Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, 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("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.4281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.26757\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(7\) | 10.2514 | 0.553524 | 0.276762 | − | 0.960938i | \(-0.410739\pi\) | ||||
0.276762 | + | 0.960938i | \(0.410739\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.3754 | 1.21633 | 0.608167 | − | 0.793809i | \(-0.291905\pi\) | ||||
0.608167 | + | 0.793809i | \(0.291905\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.8782 | −1.08547 | −0.542733 | − | 0.839905i | \(-0.682611\pi\) | ||||
−0.542733 | + | 0.839905i | \(0.682611\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.2514 | −0.360257 | −0.180128 | − | 0.983643i | \(-0.557651\pi\) | ||||
−0.180128 | + | 0.983643i | \(0.557651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.3754 | −0.378842 | −0.189421 | − | 0.981896i | \(-0.560661\pi\) | ||||
−0.189421 | + | 0.981896i | \(0.560661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −76.1296 | −0.690179 | −0.345090 | − | 0.938570i | \(-0.612151\pi\) | ||||
−0.345090 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −156.008 | −0.998963 | −0.499481 | − | 0.866325i | \(-0.666476\pi\) | ||||
−0.499481 | + | 0.866325i | \(0.666476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 134.505 | 0.779284 | 0.389642 | − | 0.920966i | \(-0.372599\pi\) | ||||
0.389642 | + | 0.920966i | \(0.372599\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −51.2571 | −0.247544 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.2423 | 0.360977 | 0.180488 | − | 0.983577i | \(-0.442232\pi\) | ||||
0.180488 | + | 0.983577i | \(0.442232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −326.256 | −1.24275 | −0.621373 | − | 0.783515i | \(-0.713425\pi\) | ||||
−0.621373 | + | 0.783515i | \(0.713425\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 422.526 | 1.49848 | 0.749240 | − | 0.662299i | \(-0.230419\pi\) | ||||
0.749240 | + | 0.662299i | \(0.230419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 452.635 | 1.40476 | 0.702379 | − | 0.711803i | \(-0.252121\pi\) | ||||
0.702379 | + | 0.711803i | \(0.252121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −237.909 | −0.693611 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −98.1105 | −0.254274 | −0.127137 | − | 0.991885i | \(-0.540579\pi\) | ||||
−0.127137 | + | 0.991885i | \(0.540579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −221.877 | −0.543961 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −540.118 | −1.19182 | −0.595910 | − | 0.803051i | \(-0.703208\pi\) | ||||
−0.595910 | + | 0.803051i | \(0.703208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 522.292 | 1.09627 | 0.548136 | − | 0.836389i | \(-0.315338\pi\) | ||||
0.548136 | + | 0.836389i | \(0.315338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 254.391 | 0.485436 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −129.272 | −0.235717 | −0.117859 | − | 0.993030i | \(-0.537603\pi\) | ||||
−0.117859 | + | 0.993030i | \(0.537603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −26.6034 | −0.0444682 | −0.0222341 | − | 0.999753i | \(-0.507078\pi\) | ||||
−0.0222341 | + | 0.999753i | \(0.507078\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −147.873 | −0.237085 | −0.118542 | − | 0.992949i | \(-0.537822\pi\) | ||||
−0.118542 | + | 0.992949i | \(0.537822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 454.910 | 0.673270 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1088.91 | −1.55079 | −0.775394 | − | 0.631478i | \(-0.782449\pi\) | ||||
−0.775394 | + | 0.631478i | \(0.782449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −594.611 | −0.786350 | −0.393175 | − | 0.919464i | \(-0.628623\pi\) | ||||
−0.393175 | + | 0.919464i | \(0.628623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 126.257 | 0.161112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −592.229 | −0.705350 | −0.352675 | − | 0.935746i | \(-0.614728\pi\) | ||||
−0.352675 | + | 0.935746i | \(0.614728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −521.573 | −0.600832 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 156.877 | 0.169423 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −666.786 | −0.697958 | −0.348979 | − | 0.937131i | \(-0.613471\pi\) | ||||
−0.348979 | + | 0.937131i | \(0.613471\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1218.56 | −1.20051 | −0.600254 | − | 0.799809i | \(-0.704934\pi\) | ||||
