Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,4,Mod(1,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.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: | \(94.4030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1 |
$q$-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 | ||||||||
\(3\) | −6.89898 | −1.32771 | −0.663855 | − | 0.747862i | \(-0.731081\pi\) | ||||
−0.663855 | + | 0.747862i | \(0.731081\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.6969 | −0.685570 | −0.342785 | − | 0.939414i | \(-0.611370\pi\) | ||||
−0.342785 | + | 0.939414i | \(0.611370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 20.5959 | 0.762812 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 59.1918 | 1.62246 | 0.811228 | − | 0.584730i | \(-0.198800\pi\) | ||||
0.811228 | + | 0.584730i | \(0.198800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.2020 | 0.900365 | 0.450182 | − | 0.892937i | \(-0.351359\pi\) | ||||
0.450182 | + | 0.892937i | \(0.351359\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −126.384 | −1.80309 | −0.901545 | − | 0.432685i | \(-0.857566\pi\) | ||||
−0.901545 | + | 0.432685i | \(0.857566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.1918 | −0.231732 | −0.115866 | − | 0.993265i | \(-0.536964\pi\) | ||||
−0.115866 | + | 0.993265i | \(0.536964\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 87.5959 | 0.910238 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 78.3133 | 0.709976 | 0.354988 | − | 0.934871i | \(-0.384485\pi\) | ||||
0.354988 | + | 0.934871i | \(0.384485\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 44.1816 | 0.314917 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 148.384 | 0.950143 | 0.475072 | − | 0.879947i | \(-0.342422\pi\) | ||||
0.475072 | + | 0.879947i | \(0.342422\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.151 | 0.806202 | 0.403101 | − | 0.915156i | \(-0.367932\pi\) | ||||
0.403101 | + | 0.915156i | \(0.367932\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −408.363 | −2.15415 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −66.5653 | −0.295764 | −0.147882 | − | 0.989005i | \(-0.547246\pi\) | ||||
−0.147882 | + | 0.989005i | \(0.547246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −291.151 | −1.19542 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −203.212 | −0.774059 | −0.387030 | − | 0.922067i | \(-0.626499\pi\) | ||||
−0.387030 | + | 0.922067i | \(0.626499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −288.879 | −1.02450 | −0.512251 | − | 0.858836i | \(-0.671188\pi\) | ||||
−0.512251 | + | 0.858836i | \(0.671188\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 360.434 | 1.11861 | 0.559305 | − | 0.828962i | \(-0.311068\pi\) | ||||
0.559305 | + | 0.828962i | \(0.311068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −181.788 | −0.529993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 871.918 | 2.39398 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −686.888 | −1.78021 | −0.890106 | − | 0.455753i | \(-0.849370\pi\) | ||||
−0.890106 | + | 0.455753i | \(0.849370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 132.404 | 0.307673 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −83.1102 | −0.183390 | −0.0916951 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916951 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 208.829 | 0.438324 | 0.219162 | − | 0.975688i | \(-0.429668\pi\) | ||||
0.219162 | + | 0.975688i | \(0.429668\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −261.505 | −0.522961 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −192.293 | −0.350632 | −0.175316 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175316 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −540.282 | −0.942642 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −500.767 | −0.837044 | −0.418522 | − | 0.908207i | \(-0.637452\pi\) | ||||
−0.418522 | + | 0.908207i | \(0.637452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −122.706 | −0.196735 | −0.0983676 | − | 0.995150i | \(-0.531362\pi\) | ||||
−0.0983676 | + | 0.995150i | \(0.531362\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −751.555 | −1.11231 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 289.616 | 0.412461 | 0.206230 | − | 0.978503i | \(-0.433880\pi\) | ||||
0.206230 | + | 0.978503i | \(0.433880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −860.898 | −1.18093 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 573.950 | 0.759026 | 0.379513 | − | 0.925186i | \(-0.376091\pi\) | ||||
0.379513 | + | 0.925186i | \(0.376091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1023.70 | −1.26151 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −565.151 | −0.673100 | −0.336550 | − | 0.941666i | \(-0.609260\pi\) | ||||
−0.336550 | + | 0.941666i | \(0.609260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −535.837 | −0.617263 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −960.000 | −1.07040 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −643.959 | −0.674063 | −0.337032 | − | 0.941493i | \(-0.609423\pi\) | ||||
−0.337032 | + | 0.941493i | \(0.609423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1219.11 | 1.23763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 745.918 | 0.734868 | 0.367434 | − | 0.930050i | \(-0.380236\pi\) | ||||
0.367434 | + | 0.930050i | \(0.380236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −738.413 | −0.706389 | −0.353194 | − | 0.935550i | \(-0.614905\pi\) | ||||
−0.353194 | + | 0.935550i | \(0.614905\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 558.536 | 0.504633 | 0.252316 | − | 0.967645i | \(-0.418808\pi\) | ||||
0.252316 | + | 0.967645i | \(0.418808\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1523.69 | 1.33893 | 0.669465 | − | 0.742843i | \(-0.266523\pi\) | ||||
