Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.957567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −4.64574 | −0.894072 | −0.447036 | − | 0.894516i | \(-0.647520\pi\) | ||||
−0.447036 | + | 0.894516i | \(0.647520\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.8729 | −1.15138 | −0.575692 | − | 0.817667i | \(-0.695267\pi\) | ||||
−0.575692 | + | 0.817667i | \(0.695267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.0540 | 1.40678 | 0.703391 | − | 0.710804i | \(-0.251669\pi\) | ||||
0.703391 | + | 0.710804i | \(0.251669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.41713 | −0.200635 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 62.8274 | 1.72211 | 0.861053 | − | 0.508515i | \(-0.169805\pi\) | ||||
0.861053 | + | 0.508515i | \(0.169805\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.3936 | −0.477759 | −0.238879 | − | 0.971049i | \(-0.576780\pi\) | ||||
−0.238879 | + | 0.971049i | \(0.576780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 59.8039 | 1.02942 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −57.9808 | −0.827201 | −0.413601 | − | 0.910458i | \(-0.635729\pi\) | ||||
−0.413601 | + | 0.910458i | \(0.635729\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −71.3143 | −0.861086 | −0.430543 | − | 0.902570i | \(-0.641678\pi\) | ||||
−0.430543 | + | 0.902570i | \(0.641678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −121.040 | −1.25776 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −49.5307 | −0.449037 | −0.224519 | − | 0.974470i | \(-0.572081\pi\) | ||||
−0.224519 | + | 0.974470i | \(0.572081\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.7104 | 0.325683 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 150.601 | 1.07345 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 62.9198 | 0.364540 | 0.182270 | − | 0.983249i | \(-0.441656\pi\) | ||||
0.182270 | + | 0.983249i | \(0.441656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −291.880 | −1.53969 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −335.389 | −1.61974 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −119.123 | −0.529288 | −0.264644 | − | 0.964346i | \(-0.585254\pi\) | ||||
−0.264644 | + | 0.964346i | \(0.585254\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 104.035 | 0.427151 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −414.916 | −1.58046 | −0.790231 | − | 0.612810i | \(-0.790039\pi\) | ||||
−0.790231 | + | 0.612810i | \(0.790039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 348.009 | 1.23421 | 0.617103 | − | 0.786882i | \(-0.288306\pi\) | ||||
0.617103 | + | 0.786882i | \(0.288306\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 69.7340 | 0.231007 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 553.259 | 1.71705 | 0.858523 | − | 0.512775i | \(-0.171382\pi\) | ||||
0.858523 | + | 0.512775i | \(0.171382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.808 | 0.979033 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 269.364 | 0.739578 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 107.308 | 0.278111 | 0.139055 | − | 0.990285i | \(-0.455593\pi\) | ||||
0.139055 | + | 0.990285i | \(0.455593\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −808.768 | −1.98280 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 331.308 | 0.769873 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −136.881 | −0.302041 | −0.151020 | − | 0.988531i | \(-0.548256\pi\) | ||||
−0.151020 | + | 0.988531i | \(0.548256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 579.408 | 1.21616 | 0.608078 | − | 0.793877i | \(-0.291941\pi\) | ||||
0.608078 | + | 0.793877i | \(0.291941\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −141.138 | −0.282249 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 288.269 | 0.550084 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −919.959 | −1.67748 | −0.838738 | − | 0.544535i | \(-0.816706\pi\) | ||||
−0.838738 | + | 0.544535i | \(0.816706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 230.106 | 0.401472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 781.802 | 1.30680 | 0.653400 | − | 0.757013i | \(-0.273342\pi\) | ||||
0.653400 | + | 0.757013i | \(0.273342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −133.237 | −0.213619 | −0.106810 | − | 0.994279i | \(-0.534064\pi\) | ||||
−0.106810 | + | 0.994279i | \(0.534064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −189.130 | −0.291185 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1636.90 | 2.42263 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 868.196 | 1.23645 | 0.618225 | − | 0.786001i | \(-0.287852\pi\) | ||||
0.618225 | + | 0.786001i | \(0.287852\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −553.392 | −0.759111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 83.3560 | 0.110235 | 0.0551175 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551175 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 746.379 | 0.952425 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −134.726 | −0.166025 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −357.919 | −0.426284 | −0.213142 | − | 0.977021i | \(-0.568370\pi\) | ||||
−0.213142 | + | 0.977021i | \(0.568370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −583.442 | −0.672102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −292.309 | −0.325925 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 918.019 | 0.991440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −187.105 | −0.195852 | −0.0979260 | − | 0.995194i | \(-0.531221\pi\) | ||||
−0.0979260 | + | 0.995194i | \(0.531221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −340.344 | −0.345514 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 959.423 | 0.945209 | 0.472605 | − | 0.881275i | \(-0.343314\pi\) | ||||
0.472605 | + | 0.881275i | \(0.343314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78.8738 | 0.0754531 | 0.0377265 | − | 0.999288i | \(-0.487988\pi\) | ||||
0.0377265 | + | 0.999288i | \(0.487988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1558.13 | 1.44817 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −713.851 | −0.644959 | −0.322479 | − | 0.946577i | \(-0.604516\pi\) | ||||
−0.322479 | + | 0.946577i | \(0.604516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −536.561 | −0.471497 | −0.235749 | − | 0.971814i | \(-0.575754\pi\) | ||||
