Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.438516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.55649\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.7265 | −1.76706 | −0.883531 | − | 0.468372i | \(-0.844841\pi\) | ||||
−0.883531 | + | 0.468372i | \(0.844841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.1055 | −0.441455 | −0.220727 | − | 0.975336i | \(-0.570843\pi\) | ||||
−0.220727 | + | 0.975336i | \(0.570843\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.4043 | 0.392649 | 0.196324 | − | 0.980539i | \(-0.437099\pi\) | ||||
0.196324 | + | 0.980539i | \(0.437099\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.5584 | −0.878242 | −0.439121 | − | 0.898428i | \(-0.644710\pi\) | ||||
−0.439121 | + | 0.898428i | \(0.644710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 118.317 | 1.42862 | 0.714308 | − | 0.699831i | \(-0.246742\pi\) | ||||
0.714308 | + | 0.699831i | \(0.246742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 132.682 | 1.20287 | 0.601436 | − | 0.798921i | \(-0.294595\pi\) | ||||
0.601436 | + | 0.798921i | \(0.294595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 240.769 | 1.54171 | 0.770856 | − | 0.637009i | \(-0.219829\pi\) | ||||
0.770856 | + | 0.637009i | \(0.219829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.4265 | 0.211045 | 0.105522 | − | 0.994417i | \(-0.466348\pi\) | ||||
0.105522 | + | 0.994417i | \(0.466348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −163.632 | −0.790254 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 65.7676 | 0.292220 | 0.146110 | − | 0.989268i | \(-0.453325\pi\) | ||||
0.146110 | + | 0.989268i | \(0.453325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −151.078 | −0.575473 | −0.287737 | − | 0.957710i | \(-0.592903\pi\) | ||||
−0.287737 | + | 0.957710i | \(0.592903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 293.221 | 1.03990 | 0.519951 | − | 0.854196i | \(-0.325950\pi\) | ||||
0.519951 | + | 0.854196i | \(0.325950\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −354.799 | −1.10112 | −0.550561 | − | 0.834795i | \(-0.685586\pi\) | ||||
−0.550561 | + | 0.834795i | \(0.685586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 728.021 | 2.12251 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −708.587 | −1.83645 | −0.918225 | − | 0.396059i | \(-0.870378\pi\) | ||||
−0.918225 | + | 0.396059i | \(0.870378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −80.5277 | −0.197424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 220.003 | 0.485457 | 0.242729 | − | 0.970094i | \(-0.421958\pi\) | ||||
0.242729 | + | 0.970094i | \(0.421958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −893.735 | −1.87592 | −0.937960 | − | 0.346744i | \(-0.887287\pi\) | ||||
−0.937960 | + | 0.346744i | \(0.887287\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 92.0215 | 0.175598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31.0366 | 0.0565929 | 0.0282965 | − | 0.999600i | \(-0.490992\pi\) | ||||
0.0282965 | + | 0.999600i | \(0.490992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −196.045 | −0.327694 | −0.163847 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163847 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −975.957 | −1.56475 | −0.782377 | − | 0.622805i | \(-0.785993\pi\) | ||||
−0.782377 | + | 0.622805i | \(0.785993\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 527.077 | 0.780078 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −844.463 | −1.20265 | −0.601326 | − | 0.799004i | \(-0.705361\pi\) | ||||
−0.601326 | + | 0.799004i | \(0.705361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.8533 | −0.0169980 | −0.00849900 | − | 0.999964i | \(-0.502705\pi\) | ||||
−0.00849900 | + | 0.999964i | \(0.502705\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −307.792 | −0.392762 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 892.671 | 1.06318 | 0.531590 | − | 0.847002i | \(-0.321595\pi\) | ||||
0.531590 | + | 0.847002i | \(0.321595\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −602.308 | −0.693835 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 591.583 | 0.638897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −757.518 | −0.792931 | −0.396466 | − | 0.918050i | \(-0.629763\pi\) | ||||
−0.396466 | + | 0.918050i | \(0.629763\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 35.2237 | 0.0347019 | 0.0173509 | − | 0.999849i | \(-0.494477\pi\) | ||||
0.0173509 | + | 0.999849i | \(0.494477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 610.290 | 0.583822 | 0.291911 | − | 0.956446i | \(-0.405709\pi\) | ||||
0.291911 | + | 0.956446i | \(0.405709\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1094.01 | −0.988430 | −0.494215 | − | 0.869340i | \(-0.664545\pi\) | ||||
−0.494215 | + | 0.869340i | \(0.664545\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1818.81 | −1.59826 | −0.799129 | − | 0.601159i | \(-0.794706\pi\) | ||||
