Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.136768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 23x^{2} + 18x + 119 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.31012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 | ||||||||
\(5\) | −16.6547 | −1.48964 | −0.744820 | − | 0.667265i | \(-0.767465\pi\) | ||||
−0.744820 | + | 0.667265i | \(0.767465\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −71.7600 | −1.96695 | −0.983475 | − | 0.181044i | \(-0.942052\pi\) | ||||
−0.983475 | + | 0.181044i | \(0.942052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −65.3878 | −1.39502 | −0.697512 | − | 0.716573i | \(-0.745709\pi\) | ||||
−0.697512 | + | 0.716573i | \(0.745709\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −49.9641 | −0.860044 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 90.4316 | 1.29017 | 0.645085 | − | 0.764111i | \(-0.276822\pi\) | ||||
0.645085 | + | 0.764111i | \(0.276822\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 163.818 | 1.97803 | 0.989014 | − | 0.147824i | \(-0.0472268\pi\) | ||||
0.989014 | + | 0.147824i | \(0.0472268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 79.2288 | 0.718276 | 0.359138 | − | 0.933284i | \(-0.383071\pi\) | ||||
0.359138 | + | 0.933284i | \(0.383071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 152.379 | 1.21903 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −43.2995 | −0.277259 | −0.138630 | − | 0.990344i | \(-0.544270\pi\) | ||||
−0.138630 | + | 0.990344i | \(0.544270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 135.636 | 0.785836 | 0.392918 | − | 0.919574i | \(-0.371466\pi\) | ||||
0.392918 | + | 0.919574i | \(0.371466\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −215.280 | −1.13562 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 270.740 | 1.20296 | 0.601479 | − | 0.798889i | \(-0.294578\pi\) | ||||
0.601479 | + | 0.798889i | \(0.294578\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −196.163 | −0.805417 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 152.241 | 0.579902 | 0.289951 | − | 0.957041i | \(-0.406361\pi\) | ||||
0.289951 | + | 0.957041i | \(0.406361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −177.641 | −0.630001 | −0.315001 | − | 0.949091i | \(-0.602005\pi\) | ||||
−0.315001 | + | 0.949091i | \(0.602005\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −149.892 | −0.496547 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.6331 | −0.141623 | −0.0708114 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708114 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 271.295 | 0.744880 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −158.438 | −0.410624 | −0.205312 | − | 0.978697i | \(-0.565821\pi\) | ||||
−0.205312 | + | 0.978697i | \(0.565821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1195.14 | 2.93005 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 491.455 | 1.14201 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −391.769 | −0.864474 | −0.432237 | − | 0.901760i | \(-0.642276\pi\) | ||||
−0.432237 | + | 0.901760i | \(0.642276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 551.295 | 1.15715 | 0.578574 | − | 0.815630i | \(-0.303609\pi\) | ||||
0.578574 | + | 0.815630i | \(0.303609\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1089.01 | 2.07808 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 458.630 | 0.836277 | 0.418139 | − | 0.908383i | \(-0.362683\pi\) | ||||
0.418139 | + | 0.908383i | \(0.362683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 237.687 | 0.414697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −486.786 | −0.813674 | −0.406837 | − | 0.913501i | \(-0.633368\pi\) | ||||
−0.406837 | + | 0.913501i | \(0.633368\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 574.892 | 0.921726 | 0.460863 | − | 0.887471i | \(-0.347540\pi\) | ||||
0.460863 | + | 0.887471i | \(0.347540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 457.136 | 0.703806 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −668.319 | −0.951795 | −0.475897 | − | 0.879501i | \(-0.657877\pi\) | ||||
−0.475897 | + | 0.879501i | \(0.657877\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.2450 | 0.100831 | 0.0504155 | − | 0.998728i | \(-0.483945\pi\) | ||||
0.0504155 | + | 0.998728i | \(0.483945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1506.11 | −1.92189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −129.899 | −0.160076 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1366.80 | 1.62787 | 0.813937 | − | 0.580953i | \(-0.197320\pi\) | ||||
0.813937 | + | 0.580953i | \(0.197320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 406.907 | 0.453702 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2728.34 | −2.94655 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 242.655 | 0.253999 | 0.127000 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127000 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −645.840 | −0.655650 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 694.743 | 0.684450 | 0.342225 | − | 0.939618i | \(-0.388819\pi\) | ||||
0.342225 | + | 0.939618i | \(0.388819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −174.218 | −0.166662 | −0.0833310 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833310 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 47.6051 | 0.0430108 | 0.0215054 | − | 0.999769i | \(-0.493154\pi\) | ||||
0.0215054 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1633.10 | −1.43507 | −0.717534 | − | 0.696523i | \(-0.754729\pi\) | ||||
−0.717534 | + | 0.696523i | \(0.754729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 812.221 | 0.694528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1127.29 | −0.938464 | −0.469232 | − | 0.883075i | \(-0.655469\pi\) | ||||
