Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 19x^{6} + 92x^{4} - 51x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.354810\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.50343 | −0.674235 | −0.337118 | − | 0.941463i | \(-0.609452\pi\) | ||||
−0.337118 | + | 0.941463i | \(0.609452\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.74822 | −0.603579 | −0.301790 | − | 0.953375i | \(-0.597584\pi\) | ||||
−0.301790 | + | 0.953375i | \(0.597584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.06823 | −0.273659 | −0.136829 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136829 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.7260 | −0.545407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.4509 | 0.615383 | 0.307692 | − | 0.951486i | \(-0.400443\pi\) | ||||
0.307692 | + | 0.951486i | \(0.400443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.4464 | 0.436216 | 0.218108 | − | 0.975925i | \(-0.430011\pi\) | ||||
0.218108 | + | 0.975925i | \(0.430011\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 23.6419 | 0.406954 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 45.3575 | 0.647106 | 0.323553 | − | 0.946210i | \(-0.395123\pi\) | ||||
0.323553 | + | 0.946210i | \(0.395123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −79.8869 | −0.964595 | −0.482298 | − | 0.876007i | \(-0.660198\pi\) | ||||
−0.482298 | + | 0.876007i | \(0.660198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.7562 | 0.184510 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −67.4136 | −0.611161 | −0.305581 | − | 0.952166i | \(-0.598851\pi\) | ||||
−0.305581 | + | 0.952166i | \(0.598851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −79.4615 | −0.635692 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 146.184 | 1.04197 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 133.881 | 0.775669 | 0.387834 | − | 0.921729i | \(-0.373223\pi\) | ||||
0.387834 | + | 0.921729i | \(0.373223\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −78.6553 | −0.414913 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34.2015 | 0.165175 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 343.446 | 1.52600 | 0.763002 | − | 0.646396i | \(-0.223725\pi\) | ||||
0.763002 | + | 0.646396i | \(0.223725\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −71.6325 | −0.294112 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 72.7396 | 0.277074 | 0.138537 | − | 0.990357i | \(-0.455760\pi\) | ||||
0.138537 | + | 0.990357i | \(0.455760\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 232.616 | 0.824968 | 0.412484 | − | 0.910965i | \(-0.364661\pi\) | ||||
0.412484 | + | 0.910965i | \(0.364661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 99.3742 | 0.329196 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −416.631 | −1.29302 | −0.646510 | − | 0.762906i | \(-0.723772\pi\) | ||||
−0.646510 | + | 0.762906i | \(0.723772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −317.313 | −0.925111 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −158.907 | −0.436302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 136.783 | 0.354502 | 0.177251 | − | 0.984166i | \(-0.443280\pi\) | ||||
0.177251 | + | 0.984166i | \(0.443280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −151.504 | −0.371433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 279.878 | 0.650364 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 586.105 | 1.29329 | 0.646647 | − | 0.762789i | \(-0.276171\pi\) | ||||
0.646647 | + | 0.762789i | \(0.276171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 212.320 | 0.445653 | 0.222826 | − | 0.974858i | \(-0.428472\pi\) | ||||
0.222826 | + | 0.974858i | \(0.428472\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 74.6346 | 0.149255 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −137.977 | −0.263291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −138.963 | −0.253389 | −0.126694 | − | 0.991942i | \(-0.540437\pi\) | ||||
−0.126694 | + | 0.991942i | \(0.540437\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 236.179 | 0.412066 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 812.301 | 1.35778 | 0.678890 | − | 0.734240i | \(-0.262461\pi\) | ||||
0.678890 | + | 0.734240i | \(0.262461\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 163.327 | 0.261862 | 0.130931 | − | 0.991391i | \(-0.458203\pi\) | ||||
0.130931 | + | 0.991391i | \(0.458203\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 278.388 | 0.428606 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −113.787 | −0.168405 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 926.444 | 1.31941 | 0.659703 | − | 0.751526i | \(-0.270682\pi\) | ||||
0.659703 | + | 0.751526i | \(0.270682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −114.544 | −0.157125 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 539.330 | 0.713243 | 0.356621 | − | 0.934249i | \(-0.383929\pi\) | ||||
0.356621 | + | 0.934249i | \(0.383929\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −306.082 | −0.390580 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 101.599 | 0.125202 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −196.223 | −0.233703 | −0.116852 | − | 0.993149i | \(-0.537280\pi\) | ||||
−0.116852 | + | 0.993149i | \(0.537280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −103.627 | −0.119374 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −469.043 | −0.522983 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 539.094 | 0.582209 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1858.85 | −1.94575 | −0.972874 | − | 0.231338i | \(-0.925690\pi\) | ||||
−0.972874 | + | 0.231338i | \(0.925690\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −330.612 | −0.335634 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −169.178 | −0.166671 | −0.0833356 | − | 0.996522i | \(-0.526557\pi\) | ||||
−0.0833356 | + | 0.996522i | \(0.526557\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −601.801 | −0.575701 | −0.287850 | − | 0.957675i | \(-0.592941\pi\) | ||||
−0.287850 | + | 0.957675i | \(0.592941\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −119.823 | −0.111367 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 599.520 | 0.541662 | 0.270831 | − | 0.962627i | \(-0.412702\pi\) | ||||
0.270831 | + | 0.962627i | \(0.412702\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 67.3011 | 0.0591401 | 0.0295701 | − | 0.999563i | \(-0.490586\pi\) | ||||