−0.799129 | + | 0.601159i | \(0.794706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −961.999 | −0.800861 | −0.400430 | − | 0.916327i | \(-0.631139\pi\) | ||||
−0.400430 | + | 0.916327i | \(0.631139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 663.409 | 0.537941 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2014.59 | 1.55191 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1071.61 | −0.805118 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −833.065 | −0.582067 | −0.291034 | − | 0.956713i | \(-0.593999\pi\) | ||||
−0.291034 | + | 0.956713i | \(0.593999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −562.201 | −0.374960 | −0.187480 | − | 0.982268i | \(-0.560032\pi\) | ||||
−0.187480 | + | 0.982268i | \(0.560032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3872.09 | −2.52445 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1061.62 | −0.662045 | −0.331022 | − | 0.943623i | \(-0.607394\pi\) | ||||
−0.331022 | + | 0.943623i | \(0.607394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −212.848 | −0.129882 | −0.0649409 | − | 0.997889i | \(-0.520686\pi\) | ||||
−0.0649409 | + | 0.997889i | \(0.520686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −296.411 | −0.173337 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1203.84 | 0.689475 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1758.09 | 0.966631 | 0.483315 | − | 0.875446i | \(-0.339432\pi\) | ||||
0.483315 | + | 0.875446i | \(0.339432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1672.32 | 0.901268 | 0.450634 | − | 0.892709i | \(-0.351198\pi\) | ||||
0.450634 | + | 0.892709i | \(0.351198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 182.133 | 0.0943822 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2654.46 | −1.34936 | −0.674679 | − | 0.738111i | \(-0.735718\pi\) | ||||
−0.674679 | + | 0.738111i | \(0.735718\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4342.21 | −2.12555 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1825.20 | 0.877058 | 0.438529 | − | 0.898717i | \(-0.355500\pi\) | ||||
0.438529 | + | 0.898717i | \(0.355500\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4234.49 | 1.96213 | 0.981063 | − | 0.193691i | \(-0.0620460\pi\) | ||||
0.981063 | + | 0.193691i | \(0.0620460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1858.28 | −0.845827 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2327.00 | −1.02265 | −0.511326 | − | 0.859387i | \(-0.670846\pi\) | ||||
−0.511326 | + | 0.859387i | \(0.670846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −818.161 | −0.353412 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3754.31 | 1.56766 | 0.783828 | − | 0.620978i | \(-0.213264\pi\) | ||||
0.783828 | + | 0.620978i | \(0.213264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 44.8828 | 0.0184315 | 0.00921577 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921577 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 328.838 | 0.130685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 991.431 | 0.387704 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4536.78 | 1.71869 | 0.859346 | − | 0.511394i | \(-0.170871\pi\) | ||||
0.859346 | + | 0.511394i | \(0.170871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 240.123 | 0.0895567 | 0.0447783 | − | 0.998997i | \(-0.485742\pi\) | ||||
0.0447783 | + | 0.998997i | \(0.485742\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3708.98 | 1.34139 | 0.670694 | − | 0.741734i | \(-0.265996\pi\) | ||||
0.670694 | + | 0.741734i | \(0.265996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −975.782 | −0.347595 | −0.173797 | − | 0.984781i | \(-0.555604\pi\) | ||||
−0.173797 | + | 0.984781i | \(0.555604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7879.51 | −2.72430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −755.390 | −0.257360 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1905.55 | −0.630669 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5494.82 | −1.79279 | −0.896396 | − | 0.443255i | \(-0.853824\pi\) | ||||
−0.896396 | + | 0.443255i | \(0.853824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1466.11 | 0.465058 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1192.11 | −0.372930 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1132.94 | −0.344841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4116.81 | 1.23624 | 0.618121 | − | 0.786083i | \(-0.287894\pi\) | ||||
0.618121 | + | 0.786083i | \(0.287894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3360.00 | −0.982429 | −0.491214 | − | 0.871039i | \(-0.663447\pi\) | ||||
−0.491214 | + | 0.871039i | \(0.663447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.31590 | −0.00239969 | −0.00119985 | − | 0.999999i | \(-0.500382\pi\) | ||||
−0.00119985 | + | 0.999999i | \(0.500382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1751.22 | 0.492386 | 0.246193 | − | 0.969221i | \(-0.420820\pi\) | ||||
