Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | 12.8248 | 1.14708 | 0.573540 | − | 0.819177i | \(-0.305570\pi\) | ||||
0.573540 | + | 0.819177i | \(0.305570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.8248 | 1.00937 | 0.504685 | − | 0.863303i | \(-0.331608\pi\) | ||||
0.504685 | + | 0.863303i | \(0.331608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.1238 | −1.85875 | −0.929376 | − | 0.369134i | \(-0.879654\pi\) | ||||
−0.929376 | + | 0.369134i | \(0.879654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −38.4743 | −0.662267 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −102.598 | −1.46375 | −0.731873 | − | 0.681441i | \(-0.761353\pi\) | ||||
−0.731873 | + | 0.681441i | \(0.761353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 95.8248 | 1.15704 | 0.578519 | − | 0.815669i | \(-0.303631\pi\) | ||||
0.578519 | + | 0.815669i | \(0.303631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 96.0000 | 0.870321 | 0.435161 | − | 0.900353i | \(-0.356692\pi\) | ||||
0.435161 | + | 0.900353i | \(0.356692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 39.4743 | 0.315794 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −212.021 | −1.35763 | −0.678815 | − | 0.734309i | \(-0.737506\pi\) | ||||
−0.678815 | + | 0.734309i | \(0.737506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −159.248 | −0.922635 | −0.461318 | − | 0.887235i | \(-0.652623\pi\) | ||||
−0.461318 | + | 0.887235i | \(0.652623\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −110.474 | −0.582761 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 128.670 | 0.571710 | 0.285855 | − | 0.958273i | \(-0.407722\pi\) | ||||
0.285855 | + | 0.958273i | \(0.407722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 261.371 | 1.07315 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 298.042 | 1.13527 | 0.567637 | − | 0.823279i | \(-0.307858\pi\) | ||||
0.567637 | + | 0.823279i | \(0.307858\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.3297 | 0.118203 | 0.0591016 | − | 0.998252i | \(-0.481176\pi\) | ||||
0.0591016 | + | 0.998252i | \(0.481176\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 115.423 | 0.382360 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 271.196 | 0.841660 | 0.420830 | − | 0.907140i | \(-0.361739\pi\) | ||||
0.420830 | + | 0.907140i | \(0.361739\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 307.794 | 0.845094 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 448.268 | 1.16178 | 0.580890 | − | 0.813982i | \(-0.302704\pi\) | ||||
0.580890 | + | 0.813982i | \(0.302704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 472.268 | 1.15783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −287.474 | −0.668016 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −668.474 | −1.47505 | −0.737525 | − | 0.675320i | \(-0.764006\pi\) | ||||
−0.737525 | + | 0.675320i | \(0.764006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 243.691 | 0.511499 | 0.255750 | − | 0.966743i | \(-0.417678\pi\) | ||||
0.255750 | + | 0.966743i | \(0.417678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1117.34 | −2.13214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 335.577 | 0.611900 | 0.305950 | − | 0.952048i | \(-0.401026\pi\) | ||||
0.305950 | + | 0.952048i | \(0.401026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −288.000 | −0.502480 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 339.608 | 0.567663 | 0.283831 | − | 0.958874i | \(-0.408394\pi\) | ||||
0.283831 | + | 0.958874i | \(0.408394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 918.320 | 1.47235 | 0.736173 | − | 0.676794i | \(-0.236631\pi\) | ||||
0.736173 | + | 0.676794i | \(0.236631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −118.423 | −0.182324 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 136.299 | 0.194112 | 0.0970559 | − | 0.995279i | \(-0.469057\pi\) | ||||
0.0970559 | + | 0.995279i | \(0.469057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 287.464 | 0.380160 | 0.190080 | − | 0.981769i | \(-0.439125\pi\) | ||||
0.190080 | + | 0.981769i | \(0.439125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1315.79 | −1.67903 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 636.062 | 0.783828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −161.855 | −0.192771 | −0.0963856 | − | 0.995344i | \(-0.530728\pi\) | ||||
−0.0963856 | + | 0.995344i | \(0.530728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 477.743 | 0.532684 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1228.93 | 1.32721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −182.680 | −0.191220 | −0.0956101 | − | 0.995419i | \(-0.530480\pi\) | ||||
−0.0956101 | + | 0.995419i | \(0.530480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 331.423 | 0.336457 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1532.10 | 1.50941 | 0.754703 | − | 0.656067i | \(-0.227781\pi\) | ||||
0.754703 | + | 0.656067i | \(0.227781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 487.908 | 0.466747 | 0.233374 | − | 0.972387i | \(-0.425023\pi\) | ||||
0.233374 | + | 0.972387i | \(0.425023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −492.351 | −0.444836 | −0.222418 | − | 0.974951i | \(-0.571395\pi\) | ||||
−0.222418 | + | 0.974951i | \(0.571395\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 848.072 | 0.745235 | 0.372617 | − | 0.927985i | \(-0.378460\pi\) | ||||
0.372617 | + | 0.927985i | \(0.378460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −386.011 | −0.330077 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −736.350 | −0.613009 | −0.306505 | − | 0.951869i | \(-0.599159\pi\) | ||||