−0.235749 | + | 0.971814i | \(0.575754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 553.412 | 0.473222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1946.36 | 1.62034 | 0.810170 | − | 0.586195i | \(-0.199375\pi\) | ||||
0.810170 | + | 0.586195i | \(0.199375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 637.601 | 0.517014 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 121.309 | 0.0958549 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1510.63 | −1.16369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2616.28 | 1.96565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1927.59 | 1.41305 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1085.05 | 0.776397 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1995.14 | −1.39402 | −0.697009 | − | 0.717062i | \(-0.745486\pi\) | ||||
−0.697009 | + | 0.717062i | \(0.745486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1616.76 | −1.10347 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1544.84 | −1.03033 | −0.515164 | − | 0.857092i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857092i | \(0.672269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1858.02 | −1.21136 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1938.67 | −1.23596 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1294.93 | −0.807543 | −0.403771 | − | 0.914860i | \(-0.632301\pi\) | ||||
−0.403771 | + | 0.914860i | \(0.632301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1999.66 | −1.22021 | −0.610105 | − | 0.792320i | \(-0.708873\pi\) | ||||
−0.610105 | + | 0.792320i | \(0.708873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2570.30 | −1.53516 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1406.93 | −0.822752 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −373.313 | −0.213807 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1560.08 | −0.875326 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1187.63 | −0.652984 | −0.326492 | − | 0.945200i | \(-0.605867\pi\) | ||||
−0.326492 | + | 0.945200i | \(0.605867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2257.61 | −1.21670 | −0.608350 | − | 0.793669i | \(-0.708168\pi\) | ||||
−0.608350 | + | 0.793669i | \(0.708168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 314.090 | 0.165965 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −809.958 | −0.419725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1188.18 | −0.603995 | −0.301997 | − | 0.953309i | \(-0.597653\pi\) | ||||
−0.301997 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −498.524 | −0.248651 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1290.47 | −0.631697 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2452.33 | 1.17841 | 0.589207 | − | 0.807982i | \(-0.299440\pi\) | ||||
0.589207 | + | 0.807982i | \(0.299440\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3757.32 | 1.77277 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2020.14 | −0.936067 | −0.468034 | − | 0.883711i | \(-0.655037\pi\) | ||||
−0.468034 | + | 0.883711i | \(0.655037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1695.53 | −0.771746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 386.319 | 0.172764 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2862.12 | −1.25782 | −0.628910 | − | 0.777478i | \(-0.716499\pi\) | ||||
−0.628910 | + | 0.777478i | \(0.716499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1060.67 | 0.458165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 635.914 | 0.270046 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 232.651 | 0.0971460 | 0.0485730 | − | 0.998820i | \(-0.484533\pi\) | ||||
0.0485730 | + | 0.998820i | \(0.484533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2607.67 | 1.07086 | 0.535432 | − | 0.844578i | \(-0.320149\pi\) | ||||
0.535432 | + | 0.844578i | \(0.320149\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2691.78 | −1.08733 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1533.45 | 0.609413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3642.78 | −1.42453 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3923.76 | 1.51012 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1528.90 | 0.579202 | 0.289601 | − | 0.957147i | \(-0.406477\pi\) | ||||
0.289601 | + | 0.957147i | \(0.406477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1017.58 | 0.379518 | 0.189759 | − | 0.981831i | \(-0.439229\pi\) | ||||
0.189759 | + | 0.981831i | \(0.439229\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1339.22 | −0.491815 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3290.20 | −1.18994 | −0.594968 | − | 0.803749i | \(-0.702835\pi\) | ||||
−0.594968 | + | 0.803749i | \(0.702835\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −29.9190 | −0.0106578 | −0.00532891 | − | 0.999986i | \(-0.501696\pi\) | ||||
−0.00532891 | + | 0.999986i | \(0.501696\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4273.89 | 1.49979 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 755.565 | 0.261233 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5341.15 | 1.81972 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 268.314 | 0.0900924 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4480.49 | −1.48288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2267.20 | −0.739717 | −0.369859 | − | 0.929088i | \(-0.620594\pi\) | ||||
−0.369859 | + | 0.929088i | \(0.620594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3632.05 | −1.16837 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4479.87 | −1.42105 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1639.31 | 0.512828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 618.984 | 0.190991 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1298.40 | 0.395203 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4945.03 | 1.48495 | 0.742474 | − | 0.669875i | \(-0.233652\pi\) | ||||
0.742474 | + | 0.669875i | \(0.233652\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −220.534 | −0.0653433 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3559.46 | 1.04075 | 0.520374 | − | 0.853938i | \(-0.325792\pi\) | ||||
0.520374 | + | 0.853938i | \(0.325792\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6143.40 | −1.77278 | −0.886391 | − | 0.462937i | \(-0.846796\pi\) | ||||
−0.886391 | + | 0.462937i | \(0.846796\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7604.61 | −2.16600 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1087.06 | −0.305648 | −0.152824 | − | 0.988253i | \(-0.548837\pi\) | ||||
