Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, 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("336.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(19.8246417619\) |
Analytic rank: | \(1\) |
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: | \( 2 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-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 | ||||||||
\(5\) | −4.54983 | −0.406950 | −0.203475 | − | 0.979080i | \(-0.565223\pi\) | ||||
−0.203475 | + | 0.979080i | \(0.565223\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.7492 | 1.11694 | 0.558470 | − | 0.829525i | \(-0.311389\pi\) | ||||
0.558470 | + | 0.829525i | \(0.311389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 53.2990 | 1.13711 | 0.568557 | − | 0.822644i | \(-0.307502\pi\) | ||||
0.568557 | + | 0.822644i | \(0.307502\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.6495 | 0.234952 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54983 | 0.0649116 | 0.0324558 | − | 0.999473i | \(-0.489667\pi\) | ||||
0.0324558 | + | 0.999473i | \(0.489667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −122.598 | −1.48031 | −0.740156 | − | 0.672436i | \(-0.765248\pi\) | ||||
−0.740156 | + | 0.672436i | \(0.765248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −131.347 | −1.19077 | −0.595387 | − | 0.803439i | \(-0.703001\pi\) | ||||
−0.595387 | + | 0.803439i | \(0.703001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.299 | −0.834392 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −216.598 | −1.38694 | −0.693470 | − | 0.720486i | \(-0.743919\pi\) | ||||
−0.693470 | + | 0.720486i | \(0.743919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 251.794 | 1.45882 | 0.729412 | − | 0.684075i | \(-0.239794\pi\) | ||||
0.729412 | + | 0.684075i | \(0.239794\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −122.248 | −0.644865 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.8488 | 0.153812 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8970 | 0.0528610 | 0.0264305 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264305 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −159.897 | −0.656513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −111.752 | −0.425678 | −0.212839 | − | 0.977087i | \(-0.568271\pi\) | ||||
−0.212839 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.196 | −1.30935 | −0.654673 | − | 0.755912i | \(-0.727194\pi\) | ||||
−0.654673 | + | 0.755912i | \(0.727194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −40.9485 | −0.135650 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 262.694 | 0.815275 | 0.407637 | − | 0.913144i | \(-0.366353\pi\) | ||||
0.407637 | + | 0.913144i | \(0.366353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.6495 | −0.0374767 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −567.100 | −1.46976 | −0.734879 | − | 0.678199i | \(-0.762761\pi\) | ||||
−0.734879 | + | 0.678199i | \(0.762761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.402 | −0.454538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 367.794 | 0.854658 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −839.890 | −1.85330 | −0.926648 | − | 0.375931i | \(-0.877323\pi\) | ||||
−0.926648 | + | 0.375931i | \(0.877323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −485.794 | −1.01966 | −0.509832 | − | 0.860274i | \(-0.670293\pi\) | ||||
−0.509832 | + | 0.860274i | \(0.670293\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −242.502 | −0.462748 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 333.691 | 0.608460 | 0.304230 | − | 0.952599i | \(-0.401601\pi\) | ||||
0.304230 | + | 0.952599i | \(0.401601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 394.042 | 0.687493 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −590.248 | −0.986613 | −0.493306 | − | 0.869856i | \(-0.664212\pi\) | ||||
−0.493306 | + | 0.869856i | \(0.664212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 490.701 | 0.786743 | 0.393371 | − | 0.919380i | \(-0.371309\pi\) | ||||
0.393371 | + | 0.919380i | \(0.371309\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 312.897 | 0.481736 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −285.244 | −0.422164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −121.691 | −0.173308 | −0.0866539 | − | 0.996238i | \(-0.527617\pi\) | ||||
−0.0866539 | + | 0.996238i | \(0.527617\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −609.608 | −0.806183 | −0.403091 | − | 0.915160i | \(-0.632064\pi\) | ||||
−0.403091 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7010 | −0.0264157 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 649.794 | 0.800750 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 719.038 | 0.856381 | 0.428190 | − | 0.903689i | \(-0.359151\pi\) | ||||
0.428190 | + | 0.903689i | \(0.359151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −373.093 | −0.429789 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −755.382 | −0.842252 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 557.801 | 0.602412 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −637.877 | −0.667697 | −0.333849 | − | 0.942627i | \(-0.608347\pi\) | ||||
−0.333849 | + | 0.942627i | \(0.608347\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 366.743 | 0.372313 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 671.148 | 0.661205 | 0.330603 | − | 0.943770i | \(-0.392748\pi\) | ||||
0.330603 | + | 0.943770i | \(0.392748\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 912.412 | 0.872841 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −95.5465 | −0.0888037 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 116.736 | 0.105470 | 0.0527350 | − | 0.998609i | \(-0.483206\pi\) | ||||
0.0527350 | + | 0.998609i | \(0.483206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 837.176 | 0.735660 | 0.367830 | − | 0.929893i | \(-0.380101\pi\) | ||||
0.367830 | + | 0.929893i | \(0.380101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −35.6911 | −0.0305193 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1086.58 | −0.904572 | −0.452286 | − | 0.891873i | \(-0.649391\pi\) | ||||
−0.452286 | + | 0.891873i | \(0.649391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 597.608 | 0.484585 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 479.691 | 0.379038 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31.8488 | −0.0245343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 329.495 | 0.247554 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 335.257 | 0.245765 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1043.27 | 0.746505 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 537.113 | 0.375284 | 0.187642 | − | 0.982237i | \(-0.439916\pi\) | ||||
