Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.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: | \(60.4179558459\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 36x^{8} + 405x^{6} - 1380x^{4} + 420x^{2} - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.357936\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-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 | ||||||||
\(3\) | −7.77277 | −1.49587 | −0.747935 | − | 0.663771i | \(-0.768955\pi\) | ||||
−0.747935 | + | 0.663771i | \(0.768955\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.59550 | 0.589919 | 0.294960 | − | 0.955510i | \(-0.404694\pi\) | ||||
0.294960 | + | 0.955510i | \(0.404694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.8965 | −1.34429 | −0.672143 | − | 0.740422i | \(-0.734626\pi\) | ||||
−0.672143 | + | 0.740422i | \(0.734626\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 33.4160 | 1.23763 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.5979 | −0.866103 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9402 | 0.340078 | 0.170039 | − | 0.985437i | \(-0.445611\pi\) | ||||
0.170039 | + | 0.985437i | \(0.445611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −51.2653 | −0.882443 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 88.4846 | 1.26239 | 0.631196 | − | 0.775623i | \(-0.282564\pi\) | ||||
0.631196 | + | 0.775623i | \(0.282564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.4838 | 0.645790 | 0.322895 | − | 0.946435i | \(-0.395344\pi\) | ||||
0.322895 | + | 0.946435i | \(0.395344\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 193.515 | 2.01088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.1224 | −0.436270 | −0.218135 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218135 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −81.4994 | −0.651995 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −49.8702 | −0.355464 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.7689 | 0.0945692 | 0.0472846 | − | 0.998881i | \(-0.484943\pi\) | ||||
0.0472846 | + | 0.998881i | \(0.484943\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 96.9578 | 0.561746 | 0.280873 | − | 0.959745i | \(-0.409376\pi\) | ||||
0.280873 | + | 0.959745i | \(0.409376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 245.604 | 1.29558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −164.205 | −0.793020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 230.911 | 1.02599 | 0.512994 | − | 0.858392i | \(-0.328536\pi\) | ||||
0.512994 | + | 0.858392i | \(0.328536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −123.899 | −0.508713 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.519 | −1.37326 | −0.686629 | − | 0.727008i | \(-0.740910\pi\) | ||||
−0.686629 | + | 0.727008i | \(0.740910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 141.774 | 0.502797 | 0.251398 | − | 0.967884i | \(-0.419110\pi\) | ||||
0.251398 | + | 0.967884i | \(0.419110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 220.395 | 0.730102 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 220.669 | 0.684849 | 0.342425 | − | 0.939545i | \(-0.388752\pi\) | ||||
0.342425 | + | 0.939545i | \(0.388752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 276.837 | 0.807104 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −687.771 | −1.88838 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −248.551 | −0.644172 | −0.322086 | − | 0.946710i | \(-0.604384\pi\) | ||||
−0.322086 | + | 0.946710i | \(0.604384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −208.404 | −0.510931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −415.717 | −0.966019 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 572.767 | 1.26386 | 0.631932 | − | 0.775024i | \(-0.282262\pi\) | ||||
0.631932 | + | 0.775024i | \(0.282262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 939.852 | 1.97272 | 0.986358 | − | 0.164614i | \(-0.0526377\pi\) | ||||
0.986358 | + | 0.164614i | \(0.0526377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −831.942 | −1.66373 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 105.133 | 0.200619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 151.854 | 0.276894 | 0.138447 | − | 0.990370i | \(-0.455789\pi\) | ||||
0.138447 | + | 0.990370i | \(0.455789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 374.045 | 0.652604 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 215.050 | 0.359461 | 0.179731 | − | 0.983716i | \(-0.442477\pi\) | ||||
0.179731 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −668.587 | −1.07195 | −0.535974 | − | 0.844235i | \(-0.680055\pi\) | ||||
−0.535974 | + | 0.844235i | \(0.680055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 633.476 | 0.975300 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 786.679 | 1.16429 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −822.956 | −1.17202 | −0.586012 | − | 0.810303i | \(-0.699303\pi\) | ||||
−0.586012 | + | 0.810303i | \(0.699303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −514.603 | −0.705902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 462.269 | 0.611332 | 0.305666 | − | 0.952139i | \(-0.401121\pi\) | ||||
0.305666 | + | 0.952139i | \(0.401121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 583.600 | 0.744710 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −114.795 | −0.141463 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 262.733 | 0.312918 | 0.156459 | − | 0.987684i | \(-0.449992\pi\) | ||||
0.156459 | + | 0.987684i | \(0.449992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −396.855 | −0.457162 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −753.631 | −0.840300 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 352.752 | 0.380964 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −150.801 | −0.157850 | −0.0789251 | − | 0.996881i | \(-0.525149\pi\) | ||||
−0.0789251 | + | 0.996881i | \(0.525149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1055.88 | −1.07192 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −690.115 | −0.679891 | −0.339945 | − | 0.940445i | \(-0.610409\pi\) | ||||
−0.339945 | + | 0.940445i | \(0.610409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1840.58 | −1.76075 | −0.880377 | − | 0.474275i | \(-0.842710\pi\) | ||||
−0.880377 | + | 0.474275i | \(0.842710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1276.33 | 1.18626 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 112.302 | 0.101464 | 0.0507322 | − | 0.998712i | \(-0.483845\pi\) | ||||
0.0507322 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1347.72 | −1.18429 | −0.592146 | − | 0.805831i | \(-0.701719\pi\) | ||||