−0.152824 | + | 0.988253i | \(0.548837\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7122.03 | −1.97698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4033.41 | −1.10548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1079.00 | 0.292027 | 0.146013 | − | 0.989283i | \(-0.453356\pi\) | ||||
0.146013 | + | 0.989283i | \(0.453356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −989.224 | −0.264405 | −0.132202 | − | 0.991223i | \(-0.542205\pi\) | ||||
−0.132202 | + | 0.991223i | \(0.542205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1495.33 | −0.394754 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4322.81 | −1.12724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1596.98 | 0.411391 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −387.250 | −0.0985581 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −900.246 | −0.226386 | −0.113193 | − | 0.993573i | \(-0.536108\pi\) | ||||
−0.113193 | + | 0.993573i | \(0.536108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3111.88 | −0.773290 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3467.48 | −0.851537 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3125.18 | −0.758534 | −0.379267 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379267 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3103.62 | −0.744592 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −157.097 | −0.0372569 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2814.89 | 0.659976 | 0.329988 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329988 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1381.36 | −0.320212 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1662.80 | 0.381129 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4409.28 | −0.999400 | −0.499700 | − | 0.866199i | \(-0.666556\pi\) | ||||
−0.499700 | + | 0.866199i | \(0.666556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4417.97 | −0.990304 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2710.52 | 0.600908 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2557.73 | 0.560862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 887.577 | 0.192525 | 0.0962624 | − | 0.995356i | \(-0.469311\pi\) | ||||
0.0962624 | + | 0.995356i | \(0.469311\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −340.845 | −0.0731393 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4286.58 | −0.910021 | −0.455010 | − | 0.890486i | \(-0.650364\pi\) | ||||
−0.455010 | + | 0.890486i | \(0.650364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1709.59 | 0.359097 | 0.179549 | − | 0.983749i | \(-0.442536\pi\) | ||||
0.179549 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4264.88 | −0.886419 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10810.2 | −2.22336 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1551.22 | −0.315738 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 869.241 | 0.175106 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1145.01 | −0.228301 | −0.114151 | − | 0.993463i | \(-0.536415\pi\) | ||||
−0.114151 | + | 0.993463i | \(0.536415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1762.05 | 0.347765 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9461.90 | 1.84860 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1109.17 | 0.214532 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9067.01 | 1.73626 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4457.23 | −0.845086 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7458.63 | −1.40026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1079.39 | −0.200665 | −0.100333 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100333 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −366.427 | −0.0674605 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2313.90 | 0.421895 | 0.210947 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210947 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7653.19 | −1.38206 | −0.691029 | − | 0.722827i | \(-0.742842\pi\) | ||||
−0.691029 | + | 0.722827i | \(0.742842\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1816.85 | 0.324977 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3657.23 | 0.647982 | 0.323991 | − | 0.946060i | \(-0.394975\pi\) | ||||
0.323991 | + | 0.946060i | \(0.394975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1821.99 | 0.319787 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3316.36 | 0.576640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4134.86 | 0.712291 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −911.653 | −0.155598 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2492.72 | 0.421553 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14414.6 | 2.41551 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3237.92 | −0.537681 | −0.268841 | − | 0.963185i | \(-0.586640\pi\) | ||||
−0.268841 | + | 0.963185i | \(0.586640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 645.303 | 0.106193 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11842.5 | 1.93142 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7976.89 | −1.28940 | −0.644702 | − | 0.764434i | \(-0.723018\pi\) | ||||
−0.644702 | + | 0.764434i | \(0.723018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9042.29 | −1.44870 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3953.09 | 0.627777 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −187.371 | −0.0294959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2962.13 | −0.462248 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8355.93 | 1.29271 | 0.646354 | − | 0.763037i | \(-0.276293\pi\) | ||||
0.646354 | + | 0.763037i | \(0.276293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5544.56 | −0.850411 | −0.425205 | − | 0.905097i | \(-0.639798\pi\) | ||||
−0.425205 | + | 0.905097i | \(0.639798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3372.51 | −0.512852 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1682.79 | −0.253727 | −0.126864 | − | 0.991920i | \(-0.540491\pi\) | ||||
−0.126864 | + | 0.991920i | \(0.540491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10064.0 | −1.50463 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7017.99 | 1.04042 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7143.13 | 1.05014 | 0.525069 | − | 0.851059i | \(-0.324039\pi\) | ||||
