Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.10672 | 1.09839 | 0.549195 | − | 0.835694i | \(-0.314934\pi\) | ||||
0.549195 | + | 0.835694i | \(0.314934\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.65170 | 0.206462 | ||||||||
\(5\) | 17.8784 | 1.59909 | 0.799545 | − | 0.600607i | \(-0.205074\pi\) | ||||
0.799545 | + | 0.600607i | \(0.205074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.745718 | 0.0402650 | 0.0201325 | − | 0.999797i | \(-0.493591\pi\) | ||||
0.0201325 | + | 0.999797i | \(0.493591\pi\) | |||||||
\(8\) | −19.7224 | −0.871614 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 55.5430 | 1.75643 | ||||||||
\(11\) | 24.7007 | 0.677048 | 0.338524 | − | 0.940958i | \(-0.390072\pi\) | ||||
0.338524 | + | 0.940958i | \(0.390072\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.8856 | −1.04296 | −0.521478 | − | 0.853265i | \(-0.674619\pi\) | ||||
−0.521478 | + | 0.853265i | \(0.674619\pi\) | |||||||
\(14\) | 2.31673 | 0.0442267 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −74.4855 | −1.16384 | ||||||||
\(17\) | −98.7517 | −1.40887 | −0.704435 | − | 0.709768i | \(-0.748800\pi\) | ||||
−0.704435 | + | 0.709768i | \(0.748800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.0037 | 0.350206 | 0.175103 | − | 0.984550i | \(-0.443974\pi\) | ||||
0.175103 | + | 0.984550i | \(0.443974\pi\) | |||||||
\(20\) | 29.5297 | 0.330152 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 76.7380 | 0.743664 | ||||||||
\(23\) | −104.592 | −0.948214 | −0.474107 | − | 0.880467i | \(-0.657229\pi\) | ||||
−0.474107 | + | 0.880467i | \(0.657229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 194.636 | 1.55709 | ||||||||
\(26\) | −151.874 | −1.14557 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.23170 | 0.00831320 | ||||||||
\(29\) | 143.025 | 0.915831 | 0.457915 | − | 0.888996i | \(-0.348596\pi\) | ||||
0.457915 | + | 0.888996i | \(0.348596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.12534 | −0.0528697 | −0.0264348 | − | 0.999651i | \(-0.508415\pi\) | ||||
−0.0264348 | + | 0.999651i | \(0.508415\pi\) | |||||||
\(32\) | −73.6264 | −0.406732 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −306.794 | −1.54749 | ||||||||
\(35\) | 13.3322 | 0.0643873 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −280.097 | −1.24453 | −0.622267 | − | 0.782805i | \(-0.713788\pi\) | ||||
−0.622267 | + | 0.782805i | \(0.713788\pi\) | |||||||
\(38\) | 90.1064 | 0.384663 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −352.604 | −1.39379 | ||||||||
\(41\) | −350.333 | −1.33446 | −0.667230 | − | 0.744852i | \(-0.732520\pi\) | ||||
−0.667230 | + | 0.744852i | \(0.732520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −161.036 | −0.571109 | −0.285555 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285555 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(44\) | 40.7981 | 0.139785 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −324.938 | −1.04151 | ||||||||
\(47\) | 160.894 | 0.499337 | 0.249669 | − | 0.968331i | \(-0.419678\pi\) | ||||
0.249669 | + | 0.968331i | \(0.419678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.444 | −0.998379 | ||||||||
\(50\) | 604.679 | 1.71029 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −80.7443 | −0.215331 | ||||||||
\(53\) | 316.963 | 0.821476 | 0.410738 | − | 0.911754i | \(-0.365271\pi\) | ||||
0.410738 | + | 0.911754i | \(0.365271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 441.607 | 1.08266 | ||||||||
\(56\) | −14.7073 | −0.0350955 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 444.339 | 1.00594 | ||||||||
\(59\) | −295.547 | −0.652151 | −0.326076 | − | 0.945344i | \(-0.605726\pi\) | ||||
−0.326076 | + | 0.945344i | \(0.605726\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −431.505 | −0.905713 | −0.452857 | − | 0.891583i | \(-0.649595\pi\) | ||||
−0.452857 | + | 0.891583i | \(0.649595\pi\) | |||||||
\(62\) | −28.3499 | −0.0580715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 367.147 | 0.717085 | ||||||||
\(65\) | −873.994 | −1.66778 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −547.646 | −0.998591 | −0.499296 | − | 0.866432i | \(-0.666408\pi\) | ||||
−0.499296 | + | 0.866432i | \(0.666408\pi\) | |||||||
\(68\) | −163.108 | −0.290879 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 41.4194 | 0.0707224 | ||||||||
\(71\) | −841.853 | −1.40718 | −0.703588 | − | 0.710608i | \(-0.748420\pi\) | ||||
−0.703588 | + | 0.710608i | \(0.748420\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 189.720 | 0.304178 | 0.152089 | − | 0.988367i | \(-0.451400\pi\) | ||||
0.152089 | + | 0.988367i | \(0.451400\pi\) | |||||||
\(74\) | −870.184 | −1.36698 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 47.9054 | 0.0723043 | ||||||||
\(77\) | 18.4197 | 0.0272613 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −587.506 | −0.836703 | −0.418352 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418352 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(80\) | −1331.68 | −1.86108 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1088.39 | −1.46576 | ||||||||
\(83\) | −237.277 | −0.313790 | −0.156895 | − | 0.987615i | \(-0.550148\pi\) | ||||
−0.156895 | + | 0.987615i | \(0.550148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1765.52 | −2.25291 | ||||||||
\(86\) | −500.292 | −0.627301 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −487.156 | −0.590125 | ||||||||
\(89\) | 1303.76 | 1.55279 | 0.776394 | − | 0.630248i | \(-0.217047\pi\) | ||||
0.776394 | + | 0.630248i | \(0.217047\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −36.4548 | −0.0419946 | ||||||||
\(92\) | −172.754 | −0.195771 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 499.854 | 0.548468 | ||||||||
\(95\) | 518.539 | 0.560010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −364.918 | −0.381977 | −0.190989 | − | 0.981592i | \(-0.561169\pi\) | ||||
−0.190989 | + | 0.981592i | \(0.561169\pi\) | |||||||
\(98\) | −1063.88 | −1.09661 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 321.480 | 0.321480 | ||||||||
\(101\) | 1684.17 | 1.65922 | 0.829610 | − | 0.558344i | \(-0.188563\pi\) | ||||
0.829610 | + | 0.558344i | \(0.188563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −29.1605 | −0.0278958 | −0.0139479 | − | 0.999903i | \(-0.504440\pi\) | ||||
−0.0139479 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(104\) | 964.140 | 0.909055 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 984.715 | 0.902301 | ||||||||
\(107\) | 1521.44 | 1.37461 | 0.687304 | − | 0.726370i | \(-0.258794\pi\) | ||||
0.687304 | + | 0.726370i | \(0.258794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1470.92 | 1.29256 | 0.646278 | − | 0.763102i | \(-0.276325\pi\) | ||||