−0.592146 | + | 0.805831i | \(0.701719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1794.82 | −1.53475 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 720.469 | 0.599788 | 0.299894 | − | 0.953973i | \(-0.403049\pi\) | ||||
0.299894 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −317.391 | −0.257364 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 532.657 | 0.420890 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2202.96 | −1.69702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −332.571 | −0.249865 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2802.23 | 2.05422 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1361.97 | −0.974544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2622.35 | −1.83225 | −0.916124 | − | 0.400895i | \(-0.868699\pi\) | ||||
−0.916124 | + | 0.400895i | \(0.868699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1101.97 | −0.752119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −929.950 | −0.620230 | −0.310115 | − | 0.950699i | \(-0.600368\pi\) | ||||
−0.310115 | + | 0.950699i | \(0.600368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1331.56 | −0.868127 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −328.919 | −0.209695 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2511.52 | 1.56623 | 0.783117 | − | 0.621874i | \(-0.213629\pi\) | ||||
0.783117 | + | 0.621874i | \(0.213629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1535.86 | 0.937195 | 0.468598 | − | 0.883412i | \(-0.344759\pi\) | ||||
0.468598 | + | 0.883412i | \(0.344759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1715.21 | −1.02445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −503.677 | −0.294543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 97.4080 | 0.0557882 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2151.79 | −1.20732 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3230.96 | −1.77645 | −0.888223 | − | 0.459413i | \(-0.848060\pi\) | ||||
−0.888223 | + | 0.459413i | \(0.848060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2814.39 | 1.51677 | 0.758383 | − | 0.651809i | \(-0.225990\pi\) | ||||
0.758383 | + | 0.651809i | \(0.225990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2956.80 | 1.56237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 639.485 | 0.331385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1281.71 | −0.651541 | −0.325770 | − | 0.945449i | \(-0.605624\pi\) | ||||
−0.325770 | + | 0.945449i | \(0.605624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1931.93 | 0.963598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1198.08 | 0.586472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1969.09 | −0.946204 | −0.473102 | − | 0.881008i | \(-0.656866\pi\) | ||||
−0.473102 | + | 0.881008i | \(0.656866\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1619.88 | 0.764287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1221.66 | −0.566075 | −0.283038 | − | 0.959109i | \(-0.591342\pi\) | ||||
−0.283038 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1942.91 | −0.884347 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1787.21 | 0.799249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 796.794 | 0.350168 | 0.175084 | − | 0.984553i | \(-0.443980\pi\) | ||||
0.175084 | + | 0.984553i | \(0.443980\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2029.05 | 0.876468 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4451.99 | −1.89058 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3114.42 | −1.30046 | −0.650230 | − | 0.759737i | \(-0.725328\pi\) | ||||
−0.650230 | + | 0.759737i | \(0.725328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 171.535 | 0.0704425 | 0.0352213 | − | 0.999380i | \(-0.488786\pi\) | ||||
0.0352213 | + | 0.999380i | \(0.488786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7305.26 | −2.95093 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1522.98 | 0.605251 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2795.93 | −1.09336 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1241.59 | 0.477845 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3927.65 | −1.48793 | −0.743966 | − | 0.668218i | \(-0.767058\pi\) | ||||
−0.743966 | + | 0.668218i | \(0.767058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3249.02 | −1.21176 | −0.605880 | − | 0.795556i | \(-0.707179\pi\) | ||||
−0.605880 | + | 0.795556i | \(0.707179\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −817.179 | −0.300099 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3423.68 | −1.23821 | −0.619103 | − | 0.785309i | \(-0.712504\pi\) | ||||
−0.619103 | + | 0.785309i | \(0.712504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1371.30 | 0.488488 | 0.244244 | − | 0.969714i | \(-0.421460\pi\) | ||||
0.244244 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1180.33 | −0.414198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −367.693 | −0.127128 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2377.80 | −0.810112 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1608.06 | −0.539941 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1689.98 | −0.559321 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2291.73 | −0.747721 | −0.373861 | − | 0.927485i | \(-0.621966\pi\) | ||||
−0.373861 | + | 0.927485i | \(0.621966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1671.54 | −0.537708 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 935.068 | 0.296610 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2413.91 | −0.755148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5196.77 | 1.60349 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1410.46 | 0.429312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 419.617 | 0.126007 | 0.0630036 | − | 0.998013i | \(-0.479932\pi\) | ||||
0.0630036 | + | 0.998013i | \(0.479932\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2723.38 | −0.806929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3017.42 | 0.882262 | 0.441131 | − | 0.897443i | \(-0.354577\pi\) | ||||
0.441131 | + | 0.897443i | \(0.354577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2226.56 | 0.642513 | 0.321256 | − | 0.946992i | \(-0.395895\pi\) | ||||
0.321256 | + | 0.946992i | \(0.395895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6114.67 | −1.74163 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1194.86 | 0.335957 | 0.167978 | − | 0.985791i | \(-0.446276\pi\) | ||||
0.167978 | + | 0.985791i | \(0.446276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1455.42 | 0.404006 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6396.65 | 1.75320 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4241.03 | −1.14782 | −0.573911 | − | 0.818917i | \(-0.694575\pi\) | ||||