0.525069 | + | 0.851059i | \(0.324039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1773.27 | −0.258531 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12154.6 | −1.75743 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1715.14 | 0.245958 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4456.16 | −0.633814 | −0.316907 | − | 0.948457i | \(-0.602644\pi\) | ||||
−0.316907 | + | 0.948457i | \(0.602644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2247.65 | 0.317095 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2795.79 | 0.391241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2508.28 | −0.348187 | −0.174094 | − | 0.984729i | \(-0.555700\pi\) | ||||
−0.174094 | + | 0.984729i | \(0.555700\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5040.85 | −0.694155 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −649.414 | −0.0887176 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12733.9 | 1.72585 | 0.862926 | − | 0.505331i | \(-0.168629\pi\) | ||||
0.862926 | + | 0.505331i | \(0.168629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9268.91 | 1.24635 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1027.19 | −0.137042 | −0.0685209 | − | 0.997650i | \(-0.521828\pi\) | ||||
−0.0685209 | + | 0.997650i | \(0.521828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21071.6 | −2.78937 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1885.21 | −0.247624 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5153.35 | −0.671684 | −0.335842 | − | 0.941918i | \(-0.609021\pi\) | ||||
−0.335842 | + | 0.941918i | \(0.609021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2871.83 | 0.371444 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7176.90 | 0.921187 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11176.2 | −1.42363 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6250.95 | −0.790242 | −0.395121 | − | 0.918629i | \(-0.629297\pi\) | ||||
−0.395121 | + | 0.918629i | \(0.629297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8631.87 | 1.08304 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11083.8 | 1.38029 | 0.690145 | − | 0.723671i | \(-0.257547\pi\) | ||||
0.690145 | + | 0.723671i | \(0.257547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1409.00 | −0.174162 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7123.74 | 0.874028 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7484.17 | −0.911490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3375.43 | −0.408079 | −0.204039 | − | 0.978963i | \(-0.565407\pi\) | ||||
−0.204039 | + | 0.978963i | \(0.565407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6015.91 | 0.722002 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3566.29 | −0.424905 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1073.03 | −0.126923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9289.91 | 1.09096 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6486.50 | −0.756292 | −0.378146 | − | 0.925746i | \(-0.623438\pi\) | ||||
−0.378146 | + | 0.925746i | \(0.623438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10938.6 | 1.26631 | 0.633153 | − | 0.774026i | \(-0.281760\pi\) | ||||
0.633153 | + | 0.774026i | \(0.281760\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2997.08 | −0.344499 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2360.42 | −0.269406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15095.9 | 1.71087 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6536.23 | 0.735600 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4124.34 | 0.460934 | 0.230467 | − | 0.973080i | \(-0.425975\pi\) | ||||
0.230467 | + | 0.973080i | \(0.425975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1561.41 | −0.173295 | −0.0866473 | − | 0.996239i | \(-0.527615\pi\) | ||||
−0.0866473 | + | 0.996239i | \(0.527615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1734.31 | 0.191158 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3532.25 | 0.386660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15712.7 | −1.70826 | −0.854130 | − | 0.520060i | \(-0.825909\pi\) | ||||
−0.854130 | + | 0.520060i | \(0.825909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1819.12 | −0.196428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12763.5 | −1.36888 | −0.684439 | − | 0.729070i | \(-0.739953\pi\) | ||||
−0.684439 | + | 0.729070i | \(0.739953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4607.44 | 0.490817 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5517.42 | 0.583815 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3117.88 | 0.327710 | 0.163855 | − | 0.986484i | \(-0.447607\pi\) | ||||
0.163855 | + | 0.986484i | \(0.447607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26068.1 | −2.72172 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10488.3 | 1.08782 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7510.56 | 0.773847 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8479.41 | −0.867943 | −0.433972 | − | 0.900927i | \(-0.642888\pi\) | ||||
−0.433972 | + | 0.900927i | \(0.642888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8732.00 | −0.887962 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9253.32 | −0.934859 | −0.467430 | − | 0.884030i | \(-0.654820\pi\) | ||||
−0.467430 | + | 0.884030i | \(0.654820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 521.395 | 0.0523354 | 0.0261677 | − | 0.999658i | \(-0.491670\pi\) | ||||
0.0261677 | + | 0.999658i | \(0.491670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3762.85 | 0.375265 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4337.35 | −0.429783 | −0.214891 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214891 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23968.6 | −2.35984 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5519.98 | 0.540015 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21864.5 | 2.12544 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2903.24 | −0.280441 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −581.300 | −0.0557986 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11258.1 | −1.07390 | −0.536949 | − | 0.843615i | \(-0.680423\pi\) | ||||
−0.536949 | + | 0.843615i | \(0.680423\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2667.58 | 0.252872 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5995.18 | 0.564783 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2408.58 | 0.225501 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4353.54 | 0.405088 | 0.202544 | − | 0.979273i | \(-0.435079\pi\) | ||||