−0.600254 | + | 0.799809i | \(0.704934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −231.789 | −0.221736 | −0.110868 | − | 0.993835i | \(-0.535363\pi\) | ||||
−0.110868 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1979.96 | −1.78888 | −0.894439 | − | 0.447189i | \(-0.852425\pi\) | ||||
−0.894439 | + | 0.447189i | \(0.852425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1075.41 | 0.945005 | 0.472502 | − | 0.881329i | \(-0.343351\pi\) | ||||
0.472502 | + | 0.881329i | \(0.343351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −693.410 | −0.577261 | −0.288631 | − | 0.957441i | \(-0.593200\pi\) | ||||
−0.288631 | + | 0.957441i | \(0.593200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 380.648 | 0.308657 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −258.863 | −0.199411 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 638.173 | 0.479469 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −833.579 | −0.582427 | −0.291213 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291213 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −353.721 | −0.235914 | −0.117957 | − | 0.993019i | \(-0.537635\pi\) | ||||
−0.117957 | + | 0.993019i | \(0.537635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −321.642 | −0.209698 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1509.90 | −0.941601 | −0.470800 | − | 0.882240i | \(-0.656035\pi\) | ||||
−0.470800 | + | 0.882240i | \(0.656035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −618.485 | −0.377404 | −0.188702 | − | 0.982034i | \(-0.560428\pi\) | ||||
−0.188702 | + | 0.982034i | \(0.560428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2257.74 | −1.32029 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 780.039 | 0.446750 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2405.41 | −1.32254 | −0.661271 | − | 0.750147i | \(-0.729983\pi\) | ||||
−0.661271 | + | 0.750147i | \(0.729983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1601.13 | 0.862900 | 0.431450 | − | 0.902137i | \(-0.358002\pi\) | ||||
0.431450 | + | 0.902137i | \(0.358002\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −672.525 | −0.348506 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3208.39 | 1.63094 | 0.815470 | − | 0.578799i | \(-0.196479\pi\) | ||||
0.815470 | + | 0.578799i | \(0.196479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −780.436 | −0.382031 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −392.481 | −0.188598 | −0.0942991 | − | 0.995544i | \(-0.530061\pi\) | ||||
−0.0942991 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 260.818 | 0.120854 | 0.0604272 | − | 0.998173i | \(-0.480754\pi\) | ||||
0.0604272 | + | 0.998173i | \(0.480754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 391.590 | 0.178239 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 204.870 | 0.0900346 | 0.0450173 | − | 0.998986i | \(-0.485666\pi\) | ||||
0.0450173 | + | 0.998986i | \(0.485666\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 256.285 | 0.110705 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1836.92 | 0.767029 | 0.383514 | − | 0.923535i | \(-0.374714\pi\) | ||||
0.383514 | + | 0.923535i | \(0.374714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2880.67 | −1.18298 | −0.591488 | − | 0.806314i | \(-0.701459\pi\) | ||||
−0.591488 | + | 0.806314i | \(0.701459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −406.211 | −0.161434 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1120.54 | −0.438193 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −748.242 | −0.283460 | −0.141730 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141730 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 621.620 | 0.231840 | 0.115920 | − | 0.993259i | \(-0.463018\pi\) | ||||
0.115920 | + | 0.993259i | \(0.463018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −588.243 | −0.212744 | −0.106372 | − | 0.994326i | \(-0.533923\pi\) | ||||
−0.106372 | + | 0.994326i | \(0.533923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4015.31 | −1.43034 | −0.715171 | − | 0.698950i | \(-0.753651\pi\) | ||||
−0.715171 | + | 0.698950i | \(0.753651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1599.30 | −0.552950 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1631.28 | 0.555773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1392.29 | −0.460799 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −640.632 | −0.209019 | −0.104509 | − | 0.994524i | \(-0.533327\pi\) | ||||
