Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.22700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 28x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.424864\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −15.3946 | −1.37694 | −0.688469 | − | 0.725266i | \(-0.741717\pi\) | ||||
−0.688469 | + | 0.725266i | \(0.741717\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.9957 | 0.493265 | 0.246632 | − | 0.969109i | \(-0.420676\pi\) | ||||
0.246632 | + | 0.969109i | \(0.420676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.3989 | 0.371199 | 0.185600 | − | 0.982625i | \(-0.440577\pi\) | ||||
0.185600 | + | 0.982625i | \(0.440577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −46.1839 | −0.794975 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84.3720 | −1.20372 | −0.601860 | − | 0.798602i | \(-0.705573\pi\) | ||||
−0.601860 | + | 0.798602i | \(0.705573\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 159.767 | 1.92910 | 0.964552 | − | 0.263892i | \(-0.0850061\pi\) | ||||
0.964552 | + | 0.263892i | \(0.0850061\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −115.968 | −1.05134 | −0.525672 | − | 0.850687i | \(-0.676186\pi\) | ||||
−0.525672 | + | 0.850687i | \(0.676186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 111.995 | 0.895956 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −215.362 | −1.37903 | −0.689513 | − | 0.724273i | \(-0.742176\pi\) | ||||
−0.689513 | + | 0.724273i | \(0.742176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 144.160 | 0.835223 | 0.417612 | − | 0.908626i | \(-0.362867\pi\) | ||||
0.417612 | + | 0.908626i | \(0.362867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 53.9872 | 0.284787 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −107.762 | −0.520433 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −150.960 | −0.670749 | −0.335375 | − | 0.942085i | \(-0.608863\pi\) | ||||
−0.335375 | + | 0.942085i | \(0.608863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.1967 | 0.214312 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −229.492 | −0.874163 | −0.437082 | − | 0.899422i | \(-0.643988\pi\) | ||||
−0.437082 | + | 0.899422i | \(0.643988\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 411.157 | 1.45816 | 0.729080 | − | 0.684429i | \(-0.239948\pi\) | ||||
0.729080 | + | 0.684429i | \(0.239948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −138.552 | −0.458979 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −45.2107 | −0.140312 | −0.0701560 | − | 0.997536i | \(-0.522350\pi\) | ||||
−0.0701560 | + | 0.997536i | \(0.522350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −253.116 | −0.694968 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 604.016 | 1.56543 | 0.782717 | − | 0.622378i | \(-0.213833\pi\) | ||||
0.782717 | + | 0.622378i | \(0.213833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −277.037 | −0.679195 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 479.300 | 1.11377 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 315.649 | 0.696509 | 0.348255 | − | 0.937400i | \(-0.386774\pi\) | ||||
0.348255 | + | 0.937400i | \(0.386774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −595.147 | −1.24919 | −0.624597 | − | 0.780947i | \(-0.714737\pi\) | ||||
−0.624597 | + | 0.780947i | \(0.714737\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −267.850 | −0.511118 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 311.632 | 0.568238 | 0.284119 | − | 0.958789i | \(-0.408299\pi\) | ||||
0.284119 | + | 0.958789i | \(0.408299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −347.903 | −0.606994 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 358.260 | 0.598840 | 0.299420 | − | 0.954121i | \(-0.403207\pi\) | ||||
0.299420 | + | 0.954121i | \(0.403207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −816.660 | −1.30935 | −0.654677 | − | 0.755909i | \(-0.727195\pi\) | ||||
−0.654677 | + | 0.755909i | \(0.727195\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 335.984 | 0.517281 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 125.970 | 0.186437 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 137.873 | 0.196354 | 0.0981768 | − | 0.995169i | \(-0.468699\pi\) | ||||
0.0981768 | + | 0.995169i | \(0.468699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64.5399 | 0.0853514 | 0.0426757 | − | 0.999089i | \(-0.486412\pi\) | ||||
0.0426757 | + | 0.999089i | \(0.486412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1298.88 | 1.65745 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −646.087 | −0.796181 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 487.439 | 0.580544 | 0.290272 | − | 0.956944i | \(-0.406254\pi\) | ||||
0.290272 | + | 0.956944i | \(0.406254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 121.792 | 0.140300 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 432.480 | 0.482216 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2459.55 | −2.65626 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1285.20 | 1.34528 | 0.672639 | − | 0.739970i | \(-0.265161\pi\) | ||||
0.672639 | + | 0.739970i | \(0.265161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 161.961 | 0.164422 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1114.36 | 1.09785 | 0.548925 | − | 0.835872i | \(-0.315037\pi\) | ||||
0.548925 | + | 0.835872i | \(0.315037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 860.304 | 0.822993 | 0.411497 | − | 0.911411i | \(-0.365006\pi\) | ||||
0.411497 | + | 0.911411i | \(0.365006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −323.287 | −0.300472 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1241.76 | 1.12192 | 0.560962 | − | 0.827842i | \(-0.310431\pi\) | ||||
0.560962 | + | 0.827842i | \(0.310431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1640.96 | 1.44198 | 0.720990 | − | 0.692945i | \(-0.243687\pi\) | ||||
0.720990 | + | 0.692945i | \(0.243687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −452.881 | −0.387257 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1945.07 | 1.61926 | 0.809632 | − | 0.586938i | \(-0.199667\pi\) | ||||