−0.306505 | + | 0.951869i | \(0.599159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1231.18 | 0.998328 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −784.114 | −0.619584 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.0623 | 0.0188297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −894.125 | −0.655451 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1096.85 | −0.784839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2511.37 | 1.75471 | 0.877355 | − | 0.479841i | \(-0.159306\pi\) | ||||
0.877355 | + | 0.479841i | \(0.159306\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −99.9892 | −0.0682446 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −679.423 | −0.453141 | −0.226570 | − | 0.973995i | \(-0.572751\pi\) | ||||
−0.226570 | + | 0.973995i | \(0.572751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −346.268 | −0.220756 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −164.537 | −0.102608 | −0.0513040 | − | 0.998683i | \(-0.516338\pi\) | ||||
−0.0513040 | + | 0.998683i | \(0.516338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −521.991 | −0.318523 | −0.159261 | − | 0.987236i | \(-0.550911\pi\) | ||||
−0.159261 | + | 0.987236i | \(0.550911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −813.588 | −0.485932 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3208.31 | −1.87617 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2719.11 | −1.55731 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2412.12 | −1.32623 | −0.663117 | − | 0.748516i | \(-0.730767\pi\) | ||||
−0.663117 | + | 0.748516i | \(0.730767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1574.58 | 0.848591 | 0.424296 | − | 0.905524i | \(-0.360522\pi\) | ||||
0.424296 | + | 0.905524i | \(0.360522\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −923.382 | −0.487915 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2042.31 | −1.05834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2078.74 | −1.05670 | −0.528349 | − | 0.849027i | \(-0.677189\pi\) | ||||
−0.528349 | + | 0.849027i | \(0.677189\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1344.80 | −0.670754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3179.43 | 1.52780 | 0.763901 | − | 0.645333i | \(-0.223281\pi\) | ||||
0.763901 | + | 0.645333i | \(0.223281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1416.80 | −0.668473 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2979.28 | −1.38050 | −0.690250 | − | 0.723571i | \(-0.742500\pi\) | ||||
−0.690250 | + | 0.723571i | \(0.742500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5393.55 | 2.45496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 862.423 | 0.385679 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.3704 | −0.00719431 | −0.00359716 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359716 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2005.42 | 0.851620 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2698.29 | −1.12670 | −0.563351 | − | 0.826218i | \(-0.690488\pi\) | ||||
−0.563351 | + | 0.826218i | \(0.690488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −31.3297 | −0.0128659 | −0.00643293 | − | 0.999979i | \(-0.502048\pi\) | ||||
−0.00643293 | + | 0.999979i | \(0.502048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −731.073 | −0.295314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1650.16 | 0.655797 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3778.15 | −1.47746 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1545.17 | 0.585366 | 0.292683 | − | 0.956210i | \(-0.405452\pi\) | ||||
0.292683 | + | 0.956210i | \(0.405452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1830.20 | −0.682593 | −0.341297 | − | 0.939956i | \(-0.610866\pi\) | ||||
−0.341297 | + | 0.939956i | \(0.610866\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3352.02 | 1.23099 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4728.45 | 1.71009 | 0.855047 | − | 0.518551i | \(-0.173528\pi\) | ||||
0.855047 | + | 0.518551i | \(0.173528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −328.249 | −0.116930 | −0.0584648 | − | 0.998289i | \(-0.518621\pi\) | ||||
−0.0584648 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1006.73 | −0.353280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3822.31 | 1.30225 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 864.000 | 0.290107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3528.72 | 1.16788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4935.76 | 1.61039 | 0.805193 | − | 0.593013i | \(-0.202062\pi\) | ||||
0.805193 | + | 0.593013i | \(0.202062\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1018.82 | −0.327740 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 427.445 | 0.135589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2754.96 | −0.850059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8938.72 | 2.72074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3446.00 | 1.03480 | 0.517402 | − | 0.855742i | \(-0.326899\pi\) | ||||
0.517402 | + | 0.855742i | \(0.326899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 355.268 | 0.105265 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5724.75 | 1.67385 | 0.836927 | − | 0.547315i | \(-0.184350\pi\) | ||||
0.836927 | + | 0.547315i | \(0.184350\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3017.15 | −0.870649 | −0.435325 | − | 0.900274i | \(-0.643366\pi\) | ||||
−0.435325 | + | 0.900274i | \(0.643366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 381.713 | 0.107325 | 0.0536627 | − | 0.998559i | \(-0.482910\pi\) | ||||
0.0536627 | + | 0.998559i | \(0.482910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3478.02 | 0.965452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −408.897 | −0.112071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1377.38 | 0.372785 | 0.186392 | − | 0.982475i | \(-0.440320\pi\) | ||||
0.186392 | + | 0.982475i | \(0.440320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5806.72 | −1.55205 | −0.776025 | − | 0.630702i | \(-0.782767\pi\) | ||||