0.0295701 | + | 0.999563i | \(0.490586\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1203.24 | −1.02889 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1809.72 | −1.50659 | −0.753294 | − | 0.657683i | \(-0.771536\pi\) | ||||
−0.753294 | + | 0.657683i | \(0.771536\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 454.922 | 0.368884 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −301.093 | −0.237915 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −229.882 | −0.177086 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −826.955 | −0.621303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −254.838 | −0.186813 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1379.75 | 0.987270 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1759.44 | 1.22933 | 0.614665 | − | 0.788788i | \(-0.289291\pi\) | ||||
0.614665 | + | 0.788788i | \(0.289291\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −814.954 | −0.556223 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2743.56 | −1.82981 | −0.914907 | − | 0.403664i | \(-0.867736\pi\) | ||||
−0.914907 | + | 0.403664i | \(0.867736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 404.885 | 0.263970 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −986.482 | −0.628910 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1443.11 | −0.899952 | −0.449976 | − | 0.893041i | \(-0.648567\pi\) | ||||
−0.449976 | + | 0.893041i | \(0.648567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1737.45 | −1.06021 | −0.530103 | − | 0.847934i | \(-0.677847\pi\) | ||||
−0.530103 | + | 0.847934i | \(0.677847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1459.64 | 0.871800 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 459.041 | 0.268440 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 195.698 | 0.112082 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1111.68 | 0.623742 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −859.701 | −0.472681 | −0.236340 | − | 0.971670i | \(-0.575948\pi\) | ||||
−0.236340 | + | 0.971670i | \(0.575948\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 474.299 | 0.255615 | 0.127808 | − | 0.991799i | \(-0.459206\pi\) | ||||
0.127808 | + | 0.991799i | \(0.459206\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −667.933 | −0.352936 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −903.458 | −0.468177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 338.908 | 0.172279 | 0.0861396 | − | 0.996283i | \(-0.472547\pi\) | ||||
0.0861396 | + | 0.996283i | \(0.472547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −479.210 | −0.239018 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 341.667 | 0.167249 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1484.38 | 0.713287 | 0.356643 | − | 0.934241i | \(-0.383921\pi\) | ||||
0.356643 | + | 0.934241i | \(0.383921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 530.783 | 0.250433 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1790.86 | 0.829824 | 0.414912 | − | 0.909862i | \(-0.363812\pi\) | ||||
0.414912 | + | 0.909862i | \(0.363812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1778.94 | −0.809715 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1176.41 | 0.526097 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1671.46 | −0.734561 | −0.367281 | − | 0.930110i | \(-0.619711\pi\) | ||||
−0.367281 | + | 0.930110i | \(0.619711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 402.729 | 0.173963 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2053.38 | −0.871985 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2111.96 | −0.881874 | −0.440937 | − | 0.897538i | \(-0.645354\pi\) | ||||
−0.440937 | + | 0.897538i | \(0.645354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1746.36 | 0.717161 | 0.358581 | − | 0.933499i | \(-0.383261\pi\) | ||||
0.358581 | + | 0.933499i | \(0.383261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −743.849 | −0.300475 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2317.65 | −0.921064 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1018.32 | 0.398218 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −740.894 | −0.285143 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1904.98 | −0.721672 | −0.360836 | − | 0.932629i | \(-0.617509\pi\) | ||||
−0.360836 | + | 0.932629i | \(0.617509\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4758.65 | −1.77479 | −0.887397 | − | 0.461007i | \(-0.847488\pi\) | ||||
−0.887397 | + | 0.461007i | \(0.847488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 483.392 | 0.177520 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 664.799 | 0.240431 | 0.120216 | − | 0.992748i | \(-0.461641\pi\) | ||||
0.120216 | + | 0.992748i | \(0.461641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2902.16 | 1.03381 | 0.516907 | − | 0.856042i | \(-0.327083\pi\) | ||||
0.516907 | + | 0.856042i | \(0.327083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 486.848 | 0.170844 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 146.979 | 0.0508171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −490.863 | −0.167236 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 992.731 | 0.333331 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1793.54 | −0.593596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3698.14 | 1.20659 | 0.603296 | − | 0.797518i | \(-0.293854\pi\) | ||||
0.603296 | + | 0.797518i | \(0.293854\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2845.84 | −0.915463 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1569.74 | −0.497934 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −678.539 | −0.212268 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −572.204 | −0.176557 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 927.397 | 0.282278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1381.34 | −0.414805 | −0.207402 | − | 0.978256i | \(-0.566501\pi\) | ||||
−0.207402 | + | 0.978256i | \(0.566501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1170.15 | 0.346711 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2632.75 | −0.769789 | −0.384894 | − | 0.922961i | \(-0.625762\pi\) | ||||
−0.384894 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2921.66 | −0.843094 | −0.421547 | − | 0.906806i | \(-0.638513\pi\) | ||||
−0.421547 | + | 0.906806i | \(0.638513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 398.643 | 0.113545 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2704.54 | 0.760431 | 0.380216 | − | 0.924898i | \(-0.375850\pi\) | ||||