0.669465 | + | 0.742843i | \(0.266523\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 459.233 | 0.392689 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.4245 | 0.0486382 | 0.0243191 | − | 0.999704i | \(-0.492258\pi\) | ||||
0.0243191 | + | 0.999704i | \(0.492258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 869.190 | 0.686809 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1604.69 | 1.23615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2172.67 | 1.63236 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1401.96 | 1.02773 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 941.283 | 0.657680 | 0.328840 | − | 0.944386i | \(-0.393342\pi\) | ||||
0.328840 | + | 0.944386i | \(0.393342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1992.97 | 1.36024 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −214.343 | −0.142956 | −0.0714779 | − | 0.997442i | \(-0.522772\pi\) | ||||
−0.0714779 | + | 0.997442i | \(0.522772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 243.678 | 0.158869 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 499.514 | 0.311506 | 0.155753 | − | 0.987796i | \(-0.450220\pi\) | ||||
0.155753 | + | 0.987796i | \(0.450220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2660.48 | 1.62345 | 0.811723 | − | 0.584042i | \(-0.198530\pi\) | ||||
0.811723 | + | 0.584042i | \(0.198530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2486.62 | −1.48519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2498.02 | 1.46080 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1254.15 | 0.703677 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1334.89 | −0.733947 | −0.366973 | − | 0.930231i | \(-0.619606\pi\) | ||||
−0.366973 | + | 0.930231i | \(0.619606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 259.478 | 0.139841 | 0.0699205 | − | 0.997553i | \(-0.477725\pi\) | ||||
0.0699205 | + | 0.997553i | \(0.477725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2602.99 | −1.37542 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1063.58 | 0.540654 | 0.270327 | − | 0.962769i | \(-0.412868\pi\) | ||||
0.270327 | + | 0.962769i | \(0.412868\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4738.82 | 2.36361 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −994.339 | −0.486738 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3139.67 | −1.50870 | −0.754349 | − | 0.656474i | \(-0.772047\pi\) | ||||
−0.754349 | + | 0.656474i | \(0.772047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −936.411 | −0.433902 | −0.216951 | − | 0.976182i | \(-0.569611\pi\) | ||||
−0.216951 | + | 0.976182i | \(0.569611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −415.988 | −0.189344 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −395.273 | −0.176768 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1439.78 | 0.632741 | 0.316371 | − | 0.948636i | \(-0.397536\pi\) | ||||
0.316371 | + | 0.948636i | \(0.397536\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 573.376 | 0.243489 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2494.42 | 1.04158 | 0.520788 | − | 0.853686i | \(-0.325638\pi\) | ||||
0.520788 | + | 0.853686i | \(0.325638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1590.36 | 0.653096 | 0.326548 | − | 0.945181i | \(-0.394114\pi\) | ||||
0.326548 | + | 0.945181i | \(0.394114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1440.70 | −0.581967 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7480.88 | −2.92543 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −560.971 | −0.215898 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2652.77 | 1.00496 | 0.502480 | − | 0.864589i | \(-0.332421\pi\) | ||||
0.502480 | + | 0.864589i | \(0.332421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3001.61 | 1.11948 | 0.559742 | − | 0.828667i | \(-0.310900\pi\) | ||||
0.559742 | + | 0.828667i | \(0.310900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2176.06 | −0.786994 | −0.393497 | − | 0.919326i | \(-0.628735\pi\) | ||||
−0.393497 | + | 0.919326i | \(0.628735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4270.30 | 1.52117 | 0.760587 | − | 0.649236i | \(-0.224911\pi\) | ||||
0.760587 | + | 0.649236i | \(0.224911\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1326.62 | 0.465537 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1884.02 | −0.651390 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1612.93 | 0.541578 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1136.00 | −0.375975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2978.78 | −0.971886 | −0.485943 | − | 0.873991i | \(-0.661524\pi\) | ||||
−0.485943 | + | 0.873991i | \(0.661524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3454.78 | 1.11135 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1766.79 | −0.552708 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 846.547 | 0.261207 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5333.65 | −1.62344 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3183.16 | 0.955875 | 0.477937 | − | 0.878394i | \(-0.341385\pi\) | ||||
0.477937 | + | 0.878394i | \(0.341385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5910.41 | 1.72814 | 0.864070 | − | 0.503372i | \(-0.167908\pi\) | ||||
0.864070 | + | 0.503372i | \(0.167908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3465.59 | −1.00006 | −0.500028 | − | 0.866009i | \(-0.666677\pi\) | ||||
−0.500028 | + | 0.866009i | \(0.666677\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5184.96 | 1.47682 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4611.51 | 1.29661 | 0.648305 | − | 0.761380i | \(-0.275478\pi\) | ||||