−0.776025 | + | 0.630702i | \(0.782767\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8348.61 | −2.15065 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −862.393 | −0.219486 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4348.52 | −1.09353 | −0.546765 | − | 0.837286i | \(-0.684141\pi\) | ||||
−0.546765 | + | 0.837286i | \(0.684141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3535.18 | 0.878477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3947.38 | 0.969391 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4691.11 | 1.13861 | 0.569307 | − | 0.822125i | \(-0.307212\pi\) | ||||
0.569307 | + | 0.822125i | \(0.307212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1908.19 | −0.452543 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7581.61 | 1.77758 | 0.888788 | − | 0.458319i | \(-0.151548\pi\) | ||||
0.888788 | + | 0.458319i | \(0.151548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5748.93 | 1.33266 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 485.566 | 0.111297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3601.90 | 0.816400 | 0.408200 | − | 0.912893i | \(-0.366157\pi\) | ||||
0.408200 | + | 0.912893i | \(0.366157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3836.27 | −0.859914 | −0.429957 | − | 0.902849i | \(-0.641471\pi\) | ||||
−0.429957 | + | 0.902849i | \(0.641471\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1453.63 | 0.318753 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5403.04 | 1.17198 | 0.585988 | − | 0.810320i | \(-0.300706\pi\) | ||||
0.585988 | + | 0.810320i | \(0.300706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1433.23 | −0.307545 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 150.842 | 0.0320230 | 0.0160115 | − | 0.999872i | \(-0.494903\pi\) | ||||
0.0160115 | + | 0.999872i | \(0.494903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1817.14 | 0.381689 | 0.190844 | − | 0.981620i | \(-0.438877\pi\) | ||||
0.190844 | + | 0.981620i | \(0.438877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3686.79 | −0.766268 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5613.35 | 1.14255 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 548.041 | 0.110401 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2817.59 | 0.561792 | 0.280896 | − | 0.959738i | \(-0.409368\pi\) | ||||
0.280896 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8573.02 | −1.69200 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −994.268 | −0.194254 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8363.88 | −1.61771 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4596.31 | −0.871456 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3125.28 | 0.586731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8589.21 | 1.59678 | 0.798391 | − | 0.602139i | \(-0.205685\pi\) | ||||
0.798391 | + | 0.602139i | \(0.205685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1463.72 | −0.269477 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5998.29 | −1.09367 | −0.546836 | − | 0.837240i | \(-0.684168\pi\) | ||||
−0.546836 | + | 0.837240i | \(0.684168\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4963.27 | 0.896297 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3904.60 | −0.691812 | −0.345906 | − | 0.938269i | \(-0.612428\pi\) | ||||
−0.345906 | + | 0.938269i | \(0.612428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7807.61 | −1.37035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1477.05 | 0.256826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9831.43 | −1.69361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3439.15 | −0.586983 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2544.22 | −0.430262 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2449.73 | 0.406795 | 0.203397 | − | 0.979096i | \(-0.434802\pi\) | ||||
0.203397 | + | 0.979096i | \(0.434802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1158.03 | 0.190570 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4303.69 | 0.701898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1770.59 | −0.286203 | −0.143101 | − | 0.989708i | \(-0.545707\pi\) | ||||
−0.143101 | + | 0.989708i | \(0.545707\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2209.05 | 0.353921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5864.25 | −0.931281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3693.53 | −0.576385 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4034.72 | 0.624194 | 0.312097 | − | 0.950050i | \(-0.398969\pi\) | ||||
0.312097 | + | 0.950050i | \(0.398969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6791.53 | −1.04167 | −0.520834 | − | 0.853658i | \(-0.674379\pi\) | ||||
−0.520834 | + | 0.853658i | \(0.674379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2352.34 | 0.357717 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10156.8 | 1.53142 | 0.765712 | − | 0.643184i | \(-0.222387\pi\) | ||||
0.765712 | + | 0.643184i | \(0.222387\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4355.39 | 0.651155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12842.7 | 1.88806 | 0.944029 | − | 0.329861i | \(-0.107002\pi\) | ||||
0.944029 | + | 0.329861i | \(0.107002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2323.38 | 0.338735 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −75.1870 | −0.0108713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11777.2 | 1.68890 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1914.82 | −0.272350 | −0.136175 | − | 0.990685i | \(-0.543481\pi\) | ||||
−0.136175 | + | 0.990685i | \(0.543481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2682.37 | 0.378425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5714.86 | 0.793309 | 0.396654 | − | 0.917968i | \(-0.370171\pi\) | ||||