0.202544 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11392.9 | −1.05359 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8458.77 | 0.777472 | 0.388736 | − | 0.921349i | \(-0.372912\pi\) | ||||
0.388736 | + | 0.921349i | \(0.372912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1681.44 | −0.153607 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4381.20 | 0.397819 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20369.0 | 1.83838 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14850.9 | −1.33230 | −0.666149 | − | 0.745819i | \(-0.732058\pi\) | ||||
−0.666149 | + | 0.745819i | \(0.732058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9385.04 | 0.836912 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1686.45 | −0.149493 | −0.0747464 | − | 0.997203i | \(-0.523815\pi\) | ||||
−0.0747464 | + | 0.997203i | \(0.523815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12350.5 | −1.08830 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7876.97 | 0.689997 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11113.5 | 0.967773 | 0.483887 | − | 0.875131i | \(-0.339225\pi\) | ||||
0.483887 | + | 0.875131i | \(0.339225\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3471.35 | −0.300516 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10740.0 | −0.924336 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1015.33 | −0.0868754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34759.8 | 2.95694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13296.7 | 1.12458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15931.1 | −1.33964 | −0.669820 | − | 0.742523i | \(-0.733629\pi\) | ||||
−0.669820 | + | 0.742523i | \(0.733629\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7960.43 | 0.665555 | 0.332778 | − | 0.943005i | \(-0.392014\pi\) | ||||
0.332778 | + | 0.943005i | \(0.392014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4927.58 | −0.409633 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3648.14 | −0.301548 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9713.71 | −0.798366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 741.503 | 0.0605998 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9291.45 | 0.755079 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9189.30 | 0.742594 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1080.83 | −0.0868555 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21098.0 | 1.68600 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13818.9 | −1.09819 | −0.549096 | − | 0.835760i | \(-0.685028\pi\) | ||||
−0.549096 | + | 0.835760i | \(0.685028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12114.5 | −0.957430 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6907.07 | 0.542874 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22093.3 | −1.72695 | −0.863474 | − | 0.504393i | \(-0.831716\pi\) | ||||
−0.863474 | + | 0.504393i | \(0.831716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3138.73 | −0.244003 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2068.12 | −0.159900 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22619.9 | 1.73942 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7124.00 | −0.544859 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3110.34 | 0.236606 | 0.118303 | − | 0.992978i | \(-0.462255\pi\) | ||||
0.118303 | + | 0.992978i | \(0.462255\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7793.17 | −0.589653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16923.4 | 1.27363 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13284.6 | 0.994455 | 0.497227 | − | 0.867620i | \(-0.334351\pi\) | ||||
0.497227 | + | 0.867620i | \(0.334351\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25055.2 | −1.86563 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14418.1 | −1.06790 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6809.18 | −0.501680 | −0.250840 | − | 0.968029i | \(-0.580707\pi\) | ||||
−0.250840 | + | 0.968029i | \(0.580707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13471.8 | 0.987352 | 0.493676 | − | 0.869646i | \(-0.335653\pi\) | ||||
0.493676 | + | 0.869646i | \(0.335653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7102.88 | −0.517849 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2016.41 | −0.146244 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5331.06 | 0.384636 | 0.192318 | − | 0.981333i | \(-0.438399\pi\) | ||||
0.192318 | + | 0.981333i | \(0.438399\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4727.41 | −0.339317 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2171.75 | 0.155077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6741.87 | 0.478936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1561.59 | −0.110366 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3333.96 | −0.234425 | −0.117212 | − | 0.993107i | \(-0.537396\pi\) | ||||
−0.117212 | + | 0.993107i | \(0.537396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4487.09 | −0.313900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15285.4 | 1.06389 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23405.3 | −1.62081 | −0.810404 | − | 0.585872i | \(-0.800752\pi\) | ||||
−0.810404 | + | 0.585872i | \(0.800752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19446.1 | 1.33985 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 138.996 | 0.00952886 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10352.1 | −0.706133 | −0.353067 | − | 0.935598i | \(-0.614861\pi\) | ||||
−0.353067 | + | 0.935598i | \(0.614861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15171.1 | 1.02969 | 0.514843 | − | 0.857285i | \(-0.327850\pi\) | ||||
0.514843 | + | 0.857285i | \(0.327850\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4983.54 | 0.336560 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33679.0 | −2.26322 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20823.0 | −1.39239 | −0.696193 | − | 0.717854i | \(-0.745124\pi\) | ||||
−0.696193 | + | 0.717854i | \(0.745124\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3510.15 | −0.233561 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12389.5 | −0.820334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19071.6 | 1.25660 | 0.628299 | − | 0.777972i | \(-0.283751\pi\) | ||||
0.628299 | + | 0.777972i | \(0.283751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24813.6 | −1.62696 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15200.4 | 0.991806 | 0.495903 | − | 0.868378i | \(-0.334837\pi\) | ||||