0.187642 | + | 0.982237i | \(0.439916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1107.59 | 0.755951 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1497.39 | −0.998683 | −0.499341 | − | 0.866405i | \(-0.666425\pi\) | ||||
−0.499341 | + | 0.866405i | \(0.666425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 858.186 | 0.559505 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 122.846 | 0.0783175 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1380.09 | −0.860650 | −0.430325 | − | 0.902674i | \(-0.641601\pi\) | ||||
−0.430325 | + | 0.902674i | \(0.641601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 141.980 | 0.0866374 | 0.0433187 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433187 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −788.083 | −0.470699 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2171.89 | 1.27009 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 985.485 | 0.564414 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1943.87 | −1.06878 | −0.534390 | − | 0.845238i | \(-0.679458\pi\) | ||||
−0.534390 | + | 0.845238i | \(0.679458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2654.76 | 1.43074 | 0.715370 | − | 0.698746i | \(-0.246258\pi\) | ||||
0.715370 | + | 0.698746i | \(0.246258\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.9485 | 0.0216372 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1145.62 | −0.593668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1665.22 | 0.846489 | 0.423244 | − | 0.906016i | \(-0.360891\pi\) | ||||
0.423244 | + | 0.906016i | \(0.360891\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1701.30 | 0.848565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 919.430 | 0.450070 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 33.0732 | 0.0158926 | 0.00794629 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794629 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 556.206 | 0.262428 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1654.48 | −0.766630 | −0.383315 | − | 0.923618i | \(-0.625218\pi\) | ||||
−0.383315 | + | 0.923618i | \(0.625218\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 643.784 | 0.293029 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1103.38 | −0.493437 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 64.1909 | 0.0282101 | 0.0141050 | − | 0.999901i | \(-0.495510\pi\) | ||||
0.0141050 | + | 0.999901i | \(0.495510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 730.093 | 0.315371 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2519.67 | 1.07000 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3914.68 | −1.63462 | −0.817309 | − | 0.576200i | \(-0.804535\pi\) | ||||
−0.817309 | + | 0.576200i | \(0.804535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2058.04 | −0.845156 | −0.422578 | − | 0.906327i | \(-0.638875\pi\) | ||||
−0.422578 | + | 0.906327i | \(0.638875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1457.38 | 0.588704 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −54.1295 | −0.0215118 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 185.402 | 0.0725023 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −428.048 | −0.162160 | −0.0810798 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810798 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1604.93 | 0.598576 | 0.299288 | − | 0.954163i | \(-0.403251\pi\) | ||||
0.299288 | + | 0.954163i | \(0.403251\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 727.505 | 0.267168 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3738.83 | 1.35218 | 0.676092 | − | 0.736817i | \(-0.263672\pi\) | ||||
0.676092 | + | 0.736817i | \(0.263672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 349.030 | 0.124332 | 0.0621660 | − | 0.998066i | \(-0.480199\pi\) | ||||
0.0621660 | + | 0.998066i | \(0.480199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1001.07 | −0.351295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1516.19 | 0.524214 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 508.455 | 0.173230 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1182.12 | −0.396924 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4995.77 | −1.65342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2588.58 | −0.844574 | −0.422287 | − | 0.906462i | \(-0.638773\pi\) | ||||
−0.422287 | + | 0.906462i | \(0.638773\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1770.74 | 0.569621 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1679.78 | 0.532838 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1762.56 | −0.551384 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1472.10 | −0.454226 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 242.502 | 0.0738119 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3236.21 | 0.971804 | 0.485902 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485902 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −938.691 | −0.278131 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5631.62 | 1.64662 | 0.823312 | − | 0.567589i | \(-0.192124\pi\) | ||||
0.823312 | + | 0.567589i | \(0.192124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3770.25 | 1.08797 | 0.543985 | − | 0.839095i | \(-0.316915\pi\) | ||||
0.543985 | + | 0.839095i | \(0.316915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 855.733 | 0.243736 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6560.90 | −1.84472 | −0.922358 | − | 0.386336i | \(-0.873741\pi\) | ||||
−0.922358 | + | 0.386336i | \(0.873741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1195.22 | −0.331776 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 365.073 | 0.100059 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 771.444 | 0.208789 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1252.10 | 0.334668 | 0.167334 | − | 0.985900i | \(-0.446484\pi\) | ||||
0.167334 | + | 0.985900i | \(0.446484\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −222.942 | −0.0581357 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6534.35 | −1.68328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1828.82 | 0.465450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5166.27 | −1.29917 | −0.649586 | − | 0.760288i | \(-0.725058\pi\) | ||||
