Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,4,Mod(1,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1872.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.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: | \(110.451575531\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1872.1 |
$q$-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 | ||||||||
\(5\) | −10.5830 | −0.946573 | −0.473286 | − | 0.880909i | \(-0.656932\pi\) | ||||
−0.473286 | + | 0.880909i | \(0.656932\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000 | 1.18789 | 0.593944 | − | 0.804506i | \(-0.297570\pi\) | ||||
0.593944 | + | 0.804506i | \(0.297570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29150 | 0.145041 | 0.0725204 | − | 0.997367i | \(-0.476896\pi\) | ||||
0.0725204 | + | 0.997367i | \(0.476896\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 116.413 | 1.66084 | 0.830421 | − | 0.557136i | \(-0.188100\pi\) | ||||
0.830421 | + | 0.557136i | \(0.188100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 126.000 | 1.52139 | 0.760694 | − | 0.649110i | \(-0.224859\pi\) | ||||
0.760694 | + | 0.649110i | \(0.224859\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −31.7490 | −0.287832 | −0.143916 | − | 0.989590i | \(-0.545969\pi\) | ||||
−0.143916 | + | 0.989590i | \(0.545969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.0000 | −0.104000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.9150 | 0.338830 | 0.169415 | − | 0.985545i | \(-0.445812\pi\) | ||||
0.169415 | + | 0.985545i | \(0.445812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 182.000 | 1.05446 | 0.527228 | − | 0.849724i | \(-0.323231\pi\) | ||||
0.527228 | + | 0.849724i | \(0.323231\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −232.826 | −1.12442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −86.0000 | −0.382117 | −0.191058 | − | 0.981579i | \(-0.561192\pi\) | ||||
−0.191058 | + | 0.981579i | \(0.561192\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −444.486 | −1.69310 | −0.846550 | − | 0.532310i | \(-0.821324\pi\) | ||||
−0.846550 | + | 0.532310i | \(0.821324\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −96.0000 | −0.340462 | −0.170231 | − | 0.985404i | \(-0.554451\pi\) | ||||
−0.170231 | + | 0.985404i | \(0.554451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −365.114 | −1.13313 | −0.566567 | − | 0.824016i | \(-0.691729\pi\) | ||||
−0.566567 | + | 0.824016i | \(0.691729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 141.000 | 0.411079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −190.494 | −0.493705 | −0.246853 | − | 0.969053i | \(-0.579396\pi\) | ||||
−0.246853 | + | 0.969053i | \(0.579396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −56.0000 | −0.137292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 587.357 | 1.29606 | 0.648028 | − | 0.761616i | \(-0.275594\pi\) | ||||
0.648028 | + | 0.761616i | \(0.275594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 574.000 | 1.20481 | 0.602403 | − | 0.798192i | \(-0.294210\pi\) | ||||
0.602403 | + | 0.798192i | \(0.294210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −137.579 | −0.262532 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 530.000 | 0.966415 | 0.483208 | − | 0.875506i | \(-0.339472\pi\) | ||||
0.483208 | + | 0.875506i | \(0.339472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −809.600 | −1.35327 | −0.676633 | − | 0.736321i | \(-0.736561\pi\) | ||||
−0.676633 | + | 0.736321i | \(0.736561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −154.000 | −0.246909 | −0.123454 | − | 0.992350i | \(-0.539397\pi\) | ||||
−0.123454 | + | 0.992350i | \(0.539397\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 116.413 | 0.172292 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 460.000 | 0.655114 | 0.327557 | − | 0.944831i | \(-0.393775\pi\) | ||||
0.327557 | + | 0.944831i | \(0.393775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 322.782 | 0.426866 | 0.213433 | − | 0.976958i | \(-0.431535\pi\) | ||||
0.213433 | + | 0.976958i | \(0.431535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1232.00 | −1.57211 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1439.29 | 1.71421 | 0.857103 | − | 0.515145i | \(-0.172262\pi\) | ||||
0.857103 | + | 0.515145i | \(0.172262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 286.000 | 0.329461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1333.46 | −1.44010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.0000 | 0.0732724 | 0.0366362 | − | 0.999329i | \(-0.488336\pi\) | ||||
0.0366362 | + | 0.999329i | \(0.488336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1460.45 | −1.43882 | −0.719409 | − | 0.694586i | \(-0.755587\pi\) | ||||
−0.719409 | + | 0.694586i | \(0.755587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1428.00 | 1.36607 | 0.683034 | − | 0.730387i | \(-0.260660\pi\) | ||||
0.683034 | + | 0.730387i | \(0.260660\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1619.20 | 1.46293 | 0.731467 | − | 0.681877i | \(-0.238836\pi\) | ||||