0.646278 | + | 0.763102i | \(0.276325\pi\) | |||||||
\(110\) | 1371.95 | 1.18918 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −55.5451 | −0.0468618 | ||||||||
\(113\) | 28.8054 | 0.0239804 | 0.0119902 | − | 0.999928i | \(-0.496183\pi\) | ||||
0.0119902 | + | 0.999928i | \(0.496183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1869.93 | −1.51628 | ||||||||
\(116\) | 236.235 | 0.189085 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −918.181 | −0.716317 | ||||||||
\(119\) | −73.6409 | −0.0567281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −720.877 | −0.541606 | ||||||||
\(122\) | −1340.56 | −0.994827 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0723 | −0.0109156 | ||||||||
\(125\) | 1244.98 | 0.890832 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1705.66 | 1.19175 | 0.595877 | − | 0.803076i | \(-0.296805\pi\) | ||||
0.595877 | + | 0.803076i | \(0.296805\pi\) | |||||||
\(128\) | 1729.63 | 1.19437 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2715.25 | −1.83187 | ||||||||
\(131\) | −920.292 | −0.613789 | −0.306894 | − | 0.951744i | \(-0.599290\pi\) | ||||
−0.306894 | + | 0.951744i | \(0.599290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.6286 | 0.0141010 | ||||||||
\(134\) | −1701.38 | −1.09684 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1947.62 | 1.22799 | ||||||||
\(137\) | 163.174 | 0.101758 | 0.0508791 | − | 0.998705i | \(-0.483798\pi\) | ||||
0.0508791 | + | 0.998705i | \(0.483798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2133.81 | −1.30207 | −0.651035 | − | 0.759048i | \(-0.725665\pi\) | ||||
−0.651035 | + | 0.759048i | \(0.725665\pi\) | |||||||
\(140\) | 22.0208 | 0.0132936 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2615.40 | −1.54563 | ||||||||
\(143\) | −1207.51 | −0.706131 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2557.06 | 1.46450 | ||||||||
\(146\) | 589.406 | 0.334107 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −462.637 | −0.256949 | ||||||||
\(149\) | 1922.08 | 1.05680 | 0.528398 | − | 0.848997i | \(-0.322793\pi\) | ||||
0.528398 | + | 0.848997i | \(0.322793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2674.86 | −1.44157 | −0.720784 | − | 0.693159i | \(-0.756218\pi\) | ||||
−0.720784 | + | 0.693159i | \(0.756218\pi\) | |||||||
\(152\) | −572.022 | −0.305244 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 57.2249 | 0.0299436 | ||||||||
\(155\) | −163.146 | −0.0845433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1031.87 | −0.524536 | −0.262268 | − | 0.964995i | \(-0.584470\pi\) | ||||
−0.262268 | + | 0.964995i | \(0.584470\pi\) | |||||||
\(158\) | −1825.21 | −0.919027 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1316.32 | −0.650401 | ||||||||
\(161\) | −77.9960 | −0.0381798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1046.99 | −0.503106 | −0.251553 | − | 0.967843i | \(-0.580941\pi\) | ||||
−0.251553 | + | 0.967843i | \(0.580941\pi\) | |||||||
\(164\) | −578.645 | −0.275516 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −737.153 | −0.344664 | ||||||||
\(167\) | 476.791 | 0.220929 | 0.110465 | − | 0.993880i | \(-0.464766\pi\) | ||||
0.110465 | + | 0.993880i | \(0.464766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 192.801 | 0.0877565 | ||||||||
\(170\) | −5484.97 | −2.47458 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −265.982 | −0.117913 | ||||||||
\(173\) | −1492.14 | −0.655754 | −0.327877 | − | 0.944720i | \(-0.606333\pi\) | ||||
−0.327877 | + | 0.944720i | \(0.606333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 145.143 | 0.0626961 | ||||||||
\(176\) | −1839.84 | −0.787973 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4050.41 | 1.70557 | ||||||||
\(179\) | 1851.15 | 0.772968 | 0.386484 | − | 0.922296i | \(-0.373689\pi\) | ||||
0.386484 | + | 0.922296i | \(0.373689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2034.86 | −0.835633 | −0.417817 | − | 0.908531i | \(-0.637205\pi\) | ||||
−0.417817 | + | 0.908531i | \(0.637205\pi\) | |||||||
\(182\) | −113.255 | −0.0461265 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2062.80 | 0.826477 | ||||||||
\(185\) | −5007.68 | −1.99012 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2439.23 | −0.953873 | ||||||||
\(188\) | 265.749 | 0.103094 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1610.95 | 0.615110 | ||||||||
\(191\) | −3100.11 | −1.17443 | −0.587214 | − | 0.809431i | \(-0.699775\pi\) | ||||
−0.587214 | + | 0.809431i | \(0.699775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1287.94 | 0.480353 | 0.240177 | − | 0.970729i | \(-0.422795\pi\) | ||||
0.240177 | + | 0.970729i | \(0.422795\pi\) | |||||||
\(194\) | −1133.70 | −0.419560 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −565.614 | −0.206128 | ||||||||
\(197\) | −4343.12 | −1.57073 | −0.785367 | − | 0.619031i | \(-0.787526\pi\) | ||||
−0.785367 | + | 0.619031i | \(0.787526\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −30.9425 | −0.0110224 | −0.00551120 | − | 0.999985i | \(-0.501754\pi\) | ||||
−0.00551120 | + | 0.999985i | \(0.501754\pi\) | |||||||
\(200\) | −3838.68 | −1.35718 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5232.24 | 1.82247 | ||||||||
\(203\) | 106.656 | 0.0368759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6263.39 | −2.13392 | ||||||||
\(206\) | −90.5935 | −0.0306405 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3641.27 | 1.21383 | ||||||||
\(209\) | 716.411 | 0.237106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3748.26 | 1.22294 | 0.611471 | − | 0.791267i | \(-0.290578\pi\) | ||||
0.611471 | + | 0.791267i | \(0.290578\pi\) | |||||||
\(212\) | 523.527 | 0.169604 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4726.68 | 1.50986 | ||||||||
\(215\) | −2879.05 | −0.913255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.80493 | −0.00212879 | ||||||||
\(218\) | 4569.73 | 1.41973 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 729.403 | 0.223529 | ||||||||
\(221\) | 4827.53 | 1.46939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2771.21 | −0.832171 | −0.416085 | − | 0.909326i | \(-0.636598\pi\) | ||||
−0.416085 | + | 0.909326i | \(0.636598\pi\) | |||||||
\(224\) | −54.9045 | −0.0163771 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 89.4902 | 0.0263398 | ||||||||
\(227\) | −236.430 | −0.0691296 | −0.0345648 | − | 0.999402i | \(-0.511005\pi\) | ||||
−0.0345648 | + | 0.999402i | \(0.511005\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 322.526 | 0.0930705 | 0.0465352 | − | 0.998917i | \(-0.485182\pi\) | ||||
0.0465352 | + | 0.998917i | \(0.485182\pi\) | |||||||
\(230\) | −5809.35 | −1.66547 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2820.80 | −0.798251 | ||||||||