0.396654 | + | 0.917968i | \(0.370171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3290.54 | 0.453127 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18472.0 | 2.52350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11570.3 | 1.56815 | 0.784075 | − | 0.620666i | \(-0.213138\pi\) | ||||
0.784075 | + | 0.620666i | \(0.213138\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7534.12 | −1.01308 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6118.02 | 0.816231 | 0.408115 | − | 0.912930i | \(-0.366186\pi\) | ||||
0.408115 | + | 0.912930i | \(0.366186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 299.967 | 0.0394010 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3258.46 | −0.424705 | −0.212353 | − | 0.977193i | \(-0.568113\pi\) | ||||
−0.212353 | + | 0.977193i | \(0.568113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9849.41 | −1.27393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2038.27 | 0.261621 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1748.00 | 0.222662 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −723.926 | −0.0915184 | −0.0457592 | − | 0.998952i | \(-0.514571\pi\) | ||||
−0.0457592 | + | 0.998952i | \(0.514571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11029.8 | 1.37357 | 0.686787 | − | 0.726859i | \(-0.259021\pi\) | ||||
0.686787 | + | 0.726859i | \(0.259021\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13874.2 | 1.71495 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1038.80 | 0.127453 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4738.25 | 0.577067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2683.56 | −0.324434 | −0.162217 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162217 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 493.610 | 0.0592408 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3686.66 | 0.436075 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1565.97 | 0.183899 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10024.9 | 1.16885 | 0.584427 | − | 0.811446i | \(-0.301319\pi\) | ||||
0.584427 | + | 0.811446i | \(0.301319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5560.68 | −0.643731 | −0.321866 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321866 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2440.76 | 0.280553 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4049.98 | −0.462242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9624.93 | 1.08321 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11526.2 | −1.28816 | −0.644081 | − | 0.764957i | \(-0.722760\pi\) | ||||
−0.644081 | + | 0.764957i | \(0.722760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2228.79 | −0.247365 | −0.123683 | − | 0.992322i | \(-0.539470\pi\) | ||||
−0.123683 | + | 0.992322i | \(0.539470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8157.34 | 0.899114 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9199.18 | 1.00699 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4609.26 | 0.501112 | 0.250556 | − | 0.968102i | \(-0.419387\pi\) | ||||
0.250556 | + | 0.968102i | \(0.419387\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1063.32 | −0.114041 | −0.0570203 | − | 0.998373i | \(-0.518160\pi\) | ||||
−0.0570203 | + | 0.998373i | \(0.518160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2075.76 | −0.221124 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7236.37 | 0.765702 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12265.9 | −1.28923 | −0.644613 | − | 0.764509i | \(-0.722982\pi\) | ||||
−0.644613 | + | 0.764509i | \(0.722982\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10975.3 | 1.14591 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4723.73 | −0.489934 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17791.2 | −1.82109 | −0.910543 | − | 0.413415i | \(-0.864336\pi\) | ||||
−0.910543 | + | 0.413415i | \(0.864336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2770.15 | 0.281698 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15368.9 | −1.55272 | −0.776358 | − | 0.630293i | \(-0.782935\pi\) | ||||
−0.776358 | + | 0.630293i | \(0.782935\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4104.98 | 0.412040 | 0.206020 | − | 0.978548i | \(-0.433949\pi\) | ||||
0.206020 | + | 0.978548i | \(0.433949\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6126.93 | 0.611031 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3807.36 | 0.377267 | 0.188634 | − | 0.982048i | \(-0.439594\pi\) | ||||
0.188634 | + | 0.982048i | \(0.439594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6236.23 | 0.610085 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1227.36 | 0.119311 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3782.61 | 0.365385 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4034.41 | 0.387260 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9874.65 | 0.941930 | 0.470965 | − | 0.882152i | \(-0.343906\pi\) | ||||
0.470965 | + | 0.882152i | \(0.343906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11210.2 | −1.06267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2342.83 | −0.219345 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6763.72 | 0.629350 | 0.314675 | − | 0.949199i | \(-0.398104\pi\) | ||||
0.314675 | + | 0.949199i | \(0.398104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9538.28 | −0.882077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5574.29 | 0.512351 | 0.256175 | − | 0.966630i | \(-0.417538\pi\) | ||||
0.256175 | + | 0.966630i | \(0.417538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21752.9 | 1.98722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4250.41 | 0.385943 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5787.46 | −0.519203 | −0.259601 | − | 0.965716i | \(-0.583591\pi\) | ||||