−0.649586 | + | 0.760288i | \(0.725058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5352.29 | −1.33002 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 62.1030 | 0.0152511 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2767.45 | 0.671707 | 0.335854 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335854 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −83.2791 | −0.0199796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1949.38 | −0.462313 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4101.78 | 0.961699 | 0.480849 | − | 0.876803i | \(-0.340328\pi\) | ||||
0.480849 | + | 0.876803i | \(0.340328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2580.21 | 0.598117 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2157.11 | −0.494432 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6950.84 | −1.57546 | −0.787732 | − | 0.616018i | \(-0.788745\pi\) | ||||
−0.787732 | + | 0.616018i | \(0.788745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7140.29 | 1.60052 | 0.800262 | − | 0.599651i | \(-0.204694\pi\) | ||||
0.800262 | + | 0.599651i | \(0.204694\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1119.28 | 0.248139 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4250.10 | −0.931966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1320.51 | 0.286433 | 0.143217 | − | 0.989691i | \(-0.454255\pi\) | ||||
0.143217 | + | 0.989691i | \(0.454255\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2266.15 | 0.486275 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −204.309 | −0.0433738 | −0.0216869 | − | 0.999765i | \(-0.506904\pi\) | ||||
−0.0216869 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −975.794 | −0.204964 | −0.102482 | − | 0.994735i | \(-0.532678\pi\) | ||||
−0.102482 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1673.40 | −0.347803 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 782.267 | 0.160891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4892.30 | −0.995786 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1913.63 | 0.385495 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 607.919 | 0.121212 | 0.0606058 | − | 0.998162i | \(-0.480697\pi\) | ||||
0.0606058 | + | 0.998162i | \(0.480697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3821.36 | 0.754198 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1100.23 | −0.214955 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7000.67 | −1.35405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2584.37 | 0.494886 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2013.44 | −0.381747 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2210.28 | 0.414952 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8037.08 | −1.49414 | −0.747069 | − | 0.664747i | \(-0.768539\pi\) | ||||
−0.747069 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2737.24 | −0.503935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5311.60 | −0.968468 | −0.484234 | − | 0.874939i | \(-0.660902\pi\) | ||||
−0.484234 | + | 0.874939i | \(0.660902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1531.61 | −0.276587 | −0.138293 | − | 0.990391i | \(-0.544162\pi\) | ||||
−0.138293 | + | 0.990391i | \(0.544162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 286.640 | 0.0512708 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4219.19 | 0.747549 | 0.373775 | − | 0.927520i | \(-0.378063\pi\) | ||||
0.373775 | + | 0.927520i | \(0.378063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8826.19 | −1.54913 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −350.208 | −0.0608931 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −557.801 | −0.0960893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5559.03 | −0.948799 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2511.53 | −0.424733 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1838.86 | −0.308145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8298.19 | −1.37797 | −0.688987 | − | 0.724773i | \(-0.741944\pi\) | ||||
−0.688987 | + | 0.724773i | \(0.741944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 107.073 | 0.0176203 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1518.24 | −0.247613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4348.44 | −0.702892 | −0.351446 | − | 0.936208i | \(-0.614310\pi\) | ||||
−0.351446 | + | 0.936208i | \(0.614310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3259.73 | 0.522255 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10260.4 | 1.62942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1792.82 | −0.279775 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8345.54 | 1.29110 | 0.645550 | − | 0.763718i | \(-0.276628\pi\) | ||||
0.645550 | + | 0.763718i | \(0.276628\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9982.54 | −1.53110 | −0.765549 | − | 0.643378i | \(-0.777532\pi\) | ||||
−0.765549 | + | 0.643378i | \(0.777532\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1439.07 | −0.218838 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8801.59 | 1.32709 | 0.663543 | − | 0.748138i | \(-0.269052\pi\) | ||||
0.663543 | + | 0.748138i | \(0.269052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2685.53 | 0.401502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 95.5465 | 0.0141649 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 524.039 | 0.0770409 | 0.0385205 | − | 0.999258i | \(-0.487736\pi\) | ||||
0.0385205 | + | 0.999258i | \(0.487736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8171.27 | 1.19132 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −988.485 | −0.142926 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2232.61 | −0.320165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6362.72 | 0.904991 | 0.452495 | − | 0.891767i | \(-0.350534\pi\) | ||||
0.452495 | + | 0.891767i | \(0.350534\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1005.77 | −0.141893 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3969.70 | 0.555516 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11265.8 | −1.56387 | −0.781935 | − | 0.623361i | \(-0.785767\pi\) | ||||
−0.781935 | + | 0.623361i | \(0.785767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3129.82 | −0.430995 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11544.5 | −1.57711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1151.71 | 0.156094 | 0.0780470 | − | 0.996950i | \(-0.475132\pi\) | ||||