\(233\) | −1999.92 | −0.562312 | −0.281156 | − | 0.959662i | \(-0.590718\pi\) | ||||
−0.281156 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2876.53 | 0.798485 | ||||||||
\(236\) | −488.154 | −0.134645 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −228.781 | −0.0623097 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5112.71 | −1.36655 | −0.683275 | − | 0.730161i | \(-0.739445\pi\) | ||||
−0.683275 | + | 0.730161i | \(0.739445\pi\) | |||||||
\(242\) | −2239.56 | −0.594895 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −712.716 | −0.186996 | ||||||||
\(245\) | −6122.34 | −1.59650 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1417.86 | −0.365249 | ||||||||
\(248\) | 179.973 | 0.0460820 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3867.79 | 0.978482 | ||||||||
\(251\) | 2554.30 | 0.642334 | 0.321167 | − | 0.947023i | \(-0.395925\pi\) | ||||
0.321167 | + | 0.947023i | \(0.395925\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2583.49 | −0.641987 | ||||||||
\(254\) | 5299.00 | 1.30901 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2436.31 | 0.594802 | ||||||||
\(257\) | −4075.19 | −0.989119 | −0.494559 | − | 0.869144i | \(-0.664671\pi\) | ||||
−0.494559 | + | 0.869144i | \(0.664671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −208.874 | −0.0501111 | ||||||||
\(260\) | −1443.58 | −0.344334 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2859.09 | −0.674180 | ||||||||
\(263\) | −737.047 | −0.172807 | −0.0864035 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864035 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5666.78 | 1.31361 | ||||||||
\(266\) | 67.1939 | 0.0154884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −904.547 | −0.206172 | ||||||||
\(269\) | −3909.75 | −0.886178 | −0.443089 | − | 0.896478i | \(-0.646117\pi\) | ||||
−0.443089 | + | 0.896478i | \(0.646117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −843.576 | −0.189091 | −0.0945454 | − | 0.995521i | \(-0.530140\pi\) | ||||
−0.0945454 | + | 0.995521i | \(0.530140\pi\) | |||||||
\(272\) | 7355.57 | 1.63969 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 506.935 | 0.111770 | ||||||||
\(275\) | 4807.64 | 1.05422 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1297.21 | 0.281379 | 0.140690 | − | 0.990054i | \(-0.455068\pi\) | ||||
0.140690 | + | 0.990054i | \(0.455068\pi\) | |||||||
\(278\) | −6629.16 | −1.43018 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −262.943 | −0.0561209 | ||||||||
\(281\) | 6877.66 | 1.46010 | 0.730048 | − | 0.683396i | \(-0.239498\pi\) | ||||
0.730048 | + | 0.683396i | \(0.239498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 177.597 | 0.0373041 | 0.0186520 | − | 0.999826i | \(-0.494063\pi\) | ||||
0.0186520 | + | 0.999826i | \(0.494063\pi\) | |||||||
\(284\) | −1390.49 | −0.290529 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3751.38 | −0.775608 | ||||||||
\(287\) | −261.250 | −0.0537320 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4838.90 | 0.984917 | ||||||||
\(290\) | 7944.05 | 1.60859 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 313.360 | 0.0628014 | ||||||||
\(293\) | 231.891 | 0.0462362 | 0.0231181 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231181 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5283.89 | −1.04285 | ||||||||
\(296\) | 5524.19 | 1.08475 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5971.35 | 1.16078 | ||||||||
\(299\) | 5113.04 | 0.988945 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −120.087 | −0.0229957 | ||||||||
\(302\) | −8310.03 | −1.58341 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2160.36 | −0.407582 | ||||||||
\(305\) | −7714.60 | −1.44832 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1985.03 | 0.369029 | 0.184514 | − | 0.982830i | \(-0.440929\pi\) | ||||
0.184514 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(308\) | 30.4238 | 0.00562844 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −506.849 | −0.0928616 | ||||||||
\(311\) | −3843.49 | −0.700786 | −0.350393 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350393 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3979.76 | 0.718688 | 0.359344 | − | 0.933205i | \(-0.383001\pi\) | ||||
0.359344 | + | 0.933205i | \(0.383001\pi\) | |||||||
\(314\) | −3205.73 | −0.576145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −970.383 | −0.172748 | ||||||||
\(317\) | 8025.86 | 1.42201 | 0.711005 | − | 0.703187i | \(-0.248240\pi\) | ||||
0.711005 | + | 0.703187i | \(0.248240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3532.82 | 0.620062 | ||||||||
\(320\) | 6564.00 | 1.14668 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −242.312 | −0.0419364 | ||||||||
\(323\) | −2864.17 | −0.493395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9514.89 | −1.62397 | ||||||||
\(326\) | −3252.69 | −0.552607 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6909.41 | 1.16313 | ||||||||
\(329\) | 119.982 | 0.0201058 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2201.00 | 0.365493 | 0.182746 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182746 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(332\) | −391.910 | −0.0647858 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1481.26 | 0.242667 | ||||||||
\(335\) | −9791.02 | −1.59684 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9699.26 | 1.56781 | 0.783905 | − | 0.620880i | \(-0.213225\pi\) | ||||
0.783905 | + | 0.620880i | \(0.213225\pi\) | |||||||
\(338\) | 598.978 | 0.0963909 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2916.11 | −0.465141 | ||||||||
\(341\) | −225.402 | −0.0357953 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −511.148 | −0.0804646 | ||||||||
\(344\) | 3176.01 | 0.497787 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4635.67 | −0.720274 | ||||||||
\(347\) | −9863.87 | −1.52599 | −0.762997 | − | 0.646402i | \(-0.776273\pi\) | ||||
−0.762997 | + | 0.646402i | \(0.776273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11050.6 | −1.69491 | −0.847454 | − | 0.530869i | \(-0.821866\pi\) | ||||
−0.847454 | + | 0.530869i | \(0.821866\pi\) | |||||||
\(350\) | 450.920 | 0.0688648 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1818.62 | −0.275377 | ||||||||
\(353\) | 511.811 | 0.0771698 | 0.0385849 | − | 0.999255i | \(-0.487715\pi\) | ||||
0.0385849 | + | 0.999255i | \(0.487715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15051.0 | −2.25020 | ||||||||
\(356\) | 2153.42 | 0.320592 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5750.99 | 0.849021 | ||||||||
\(359\) | −12746.3 | −1.87389 | −0.936943 | − | 0.349481i | \(-0.886358\pi\) | ||||