0.809632 | + | 0.586938i | \(0.199667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1785.28 | 1.44764 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 156.590 | 0.123733 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −590.604 | −0.454963 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1007.15 | −0.756690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −688.477 | −0.504699 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 200.214 | 0.143262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1423.59 | −0.994672 | −0.497336 | − | 0.867558i | \(-0.665688\pi\) | ||||
−0.497336 | + | 0.867558i | \(0.665688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1233.47 | 0.841869 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 861.290 | 0.574437 | 0.287219 | − | 0.957865i | \(-0.407269\pi\) | ||||
0.287219 | + | 0.957865i | \(0.407269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1118.37 | 0.729133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −415.655 | −0.264992 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1812.47 | 1.13029 | 0.565145 | − | 0.824992i | \(-0.308820\pi\) | ||||
0.565145 | + | 0.824992i | \(0.308820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2220.22 | 1.35479 | 0.677397 | − | 0.735618i | \(-0.263108\pi\) | ||||
0.677397 | + | 0.735618i | \(0.263108\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −135.632 | −0.0810092 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 313.106 | 0.183099 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3315.42 | 1.89883 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 830.283 | 0.456506 | 0.228253 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228253 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 249.611 | 0.134523 | 0.0672617 | − | 0.997735i | \(-0.478574\pi\) | ||||
0.0672617 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −759.348 | −0.401240 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2219.29 | −1.15005 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2479.96 | 1.26065 | 0.630326 | − | 0.776330i | \(-0.282921\pi\) | ||||
0.630326 | + | 0.776330i | \(0.282921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1812.05 | 0.903804 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −811.774 | −0.397371 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 924.909 | 0.444444 | 0.222222 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222222 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −831.112 | −0.392133 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2508.91 | −1.16255 | −0.581273 | − | 0.813708i | \(-0.697445\pi\) | ||||
−0.581273 | + | 0.813708i | \(0.697445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1894.28 | −0.862211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1437.90 | 0.643035 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3741.87 | −1.64445 | −0.822224 | − | 0.569164i | \(-0.807267\pi\) | ||||
−0.822224 | + | 0.569164i | \(0.807267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 783.962 | 0.338640 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 946.948 | 0.402130 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2806.16 | −1.17174 | −0.585872 | − | 0.810404i | \(-0.699248\pi\) | ||||
−0.585872 | + | 0.810404i | \(0.699248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2078.69 | 0.853635 | 0.426817 | − | 0.904338i | \(-0.359635\pi\) | ||||
0.426817 | + | 0.904338i | \(0.359635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1785.44 | −0.721222 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2323.98 | 0.923580 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1518.34 | −0.593752 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3860.97 | 1.46267 | 0.731334 | − | 0.682019i | \(-0.238898\pi\) | ||||
0.731334 | + | 0.682019i | \(0.238898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2486.23 | −0.927268 | −0.463634 | − | 0.886027i | \(-0.653455\pi\) | ||||
−0.463634 | + | 0.886027i | \(0.653455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −803.549 | −0.295094 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2256.81 | −0.816200 | −0.408100 | − | 0.912937i | \(-0.633809\pi\) | ||||
−0.408100 | + | 0.912937i | \(0.633809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3025.28 | 1.07767 | 0.538835 | − | 0.842411i | \(-0.318865\pi\) | ||||
0.538835 | + | 0.842411i | \(0.318865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 934.897 | 0.328072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1507.54 | −0.521223 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3532.95 | 1.20367 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1043.71 | −0.350448 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2875.12 | 0.951559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4415.84 | −1.44075 | −0.720377 | − | 0.693583i | \(-0.756031\pi\) | ||||
−0.720377 | + | 0.693583i | \(0.756031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1074.78 | 0.345740 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6329.61 | −2.00779 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1009.12 | 0.315685 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2449.98 | −0.755956 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1467.98 | −0.446820 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1159.22 | −0.348105 | −0.174052 | − | 0.984736i | \(-0.555686\pi\) | ||||
−0.174052 | + | 0.984736i | \(0.555686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1007.95 | 0.298652 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3861.19 | −1.12897 | −0.564485 | − | 0.825443i | \(-0.690925\pi\) | ||||
−0.564485 | + | 0.825443i | \(0.690925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3141.40 | 0.906504 | 0.453252 | − | 0.891382i | \(-0.350264\pi\) | ||||
0.453252 | + | 0.891382i | \(0.350264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 377.910 | 0.107639 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3317.81 | 0.932863 | 0.466431 | − | 0.884557i | \(-0.345539\pi\) | ||||
0.466431 | + | 0.884557i | \(0.345539\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 696.003 | 0.193201 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 413.619 | 0.113365 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3309.41 | 0.895681 | 0.447840 | − | 0.894114i | \(-0.352193\pi\) | ||||