0.648305 | + | 0.761380i | \(0.275478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1998.06 | −0.547628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4816.47 | −1.30356 | −0.651782 | − | 0.758406i | \(-0.725978\pi\) | ||||
−0.651782 | + | 0.758406i | \(0.725978\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3057.47 | 0.817217 | 0.408608 | − | 0.912710i | \(-0.366014\pi\) | ||||
0.408608 | + | 0.912710i | \(0.366014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4746.41 | 1.25301 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −809.935 | −0.208643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3959.67 | −1.00777 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7498.54 | 1.88567 | 0.942836 | − | 0.333258i | \(-0.108148\pi\) | ||||
0.942836 | + | 0.333258i | \(0.108148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4635.51 | 1.15190 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2272.33 | 0.551532 | 0.275766 | − | 0.961225i | \(-0.411068\pi\) | ||||
0.275766 | + | 0.961225i | \(0.411068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 845.176 | 0.202767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3056.10 | 0.724781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5271.34 | −1.23591 | −0.617955 | − | 0.786213i | \(-0.712039\pi\) | ||||
−0.617955 | + | 0.786213i | \(0.712039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3898.97 | 0.893681 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4315.61 | 0.978169 | 0.489085 | − | 0.872236i | \(-0.337331\pi\) | ||||
0.489085 | + | 0.872236i | \(0.337331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4471.27 | −1.00225 | −0.501125 | − | 0.865375i | \(-0.667081\pi\) | ||||
−0.501125 | + | 0.865375i | \(0.667081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3696.73 | 0.819546 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8112.09 | 1.75960 | 0.879798 | − | 0.475348i | \(-0.157678\pi\) | ||||
0.879798 | + | 0.475348i | \(0.157678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2865.94 | 0.614980 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3811.46 | −0.809155 | −0.404577 | − | 0.914504i | \(-0.632581\pi\) | ||||
−0.404577 | + | 0.914504i | \(0.632581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2362.60 | 0.496261 | 0.248131 | − | 0.968727i | \(-0.420184\pi\) | ||||
0.248131 | + | 0.968727i | \(0.420184\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2580.17 | 0.530672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11059.8 | 2.25114 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4442.66 | 0.894960 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6337.79 | −1.26368 | −0.631839 | − | 0.775099i | \(-0.717700\pi\) | ||||
−0.631839 | + | 0.775099i | \(0.717700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2615.19 | 0.510939 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3304.98 | 0.639237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3667.87 | 0.702368 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5146.08 | −0.975691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4170.44 | 0.775308 | 0.387654 | − | 0.921805i | \(-0.373285\pi\) | ||||
0.387654 | + | 0.921805i | \(0.373285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5094.30 | 0.937879 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5083.71 | 0.926915 | 0.463457 | − | 0.886119i | \(-0.346609\pi\) | ||||
0.463457 | + | 0.886119i | \(0.346609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1522.86 | 0.275007 | 0.137504 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137504 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4996.09 | 0.885200 | 0.442600 | − | 0.896719i | \(-0.354056\pi\) | ||||
0.442600 | + | 0.896719i | \(0.354056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8783.10 | 1.54157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3853.33 | −0.670005 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2425.53 | 0.417834 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10511.9 | −1.77771 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4576.40 | −0.766885 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2832.04 | 0.470281 | 0.235141 | − | 0.971961i | \(-0.424445\pi\) | ||||
0.235141 | + | 0.971961i | \(0.424445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1370.97 | −0.225612 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1684.43 | 0.272276 | 0.136138 | − | 0.990690i | \(-0.456531\pi\) | ||||
0.136138 | + | 0.990690i | \(0.456531\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −403.069 | −0.0645774 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8236.60 | 1.30803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6663.20 | 1.04892 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9350.30 | −1.44654 | −0.723271 | − | 0.690564i | \(-0.757362\pi\) | ||||
−0.723271 | + | 0.690564i | \(0.757362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4174.20 | −0.640228 | −0.320114 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320114 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1864.55 | 0.283540 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6217.04 | −0.937394 | −0.468697 | − | 0.883359i | \(-0.655276\pi\) | ||||
−0.468697 | + | 0.883359i | \(0.655276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11070.7 | −1.64124 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8149.73 | −1.19812 | −0.599062 | − | 0.800703i | \(-0.704460\pi\) | ||||
−0.599062 | + | 0.800703i | \(0.704460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6490.67 | −0.946300 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14989.2 | −2.16730 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11868.2 | 1.68806 | 0.844028 | − | 0.536299i | \(-0.180178\pi\) | ||||