0.380216 | + | 0.924898i | \(0.375850\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2811.52 | 0.780440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3245.73 | −0.889590 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 320.582 | 0.0867645 | 0.0433823 | − | 0.999059i | \(-0.486187\pi\) | ||||
0.0433823 | + | 0.999059i | \(0.486187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1545.98 | 0.413216 | 0.206608 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206608 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3545.67 | −0.936029 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2141.30 | 0.558378 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1633.40 | −0.420772 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1889.50 | −0.480893 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2528.06 | 0.635737 | 0.317868 | − | 0.948135i | \(-0.397033\pi\) | ||||
0.317868 | + | 0.948135i | \(0.397033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1513.50 | −0.376098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1072.34 | 0.263343 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3050.82 | −0.740487 | −0.370244 | − | 0.928935i | \(-0.620726\pi\) | ||||
−0.370244 | + | 0.928935i | \(0.620726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1740.66 | −0.417604 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 427.054 | 0.101279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8361.56 | −1.96044 | −0.980220 | − | 0.197910i | \(-0.936585\pi\) | ||||
−0.980220 | + | 0.197910i | \(0.936585\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −923.043 | −0.213970 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 687.453 | 0.157571 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1623.45 | −0.367968 | −0.183984 | − | 0.982929i | \(-0.558899\pi\) | ||||
−0.183984 | + | 0.982929i | \(0.558899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1624.69 | −0.364181 | −0.182091 | − | 0.983282i | \(-0.558286\pi\) | ||||
−0.182091 | + | 0.983282i | \(0.558286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 363.050 | 0.0804864 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1783.99 | −0.391194 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5176.32 | −1.12280 | −0.561399 | − | 0.827546i | \(-0.689737\pi\) | ||||
−0.561399 | + | 0.827546i | \(0.689737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1971.53 | −0.423055 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1227.99 | −0.260696 | −0.130348 | − | 0.991468i | \(-0.541609\pi\) | ||||
−0.130348 | + | 0.991468i | \(0.541609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2760.21 | −0.579779 | −0.289889 | − | 0.957060i | \(-0.593619\pi\) | ||||
−0.289889 | + | 0.957060i | \(0.593619\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1888.68 | −0.392546 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −368.661 | −0.0758235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2855.70 | −0.581254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6512.34 | 1.31189 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7974.31 | −1.58998 | −0.794990 | − | 0.606623i | \(-0.792524\pi\) | ||||
−0.794990 | + | 0.606623i | \(0.792524\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3955.17 | −0.780605 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3281.97 | 0.641210 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1378.37 | −0.266598 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1178.95 | −0.225760 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 592.701 | 0.112376 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1432.78 | −0.268987 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5816.97 | −1.08141 | −0.540704 | − | 0.841213i | \(-0.681842\pi\) | ||||
−0.540704 | + | 0.841213i | \(0.681842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2108.37 | 0.388158 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9625.16 | 1.75496 | 0.877481 | − | 0.479612i | \(-0.159223\pi\) | ||||
0.877481 | + | 0.479612i | \(0.159223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2115.31 | 0.381994 | 0.190997 | − | 0.981591i | \(-0.438828\pi\) | ||||
0.190997 | + | 0.981591i | \(0.438828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −503.651 | −0.0900873 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2421.51 | 0.429040 | 0.214520 | − | 0.976720i | \(-0.431181\pi\) | ||||
0.214520 | + | 0.976720i | \(0.431181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −651.078 | −0.114274 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2100.38 | −0.365208 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3623.47 | −0.624195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1624.70 | −0.277299 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −235.785 | −0.0398744 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2111.58 | 0.353846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4071.96 | 0.676179 | 0.338090 | − | 0.941114i | \(-0.390219\pi\) | ||||
0.338090 | + | 0.941114i | \(0.390219\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5057.58 | −0.832293 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 937.754 | 0.152940 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2924.95 | −0.472796 | −0.236398 | − | 0.971656i | \(-0.575967\pi\) | ||||
−0.236398 | + | 0.971656i | \(0.575967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6340.24 | 1.01580 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3005.75 | 0.477334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3346.62 | 0.526823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1593.79 | −0.248715 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2274.16 | 0.351824 | 0.175912 | − | 0.984406i | \(-0.443713\pi\) | ||||
0.175912 | + | 0.984406i | \(0.443713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1314.05 | −0.201546 | −0.100773 | − | 0.994909i | \(-0.532132\pi\) | ||||
−0.100773 | + | 0.994909i | \(0.532132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2988.94 | 0.454523 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5773.23 | 0.870476 | 0.435238 | − | 0.900315i | \(-0.356664\pi\) | ||||
0.435238 | + | 0.900315i | \(0.356664\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5481.59 | −0.819528 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 805.375 | 0.119398 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13138.8 | −1.93159 | −0.965794 | − | 0.259311i | \(-0.916505\pi\) | ||||