0.447840 | + | 0.894114i | \(0.352193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −278.021 | −0.0743108 | −0.0371554 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371554 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −754.337 | −0.196705 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2779.77 | 0.716082 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 193.620 | 0.0492777 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2957.60 | 0.743753 | 0.371877 | − | 0.928282i | \(-0.378714\pi\) | ||||
0.371877 | + | 0.928282i | \(0.378714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2086.92 | −0.518591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3896.63 | 0.956927 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3008.66 | 0.730254 | 0.365127 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365127 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1056.72 | −0.253519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1938.26 | −0.459676 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 219.859 | 0.0515480 | 0.0257740 | − | 0.999668i | \(-0.491795\pi\) | ||||
0.0257740 | + | 0.999668i | \(0.491795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9298.60 | −2.15550 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1462.32 | 0.335177 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5831.35 | 1.32172 | 0.660862 | − | 0.750507i | \(-0.270191\pi\) | ||||
0.660862 | + | 0.750507i | \(0.270191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3306.95 | 0.741266 | 0.370633 | − | 0.928779i | \(-0.379141\pi\) | ||||
0.370633 | + | 0.928779i | \(0.379141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 365.377 | 0.0810023 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2015.42 | 0.441944 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −729.382 | −0.158210 | −0.0791052 | − | 0.996866i | \(-0.525206\pi\) | ||||
−0.0791052 | + | 0.996866i | \(0.525206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1297.44 | 0.278408 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4339.86 | −0.921333 | −0.460666 | − | 0.887573i | \(-0.652390\pi\) | ||||
−0.460666 | + | 0.887573i | \(0.652390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9156.94 | 1.92341 | 0.961703 | − | 0.274095i | \(-0.0883782\pi\) | ||||
0.961703 | + | 0.274095i | \(0.0883782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7378.65 | −1.53359 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1606.45 | −0.330403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2205.64 | 0.448940 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3855.59 | 0.776697 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 603.692 | 0.120369 | 0.0601844 | − | 0.998187i | \(-0.480831\pi\) | ||||
0.0601844 | + | 0.998187i | \(0.480831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4859.30 | −0.959050 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 485.884 | 0.0949289 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2017.71 | −0.390258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2878.10 | 0.551132 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3343.08 | 0.633844 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9162.07 | 1.72006 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9123.78 | −1.69616 | −0.848081 | − | 0.529867i | \(-0.822242\pi\) | ||||
−0.848081 | + | 0.529867i | \(0.822242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2580.91 | 0.475155 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3679.09 | 0.670811 | 0.335405 | − | 0.942074i | \(-0.391127\pi\) | ||||
0.335405 | + | 0.942074i | \(0.391127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6446.62 | −1.16417 | −0.582084 | − | 0.813128i | \(-0.697763\pi\) | ||||
−0.582084 | + | 0.813128i | \(0.697763\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −969.862 | −0.173478 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4458.32 | 0.789919 | 0.394960 | − | 0.918698i | \(-0.370759\pi\) | ||||
0.394960 | + | 0.918698i | \(0.370759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3875.60 | −0.680225 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3725.29 | 0.647743 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13479.8 | −2.32210 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1948.58 | 0.332578 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4922.89 | 0.832528 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −316.475 | −0.0530330 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4027.46 | −0.668789 | −0.334394 | − | 0.942433i | \(-0.608532\pi\) | ||||
−0.334394 | + | 0.942433i | \(0.608532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1358.64 | −0.223583 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4797.46 | −0.782428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6213.49 | −1.00436 | −0.502182 | − | 0.864762i | \(-0.667469\pi\) | ||||
−0.502182 | + | 0.864762i | \(0.667469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5835.21 | 0.934882 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2594.27 | 0.411986 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5355.84 | 0.835793 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7962.17 | −1.23179 | −0.615895 | − | 0.787828i | \(-0.711206\pi\) | ||||
−0.615895 | + | 0.787828i | \(0.711206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9690.48 | 1.48630 | 0.743151 | − | 0.669124i | \(-0.233330\pi\) | ||||
0.743151 | + | 0.669124i | \(0.233330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 469.771 | 0.0714373 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6649.02 | −1.00253 | −0.501263 | − | 0.865295i | \(-0.667131\pi\) | ||||
−0.501263 | + | 0.865295i | \(0.667131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5515.28 | −0.824565 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1771.81 | −0.262673 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 889.154 | 0.130718 | 0.0653590 | − | 0.997862i | \(-0.479181\pi\) | ||||
0.0653590 | + | 0.997862i | \(0.479181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18666.4 | 2.72144 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3021.46 | −0.436875 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12572.2 | 1.80290 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5047.48 | 0.717920 | 0.358960 | − | 0.933353i | \(-0.383132\pi\) | ||||