−0.573911 | + | 0.818917i | \(0.694575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5571.19 | 1.48910 | 0.744548 | − | 0.667569i | \(-0.232665\pi\) | ||||
0.744548 | + | 0.667569i | \(0.232665\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5346.38 | 1.41140 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1825.88 | 0.476126 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 852.541 | 0.219619 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3593.11 | −0.914474 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −682.681 | −0.171675 | −0.0858375 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858375 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1520.57 | 0.377855 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4536.19 | −1.11399 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8093.12 | 1.96434 | 0.982169 | − | 0.188002i | \(-0.0602013\pi\) | ||||
0.982169 | + | 0.188002i | \(0.0602013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5748.89 | −1.37922 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 493.516 | 0.117042 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −410.300 | −0.0961984 | −0.0480992 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480992 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1639.32 | −0.380009 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2042.17 | −0.468085 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.75940 | 0.00153207 | 0.000766037 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000766037 | 1.00000i | \(0.499756\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2833.98 | −0.635247 | −0.317623 | − | 0.948217i | \(-0.602885\pi\) | ||||
−0.317623 | + | 0.948217i | \(0.602885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3084.67 | 0.683855 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2575.21 | 0.564695 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2157.81 | 0.468052 | 0.234026 | − | 0.972230i | \(-0.424810\pi\) | ||||
0.234026 | + | 0.972230i | \(0.424810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3239.94 | 0.695234 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4750.23 | −1.00845 | −0.504226 | − | 0.863572i | \(-0.668222\pi\) | ||||
−0.504226 | + | 0.863572i | \(0.668222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 910.900 | 0.191334 | 0.0956668 | − | 0.995413i | \(-0.469502\pi\) | ||||
0.0956668 | + | 0.995413i | \(0.469502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2741.86 | −0.569873 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8975.67 | 1.84605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2916.53 | 0.593635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1172.14 | 0.236124 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2026.80 | 0.404119 | 0.202060 | − | 0.979373i | \(-0.435237\pi\) | ||||
0.202060 | + | 0.979373i | \(0.435237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3777.69 | 0.745578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1575.79 | 0.307868 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −767.080 | −0.148366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3529.67 | −0.675903 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5364.10 | 1.01703 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6198.79 | 1.16374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −326.981 | −0.0607877 | −0.0303938 | − | 0.999538i | \(-0.509676\pi\) | ||||
−0.0303938 | + | 0.999538i | \(0.509676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14306.4 | 2.63386 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −871.410 | −0.158885 | −0.0794423 | − | 0.996839i | \(-0.525314\pi\) | ||||
−0.0794423 | + | 0.996839i | \(0.525314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3515.02 | 0.634762 | 0.317381 | − | 0.948298i | \(-0.397197\pi\) | ||||
0.317381 | + | 0.948298i | \(0.397197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5487.07 | −0.981465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6680.42 | 1.18363 | 0.591814 | − | 0.806075i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −466.665 | −0.0819067 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −872.901 | −0.151778 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4732.49 | 0.815241 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1299.12 | −0.221729 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10475.5 | 1.77155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5493.90 | −0.920633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2574.24 | 0.427471 | 0.213736 | − | 0.976892i | \(-0.431437\pi\) | ||||
0.213736 | + | 0.976892i | \(0.431437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7716.13 | 1.26979 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1001.55 | 0.163345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −74.0970 | −0.0119772 | −0.00598861 | − | 0.999982i | \(-0.501906\pi\) | ||||
−0.00598861 | + | 0.999982i | \(0.501906\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5600.04 | −0.897205 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3063.67 | −0.486530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1647.24 | 0.259307 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2467.01 | 0.384984 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2973.72 | 0.460050 | 0.230025 | − | 0.973185i | \(-0.426119\pi\) | ||||
0.230025 | + | 0.973185i | \(0.426119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9351.98 | −1.43438 | −0.717192 | − | 0.696875i | \(-0.754573\pi\) | ||||
−0.717192 | + | 0.696875i | \(0.754573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −794.940 | −0.120885 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2216.90 | 0.334259 | 0.167130 | − | 0.985935i | \(-0.446550\pi\) | ||||
0.167130 | + | 0.985935i | \(0.446550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1418.36 | 0.212053 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17123.1 | 2.53852 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2082.23 | −0.306117 | −0.153059 | − | 0.988217i | \(-0.548912\pi\) | ||||
−0.153059 | + | 0.988217i | \(0.548912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3998.49 | −0.582955 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2585.00 | 0.373766 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4409.66 | −0.632362 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4509.22 | 0.641360 | 0.320680 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320680 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12047.1 | −1.69959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6188.05 | 0.865951 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12249.3 | −1.70039 | −0.850194 | − | 0.526470i | \(-0.823515\pi\) | ||||