0.844028 | + | 0.536299i | \(0.180178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4185.34 | −0.590461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8721.37 | 1.22046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3286.85 | 0.456265 | 0.228132 | − | 0.973630i | \(-0.426738\pi\) | ||||
0.228132 | + | 0.973630i | \(0.426738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6262.09 | 0.855475 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8326.24 | 1.12847 | 0.564235 | − | 0.825614i | \(-0.309171\pi\) | ||||
0.564235 | + | 0.825614i | \(0.309171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6493.89 | −0.873207 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4249.23 | −0.566908 | −0.283454 | − | 0.958986i | \(-0.591480\pi\) | ||||
−0.283454 | + | 0.958986i | \(0.591480\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5949.72 | −0.781502 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7841.83 | 1.02210 | 0.511050 | − | 0.859551i | \(-0.329257\pi\) | ||||
0.511050 | + | 0.859551i | \(0.329257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9897.52 | −1.28015 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1478.75 | 0.189804 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −401.794 | −0.0507946 | −0.0253973 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253973 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1681.13 | −0.210931 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9732.89 | 1.21206 | 0.606032 | − | 0.795441i | \(-0.292761\pi\) | ||||
0.606032 | + | 0.795441i | \(0.292761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5872.46 | 0.725876 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3940.12 | −0.479864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5629.67 | −0.680609 | −0.340305 | − | 0.940315i | \(-0.610530\pi\) | ||||
−0.340305 | + | 0.940315i | \(0.610530\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3446.14 | −0.413590 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1055.25 | 0.125727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18354.6 | −2.15547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9773.77 | 1.13957 | 0.569785 | − | 0.821794i | \(-0.307026\pi\) | ||||
0.569785 | + | 0.821794i | \(0.307026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3037.95 | −0.351688 | −0.175844 | − | 0.984418i | \(-0.556265\pi\) | ||||
−0.175844 | + | 0.984418i | \(0.556265\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7423.46 | 0.853289 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2651.48 | −0.300502 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17233.8 | −1.93952 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1873.45 | −0.209376 | −0.104688 | − | 0.994505i | \(-0.533384\pi\) | ||||
−0.104688 | + | 0.994505i | \(0.533384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11855.8 | −1.31583 | −0.657915 | − | 0.753092i | \(-0.728561\pi\) | ||||
−0.657915 | + | 0.753092i | \(0.728561\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1502.98 | −0.164524 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16243.8 | 1.76600 | 0.882999 | − | 0.469375i | \(-0.155521\pi\) | ||||
0.882999 | + | 0.469375i | \(0.155521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3744.09 | −0.404285 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3905.52 | −0.418864 | −0.209432 | − | 0.977823i | \(-0.567161\pi\) | ||||
−0.209432 | + | 0.977823i | \(0.567161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9209.35 | 0.974468 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6852.71 | −0.720265 | −0.360133 | − | 0.932901i | \(-0.617269\pi\) | ||||
−0.360133 | + | 0.932901i | \(0.617269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12028.5 | −1.25588 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1790.13 | −0.185668 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5800.75 | −0.593758 | −0.296879 | − | 0.954915i | \(-0.595946\pi\) | ||||
−0.296879 | + | 0.954915i | \(0.595946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5583.84 | −0.567824 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5263.63 | 0.531783 | 0.265891 | − | 0.964003i | \(-0.414334\pi\) | ||||
0.265891 | + | 0.964003i | \(0.414334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13636.6 | 1.36879 | 0.684394 | − | 0.729113i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729113i | \(0.260067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13158.3 | 1.30384 | 0.651920 | − | 0.758287i | \(-0.273964\pi\) | ||||
0.651920 | + | 0.758287i | \(0.273964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2441.53 | 0.240383 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7337.60 | −0.717832 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17099.3 | −1.66221 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14147.1 | −1.35797 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6775.90 | 0.646344 | 0.323172 | − | 0.946340i | \(-0.395251\pi\) | ||||
0.323172 | + | 0.946340i | \(0.395251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2809.19 | −0.266295 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6859.92 | 0.646247 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5933.64 | −0.552113 | −0.276057 | − | 0.961141i | \(-0.589028\pi\) | ||||
−0.276057 | + | 0.961141i | \(0.589028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21660.5 | 2.00311 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11934.5 | −1.09694 | −0.548468 | − | 0.836171i | \(-0.684789\pi\) | ||||