0.495903 | + | 0.868378i | \(0.334837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4358.76 | −0.283026 | −0.141513 | − | 0.989936i | \(-0.545197\pi\) | ||||
−0.141513 | + | 0.989936i | \(0.545197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7459.39 | −0.482021 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9325.20 | −0.599689 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19056.5 | −1.21961 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20815.2 | 1.32580 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6906.83 | 0.437827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2580.66 | −0.162812 | −0.0814062 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814062 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10532.8 | 0.661361 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25683.2 | 1.60505 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7519.96 | −0.467742 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4235.12 | −0.262189 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19858.9 | 1.22368 | 0.611840 | − | 0.790982i | \(-0.290430\pi\) | ||||
0.611840 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17371.9 | −1.06545 | −0.532723 | − | 0.846290i | \(-0.678831\pi\) | ||||
−0.532723 | + | 0.846290i | \(0.678831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20812.3 | 1.27052 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3275.07 | 0.199005 | 0.0995024 | − | 0.995037i | \(-0.468275\pi\) | ||||
0.0995024 | + | 0.995037i | \(0.468275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8599.88 | −0.520146 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7615.80 | −0.458505 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20726.5 | −1.24210 | −0.621049 | − | 0.783772i | \(-0.713293\pi\) | ||||
−0.621049 | + | 0.783772i | \(0.713293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19886.4 | 1.18630 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 721.762 | 0.0428594 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18404.6 | 1.08792 | 0.543960 | − | 0.839111i | \(-0.316924\pi\) | ||||
0.543960 | + | 0.839111i | \(0.316924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7146.10 | 0.420501 | 0.210250 | − | 0.977648i | \(-0.432572\pi\) | ||||
0.210250 | + | 0.977648i | \(0.432572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6032.02 | −0.353340 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23918.0 | 1.39474 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1436.39 | −0.0833841 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22973.3 | −1.32765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36402.7 | 2.09435 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26819.0 | −1.53610 | −0.768051 | − | 0.640389i | \(-0.778773\pi\) | ||||
−0.768051 | + | 0.640389i | \(0.778773\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6131.05 | 0.349606 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20093.1 | 1.14068 | 0.570340 | − | 0.821408i | \(-0.306811\pi\) | ||||
0.570340 | + | 0.821408i | \(0.306811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4874.82 | −0.275521 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16536.3 | −0.930505 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6876.22 | 0.385229 | 0.192614 | − | 0.981275i | \(-0.438303\pi\) | ||||
0.192614 | + | 0.981275i | \(0.438303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16669.5 | 0.929791 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28540.6 | 1.58500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2403.01 | −0.132870 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17332.7 | −0.954224 | −0.477112 | − | 0.878842i | \(-0.658316\pi\) | ||||
−0.477112 | + | 0.878842i | \(0.658316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8867.31 | −0.486063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25741.4 | 1.40493 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24057.1 | 1.30736 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5050.21 | 0.273271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11127.5 | −0.599545 | −0.299772 | − | 0.954011i | \(-0.596911\pi\) | ||||
−0.299772 | + | 0.954011i | \(0.596911\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8495.15 | 0.455762 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33087.1 | 1.76756 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24996.8 | 1.32970 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17432.0 | −0.923374 | −0.461687 | − | 0.887043i | \(-0.652756\pi\) | ||||
−0.461687 | + | 0.887043i | \(0.652756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4703.13 | −0.248075 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3116.46 | −0.163692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18111.2 | 0.947302 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5012.73 | −0.261093 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21082.7 | 1.09353 | 0.546767 | − | 0.837285i | \(-0.315858\pi\) | ||||
0.546767 | + | 0.837285i | \(0.315858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2054.97 | 0.106146 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4595.68 | 0.236397 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1180.60 | 0.0604779 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25839.1 | −1.31818 | −0.659091 | − | 0.752063i | \(-0.729059\pi\) | ||||
−0.659091 | + | 0.752063i | \(0.729059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21888.5 | 1.11205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20177.9 | −1.02094 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1278.54 | −0.0644256 | −0.0322128 | − | 0.999481i | \(-0.510255\pi\) | ||||
−0.0322128 | + | 0.999481i | \(0.510255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20082.6 | 1.00784 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −57798.6 | −2.88879 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4224.54 | −0.210287 | −0.105144 | − | 0.994457i | \(-0.533530\pi\) | ||||
−0.105144 | + | 0.994457i | \(0.533530\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7419.17 | −0.367814 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17992.3 | −0.888390 | −0.444195 | − | 0.895930i | \(-0.646510\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15288.2 | 0.751835 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −451.550 | −0.0221170 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18598.6 | −0.907316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10082.4 | −0.489895 | −0.244948 | − | 0.969536i | \(-0.578771\pi\) | ||||