0.246193 | + | 0.969221i | \(0.420820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1773.99 | −0.492436 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4681.54 | −1.26704 | −0.633522 | − | 0.773724i | \(-0.718392\pi\) | ||||
−0.633522 | + | 0.773724i | \(0.718392\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5198.33 | 1.38944 | 0.694718 | − | 0.719282i | \(-0.255529\pi\) | ||||
0.694718 | + | 0.719282i | \(0.255529\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3640.10 | 0.949215 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2177.54 | 0.560945 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3667.47 | 0.922265 | 0.461133 | − | 0.887331i | \(-0.347443\pi\) | ||||
0.461133 | + | 0.887331i | \(0.347443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2136.91 | −0.531014 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3036.67 | −0.737052 | −0.368526 | − | 0.929617i | \(-0.620137\pi\) | ||||
−0.368526 | + | 0.929617i | \(0.620137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2152.34 | −0.516370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7370.91 | −1.72817 | −0.864087 | − | 0.503342i | \(-0.832103\pi\) | ||||
−0.864087 | + | 0.503342i | \(0.832103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3542.93 | −0.821286 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1442.57 | 0.326970 | 0.163485 | − | 0.986546i | \(-0.447726\pi\) | ||||
0.163485 | + | 0.986546i | \(0.447726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1068.01 | −0.239400 | −0.119700 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119700 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −402.638 | −0.0882909 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8644.61 | −1.87511 | −0.937553 | − | 0.347843i | \(-0.886914\pi\) | ||||
−0.937553 | + | 0.347843i | \(0.886914\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1874.83 | −0.398017 | −0.199008 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199008 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6463.16 | −1.35758 | −0.678790 | − | 0.734332i | \(-0.737495\pi\) | ||||
−0.678790 | + | 0.734332i | \(0.737495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4944.25 | 1.01690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1123.56 | −0.228691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6949.70 | 1.38569 | 0.692843 | − | 0.721089i | \(-0.256358\pi\) | ||||
0.692843 | + | 0.721089i | \(0.256358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1100.02 | 0.217103 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2441.92 | 0.472307 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9596.08 | −1.83757 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4468.68 | −0.838937 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4561.23 | −0.847958 | −0.423979 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423979 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4151.60 | −0.756964 | −0.378482 | − | 0.925609i | \(-0.623554\pi\) | ||||
−0.378482 | + | 0.925609i | \(0.623554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3165.42 | −0.571630 | −0.285815 | − | 0.958285i | \(-0.592264\pi\) | ||||
−0.285815 | + | 0.958285i | \(0.592264\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6523.81 | −1.15588 | −0.577939 | − | 0.816080i | \(-0.696143\pi\) | ||||
−0.577939 | + | 0.816080i | \(0.696143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3877.71 | −0.680596 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7283.39 | −1.25467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 460.108 | 0.0785298 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11611.3 | 1.94575 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5420.61 | −0.900131 | −0.450066 | − | 0.892995i | \(-0.648599\pi\) | ||||
−0.450066 | + | 0.892995i | \(0.648599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 155.183 | 0.0253091 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5563.85 | 0.899354 | 0.449677 | − | 0.893191i | \(-0.351539\pi\) | ||||
0.449677 | + | 0.893191i | \(0.351539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −586.668 | −0.0931668 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12600.4 | −1.98354 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10236.1 | −1.58358 | −0.791790 | − | 0.610793i | \(-0.790851\pi\) | ||||
−0.791790 | + | 0.610793i | \(0.790851\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1500.29 | −0.230111 | −0.115056 | − | 0.993359i | \(-0.536705\pi\) | ||||
−0.115056 | + | 0.993359i | \(0.536705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6370.82 | 0.960580 | 0.480290 | − | 0.877110i | \(-0.340531\pi\) | ||||