−0.548468 | + | 0.836171i | \(0.684789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18753.3 | −1.71319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6358.21 | 0.573853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1567.65 | −0.140636 | −0.0703182 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703182 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6460.28 | 0.576096 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 450.509 | 0.0399348 | 0.0199674 | − | 0.999801i | \(-0.493644\pi\) | ||||
0.0199674 | + | 0.999801i | \(0.493644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2869.89 | 0.251393 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7016.11 | 0.610969 | 0.305485 | − | 0.952197i | \(-0.401182\pi\) | ||||
0.305485 | + | 0.952197i | \(0.401182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1557.99 | 0.134876 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −847.927 | −0.0729764 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21334.7 | 1.81489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9933.00 | −0.840097 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16356.0 | −1.37538 | −0.687688 | − | 0.726006i | \(-0.741374\pi\) | ||||
−0.687688 | + | 0.726006i | \(0.741374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13190.5 | 1.10283 | 0.551414 | − | 0.834232i | \(-0.314089\pi\) | ||||
0.551414 | + | 0.834232i | \(0.314089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17586.4 | −1.45366 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6034.03 | −0.495934 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1711.73 | −0.139892 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8575.97 | −0.696935 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17209.0 | −1.38291 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10760.4 | −0.859891 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21997.6 | −1.74815 | −0.874076 | − | 0.485789i | \(-0.838532\pi\) | ||||
−0.874076 | + | 0.485789i | \(0.838532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10971.9 | −0.867122 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 212.663 | 0.0166230 | 0.00831151 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831151 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4301.02 | 0.334359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2847.76 | −0.220179 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3677.24 | −0.282771 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6641.66 | 0.505235 | 0.252618 | − | 0.967566i | \(-0.418709\pi\) | ||||
0.252618 | + | 0.967566i | \(0.418709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12191.3 | −0.922425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51610.4 | 3.88413 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7122.94 | −0.533208 | −0.266604 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266604 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10930.8 | 0.809610 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5951.39 | 0.438480 | 0.219240 | − | 0.975671i | \(-0.429642\pi\) | ||||
0.219240 | + | 0.975671i | \(0.429642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23612.2 | −1.73054 | −0.865272 | − | 0.501303i | \(-0.832854\pi\) | ||||
−0.865272 | + | 0.501303i | \(0.832854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18301.4 | −1.33430 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25398.1 | 1.83247 | 0.916237 | − | 0.400636i | \(-0.131211\pi\) | ||||
0.916237 | + | 0.400636i | \(0.131211\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20708.0 | −1.48635 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7287.41 | −0.520366 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40658.1 | −2.88832 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17994.6 | −1.26528 | −0.632638 | − | 0.774448i | \(-0.718028\pi\) | ||||
−0.632638 | + | 0.774448i | \(0.718028\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2670.56 | −0.186823 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15012.6 | 1.04490 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14842.0 | 1.02780 | 0.513900 | − | 0.857850i | \(-0.328200\pi\) | ||||
0.513900 | + | 0.857850i | \(0.328200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29460.7 | −2.01968 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25071.6 | −1.71018 | −0.855089 | − | 0.518481i | \(-0.826498\pi\) | ||||
−0.855089 | + | 0.518481i | \(0.826498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2772.27 | −0.188159 | −0.0940794 | − | 0.995565i | \(-0.529991\pi\) | ||||
−0.0940794 | + | 0.995565i | \(0.529991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3960.45 | −0.267466 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19585.8 | −1.30966 | −0.654830 | − | 0.755776i | \(-0.727260\pi\) | ||||
−0.654830 | + | 0.755776i | \(0.727260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12997.8 | 0.864856 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15211.0 | 1.00716 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24247.5 | 1.59763 | 0.798814 | − | 0.601579i | \(-0.205461\pi\) | ||||
0.798814 | + | 0.601579i | \(0.205461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1225.83 | −0.0799841 | −0.0399920 | − | 0.999200i | \(-0.512733\pi\) | ||||
−0.0399920 | + | 0.999200i | \(0.512733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12430.1 | −0.807122 | −0.403561 | − | 0.914953i | \(-0.632228\pi\) | ||||
−0.403561 | + | 0.914953i | \(0.632228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3460.01 | 0.223583 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7175.69 | 0.461457 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7837.24 | 0.499185 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8412.77 | 0.533289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6215.00 | 0.392100 | 0.196050 | − | 0.980594i | \(-0.437188\pi\) | ||||