0.731467 | + | 0.681877i | \(0.238836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −338.000 | −0.297014 | −0.148507 | − | 0.988911i | \(-0.547447\pi\) | ||||
−0.148507 | + | 0.988911i | \(0.547447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1682.70 | −1.40084 | −0.700420 | − | 0.713731i | \(-0.747004\pi\) | ||||
−0.700420 | + | 0.713731i | \(0.747004\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 336.000 | 0.272454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2561.09 | 1.97289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1303.00 | −0.978963 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1460.45 | 1.04502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 376.000 | 0.262713 | 0.131357 | − | 0.991335i | \(-0.458067\pi\) | ||||
0.131357 | + | 0.991335i | \(0.458067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 687.895 | 0.458792 | 0.229396 | − | 0.973333i | \(-0.426325\pi\) | ||||
0.229396 | + | 0.973333i | \(0.426325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2772.00 | 1.80724 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1396.96 | 0.871168 | 0.435584 | − | 0.900148i | \(-0.356542\pi\) | ||||
0.435584 | + | 0.900148i | \(0.356542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2100.00 | −1.28144 | −0.640718 | − | 0.767776i | \(-0.721363\pi\) | ||||
−0.640718 | + | 0.767776i | \(0.721363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 68.7895 | 0.0402271 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −560.000 | −0.320727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2000.19 | −1.09974 | −0.549872 | − | 0.835249i | \(-0.685323\pi\) | ||||
−0.549872 | + | 0.835249i | \(0.685323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3526.00 | −1.90028 | −0.950138 | − | 0.311828i | \(-0.899059\pi\) | ||||
−0.950138 | + | 0.311828i | \(0.899059\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1926.11 | −0.998120 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3066.00 | 1.55856 | 0.779278 | − | 0.626678i | \(-0.215586\pi\) | ||||
0.779278 | + | 0.626678i | \(0.215586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −698.478 | −0.341912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3442.00 | 1.65398 | 0.826988 | − | 0.562219i | \(-0.190052\pi\) | ||||
0.826988 | + | 0.562219i | \(0.190052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2693.37 | −1.24802 | −0.624011 | − | 0.781416i | \(-0.714498\pi\) | ||||
−0.624011 | + | 0.781416i | \(0.714498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3492.39 | 1.53481 | 0.767404 | − | 0.641164i | \(-0.221548\pi\) | ||||
0.767404 | + | 0.641164i | \(0.221548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −286.000 | −0.123540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −169.328 | −0.0707049 | −0.0353524 | − | 0.999375i | \(-0.511255\pi\) | ||||
−0.0353524 | + | 0.999375i | \(0.511255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3374.00 | 1.38557 | 0.692783 | − | 0.721146i | \(-0.256384\pi\) | ||||
0.692783 | + | 0.721146i | \(0.256384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 910.138 | 0.361701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 616.000 | 0.240890 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1185.30 | 0.449032 | 0.224516 | − | 0.974470i | \(-0.427920\pi\) | ||||
0.224516 | + | 0.974470i | \(0.427920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1542.00 | −0.575107 | −0.287553 | − | 0.957765i | \(-0.592842\pi\) | ||||
−0.287553 | + | 0.957765i | \(0.592842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2127.18 | 0.769318 | 0.384659 | − | 0.923059i | \(-0.374319\pi\) | ||||
0.384659 | + | 0.923059i | \(0.374319\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 952.000 | 0.339123 | 0.169562 | − | 0.985520i | \(-0.445765\pi\) | ||||
0.169562 | + | 0.985520i | \(0.445765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1164.13 | 0.402492 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4704.00 | 1.60264 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 666.729 | 0.220663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1640.00 | 0.535082 | 0.267541 | − | 0.963547i | \(-0.413789\pi\) | ||||
0.267541 | + | 0.963547i | \(0.413789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1015.97 | 0.322272 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4004.00 | 1.25258 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1513.37 | 0.460635 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4886.00 | 1.46722 | 0.733612 | − | 0.679569i | \(-0.237833\pi\) | ||||
0.733612 | + | 0.679569i | \(0.237833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1867.90 | −0.546154 | −0.273077 | − | 0.961992i | \(-0.588041\pi\) | ||||
−0.273077 | + | 0.961992i | \(0.588041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5558.00 | 1.60386 | 0.801928 | − | 0.597421i | \(-0.203808\pi\) | ||||