−0.850194 | + | 0.526470i | \(0.823515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10586.3 | 1.45779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 235.418 | 0.0321609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4981.51 | 0.675153 | 0.337576 | − | 0.941298i | \(-0.390393\pi\) | ||||
0.337576 | + | 0.941298i | \(0.390393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20382.9 | 2.74081 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3044.88 | −0.406229 | −0.203115 | − | 0.979155i | \(-0.565106\pi\) | ||||
−0.203115 | + | 0.979155i | \(0.565106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5188.54 | 0.686837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4737.51 | 0.622277 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2733.30 | −0.356256 | −0.178128 | − | 0.984007i | \(-0.557004\pi\) | ||||
−0.178128 | + | 0.984007i | \(0.557004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4258.09 | −0.550744 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7228.29 | 0.927784 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5427.81 | −0.691399 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 950.997 | 0.120225 | 0.0601123 | − | 0.998192i | \(-0.480854\pi\) | ||||
0.0601123 | + | 0.998192i | \(0.480854\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10349.9 | 1.29861 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7606.74 | 0.947288 | 0.473644 | − | 0.880716i | \(-0.342938\pi\) | ||||
0.473644 | + | 0.880716i | \(0.342938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1545.53 | 0.191037 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3394.06 | −0.416425 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7296.32 | −0.888612 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4981.58 | −0.602257 | −0.301129 | − | 0.953584i | \(-0.597363\pi\) | ||||
−0.301129 | + | 0.953584i | \(0.597363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19521.5 | −2.34288 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14259.9 | −1.69899 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3048.89 | 0.360637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11937.9 | −1.40192 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4855.53 | 0.566129 | 0.283065 | − | 0.959101i | \(-0.408649\pi\) | ||||
0.283065 | + | 0.959101i | \(0.408649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11276.5 | −1.30543 | −0.652714 | − | 0.757604i | \(-0.726370\pi\) | ||||
−0.652714 | + | 0.757604i | \(0.726370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7373.88 | 0.847590 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7211.44 | −0.823074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23399.0 | −2.65189 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3914.97 | 0.440598 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4800.16 | 0.536463 | 0.268232 | − | 0.963354i | \(-0.413561\pi\) | ||||
0.268232 | + | 0.963354i | \(0.413561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6242.32 | −0.692810 | −0.346405 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346405 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −757.130 | −0.0834520 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2573.77 | −0.281739 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4929.27 | −0.535903 | −0.267951 | − | 0.963432i | \(-0.586347\pi\) | ||||
−0.267951 | + | 0.963432i | \(0.586347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9250.77 | 0.998896 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10848.0 | −1.16344 | −0.581718 | − | 0.813390i | \(-0.697619\pi\) | ||||
−0.581718 | + | 0.813390i | \(0.697619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1732.86 | 0.184596 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25113.5 | 2.65733 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11515.2 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11391.7 | 1.18938 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21875.6 | −2.26889 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2617.46 | −0.269689 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4829.89 | 0.494383 | 0.247191 | − | 0.968967i | \(-0.420492\pi\) | ||||
0.247191 | + | 0.968967i | \(0.420492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4412.74 | −0.448735 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11689.6 | −1.18100 | −0.590498 | − | 0.807039i | \(-0.701069\pi\) | ||||
−0.590498 | + | 0.807039i | \(0.701069\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5043.86 | −0.506281 | −0.253141 | − | 0.967430i | \(-0.581464\pi\) | ||||
−0.253141 | + | 0.967430i | \(0.581464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4970.57 | −0.495709 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17591.1 | 1.74308 | 0.871542 | − | 0.490321i | \(-0.163120\pi\) | ||||
0.871542 | + | 0.490321i | \(0.163120\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3780.63 | −0.372225 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9962.47 | 0.974621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4479.75 | −0.435474 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4358.89 | −0.421052 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8305.58 | −0.797246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13059.7 | −1.24575 | −0.622875 | − | 0.782321i | \(-0.714036\pi\) | ||||
−0.622875 | + | 0.782321i | \(0.714036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3680.77 | 0.348916 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9312.41 | −0.877286 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −994.605 | −0.0931189 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15549.3 | 1.44683 | 0.723414 | − | 0.690414i | \(-0.242572\pi\) | ||||
0.723414 | + | 0.690414i | \(0.242572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15305.3 | 1.41540 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12202.3 | 1.12155 | 0.560777 | − | 0.827967i | \(-0.310503\pi\) | ||||
0.560777 | + | 0.827967i | \(0.310503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1306.82 | 0.119383 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6964.03 | −0.632344 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5354.00 | −0.483219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2450.01 | 0.219794 | 0.109897 | − | 0.993943i | \(-0.464948\pi\) | ||||