0.0780470 | + | 0.996950i | \(0.475132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1611.34 | −0.216670 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 151.554 | 0.0202195 | 0.0101097 | − | 0.999949i | \(-0.496782\pi\) | ||||
0.0101097 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1297.81 | 0.171799 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3322.76 | −0.436449 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4794.18 | 0.624870 | 0.312435 | − | 0.949939i | \(-0.398855\pi\) | ||||
0.312435 | + | 0.949939i | \(0.398855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −597.608 | −0.0772950 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4492.17 | 0.576590 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 553.674 | 0.0705275 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4623.94 | −0.584556 | −0.292278 | − | 0.956333i | \(-0.594413\pi\) | ||||
−0.292278 | + | 0.956333i | \(0.594413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2574.56 | −0.323030 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3610.63 | −0.449642 | −0.224821 | − | 0.974400i | \(-0.572180\pi\) | ||||
−0.224821 | + | 0.974400i | \(0.572180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13420.4 | 1.65885 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −368.537 | −0.0452166 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 484.794 | 0.0590426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8959.57 | 1.08318 | 0.541592 | − | 0.840641i | \(-0.317822\pi\) | ||||
0.541592 | + | 0.840641i | \(0.317822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4140.27 | 0.496896 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5879.23 | 0.700480 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2773.62 | 0.328076 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −425.940 | −0.0500201 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7078.28 | 0.825290 | 0.412645 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412645 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11551.5 | 1.33725 | 0.668626 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668626 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2364.25 | 0.271758 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −474.543 | −0.0541617 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3400.56 | 0.385397 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6515.67 | −0.733286 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4064.38 | 0.454232 | 0.227116 | − | 0.973868i | \(-0.427070\pi\) | ||||
0.227116 | + | 0.973868i | \(0.427070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17456.3 | 1.93740 | 0.968701 | − | 0.248229i | \(-0.0798487\pi\) | ||||
0.968701 | + | 0.248229i | \(0.0798487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2956.46 | −0.325865 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16102.9 | 1.76271 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4595.39 | −0.499604 | −0.249802 | − | 0.968297i | \(-0.580365\pi\) | ||||
−0.249802 | + | 0.968297i | \(0.580365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 306.214 | 0.0328412 | 0.0164206 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164206 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3271.50 | −0.348504 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5831.61 | 0.617060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9229.22 | 0.970053 | 0.485026 | − | 0.874500i | \(-0.338810\pi\) | ||||
0.485026 | + | 0.874500i | \(0.338810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4553.82 | −0.475457 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7964.29 | −0.826038 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1697.51 | 0.174902 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10992.2 | −1.12515 | −0.562577 | − | 0.826745i | \(-0.690190\pi\) | ||||
−0.562577 | + | 0.826745i | \(0.690190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −122.846 | −0.0124922 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7387.88 | 0.746394 | 0.373197 | − | 0.927752i | \(-0.378261\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10163.8 | −1.02020 | −0.510101 | − | 0.860114i | \(-0.670392\pi\) | ||||
−0.510101 | + | 0.860114i | \(0.670392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3436.86 | 0.342754 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15814.6 | 1.56705 | 0.783524 | − | 0.621362i | \(-0.213420\pi\) | ||||
0.783524 | + | 0.621362i | \(0.213420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2335.84 | −0.229976 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4995.65 | −0.488720 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15044.4 | −1.46246 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12786.9 | 1.23516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5103.90 | −0.489919 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1444.85 | 0.137823 | 0.0689113 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689113 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 634.099 | 0.0601090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2758.29 | −0.259848 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2902.24 | 0.271719 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 489.402 | 0.0455378 | 0.0227689 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227689 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −99.2195 | −0.00917559 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3941.30 | 0.362257 | 0.181129 | − | 0.983459i | \(-0.442025\pi\) | ||||
0.181129 | + | 0.983459i | \(0.442025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −985.485 | −0.0900284 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1668.62 | −0.151513 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4131.73 | 0.372905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0894 | −0.000994850 0 | −0.000497425 | − | 1.00000i | \(-0.500158\pi\) | ||||
−0.000497425 | 1.00000i | \(0.500158\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4963.43 | 0.442614 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7088.41 | −0.628343 | −0.314172 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314172 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3053.61 | −0.269077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1931.35 | −0.169180 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17588.4 | 1.53162 | 0.765810 | − | 0.643067i | \(-0.222338\pi\) | ||||