−0.259601 | + | 0.965716i | \(0.583591\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8937.84 | 0.797032 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8296.10 | 0.735397 | 0.367699 | − | 0.929945i | \(-0.380146\pi\) | ||||
0.367699 | + | 0.929945i | \(0.380146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19648.8 | 1.73141 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16180.6 | −1.41737 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9760.38 | 0.849943 | 0.424972 | − | 0.905207i | \(-0.360284\pi\) | ||||
0.424972 | + | 0.905207i | \(0.360284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2587.27 | −0.222672 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6257.30 | 0.535397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9986.73 | 0.849547 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.1111 | 0.00415364 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6537.98 | 0.549778 | 0.274889 | − | 0.961476i | \(-0.411359\pi\) | ||||
0.274889 | + | 0.961476i | \(0.411359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10343.8 | −0.864826 | −0.432413 | − | 0.901676i | \(-0.642338\pi\) | ||||
−0.432413 | + | 0.901676i | \(0.642338\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16338.5 | 1.35050 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2951.00 | −0.242541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6016.27 | −0.491683 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25966.5 | −2.11020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6314.28 | −0.510262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8094.87 | 0.650502 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6843.19 | −0.543829 | −0.271915 | − | 0.962321i | \(-0.587657\pi\) | ||||
−0.271915 | + | 0.962321i | \(0.587657\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 93.9892 | 0.00742810 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10876.3 | 0.854844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18402.1 | 1.43842 | 0.719211 | − | 0.694791i | \(-0.244503\pi\) | ||||
0.719211 | + | 0.694791i | \(0.244503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2193.22 | 0.170500 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20316.8 | −1.57083 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4950.49 | −0.378625 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 646.478 | 0.0491780 | 0.0245890 | − | 0.999698i | \(-0.492172\pi\) | ||||
0.0245890 | + | 0.999698i | \(0.492172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2903.81 | −0.219710 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11334.4 | 0.853013 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6174.80 | 0.462232 | 0.231116 | − | 0.972926i | \(-0.425762\pi\) | ||||
0.231116 | + | 0.972926i | \(0.425762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9443.51 | −0.703171 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6837.17 | −0.503742 | −0.251871 | − | 0.967761i | \(-0.581046\pi\) | ||||
−0.251871 | + | 0.967761i | \(0.581046\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5885.54 | 0.431353 | 0.215676 | − | 0.976465i | \(-0.430804\pi\) | ||||
0.215676 | + | 0.976465i | \(0.430804\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4635.52 | −0.337961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3789.53 | 0.274842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12003.2 | 0.866033 | 0.433017 | − | 0.901386i | \(-0.357449\pi\) | ||||
0.433017 | + | 0.901386i | \(0.357449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5490.59 | 0.394095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16507.4 | 1.17267 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10056.1 | −0.710713 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12719.4 | −0.894358 | −0.447179 | − | 0.894445i | \(-0.647571\pi\) | ||||
−0.447179 | + | 0.894445i | \(0.647571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15259.9 | −1.06752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14185.4 | −0.987323 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19160.4 | −1.32685 | −0.663426 | − | 0.748242i | \(-0.730898\pi\) | ||||
−0.663426 | + | 0.748242i | \(0.730898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 984.748 | 0.0675093 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1067.97 | −0.0728479 | −0.0364240 | − | 0.999336i | \(-0.511597\pi\) | ||||
−0.0364240 | + | 0.999336i | \(0.511597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7554.96 | −0.512768 | −0.256384 | − | 0.966575i | \(-0.582531\pi\) | ||||
−0.256384 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3020.20 | 0.203967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 321.418 | 0.0215992 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11777.4 | −0.787529 | −0.393765 | − | 0.919211i | \(-0.628828\pi\) | ||||
−0.393765 | + | 0.919211i | \(0.628828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23627.6 | −1.56444 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26852.9 | 1.76930 | 0.884649 | − | 0.466258i | \(-0.154398\pi\) | ||||
0.884649 | + | 0.466258i | \(0.154398\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11466.9 | −0.751855 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6816.72 | −0.444782 | −0.222391 | − | 0.974958i | \(-0.571386\pi\) | ||||
−0.222391 | + | 0.974958i | \(0.571386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16713.5 | −1.08525 | −0.542627 | − | 0.839974i | \(-0.682570\pi\) | ||||
−0.542627 | + | 0.839974i | \(0.682570\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2592.00 | −0.167493 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19001.1 | −1.21607 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10586.2 | −0.674276 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13201.3 | −0.836838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −592.225 | −0.0373631 | −0.0186815 | − | 0.999825i | \(-0.505947\pi\) | ||||