0.109897 | + | 0.993943i | \(0.464948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9495.65 | 0.846775 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16579.6 | 1.46968 | 0.734839 | − | 0.678241i | \(-0.237258\pi\) | ||||
0.734839 | + | 0.678241i | \(0.237258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4551.65 | −0.401081 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15101.8 | 1.32287 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11074.6 | −0.964387 | −0.482193 | − | 0.876065i | \(-0.660160\pi\) | ||||
−0.482193 | + | 0.876065i | \(0.660160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16645.5 | 1.44100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2667.24 | −0.229555 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12139.5 | −1.03870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6972.69 | −0.593150 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6193.30 | −0.523807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3400.02 | −0.285907 | −0.142953 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142953 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2856.01 | 0.238785 | 0.119393 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119393 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −15771.4 | −1.31108 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8579.28 | 0.709144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9851.23 | −0.809668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19139.6 | 1.56420 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5746.74 | −0.467015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 740.691 | 0.0598558 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24207.7 | 1.94532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8747.47 | −0.699035 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18996.6 | −1.50966 | −0.754829 | − | 0.655921i | \(-0.772280\pi\) | ||||
−0.754829 | + | 0.655921i | \(0.772280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1333.30 | −0.105373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8888.86 | −0.698637 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7603.46 | 0.594333 | 0.297167 | − | 0.954826i | \(-0.403958\pi\) | ||||
0.297167 | + | 0.954826i | \(0.403958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31406.1 | 2.44149 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 789.894 | 0.0610719 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20488.7 | 1.57553 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11837.7 | −0.905377 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2936.30 | 0.223367 | 0.111683 | − | 0.993744i | \(-0.464376\pi\) | ||||
0.111683 | + | 0.993744i | \(0.464376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2259.90 | 0.170990 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21732.1 | 1.63553 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23536.9 | −1.76192 | −0.880961 | − | 0.473188i | \(-0.843103\pi\) | ||||
−0.880961 | + | 0.473188i | \(0.843103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4751.85 | 0.353826 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12811.8 | 0.948934 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5659.60 | −0.416982 | −0.208491 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208491 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6891.00 | 0.505043 | 0.252521 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252521 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30528.8 | 2.22575 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3921.95 | 0.284446 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10652.2 | 0.768556 | 0.384278 | − | 0.923217i | \(-0.374450\pi\) | ||||
0.384278 | + | 0.923217i | \(0.374450\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25253.9 | 1.81264 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11508.9 | −0.821805 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7853.69 | 0.557919 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3513.14 | 0.248291 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14006.3 | −0.984841 | −0.492421 | − | 0.870357i | \(-0.663888\pi\) | ||||
−0.492421 | + | 0.870357i | \(0.663888\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5185.67 | 0.362770 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26611.5 | 1.85220 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3528.04 | 0.244316 | 0.122158 | − | 0.992511i | \(-0.461019\pi\) | ||||
0.122158 | + | 0.992511i | \(0.461019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14529.6 | −1.00110 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10658.8 | −0.730715 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19024.9 | −1.29772 | −0.648861 | − | 0.760907i | \(-0.724754\pi\) | ||||
−0.648861 | + | 0.760907i | \(0.724754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1065.92 | −0.0723460 | −0.0361730 | − | 0.999346i | \(-0.511517\pi\) | ||||
−0.0361730 | + | 0.999346i | \(0.511517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5074.35 | 0.342692 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2193.47 | −0.147400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12909.7 | −0.863242 | −0.431621 | − | 0.902055i | \(-0.642058\pi\) | ||||
−0.431621 | + | 0.902055i | \(0.642058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2858.00 | 0.190167 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3517.51 | 0.232902 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12393.3 | 0.816578 | 0.408289 | − | 0.912853i | \(-0.366126\pi\) | ||||
0.408289 | + | 0.912853i | \(0.366126\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18482.1 | 1.21182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18921.2 | −1.23459 | −0.617293 | − | 0.786733i | \(-0.711771\pi\) | ||||
−0.617293 | + | 0.786733i | \(0.711771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21378.2 | 1.38814 | 0.694072 | − | 0.719906i | \(-0.255815\pi\) | ||||
0.694072 | + | 0.719906i | \(0.255815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2399.87 | 0.155078 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6541.15 | −0.420651 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1204.57 | 0.0770926 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13135.8 | 0.836672 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20432.1 | 1.29520 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9602.80 | 0.605834 | 0.302917 | − | 0.953017i | \(-0.402039\pi\) | ||||