−0.104509 | + | 0.994524i | \(0.533327\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2112.63 | −0.670141 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1378.87 | 0.431353 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1284.75 | 0.391047 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4147.71 | −1.24552 | −0.622761 | − | 0.782412i | \(-0.713989\pi\) | ||||
−0.622761 | + | 0.782412i | \(0.713989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5012.97 | −1.46574 | −0.732869 | − | 0.680370i | \(-0.761819\pi\) | ||||
−0.732869 | + | 0.680370i | \(0.761819\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6763.07 | 1.95160 | 0.975800 | − | 0.218664i | \(-0.0701700\pi\) | ||||
0.975800 | + | 0.218664i | \(0.0701700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1995.20 | 0.560987 | 0.280493 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280493 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2263.18 | −0.628227 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1681.95 | −0.455213 | −0.227607 | − | 0.973753i | \(-0.573090\pi\) | ||||
−0.227607 | + | 0.973753i | \(0.573090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3573.58 | 0.955164 | 0.477582 | − | 0.878587i | \(-0.341513\pi\) | ||||
0.477582 | + | 0.878587i | \(0.341513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1189.54 | 0.310192 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1596.32 | 0.411221 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −808.137 | −0.203224 | −0.101612 | − | 0.994824i | \(-0.532400\pi\) | ||||
−0.101612 | + | 0.994824i | \(0.532400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3378.28 | −0.839488 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4824.76 | −1.17105 | −0.585526 | − | 0.810654i | \(-0.699112\pi\) | ||||
−0.585526 | + | 0.810654i | \(0.699112\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 832.848 | 0.199809 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4252.92 | 0.997134 | 0.498567 | − | 0.866851i | \(-0.333860\pi\) | ||||
0.498567 | + | 0.866851i | \(0.333860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 490.553 | 0.113715 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2198.92 | 0.498403 | 0.249202 | − | 0.968452i | \(-0.419832\pi\) | ||||
0.249202 | + | 0.968452i | \(0.419832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4904.13 | −1.09928 | −0.549639 | − | 0.835402i | \(-0.685235\pi\) | ||||
−0.549639 | + | 0.835402i | \(0.685235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1109.38 | 0.243267 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 933.019 | 0.202382 | 0.101191 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101191 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4412.79 | −0.936814 | −0.468407 | − | 0.883513i | \(-0.655172\pi\) | ||||
−0.468407 | + | 0.883513i | \(0.655172\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 748.931 | 0.157312 | 0.0786561 | − | 0.996902i | \(-0.474937\pi\) | ||||
0.0786561 | + | 0.996902i | \(0.474937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3344.58 | −0.687890 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4275.37 | −0.870215 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1706.45 | −0.340246 | −0.170123 | − | 0.985423i | \(-0.554416\pi\) | ||||
−0.170123 | + | 0.985423i | \(0.554416\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2700.59 | 0.532998 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3873.34 | 0.749167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4331.49 | 0.829445 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2611.46 | −0.490268 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5773.97 | 1.07341 | 0.536706 | − | 0.843769i | \(-0.319668\pi\) | ||||
0.536706 | + | 0.843769i | \(0.319668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3777.25 | −0.688709 | −0.344354 | − | 0.938840i | \(-0.611902\pi\) | ||||
−0.344354 | + | 0.938840i | \(0.611902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6966.88 | 1.25812 | 0.629060 | − | 0.777357i | \(-0.283440\pi\) | ||||
0.629060 | + | 0.777357i | \(0.283440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8482.29 | 1.50288 | 0.751440 | − | 0.659801i | \(-0.229360\pi\) | ||||
0.751440 | + | 0.659801i | \(0.229360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6922.90 | −1.21507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 792.272 | 0.136481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1271.95 | −0.217093 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4640.15 | 0.777568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7673.68 | −1.27427 | −0.637136 | − | 0.770752i | \(-0.719881\pi\) | ||||