0.358960 | + | 0.933353i | \(0.383132\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2065.43 | −0.291388 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4228.11 | 0.591678 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1435.50 | −0.199270 | −0.0996348 | − | 0.995024i | \(-0.531767\pi\) | ||||
−0.0996348 | + | 0.995024i | \(0.531767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 600.642 | 0.0827121 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3747.07 | −0.511894 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3653.10 | −0.495112 | −0.247556 | − | 0.968874i | \(-0.579627\pi\) | ||||
−0.247556 | + | 0.968874i | \(0.579627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4270.77 | −0.574274 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12685.9 | 1.69248 | 0.846239 | − | 0.532804i | \(-0.178862\pi\) | ||||
0.846239 | + | 0.532804i | \(0.178862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1939.26 | −0.256711 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3700.41 | 0.486053 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8256.58 | −1.07616 | −0.538079 | − | 0.842895i | \(-0.680850\pi\) | ||||
−0.538079 | + | 0.842895i | \(0.680850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9784.43 | 1.26552 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2583.87 | 0.331652 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2122.50 | −0.270367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8693.84 | 1.09907 | 0.549536 | − | 0.835470i | \(-0.314805\pi\) | ||||
0.549536 | + | 0.835470i | \(0.314805\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3355.10 | 0.420965 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8905.25 | 1.10899 | 0.554497 | − | 0.832185i | \(-0.312911\pi\) | ||||
0.554497 | + | 0.832185i | \(0.312911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2508.23 | 0.310034 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1246.96 | −0.152993 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2716.64 | −0.330857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2343.87 | −0.283367 | −0.141683 | − | 0.989912i | \(-0.545251\pi\) | ||||
−0.141683 | + | 0.989912i | \(0.545251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5437.41 | 0.652573 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2209.55 | 0.263256 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −993.567 | −0.117524 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6660.65 | 0.782191 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9025.01 | 1.05227 | 0.526134 | − | 0.850402i | \(-0.323641\pi\) | ||||
0.526134 | + | 0.850402i | \(0.323641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4426.02 | −0.512378 | −0.256189 | − | 0.966627i | \(-0.582467\pi\) | ||||
−0.256189 | + | 0.966627i | \(0.582467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −406.897 | −0.0467707 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9449.21 | −1.07848 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4166.03 | −0.472151 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 939.318 | 0.105713 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 347.465 | 0.0388325 | 0.0194162 | − | 0.999811i | \(-0.493819\pi\) | ||||
0.0194162 | + | 0.999811i | \(0.493819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1984.35 | −0.220235 | −0.110117 | − | 0.993919i | \(-0.535123\pi\) | ||||
−0.110117 | + | 0.993919i | \(0.535123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9946.27 | 1.09629 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18527.8 | −2.02815 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10528.3 | 1.14462 | 0.572310 | − | 0.820037i | \(-0.306047\pi\) | ||||
0.572310 | + | 0.820037i | \(0.306047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3723.08 | 0.399297 | 0.199649 | − | 0.979868i | \(-0.436020\pi\) | ||||
0.199649 | + | 0.979868i | \(0.436020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7503.94 | −0.799372 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2490.85 | 0.263564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 501.935 | 0.0527567 | 0.0263784 | − | 0.999652i | \(-0.491603\pi\) | ||||
0.0263784 | + | 0.999652i | \(0.491603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4129.88 | −0.431194 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 748.832 | 0.0776671 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1874.95 | −0.193184 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7205.28 | −0.737525 | −0.368763 | − | 0.929524i | \(-0.620218\pi\) | ||||
−0.368763 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2278.05 | −0.231656 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2264.90 | 0.228822 | 0.114411 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114411 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9703.82 | −0.974027 | −0.487014 | − | 0.873394i | \(-0.661914\pi\) | ||||
−0.487014 | + | 0.873394i | \(0.661914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6657.87 | −0.663982 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13418.1 | 1.32959 | 0.664794 | − | 0.747027i | \(-0.268519\pi\) | ||||
0.664794 | + | 0.747027i | \(0.268519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2181.43 | 0.214774 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7439.88 | 0.727838 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7399.07 | 0.719259 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17893.0 | 1.72839 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5436.14 | 0.521811 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8508.95 | −0.811658 | −0.405829 | − | 0.913949i | \(-0.633017\pi\) | ||||
−0.405829 | + | 0.913949i | \(0.633017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2626.54 | −0.248982 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2435.32 | −0.229422 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19785.1 | −1.85236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3185.29 | −0.296385 | −0.148192 | − | 0.988959i | \(-0.547345\pi\) | ||||
−0.148192 | + | 0.988959i | \(0.547345\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2774.73 | 0.256600 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15198.0 | −1.39690 | −0.698449 | − | 0.715660i | \(-0.746126\pi\) | ||||