0.302917 | + | 0.953017i | \(0.402039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17813.1 | 1.11849 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17295.7 | −1.08088 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4412.83 | 0.274478 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7186.12 | 0.444880 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4450.84 | 0.274256 | 0.137128 | − | 0.990553i | \(-0.456213\pi\) | ||||
0.137128 | + | 0.990553i | \(0.456213\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9180.04 | −0.563026 | −0.281513 | − | 0.959557i | \(-0.590836\pi\) | ||||
−0.281513 | + | 0.959557i | \(0.590836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7268.07 | −0.443690 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5546.17 | −0.337005 | −0.168503 | − | 0.985701i | \(-0.553893\pi\) | ||||
−0.168503 | + | 0.985701i | \(0.553893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18098.3 | −1.09464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18762.8 | 1.12960 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8948.56 | −0.536270 | −0.268135 | − | 0.963381i | \(-0.586407\pi\) | ||||
−0.268135 | + | 0.963381i | \(0.586407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6133.49 | −0.365886 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22341.5 | −1.32667 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21404.4 | 1.26525 | 0.632623 | − | 0.774460i | \(-0.281978\pi\) | ||||
0.632623 | + | 0.774460i | \(0.281978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33177.6 | −1.95228 | −0.976140 | − | 0.217140i | \(-0.930327\pi\) | ||||
−0.976140 | + | 0.217140i | \(0.930327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10963.2 | −0.642195 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8782.30 | −0.512125 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −710.713 | −0.0412577 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3261.59 | −0.188491 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29697.4 | −1.70858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30638.5 | 1.75487 | 0.877436 | − | 0.479694i | \(-0.159252\pi\) | ||||
0.877436 | + | 0.479694i | \(0.159252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4064.39 | 0.231760 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17633.7 | 1.00106 | 0.500529 | − | 0.865720i | \(-0.333139\pi\) | ||||
0.500529 | + | 0.865720i | \(0.333139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3754.41 | 0.212196 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23453.8 | −1.31975 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19570.6 | −1.09641 | −0.548206 | − | 0.836344i | \(-0.684689\pi\) | ||||
−0.548206 | + | 0.836344i | \(0.684689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16564.8 | 0.923952 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17306.6 | −0.961116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3961.95 | −0.219068 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −149.923 | −0.00825375 | −0.00412688 | − | 0.999991i | \(-0.501314\pi\) | ||||
−0.00412688 | + | 0.999991i | \(0.501314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26287.7 | 1.44096 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10129.8 | 0.552870 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31900.4 | −1.73359 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9287.38 | −0.502548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11086.5 | 0.597335 | 0.298667 | − | 0.954357i | \(-0.403458\pi\) | ||||
0.298667 | + | 0.954357i | \(0.403458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12350.0 | 0.662574 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11312.7 | −0.604341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17181.5 | 0.913968 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3858.40 | −0.204380 | −0.102190 | − | 0.994765i | \(-0.532585\pi\) | ||||
−0.102190 | + | 0.994765i | \(0.532585\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27499.9 | −1.45053 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4665.84 | −0.245073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3322.00 | −0.173756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32964.6 | 1.71699 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32717.8 | −1.69704 | −0.848519 | − | 0.529166i | \(-0.822505\pi\) | ||||
−0.848519 | + | 0.529166i | \(0.822505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45824.0 | 2.36696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43303.6 | −2.22750 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1203.65 | −0.0616587 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25847.2 | −1.31859 | −0.659297 | − | 0.751883i | \(-0.729146\pi\) | ||||
−0.659297 | + | 0.751883i | \(0.729146\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27662.0 | −1.40537 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12544.8 | 0.634727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14328.7 | 0.722023 | 0.361011 | − | 0.932561i | \(-0.382432\pi\) | ||||
0.361011 | + | 0.932561i | \(0.382432\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14192.1 | −0.712223 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4798.27 | −0.239819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27101.5 | −1.34905 | −0.674524 | − | 0.738253i | \(-0.735651\pi\) | ||||
−0.674524 | + | 0.738253i | \(0.735651\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6626.61 | −0.328522 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23322.1 | −1.15155 | −0.575777 | − | 0.817607i | \(-0.695301\pi\) | ||||
−0.575777 | + | 0.817607i | \(0.695301\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21309.8 | −1.04796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15447.2 | 0.756603 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2795.94 | −0.136397 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25994.0 | 1.26303 | 0.631515 | − | 0.775364i | \(-0.282434\pi\) | ||||
0.631515 | + | 0.775364i | \(0.282434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5306.32 | 0.256804 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18562.3 | 0.894770 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31317.8 | 1.50365 | 0.751825 | − | 0.659363i | \(-0.229174\pi\) | ||||
0.751825 | + | 0.659363i | \(0.229174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11819.0 | −0.565222 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16497.5 | −0.785853 | −0.392926 | − | 0.919570i | \(-0.628537\pi\) | ||||
−0.392926 | + | 0.919570i | \(0.628537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33553.4 | 1.59203 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19501.6 | 0.921675 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9130.02 | 0.429812 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24867.3 | −1.16611 | −0.583055 | − | 0.812433i | \(-0.698143\pi\) | ||||