−0.965794 | + | 0.259311i | \(0.916505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −477.087 | −0.0695563 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2897.18 | 0.418905 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1102.17 | −0.158055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2954.04 | 0.420162 | 0.210081 | − | 0.977684i | \(-0.432627\pi\) | ||||
0.210081 | + | 0.977684i | \(0.432627\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1071.16 | −0.151118 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −693.248 | −0.0970126 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2476.76 | −0.343812 | −0.171906 | − | 0.985113i | \(-0.554993\pi\) | ||||
−0.171906 | + | 0.985113i | \(0.554993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4833.86 | −0.665652 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −592.946 | −0.0810033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9969.57 | −1.35119 | −0.675597 | − | 0.737272i | \(-0.736114\pi\) | ||||
−0.675597 | + | 0.737272i | \(0.736114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6164.07 | −0.828858 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −65.3323 | −0.00871626 | −0.00435813 | − | 0.999991i | \(-0.501387\pi\) | ||||
−0.00435813 | + | 0.999991i | \(0.501387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 767.856 | 0.101646 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3425.50 | −0.449943 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −958.325 | −0.124907 | −0.0624537 | − | 0.998048i | \(-0.519893\pi\) | ||||
−0.0624537 | + | 0.998048i | \(0.519893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3057.71 | −0.395486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9611.86 | 1.23373 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6251.85 | −0.796366 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6593.27 | −0.833518 | −0.416759 | − | 0.909017i | \(-0.636834\pi\) | ||||
−0.416759 | + | 0.909017i | \(0.636834\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1418.49 | −0.177978 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1027.58 | −0.127967 | −0.0639834 | − | 0.997951i | \(-0.520380\pi\) | ||||
−0.0639834 | + | 0.997951i | \(0.520380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2737.38 | 0.338359 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 772.967 | 0.0948372 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7710.68 | 0.939077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1733.46 | 0.209570 | 0.104785 | − | 0.994495i | \(-0.466585\pi\) | ||||
0.104785 | + | 0.994495i | \(0.466585\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5055.84 | 0.606779 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2970.51 | −0.353921 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3639.52 | −0.430498 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6087.03 | 0.714828 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7022.33 | 0.818767 | 0.409384 | − | 0.912362i | \(-0.365744\pi\) | ||||
0.409384 | + | 0.912362i | \(0.365744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14218.0 | −1.64594 | −0.822971 | − | 0.568083i | \(-0.807685\pi\) | ||||
−0.822971 | + | 0.568083i | \(0.807685\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6135.31 | 0.705222 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3604.17 | −0.411360 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1076.09 | −0.121957 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1608.22 | −0.180992 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5156.37 | 0.576273 | 0.288136 | − | 0.957589i | \(-0.406964\pi\) | ||||
0.288136 | + | 0.957589i | \(0.406964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8676.62 | −0.962983 | −0.481492 | − | 0.876451i | \(-0.659905\pi\) | ||||
−0.481492 | + | 0.876451i | \(0.659905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −685.615 | −0.0755695 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5385.46 | 0.589523 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5758.81 | −0.626089 | −0.313045 | − | 0.949738i | \(-0.601349\pi\) | ||||
−0.313045 | + | 0.949738i | \(0.601349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4672.75 | 0.504562 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1755.56 | −0.188283 | −0.0941415 | − | 0.995559i | \(-0.530011\pi\) | ||||
−0.0941415 | + | 0.995559i | \(0.530011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1324.16 | 0.141058 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3011.90 | 0.318698 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10362.4 | 1.08915 | 0.544577 | − | 0.838711i | \(-0.316690\pi\) | ||||
0.544577 | + | 0.838711i | \(0.316690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1633.07 | 0.170506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1661.67 | −0.172345 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 699.298 | 0.0720519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2767.51 | −0.283280 | −0.141640 | − | 0.989918i | \(-0.545237\pi\) | ||||
−0.141640 | + | 0.989918i | \(0.545237\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6630.54 | 0.674263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7136.27 | −0.720974 | −0.360487 | − | 0.932764i | \(-0.617390\pi\) | ||||
−0.360487 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2046.79 | 0.205448 | 0.102724 | − | 0.994710i | \(-0.467244\pi\) | ||||
0.102724 | + | 0.994710i | \(0.467244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3165.20 | 0.315662 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9820.16 | −0.973068 | −0.486534 | − | 0.873662i | \(-0.661739\pi\) | ||||
−0.486534 | + | 0.873662i | \(0.661739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 704.297 | 0.0693420 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1187.34 | −0.116157 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5222.45 | 0.507672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6347.93 | 0.613186 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2014.27 | −0.193348 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5722.78 | 0.545888 | 0.272944 | − | 0.962030i | \(-0.412003\pi\) | ||||
0.272944 | + | 0.962030i | \(0.412003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7022.23 | 0.665668 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1197.01 | −0.112765 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12543.9 | 1.17441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14805.4 | 1.37761 | 0.688805 | − | 0.724946i | \(-0.258136\pi\) | ||||