0.765810 | + | 0.643067i | \(0.222338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3434.91 | −0.297361 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3310.15 | 0.284886 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4151.32 | −0.355202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10704.6 | 0.910613 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −192.573 | −0.0162871 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11646.6 | −0.979360 | −0.489680 | − | 0.871902i | \(-0.662886\pi\) | ||||
−0.489680 | + | 0.871902i | \(0.662886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8965.82 | −0.749614 | −0.374807 | − | 0.927103i | \(-0.622291\pi\) | ||||
−0.374807 | + | 0.927103i | \(0.622291\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2190.28 | −0.182079 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1145.62 | 0.0946946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5085.08 | 0.417941 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7559.01 | −0.617765 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5956.30 | −0.484045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −531.129 | −0.0429210 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11744.0 | 0.943747 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1996.71 | 0.159563 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −195.272 | −0.0155183 | −0.00775914 | − | 0.999970i | \(-0.502470\pi\) | ||||
−0.00775914 | + | 0.999970i | \(0.502470\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6174.13 | 0.487951 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3809.01 | −0.299376 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1399.26 | 0.109375 | 0.0546874 | − | 0.998504i | \(-0.482584\pi\) | ||||
0.0546874 | + | 0.998504i | \(0.482584\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4372.15 | −0.339888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26554.5 | 2.05310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 851.837 | 0.0655042 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 162.388 | 0.0124198 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0467 | 0.00327459 | 0.00163730 | − | 0.999999i | \(-0.499479\pi\) | ||||
0.00163730 | + | 0.999999i | \(0.499479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19677.8 | −1.48888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −556.206 | −0.0418592 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19232.9 | 1.43973 | 0.719865 | − | 0.694114i | \(-0.244203\pi\) | ||||
0.719865 | + | 0.694114i | \(0.244203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4943.75 | 0.368115 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5163.98 | 0.380466 | 0.190233 | − | 0.981739i | \(-0.439076\pi\) | ||||
0.190233 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10231.9 | 0.749899 | 0.374950 | − | 0.927045i | \(-0.377660\pi\) | ||||
0.374950 | + | 0.927045i | \(0.377660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1284.14 | 0.0936229 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13699.4 | 0.993572 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16563.7 | 1.19507 | 0.597537 | − | 0.801842i | \(-0.296146\pi\) | ||||
0.597537 | + | 0.801842i | \(0.296146\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4814.78 | −0.345588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4267.26 | 0.304708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23108.8 | −1.64163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2182.51 | −0.154249 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16020.6 | −1.12648 | −0.563239 | − | 0.826294i | \(-0.690445\pi\) | ||||
−0.563239 | + | 0.826294i | \(0.690445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30869.4 | −2.15951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11216.5 | −0.780684 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6771.14 | −0.468900 | −0.234450 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234450 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 144.907 | 0.00998421 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1047.09 | −0.0717831 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11070.2 | −0.755120 | −0.377560 | − | 0.925985i | \(-0.623237\pi\) | ||||
−0.377560 | + | 0.925985i | \(0.623237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24187.7 | −1.64166 | −0.820830 | − | 0.571173i | \(-0.806489\pi\) | ||||
−0.820830 | + | 0.571173i | \(0.806489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3003.22 | 0.202820 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1499.15 | −0.100742 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10074.1 | 0.673631 | 0.336816 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4548.56 | −0.302655 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14001.3 | 0.927060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11114.6 | −0.732323 | −0.366161 | − | 0.930551i | \(-0.619328\pi\) | ||||
−0.366161 | + | 0.930551i | \(0.619328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1525.37 | −0.100014 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20496.4 | 1.33737 | 0.668683 | − | 0.743548i | \(-0.266858\pi\) | ||||
0.668683 | + | 0.743548i | \(0.266858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16714.4 | 1.08532 | 0.542658 | − | 0.839954i | \(-0.317418\pi\) | ||||
0.542658 | + | 0.839954i | \(0.317418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3546.37 | 0.229164 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5033.27 | −0.323682 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8290.66 | 0.530602 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14987.3 | 0.954602 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 54.1295 | 0.00343129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9168.53 | −0.578437 | −0.289218 | − | 0.957263i | \(-0.593395\pi\) | ||||
−0.289218 | + | 0.957263i | \(0.593395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7765.73 | 0.487615 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2443.77 | −0.152722 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2611.65 | 0.162445 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5312.23 | −0.328871 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4273.37 | −0.263319 | −0.131660 | − | 0.991295i | \(-0.542031\pi\) | ||||