−0.583055 | + | 0.812433i | \(0.698143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62905.9 | −2.93839 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2661.15 | −0.123823 | −0.0619114 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619114 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7902.00 | −0.366256 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44684.8 | 2.06314 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19281.9 | −0.886837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6795.14 | −0.311331 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −736.525 | −0.0336159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8453.54 | −0.384356 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11018.1 | −0.499049 | −0.249524 | − | 0.968369i | \(-0.580274\pi\) | ||||
−0.249524 | + | 0.968369i | \(0.580274\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3189.17 | 0.143900 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17937.2 | −0.806286 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14981.4 | 0.670877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12742.0 | 0.568445 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5953.61 | −0.264602 | −0.132301 | − | 0.991210i | \(-0.542237\pi\) | ||||
−0.132301 | + | 0.991210i | \(0.542237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19525.8 | 0.864549 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8779.50 | 0.387276 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21126.0 | 0.928417 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7901.94 | 0.345971 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −52.5393 | −0.00229178 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27554.3 | 1.19747 | 0.598737 | − | 0.800946i | \(-0.295670\pi\) | ||||
0.598737 | + | 0.800946i | \(0.295670\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4817.57 | −0.208592 | −0.104296 | − | 0.994546i | \(-0.533259\pi\) | ||||
−0.104296 | + | 0.994546i | \(0.533259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22027.9 | 0.950247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12987.1 | −0.558184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7582.59 | 0.324701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13261.3 | −0.565797 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13914.6 | −0.591504 | −0.295752 | − | 0.955265i | \(-0.595570\pi\) | ||||
−0.295752 | + | 0.955265i | \(0.595570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36653.5 | 1.55244 | 0.776221 | − | 0.630461i | \(-0.217134\pi\) | ||||
0.776221 | + | 0.630461i | \(0.217134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20016.5 | −0.844711 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31428.3 | −1.32149 | −0.660743 | − | 0.750612i | \(-0.729759\pi\) | ||||
−0.660743 | + | 0.750612i | \(0.729759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20810.9 | 0.871885 | 0.435942 | − | 0.899975i | \(-0.356415\pi\) | ||||
0.435942 | + | 0.899975i | \(0.356415\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16772.2 | −0.700145 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24495.8 | 1.01888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8057.43 | −0.333939 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4835.30 | −0.199680 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11010.0 | −0.453050 | −0.226525 | − | 0.974005i | \(-0.572737\pi\) | ||||
−0.226525 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24170.9 | −0.991057 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36922.5 | 1.50852 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12814.5 | −0.521694 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8279.85 | 0.335890 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7080.22 | −0.286210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11112.0 | −0.447608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18116.0 | 0.727175 | 0.363587 | − | 0.931560i | \(-0.381552\pi\) | ||||
0.363587 | + | 0.931560i | \(0.381552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11787.6 | 0.471493 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38510.8 | 1.53501 | 0.767505 | − | 0.641043i | \(-0.221498\pi\) | ||||
0.767505 | + | 0.641043i | \(0.221498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32858.7 | 1.30515 | 0.652576 | − | 0.757723i | \(-0.273688\pi\) | ||||
0.652576 | + | 0.757723i | \(0.273688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −69765.8 | −2.76146 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22079.5 | 0.870911 | 0.435456 | − | 0.900210i | \(-0.356587\pi\) | ||||
0.435456 | + | 0.900210i | \(0.356587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5255.26 | 0.206571 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22669.5 | −0.888001 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26003.7 | 1.01509 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2420.58 | 0.0941656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5039.15 | −0.195360 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33908.2 | 1.31007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5773.00 | −0.222281 | −0.111140 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111140 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15753.9 | −0.604510 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7132.59 | −0.272762 | −0.136381 | − | 0.990656i | \(-0.543547\pi\) | ||||
−0.136381 | + | 0.990656i | \(0.543547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27110.4 | 1.03323 | 0.516613 | − | 0.856219i | \(-0.327193\pi\) | ||||
0.516613 | + | 0.856219i | \(0.327193\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29363.1 | −1.11529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45045.7 | −1.70517 | −0.852585 | − | 0.522589i | \(-0.824966\pi\) | ||||
−0.852585 | + | 0.522589i | \(0.824966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 65287.3 | 2.46306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16260.4 | 0.611384 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11802.2 | 0.442269 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20541.1 | −0.767167 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5962.34 | 0.221936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1431.96 | 0.0531239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21992.9 | −0.813197 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27435.3 | 1.01106 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1131.36 | 0.0415554 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47599.9 | 1.74259 | 0.871295 | − | 0.490760i | \(-0.163281\pi\) | ||||