0.688805 | + | 0.724946i | \(0.258136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5200.43 | −0.480923 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2100.56 | 0.193069 | 0.0965343 | − | 0.995330i | \(-0.469224\pi\) | ||||
0.0965343 | + | 0.995330i | \(0.469224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1315.37 | −0.120165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2231.04 | 0.202582 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4116.93 | −0.371568 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17495.0 | −1.56950 | −0.784752 | − | 0.619810i | \(-0.787210\pi\) | ||||
−0.784752 | + | 0.619810i | \(0.787210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6274.13 | −0.559496 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 657.285 | 0.0582642 | 0.0291321 | − | 0.999576i | \(-0.490726\pi\) | ||||
0.0291321 | + | 0.999576i | \(0.490726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1141.65 | 0.100599 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6232.41 | 0.545939 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −416.399 | −0.0362604 | −0.0181302 | − | 0.999836i | \(-0.505771\pi\) | ||||
−0.0181302 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −827.777 | −0.0716609 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11678.2 | −1.00508 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4061.08 | 0.347481 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9353.77 | −0.795703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5855.86 | 0.495267 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12612.5 | 1.06058 | 0.530291 | − | 0.847816i | \(-0.322083\pi\) | ||||
0.530291 | + | 0.847816i | \(0.322083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1894.84 | −0.158424 | −0.0792118 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792118 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1410.93 | −0.117292 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6072.50 | 0.501940 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7622.41 | −0.626482 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8630.97 | −0.705371 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1487.26 | 0.120864 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4045.70 | −0.326936 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7399.11 | 0.594591 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7123.98 | −0.569298 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16807.5 | −1.33569 | −0.667846 | − | 0.744300i | \(-0.732783\pi\) | ||||
−0.667846 | + | 0.744300i | \(0.732783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6118.26 | −0.483535 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −454.163 | −0.0356958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12610.7 | 0.985733 | 0.492866 | − | 0.870105i | \(-0.335949\pi\) | ||||
0.492866 | + | 0.870105i | \(0.335949\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3126.62 | −0.243062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2316.72 | 0.179121 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4695.43 | −0.361067 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8119.72 | 0.621014 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 755.062 | 0.0574381 | 0.0287190 | − | 0.999588i | \(-0.490857\pi\) | ||||
0.0287190 | + | 0.999588i | \(0.490857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4756.16 | 0.359865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3567.60 | −0.268493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16459.1 | 1.23209 | 0.616045 | − | 0.787711i | \(-0.288734\pi\) | ||||
0.616045 | + | 0.787711i | \(0.288734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12212.4 | 0.909346 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 580.535 | 0.0429985 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2566.16 | 0.189067 | 0.0945335 | − | 0.995522i | \(-0.469864\pi\) | ||||
0.0945335 | + | 0.995522i | \(0.469864\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2946.30 | −0.215935 | −0.107968 | − | 0.994154i | \(-0.534434\pi\) | ||||
−0.107968 | + | 0.994154i | \(0.534434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6673.95 | 0.486577 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5356.79 | 0.388510 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16439.8 | 1.18613 | 0.593065 | − | 0.805154i | \(-0.297918\pi\) | ||||
0.593065 | + | 0.805154i | \(0.297918\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16671.6 | 1.19663 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2733.45 | −0.195185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3070.91 | 0.218155 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2031.84 | 0.143601 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8578.20 | 0.603169 | 0.301585 | − | 0.953439i | \(-0.402484\pi\) | ||||
0.301585 | + | 0.953439i | \(0.402484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10695.3 | −0.748206 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2329.08 | −0.162107 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10209.1 | −0.706979 | −0.353490 | − | 0.935438i | \(-0.615005\pi\) | ||||
−0.353490 | + | 0.935438i | \(0.615005\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1551.29 | 0.106885 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10167.5 | −0.697033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28912.5 | −1.97217 | −0.986087 | − | 0.166232i | \(-0.946840\pi\) | ||||
−0.986087 | + | 0.166232i | \(0.946840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18387.2 | 1.24797 | 0.623986 | − | 0.781435i | \(-0.285512\pi\) | ||||
0.623986 | + | 0.781435i | \(0.285512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2046.37 | 0.138200 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5580.47 | 0.375006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8495.13 | 0.568051 | 0.284025 | − | 0.958817i | \(-0.408330\pi\) | ||||
0.284025 | + | 0.958817i | \(0.408330\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −514.929 | −0.0342627 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8518.61 | −0.564036 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2054.08 | 0.135340 | 0.0676700 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676700 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1719.70 | 0.112756 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5368.22 | −0.350270 | −0.175135 | − | 0.984544i | \(-0.556036\pi\) | ||||