−0.698449 | + | 0.715660i | \(0.746126\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18170.6 | 1.65996 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2493.34 | −0.226398 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2507.82 | 0.226340 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2209.48 | 0.198216 | 0.0991082 | − | 0.995077i | \(-0.468401\pi\) | ||||
0.0991082 | + | 0.995077i | \(0.468401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7526.73 | −0.671197 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10573.7 | −0.937291 | −0.468645 | − | 0.883386i | \(-0.655258\pi\) | ||||
−0.468645 | + | 0.883386i | \(0.655258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17155.1 | −1.51167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5682.83 | −0.497798 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17028.6 | −1.48287 | −0.741434 | − | 0.671026i | \(-0.765854\pi\) | ||||
−0.741434 | + | 0.671026i | \(0.765854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5716.62 | −0.494889 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4313.70 | 0.371256 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13244.1 | −1.13321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −813.600 | −0.0692110 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11225.6 | −0.949422 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10214.0 | −0.858896 | −0.429448 | − | 0.903092i | \(-0.641292\pi\) | ||||
−0.429448 | + | 0.903092i | \(0.641292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21393.1 | 1.78863 | 0.894316 | − | 0.447437i | \(-0.147663\pi\) | ||||
0.894316 | + | 0.447437i | \(0.147663\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2351.89 | 0.195514 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12163.1 | −1.00537 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1281.50 | 0.105326 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2840.84 | 0.232170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3992.92 | −0.324489 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19116.5 | −1.54482 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8418.48 | −0.676507 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 881.790 | 0.0704664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25094.8 | −1.99429 | −0.997145 | − | 0.0755138i | \(-0.975940\pi\) | ||||
−0.997145 | + | 0.0755138i | \(0.975940\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6236.07 | 0.492846 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25262.0 | −1.98552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17839.9 | 1.39447 | 0.697237 | − | 0.716841i | \(-0.254412\pi\) | ||||
0.697237 | + | 0.716841i | \(0.254412\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5356.33 | −0.416398 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34407.7 | −2.66029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 965.112 | 0.0742147 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6971.93 | 0.533229 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15032.1 | −1.14350 | −0.571749 | − | 0.820428i | \(-0.693735\pi\) | ||||
−0.571749 | + | 0.820428i | \(0.693735\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7153.68 | 0.541268 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4555.01 | −0.342803 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5211.21 | −0.390100 | −0.195050 | − | 0.980793i | \(-0.562487\pi\) | ||||
−0.195050 | + | 0.980793i | \(0.562487\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29943.6 | −2.22962 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17148.5 | 1.26345 | 0.631723 | − | 0.775194i | \(-0.282348\pi\) | ||||
0.631723 | + | 0.775194i | \(0.282348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5712.23 | 0.418650 | 0.209325 | − | 0.977846i | \(-0.432873\pi\) | ||||
0.209325 | + | 0.977846i | \(0.432873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11582.9 | 0.844472 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12987.7 | −0.941959 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9198.45 | 0.663668 | 0.331834 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331834 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7458.69 | −0.535359 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 451.779 | 0.0322598 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10869.7 | 0.772173 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2410.65 | −0.170373 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20649.4 | −1.45194 | −0.725971 | − | 0.687725i | \(-0.758609\pi\) | ||||
−0.725971 | + | 0.687725i | \(0.758609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23032.0 | 1.61123 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6770.44 | −0.471233 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5262.45 | −0.364423 | −0.182212 | − | 0.983259i | \(-0.558326\pi\) | ||||
−0.182212 | + | 0.983259i | \(0.558326\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9092.13 | 0.626456 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9075.84 | 0.622193 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6825.01 | −0.465547 | −0.232773 | − | 0.972531i | \(-0.574780\pi\) | ||||
−0.232773 | + | 0.972531i | \(0.574780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25287.1 | −1.71628 | −0.858139 | − | 0.513418i | \(-0.828379\pi\) | ||||
−0.858139 | + | 0.513418i | \(0.828379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2804.69 | 0.189413 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15504.8 | 1.04191 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15067.9 | 1.00755 | 0.503777 | − | 0.863833i | \(-0.331943\pi\) | ||||
0.503777 | + | 0.863833i | \(0.331943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4522.61 | −0.300928 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −786.618 | −0.0520837 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17249.8 | −1.13656 | −0.568282 | − | 0.822834i | \(-0.692392\pi\) | ||||
−0.568282 | + | 0.822834i | \(0.692392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10598.9 | 0.694938 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6229.57 | −0.406471 | −0.203236 | − | 0.979130i | \(-0.565146\pi\) | ||||
−0.203236 | + | 0.979130i | \(0.565146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11372.9 | −0.738472 | −0.369236 | − | 0.929336i | \(-0.620381\pi\) | ||||