−0.131660 | + | 0.991295i | \(0.542031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2955.75 | −0.181281 | −0.0906404 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5039.34 | −0.307634 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22701.2 | −1.37941 | −0.689704 | − | 0.724091i | \(-0.742259\pi\) | ||||
−0.689704 | + | 0.724091i | \(0.742259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34224.8 | −2.07002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5287.67 | 0.318341 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1537.81 | 0.0921582 | 0.0460791 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460791 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6812.87 | 0.406414 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4416.31 | 0.262248 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12338.1 | −0.729323 | −0.364661 | − | 0.931140i | \(-0.618815\pi\) | ||||
−0.364661 | + | 0.931140i | \(0.618815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1845.10 | 0.108572 | 0.0542859 | − | 0.998525i | \(-0.482712\pi\) | ||||
0.0542859 | + | 0.998525i | \(0.482712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −727.505 | −0.0426153 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3904.60 | −0.227690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28449.5 | 1.65153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9708.62 | −0.561072 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19795.7 | −1.13890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23955.4 | 1.37208 | 0.686041 | − | 0.727563i | \(-0.259347\pi\) | ||||
0.686041 | + | 0.727563i | \(0.259347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2816.07 | 0.160579 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3678.26 | −0.208814 | −0.104407 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104407 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4465.14 | 0.252366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16894.9 | −0.950679 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4390.87 | −0.245991 | −0.122996 | − | 0.992407i | \(-0.539250\pi\) | ||||
−0.122996 | + | 0.992407i | \(0.539250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6279.18 | 0.350241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11310.7 | −0.628140 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30225.8 | −1.67128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10371.7 | −0.570994 | −0.285497 | − | 0.958380i | \(-0.592159\pi\) | ||||
−0.285497 | + | 0.958380i | \(0.592159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2567.20 | −0.140721 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −645.986 | −0.0352570 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −508.455 | −0.0276314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19682.7 | 1.06505 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 109.675 | 0.00590922 | 0.00295461 | − | 0.999996i | \(-0.499060\pi\) | ||||
0.00295461 | + | 0.999996i | \(0.499060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1458.55 | −0.0782508 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3585.65 | 0.191551 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4698.03 | −0.249912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26918.8 | 1.42589 | 0.712944 | − | 0.701221i | \(-0.247361\pi\) | ||||
0.712944 | + | 0.701221i | \(0.247361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1095.22 | −0.0577693 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33072.4 | −1.73713 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9881.74 | −0.516862 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2314.33 | −0.120544 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15170.8 | −0.786889 | −0.393445 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6386.88 | −0.329903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3756.31 | −0.193221 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22591.0 | 1.15725 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33286.9 | 1.69813 | 0.849066 | − | 0.528288i | \(-0.177166\pi\) | ||||
0.849066 | + | 0.528288i | \(0.177166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1679.78 | −0.0849917 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20544.0 | 1.03521 | 0.517607 | − | 0.855619i | \(-0.326823\pi\) | ||||
0.517607 | + | 0.855619i | \(0.326823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 668.826 | 0.0335646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13597.6 | 0.679614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34357.2 | −1.71022 | −0.855109 | − | 0.518449i | \(-0.826510\pi\) | ||||
−0.855109 | + | 0.518449i | \(0.826510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19603.1 | 0.971844 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8166.99 | −0.403254 | −0.201627 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201627 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8844.29 | 0.434939 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5486.47 | −0.268728 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −817.151 | −0.0398639 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17080.1 | −0.829909 | −0.414954 | − | 0.909842i | \(-0.636202\pi\) | ||||
−0.414954 | + | 0.909842i | \(0.636202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15498.8 | 0.750077 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12078.7 | −0.582239 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16324.0 | −0.783758 | −0.391879 | − | 0.920017i | \(-0.628175\pi\) | ||||
−0.391879 | + | 0.920017i | \(0.628175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16056.9 | 0.767888 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32366.2 | −1.54175 | −0.770875 | − | 0.636986i | \(-0.780181\pi\) | ||||
−0.770875 | + | 0.636986i | \(0.780181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5860.23 | −0.278053 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −186.309 | −0.00880525 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44765.3 | −2.10741 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7948.44 | −0.372728 | −0.186364 | − | 0.982481i | \(-0.559670\pi\) | ||||
−0.186364 | + | 0.982481i | \(0.559670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8302.35 | −0.387810 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17819.3 | 0.829127 | 0.414564 | − | 0.910020i | \(-0.363934\pi\) | ||||