0.480290 | + | 0.877110i | \(0.340531\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −980.226 | −0.146549 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2837.15 | 0.417100 | 0.208550 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208550 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7139.84 | 1.04094 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4879.78 | −0.699780 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4703.76 | −0.669030 | −0.334515 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334515 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23189.5 | 3.24512 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5076.15 | −0.704647 | −0.352323 | − | 0.935878i | \(-0.614608\pi\) | ||||
−0.352323 | + | 0.935878i | \(0.614608\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4431.19 | 0.605352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 559.935 | 0.0758890 | 0.0379445 | − | 0.999280i | \(-0.487919\pi\) | ||||
0.0379445 | + | 0.999280i | \(0.487919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5773.83 | 0.770310 | 0.385155 | − | 0.922852i | \(-0.374148\pi\) | ||||
0.385155 | + | 0.922852i | \(0.374148\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2635.38 | 0.348861 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12668.3 | −1.65118 | −0.825590 | − | 0.564271i | \(-0.809157\pi\) | ||||
−0.825590 | + | 0.564271i | \(0.809157\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8167.69 | −1.05641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4222.32 | −0.537843 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1138.65 | −0.143947 | −0.0719736 | − | 0.997407i | \(-0.522930\pi\) | ||||
−0.0719736 | + | 0.997407i | \(0.522930\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3371.61 | 0.419875 | 0.209938 | − | 0.977715i | \(-0.432674\pi\) | ||||
0.209938 | + | 0.977715i | \(0.432674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 670.405 | 0.0828666 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1059.22 | −0.129002 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2098.28 | 0.253676 | 0.126838 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126838 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7199.92 | −0.857833 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −64.2666 | −0.00760174 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1978.06 | 0.230631 | 0.115316 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115316 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1647.35 | −0.190706 | −0.0953529 | − | 0.995444i | \(-0.530398\pi\) | ||||
−0.0953529 | + | 0.995444i | \(0.530398\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1538.96 | −0.175648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29248.8 | 3.31487 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9716.13 | −1.08587 | −0.542934 | − | 0.839775i | \(-0.682687\pi\) | ||||
−0.542934 | + | 0.839775i | \(0.682687\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12751.3 | 1.41522 | 0.707610 | − | 0.706604i | \(-0.249774\pi\) | ||||
0.707610 | + | 0.706604i | \(0.249774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15698.5 | 1.71844 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1135.01 | 0.123396 | 0.0616980 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0616980 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1587.02 | 0.170207 | 0.0851033 | − | 0.996372i | \(-0.472878\pi\) | ||||
0.0851033 | + | 0.996372i | \(0.472878\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4463.36 | 0.475468 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11255.5 | −1.18302 | −0.591512 | − | 0.806296i | \(-0.701469\pi\) | ||||
−0.591512 | + | 0.806296i | \(0.701469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2433.19 | 0.254045 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3011.54 | −0.310293 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13549.3 | −1.38689 | −0.693444 | − | 0.720511i | \(-0.743907\pi\) | ||||
−0.693444 | + | 0.720511i | \(0.743907\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1628.83 | 0.164560 | 0.0822800 | − | 0.996609i | \(-0.473780\pi\) | ||||
0.0822800 | + | 0.996609i | \(0.473780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6960.47 | 0.698662 | 0.349331 | − | 0.936999i | \(-0.386409\pi\) | ||||
0.349331 | + | 0.936999i | \(0.386409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1221.07 | 0.120994 | 0.0604970 | − | 0.998168i | \(-0.480731\pi\) | ||||
0.0604970 | + | 0.998168i | \(0.480731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1015.72 | −0.100003 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4722.48 | −0.459070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2957.92 | 0.285723 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16552.1 | −1.57888 | −0.789442 | − | 0.613826i | \(-0.789630\pi\) | ||||
−0.789442 | + | 0.613826i | \(0.789630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1210.41 | 0.114740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3787.59 | −0.354610 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3739.16 | −0.347921 | −0.173960 | − | 0.984753i | \(-0.555656\pi\) | ||||