−0.244948 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4182.30 | 0.202406 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29061.9 | 1.40089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10806.5 | −0.518851 | −0.259425 | − | 0.965763i | \(-0.583533\pi\) | ||||
−0.259425 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14457.0 | 0.691377 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30710.4 | −1.46288 | −0.731439 | − | 0.681907i | \(-0.761151\pi\) | ||||
−0.731439 | + | 0.681907i | \(0.761151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13979.5 | −0.663293 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4043.23 | −0.191089 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3065.26 | 0.144303 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10757.1 | 0.504436 | 0.252218 | − | 0.967670i | \(-0.418840\pi\) | ||||
0.252218 | + | 0.967670i | \(0.418840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14518.8 | 0.678185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18077.2 | 0.841125 | 0.420563 | − | 0.907263i | \(-0.361833\pi\) | ||||
0.420563 | + | 0.907263i | \(0.361833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2561.49 | 0.118725 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14418.6 | 0.665719 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29589.4 | 1.36091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49118.6 | 2.25045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4367.44 | 0.199335 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15295.3 | 0.695430 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31543.7 | 1.42873 | 0.714366 | − | 0.699773i | \(-0.246715\pi\) | ||||
0.714366 | + | 0.699773i | \(0.246715\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13077.3 | −0.590066 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50710.4 | 2.27946 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12975.0 | −0.581030 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6417.42 | 0.286293 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18280.9 | −0.812477 | −0.406239 | − | 0.913767i | \(-0.633160\pi\) | ||||
−0.406239 | + | 0.913767i | \(0.633160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32078.4 | −1.42034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1938.89 | 0.0855273 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8370.93 | −0.367875 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16612.0 | 0.727326 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20484.4 | 0.893536 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21776.3 | 0.946372 | 0.473186 | − | 0.880963i | \(-0.343104\pi\) | ||||
0.473186 | + | 0.880963i | \(0.343104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17035.7 | −0.737612 | −0.368806 | − | 0.929506i | \(-0.620233\pi\) | ||||
−0.368806 | + | 0.929506i | \(0.620233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20524.7 | 0.885404 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31568.5 | −1.35681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24818.0 | −1.06276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3160.58 | 0.134847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45120.7 | 1.91805 | 0.959027 | − | 0.283314i | \(-0.0914339\pi\) | ||||
0.959027 | + | 0.283314i | \(0.0914339\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22261.7 | 0.942883 | 0.471442 | − | 0.881897i | \(-0.343734\pi\) | ||||
0.471442 | + | 0.881897i | \(0.343734\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11882.5 | −0.501451 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10280.4 | −0.432266 | −0.216133 | − | 0.976364i | \(-0.569345\pi\) | ||||
−0.216133 | + | 0.976364i | \(0.569345\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28509.2 | −1.19441 | −0.597206 | − | 0.802088i | \(-0.703722\pi\) | ||||
−0.597206 | + | 0.802088i | \(0.703722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4123.45 | −0.172131 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19470.4 | −0.809857 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26005.0 | 1.07777 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9475.82 | 0.391317 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4746.97 | 0.195332 | 0.0976661 | − | 0.995219i | \(-0.468862\pi\) | ||||
0.0976661 | + | 0.995219i | \(0.468862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19914.3 | 0.813625 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21826.3 | 0.888576 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 68164.5 | 2.76524 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7942.30 | −0.321059 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5900.22 | 0.237670 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35313.3 | −1.41747 | −0.708736 | − | 0.705473i | \(-0.750734\pi\) | ||||
−0.708736 | + | 0.705473i | \(0.750734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4973.03 | −0.198917 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32142.8 | 1.28119 | 0.640594 | − | 0.767880i | \(-0.278688\pi\) | ||||
0.640594 | + | 0.767880i | \(0.278688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37568.2 | −1.49221 | −0.746107 | − | 0.665826i | \(-0.768079\pi\) | ||||
−0.746107 | + | 0.665826i | \(0.768079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50221.3 | 1.98785 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3416.95 | 0.134779 | 0.0673896 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673896 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36843.6 | 1.44823 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7206.57 | 0.282293 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54546.5 | 2.12930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20601.2 | 0.801429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1013.57 | 0.0392947 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28269.8 | 1.09222 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11891.0 | 0.457847 | 0.228923 | − | 0.973444i | \(-0.426479\pi\) | ||||
0.228923 | + | 0.973444i | \(0.426479\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5319.42 | 0.204118 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20042.7 | 0.766464 | 0.383232 | − | 0.923652i | \(-0.374811\pi\) | ||||