−0.369236 | + | 0.929336i | \(0.620381\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3131.13 | −0.202331 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3412.07 | 0.219425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17081.5 | −1.09322 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8625.35 | 0.549383 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12736.8 | 0.807394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8041.72 | 0.507347 | 0.253673 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253673 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13247.5 | −0.831819 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21915.7 | 1.36960 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 852.547 | 0.0530285 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3224.34 | 0.199613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12462.1 | 0.767898 | 0.383949 | − | 0.923354i | \(-0.374564\pi\) | ||||
0.383949 | + | 0.923354i | \(0.374564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7116.38 | −0.436458 | −0.218229 | − | 0.975898i | \(-0.570028\pi\) | ||||
−0.218229 | + | 0.975898i | \(0.570028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18988.8 | −1.15920 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12695.1 | 0.771398 | 0.385699 | − | 0.922625i | \(-0.373960\pi\) | ||||
0.385699 | + | 0.922625i | \(0.373960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5680.34 | 0.343564 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3027.36 | 0.182261 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28102.2 | 1.68411 | 0.842056 | − | 0.539391i | \(-0.181345\pi\) | ||||
0.842056 | + | 0.539391i | \(0.181345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13259.2 | −0.790964 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7349.94 | −0.436451 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25203.9 | −1.48984 | −0.744921 | − | 0.667152i | \(-0.767513\pi\) | ||||
−0.744921 | + | 0.667152i | \(0.767513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28508.6 | 1.67754 | 0.838772 | − | 0.544483i | \(-0.183274\pi\) | ||||
0.838772 | + | 0.544483i | \(0.183274\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4403.94 | −0.257971 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17216.8 | −1.00397 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24975.1 | 1.44983 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3477.67 | −0.200978 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10710.1 | −0.616183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1549.88 | −0.0887720 | −0.0443860 | − | 0.999014i | \(-0.514133\pi\) | ||||
−0.0443860 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3023.85 | 0.172427 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30216.3 | −1.71537 | −0.857686 | − | 0.514173i | \(-0.828099\pi\) | ||||
−0.857686 | + | 0.514173i | \(0.828099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8996.38 | 0.508468 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11583.6 | −0.651811 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8620.18 | 0.482931 | 0.241466 | − | 0.970409i | \(-0.422372\pi\) | ||||
0.241466 | + | 0.970409i | \(0.422372\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27902.3 | −1.55634 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9424.20 | 0.523371 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10509.2 | 0.581088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23194.7 | −1.27694 | −0.638472 | − | 0.769645i | \(-0.720433\pi\) | ||||
−0.638472 | + | 0.769645i | \(0.720433\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1133.73 | 0.0621455 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34179.4 | −1.86547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19362.7 | 1.05225 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9953.43 | 0.538589 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19232.3 | −1.03622 | −0.518111 | − | 0.855313i | \(-0.673365\pi\) | ||||
−0.518111 | + | 0.855313i | \(0.673365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24118.4 | −1.29395 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2088.01 | 0.111545 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7800.51 | 0.414948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28157.2 | −1.49149 | −0.745744 | − | 0.666233i | \(-0.767906\pi\) | ||||
−0.745744 | + | 0.666233i | \(0.767906\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1240.86 | 0.0654512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16717.9 | −0.878108 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4820.15 | −0.252117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9928.22 | 0.517121 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5511.45 | 0.285873 | 0.142936 | − | 0.989732i | \(-0.454346\pi\) | ||||
0.142936 | + | 0.989732i | \(0.454346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6022.13 | 0.311062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −834.063 | −0.0429034 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24119.4 | −1.23555 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32419.8 | 1.65390 | 0.826948 | − | 0.562278i | \(-0.190075\pi\) | ||||
0.826948 | + | 0.562278i | \(0.190075\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34690.2 | −1.75521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1919.18 | 0.0967076 | 0.0483538 | − | 0.998830i | \(-0.484603\pi\) | ||||
0.0483538 | + | 0.998830i | \(0.484603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2263.01 | −0.113568 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5608.05 | 0.280292 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17633.0 | 0.877729 | 0.438865 | − | 0.898553i | \(-0.355381\pi\) | ||||
0.438865 | + | 0.898553i | \(0.355381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8339.30 | 0.413430 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12128.6 | −0.598865 | −0.299433 | − | 0.954117i | \(-0.596797\pi\) | ||||
−0.299433 | + | 0.954117i | \(0.596797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12781.9 | −0.628581 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 580.859 | 0.0284505 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8692.35 | 0.424047 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26822.2 | −1.30327 | −0.651634 | − | 0.758533i | \(-0.725916\pi\) | ||||