−0.173960 | + | 0.984753i | \(0.555656\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15633.3 | 1.43691 | 0.718453 | − | 0.695576i | \(-0.244851\pi\) | ||||
0.718453 | + | 0.695576i | \(0.244851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14821.4 | −1.35400 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6415.86 | 0.579056 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9221.21 | 0.827251 | 0.413625 | − | 0.910447i | \(-0.364262\pi\) | ||||
0.413625 | + | 0.910447i | \(0.364262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15565.7 | 1.37980 | 0.689901 | − | 0.723903i | \(-0.257654\pi\) | ||||
0.689901 | + | 0.723903i | \(0.257654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 176.119 | 0.0155192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2653.76 | −0.231092 | −0.115546 | − | 0.993302i | \(-0.536862\pi\) | ||||
−0.115546 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31939.6 | 2.76502 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3051.45 | 0.261093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5714.22 | 0.486095 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4708.79 | −0.395962 | −0.197981 | − | 0.980206i | \(-0.563438\pi\) | ||||
−0.197981 | + | 0.980206i | \(0.563438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2586.36 | −0.216240 | −0.108120 | − | 0.994138i | \(-0.534483\pi\) | ||||
−0.108120 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2242.36 | −0.185349 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5437.47 | 0.446903 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2780.49 | −0.225959 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5470.06 | −0.442040 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11725.2 | −0.936991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12767.5 | −1.01464 | −0.507319 | − | 0.861758i | \(-0.669363\pi\) | ||||
−0.507319 | + | 0.861758i | \(0.669363\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9094.04 | −0.714763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1062.83 | −0.0830770 | −0.0415385 | − | 0.999137i | \(-0.513226\pi\) | ||||
−0.0415385 | + | 0.999137i | \(0.513226\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28487.0 | 2.20252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27636.3 | 2.12516 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19202.4 | 1.46074 | 0.730369 | − | 0.683053i | \(-0.239348\pi\) | ||||
0.730369 | + | 0.683053i | \(0.239348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5396.53 | 0.408316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5879.05 | 0.440093 | 0.220046 | − | 0.975489i | \(-0.429379\pi\) | ||||
0.220046 | + | 0.975489i | \(0.429379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4809.99 | −0.358156 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9008.59 | 0.663726 | 0.331863 | − | 0.943328i | \(-0.392323\pi\) | ||||
0.331863 | + | 0.943328i | \(0.392323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9763.61 | 0.715577 | 0.357788 | − | 0.933803i | \(-0.383531\pi\) | ||||
0.357788 | + | 0.933803i | \(0.383531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3317.05 | 0.240575 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20212.3 | −1.45832 | −0.729159 | − | 0.684344i | \(-0.760089\pi\) | ||||
−0.729159 | + | 0.684344i | \(0.760089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 420.643 | 0.0300365 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11412.2 | 0.810709 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3458.92 | −0.243211 | −0.121605 | − | 0.992579i | \(-0.538804\pi\) | ||||
−0.121605 | + | 0.992579i | \(0.538804\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4309.86 | 0.301502 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6880.71 | 0.476487 | 0.238243 | − | 0.971205i | \(-0.423428\pi\) | ||||
0.238243 | + | 0.971205i | \(0.423428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10072.9 | 0.694034 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12564.8 | −0.857071 | −0.428536 | − | 0.903525i | \(-0.640970\pi\) | ||||
−0.428536 | + | 0.903525i | \(0.640970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13392.7 | 0.908986 | 0.454493 | − | 0.890750i | \(-0.349821\pi\) | ||||
0.454493 | + | 0.890750i | \(0.349821\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5358.06 | −0.360060 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20209.4 | −1.35136 | −0.675679 | − | 0.737196i | \(-0.736149\pi\) | ||||
−0.675679 | + | 0.737196i | \(0.736149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6529.82 | −0.432354 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16892.6 | 1.11303 | 0.556513 | − | 0.830839i | \(-0.312139\pi\) | ||||
0.556513 | + | 0.830839i | \(0.312139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26113.6 | 1.70388 | 0.851939 | − | 0.523640i | \(-0.175426\pi\) | ||||