0.196050 | + | 0.980594i | \(0.437188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20550.6 | 1.29038 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7671.81 | −0.477187 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10313.8 | −0.638507 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5059.76 | 0.311776 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8676.69 | −0.532154 | −0.266077 | − | 0.963952i | \(-0.585728\pi\) | ||||
−0.266077 | + | 0.963952i | \(0.585728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22787.4 | 1.38465 | 0.692323 | − | 0.721587i | \(-0.256587\pi\) | ||||
0.692323 | + | 0.721587i | \(0.256587\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4919.45 | −0.297543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12189.1 | 0.733836 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26813.1 | 1.60686 | 0.803428 | − | 0.595402i | \(-0.203007\pi\) | ||||
0.803428 | + | 0.595402i | \(0.203007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2527.25 | −0.150072 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1935.78 | −0.114427 | −0.0572134 | − | 0.998362i | \(-0.518222\pi\) | ||||
−0.0572134 | + | 0.998362i | \(0.518222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3371.84 | −0.198411 | −0.0992053 | − | 0.995067i | \(-0.531630\pi\) | ||||
−0.0992053 | + | 0.995067i | \(0.531630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36796.7 | 2.15546 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11620.4 | 0.674579 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21960.5 | −1.26912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12360.9 | 0.711161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22061.3 | 1.26360 | 0.631798 | − | 0.775133i | \(-0.282317\pi\) | ||||
0.631798 | + | 0.775133i | \(0.282317\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12747.5 | 0.723674 | 0.361837 | − | 0.932241i | \(-0.382150\pi\) | ||||
0.361837 | + | 0.932241i | \(0.382150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8176.31 | 0.462118 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40775.8 | −2.29447 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24562.0 | 1.37605 | 0.688023 | − | 0.725689i | \(-0.258479\pi\) | ||||
0.688023 | + | 0.725689i | \(0.258479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23909.0 | 1.32778 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28988.1 | −1.60284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15853.1 | −0.872767 | −0.436383 | − | 0.899761i | \(-0.643741\pi\) | ||||
−0.436383 | + | 0.899761i | \(0.643741\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15479.0 | −0.848481 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25682.7 | 1.39570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31814.7 | −1.72152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18288.0 | 0.985347 | 0.492673 | − | 0.870214i | \(-0.336020\pi\) | ||||
0.492673 | + | 0.870214i | \(0.336020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1277.51 | 0.0685380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9470.88 | −0.503804 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11985.3 | −0.634864 | −0.317432 | − | 0.948281i | \(-0.602821\pi\) | ||||
−0.317432 | + | 0.948281i | \(0.602821\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5964.91 | 0.314630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10897.4 | 0.572384 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33228.8 | 1.73075 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17036.3 | −0.883653 | −0.441827 | − | 0.897101i | \(-0.645669\pi\) | ||||
−0.441827 | + | 0.897101i | \(0.645669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9375.59 | 0.484279 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21093.4 | −1.08503 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1219.85 | 0.0622307 | 0.0311154 | − | 0.999516i | \(-0.490094\pi\) | ||||
0.0311154 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9501.16 | −0.482709 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36509.5 | 1.84727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17750.6 | 0.894453 | 0.447226 | − | 0.894421i | \(-0.352412\pi\) | ||||
0.447226 | + | 0.894421i | \(0.352412\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11382.2 | −0.568884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25825.4 | −1.28553 | −0.642763 | − | 0.766065i | \(-0.722212\pi\) | ||||
−0.642763 | + | 0.766065i | \(0.722212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5587.72 | 0.277018 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11549.8 | −0.570282 | −0.285141 | − | 0.958486i | \(-0.592041\pi\) | ||||
−0.285141 | + | 0.958486i | \(0.592041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11821.0 | 0.578994 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7091.69 | −0.345961 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29468.3 | −1.43184 | −0.715921 | − | 0.698182i | \(-0.753993\pi\) | ||||
−0.715921 | + | 0.698182i | \(0.753993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −51732.3 | −2.50362 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13820.2 | −0.663545 | −0.331772 | − | 0.943359i | \(-0.607647\pi\) | ||||
−0.331772 | + | 0.943359i | \(0.607647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31980.3 | −1.52939 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1188.09 | −0.0565943 | −0.0282971 | − | 0.999600i | \(-0.509008\pi\) | ||||
−0.0282971 | + | 0.999600i | \(0.509008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19346.2 | −0.917931 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3507.42 | −0.165118 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29907.3 | 1.40245 | 0.701225 | − | 0.712940i | \(-0.252637\pi\) | ||||