−0.469232 | + | 0.883075i | \(0.655469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1319.53 | −1.06997 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −588.490 | −0.465008 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3818.50 | 2.86889 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 456.722 | 0.334807 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −455.982 | −0.326274 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2398.66 | 1.67596 | 0.837979 | − | 0.545702i | \(-0.183737\pi\) | ||||
0.837979 | + | 0.545702i | \(0.183737\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −532.924 | −0.363731 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1548.96 | 1.03308 | 0.516541 | − | 0.856263i | \(-0.327219\pi\) | ||||
0.516541 | + | 0.856263i | \(0.327219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −449.677 | −0.286681 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1523.27 | 0.949939 | 0.474969 | − | 0.880002i | \(-0.342459\pi\) | ||||
0.474969 | + | 0.880002i | \(0.342459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 551.445 | 0.336496 | 0.168248 | − | 0.985745i | \(-0.446189\pi\) | ||||
0.168248 | + | 0.985745i | \(0.446189\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −136.899 | −0.0817660 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4692.23 | 2.74394 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 721.140 | 0.413017 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2400.24 | −1.31970 | −0.659851 | − | 0.751397i | \(-0.729381\pi\) | ||||
−0.659851 | + | 0.751397i | \(0.729381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 621.560 | 0.334979 | 0.167490 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167490 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 813.884 | 0.430056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2258.97 | −1.17061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2691.58 | −1.36822 | −0.684112 | − | 0.729377i | \(-0.739810\pi\) | ||||
−0.684112 | + | 0.729377i | \(0.739810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −475.313 | −0.237074 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1057.31 | 0.508065 | 0.254032 | − | 0.967196i | \(-0.418243\pi\) | ||||
0.254032 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3585.42 | 1.69166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −243.840 | −0.112987 | −0.0564937 | − | 0.998403i | \(-0.517992\pi\) | ||||
−0.0564937 | + | 0.998403i | \(0.517992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2078.56 | 0.946090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1474.37 | 0.659342 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1687.26 | −0.741505 | −0.370753 | − | 0.928732i | \(-0.620900\pi\) | ||||
−0.370753 | + | 0.928732i | \(0.620900\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1175.31 | −0.499104 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −359.139 | −0.149963 | −0.0749814 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749814 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2982.58 | 1.22483 | 0.612413 | − | 0.790538i | \(-0.290199\pi\) | ||||
0.612413 | + | 0.790538i | \(0.290199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1653.88 | 0.668080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4509.10 | −1.79198 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6489.37 | −2.53770 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3490.77 | 1.32243 | 0.661213 | − | 0.750198i | \(-0.270042\pi\) | ||||
0.661213 | + | 0.750198i | \(0.270042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1604.23 | 0.598315 | 0.299158 | − | 0.954204i | \(-0.403294\pi\) | ||||
0.299158 | + | 0.954204i | \(0.403294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3267.04 | 1.19978 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −455.935 | −0.164893 | −0.0824467 | − | 0.996595i | \(-0.526273\pi\) | ||||
−0.0824467 | + | 0.996595i | \(0.526273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2084.16 | 0.742423 | 0.371212 | − | 0.928548i | \(-0.378942\pi\) | ||||
0.371212 | + | 0.928548i | \(0.378942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1375.89 | 0.482825 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2535.52 | −0.863846 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 713.060 | 0.239425 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11755.6 | −3.89068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2568.06 | 0.837880 | 0.418940 | − | 0.908014i | \(-0.362402\pi\) | ||||
0.418940 | + | 0.908014i | \(0.362402\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1460.36 | −0.469775 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2958.56 | 0.938475 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1724.68 | 0.532159 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5913.12 | −1.79982 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4659.55 | −1.39922 | −0.699612 | − | 0.714523i | \(-0.746644\pi\) | ||||
−0.699612 | + | 0.714523i | \(0.746644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1371.41 | 0.406343 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4828.77 | 1.41188 | 0.705940 | − | 0.708271i | \(-0.250525\pi\) | ||||
0.705940 | + | 0.708271i | \(0.250525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3222.59 | −0.929932 | −0.464966 | − | 0.885328i | \(-0.653934\pi\) | ||||
−0.464966 | + | 0.885328i | \(0.653934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5702.42 | −1.60334 | −0.801670 | − | 0.597767i | \(-0.796055\pi\) | ||||
−0.801670 | + | 0.597767i | \(0.796055\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 760.005 | 0.210967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2004.96 | −0.549519 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1994.47 | 0.539796 | 0.269898 | − | 0.962889i | \(-0.413010\pi\) | ||||