0.383232 | + | 0.923652i | \(0.374811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18042.8 | 0.687641 | 0.343821 | − | 0.939035i | \(-0.388279\pi\) | ||||
0.343821 | + | 0.939035i | \(0.388279\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8186.02 | −0.310927 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2247.91 | 0.0850929 | 0.0425464 | − | 0.999094i | \(-0.486453\pi\) | ||||
0.0425464 | + | 0.999094i | \(0.486453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51981.4 | −1.96108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34768.2 | −1.30727 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39455.3 | −1.47852 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2994.88 | −0.111852 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5152.91 | −0.191807 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1824.68 | 0.0676934 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6221.80 | −0.230053 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42123.0 | −1.55234 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33568.1 | −1.23298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1798.34 | 0.0658354 | 0.0329177 | − | 0.999458i | \(-0.489520\pi\) | ||||
0.0329177 | + | 0.999458i | \(0.489520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5197.32 | −0.189642 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4602.02 | 0.167367 | 0.0836837 | − | 0.996492i | \(-0.473331\pi\) | ||||
0.0836837 | + | 0.996492i | \(0.473331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5237.04 | 0.189836 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34650.8 | 1.25194 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40249.1 | −1.44944 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20622.0 | 0.740215 | 0.370107 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370107 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5014.58 | 0.179409 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17507.4 | −0.624335 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4849.53 | −0.172380 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −427.270 | −0.0151385 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24061.8 | −0.849777 | −0.424889 | − | 0.905246i | \(-0.639687\pi\) | ||||
−0.424889 | + | 0.905246i | \(0.639687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23947.9 | −0.843032 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10749.8 | −0.377204 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46893.0 | 1.64018 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6581.96 | −0.229481 | −0.114740 | − | 0.993396i | \(-0.536604\pi\) | ||||
−0.114740 | + | 0.993396i | \(0.536604\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35554.7 | 1.23566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23579.7 | −0.816873 | −0.408436 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408436 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20551.0 | 0.709686 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50510.0 | −1.73872 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36368.6 | 1.24796 | 0.623982 | − | 0.781439i | \(-0.285514\pi\) | ||||
0.623982 | + | 0.781439i | \(0.285514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2983.65 | 0.102058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16990.5 | −0.579343 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44404.3 | 1.50933 | 0.754667 | − | 0.656108i | \(-0.227798\pi\) | ||||
0.754667 | + | 0.656108i | \(0.227798\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19681.4 | −0.666884 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8464.51 | −0.285913 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33738.1 | −1.13604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25832.1 | −0.867111 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3867.02 | 0.129401 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13099.2 | −0.436971 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21928.3 | 0.729230 | 0.364615 | − | 0.931158i | \(-0.381201\pi\) | ||||
0.364615 | + | 0.931158i | \(0.381201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19209.5 | −0.636840 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6352.95 | 0.209965 | 0.104982 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104982 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52099.1 | −1.71657 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4235.30 | 0.139116 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12792.8 | 0.418913 | 0.209456 | − | 0.977818i | \(-0.432831\pi\) | ||||
0.209456 | + | 0.977818i | \(0.432831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22487.1 | −0.734107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2906.62 | 0.0945986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7536.73 | 0.244542 | 0.122271 | − | 0.992497i | \(-0.460982\pi\) | ||||
0.122271 | + | 0.992497i | \(0.460982\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42354.3 | 1.37007 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −66966.4 | −2.15964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17237.1 | −0.554205 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28088.3 | −0.900357 | −0.450179 | − | 0.892938i | \(-0.648640\pi\) | ||||
−0.450179 | + | 0.892938i | \(0.648640\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15042.5 | 0.480726 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 385.144 | 0.0122712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44951.9 | 1.42793 | 0.713963 | − | 0.700184i | \(-0.246899\pi\) | ||||
0.713963 | + | 0.700184i | \(0.246899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17940.0 | −0.568166 |
(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 | 1856.4.a.y.1.2 | 5 | ||
4.3 | odd | 2 | 1856.4.a.bb.1.4 | 5 | |||
8.3 | odd | 2 | 464.4.a.l.1.2 | 5 | |||
8.5 | even | 2 | 29.4.a.b.1.2 | ✓ | 5 | ||
24.5 | odd | 2 | 261.4.a.f.1.4 | 5 | |||
40.29 | even | 2 | 725.4.a.c.1.4 | 5 | |||
56.13 | odd | 2 | 1421.4.a.e.1.2 | 5 | |||
232.173 | even | 2 | 841.4.a.b.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.2 | ✓ | 5 | 8.5 | even | 2 | ||
261.4.a.f.1.4 | 5 | 24.5 | odd | 2 | |||
464.4.a.l.1.2 | 5 | 8.3 | odd | 2 | |||
725.4.a.c.1.4 | 5 | 40.29 | even | 2 | |||
841.4.a.b.1.4 | 5 | 232.173 | even | 2 | |||
1421.4.a.e.1.2 | 5 | 56.13 | odd | 2 | |||
1856.4.a.y.1.2 | 5 | 1.1 | even | 1 | trivial | ||
1856.4.a.bb.1.4 | 5 | 4.3 | odd | 2 |