0.414564 | + | 0.910020i | \(0.363934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26261.9 | −1.21723 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 249.837 | 0.0115352 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13700.6 | 0.630136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24052.1 | −1.10199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5848.15 | 0.266917 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7576.46 | −0.344478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2912.38 | −0.131912 | −0.0659562 | − | 0.997823i | \(-0.521010\pi\) | ||||
−0.0659562 | + | 0.997823i | \(0.521010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12305.3 | −0.555237 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7606.05 | 0.341896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25892.3 | −1.15948 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7740.63 | −0.345323 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33789.1 | −1.50172 | −0.750861 | − | 0.660460i | \(-0.770361\pi\) | ||||
−0.750861 | + | 0.660460i | \(0.770361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1195.22 | 0.0529208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6471.34 | 0.285460 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19995.7 | 0.878744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4183.26 | −0.183156 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20852.5 | 0.909595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1252.13 | 0.0544159 | 0.0272079 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272079 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31913.1 | 1.38178 | 0.690889 | − | 0.722961i | \(-0.257219\pi\) | ||||
0.690889 | + | 0.722961i | \(0.257219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21420.9 | −0.924063 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −150.477 | −0.00646748 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45262.7 | 1.93824 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3357.84 | −0.143263 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30742.4 | 1.30684 | 0.653421 | − | 0.756995i | \(-0.273333\pi\) | ||||
0.653421 | + | 0.756995i | \(0.273333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13822.6 | 0.585449 | 0.292724 | − | 0.956197i | \(-0.405438\pi\) | ||||
0.292724 | + | 0.956197i | \(0.405438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12750.3 | 0.538071 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42107.1 | 1.77051 | 0.885253 | − | 0.465110i | \(-0.153985\pi\) | ||||
0.885253 | + | 0.465110i | \(0.153985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38763.8 | −1.62403 | −0.812015 | − | 0.583636i | \(-0.801629\pi\) | ||||
−0.812015 | + | 0.583636i | \(0.801629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3961.54 | −0.165372 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 222.942 | 0.00927308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7527.59 | 0.311980 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6798.44 | −0.280751 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16896.3 | −0.695262 | −0.347631 | − | 0.937631i | \(-0.613014\pi\) | ||||
−0.347631 | + | 0.937631i | \(0.613014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22525.7 | 0.923601 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 612.927 | 0.0250419 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2929.11 | −0.119248 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2306.47 | −0.0935668 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2927.38 | 0.118336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1562.64 | −0.0629455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46429.3 | 1.86367 | 0.931833 | − | 0.362887i | \(-0.118209\pi\) | ||||
0.931833 | + | 0.362887i | \(0.118209\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5020.21 | 0.200804 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21206.4 | 0.845272 | 0.422636 | − | 0.906300i | \(-0.361105\pi\) | ||||
0.422636 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13876.2 | −0.551163 | −0.275581 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275581 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2346.80 | −0.0928906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14337.1 | −0.565515 | −0.282757 | − | 0.959191i | \(-0.591249\pi\) | ||||
−0.282757 | + | 0.959191i | \(0.591249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −292.058 | −0.0114801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14676.9 | 0.574918 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4958.81 | −0.193574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17785.4 | 0.691889 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5740.89 | −0.222566 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7302.91 | −0.282152 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24369.3 | −0.938304 | −0.469152 | − | 0.883118i | \(-0.655440\pi\) | ||||
−0.469152 | + | 0.883118i | \(0.655440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1823.76 | −0.0699815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26127.0 | −0.999140 | −0.499570 | − | 0.866273i | \(-0.666509\pi\) | ||||
−0.499570 | + | 0.866273i | \(0.666509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15713.1 | 0.598855 | 0.299428 | − | 0.954119i | \(-0.403204\pi\) | ||||
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11464.1 | −0.435436 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13139.5 | −0.497385 | −0.248692 | − | 0.968583i | \(-0.580001\pi\) | ||||
−0.248692 | + | 0.968583i | \(0.580001\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3759.79 | −0.141844 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3300.68 | 0.124104 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32205.8 | −1.20686 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17811.1 | 0.665207 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21002.0 | 0.781758 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54538.1 | −2.02330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2580.21 | −0.0954043 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7753.12 | −0.285723 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9363.76 | 0.343936 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3799.71 | 0.139104 | 0.0695519 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695519 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6040.33 | 0.220402 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51528.4 | 1.87400 | 0.936998 | − | 0.349334i | \(-0.113592\pi\) | ||||