0.801928 | + | 0.597421i | \(0.203808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3577.06 | −1.00575 | −0.502877 | − | 0.864358i | \(-0.667725\pi\) | ||||
−0.502877 | + | 0.864358i | \(0.667725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3864.00 | 1.07259 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2936.78 | 0.794832 | 0.397416 | − | 0.917639i | \(-0.369907\pi\) | ||||
0.397416 | + | 0.917639i | \(0.369907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −602.000 | −0.160906 | −0.0804528 | − | 0.996758i | \(-0.525637\pi\) | ||||
−0.0804528 | + | 0.996758i | \(0.525637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1492.20 | −0.389116 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1638.00 | 0.421957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3524.14 | 0.886222 | 0.443111 | − | 0.896467i | \(-0.353875\pi\) | ||||
0.443111 | + | 0.896467i | \(0.353875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −168.000 | −0.0417473 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2942.08 | 0.714092 | 0.357046 | − | 0.934087i | \(-0.383784\pi\) | ||||
0.357046 | + | 0.934087i | \(0.383784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1892.00 | −0.453912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −857.223 | −0.200984 | −0.100492 | − | 0.994938i | \(-0.532042\pi\) | ||||
−0.100492 | + | 0.994938i | \(0.532042\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2016.00 | 0.467328 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 328.073 | 0.0743605 | 0.0371802 | − | 0.999309i | \(-0.488162\pi\) | ||||
0.0371802 | + | 0.999309i | \(0.488162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2814.00 | 0.630769 | 0.315384 | − | 0.948964i | \(-0.397867\pi\) | ||||
0.315384 | + | 0.948964i | \(0.397867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68.7895 | −0.0150842 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3190.00 | −0.691944 | −0.345972 | − | 0.938245i | \(-0.612451\pi\) | ||||
−0.345972 | + | 0.938245i | \(0.612451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6116.98 | 1.29861 | 0.649303 | − | 0.760530i | \(-0.275061\pi\) | ||||
0.649303 | + | 0.760530i | \(0.275061\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4788.00 | 1.00571 | 0.502857 | − | 0.864370i | \(-0.332282\pi\) | ||||
0.502857 | + | 0.864370i | \(0.332282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9778.70 | −2.01121 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8639.00 | 1.75840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6699.04 | −1.33571 | −0.667854 | − | 0.744293i | \(-0.732787\pi\) | ||||
−0.667854 | + | 0.744293i | \(0.732787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6216.00 | −1.22681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −412.737 | −0.0798301 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2112.00 | −0.404431 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6074.65 | −1.14044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 406.000 | 0.0754777 | 0.0377388 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377388 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8286.49 | −1.51088 | −0.755440 | − | 0.655217i | \(-0.772577\pi\) | ||||
−0.755440 | + | 0.655217i | \(0.772577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5586.00 | −1.00875 | −0.504376 | − | 0.863484i | \(-0.668277\pi\) | ||||
−0.504376 | + | 0.863484i | \(0.668277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8392.32 | −1.48694 | −0.743470 | − | 0.668770i | \(-0.766821\pi\) | ||||
−0.743470 | + | 0.668770i | \(0.766821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 280.000 | 0.0491442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14668.0 | 2.52679 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −169.000 | −0.0288444 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8032.50 | −1.34604 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4426.00 | 0.734970 | 0.367485 | − | 0.930030i | \(-0.380219\pi\) | ||||
0.367485 | + | 0.930030i | \(0.380219\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5608.99 | −0.914782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8370.00 | 1.35295 | 0.676473 | − | 0.736467i | \(-0.263507\pi\) | ||||
0.676473 | + | 0.736467i | \(0.263507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 963.053 | 0.152939 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4444.00 | −0.699573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6095.81 | −0.943056 | −0.471528 | − | 0.881851i | \(-0.656297\pi\) | ||||
−0.471528 | + | 0.881851i | \(0.656297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4354.00 | 0.667806 | 0.333903 | − | 0.942607i | \(-0.391634\pi\) | ||||
0.333903 | + | 0.942607i | \(0.391634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3407.73 | 0.513810 | 0.256905 | − | 0.966437i | \(-0.417297\pi\) | ||||