0.871295 | + | 0.490760i | \(0.163281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23060.9 | −0.841453 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42503.8 | −1.54579 | −0.772895 | − | 0.634534i | \(-0.781192\pi\) | ||||
−0.772895 | + | 0.634534i | \(0.781192\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14606.7 | −0.529477 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −48181.8 | −1.74081 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23152.5 | 0.833766 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8819.41 | −0.316568 | −0.158284 | − | 0.987394i | \(-0.550596\pi\) | ||||
−0.158284 | + | 0.987394i | \(0.550596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2541.55 | 0.0909305 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3427.94 | 0.122245 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18819.1 | −0.668940 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −61504.8 | −2.17916 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14155.6 | −0.499925 | −0.249963 | − | 0.968256i | \(-0.580418\pi\) | ||||
−0.249963 | + | 0.968256i | \(0.580418\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14806.3 | 0.521220 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6773.27 | 0.237671 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18440.6 | −0.644996 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38518.7 | 1.34296 | 0.671479 | − | 0.741023i | \(-0.265659\pi\) | ||||
0.671479 | + | 0.741023i | \(0.265659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27321.4 | −0.949523 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39595.4 | −1.37170 | −0.685852 | − | 0.727741i | \(-0.740570\pi\) | ||||
−0.685852 | + | 0.727741i | \(0.740570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17349.0 | 0.599112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8188.93 | 0.281890 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46442.1 | −1.59363 | −0.796814 | − | 0.604225i | \(-0.793483\pi\) | ||||
−0.796814 | + | 0.604225i | \(0.793483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10657.4 | −0.364545 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51925.4 | −1.77055 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20600.1 | −0.700211 | −0.350106 | − | 0.936710i | \(-0.613854\pi\) | ||||
−0.350106 | + | 0.936710i | \(0.613854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25904.8 | −0.877760 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3627.28 | 0.122522 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −62528.2 | −2.10547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20390.2 | −0.684441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3752.70 | 0.125575 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21428.9 | −0.714841 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38210.9 | −1.27071 | −0.635356 | − | 0.772219i | \(-0.719147\pi\) | ||||
−0.635356 | + | 0.772219i | \(0.719147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36784.6 | −1.21950 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52643.9 | −1.73988 | −0.869941 | − | 0.493157i | \(-0.835843\pi\) | ||||
−0.869941 | + | 0.493157i | \(0.835843\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38237.6 | −1.25986 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10097.7 | 0.331678 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7985.95 | −0.261508 | −0.130754 | − | 0.991415i | \(-0.541740\pi\) | ||||
−0.130754 | + | 0.991415i | \(0.541740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8301.83 | −0.271019 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45035.3 | −1.46571 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10703.1 | −0.347279 | −0.173639 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173639 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22580.9 | −0.730442 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42702.8 | 1.37715 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6822.49 | −0.219355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23945.4 | 0.767558 | 0.383779 | − | 0.923425i | \(-0.374623\pi\) | ||||
0.383779 | + | 0.923425i | \(0.374623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20009.0 | −0.639442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9044.42 | 0.288168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20212.7 | 0.642068 | 0.321034 | − | 0.947068i | \(-0.395970\pi\) | ||||
0.321034 | + | 0.947068i | \(0.395970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11515.6 | −0.364702 |
(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 | 1024.4.a.m.1.2 | 10 | ||
4.3 | odd | 2 | 1024.4.a.n.1.9 | 10 | |||
8.3 | odd | 2 | 1024.4.a.n.1.2 | 10 | |||
8.5 | even | 2 | inner | 1024.4.a.m.1.9 | 10 | ||
16.3 | odd | 4 | 1024.4.b.j.513.9 | 10 | |||
16.5 | even | 4 | 1024.4.b.k.513.9 | 10 | |||
16.11 | odd | 4 | 1024.4.b.j.513.2 | 10 | |||
16.13 | even | 4 | 1024.4.b.k.513.2 | 10 | |||
32.3 | odd | 8 | 16.4.e.a.13.1 | yes | 10 | ||
32.5 | even | 8 | 128.4.e.a.97.5 | 10 | |||
32.11 | odd | 8 | 16.4.e.a.5.1 | ✓ | 10 | ||
32.13 | even | 8 | 128.4.e.a.33.5 | 10 | |||
32.19 | odd | 8 | 128.4.e.b.33.1 | 10 | |||
32.21 | even | 8 | 64.4.e.a.49.1 | 10 | |||
32.27 | odd | 8 | 128.4.e.b.97.1 | 10 | |||
32.29 | even | 8 | 64.4.e.a.17.1 | 10 | |||
96.11 | even | 8 | 144.4.k.a.37.5 | 10 | |||
96.29 | odd | 8 | 576.4.k.a.145.4 | 10 | |||
96.35 | even | 8 | 144.4.k.a.109.5 | 10 | |||
96.53 | odd | 8 | 576.4.k.a.433.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.1 | ✓ | 10 | 32.11 | odd | 8 | ||
16.4.e.a.13.1 | yes | 10 | 32.3 | odd | 8 | ||
64.4.e.a.17.1 | 10 | 32.29 | even | 8 | |||
64.4.e.a.49.1 | 10 | 32.21 | even | 8 | |||
128.4.e.a.33.5 | 10 | 32.13 | even | 8 | |||
128.4.e.a.97.5 | 10 | 32.5 | even | 8 | |||
128.4.e.b.33.1 | 10 | 32.19 | odd | 8 | |||
128.4.e.b.97.1 | 10 | 32.27 | odd | 8 | |||
144.4.k.a.37.5 | 10 | 96.11 | even | 8 | |||
144.4.k.a.109.5 | 10 | 96.35 | even | 8 | |||
576.4.k.a.145.4 | 10 | 96.29 | odd | 8 | |||
576.4.k.a.433.4 | 10 | 96.53 | odd | 8 | |||
1024.4.a.m.1.2 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.a.m.1.9 | 10 | 8.5 | even | 2 | inner | ||
1024.4.a.n.1.2 | 10 | 8.3 | odd | 2 | |||
1024.4.a.n.1.9 | 10 | 4.3 | odd | 2 | |||
1024.4.b.j.513.2 | 10 | 16.11 | odd | 4 | |||
1024.4.b.j.513.9 | 10 | 16.3 | odd | 4 | |||
1024.4.b.k.513.2 | 10 | 16.13 | even | 4 | |||
1024.4.b.k.513.9 | 10 | 16.5 | even | 4 |