0.269898 | + | 0.962889i | \(0.413010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1420.89 | −0.379781 | −0.189891 | − | 0.981805i | \(-0.560813\pi\) | ||||
−0.189891 | + | 0.981805i | \(0.560813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10711.7 | −2.75939 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 228.735 | 0.0582148 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3855.44 | −0.969534 | −0.484767 | − | 0.874643i | \(-0.661096\pi\) | ||||
−0.484767 | + | 0.874643i | \(0.661096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5685.46 | −1.41281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4518.33 | −1.10960 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4053.28 | 0.983800 | 0.491900 | − | 0.870652i | \(-0.336303\pi\) | ||||
0.491900 | + | 0.870652i | \(0.336303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −389.696 | −0.0924198 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −500.787 | −0.117414 | −0.0587069 | − | 0.998275i | \(-0.518698\pi\) | ||||
−0.0587069 | + | 0.998275i | \(0.518698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2638.73 | 0.611683 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4100.41 | 0.939853 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3281.74 | 0.743834 | 0.371917 | − | 0.928266i | \(-0.378701\pi\) | ||||
0.371917 | + | 0.928266i | \(0.378701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3324.36 | 0.745168 | 0.372584 | − | 0.927999i | \(-0.378472\pi\) | ||||
0.372584 | + | 0.927999i | \(0.378472\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10934.7 | −2.39777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8619.75 | 1.86971 | 0.934856 | − | 0.355026i | \(-0.115528\pi\) | ||||
0.934856 | + | 0.355026i | \(0.115528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1220.72 | 0.261945 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7710.80 | −1.63697 | −0.818484 | − | 0.574529i | \(-0.805185\pi\) | ||||
−0.818484 | + | 0.574529i | \(0.805185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −139.271 | −0.0292537 | −0.0146268 | − | 0.999893i | \(-0.504656\pi\) | ||||
−0.0146268 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8185.03 | −1.70119 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3264.87 | 0.664537 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 727.966 | 0.146646 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4437.09 | −0.884702 | −0.442351 | − | 0.896842i | \(-0.645855\pi\) | ||||
−0.442351 | + | 0.896842i | \(0.645855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6524.79 | 1.28776 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1937.52 | −0.378540 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5180.60 | −1.00201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2084.23 | 0.395168 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9181.64 | −1.72373 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −299.480 | −0.0556749 | −0.0278375 | − | 0.999612i | \(-0.508862\pi\) | ||||
−0.0278375 | + | 0.999612i | \(0.508862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −522.654 | −0.0962224 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 913.944 | 0.166640 | 0.0833199 | − | 0.996523i | \(-0.473448\pi\) | ||||
0.0833199 | + | 0.996523i | \(0.473448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3887.38 | 0.702005 | 0.351002 | − | 0.936375i | \(-0.385841\pi\) | ||||
0.351002 | + | 0.936375i | \(0.385841\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2879.30 | 0.510151 | 0.255075 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255075 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3107.17 | 0.545355 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 142.815 | 0.0248323 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14814.4 | 2.55199 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9963.70 | −1.70057 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4899.29 | −0.828537 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2810.79 | −0.466752 | −0.233376 | − | 0.972387i | \(-0.574977\pi\) | ||||
−0.233376 | + | 0.972387i | \(0.574977\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2436.66 | 0.400986 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7638.34 | −1.24575 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2960.90 | 0.478607 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3381.87 | −0.541823 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9733.22 | −1.54570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3958.59 | −0.617749 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4284.51 | −0.662838 | −0.331419 | − | 0.943484i | \(-0.607527\pi\) | ||||
−0.331419 | + | 0.943484i | \(0.607527\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3295.36 | 0.505434 | 0.252717 | − | 0.967540i | \(-0.418676\pi\) | ||||
0.252717 | + | 0.967540i | \(0.418676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1765.47 | −0.268472 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10629.7 | −1.60272 | −0.801360 | − | 0.598183i | \(-0.795890\pi\) | ||||
−0.801360 | + | 0.598183i | \(0.795890\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8107.26 | 1.21208 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3185.01 | 0.468241 | 0.234121 | − | 0.972208i | \(-0.424779\pi\) | ||||
0.234121 | + | 0.972208i | \(0.424779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19977.5 | 2.91259 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11455.5 | 1.65636 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9574.65 | −1.37304 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7603.03 | 1.08140 | 0.540702 | − | 0.841214i | \(-0.318159\pi\) | ||||
0.540702 | + | 0.841214i | \(0.318159\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1370.17 | 0.193301 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1511.96 | 0.209882 | 0.104941 | − | 0.994478i | \(-0.466535\pi\) | ||||