−0.936943 | + | 0.349481i | \(0.886358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6017.78 | −0.877356 | ||||||||
\(362\) | −6321.72 | −0.917852 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −60.2124 | −0.00867030 | ||||||||
\(365\) | 3391.88 | 0.486409 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7419.01 | 1.05523 | 0.527615 | − | 0.849484i | \(-0.323086\pi\) | ||||
0.527615 | + | 0.849484i | \(0.323086\pi\) | |||||||
\(368\) | 7790.58 | 1.10357 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15557.5 | −2.18593 | ||||||||
\(371\) | 236.365 | 0.0330767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1108.86 | −0.153927 | −0.0769633 | − | 0.997034i | \(-0.524522\pi\) | ||||
−0.0769633 | + | 0.997034i | \(0.524522\pi\) | |||||||
\(374\) | −7578.01 | −1.04773 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3173.22 | −0.435230 | ||||||||
\(377\) | −6991.87 | −0.955171 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10686.4 | 1.44835 | 0.724173 | − | 0.689618i | \(-0.242222\pi\) | ||||
0.724173 | + | 0.689618i | \(0.242222\pi\) | |||||||
\(380\) | 856.471 | 0.115621 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9631.16 | −1.28998 | ||||||||
\(383\) | 12048.2 | 1.60740 | 0.803702 | − | 0.595031i | \(-0.202860\pi\) | ||||
0.803702 | + | 0.595031i | \(0.202860\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 329.314 | 0.0435933 | ||||||||
\(386\) | 4001.28 | 0.527615 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −602.734 | −0.0788639 | ||||||||
\(389\) | 1473.17 | 0.192011 | 0.0960057 | − | 0.995381i | \(-0.469393\pi\) | ||||
0.0960057 | + | 0.995381i | \(0.469393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10328.6 | 1.33591 | ||||||||
\(392\) | 6753.81 | 0.870201 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13492.9 | −1.72528 | ||||||||
\(395\) | −10503.6 | −1.33796 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5818.69 | 0.735596 | 0.367798 | − | 0.929906i | \(-0.380112\pi\) | ||||
0.367798 | + | 0.929906i | \(0.380112\pi\) | |||||||
\(398\) | −96.1297 | −0.0121069 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14497.5 | −1.81219 | ||||||||
\(401\) | 3009.09 | 0.374730 | 0.187365 | − | 0.982290i | \(-0.440005\pi\) | ||||
0.187365 | + | 0.982290i | \(0.440005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 446.098 | 0.0551407 | ||||||||
\(404\) | 2781.74 | 0.342566 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 331.351 | 0.0405042 | ||||||||
\(407\) | −6918.59 | −0.842609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12146.2 | −1.46844 | −0.734218 | − | 0.678914i | \(-0.762451\pi\) | ||||
−0.734218 | + | 0.678914i | \(0.762451\pi\) | |||||||
\(410\) | −19458.6 | −2.34388 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −48.1644 | −0.00575944 | ||||||||
\(413\) | −220.394 | −0.0262588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4242.13 | −0.501778 | ||||||||
\(416\) | 3599.27 | 0.424203 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2225.69 | 0.260435 | ||||||||
\(419\) | −7078.38 | −0.825302 | −0.412651 | − | 0.910889i | \(-0.635397\pi\) | ||||
−0.412651 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1350.43 | −0.156332 | −0.0781662 | − | 0.996940i | \(-0.524906\pi\) | ||||
−0.0781662 | + | 0.996940i | \(0.524906\pi\) | |||||||
\(422\) | 11644.8 | 1.34327 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6251.26 | −0.716010 | ||||||||
\(425\) | −19220.6 | −2.19373 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −321.781 | −0.0364685 | ||||||||
\(428\) | 2512.96 | 0.283805 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8944.41 | −1.00311 | ||||||||
\(431\) | 6841.23 | 0.764572 | 0.382286 | − | 0.924044i | \(-0.375137\pi\) | ||||
0.382286 | + | 0.924044i | \(0.375137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14287.5 | 1.58572 | 0.792859 | − | 0.609406i | \(-0.208592\pi\) | ||||
0.792859 | + | 0.609406i | \(0.208592\pi\) | |||||||
\(434\) | −21.1410 | −0.00233825 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2429.52 | 0.266864 | ||||||||
\(437\) | −3033.56 | −0.332070 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1490.40 | 0.162034 | 0.0810171 | − | 0.996713i | \(-0.474183\pi\) | ||||
0.0810171 | + | 0.996713i | \(0.474183\pi\) | |||||||
\(440\) | −8709.55 | −0.943663 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14997.8 | 1.61396 | ||||||||
\(443\) | −11204.7 | −1.20169 | −0.600847 | − | 0.799364i | \(-0.705170\pi\) | ||||
−0.600847 | + | 0.799364i | \(0.705170\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23309.1 | 2.48305 | ||||||||
\(446\) | −8609.37 | −0.914049 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 273.788 | 0.0288734 | ||||||||
\(449\) | −15726.5 | −1.65296 | −0.826480 | − | 0.562966i | \(-0.809660\pi\) | ||||
−0.826480 | + | 0.562966i | \(0.809660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8653.47 | −0.903494 | ||||||||
\(452\) | 47.5778 | 0.00495104 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −734.522 | −0.0759313 | ||||||||
\(455\) | −651.753 | −0.0671531 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9442.99 | 0.966574 | 0.483287 | − | 0.875462i | \(-0.339443\pi\) | ||||
0.483287 | + | 0.875462i | \(0.339443\pi\) | |||||||
\(458\) | 1002.00 | 0.102228 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3088.57 | −0.313055 | ||||||||
\(461\) | −4345.33 | −0.439007 | −0.219504 | − | 0.975612i | \(-0.570444\pi\) | ||||
−0.219504 | + | 0.975612i | \(0.570444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11702.1 | 1.17461 | 0.587303 | − | 0.809367i | \(-0.300190\pi\) | ||||
0.587303 | + | 0.809367i | \(0.300190\pi\) | |||||||
\(464\) | −10653.3 | −1.06588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6213.17 | −0.617639 | ||||||||
\(467\) | 10980.5 | 1.08805 | 0.544023 | − | 0.839070i | \(-0.316900\pi\) | ||||
0.544023 | + | 0.839070i | \(0.316900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −408.389 | −0.0402082 | ||||||||
\(470\) | 8936.56 | 0.877049 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5828.89 | 0.568424 | ||||||||
\(473\) | −3977.69 | −0.386669 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5645.16 | 0.545301 | ||||||||
\(476\) | −121.633 | −0.0117122 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 742.506 | 0.0710490 | ||||||||
\(479\) | −16368.3 | −1.56135 | −0.780673 | − | 0.624939i | \(-0.785124\pi\) | ||||
−0.780673 | + | 0.624939i | \(0.785124\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13692.7 | 1.29799 | ||||||||
\(482\) | −15883.8 | −1.50101 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1190.67 | −0.111821 | ||||||||