0.851939 | + | 0.523640i | \(0.175426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8267.32 | −0.536820 | −0.268410 | − | 0.963305i | \(-0.586498\pi\) | ||||
−0.268410 | + | 0.963305i | \(0.586498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29214.0 | −1.87870 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4048.55 | −0.256639 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29318.5 | 1.84968 | 0.924841 | − | 0.380353i | \(-0.124198\pi\) | ||||
0.924841 | + | 0.380353i | \(0.124198\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4165.32 | −0.260308 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13398.7 | 0.833401 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13322.0 | 0.820884 | 0.410442 | − | 0.911887i | \(-0.365374\pi\) | ||||
0.410442 | + | 0.911887i | \(0.365374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13836.6 | −0.848617 | −0.424308 | − | 0.905518i | \(-0.639483\pi\) | ||||
−0.424308 | + | 0.905518i | \(0.639483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2485.83 | −0.151048 | −0.0755239 | − | 0.997144i | \(-0.524063\pi\) | ||||
−0.0755239 | + | 0.997144i | \(0.524063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3543.27 | −0.214307 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28397.2 | −1.70179 | −0.850894 | − | 0.525338i | \(-0.823939\pi\) | ||||
−0.850894 | + | 0.525338i | \(0.823939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2811.01 | −0.167687 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21563.6 | −1.27465 | −0.637327 | − | 0.770593i | \(-0.719960\pi\) | ||||
−0.637327 | + | 0.770593i | \(0.719960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29325.9 | −1.72564 | −0.862819 | − | 0.505513i | \(-0.831303\pi\) | ||||
−0.862819 | + | 0.505513i | \(0.831303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19360.4 | −1.12897 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31945.7 | 1.85448 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14394.1 | 0.828133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3823.52 | −0.218998 | −0.109499 | − | 0.993987i | \(-0.534925\pi\) | ||||
−0.109499 | + | 0.993987i | \(0.534925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4502.69 | −0.255617 | −0.127808 | − | 0.991799i | \(-0.540794\pi\) | ||||
−0.127808 | + | 0.991799i | \(0.540794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24790.9 | 1.40116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25841.5 | −1.44773 | −0.723863 | − | 0.689944i | \(-0.757635\pi\) | ||||
−0.723863 | + | 0.689944i | \(0.757635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5308.09 | −0.296075 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13041.0 | −0.721080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25894.2 | −1.42556 | −0.712780 | − | 0.701387i | \(-0.752564\pi\) | ||||
−0.712780 | + | 0.701387i | \(0.752564\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1064.24 | −0.0580849 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9300.12 | 0.505405 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30603.6 | 1.64890 | 0.824452 | − | 0.565932i | \(-0.191484\pi\) | ||||
0.824452 | + | 0.565932i | \(0.191484\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7781.40 | 0.417470 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1152.75 | −0.0613204 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12245.5 | −0.648646 | −0.324323 | − | 0.945946i | \(-0.605136\pi\) | ||||
−0.324323 | + | 0.945946i | \(0.605136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4833.14 | 0.253860 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1482.06 | −0.0775185 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16585.7 | 0.860282 | 0.430141 | − | 0.902762i | \(-0.358464\pi\) | ||||
0.430141 | + | 0.902762i | \(0.358464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19972.6 | −1.03165 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6019.22 | 0.308343 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8074.43 | 0.411918 | 0.205959 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205959 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18050.2 | −0.913286 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12009.3 | −0.605147 | −0.302573 | − | 0.953126i | \(-0.597846\pi\) | ||||
−0.302573 | + | 0.953126i | \(0.597846\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −499.861 | −0.0249832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8208.53 | 0.408600 | 0.204300 | − | 0.978908i | \(-0.434508\pi\) | ||||
0.204300 | + | 0.978908i | \(0.434508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1904.13 | 0.0940185 | 0.0470093 | − | 0.998894i | \(-0.485031\pi\) | ||||
0.0470093 | + | 0.998894i | \(0.485031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8790.43 | 0.432290 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35803.1 | 1.74662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8188.19 | −0.397858 | −0.198929 | − | 0.980014i | \(-0.563746\pi\) | ||||