0.104941 | + | 0.994478i | \(0.466535\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1367.94 | −0.188374 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2831.26 | 0.386783 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8848.36 | 1.19923 | 0.599617 | − | 0.800287i | \(-0.295320\pi\) | ||||
0.599617 | + | 0.800287i | \(0.295320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7195.98 | 0.967615 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4134.10 | 0.551548 | 0.275774 | − | 0.961223i | \(-0.411066\pi\) | ||||
0.275774 | + | 0.961223i | \(0.411066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1598.77 | −0.210000 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7630.61 | 0.994569 | 0.497284 | − | 0.867588i | \(-0.334331\pi\) | ||||
0.497284 | + | 0.867588i | \(0.334331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7164.79 | 0.926698 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4646.89 | 0.596450 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11130.6 | 1.41783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11618.5 | −1.46881 | −0.734403 | − | 0.678714i | \(-0.762538\pi\) | ||||
−0.734403 | + | 0.678714i | \(0.762538\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3047.01 | 0.379453 | 0.189726 | − | 0.981837i | \(-0.439240\pi\) | ||||
0.189726 | + | 0.981837i | \(0.439240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8868.92 | −1.09626 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1349.03 | −0.165516 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19428.3 | −2.36616 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11582.8 | 1.40033 | 0.700164 | − | 0.713982i | \(-0.253110\pi\) | ||||
0.700164 | + | 0.713982i | \(0.253110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4569.80 | 0.548447 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1269.84 | −0.150202 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1654.33 | 0.194276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1318.83 | −0.153768 | −0.0768841 | − | 0.997040i | \(-0.524497\pi\) | ||||
−0.0768841 | + | 0.997040i | \(0.524497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9733.56 | −1.12680 | −0.563402 | − | 0.826183i | \(-0.690508\pi\) | ||||
−0.563402 | + | 0.826183i | \(0.690508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −410.698 | −0.0472076 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13779.8 | 1.57275 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14076.7 | 1.58422 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14428.9 | −1.61257 | −0.806284 | − | 0.591528i | \(-0.798525\pi\) | ||||
−0.806284 | + | 0.591528i | \(0.798525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16620.3 | −1.84463 | −0.922313 | − | 0.386444i | \(-0.873703\pi\) | ||||
−0.922313 | + | 0.386444i | \(0.873703\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2163.42 | 0.238455 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12979.1 | 1.42077 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −515.565 | −0.0560515 | −0.0280257 | − | 0.999607i | \(-0.508922\pi\) | ||||
−0.0280257 | + | 0.999607i | \(0.508922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8976.09 | 0.962679 | 0.481340 | − | 0.876534i | \(-0.340150\pi\) | ||||
0.481340 | + | 0.876534i | \(0.340150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22763.7 | −2.42495 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7200.73 | −0.761930 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2106.83 | 0.221442 | 0.110721 | − | 0.993852i | \(-0.464684\pi\) | ||||
0.110721 | + | 0.993852i | \(0.464684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10924.8 | −1.14064 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1864.68 | 0.193400 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15726.2 | 1.60971 | 0.804857 | − | 0.593469i | \(-0.202242\pi\) | ||||
0.804857 | + | 0.593469i | \(0.202242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2441.65 | 0.248293 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7921.16 | −0.800272 | −0.400136 | − | 0.916456i | \(-0.631037\pi\) | ||||
−0.400136 | + | 0.916456i | \(0.631037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5821.20 | −0.584306 | −0.292153 | − | 0.956372i | \(-0.594372\pi\) | ||||
−0.292153 | + | 0.956372i | \(0.594372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6776.92 | −0.675854 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11787.9 | 1.16805 | 0.584024 | − | 0.811737i | \(-0.301477\pi\) | ||||
0.584024 | + | 0.811737i | \(0.301477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8074.73 | −0.789944 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12747.5 | 1.23918 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24962.4 | 2.41127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1425.94 | −0.136875 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5314.43 | −0.506936 | −0.253468 | − | 0.967344i | \(-0.581571\pi\) | ||||
−0.253468 | + | 0.967344i | \(0.581571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17703.1 | −1.67816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4041.35 | −0.378367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18662.7 | −1.73652 | −0.868261 | − | 0.496107i | \(-0.834762\pi\) | ||||
−0.868261 | + | 0.496107i | \(0.834762\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3171.92 | 0.293331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13519.1 | 1.24259 | 0.621293 | − | 0.783578i | \(-0.286608\pi\) | ||||
0.621293 | + | 0.783578i | \(0.286608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3915.64 | −0.357711 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10756.3 | 0.976683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13832.3 | 1.24092 | 0.620462 | − | 0.784237i | \(-0.286945\pi\) | ||||