0.256905 | + | 0.966437i | \(0.417297\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8568.00 | 1.28096 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7762.63 | 1.14121 | 0.570607 | − | 0.821223i | \(-0.306708\pi\) | ||||
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9017.00 | 1.31462 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1629.78 | 0.233717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7784.00 | 1.10714 | 0.553572 | − | 0.832802i | \(-0.313265\pi\) | ||||
0.553572 | + | 0.832802i | \(0.313265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4190.87 | −0.586467 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8510.00 | −1.18132 | −0.590658 | − | 0.806922i | \(-0.701132\pi\) | ||||
−0.590658 | + | 0.806922i | \(0.701132\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 687.895 | 0.0939746 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1650.00 | −0.223627 | −0.111814 | − | 0.993729i | \(-0.535666\pi\) | ||||
−0.111814 | + | 0.993729i | \(0.535666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8662.19 | 1.15566 | 0.577829 | − | 0.816158i | \(-0.303900\pi\) | ||||
0.577829 | + | 0.816158i | \(0.303900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1232.00 | −0.163087 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2423.51 | 0.315879 | 0.157939 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157939 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3696.00 | −0.478043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4868.18 | −0.620114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1414.00 | −0.178757 | −0.0893786 | − | 0.995998i | \(-0.528488\pi\) | ||||
−0.0893786 | + | 0.995998i | \(0.528488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5228.00 | −0.651058 | −0.325529 | − | 0.945532i | \(-0.605542\pi\) | ||||
−0.325529 | + | 0.945532i | \(0.605542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2366.00 | 0.292454 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −455.069 | −0.0554225 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5782.00 | 0.699026 | 0.349513 | − | 0.936932i | \(-0.386347\pi\) | ||||
0.349513 | + | 0.936932i | \(0.386347\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12921.8 | 1.53957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3416.00 | −0.404060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11482.6 | 1.33881 | 0.669403 | − | 0.742899i | \(-0.266550\pi\) | ||||
0.669403 | + | 0.742899i | \(0.266550\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14194.0 | −1.64317 | −0.821583 | − | 0.570088i | \(-0.806909\pi\) | ||||
−0.821583 | + | 0.570088i | \(0.806909\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1513.37 | −0.172728 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12628.0 | 1.43118 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5222.71 | −0.583687 | −0.291844 | − | 0.956466i | \(-0.594269\pi\) | ||||
−0.291844 | + | 0.956466i | \(0.594269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −686.000 | −0.0761364 | −0.0380682 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380682 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4000.38 | −0.437904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1372.00 | 0.149162 | 0.0745809 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745809 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2338.84 | −0.250839 | −0.125420 | − | 0.992104i | \(-0.540028\pi\) | ||||
−0.125420 | + | 0.992104i | \(0.540028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15232.0 | −1.62262 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17250.3 | 1.81312 | 0.906561 | − | 0.422074i | \(-0.138698\pi\) | ||||
0.906561 | + | 0.422074i | \(0.138698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2352.00 | −0.245568 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3026.74 | −0.311859 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17866.0 | −1.82874 | −0.914372 | − | 0.404875i | \(-0.867315\pi\) | ||||
−0.914372 | + | 0.404875i | \(0.867315\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2106.02 | 0.212770 | 0.106385 | − | 0.994325i | \(-0.466072\pi\) | ||||
0.106385 | + | 0.994325i | \(0.466072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13718.0 | 1.37695 | 0.688477 | − | 0.725258i | \(-0.258280\pi\) | ||||
0.688477 | + | 0.725258i | \(0.258280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4095.62 | −0.405830 | −0.202915 | − | 0.979196i | \(-0.565042\pi\) | ||||
−0.202915 | + | 0.979196i | \(0.565042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11660.0 | 1.14799 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −507.984 | −0.0493808 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1638.00 | −0.158224 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8715.10 | −0.831322 | −0.415661 | − | 0.909520i | \(-0.636450\pi\) | ||||
−0.415661 | + | 0.909520i | \(0.636450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1118.00 | −0.105980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −740.810 | −0.0693577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4506.00 | −0.419274 | −0.209637 | − | 0.977779i | \(-0.567228\pi\) | ||||