−0.0186815 | + | 0.999825i | \(0.505947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14807.3 | −0.929757 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32207.7 | 2.01279 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3056.47 | 0.189221 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6963.91 | 0.429108 | 0.214554 | − | 0.976712i | \(-0.431170\pi\) | ||||
0.214554 | + | 0.976712i | \(0.431170\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5466.06 | 0.335242 | 0.167621 | − | 0.985852i | \(-0.446392\pi\) | ||||
0.167621 | + | 0.985852i | \(0.446392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1282.34 | −0.0782821 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1237.27 | −0.0751808 | −0.0375904 | − | 0.999293i | \(-0.511968\pi\) | ||||
−0.0375904 | + | 0.999293i | \(0.511968\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24616.4 | −1.48887 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27151.8 | 1.62716 | 0.813578 | − | 0.581455i | \(-0.197516\pi\) | ||||
0.813578 | + | 0.581455i | \(0.197516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8713.43 | −0.519789 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8264.88 | 0.490782 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5900.66 | −0.348797 | −0.174398 | − | 0.984675i | \(-0.555798\pi\) | ||||
−0.174398 | + | 0.984675i | \(0.555798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3618.98 | −0.212953 | −0.106477 | − | 0.994315i | \(-0.533957\pi\) | ||||
−0.106477 | + | 0.994315i | \(0.533957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26816.2 | −1.57082 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20354.0 | −1.18157 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10338.0 | −0.597445 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8973.86 | 0.516292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13952.5 | −0.799151 | −0.399576 | − | 0.916700i | \(-0.630842\pi\) | ||||
−0.399576 | + | 0.916700i | \(0.630842\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1065.80 | −0.0607746 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28918.9 | 1.64172 | 0.820859 | − | 0.571131i | \(-0.193495\pi\) | ||||
0.820859 | + | 0.571131i | \(0.193495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17174.2 | −0.966400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11130.1 | 0.623547 | 0.311773 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311773 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2110.14 | −0.117700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9051.44 | 0.502670 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39054.8 | −2.15946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14025.3 | −0.772137 | −0.386069 | − | 0.922470i | \(-0.626167\pi\) | ||||
−0.386069 | + | 0.922470i | \(0.626167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6694.40 | −0.365372 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30578.5 | −1.66175 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1145.14 | −0.0619644 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30366.7 | 1.63614 | 0.818070 | − | 0.575119i | \(-0.195044\pi\) | ||||
0.818070 | + | 0.575119i | \(0.195044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12329.8 | 0.661490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10434.1 | −0.557404 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16891.0 | 0.894716 | 0.447358 | − | 0.894355i | \(-0.352365\pi\) | ||||
0.447358 | + | 0.894355i | \(0.352365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1226.69 | 0.0647040 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15287.8 | −0.802989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41145.8 | −2.15212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4132.15 | −0.215227 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11007.2 | 0.570932 | 0.285466 | − | 0.958389i | \(-0.407852\pi\) | ||||
0.285466 | + | 0.958389i | \(0.407852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17420.2 | 0.896076 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8369.36 | −0.428731 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14618.0 | −0.745737 | −0.372869 | − | 0.927884i | \(-0.621626\pi\) | ||||
−0.372869 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3419.56 | −0.173019 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28522.2 | 1.43723 | 0.718617 | − | 0.695406i | \(-0.244775\pi\) | ||||
0.718617 | + | 0.695406i | \(0.244775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12357.5 | 0.617634 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20239.5 | −1.00747 | −0.503735 | − | 0.863858i | \(-0.668041\pi\) | ||||
−0.503735 | + | 0.863858i | \(0.668041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25045.8 | 1.24168 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13977.6 | −0.690159 | −0.345079 | − | 0.938573i | \(-0.612148\pi\) | ||||
−0.345079 | + | 0.938573i | \(0.612148\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30934.9 | −1.52130 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2587.18 | 0.126720 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15027.8 | −0.730190 | −0.365095 | − | 0.930970i | \(-0.618963\pi\) | ||||
−0.365095 | + | 0.930970i | \(0.618963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13045.6 | 0.631350 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20193.6 | 0.973403 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20769.4 | 0.997196 | 0.498598 | − | 0.866833i | \(-0.333848\pi\) | ||||
0.498598 | + | 0.866833i | \(0.333848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10605.5 | −0.507189 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11211.1 | −0.534039 | −0.267019 | − | 0.963691i | \(-0.586039\pi\) | ||||