0.620462 | + | 0.784237i | \(0.286945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −731.520 | −0.0652334 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13469.0 | 1.19394 | 0.596970 | − | 0.802264i | \(-0.296371\pi\) | ||||
0.596970 | + | 0.802264i | \(0.296371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11570.7 | −1.01958 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6235.68 | 0.546226 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8775.25 | 0.764157 | 0.382079 | − | 0.924130i | \(-0.375208\pi\) | ||||
0.382079 | + | 0.924130i | \(0.375208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4423.10 | 0.380672 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2901.54 | 0.248267 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3274.63 | 0.278565 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5061.79 | −0.428108 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1660.76 | −0.139653 | −0.0698267 | − | 0.997559i | \(-0.522245\pi\) | ||||
−0.0698267 | + | 0.997559i | \(0.522245\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6324.82 | 0.528805 | 0.264402 | − | 0.964412i | \(-0.414825\pi\) | ||||
0.264402 | + | 0.964412i | \(0.414825\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12265.8 | 1.01386 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5889.79 | −0.484079 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3525.92 | −0.288158 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9954.68 | −0.808977 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −792.848 | −0.0640707 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1077.42 | −0.0865810 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4467.88 | 0.355063 | 0.177532 | − | 0.984115i | \(-0.443189\pi\) | ||||
0.177532 | + | 0.984115i | \(0.443189\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8947.74 | 0.707153 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27198.7 | 2.13774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10939.0 | −0.855063 | −0.427531 | − | 0.904000i | \(-0.640617\pi\) | ||||
−0.427531 | + | 0.904000i | \(0.640617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4961.65 | 0.385716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7093.26 | −0.548427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13527.3 | −1.03460 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14325.1 | −1.08972 | −0.544862 | − | 0.838526i | \(-0.683418\pi\) | ||||
−0.544862 | + | 0.838526i | \(0.683418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11615.6 | 0.878867 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19468.1 | −1.46514 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20402.8 | 1.52731 | 0.763656 | − | 0.645624i | \(-0.223402\pi\) | ||||
0.763656 | + | 0.645624i | \(0.223402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18774.6 | 1.39797 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7250.43 | −0.534189 | −0.267095 | − | 0.963670i | \(-0.586064\pi\) | ||||
−0.267095 | + | 0.963670i | \(0.586064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24894.8 | 1.82454 | 0.912272 | − | 0.409586i | \(-0.134327\pi\) | ||||
0.912272 | + | 0.409586i | \(0.134327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10472.3 | 0.763503 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12072.8 | 0.875599 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1363.45 | 0.0983726 | 0.0491863 | − | 0.998790i | \(-0.484337\pi\) | ||||
0.0491863 | + | 0.998790i | \(0.484337\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4812.68 | 0.345437 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11369.5 | 0.807677 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9801.12 | 0.692694 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23854.8 | 1.67733 | 0.838666 | − | 0.544647i | \(-0.183336\pi\) | ||||
0.838666 | + | 0.544647i | \(0.183336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22219.6 | 1.55440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1367.80 | −0.0952013 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3437.20 | 0.238025 | 0.119013 | − | 0.992893i | \(-0.462027\pi\) | ||||
0.119013 | + | 0.992893i | \(0.462027\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6252.48 | 0.428638 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16511.7 | 1.12630 | 0.563148 | − | 0.826356i | \(-0.309590\pi\) | ||||
0.563148 | + | 0.826356i | \(0.309590\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11148.3 | −0.756656 | −0.378328 | − | 0.925672i | \(-0.623501\pi\) | ||||
−0.378328 | + | 0.925672i | \(0.623501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4127.67 | 0.278759 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −63595.8 | −4.27362 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −391.583 | −0.0261843 | −0.0130921 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130921 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2983.85 | 0.197567 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11740.5 | −0.773563 | −0.386782 | − | 0.922171i | \(-0.626413\pi\) | ||||
−0.386782 | + | 0.922171i | \(0.626413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7606.56 | −0.498742 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8818.95 | −0.575426 | −0.287713 | − | 0.957717i | \(-0.592895\pi\) | ||||
−0.287713 | + | 0.957717i | \(0.592895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15924.7 | −1.03404 | −0.517018 | − | 0.855975i | \(-0.672958\pi\) | ||||
−0.517018 | + | 0.855975i | \(0.672958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2139.18 | 0.138232 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11453.1 | −0.732998 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35266.8 | −2.24629 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24483.5 | 1.55202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29206.4 | 1.84261 | 0.921307 | − | 0.388836i | \(-0.127123\pi\) | ||||