−0.209637 | + | 0.977779i | \(0.567228\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21621.1 | 1.98726 | 0.993631 | − | 0.112683i | \(-0.0359443\pi\) | ||||
0.993631 | + | 0.112683i | \(0.0359443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6160.00 | 0.562743 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17811.2 | −1.60753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 786.000 | 0.0705134 | 0.0352567 | − | 0.999378i | \(-0.488775\pi\) | ||||
0.0352567 | + | 0.999378i | \(0.488775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2106.02 | −0.186685 | −0.0933426 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933426 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15456.0 | 1.36195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8392.32 | 0.730812 | 0.365406 | − | 0.930848i | \(-0.380930\pi\) | ||||
0.365406 | + | 0.930848i | \(0.380930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3388.00 | −0.293300 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15112.5 | −1.29308 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1932.00 | −0.164351 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3905.13 | 0.328382 | 0.164191 | − | 0.986429i | \(-0.447499\pi\) | ||||
0.164191 | + | 0.986429i | \(0.447499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17668.0 | 1.47718 | 0.738592 | − | 0.674152i | \(-0.235491\pi\) | ||||
0.738592 | + | 0.674152i | \(0.235491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21187.2 | 1.75129 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11159.0 | −0.917153 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5778.32 | −0.469581 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17136.0 | −1.38477 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 746.102 | 0.0596232 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1650.00 | −0.131126 | −0.0655629 | − | 0.997848i | \(-0.520884\pi\) | ||||
−0.0655629 | + | 0.997848i | \(0.520884\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3577.06 | 0.281145 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3796.00 | −0.296719 | −0.148359 | − | 0.988934i | \(-0.547399\pi\) | ||||
−0.148359 | + | 0.988934i | \(0.547399\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6667.29 | 0.515492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10120.0 | 0.778203 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2063.69 | −0.156986 | −0.0784930 | − | 0.996915i | \(-0.525011\pi\) | ||||
−0.0784930 | + | 0.996915i | \(0.525011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1248.00 | −0.0944271 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26034.2 | −1.94886 | −0.974432 | − | 0.224683i | \(-0.927865\pi\) | ||||
−0.974432 | + | 0.224683i | \(0.927865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17808.0 | 1.32600 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3640.55 | −0.268225 | −0.134112 | − | 0.990966i | \(-0.542818\pi\) | ||||
−0.134112 | + | 0.990966i | \(0.542818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19612.0 | 1.43737 | 0.718684 | − | 0.695337i | \(-0.244745\pi\) | ||||
0.718684 | + | 0.695337i | \(0.244745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 412.737 | 0.0299345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15722.0 | 1.13434 | 0.567171 | − | 0.823600i | \(-0.308038\pi\) | ||||
0.567171 | + | 0.823600i | \(0.308038\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7101.20 | 0.507069 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1008.00 | −0.0716074 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2725.12 | −0.191615 | −0.0958074 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958074 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22932.0 | 1.60424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18012.3 | 1.24734 | 0.623672 | − | 0.781686i | \(-0.285640\pi\) | ||||
0.623672 | + | 0.781686i | \(0.285640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27104.0 | −1.86749 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12181.0 | −0.830891 | −0.415446 | − | 0.909618i | \(-0.636374\pi\) | ||||
−0.415446 | + | 0.909618i | \(0.636374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5950.00 | 0.403836 | 0.201918 | − | 0.979402i | \(-0.435283\pi\) | ||||
0.201918 | + | 0.979402i | \(0.435283\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13789.7 | 0.926660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14168.0 | −0.947383 | −0.473691 | − | 0.880691i | \(-0.657079\pi\) | ||||
−0.473691 | + | 0.880691i | \(0.657079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4746.48 | −0.314275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6326.00 | −0.416810 | −0.208405 | − | 0.978043i | \(-0.566827\pi\) | ||||