−0.651634 | + | 0.758533i | \(0.725916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8872.80 | 0.429406 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3842.66 | −0.185230 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10169.2 | −0.488251 | −0.244126 | − | 0.969744i | \(-0.578501\pi\) | ||||
−0.244126 | + | 0.969744i | \(0.578501\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6260.77 | −0.299409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23389.5 | 1.11415 | 0.557075 | − | 0.830462i | \(-0.311924\pi\) | ||||
0.557075 | + | 0.830462i | \(0.311924\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11486.7 | 0.545017 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11689.9 | 0.552482 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5491.95 | 0.258544 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7009.66 | 0.328706 | 0.164353 | − | 0.986402i | \(-0.447446\pi\) | ||||
0.164353 | + | 0.986402i | \(0.447446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9025.99 | 0.421613 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23176.3 | 1.07839 | 0.539195 | − | 0.842181i | \(-0.318729\pi\) | ||||
0.539195 | + | 0.842181i | \(0.318729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16145.1 | 0.748324 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3170.17 | −0.146369 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36665.2 | −1.68635 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6447.14 | 0.295387 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5814.78 | −0.265394 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38178.1 | −1.73584 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24261.8 | 1.09891 | 0.549454 | − | 0.835524i | \(-0.314836\pi\) | ||||
0.549454 | + | 0.835524i | \(0.314836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 659.578 | 0.0297612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13615.5 | 0.612024 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10354.9 | −0.463700 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27895.8 | −1.24448 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8259.57 | 0.367088 | 0.183544 | − | 0.983012i | \(-0.441243\pi\) | ||||
0.183544 | + | 0.983012i | \(0.441243\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3814.52 | 0.168896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4386.95 | 0.193515 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14696.4 | −0.645858 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12497.0 | 0.547155 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17494.1 | 0.763098 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32589.7 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20365.5 | 0.881785 | 0.440893 | − | 0.897560i | \(-0.354662\pi\) | ||||
0.440893 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9920.86 | 0.427970 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14238.6 | −0.611972 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65689.2 | 2.81294 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1096.13 | 0.0467667 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44152.7 | 1.87691 | 0.938453 | − | 0.345407i | \(-0.112259\pi\) | ||||
0.938453 | + | 0.345407i | \(0.112259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35201.7 | 1.49095 | 0.745477 | − | 0.666531i | \(-0.232222\pi\) | ||||
0.745477 | + | 0.666531i | \(0.232222\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6046.27 | 0.255156 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38376.9 | 1.61366 | 0.806830 | − | 0.590784i | \(-0.201181\pi\) | ||||
0.806830 | + | 0.590784i | \(0.201181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20449.0 | −0.856722 | −0.428361 | − | 0.903608i | \(-0.640909\pi\) | ||||
−0.428361 | + | 0.903608i | \(0.640909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2188.15 | −0.0913429 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4134.23 | −0.171960 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38623.7 | 1.60075 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3892.32 | 0.160739 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11967.4 | 0.492443 | 0.246221 | − | 0.969214i | \(-0.420811\pi\) | ||||
0.246221 | + | 0.969214i | \(0.420811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21991.9 | 0.901715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13019.6 | −0.531932 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29161.7 | 1.18721 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7050.08 | −0.286002 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27470.8 | 1.11048 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17506.5 | 0.705189 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18703.4 | −0.750754 | −0.375377 | − | 0.926872i | \(-0.622487\pi\) | ||||
−0.375377 | + | 0.926872i | \(0.622487\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22135.9 | −0.885419 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31430.5 | −1.25279 | −0.626397 | − | 0.779504i | \(-0.715471\pi\) | ||||
−0.626397 | + | 0.779504i | \(0.715471\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6183.40 | −0.245605 | −0.122803 | − | 0.992431i | \(-0.539188\pi\) | ||||
−0.122803 | + | 0.992431i | \(0.539188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4819.34 | −0.190758 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6480.22 | 0.255608 | 0.127804 | − | 0.991799i | \(-0.459207\pi\) | ||||
0.127804 | + | 0.991799i | \(0.459207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57604.8 | 2.26430 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6616.93 | 0.259196 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2481.12 | 0.0968543 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5422.06 | 0.210929 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11566.8 | 0.448426 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1401.50 | 0.0541478 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14697.9 | −0.565922 | −0.282961 | − | 0.959131i | \(-0.591317\pi\) | ||||
−0.282961 | + | 0.959131i | \(0.591317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1811.07 | 0.0694949 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47733.9 | 1.82542 | 0.912711 | − | 0.408605i | \(-0.133985\pi\) | ||||