\(485\) | −6524.13 | −0.610815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5105.40 | −0.475047 | −0.237523 | − | 0.971382i | \(-0.576336\pi\) | ||||
−0.237523 | + | 0.971382i | \(0.576336\pi\) | |||||||
\(488\) | 8510.30 | 0.789433 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19020.4 | −1.75358 | ||||||||
\(491\) | −1265.56 | −0.116322 | −0.0581608 | − | 0.998307i | \(-0.518524\pi\) | ||||
−0.0581608 | + | 0.998307i | \(0.518524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14124.0 | −1.29029 | ||||||||
\(494\) | −4404.90 | −0.401186 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 679.705 | 0.0615316 | ||||||||
\(497\) | −627.784 | −0.0566599 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4373.23 | 0.392330 | 0.196165 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196165 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(500\) | 2056.33 | 0.183923 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7935.48 | 0.705534 | ||||||||
\(503\) | 19926.2 | 1.76633 | 0.883164 | − | 0.469064i | \(-0.155409\pi\) | ||||
0.883164 | + | 0.469064i | \(0.155409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30110.2 | 2.65324 | ||||||||
\(506\) | −8026.18 | −0.705152 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2817.23 | 0.246052 | ||||||||
\(509\) | 15679.4 | 1.36538 | 0.682691 | − | 0.730708i | \(-0.260810\pi\) | ||||
0.682691 | + | 0.730708i | \(0.260810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 141.477 | 0.0122477 | ||||||||
\(512\) | −6268.15 | −0.541047 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12660.5 | −1.08644 | ||||||||
\(515\) | −521.343 | −0.0446080 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3974.20 | 0.338075 | ||||||||
\(518\) | −648.911 | −0.0550416 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17237.3 | 1.45366 | ||||||||
\(521\) | −16954.5 | −1.42570 | −0.712850 | − | 0.701316i | \(-0.752596\pi\) | ||||
−0.712850 | + | 0.701316i | \(0.752596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20850.4 | 1.74326 | 0.871628 | − | 0.490167i | \(-0.163064\pi\) | ||||
0.871628 | + | 0.490167i | \(0.163064\pi\) | |||||||
\(524\) | −1520.05 | −0.126724 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2289.80 | −0.189810 | ||||||||
\(527\) | 901.143 | 0.0744865 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1227.53 | −0.100890 | ||||||||
\(530\) | 17605.1 | 1.44286 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 35.7239 | 0.00291133 | ||||||||
\(533\) | 17126.3 | 1.39178 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27200.8 | 2.19812 | ||||||||
\(536\) | 10800.9 | 0.870387 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12146.5 | −0.973370 | ||||||||
\(539\) | −8458.59 | −0.675951 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3440.60 | 0.273425 | 0.136712 | − | 0.990611i | \(-0.456346\pi\) | ||||
0.136712 | + | 0.990611i | \(0.456346\pi\) | |||||||
\(542\) | −2620.75 | −0.207696 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7270.73 | 0.573033 | ||||||||
\(545\) | 26297.6 | 2.06691 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11784.0 | 0.921113 | 0.460556 | − | 0.887630i | \(-0.347650\pi\) | ||||
0.460556 | + | 0.887630i | \(0.347650\pi\) | |||||||
\(548\) | 269.514 | 0.0210092 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14936.0 | 1.15795 | ||||||||
\(551\) | 4148.26 | 0.320729 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −438.113 | −0.0336898 | ||||||||
\(554\) | 4030.08 | 0.309064 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3524.42 | −0.268829 | ||||||||
\(557\) | 620.891 | 0.0472316 | 0.0236158 | − | 0.999721i | \(-0.492482\pi\) | ||||
0.0236158 | + | 0.999721i | \(0.492482\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7872.32 | 0.595642 | ||||||||
\(560\) | −993.056 | −0.0749362 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21366.9 | 1.60376 | ||||||||
\(563\) | −26002.2 | −1.94647 | −0.973233 | − | 0.229821i | \(-0.926186\pi\) | ||||
−0.973233 | + | 0.229821i | \(0.926186\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 514.993 | 0.0383467 | ||||||||
\(566\) | 551.744 | 0.0409745 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16603.3 | 1.22652 | ||||||||
\(569\) | 10004.8 | 0.737120 | 0.368560 | − | 0.929604i | \(-0.379851\pi\) | ||||
0.368560 | + | 0.929604i | \(0.379851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9283.06 | −0.680357 | −0.340179 | − | 0.940361i | \(-0.610488\pi\) | ||||
−0.340179 | + | 0.940361i | \(0.610488\pi\) | |||||||
\(572\) | −1994.44 | −0.145790 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −811.629 | −0.0590187 | ||||||||
\(575\) | −20357.3 | −1.47645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4371.52 | −0.315405 | −0.157703 | − | 0.987487i | \(-0.550409\pi\) | ||||
−0.157703 | + | 0.987487i | \(0.550409\pi\) | |||||||
\(578\) | 15033.1 | 1.08182 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4223.49 | 0.302363 | ||||||||
\(581\) | −176.942 | −0.0126347 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7829.19 | 0.556179 | ||||||||
\(584\) | −3741.73 | −0.265126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 720.419 | 0.0507854 | ||||||||
\(587\) | −5076.25 | −0.356932 | −0.178466 | − | 0.983946i | \(-0.557114\pi\) | ||||
−0.178466 | + | 0.983946i | \(0.557114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −264.669 | −0.0185153 | ||||||||
\(590\) | −16415.6 | −1.14545 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20863.2 | 1.44843 | ||||||||
\(593\) | 14397.4 | 0.997019 | 0.498509 | − | 0.866884i | \(-0.333881\pi\) | ||||
0.498509 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1316.58 | −0.0907134 | ||||||||
\(596\) | 3174.69 | 0.218189 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15884.8 | 1.08625 | ||||||||
\(599\) | 13497.3 | 0.920676 | 0.460338 | − | 0.887744i | \(-0.347728\pi\) | ||||
0.460338 | + | 0.887744i | \(0.347728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7012.74 | 0.475966 | 0.237983 | − | 0.971269i | \(-0.423514\pi\) | ||||
0.237983 | + | 0.971269i | \(0.423514\pi\) | |||||||
\(602\) | −373.077 | −0.0252583 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4418.06 | −0.297630 | ||||||||
\(605\) | −12888.1 | −0.866076 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22822.2 | −1.52607 | −0.763035 | − | 0.646357i | \(-0.776292\pi\) | ||||
−0.763035 | + | 0.646357i | \(0.776292\pi\) | |||||||
\(608\) | −2135.44 | −0.142440 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23967.1 | −1.59082 | ||||||||
\(611\) | −7865.42 | −0.520787 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12441.8 | −0.819771 | −0.409885 | − | 0.912137i | \(-0.634431\pi\) | ||||