−0.208405 | + | 0.978043i | \(0.566827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8805.06 | 0.574519 | 0.287260 | − | 0.957853i | \(-0.407256\pi\) | ||||
0.287260 | + | 0.957853i | \(0.407256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24486.0 | 1.58994 | 0.794972 | − | 0.606646i | \(-0.207485\pi\) | ||||
0.794972 | + | 0.606646i | \(0.207485\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31664.4 | 2.03628 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10011.5 | −0.634635 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22430.0 | −1.41509 | −0.707547 | − | 0.706666i | \(-0.750198\pi\) | ||||
−0.707547 | + | 0.706666i | \(0.750198\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3979.21 | −0.248677 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1833.00 | 0.114013 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27484.1 | 1.69353 | 0.846767 | − | 0.531964i | \(-0.178546\pi\) | ||||
0.846767 | + | 0.531964i | \(0.178546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16478.0 | −1.01062 | −0.505310 | − | 0.862938i | \(-0.668622\pi\) | ||||
−0.505310 | + | 0.862938i | \(0.668622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26563.3 | 1.61408 | 0.807042 | − | 0.590494i | \(-0.201067\pi\) | ||||
0.807042 | + | 0.590494i | \(0.201067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3108.00 | 0.187981 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20287.6 | −1.21580 | −0.607899 | − | 0.794014i | \(-0.707987\pi\) | ||||
−0.607899 | + | 0.794014i | \(0.707987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7280.00 | −0.434280 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 656.146 | 0.0387858 | 0.0193929 | − | 0.999812i | \(-0.493827\pi\) | ||||
0.0193929 | + | 0.999812i | \(0.493827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14238.0 | −0.837812 | −0.418906 | − | 0.908030i | \(-0.637586\pi\) | ||||
−0.418906 | + | 0.908030i | \(0.637586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29336.1 | −1.71068 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1680.00 | −0.0975260 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3037.32 | 0.174746 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4874.00 | −0.279166 | −0.139583 | − | 0.990210i | \(-0.544576\pi\) | ||||
−0.139583 | + | 0.990210i | \(0.544576\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21801.0 | −1.23764 | −0.618818 | − | 0.785534i | \(-0.712388\pi\) | ||||
−0.618818 | + | 0.785534i | \(0.712388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1540.00 | 0.0870394 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8746.85 | 0.490028 | 0.245014 | − | 0.969520i | \(-0.421207\pi\) | ||||
0.245014 | + | 0.969520i | \(0.421207\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14784.0 | −0.824624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2476.42 | −0.136929 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −294.000 | −0.0161857 | −0.00809283 | − | 0.999967i | \(-0.502576\pi\) | ||||
−0.00809283 | + | 0.999967i | \(0.502576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22224.3 | 1.21297 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51744.0 | −2.81197 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15758.1 | −0.849037 | −0.424519 | − | 0.905419i | \(-0.639557\pi\) | ||||
−0.424519 | + | 0.905419i | \(0.639557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10836.0 | −0.581348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32130.0 | −1.70916 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6722.00 | −0.356065 | −0.178032 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178032 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5778.32 | −0.303506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −728.000 | −0.0380778 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.7490 | −0.00164679 | −0.000823393 | − | 1.00000i | \(-0.500262\pi\) | ||||
−0.000823393 | 1.00000i | \(0.500262\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31416.0 | 1.62274 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −687.895 | −0.0352383 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12824.0 | −0.654217 | −0.327109 | − | 0.944987i | \(-0.606074\pi\) | ||||
−0.327109 | + | 0.944987i | \(0.606074\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11175.7 | −0.565453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29610.0 | −1.49205 | −0.746023 | − | 0.665920i | \(-0.768039\pi\) | ||||
−0.746023 | + | 0.665920i | \(0.768039\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2804.50 | 0.140170 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15622.0 | 0.777625 | 0.388812 | − | 0.921317i | \(-0.372885\pi\) | ||||
0.388812 | + | 0.921317i | \(0.372885\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8588.11 | 0.424047 | 0.212024 | − | 0.977265i | \(-0.431995\pi\) | ||||
0.212024 | + | 0.977265i | \(0.431995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21168.0 | 1.04099 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35622.4 | 1.73780 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29468.0 | −1.43183 | −0.715914 | − | 0.698189i | \(-0.753990\pi\) | ||||