−0.175135 | + | 0.984544i | \(0.556036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12026.5 | 0.780916 | 0.390458 | − | 0.920621i | \(-0.372317\pi\) | ||||
0.390458 | + | 0.920621i | \(0.372317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9854.79 | −0.636810 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 994.502 | 0.0639549 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 621.824 | 0.0397967 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6283.53 | 0.400223 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15577.8 | 0.987486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5964.45 | −0.376293 | −0.188147 | − | 0.982141i | \(-0.560248\pi\) | ||||
−0.188147 | + | 0.982141i | \(0.560248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12956.2 | −0.813526 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11873.1 | −0.741999 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6487.91 | −0.403549 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11961.9 | −0.740543 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18376.9 | −1.13236 | −0.566181 | − | 0.824281i | \(-0.691580\pi\) | ||||
−0.566181 | + | 0.824281i | \(0.691580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1716.99 | 0.105306 | 0.0526529 | − | 0.998613i | \(-0.483232\pi\) | ||||
0.0526529 | + | 0.998613i | \(0.483232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5499.49 | 0.335724 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15572.9 | −0.946266 | −0.473133 | − | 0.880991i | \(-0.656877\pi\) | ||||
−0.473133 | + | 0.880991i | \(0.656877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13158.6 | 0.795872 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2377.21 | 0.143119 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 408.474 | 0.0244790 | 0.0122395 | − | 0.999925i | \(-0.496104\pi\) | ||||
0.0122395 | + | 0.999925i | \(0.496104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18514.1 | 1.10444 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2405.15 | −0.142822 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2482.85 | 0.146765 | 0.0733824 | − | 0.997304i | \(-0.476621\pi\) | ||||
0.0733824 | + | 0.997304i | \(0.476621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18389.9 | 1.08212 | 0.541061 | − | 0.840983i | \(-0.318023\pi\) | ||||
0.541061 | + | 0.840983i | \(0.318023\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3249.07 | −0.190322 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2732.25 | −0.159327 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1954.99 | 0.113490 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4839.43 | 0.279676 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4766.79 | 0.274247 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7094.41 | 0.406344 | 0.203172 | − | 0.979143i | \(-0.434875\pi\) | ||||
0.203172 | + | 0.979143i | \(0.434875\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11616.0 | −0.662371 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34603.8 | 1.96445 | 0.982224 | − | 0.187715i | \(-0.0601080\pi\) | ||||
0.982224 | + | 0.187715i | \(0.0601080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9421.07 | 0.532470 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9223.67 | 0.519019 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9849.61 | 0.551808 | 0.275904 | − | 0.961185i | \(-0.411023\pi\) | ||||
0.275904 | + | 0.961185i | \(0.411023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9738.44 | 0.543192 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10235.8 | 0.568444 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2796.72 | 0.154640 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25353.4 | −1.39579 | −0.697894 | − | 0.716201i | \(-0.745879\pi\) | ||||
−0.697894 | + | 0.716201i | \(0.745879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1675.62 | 0.0918492 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11724.7 | 0.639918 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3299.28 | 0.179296 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9475.17 | −0.512710 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25751.8 | 1.38749 | 0.693746 | − | 0.720220i | \(-0.255959\pi\) | ||||
0.693746 | + | 0.720220i | \(0.255959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27436.8 | −1.47198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9849.96 | −0.526200 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 857.430 | 0.0456110 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36751.0 | 1.94670 | 0.973352 | − | 0.229317i | \(-0.0736492\pi\) | ||||
0.973352 | + | 0.229317i | \(0.0736492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13642.8 | −0.719613 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9025.40 | −0.474059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3097.71 | −0.162025 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1123.14 | −0.0584997 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6541.00 | −0.339274 | −0.169637 | − | 0.985507i | \(-0.554260\pi\) | ||||
−0.169637 | + | 0.985507i | \(0.554260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3050.06 | 0.157545 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5416.22 | −0.278605 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2304.38 | 0.118045 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17838.1 | −0.910014 | −0.455007 | − | 0.890488i | \(-0.650363\pi\) | ||||
−0.455007 | + | 0.890488i | \(0.650363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15514.7 | 0.788228 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10550.9 | 0.533842 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24295.4 | −1.22424 | −0.612121 | − | 0.790764i | \(-0.709684\pi\) | ||||
−0.612121 | + | 0.790764i | \(0.709684\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7501.89 | −0.376478 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3119.85 | −0.155931 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38041.0 | 1.89359 | 0.946794 | − | 0.321840i | \(-0.104301\pi\) | ||||
0.946794 | + | 0.321840i | \(0.104301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5722.50 | 0.283699 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21176.9 | 1.04563 | 0.522816 | − | 0.852446i | \(-0.324882\pi\) | ||||