−0.267019 | + | 0.963691i | \(0.586039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11842.1 | −0.559678 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58240.0 | 2.74175 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4305.86 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14073.3 | −0.657379 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16640.5 | −0.774277 | −0.387139 | − | 0.922022i | \(-0.626536\pi\) | ||||
−0.387139 | + | 0.922022i | \(0.626536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6286.18 | −0.291363 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28559.8 | 1.31356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12506.0 | 0.572982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5724.56 | 0.261276 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26659.4 | −1.21212 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9767.05 | −0.442386 | −0.221193 | − | 0.975230i | \(-0.570995\pi\) | ||||
−0.221193 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22744.8 | −1.02628 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21231.3 | −0.950750 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17246.8 | −0.769410 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23118.5 | −1.02748 | −0.513738 | − | 0.857947i | \(-0.671740\pi\) | ||||
−0.513738 | + | 0.857947i | \(0.671740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27824.2 | −1.23198 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1456.70 | −0.0642571 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33816.9 | 1.48614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10805.7 | −0.471349 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10460.7 | 0.454607 | 0.227304 | − | 0.973824i | \(-0.427009\pi\) | ||||
0.227304 | + | 0.973824i | \(0.427009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9167.55 | −0.396937 | −0.198469 | − | 0.980107i | \(-0.563597\pi\) | ||||
−0.198469 | + | 0.980107i | \(0.563597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11508.8 | 0.496472 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40775.3 | 1.75251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3193.81 | 0.136765 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28827.3 | 1.22543 | 0.612717 | − | 0.790303i | \(-0.290077\pi\) | ||||
0.612717 | + | 0.790303i | \(0.290077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42794.3 | −1.81254 | −0.906268 | − | 0.422704i | \(-0.861081\pi\) | ||||
−0.906268 | + | 0.422704i | \(0.861081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4360.89 | −0.184032 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6028.87 | 0.253500 | 0.126750 | − | 0.991935i | \(-0.459545\pi\) | ||||
0.126750 | + | 0.991935i | \(0.459545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19407.4 | 0.813085 | 0.406542 | − | 0.913632i | \(-0.366734\pi\) | ||||
0.406542 | + | 0.913632i | \(0.366734\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16209.1 | −0.676641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38208.5 | −1.58355 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4299.68 | 0.177561 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10599.5 | −0.436156 | −0.218078 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218078 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20563.8 | 0.843159 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −452.526 | −0.0184885 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 69170.9 | 2.81604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5451.43 | −0.220368 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12352.3 | 0.497571 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34766.1 | 1.39551 | 0.697754 | − | 0.716338i | \(-0.254183\pi\) | ||||
0.697754 | + | 0.716338i | \(0.254183\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11060.4 | 0.442405 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30004.0 | −1.19594 | −0.597968 | − | 0.801520i | \(-0.704025\pi\) | ||||
−0.597968 | + | 0.801520i | \(0.704025\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26130.6 | −1.03791 | −0.518955 | − | 0.854802i | \(-0.673679\pi\) | ||||
−0.518955 | + | 0.854802i | \(0.673679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44668.3 | −1.76191 | −0.880955 | − | 0.473201i | \(-0.843099\pi\) | ||||
−0.880955 | + | 0.473201i | \(0.843099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −209.946 | −0.00825245 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16840.1 | −0.659652 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5019.18 | 0.195931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29236.7 | −1.13737 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1644.12 | −0.0637401 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3678.56 | 0.141637 | 0.0708187 | − | 0.997489i | \(-0.477439\pi\) | ||||
0.0708187 | + | 0.997489i | \(0.477439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8452.76 | −0.324351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33443.6 | 1.27894 | 0.639468 | − | 0.768817i | \(-0.279154\pi\) | ||||
0.639468 | + | 0.768817i | \(0.279154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21095.4 | 0.803983 | 0.401991 | − | 0.915644i | \(-0.368318\pi\) | ||||
0.401991 | + | 0.915644i | \(0.368318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25719.0 | 0.976877 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14453.3 | 0.547119 | 0.273560 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273560 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2982.80 | 0.112152 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25987.3 | 0.973832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34604.9 | −1.29242 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25091.6 | 0.933986 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33763.8 | 1.25260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45991.4 | −1.70055 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −401.796 | −0.0147582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5204.09 | 0.190517 | 0.0952584 | − | 0.995453i | \(-0.469632\pi\) | ||||