−0.409885 | + | 0.912137i | \(0.634431\pi\) | |||||||
\(614\) | 6166.94 | 0.405338 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −363.281 | −0.0237614 | ||||||||
\(617\) | −8903.80 | −0.580962 | −0.290481 | − | 0.956881i | \(-0.593815\pi\) | ||||
−0.290481 | + | 0.956881i | \(0.593815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1315.39 | −0.0854120 | −0.0427060 | − | 0.999088i | \(-0.513598\pi\) | ||||
−0.0427060 | + | 0.999088i | \(0.513598\pi\) | |||||||
\(620\) | −269.468 | −0.0174550 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11940.7 | −0.769737 | ||||||||
\(623\) | 972.236 | 0.0625230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2071.36 | −0.132567 | ||||||||
\(626\) | 12364.0 | 0.789400 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1704.34 | −0.108297 | ||||||||
\(629\) | 27660.1 | 1.75339 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27108.3 | 1.71024 | 0.855121 | − | 0.518429i | \(-0.173483\pi\) | ||||
0.855121 | + | 0.518429i | \(0.173483\pi\) | |||||||
\(632\) | 11587.0 | 0.729282 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24934.1 | 1.56192 | ||||||||
\(635\) | 30494.4 | 1.90572 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16740.6 | 1.04126 | ||||||||
\(638\) | 10975.5 | 0.681070 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30923.0 | 1.90991 | ||||||||
\(641\) | −11334.4 | −0.698409 | −0.349204 | − | 0.937047i | \(-0.613548\pi\) | ||||
−0.349204 | + | 0.937047i | \(0.613548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1526.23 | 0.0936063 | 0.0468031 | − | 0.998904i | \(-0.485097\pi\) | ||||
0.0468031 | + | 0.998904i | \(0.485097\pi\) | |||||||
\(644\) | −128.826 | −0.00788270 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8898.16 | −0.541940 | ||||||||
\(647\) | 1836.25 | 0.111577 | 0.0557886 | − | 0.998443i | \(-0.482233\pi\) | ||||
0.0557886 | + | 0.998443i | \(0.482233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7300.20 | −0.441538 | ||||||||
\(650\) | −29560.1 | −1.78376 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1729.31 | −0.103873 | ||||||||
\(653\) | 18006.4 | 1.07909 | 0.539543 | − | 0.841958i | \(-0.318597\pi\) | ||||
0.539543 | + | 0.841958i | \(0.318597\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16453.3 | −0.981503 | ||||||||
\(656\) | 26094.7 | 1.55309 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 372.750 | 0.0220840 | ||||||||
\(659\) | −13881.1 | −0.820531 | −0.410266 | − | 0.911966i | \(-0.634564\pi\) | ||||
−0.410266 | + | 0.911966i | \(0.634564\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13229.9 | −0.778495 | −0.389247 | − | 0.921133i | \(-0.627265\pi\) | ||||
−0.389247 | + | 0.921133i | \(0.627265\pi\) | |||||||
\(662\) | 6837.90 | 0.401454 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4679.67 | 0.273504 | ||||||||
\(665\) | 386.684 | 0.0225488 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14959.3 | −0.868404 | ||||||||
\(668\) | 787.515 | 0.0456136 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30417.9 | −1.75395 | ||||||||
\(671\) | −10658.4 | −0.613211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6521.08 | 0.373505 | 0.186753 | − | 0.982407i | \(-0.440204\pi\) | ||||
0.186753 | + | 0.982407i | \(0.440204\pi\) | |||||||
\(674\) | 30132.9 | 1.72207 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 318.449 | 0.0181184 | ||||||||
\(677\) | 14707.0 | 0.834914 | 0.417457 | − | 0.908697i | \(-0.362921\pi\) | ||||
0.417457 | + | 0.908697i | \(0.362921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −272.125 | −0.0153803 | ||||||||
\(680\) | 34820.2 | 1.96367 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −700.260 | −0.0393172 | ||||||||
\(683\) | 30336.2 | 1.69954 | 0.849768 | − | 0.527157i | \(-0.176742\pi\) | ||||
0.849768 | + | 0.527157i | \(0.176742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2917.28 | 0.162720 | ||||||||
\(686\) | −1587.99 | −0.0883816 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11994.8 | 0.664677 | ||||||||
\(689\) | −15494.9 | −0.856763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22793.2 | 1.25484 | 0.627421 | − | 0.778680i | \(-0.284110\pi\) | ||||
0.627421 | + | 0.778680i | \(0.284110\pi\) | |||||||
\(692\) | −2464.57 | −0.135389 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30644.3 | −1.67614 | ||||||||
\(695\) | −38149.1 | −2.08213 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34596.0 | 1.88008 | ||||||||
\(698\) | −34331.0 | −1.86167 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 239.733 | 0.0129444 | ||||||||
\(701\) | −4226.10 | −0.227700 | −0.113850 | − | 0.993498i | \(-0.536318\pi\) | ||||
−0.113850 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8123.87 | −0.435843 | ||||||||
\(704\) | 9068.79 | 0.485501 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1590.05 | 0.0847626 | ||||||||
\(707\) | 1255.91 | 0.0668084 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29662.6 | −1.57123 | −0.785615 | − | 0.618715i | \(-0.787653\pi\) | ||||
−0.785615 | + | 0.618715i | \(0.787653\pi\) | |||||||
\(710\) | −46759.1 | −2.47160 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25713.2 | −1.35343 | ||||||||
\(713\) | 954.437 | 0.0501318 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21588.2 | −1.12917 | ||||||||
\(716\) | 3057.54 | 0.159589 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −39599.2 | −2.05826 | ||||||||
\(719\) | 28079.9 | 1.45647 | 0.728237 | − | 0.685325i | \(-0.240340\pi\) | ||||
0.728237 | + | 0.685325i | \(0.240340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.7455 | −0.00112323 | ||||||||
\(722\) | −18695.6 | −0.963680 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3360.97 | −0.172527 | ||||||||
\(725\) | 27837.8 | 1.42603 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6488.86 | 0.331030 | 0.165515 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165515 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(728\) | 718.976 | 0.0366031 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10537.6 | 0.534267 | ||||||||
\(731\) | 15902.5 | 0.804619 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5082.45 | 0.256104 | 0.128052 | − | 0.991767i | \(-0.459127\pi\) | ||||
0.128052 | + | 0.991767i | \(0.459127\pi\) | |||||||
\(734\) | 23048.8 | 1.15905 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7700.72 | 0.385669 | ||||||||
\(737\) | −13527.2 | −0.676094 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2586.05 | −0.128727 | −0.0643635 | − | 0.997927i | \(-0.520502\pi\) | ||||
−0.0643635 | + | 0.997927i | \(0.520502\pi\) | |||||||
\(740\) | −8271.19 | −0.410885 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 734.319 | 0.0363311 | ||||||||