0.921307 | + | 0.388836i | \(0.127123\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7704.18 | 0.483750 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −39948.9 | −2.49658 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4381.07 | −0.271225 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5613.01 | 0.345867 | 0.172933 | − | 0.984934i | \(-0.444675\pi\) | ||||
0.172933 | + | 0.984934i | \(0.444675\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18995.0 | −1.16499 | −0.582496 | − | 0.812834i | \(-0.697924\pi\) | ||||
−0.582496 | + | 0.812834i | \(0.697924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8875.68 | 0.541829 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22665.0 | 1.37721 | 0.688604 | − | 0.725138i | \(-0.258224\pi\) | ||||
0.688604 | + | 0.725138i | \(0.258224\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28113.3 | 1.70038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26527.8 | 1.58976 | 0.794879 | − | 0.606768i | \(-0.207534\pi\) | ||||
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25797.5 | −1.53892 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5174.03 | 0.307242 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17114.8 | −1.01168 | −0.505839 | − | 0.862628i | \(-0.668817\pi\) | ||||
−0.505839 | + | 0.862628i | \(0.668817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1191.82 | −0.0701305 | −0.0350653 | − | 0.999385i | \(-0.511164\pi\) | ||||
−0.0350653 | + | 0.999385i | \(0.511164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17739.4 | −1.03912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3430.57 | −0.199149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13978.7 | −0.807842 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39560.9 | −2.27605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9415.20 | −0.539271 | −0.269636 | − | 0.962962i | \(-0.586903\pi\) | ||||
−0.269636 | + | 0.962962i | \(0.586903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4114.22 | 0.234602 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7917.13 | 0.449453 | 0.224727 | − | 0.974422i | \(-0.427851\pi\) | ||||
0.224727 | + | 0.974422i | \(0.427851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14486.3 | 0.815150 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29234.4 | 1.63781 | 0.818904 | − | 0.573930i | \(-0.194582\pi\) | ||||
0.818904 | + | 0.573930i | \(0.194582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25369.6 | −1.41507 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9667.76 | −0.536897 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10359.9 | 0.572831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1222.46 | −0.0673001 | −0.0336501 | − | 0.999434i | \(-0.510713\pi\) | ||||
−0.0336501 | + | 0.999434i | \(0.510713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9184.14 | −0.501258 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13767.4 | 0.748172 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17107.3 | −0.925688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13054.6 | 0.703372 | 0.351686 | − | 0.936118i | \(-0.385608\pi\) | ||||
0.351686 | + | 0.936118i | \(0.385608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44352.3 | 2.37948 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2280.02 | 0.121802 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19975.7 | −1.05812 | −0.529058 | − | 0.848585i | \(-0.677455\pi\) | ||||
−0.529058 | + | 0.848585i | \(0.677455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6014.87 | −0.317265 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10746.3 | 0.564447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −78147.5 | −4.08749 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5983.40 | 0.311651 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6512.26 | 0.337783 | 0.168892 | − | 0.985635i | \(-0.445981\pi\) | ||||
0.168892 | + | 0.985635i | \(0.445981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4262.66 | −0.219267 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6597.92 | −0.337987 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11437.1 | 0.583467 | 0.291733 | − | 0.956500i | \(-0.405768\pi\) | ||||
0.291733 | + | 0.956500i | \(0.405768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16064.4 | −0.812808 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12276.0 | −0.618589 | −0.309295 | − | 0.950966i | \(-0.600093\pi\) | ||||
−0.309295 | + | 0.950966i | \(0.600093\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32911.3 | −1.64492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12093.8 | 0.602000 | 0.301000 | − | 0.953624i | \(-0.402680\pi\) | ||||
0.301000 | + | 0.953624i | \(0.402680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32135.2 | −1.59314 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34331.6 | 1.69516 | 0.847580 | − | 0.530668i | \(-0.178059\pi\) | ||||
0.847580 | + | 0.530668i | \(0.178059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39975.3 | 1.96588 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 686.205 | 0.0336103 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14557.9 | −0.707358 | −0.353679 | − | 0.935367i | \(-0.615070\pi\) | ||||
−0.353679 | + | 0.935367i | \(0.615070\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11566.3 | −0.559761 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10351.9 | −0.498998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27115.5 | 1.30189 | 0.650944 | − | 0.759126i | \(-0.274373\pi\) | ||||
0.650944 | + | 0.759126i | \(0.274373\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17056.4 | −0.815688 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10964.0 | −0.522264 | −0.261132 | − | 0.965303i | \(-0.584096\pi\) | ||||