0.0952584 | + | 0.995453i | \(0.469632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13788.9 | 0.503135 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31584.8 | −1.14868 | −0.574342 | − | 0.818616i | \(-0.694742\pi\) | ||||
−0.574342 | + | 0.818616i | \(0.694742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10585.8 | 0.383723 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9375.83 | −0.338749 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46630.6 | 1.67378 | 0.836889 | − | 0.547373i | \(-0.184372\pi\) | ||||
0.836889 | + | 0.547373i | \(0.184372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25767.6 | −0.921902 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29587.9 | −1.05514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5079.16 | 0.180543 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4391.17 | 0.155582 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38492.6 | 1.35942 | 0.679711 | − | 0.733480i | \(-0.262105\pi\) | ||||
0.679711 | + | 0.733480i | \(0.262105\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17994.9 | 0.631432 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48453.8 | −1.69477 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39893.8 | −1.39090 | −0.695450 | − | 0.718574i | \(-0.744795\pi\) | ||||
−0.695450 | + | 0.718574i | \(0.744795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14889.8 | −0.517477 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32630.7 | 1.13043 | 0.565213 | − | 0.824945i | \(-0.308794\pi\) | ||||
0.565213 | + | 0.824945i | \(0.308794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28612.0 | 0.988054 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30029.3 | −1.03043 | −0.515217 | − | 0.857060i | \(-0.672289\pi\) | ||||
−0.515217 | + | 0.857060i | \(0.672289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80007.5 | −2.73673 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11713.8 | 0.399418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34963.6 | −1.18844 | −0.594220 | − | 0.804303i | \(-0.702539\pi\) | ||||
−0.594220 | + | 0.804303i | \(0.702539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19816.5 | 0.671462 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23422.8 | 0.791173 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4431.23 | −0.148744 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4431.16 | −0.148279 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23471.8 | −0.782990 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20520.5 | −0.682414 | −0.341207 | − | 0.939988i | \(-0.610836\pi\) | ||||
−0.341207 | + | 0.939988i | \(0.610836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29494.3 | 0.977805 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39775.3 | 1.31457 | 0.657286 | − | 0.753641i | \(-0.271704\pi\) | ||||
0.657286 | + | 0.753641i | \(0.271704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10317.4 | 0.338895 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7172.04 | −0.234856 | −0.117428 | − | 0.993081i | \(-0.537465\pi\) | ||||
−0.117428 | + | 0.993081i | \(0.537465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5960.29 | −0.194578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7632.65 | 0.248412 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48348.3 | 1.56874 | 0.784369 | − | 0.620294i | \(-0.212987\pi\) | ||||
0.784369 | + | 0.620294i | \(0.212987\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 60641.2 | 1.96161 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3199.65 | 0.102875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36944.6 | −1.18424 | −0.592121 | − | 0.805849i | \(-0.701709\pi\) | ||||
−0.592121 | + | 0.805849i | \(0.701709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7349.18 | −0.234863 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4209.72 | −0.134128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56589.6 | −1.79760 | −0.898802 | − | 0.438355i | \(-0.855561\pi\) | ||||
−0.898802 | + | 0.438355i | \(0.855561\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3474.10 | −0.110026 |
(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 | 2352.4.a.bp.1.2 | 2 | ||
4.3 | odd | 2 | 588.4.a.h.1.2 | 2 | |||
7.3 | odd | 6 | 336.4.q.h.289.2 | 4 | |||
7.5 | odd | 6 | 336.4.q.h.193.2 | 4 | |||
7.6 | odd | 2 | 2352.4.a.cb.1.1 | 2 | |||
12.11 | even | 2 | 1764.4.a.p.1.1 | 2 | |||
28.3 | even | 6 | 84.4.i.b.37.2 | yes | 4 | ||
28.11 | odd | 6 | 588.4.i.i.373.1 | 4 | |||
28.19 | even | 6 | 84.4.i.b.25.2 | ✓ | 4 | ||
28.23 | odd | 6 | 588.4.i.i.361.1 | 4 | |||
28.27 | even | 2 | 588.4.a.g.1.1 | 2 | |||
84.11 | even | 6 | 1764.4.k.z.1549.2 | 4 | |||
84.23 | even | 6 | 1764.4.k.z.361.2 | 4 | |||
84.47 | odd | 6 | 252.4.k.d.109.1 | 4 | |||
84.59 | odd | 6 | 252.4.k.d.37.1 | 4 | |||
84.83 | odd | 2 | 1764.4.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.2 | ✓ | 4 | 28.19 | even | 6 | ||
84.4.i.b.37.2 | yes | 4 | 28.3 | even | 6 | ||
252.4.k.d.37.1 | 4 | 84.59 | odd | 6 | |||
252.4.k.d.109.1 | 4 | 84.47 | odd | 6 | |||
336.4.q.h.193.2 | 4 | 7.5 | odd | 6 | |||
336.4.q.h.289.2 | 4 | 7.3 | odd | 6 | |||
588.4.a.g.1.1 | 2 | 28.27 | even | 2 | |||
588.4.a.h.1.2 | 2 | 4.3 | odd | 2 | |||
588.4.i.i.361.1 | 4 | 28.23 | odd | 6 | |||
588.4.i.i.373.1 | 4 | 28.11 | odd | 6 | |||
1764.4.a.p.1.1 | 2 | 12.11 | even | 2 | |||
1764.4.a.x.1.2 | 2 | 84.83 | odd | 2 | |||
1764.4.k.z.361.2 | 4 | 84.23 | even | 6 | |||
1764.4.k.z.1549.2 | 4 | 84.11 | even | 6 | |||
2352.4.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.cb.1.1 | 2 | 7.6 | odd | 2 |