 0.987437i | \(-0.550509\pi\) | ||||
−0.158013 | + | 0.987437i | \(0.550509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 88953.4 | 3.04273 | ||||||||
\(950\) | −14663.8 | −0.500795 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2445.37 | −0.0832510 | ||||||||
\(953\) | 37747.8 | 1.28307 | 0.641537 | − | 0.767092i | \(-0.278297\pi\) | ||||
0.641537 | + | 0.767092i | \(0.278297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31009.4 | 1.05072 | ||||||||
\(956\) | 4667.84 | 0.157917 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38107.7 | −1.28518 | ||||||||
\(959\) | 1577.03 | 0.0531021 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23228.8 | −0.779726 | ||||||||
\(962\) | 146386. | 4.90611 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12680.7 | 0.423671 | ||||||||
\(965\) | 11011.6 | 0.367334 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57837.6 | 1.92340 | 0.961702 | − | 0.274099i | \(-0.0883795\pi\) | ||||
0.961702 | + | 0.274099i | \(0.0883795\pi\) | |||||||
\(968\) | −80485.8 | −2.67243 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19747.7 | 0.653671 | ||||||||
\(971\) | −47828.7 | −1.58074 | −0.790369 | − | 0.612631i | \(-0.790111\pi\) | ||||
−0.790369 | + | 0.612631i | \(0.790111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.5604 | 0.000973961 0 | ||||||||
\(974\) | 33302.1 | 1.09555 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −79443.0 | −2.60544 | ||||||||
\(977\) | −39670.3 | −1.29904 | −0.649522 | − | 0.760343i | \(-0.725031\pi\) | ||||
−0.649522 | + | 0.760343i | \(0.725031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −383.140 | −0.0125079 | ||||||||
\(980\) | 67504.8 | 2.20037 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24538.7 | −0.797413 | ||||||||
\(983\) | −51418.1 | −1.66834 | −0.834172 | − | 0.551505i | \(-0.814054\pi\) | ||||
−0.834172 | + | 0.551505i | \(0.814054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50256.4 | −1.62569 | ||||||||
\(986\) | 10622.6 | 0.343096 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −205170. | −6.60661 | ||||||||
\(989\) | 2465.86 | 0.0792820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28309.2 | 0.907438 | 0.453719 | − | 0.891145i | \(-0.350097\pi\) | ||||
0.453719 | + | 0.891145i | \(0.350097\pi\) | |||||||
\(992\) | −29310.0 | −0.938097 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1667.94 | −0.0532231 | ||||||||
\(995\) | 10608.0 | 0.337987 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25372.2 | −0.805962 | −0.402981 | − | 0.915208i | \(-0.632026\pi\) | ||||
−0.402981 | + | 0.915208i | \(0.632026\pi\) | |||||||
\(998\) | −24428.6 | −0.774824 | ||||||||
\(999\) | 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 | 2151.4.a.g.1.58 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.2 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.58 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.2 | yes | 59 | 3.2 | odd | 2 |