−0.261132 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13555.0 | −0.640629 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25616.9 | 1.20596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7835.53 | −0.367434 | −0.183717 | − | 0.982979i | \(-0.558813\pi\) | ||||
−0.183717 | + | 0.982979i | \(0.558813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12159.8 | 0.567997 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28767.7 | −1.33856 | −0.669278 | − | 0.743012i | \(-0.733396\pi\) | ||||
−0.669278 | + | 0.743012i | \(0.733396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20668.0 | 0.957956 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24939.8 | 1.14706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34931.7 | 1.60046 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1169.09 | −0.0533586 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44827.3 | 2.03816 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2695.83 | −0.122104 | −0.0610520 | − | 0.998135i | \(-0.519446\pi\) | ||||
−0.0610520 | + | 0.998135i | \(0.519446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1502.36 | −0.0677889 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36047.9 | −1.61425 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7916.19 | 0.353155 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12592.1 | 0.559643 | 0.279822 | − | 0.960052i | \(-0.409725\pi\) | ||||
0.279822 | + | 0.960052i | \(0.409725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4126.67 | −0.182717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12301.2 | 0.542625 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41254.2 | −1.81299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9845.23 | 0.429453 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7799.49 | −0.338956 | −0.169478 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169478 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19323.5 | −0.836669 | −0.418335 | − | 0.908293i | \(-0.637386\pi\) | ||||
−0.418335 | + | 0.908293i | \(0.637386\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9973.08 | 0.430223 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17609.1 | −0.756834 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29100.9 | −1.24616 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1085.30 | 0.0461354 | 0.0230677 | − | 0.999734i | \(-0.492657\pi\) | ||||
0.0230677 | + | 0.999734i | \(0.492657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24350.8 | −1.03137 | −0.515683 | − | 0.856779i | \(-0.672462\pi\) | ||||
−0.515683 | + | 0.856779i | \(0.672462\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32804.1 | −1.38435 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31664.9 | 1.33143 | 0.665716 | − | 0.746205i | \(-0.268126\pi\) | ||||
0.665716 | + | 0.746205i | \(0.268126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3418.02 | −0.143200 | −0.0716000 | − | 0.997433i | \(-0.522810\pi\) | ||||
−0.0716000 | + | 0.997433i | \(0.522810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25859.2 | 1.07948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4061.08 | 0.168311 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3662.17 | 0.151234 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9114.25 | 0.375040 | 0.187520 | − | 0.982261i | \(-0.439955\pi\) | ||||
0.187520 | + | 0.982261i | \(0.439955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22514.2 | −0.923127 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23132.4 | −0.945104 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34617.8 | −1.40933 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −417.813 | −0.0168896 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21450.5 | 0.864056 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36229.5 | −1.45425 | −0.727124 | − | 0.686506i | \(-0.759143\pi\) | ||||
−0.727124 | + | 0.686506i | \(0.759143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24555.1 | −0.982183 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8645.18 | 0.344590 | 0.172295 | − | 0.985045i | \(-0.444882\pi\) | ||||
0.172295 | + | 0.985045i | \(0.444882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8212.58 | −0.326205 | −0.163102 | − | 0.986609i | \(-0.552150\pi\) | ||||
−0.163102 | + | 0.986609i | \(0.552150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2611.61 | −0.103013 | −0.0515065 | − | 0.998673i | \(-0.516402\pi\) | ||||
−0.0515065 | + | 0.998673i | \(0.516402\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28100.9 | 1.10458 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9794.61 | 0.383670 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47958.6 | 1.87213 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29988.8 | −1.16663 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2183.90 | 0.0846664 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6446.58 | −0.248216 | −0.124108 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124108 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13311.3 | −0.510783 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37166.3 | 1.42130 | 0.710649 | − | 0.703547i | \(-0.248401\pi\) | ||||
0.710649 | + | 0.703547i | \(0.248401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24377.3 | 0.929060 | 0.464530 | − | 0.885557i | \(-0.346223\pi\) | ||||
0.464530 | + | 0.885557i | \(0.346223\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19574.4 | 0.743486 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36344.5 | −1.37579 | −0.687896 | − | 0.725809i | \(-0.741466\pi\) | ||||