0.701225 | + | 0.712940i | \(0.252637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15676.7 | −0.732275 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27528.3 | 1.28088 | 0.640442 | − | 0.768007i | \(-0.278751\pi\) | ||||
0.640442 | + | 0.768007i | \(0.278751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5830.85 | −0.269216 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3900.02 | 0.179374 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29641.3 | −1.35807 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6555.83 | 0.299216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10038.2 | −0.454666 | −0.227333 | − | 0.973817i | \(-0.573001\pi\) | ||||
−0.227333 | + | 0.973817i | \(0.573001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36366.8 | 1.64093 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −741.812 | −0.0333449 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8812.99 | 0.394651 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41075.3 | 1.82555 | 0.912773 | − | 0.408466i | \(-0.133936\pi\) | ||||
0.912773 | + | 0.408466i | \(0.133936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45552.9 | −2.01695 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11639.8 | −0.513449 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7263.20 | −0.319194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29773.3 | −1.29872 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2134.47 | −0.0927616 | −0.0463808 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463808 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5866.38 | 0.254003 | 0.127001 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127001 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30847.2 | 1.33070 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5544.11 | 0.237410 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11036.0 | −0.470856 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28572.6 | 1.21460 | 0.607301 | − | 0.794472i | \(-0.292252\pi\) | ||||
0.607301 | + | 0.794472i | \(0.292252\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15900.5 | 0.673460 | 0.336730 | − | 0.941601i | \(-0.390679\pi\) | ||||
0.336730 | + | 0.941601i | \(0.390679\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34717.6 | 1.45979 | 0.729896 | − | 0.683558i | \(-0.239569\pi\) | ||||
0.729896 | + | 0.683558i | \(0.239569\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 812.559 | 0.0340426 | 0.0170213 | − | 0.999855i | \(-0.494582\pi\) | ||||
0.0170213 | + | 0.999855i | \(0.494582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −55965.1 | −2.33623 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22975.0 | 0.955626 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6147.92 | 0.253887 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 852.588 | 0.0350829 | 0.0175415 | − | 0.999846i | \(-0.494416\pi\) | ||||
0.0175415 | + | 0.999846i | \(0.494416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2371.29 | −0.0972277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26295.2 | 1.07432 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27586.3 | −1.11910 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16299.5 | −0.658891 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5212.95 | −0.209985 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8851.54 | −0.355300 | −0.177650 | − | 0.984094i | \(-0.556850\pi\) | ||||
−0.177650 | + | 0.984094i | \(0.556850\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1712.28 | −0.0682502 | −0.0341251 | − | 0.999418i | \(-0.510864\pi\) | ||||
−0.0341251 | + | 0.999418i | \(0.510864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33276.7 | 1.32175 | 0.660877 | − | 0.750495i | \(-0.270185\pi\) | ||||
0.660877 | + | 0.750495i | \(0.270185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17800.6 | −0.704578 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5913.49 | −0.233253 | −0.116627 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116627 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −76301.6 | −2.98885 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17142.9 | 0.669199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8115.15 | −0.315696 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13262.9 | −0.514183 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38661.1 | −1.48859 | −0.744295 | − | 0.667851i | \(-0.767214\pi\) | ||||
−0.744295 | + | 0.667851i | \(0.767214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43724.3 | 1.67780 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20876.4 | 0.798348 | 0.399174 | − | 0.916875i | \(-0.369297\pi\) | ||||
0.399174 | + | 0.916875i | \(0.369297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14713.8 | 0.560770 | 0.280385 | − | 0.959888i | \(-0.409538\pi\) | ||||
0.280385 | + | 0.959888i | \(0.409538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38213.1 | 1.44653 | 0.723264 | − | 0.690571i | \(-0.242641\pi\) | ||||
0.723264 | + | 0.690571i | \(0.242641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11951.4 | −0.450886 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −50958.1 | −1.91601 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6917.38 | −0.259218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22801.0 | −0.848721 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20647.7 | 0.766007 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 86811.4 | 3.20989 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25304.6 | −0.932540 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30912.4 | 1.13168 | 0.565838 | − | 0.824516i | \(-0.308553\pi\) | ||||