\(743\) | 13473.8 | 0.665283 | 0.332641 | − | 0.943053i | \(-0.392060\pi\) | ||||
0.332641 | + | 0.943053i | \(0.392060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34363.6 | 1.68991 | ||||||||
\(746\) | −3444.92 | −0.169072 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4028.88 | −0.196939 | ||||||||
\(749\) | 1134.56 | 0.0553486 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17858.4 | 0.867724 | 0.433862 | − | 0.900979i | \(-0.357150\pi\) | ||||
0.433862 | + | 0.900979i | \(0.357150\pi\) | |||||||
\(752\) | −11984.3 | −0.581147 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21721.8 | −1.04915 | ||||||||
\(755\) | −47822.1 | −2.30520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3622.31 | −0.173917 | −0.0869583 | − | 0.996212i | \(-0.527715\pi\) | ||||
−0.0869583 | + | 0.996212i | \(0.527715\pi\) | |||||||
\(758\) | 33199.6 | 1.59085 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10226.8 | −0.488113 | ||||||||
\(761\) | 2386.44 | 0.113677 | 0.0568386 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568386 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1096.89 | 0.0520447 | ||||||||
\(764\) | −5120.45 | −0.242475 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37430.5 | 1.76556 | ||||||||
\(767\) | 14448.0 | 0.680165 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4038.92 | 0.189398 | 0.0946990 | − | 0.995506i | \(-0.469811\pi\) | ||||
0.0946990 | + | 0.995506i | \(0.469811\pi\) | |||||||
\(770\) | 1023.09 | 0.0478825 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2127.29 | 0.0991749 | ||||||||
\(773\) | 17780.2 | 0.827306 | 0.413653 | − | 0.910435i | \(-0.364253\pi\) | ||||
0.413653 | + | 0.910435i | \(0.364253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1776.12 | −0.0823227 | ||||||||
\(776\) | 7197.04 | 0.332937 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4576.71 | 0.210904 | ||||||||
\(779\) | −10161.0 | −0.467336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20794.3 | −0.952727 | ||||||||
\(782\) | 32088.1 | 1.46735 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25507.1 | 1.16195 | ||||||||
\(785\) | −18448.1 | −0.838779 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28216.2 | 1.27802 | 0.639009 | − | 0.769199i | \(-0.279345\pi\) | ||||
0.639009 | + | 0.769199i | \(0.279345\pi\) | |||||||
\(788\) | −7173.53 | −0.324298 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32631.8 | −1.46961 | ||||||||
\(791\) | 21.4807 | 0.000965568 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21094.4 | 0.944619 | ||||||||
\(794\) | 18077.0 | 0.807972 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −51.1077 | −0.00227571 | ||||||||
\(797\) | −8810.39 | −0.391568 | −0.195784 | − | 0.980647i | \(-0.562725\pi\) | ||||
−0.195784 | + | 0.980647i | \(0.562725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15888.6 | −0.703502 | ||||||||
\(800\) | −14330.3 | −0.633317 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9348.38 | 0.411600 | ||||||||
\(803\) | 4686.21 | 0.205943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1394.44 | −0.0610529 | ||||||||
\(806\) | 1385.90 | 0.0605660 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33215.8 | −1.44620 | ||||||||
\(809\) | 5436.82 | 0.236277 | 0.118139 | − | 0.992997i | \(-0.462307\pi\) | ||||
0.118139 | + | 0.992997i | \(0.462307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11563.5 | 0.500678 | 0.250339 | − | 0.968158i | \(-0.419458\pi\) | ||||
0.250339 | + | 0.968158i | \(0.419458\pi\) | |||||||
\(812\) | 176.164 | 0.00761349 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21494.1 | −0.925514 | ||||||||
\(815\) | −18718.4 | −0.804512 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4670.63 | −0.200006 | ||||||||
\(818\) | −37734.8 | −1.61292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10345.2 | −0.440575 | ||||||||
\(821\) | −25869.9 | −1.09972 | −0.549858 | − | 0.835258i | \(-0.685318\pi\) | ||||
−0.549858 | + | 0.835258i | \(0.685318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6191.18 | −0.262225 | −0.131112 | − | 0.991368i | \(-0.541855\pi\) | ||||
−0.131112 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(824\) | 575.115 | 0.0243144 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −684.703 | −0.0288425 | ||||||||
\(827\) | 33775.3 | 1.42017 | 0.710086 | − | 0.704115i | \(-0.248656\pi\) | ||||
0.710086 | + | 0.704115i | \(0.248656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9016.25 | −0.377741 | −0.188871 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188871 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(830\) | −13179.1 | −0.551148 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17948.2 | −0.747888 | ||||||||
\(833\) | 33816.9 | 1.40659 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8524.24 | 0.353286 | ||||||||
\(836\) | 1183.30 | 0.0489535 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21990.5 | −0.906504 | ||||||||
\(839\) | −45095.2 | −1.85561 | −0.927806 | − | 0.373062i | \(-0.878308\pi\) | ||||
−0.927806 | + | 0.373062i | \(0.878308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3932.81 | −0.161254 | ||||||||
\(842\) | −4195.41 | −0.171714 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6191.00 | 0.252492 | ||||||||
\(845\) | 3446.97 | 0.140330 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −537.571 | −0.0218077 | ||||||||
\(848\) | −23609.1 | −0.956063 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59713.1 | −2.40958 | ||||||||
\(851\) | 29295.9 | 1.18008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49211.7 | −1.97535 | −0.987676 | − | 0.156513i | \(-0.949975\pi\) | ||||
−0.987676 | + | 0.156513i | \(0.949975\pi\) | |||||||
\(854\) | −999.682 | −0.0400567 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30006.4 | −1.19813 | ||||||||
\(857\) | 23038.6 | 0.918300 | 0.459150 | − | 0.888359i | \(-0.348154\pi\) | ||||
0.459150 | + | 0.888359i | \(0.348154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6529.39 | −0.259348 | −0.129674 | − | 0.991557i | \(-0.541393\pi\) | ||||
−0.129674 | + | 0.991557i | \(0.541393\pi\) | |||||||
\(860\) | −4755.33 | −0.188553 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21253.8 | 0.839799 | ||||||||
\(863\) | 18172.1 | 0.716786 | 0.358393 | − | 0.933571i | \(-0.383325\pi\) | ||||
0.358393 | + | 0.933571i | \(0.383325\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26677.1 | −1.04861 | ||||||||
\(866\) | 44387.4 | 1.74174 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.2397 | −0.000439516 0 | ||||||||
\(869\) | −14511.8 | −0.566488 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26772.0 | 1.04149 | ||||||||