−0.715914 | + | 0.698189i | \(0.753990\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37315.7 | 1.79875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35030.0 | −1.68189 | −0.840943 | − | 0.541124i | \(-0.817999\pi\) | ||||
−0.840943 | + | 0.541124i | \(0.817999\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22330.1 | −1.06369 | −0.531844 | − | 0.846842i | \(-0.678501\pi\) | ||||
−0.531844 | + | 0.846842i | \(0.678501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7436.00 | −0.352819 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7635.64 | 0.359461 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27342.0 | −1.28216 | −0.641078 | − | 0.767476i | \(-0.721512\pi\) | ||||
−0.641078 | + | 0.767476i | \(0.721512\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11884.7 | 0.552993 | 0.276496 | − | 0.961015i | \(-0.410827\pi\) | ||||
0.276496 | + | 0.961015i | \(0.410827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2366.00 | −0.109664 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56005.3 | −2.57586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4284.00 | −0.196279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32447.5 | −1.47529 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22666.0 | −1.02663 | −0.513314 | − | 0.858201i | \(-0.671582\pi\) | ||||
−0.513314 | + | 0.858201i | \(0.671582\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37019.4 | −1.66404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7462.00 | 0.334153 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 582.065 | 0.0258693 | 0.0129346 | − | 0.999916i | \(-0.495883\pi\) | ||||
0.0129346 | + | 0.999916i | \(0.495883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42504.0 | −1.88196 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −814.891 | −0.0358118 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7392.00 | 0.323644 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 793.725 | 0.0344943 | 0.0172472 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172472 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9478.00 | 0.410379 | 0.205190 | − | 0.978722i | \(-0.434219\pi\) | ||||
0.205190 | + | 0.978722i | \(0.434219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36426.7 | −1.56561 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12096.0 | −0.517975 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3227.82 | 0.137213 | 0.0686063 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686063 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40476.0 | −1.71434 | −0.857172 | − | 0.515031i | \(-0.827781\pi\) | ||||
−0.857172 | + | 0.515031i | \(0.827781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7169.99 | −0.301481 | −0.150741 | − | 0.988573i | \(-0.548166\pi\) | ||||
−0.150741 | + | 0.988573i | \(0.548166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27482.0 | 1.15137 | 0.575687 | − | 0.817670i | \(-0.304735\pi\) | ||||
0.575687 | + | 0.817670i | \(0.304735\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16414.2 | 0.682737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28504.0 | 1.18134 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19128.8 | −0.787126 | −0.393563 | − | 0.919298i | \(-0.628758\pi\) | ||||
−0.393563 | + | 0.919298i | \(0.628758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21589.0 | −0.885194 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1788.53 | −0.0728133 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28666.0 | −1.16290 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2730.42 | 0.109985 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31962.0 | 1.28295 | 0.641476 | − | 0.767143i | \(-0.278322\pi\) | ||||
0.641476 | + | 0.767143i | \(0.278322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4931.68 | −0.196573 | −0.0982865 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982865 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11704.0 | −0.464884 | −0.232442 | − | 0.972610i | \(-0.574672\pi\) | ||||
−0.232442 | + | 0.972610i | \(0.574672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2280.64 | −0.0899581 | −0.0449790 | − | 0.998988i | \(-0.514322\pi\) | ||||
−0.0449790 | + | 0.998988i | \(0.514322\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36960.0 | −1.45281 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2434.09 | 0.0950183 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6890.00 | 0.268035 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32130.0 | 1.24136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1006.00 | −0.0387346 | −0.0193673 | − | 0.999812i | \(-0.506165\pi\) | ||||
−0.0193673 | + | 0.999812i | \(0.506165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40681.1 | 1.55571 | 0.777855 | − | 0.628444i | \(-0.216308\pi\) | ||||