−0.198929 | + | 0.980014i | \(0.563746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8361.60 | 0.403059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15107.8 | 0.725367 | 0.362684 | − | 0.931912i | \(-0.381861\pi\) | ||||
0.362684 | + | 0.931912i | \(0.381861\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24723.7 | −1.17770 | −0.588851 | − | 0.808241i | \(-0.700420\pi\) | ||||
−0.588851 | + | 0.808241i | \(0.700420\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 59523.1 | 2.82422 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4049.01 | 0.190614 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34299.9 | −1.60844 | −0.804218 | − | 0.594335i | \(-0.797415\pi\) | ||||
−0.804218 | + | 0.594335i | \(0.797415\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8485.24 | −0.394816 | −0.197408 | − | 0.980321i | \(-0.563252\pi\) | ||||
−0.197408 | + | 0.980321i | \(0.563252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 910.663 | 0.0422090 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17875.0 | −0.822131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3157.41 | 0.144662 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13272.3 | −0.603451 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5230.11 | −0.236891 | −0.118446 | − | 0.992961i | \(-0.537791\pi\) | ||||
−0.118446 | + | 0.992961i | \(0.537791\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31482.8 | 1.41517 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16448.6 | −0.736578 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6834.31 | 0.303744 | 0.151872 | − | 0.988400i | \(-0.451470\pi\) | ||||
0.151872 | + | 0.988400i | \(0.451470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21840.8 | 0.967051 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15718.3 | 0.690768 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21711.0 | −0.950575 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32358.8 | 1.40627 | 0.703137 | − | 0.711055i | \(-0.251782\pi\) | ||||
0.703137 | + | 0.711055i | \(0.251782\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14804.3 | 0.640997 | 0.320499 | − | 0.947249i | \(-0.396150\pi\) | ||||
0.320499 | + | 0.947249i | \(0.396150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9125.99 | 0.392232 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34692.9 | 1.48562 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19769.7 | −0.840398 | −0.420199 | − | 0.907432i | \(-0.638040\pi\) | ||||
−0.420199 | + | 0.907432i | \(0.638040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34322.1 | 1.45370 | 0.726848 | − | 0.686798i | \(-0.240984\pi\) | ||||
0.726848 | + | 0.686798i | \(0.240984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9870.43 | 0.415028 | 0.207514 | − | 0.978232i | \(-0.433463\pi\) | ||||
0.207514 | + | 0.978232i | \(0.433463\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3911.55 | −0.163876 | −0.0819382 | − | 0.996637i | \(-0.526111\pi\) | ||||
−0.0819382 | + | 0.996637i | \(0.526111\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −44815.8 | −1.86408 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21172.5 | 0.877489 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8347.07 | −0.343472 | −0.171736 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171736 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33580.7 | 1.37688 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9291.41 | −0.378265 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35070.1 | 1.42269 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8726.16 | 0.351503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5782.37 | −0.232104 | −0.116052 | − | 0.993243i | \(-0.537024\pi\) | ||||
−0.116052 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3636.13 | −0.144933 | −0.0724666 | − | 0.997371i | \(-0.523087\pi\) | ||||
−0.0724666 | + | 0.997371i | \(0.523087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34374.1 | 1.36534 | 0.682671 | − | 0.730726i | \(-0.260818\pi\) | ||||
0.682671 | + | 0.730726i | \(0.260818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28082.0 | −1.10767 | −0.553836 | − | 0.832626i | \(-0.686837\pi\) | ||||
−0.553836 | + | 0.832626i | \(0.686837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11635.0 | −0.457344 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13600.5 | 0.530916 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 571.207 | 0.0222212 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4090.81 | −0.158051 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26099.9 | −1.00494 | −0.502469 | − | 0.864595i | \(-0.667575\pi\) | ||||
−0.502469 | + | 0.864595i | \(0.667575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29982.7 | 1.14659 | 0.573294 | − | 0.819350i | \(-0.305665\pi\) | ||||