0.522816 | + | 0.852446i | \(0.324882\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5801.45 | 0.285300 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7942.16 | −0.389007 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3038.51 | −0.148230 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11864.8 | −0.576500 | −0.288250 | − | 0.957555i | \(-0.593073\pi\) | ||||
−0.288250 | + | 0.957555i | \(0.593073\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8856.89 | −0.428636 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3200.68 | −0.154284 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27080.6 | 1.30021 | 0.650105 | − | 0.759844i | \(-0.274725\pi\) | ||||
0.650105 | + | 0.759844i | \(0.274725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5302.44 | 0.253579 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7232.38 | −0.344512 | −0.172256 | − | 0.985052i | \(-0.555106\pi\) | ||||
−0.172256 | + | 0.985052i | \(0.555106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −341.097 | −0.0161842 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4507.36 | 0.213025 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11983.7 | 0.564156 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10444.7 | 0.489787 | 0.244894 | − | 0.969550i | \(-0.421247\pi\) | ||||
0.244894 | + | 0.969550i | \(0.421247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10688.3 | 0.499263 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22573.6 | 1.05035 | 0.525173 | − | 0.850995i | \(-0.324001\pi\) | ||||
0.525173 | + | 0.850995i | \(0.324001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10638.4 | −0.493087 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6098.28 | 0.281563 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5810.94 | −0.267264 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18236.9 | 0.835555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4239.34 | −0.193489 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2287.03 | −0.103984 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33268.0 | −1.50683 | −0.753415 | − | 0.657545i | \(-0.771595\pi\) | ||||
−0.753415 | + | 0.657545i | \(0.771595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29294.1 | 1.32180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9172.09 | 0.412291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4341.18 | 0.194401 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3233.82 | 0.144266 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17000.3 | 0.755561 | 0.377781 | − | 0.925895i | \(-0.376687\pi\) | ||||
0.377781 | + | 0.925895i | \(0.376687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18897.3 | −0.836721 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2889.58 | 0.127463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3666.84 | 0.161146 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2305.65 | −0.100948 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5687.64 | 0.248097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19036.8 | −0.827317 | −0.413658 | − | 0.910432i | \(-0.635749\pi\) | ||||
−0.413658 | + | 0.910432i | \(0.635749\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43037.9 | −1.86346 | −0.931729 | − | 0.363155i | \(-0.881700\pi\) | ||||
−0.931729 | + | 0.363155i | \(0.881700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5692.00 | 0.245544 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10016.9 | −0.430525 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18583.0 | −0.795760 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1526.01 | 0.0651076 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18755.1 | 0.797268 | 0.398634 | − | 0.917110i | \(-0.369484\pi\) | ||||
0.398634 | + | 0.917110i | \(0.369484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34237.8 | 1.45013 | 0.725064 | − | 0.688682i | \(-0.241810\pi\) | ||||
0.725064 | + | 0.688682i | \(0.241810\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6250.07 | 0.263757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7145.93 | 0.300470 | 0.150235 | − | 0.988650i | \(-0.451997\pi\) | ||||
0.150235 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31620.6 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730455\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18134.9 | 0.757030 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14392.5 | −0.598645 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12085.1 | −0.500864 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19571.3 | 0.808222 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −335.782 | −0.0138170 | −0.00690851 | − | 0.999976i | \(-0.502199\pi\) | ||||
−0.00690851 | + | 0.999976i | \(0.502199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4302.16 | 0.175770 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12004.7 | 0.488727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4191.20 | 0.170025 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9670.20 | 0.390907 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23152.9 | −0.932634 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2615.21 | 0.104974 | 0.0524872 | − | 0.998622i | \(-0.483285\pi\) | ||||
0.0524872 | + | 0.998622i | \(0.483285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7938.69 | −0.317541 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24072.4 | 0.959506 | 0.479753 | − | 0.877404i | \(-0.340726\pi\) | ||||
0.479753 | + | 0.877404i | \(0.340726\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21753.0 | 0.864032 | 0.432016 | − | 0.901866i | \(-0.357802\pi\) | ||||
0.432016 | + | 0.901866i | \(0.357802\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1291.58 | 0.0511229 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26023.5 | −1.02648 | −0.513239 | − | 0.858246i | \(-0.671555\pi\) | ||||
−0.513239 | + | 0.858246i | \(0.671555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11279.4 | 0.443366 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10004.7 | 0.391902 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20799.5 | 0.811940 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2841.30 | −0.110532 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27373.4 | 1.06122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6992.89 | −0.270175 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26143.6 | −1.00662 | −0.503310 | − | 0.864106i | \(-0.667885\pi\) | ||||