−0.687896 | + | 0.725809i | \(0.741466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5812.56 | −0.218550 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7475.55 | −0.280134 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5981.35 | 0.223391 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15541.8 | −0.578512 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5872.97 | −0.217880 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14327.8 | −0.529775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49673.9 | −1.82455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 326.875 | 0.0119666 | 0.00598329 | − | 0.999982i | \(-0.498095\pi\) | ||||
0.00598329 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6252.68 | 0.228150 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38230.7 | −1.39038 | −0.695191 | − | 0.718825i | \(-0.744680\pi\) | ||||
−0.695191 | + | 0.718825i | \(0.744680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5471.34 | −0.198330 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27544.9 | −0.995199 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20049.3 | −0.719659 | −0.359829 | − | 0.933018i | \(-0.617165\pi\) | ||||
−0.359829 | + | 0.933018i | \(0.617165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −898.439 | −0.0321439 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31829.8 | 1.13509 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41255.0 | 1.46644 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1567.96 | −0.0555540 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43341.5 | 1.53066 | 0.765332 | − | 0.643635i | \(-0.222575\pi\) | ||||
0.765332 | + | 0.643635i | \(0.222575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2741.83 | 0.0962095 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 108078. | 3.78026 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17530.0 | 0.611185 | 0.305592 | − | 0.952162i | \(-0.401146\pi\) | ||||
0.305592 | + | 0.952162i | \(0.401146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11662.1 | 0.405303 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32625.0 | −1.13023 | −0.565115 | − | 0.825012i | \(-0.691168\pi\) | ||||
−0.565115 | + | 0.825012i | \(0.691168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12061.9 | 0.416530 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19394.2 | −0.665497 | −0.332749 | − | 0.943016i | \(-0.607976\pi\) | ||||
−0.332749 | + | 0.943016i | \(0.607976\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37590.9 | −1.28583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8637.91 | 0.294536 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49618.5 | −1.68657 | −0.843285 | − | 0.537467i | \(-0.819381\pi\) | ||||
−0.843285 | + | 0.537467i | \(0.819381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −58137.7 | −1.96994 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9321.52 | 0.314861 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11393.9 | −0.382462 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 428.446 | 0.0143369 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26717.9 | −0.891274 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28432.8 | 0.945538 | 0.472769 | − | 0.881186i | \(-0.343254\pi\) | ||||
0.472769 | + | 0.881186i | \(0.343254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44443.1 | 1.47339 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42690.2 | 1.41091 | 0.705455 | − | 0.708755i | \(-0.250743\pi\) | ||||
0.705455 | + | 0.708755i | \(0.250743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29891.1 | −0.981827 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22735.1 | 0.744482 | 0.372241 | − | 0.928136i | \(-0.378589\pi\) | ||||
0.372241 | + | 0.928136i | \(0.378589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98081.7 | −3.20195 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14697.9 | −0.478356 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5643.83 | 0.183123 | 0.0915616 | − | 0.995799i | \(-0.470814\pi\) | ||||
0.0915616 | + | 0.995799i | \(0.470814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7593.45 | 0.245632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14074.3 | −0.452515 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54844.6 | −1.75802 | −0.879009 | − | 0.476806i | \(-0.841794\pi\) | ||||
−0.879009 | + | 0.476806i | \(0.841794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8432.36 | −0.269479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34711.0 | −1.10594 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44881.1 | 1.42568 | 0.712838 | − | 0.701328i | \(-0.247409\pi\) | ||||
0.712838 | + | 0.701328i | \(0.247409\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7309.99 | 0.231509 |
(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 | 588.4.a.k.1.1 | yes | 4 | |
3.2 | odd | 2 | 1764.4.a.ba.1.4 | 4 | |||
4.3 | odd | 2 | 2352.4.a.cl.1.1 | 4 | |||
7.2 | even | 3 | 588.4.i.k.361.4 | 8 | |||
7.3 | odd | 6 | 588.4.i.l.373.1 | 8 | |||
7.4 | even | 3 | 588.4.i.k.373.4 | 8 | |||
7.5 | odd | 6 | 588.4.i.l.361.1 | 8 | |||
7.6 | odd | 2 | 588.4.a.j.1.4 | ✓ | 4 | ||
21.2 | odd | 6 | 1764.4.k.bd.361.1 | 8 | |||
21.5 | even | 6 | 1764.4.k.bb.361.4 | 8 | |||
21.11 | odd | 6 | 1764.4.k.bd.1549.1 | 8 | |||
21.17 | even | 6 | 1764.4.k.bb.1549.4 | 8 | |||
21.20 | even | 2 | 1764.4.a.bc.1.1 | 4 | |||
28.27 | even | 2 | 2352.4.a.cq.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.j.1.4 | ✓ | 4 | 7.6 | odd | 2 | ||
588.4.a.k.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
588.4.i.k.361.4 | 8 | 7.2 | even | 3 | |||
588.4.i.k.373.4 | 8 | 7.4 | even | 3 | |||
588.4.i.l.361.1 | 8 | 7.5 | odd | 6 | |||
588.4.i.l.373.1 | 8 | 7.3 | odd | 6 | |||
1764.4.a.ba.1.4 | 4 | 3.2 | odd | 2 | |||
1764.4.a.bc.1.1 | 4 | 21.20 | even | 2 | |||
1764.4.k.bb.361.4 | 8 | 21.5 | even | 6 | |||
1764.4.k.bb.1549.4 | 8 | 21.17 | even | 6 | |||
1764.4.k.bd.361.1 | 8 | 21.2 | odd | 6 | |||
1764.4.k.bd.1549.1 | 8 | 21.11 | odd | 6 | |||
2352.4.a.cl.1.1 | 4 | 4.3 | odd | 2 | |||
2352.4.a.cq.1.4 | 4 | 28.27 | even | 2 |