0.573294 | + | 0.819350i | \(0.305665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 124.860 | 0.00475865 | 0.00237932 | − | 0.999997i | \(-0.499243\pi\) | ||||
0.00237932 | + | 0.999997i | \(0.499243\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2631.59 | −0.0996167 | −0.0498084 | − | 0.998759i | \(-0.515861\pi\) | ||||
−0.0498084 | + | 0.998759i | \(0.515861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27263.3 | 1.02855 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41978.6 | −1.57308 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18771.6 | 0.701077 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8770.37 | 0.325371 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43619.5 | 1.61285 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 224.414 | 0.00824284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29239.7 | 1.07044 | 0.535219 | − | 0.844713i | \(-0.320229\pi\) | ||||
0.535219 | + | 0.844713i | \(0.320229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46512.2 | 1.69157 | 0.845783 | − | 0.533527i | \(-0.179134\pi\) | ||||
0.845783 | + | 0.533527i | \(0.179134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 207.009 | 0.00750385 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18398.8 | 0.662577 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16873.5 | 0.605664 | 0.302832 | − | 0.953044i | \(-0.402068\pi\) | ||||
0.302832 | + | 0.953044i | \(0.402068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3608.08 | −0.128669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1644.19 | 0.0584439 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32397.2 | 1.14415 | 0.572076 | − | 0.820201i | \(-0.306138\pi\) | ||||
0.572076 | + | 0.820201i | \(0.306138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 86137.0 | 3.03225 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4957.16 | 0.173386 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5339.74 | −0.186170 | −0.0930852 | − | 0.995658i | \(-0.529673\pi\) | ||||
−0.0930852 | + | 0.995658i | \(0.529673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24451.1 | 0.847058 | 0.423529 | − | 0.905883i | \(-0.360791\pi\) | ||||
0.423529 | + | 0.905883i | \(0.360791\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20045.3 | −0.692221 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23200.1 | −0.796096 | −0.398048 | − | 0.917365i | \(-0.630312\pi\) | ||||
−0.398048 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17961.8 | −0.614399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22349.2 | −0.759666 | −0.379833 | − | 0.925055i | \(-0.624019\pi\) | ||||
−0.379833 | + | 0.925055i | \(0.624019\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22683.9 | 0.768623 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34743.0 | 1.16987 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28464.1 | −0.955460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1200.62 | 0.0400510 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2505.06 | −0.0833063 | −0.0416532 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416532 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50594.9 | 1.67216 | 0.836080 | − | 0.548607i | \(-0.184842\pi\) | ||||
0.836080 | + | 0.548607i | \(0.184842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6965.77 | 0.229509 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19735.5 | −0.646259 | −0.323130 | − | 0.946355i | \(-0.604735\pi\) | ||||
−0.323130 | + | 0.946355i | \(0.604735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14376.9 | −0.469345 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54357.7 | −1.76373 | −0.881863 | − | 0.471506i | \(-0.843711\pi\) | ||||
−0.881863 | + | 0.471506i | \(0.843711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18544.9 | 0.599887 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38905.1 | 1.25087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37794.5 | −1.21148 | −0.605742 | − | 0.795661i | \(-0.707124\pi\) | ||||
−0.605742 | + | 0.795661i | \(0.707124\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4878.91 | −0.155449 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21129.2 | −0.671182 | −0.335591 | − | 0.942008i | \(-0.608936\pi\) | ||||
−0.335591 | + | 0.942008i | \(0.608936\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.a.h.1.1 | 4 | ||
3.2 | odd | 2 | 1620.4.a.g.1.1 | 4 | |||
9.2 | odd | 6 | 180.4.i.b.121.2 | yes | 8 | ||
9.4 | even | 3 | 540.4.i.b.181.4 | 8 | |||
9.5 | odd | 6 | 180.4.i.b.61.2 | ✓ | 8 | ||
9.7 | even | 3 | 540.4.i.b.361.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.i.b.61.2 | ✓ | 8 | 9.5 | odd | 6 | ||
180.4.i.b.121.2 | yes | 8 | 9.2 | odd | 6 | ||
540.4.i.b.181.4 | 8 | 9.4 | even | 3 | |||
540.4.i.b.361.4 | 8 | 9.7 | even | 3 | |||
1620.4.a.g.1.1 | 4 | 3.2 | odd | 2 | |||
1620.4.a.h.1.1 | 4 | 1.1 | even | 1 | trivial |