0.936998 | + | 0.349334i | \(0.113592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24841.0 | −0.900458 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6630.85 | −0.239573 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10481.7 | 0.377467 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16984.7 | 0.609657 | 0.304828 | − | 0.952407i | \(-0.401401\pi\) | ||||
0.304828 | + | 0.952407i | \(0.401401\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24111.2 | 0.862641 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31459.6 | −1.12189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1240.85 | −0.0441068 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8211.71 | 0.290947 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5451.85 | −0.192540 | −0.0962699 | − | 0.995355i | \(-0.530691\pi\) | ||||
−0.0962699 | + | 0.995355i | \(0.530691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6007.30 | −0.211473 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15934.8 | 0.559145 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −843.548 | −0.0295048 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42429.4 | 1.47930 | 0.739652 | − | 0.672989i | \(-0.234990\pi\) | ||||
0.739652 | + | 0.672989i | \(0.234990\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4594.82 | 0.159687 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32977.9 | −1.14245 | −0.571226 | − | 0.820793i | \(-0.693532\pi\) | ||||
−0.571226 | + | 0.820793i | \(0.693532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14678.4 | 0.506886 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −859.919 | −0.0296012 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23753.4 | 0.815082 | 0.407541 | − | 0.913187i | \(-0.366386\pi\) | ||||
0.407541 | + | 0.913187i | \(0.366386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26153.9 | 0.894616 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12657.6 | −0.431598 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28074.3 | −0.954267 | −0.477134 | − | 0.878831i | \(-0.658324\pi\) | ||||
−0.477134 | + | 0.878831i | \(0.658324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1947.55 | 0.0659908 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26478.6 | 0.894389 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9660.63 | 0.325295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33609.2 | 1.12817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1050.62 | 0.0351567 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7302.15 | −0.243590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11150.3 | 0.370806 | 0.185403 | − | 0.982663i | \(-0.440641\pi\) | ||||
0.185403 | + | 0.982663i | \(0.440641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1673.40 | 0.0554772 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6059.04 | −0.200251 | −0.100126 | − | 0.994975i | \(-0.531924\pi\) | ||||
−0.100126 | + | 0.994975i | \(0.531924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −993.861 | −0.0327459 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16677.1 | 0.547789 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5700.49 | 0.186668 | 0.0933341 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933341 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29300.2 | 0.956526 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7534.59 | 0.245220 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −197.480 | −0.00640757 | −0.00320378 | − | 0.999995i | \(-0.501020\pi\) | ||||
−0.00320378 | + | 0.999995i | \(0.501020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17011.0 | −0.550271 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5516.58 | 0.177908 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48492.9 | 1.55913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20620.8 | −0.660990 | −0.330495 | − | 0.943808i | \(-0.607216\pi\) | ||||
−0.330495 | + | 0.943808i | \(0.607216\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24894.6 | 0.795574 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1588.03 | −0.0505969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19326.8 | 0.613928 | 0.306964 | − | 0.951721i | \(-0.400687\pi\) | ||||
0.306964 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −321.220 | −0.0101731 |
(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 | 336.4.a.m.1.1 | 2 | ||
3.2 | odd | 2 | 1008.4.a.ba.1.2 | 2 | |||
4.3 | odd | 2 | 21.4.a.c.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 2352.4.a.bz.1.2 | 2 | |||
8.3 | odd | 2 | 1344.4.a.bg.1.2 | 2 | |||
8.5 | even | 2 | 1344.4.a.bo.1.2 | 2 | |||
12.11 | even | 2 | 63.4.a.e.1.1 | 2 | |||
20.3 | even | 4 | 525.4.d.g.274.2 | 4 | |||
20.7 | even | 4 | 525.4.d.g.274.3 | 4 | |||
20.19 | odd | 2 | 525.4.a.n.1.1 | 2 | |||
28.3 | even | 6 | 147.4.e.m.79.1 | 4 | |||
28.11 | odd | 6 | 147.4.e.l.79.1 | 4 | |||
28.19 | even | 6 | 147.4.e.m.67.1 | 4 | |||
28.23 | odd | 6 | 147.4.e.l.67.1 | 4 | |||
28.27 | even | 2 | 147.4.a.i.1.2 | 2 | |||
60.59 | even | 2 | 1575.4.a.p.1.2 | 2 | |||
84.11 | even | 6 | 441.4.e.q.226.2 | 4 | |||
84.23 | even | 6 | 441.4.e.q.361.2 | 4 | |||
84.47 | odd | 6 | 441.4.e.p.361.2 | 4 | |||
84.59 | odd | 6 | 441.4.e.p.226.2 | 4 | |||
84.83 | odd | 2 | 441.4.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
63.4.a.e.1.1 | 2 | 12.11 | even | 2 | |||
147.4.a.i.1.2 | 2 | 28.27 | even | 2 | |||
147.4.e.l.67.1 | 4 | 28.23 | odd | 6 | |||
147.4.e.l.79.1 | 4 | 28.11 | odd | 6 | |||
147.4.e.m.67.1 | 4 | 28.19 | even | 6 | |||
147.4.e.m.79.1 | 4 | 28.3 | even | 6 | |||
336.4.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.a.r.1.1 | 2 | 84.83 | odd | 2 | |||
441.4.e.p.226.2 | 4 | 84.59 | odd | 6 | |||
441.4.e.p.361.2 | 4 | 84.47 | odd | 6 | |||
441.4.e.q.226.2 | 4 | 84.11 | even | 6 | |||
441.4.e.q.361.2 | 4 | 84.23 | even | 6 | |||
525.4.a.n.1.1 | 2 | 20.19 | odd | 2 | |||
525.4.d.g.274.2 | 4 | 20.3 | even | 4 | |||
525.4.d.g.274.3 | 4 | 20.7 | even | 4 | |||
1008.4.a.ba.1.2 | 2 | 3.2 | odd | 2 | |||
1344.4.a.bg.1.2 | 2 | 8.3 | odd | 2 | |||
1344.4.a.bo.1.2 | 2 | 8.5 | even | 2 | |||
1575.4.a.p.1.2 | 2 | 60.59 | even | 2 | |||
2352.4.a.bz.1.2 | 2 | 7.6 | odd | 2 |