0.777855 | + | 0.628444i | \(0.216308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −124.000 | −0.00472586 | −0.00236293 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236293 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16573.0 | 0.627358 | 0.313679 | − | 0.949529i | \(-0.398438\pi\) | ||||
0.313679 | + | 0.949529i | \(0.398438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8272.00 | 0.312074 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46004.3 | −1.72394 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1792.00 | 0.0669273 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9630.53 | 0.357282 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22176.0 | −0.819966 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35707.1 | −1.31154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42996.0 | 1.57404 | 0.787022 | − | 0.616924i | \(-0.211622\pi\) | ||||
0.787022 | + | 0.616924i | \(0.211622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53169.0 | −1.93366 | −0.966832 | − | 0.255413i | \(-0.917789\pi\) | ||||
−0.966832 | + | 0.255413i | \(0.917789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1708.00 | 0.0619130 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15133.7 | 0.544993 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8244.00 | −0.295913 | −0.147957 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147957 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10524.8 | −0.375328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1118.00 | 0.0397401 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16192.0 | 0.571843 | 0.285922 | − | 0.958253i | \(-0.407700\pi\) | ||||
0.285922 | + | 0.958253i | \(0.407700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17766.0 | 0.625410 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6519.13 | −0.228020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18214.0 | −0.635032 | −0.317516 | − | 0.948253i | \(-0.602849\pi\) | ||||
−0.317516 | + | 0.948253i | \(0.602849\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13916.7 | 0.482115 | 0.241057 | − | 0.970511i | \(-0.422506\pi\) | ||||
0.241057 | + | 0.970511i | \(0.422506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14112.0 | 0.487328 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40400.6 | 1.38632 | 0.693159 | − | 0.720784i | \(-0.256218\pi\) | ||||
0.693159 | + | 0.720784i | \(0.256218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2002.00 | −0.0684802 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21271.8 | −0.723046 | −0.361523 | − | 0.932363i | \(-0.617743\pi\) | ||||
−0.361523 | + | 0.932363i | \(0.617743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12544.0 | −0.425041 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30733.0 | 1.03485 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3333.00 | 0.111879 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16319.0 | 0.544380 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9578.00 | −0.318519 | −0.159259 | − | 0.987237i | \(-0.550911\pi\) | ||||
−0.159259 | + | 0.987237i | \(0.550911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44956.6 | 1.48581 | 0.742907 | − | 0.669394i | \(-0.233446\pi\) | ||||
0.742907 | + | 0.669394i | \(0.233446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46200.0 | −1.52220 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32765.0 | 1.07292 | 0.536461 | − | 0.843925i | \(-0.319761\pi\) | ||||
0.536461 | + | 0.843925i | \(0.319761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7616.00 | 0.248630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47438.3 | 1.53921 | 0.769607 | − | 0.638518i | \(-0.220452\pi\) | ||||
0.769607 | + | 0.638518i | \(0.220452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22512.0 | −0.728215 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3047.91 | 0.0979957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6848.00 | 0.219509 | 0.109755 | − | 0.993959i | \(-0.464993\pi\) | ||||
0.109755 | + | 0.993959i | \(0.464993\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10075.0 | −0.321005 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5810.00 | −0.184558 | −0.0922791 | − | 0.995733i | \(-0.529415\pi\) | ||||
−0.0922791 | + | 0.995733i | \(0.529415\pi\) | |||||||
\(998\) | 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 | 1872.4.a.ba.1.1 | 2 | ||
3.2 | odd | 2 | inner | 1872.4.a.ba.1.2 | 2 | ||
4.3 | odd | 2 | 117.4.a.e.1.2 | yes | 2 | ||
12.11 | even | 2 | 117.4.a.e.1.1 | ✓ | 2 | ||
52.51 | odd | 2 | 1521.4.a.p.1.1 | 2 | |||
156.155 | even | 2 | 1521.4.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.a.e.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
117.4.a.e.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1521.4.a.p.1.1 | 2 | 52.51 | odd | 2 | |||
1521.4.a.p.1.2 | 2 | 156.155 | even | 2 | |||
1872.4.a.ba.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1872.4.a.ba.1.2 | 2 | 3.2 | odd | 2 | inner |