0.912711 | + | 0.408605i | \(0.133985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43241.6 | −1.64801 | −0.824007 | − | 0.566579i | \(-0.808267\pi\) | ||||
−0.824007 | + | 0.566579i | \(0.808267\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14577.9 | −0.553708 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20412.9 | −0.772717 | −0.386358 | − | 0.922349i | \(-0.626267\pi\) | ||||
−0.386358 | + | 0.922349i | \(0.626267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9965.14 | −0.375951 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1457.65 | 0.0548072 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7223.17 | −0.270677 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43199.8 | 1.61342 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6053.13 | −0.225316 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31046.7 | −1.15180 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50962.1 | −1.88434 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8634.30 | 0.318196 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32000.7 | −1.17540 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35891.1 | −1.31394 | −0.656971 | − | 0.753916i | \(-0.728162\pi\) | ||||
−0.656971 | + | 0.753916i | \(0.728162\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10029.2 | 0.365950 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36282.8 | −1.31954 | −0.659770 | − | 0.751467i | \(-0.729346\pi\) | ||||
−0.659770 | + | 0.751467i | \(0.729346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1161.44 | 0.0421009 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27486.2 | 0.993078 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6029.03 | 0.217117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48078.2 | 1.72574 | 0.862869 | − | 0.505427i | \(-0.168665\pi\) | ||||
0.862869 | + | 0.505427i | \(0.168665\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27371.3 | −0.979279 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6233.33 | 0.222289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16906.7 | −0.600962 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7742.74 | 0.274331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10154.0 | 0.358603 | 0.179302 | − | 0.983794i | \(-0.442616\pi\) | ||||
0.179302 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7828.57 | 0.275586 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11037.3 | 0.387293 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23374.2 | 0.817560 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51206.2 | −1.78531 | −0.892654 | − | 0.450743i | \(-0.851159\pi\) | ||||
−0.892654 | + | 0.450743i | \(0.851159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19339.9 | −0.672133 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22523.6 | 0.780286 | 0.390143 | − | 0.920754i | \(-0.372426\pi\) | ||||
0.390143 | + | 0.920754i | \(0.372426\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26613.7 | 0.919047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2909.58 | −0.100157 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24323.4 | −0.834641 | −0.417321 | − | 0.908759i | \(-0.637031\pi\) | ||||
−0.417321 | + | 0.908759i | \(0.637031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14209.0 | −0.486031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13375.0 | 0.456060 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11966.4 | −0.406747 | −0.203374 | − | 0.979101i | \(-0.565191\pi\) | ||||
−0.203374 | + | 0.979101i | \(0.565191\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59438.1 | −2.01400 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11626.8 | −0.392728 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12687.3 | 0.427209 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9008.86 | −0.302402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11175.9 | 0.373975 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38274.6 | 1.27679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30595.1 | −1.01745 | −0.508724 | − | 0.860930i | \(-0.669882\pi\) | ||||
−0.508724 | + | 0.860930i | \(0.669882\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40439.5 | −1.34067 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14498.5 | 0.479174 | 0.239587 | − | 0.970875i | \(-0.422988\pi\) | ||||
0.239587 | + | 0.970875i | \(0.422988\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15541.5 | 0.512064 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5845.75 | 0.192014 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49564.0 | 1.62302 | 0.811511 | − | 0.584337i | \(-0.198645\pi\) | ||||
0.811511 | + | 0.584337i | \(0.198645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8771.81 | 0.286362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14768.7 | 0.480660 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55113.5 | −1.78825 | −0.894125 | − | 0.447818i | \(-0.852201\pi\) | ||||
−0.894125 | + | 0.447818i | \(0.852201\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34742.8 | 1.12386 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −949.426 | −0.0306186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47680.9 | −1.53303 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3342.51 | −0.107143 | −0.0535714 | − | 0.998564i | \(-0.517060\pi\) | ||||
−0.0535714 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12082.4 | −0.386125 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −46573.0 | −1.48388 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13993.3 | 0.444505 | 0.222252 | − | 0.974989i | \(-0.428659\pi\) | ||||
0.222252 | + | 0.974989i | \(0.428659\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4075.93 | −0.129086 |
(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 | 1344.4.a.bv.1.1 | 3 | ||
4.3 | odd | 2 | 1344.4.a.bt.1.1 | 3 | |||
8.3 | odd | 2 | 672.4.a.q.1.3 | yes | 3 | ||
8.5 | even | 2 | 672.4.a.o.1.3 | ✓ | 3 | ||
24.5 | odd | 2 | 2016.4.a.z.1.1 | 3 | |||
24.11 | even | 2 | 2016.4.a.y.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.o.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
672.4.a.q.1.3 | yes | 3 | 8.3 | odd | 2 | ||
1344.4.a.bt.1.1 | 3 | 4.3 | odd | 2 | |||
1344.4.a.bv.1.1 | 3 | 1.1 | even | 1 | trivial | ||
2016.4.a.y.1.1 | 3 | 24.11 | even | 2 | |||
2016.4.a.z.1.1 | 3 | 24.5 | odd | 2 |