0.565838 | + | 0.824516i | \(0.308553\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15362.9 | 0.560566 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1390.58 | 0.0505730 | 0.0252865 | − | 0.999680i | \(-0.491950\pi\) | ||||
0.0252865 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33973.2 | 1.23149 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2721.50 | 0.0980063 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14064.7 | 0.504843 | 0.252422 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28771.8 | −1.02938 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21133.4 | −0.753645 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15208.3 | −0.538841 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51692.7 | 1.82560 | 0.912799 | − | 0.408408i | \(-0.133916\pi\) | ||||
0.912799 | + | 0.408408i | \(0.133916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3488.84 | 0.122816 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35072.4 | −1.23067 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12479.3 | −0.435092 | −0.217546 | − | 0.976050i | \(-0.569805\pi\) | ||||
−0.217546 | + | 0.976050i | \(0.569805\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10506.2 | −0.365129 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41800.9 | −1.44811 | −0.724054 | − | 0.689743i | \(-0.757723\pi\) | ||||
−0.724054 | + | 0.689743i | \(0.757723\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15914.2 | −0.549563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6482.77 | −0.222452 | −0.111226 | − | 0.993795i | \(-0.535478\pi\) | ||||
−0.111226 | + | 0.993795i | \(0.535478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5178.45 | −0.177133 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34467.9 | −1.17529 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28635.8 | 0.973351 | 0.486675 | − | 0.873583i | \(-0.338209\pi\) | ||||
0.486675 | + | 0.873583i | \(0.338209\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −60594.4 | −2.04675 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6342.30 | −0.213560 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10428.0 | −0.350038 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11503.6 | 0.384940 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3086.04 | 0.102627 | 0.0513135 | − | 0.998683i | \(-0.483659\pi\) | ||||
0.0513135 | + | 0.998683i | \(0.483659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16733.7 | −0.554762 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11625.0 | 0.384205 | 0.192102 | − | 0.981375i | \(-0.438469\pi\) | ||||
0.192102 | + | 0.981375i | \(0.438469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33780.0 | −1.11299 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38232.0 | 1.25194 | 0.625972 | − | 0.779845i | \(-0.284702\pi\) | ||||
0.625972 | + | 0.779845i | \(0.284702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33452.3 | −1.09207 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31381.9 | 1.02135 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54290.3 | 1.76154 | 0.880769 | − | 0.473546i | \(-0.157026\pi\) | ||||
0.880769 | + | 0.473546i | \(0.157026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31572.5 | 1.01820 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22623.0 | −0.727371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13673.7 | −0.438303 | −0.219152 | − | 0.975691i | \(-0.570329\pi\) | ||||
−0.219152 | + | 0.975691i | \(0.570329\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19538.2 | −0.624397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3392.56 | 0.107767 | 0.0538834 | − | 0.998547i | \(-0.482840\pi\) | ||||
0.0538834 | + | 0.998547i | \(0.482840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2940.96 | −0.0931411 |
(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 | 1600.4.a.cf.1.1 | 2 | ||
4.3 | odd | 2 | 1600.4.a.cl.1.2 | 2 | |||
5.2 | odd | 4 | 320.4.c.h.129.4 | 4 | |||
5.3 | odd | 4 | 320.4.c.h.129.1 | 4 | |||
5.4 | even | 2 | 1600.4.a.cm.1.2 | 2 | |||
8.3 | odd | 2 | 200.4.a.k.1.1 | 2 | |||
8.5 | even | 2 | 400.4.a.x.1.2 | 2 | |||
20.3 | even | 4 | 320.4.c.g.129.4 | 4 | |||
20.7 | even | 4 | 320.4.c.g.129.1 | 4 | |||
20.19 | odd | 2 | 1600.4.a.ce.1.1 | 2 | |||
24.11 | even | 2 | 1800.4.a.bk.1.2 | 2 | |||
40.3 | even | 4 | 40.4.c.a.9.1 | ✓ | 4 | ||
40.13 | odd | 4 | 80.4.c.c.49.4 | 4 | |||
40.19 | odd | 2 | 200.4.a.l.1.2 | 2 | |||
40.27 | even | 4 | 40.4.c.a.9.4 | yes | 4 | ||
40.29 | even | 2 | 400.4.a.v.1.1 | 2 | |||
40.37 | odd | 4 | 80.4.c.c.49.1 | 4 | |||
120.53 | even | 4 | 720.4.f.m.289.4 | 4 | |||
120.59 | even | 2 | 1800.4.a.bp.1.1 | 2 | |||
120.77 | even | 4 | 720.4.f.m.289.3 | 4 | |||
120.83 | odd | 4 | 360.4.f.e.289.4 | 4 | |||
120.107 | odd | 4 | 360.4.f.e.289.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.c.a.9.1 | ✓ | 4 | 40.3 | even | 4 | ||
40.4.c.a.9.4 | yes | 4 | 40.27 | even | 4 | ||
80.4.c.c.49.1 | 4 | 40.37 | odd | 4 | |||
80.4.c.c.49.4 | 4 | 40.13 | odd | 4 | |||
200.4.a.k.1.1 | 2 | 8.3 | odd | 2 | |||
200.4.a.l.1.2 | 2 | 40.19 | odd | 2 | |||
320.4.c.g.129.1 | 4 | 20.7 | even | 4 | |||
320.4.c.g.129.4 | 4 | 20.3 | even | 4 | |||
320.4.c.h.129.1 | 4 | 5.3 | odd | 4 | |||
320.4.c.h.129.4 | 4 | 5.2 | odd | 4 | |||
360.4.f.e.289.3 | 4 | 120.107 | odd | 4 | |||
360.4.f.e.289.4 | 4 | 120.83 | odd | 4 | |||
400.4.a.v.1.1 | 2 | 40.29 | even | 2 | |||
400.4.a.x.1.2 | 2 | 8.5 | even | 2 | |||
720.4.f.m.289.3 | 4 | 120.77 | even | 4 | |||
720.4.f.m.289.4 | 4 | 120.53 | even | 4 | |||
1600.4.a.ce.1.1 | 2 | 20.19 | odd | 2 | |||
1600.4.a.cf.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1600.4.a.cl.1.2 | 2 | 4.3 | odd | 2 | |||
1600.4.a.cm.1.2 | 2 | 5.4 | even | 2 | |||
1800.4.a.bk.1.2 | 2 | 24.11 | even | 2 | |||
1800.4.a.bp.1.1 | 2 | 120.59 | even | 2 |