\(872\) | −29010.0 | −1.12661 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9424.40 | −0.364743 | ||||||||
\(875\) | 928.400 | 0.0358693 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9910.10 | 0.381574 | 0.190787 | − | 0.981631i | \(-0.438896\pi\) | ||||
0.190787 | + | 0.981631i | \(0.438896\pi\) | |||||||
\(878\) | 4630.26 | 0.177977 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32893.3 | −1.26004 | ||||||||
\(881\) | −3153.32 | −0.120588 | −0.0602940 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602940 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11764.5 | −0.448366 | −0.224183 | − | 0.974547i | \(-0.571971\pi\) | ||||
−0.224183 | + | 0.974547i | \(0.571971\pi\) | |||||||
\(884\) | 7973.64 | 0.303374 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34809.8 | −1.31993 | ||||||||
\(887\) | 35545.6 | 1.34555 | 0.672777 | − | 0.739846i | \(-0.265101\pi\) | ||||
0.672777 | + | 0.739846i | \(0.265101\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1271.94 | 0.0479859 | ||||||||
\(890\) | 72414.7 | 2.72736 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4577.21 | −0.171812 | ||||||||
\(893\) | 4666.54 | 0.174871 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33095.5 | 1.23604 | ||||||||
\(896\) | 1289.82 | 0.0480913 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48857.8 | −1.81560 | ||||||||
\(899\) | −1305.15 | −0.0484197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31300.6 | −1.15735 | ||||||||
\(902\) | −26883.9 | −0.992390 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −568.110 | −0.0209016 | ||||||||
\(905\) | −36379.9 | −1.33625 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7842.99 | 0.287125 | 0.143562 | − | 0.989641i | \(-0.454144\pi\) | ||||
0.143562 | + | 0.989641i | \(0.454144\pi\) | |||||||
\(908\) | −390.511 | −0.0142727 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2024.81 | −0.0737603 | ||||||||
\(911\) | 17676.5 | 0.642862 | 0.321431 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321431 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5860.90 | −0.212451 | ||||||||
\(914\) | 29336.7 | 1.06168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 532.716 | 0.0192156 | ||||||||
\(917\) | −686.278 | −0.0247142 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40448.5 | 1.45187 | 0.725937 | − | 0.687761i | \(-0.241406\pi\) | ||||
0.725937 | + | 0.687761i | \(0.241406\pi\) | |||||||
\(920\) | 36879.5 | 1.32161 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13499.7 | −0.482202 | ||||||||
\(923\) | 41154.5 | 1.46762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54517.0 | −1.93785 | ||||||||
\(926\) | 36355.1 | 1.29018 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10530.4 | −0.372498 | ||||||||
\(929\) | −18479.7 | −0.652635 | −0.326317 | − | 0.945260i | \(-0.605808\pi\) | ||||
−0.326317 | + | 0.945260i | \(0.605808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9932.15 | −0.349638 | ||||||||
\(932\) | −3303.26 | −0.116096 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34113.4 | 1.19510 | ||||||||
\(935\) | −43609.5 | −1.52533 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12551.8 | −0.437620 | −0.218810 | − | 0.975767i | \(-0.570218\pi\) | ||||
−0.218810 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(938\) | −1268.75 | −0.0441644 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4751.16 | 0.164857 | ||||||||
\(941\) | −42332.5 | −1.46652 | −0.733262 | − | 0.679946i | \(-0.762003\pi\) | ||||
−0.733262 | + | 0.679946i | \(0.762003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36642.0 | 1.26535 | ||||||||
\(944\) | 22013.9 | 0.758997 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12357.6 | −0.424713 | ||||||||
\(947\) | −12726.8 | −0.436710 | −0.218355 | − | 0.975869i | \(-0.570069\pi\) | ||||
−0.218355 | + | 0.975869i | \(0.570069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9274.57 | −0.317245 | ||||||||
\(950\) | 17537.9 | 0.598953 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1452.37 | 0.0494451 | ||||||||
\(953\) | 14939.7 | 0.507812 | 0.253906 | − | 0.967229i | \(-0.418285\pi\) | ||||
0.253906 | + | 0.967229i | \(0.418285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55424.8 | −1.87802 | ||||||||
\(956\) | 394.756 | 0.0133549 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50851.6 | −1.71497 | ||||||||
\(959\) | 121.682 | 0.00409729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29707.7 | −0.997205 | ||||||||
\(962\) | 42539.4 | 1.42570 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8444.66 | −0.282141 | ||||||||
\(965\) | 23026.3 | 0.768128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3191.74 | 0.106142 | 0.0530710 | − | 0.998591i | \(-0.483099\pi\) | ||||
0.0530710 | + | 0.998591i | \(0.483099\pi\) | |||||||
\(968\) | 14217.4 | 0.472071 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20268.6 | −0.670914 | ||||||||
\(971\) | 43380.7 | 1.43373 | 0.716866 | − | 0.697211i | \(-0.245576\pi\) | ||||
0.716866 | + | 0.697211i | \(0.245576\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1591.22 | −0.0524278 | ||||||||
\(974\) | −15861.0 | −0.521787 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32140.8 | 1.05410 | ||||||||
\(977\) | −57824.4 | −1.89352 | −0.946759 | − | 0.321945i | \(-0.895664\pi\) | ||||
−0.946759 | + | 0.321945i | \(0.895664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32203.7 | 1.05131 | ||||||||
\(980\) | −10112.3 | −0.329617 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3931.74 | −0.127767 | ||||||||
\(983\) | −36789.7 | −1.19370 | −0.596851 | − | 0.802352i | \(-0.703582\pi\) | ||||
−0.596851 | + | 0.802352i | \(0.703582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −77647.9 | −2.51174 | ||||||||
\(986\) | −43879.2 | −1.41724 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2341.88 | −0.0754102 | ||||||||
\(989\) | 16843.0 | 0.541534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59886.2 | 1.91963 | 0.959813 | − | 0.280641i | \(-0.0905470\pi\) | ||||
0.959813 | + | 0.280641i | \(0.0905470\pi\) | |||||||
\(992\) | 671.866 | 0.0215038 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1950.35 | −0.0622347 | ||||||||
\(995\) | −553.202 | −0.0176258 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39148.2 | 1.24357 | 0.621784 | − | 0.783189i | \(-0.286408\pi\) | ||||
0.621784 | + | 0.783189i | \(0.286408\pi\) | |||||||
\(998\) | 13586.4 | 0.430932 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.g.1.46 | ✓ | 59 | |
3.2 | odd | 2 | 2151.4.a.h.1.14 | yes | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.46 | ✓ | 59 | 1.1 | even | 1 | trivial | |
2151.4.a.h.1.14 | yes | 59 | 3.2 | odd | 2 |