−0.503310 | + | 0.864106i | \(0.667885\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27937.4 | 1.07202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24084.2 | 0.921019 | 0.460510 | − | 0.887655i | \(-0.347667\pi\) | ||||
0.460510 | + | 0.887655i | \(0.347667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −861.933 | −0.0328498 | −0.0164249 | − | 0.999865i | \(-0.505228\pi\) | ||||
−0.0164249 | + | 0.999865i | \(0.505228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13856.6 | 0.526312 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24546.4 | 0.929187 | 0.464594 | − | 0.885524i | \(-0.346200\pi\) | ||||
0.464594 | + | 0.885524i | \(0.346200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8917.24 | −0.336417 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2571.62 | −0.0966919 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33283.4 | 1.24724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14252.0 | 0.532281 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4829.01 | 0.179750 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3882.55 | −0.144038 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6204.14 | 0.229400 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4130.37 | 0.152215 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11784.8 | −0.432863 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38997.7 | −1.42767 | −0.713835 | − | 0.700313i | \(-0.753044\pi\) | ||||
−0.713835 | + | 0.700313i | \(0.753044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2491.31 | 0.0909036 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49929.6 | −1.81585 | −0.907927 | − | 0.419129i | \(-0.862336\pi\) | ||||
−0.907927 | + | 0.419129i | \(0.862336\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12108.5 | 0.438918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5019.66 | 0.181360 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13905.0 | 0.500744 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20227.7 | −0.726062 | −0.363031 | − | 0.931777i | \(-0.618258\pi\) | ||||
−0.363031 | + | 0.931777i | \(0.618258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20379.3 | 0.729123 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16608.6 | 0.592286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27290.7 | −0.970069 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8862.11 | 0.313991 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26106.4 | −0.921983 | −0.460992 | − | 0.887405i | \(-0.652506\pi\) | ||||
−0.460992 | + | 0.887405i | \(0.652506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25349.2 | 0.892358 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33721.1 | −1.18326 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6871.83 | −0.240356 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3449.56 | 0.120269 | 0.0601346 | − | 0.998190i | \(-0.480847\pi\) | ||||
0.0601346 | + | 0.998190i | \(0.480847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7410.83 | −0.257554 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14748.8 | 0.510941 | 0.255471 | − | 0.966817i | \(-0.417770\pi\) | ||||
0.255471 | + | 0.966817i | \(0.417770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4903.64 | −0.169337 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4999.72 | 0.172107 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35707.9 | 1.22529 | 0.612646 | − | 0.790358i | \(-0.290105\pi\) | ||||
0.612646 | + | 0.790358i | \(0.290105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3339.45 | 0.114229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8483.60 | −0.289274 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12441.5 | 0.422896 | 0.211448 | − | 0.977389i | \(-0.432182\pi\) | ||||
0.211448 | + | 0.977389i | \(0.432182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12855.2 | 0.435586 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2281.00 | 0.0770474 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7314.02 | 0.246280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11866.9 | −0.398338 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8828.53 | −0.295426 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32112.4 | 1.07123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2697.84 | −0.0897172 | −0.0448586 | − | 0.998993i | \(-0.514284\pi\) | ||||
−0.0448586 | + | 0.998993i | \(0.514284\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12694.6 | 0.420854 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51090.8 | −1.68855 | −0.844275 | − | 0.535910i | \(-0.819969\pi\) | ||||
−0.844275 | + | 0.535910i | \(0.819969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8805.79 | 0.290134 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5692.03 | 0.186965 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36334.4 | −1.18981 | −0.594903 | − | 0.803797i | \(-0.702810\pi\) | ||||
−0.594903 | + | 0.803797i | \(0.702810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4405.39 | −0.143817 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −991.075 | −0.0322554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11595.3 | −0.376227 | −0.188114 | − | 0.982147i | \(-0.560237\pi\) | ||||
−0.188114 | + | 0.982147i | \(0.560237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4486.21 | −0.145119 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7397.78 | −0.238575 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15681.5 | −0.504188 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37459.3 | 1.20074 | 0.600369 | − | 0.799723i | \(-0.295020\pi\) | ||||
0.600369 | + | 0.799723i | \(0.295020\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14265.8 | −0.455904 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19584.4 | −0.623988 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35586.7 | −1.13043 | −0.565216 | − | 0.824943i | \(-0.691207\pi\) | ||||
−0.565216 | + | 0.824943i | \(0.691207\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50206.3 | 1.59005 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1856.4.a.be.1.4 | 8 | ||
4.3 | odd | 2 | inner | 1856.4.a.be.1.5 | 8 | ||
8.3 | odd | 2 | 928.4.a.c.1.4 | ✓ | 8 | ||
8.5 | even | 2 | 928.4.a.c.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.c.1.4 | ✓ | 8 | 8.3 | odd | 2 | ||
928.4.a.c.1.5 | yes | 8 | 8.5 | even | 2 | ||
1856.4.a.be.1.4 | 8 | 1.1 | even | 1 | trivial | ||
1856.4.a.be.1.5 | 8 | 4.3 | odd | 2 | inner |