−0.637136 | + | 0.770752i | \(0.719881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 646.359 | 0.105416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7135.56 | 1.15341 | 0.576704 | − | 0.816953i | \(-0.304339\pi\) | ||||
0.576704 | + | 0.816953i | \(0.304339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5968.71 | 0.947870 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5955.13 | −0.937455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6809.59 | 1.05348 | 0.526741 | − | 0.850026i | \(-0.323414\pi\) | ||||
0.526741 | + | 0.850026i | \(0.323414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10666.0 | −1.63593 | −0.817963 | − | 0.575271i | \(-0.804897\pi\) | ||||
−0.817963 | + | 0.575271i | \(0.804897\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6399.50 | −0.964904 | −0.482452 | − | 0.875922i | \(-0.660254\pi\) | ||||
−0.482452 | + | 0.875922i | \(0.660254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 133.017 | 0.0198868 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1340.16 | 0.197022 | 0.0985112 | − | 0.995136i | \(-0.468592\pi\) | ||||
0.0985112 | + | 0.995136i | \(0.468592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5874.59 | −0.856479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 739.363 | 0.106027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2856.96 | 0.406354 | 0.203177 | − | 0.979142i | \(-0.434873\pi\) | ||||
0.203177 | + | 0.979142i | \(0.434873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1005.77 | −0.140747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9057.97 | 1.25738 | 0.628691 | − | 0.777655i | \(-0.283591\pi\) | ||||
0.628691 | + | 0.777655i | \(0.283591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7937.39 | 1.08434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10770.0 | −1.45968 | −0.729839 | − | 0.683619i | \(-0.760405\pi\) | ||||
−0.729839 | + | 0.683619i | \(0.760405\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1249.75 | −0.166734 | −0.0833671 | − | 0.996519i | \(-0.526567\pi\) | ||||
−0.0833671 | + | 0.996519i | \(0.526567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2274.55 | −0.301096 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14409.5 | −1.87812 | −0.939060 | − | 0.343753i | \(-0.888302\pi\) | ||||
−0.939060 | + | 0.343753i | \(0.888302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1922.38 | 0.248642 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5444.56 | 0.693533 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8504.39 | 1.07512 | 0.537561 | − | 0.843225i | \(-0.319346\pi\) | ||||
0.537561 | + | 0.843225i | \(0.319346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11812.6 | 1.47106 | 0.735528 | − | 0.677494i | \(-0.236934\pi\) | ||||
0.735528 | + | 0.677494i | \(0.236934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6843.37 | −0.845887 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3605.16 | 0.439069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3009.71 | −0.363864 | −0.181932 | − | 0.983311i | \(-0.558235\pi\) | ||||
−0.181932 | + | 0.983311i | \(0.558235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5536.97 | −0.659701 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2973.06 | 0.351667 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1354.28 | 0.157902 | 0.0789510 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789510 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14411.5 | 1.66835 | 0.834175 | − | 0.551500i | \(-0.185944\pi\) | ||||
0.834175 | + | 0.551500i | \(0.185944\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −631.285 | −0.0720514 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5354.23 | 0.606813 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6762.24 | 0.755744 | 0.377872 | − | 0.925858i | \(-0.376656\pi\) | ||||
0.377872 | + | 0.925858i | \(0.376656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3323.67 | −0.368881 | −0.184440 | − | 0.982844i | \(-0.559047\pi\) | ||||
−0.184440 | + | 0.982844i | \(0.559047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2388.59 | 0.261469 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4649.90 | 0.505530 | 0.252765 | − | 0.967528i | \(-0.418660\pi\) | ||||
0.252765 | + | 0.967528i | \(0.418660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14434.0 | 1.54804 | 0.774019 | − | 0.633162i | \(-0.218243\pi\) | ||||
0.774019 | + | 0.633162i | \(0.218243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2961.14 | 0.315442 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3428.29 | −0.360336 | −0.180168 | − | 0.983636i | \(-0.557664\pi\) | ||||
−0.180168 | + | 0.983636i | \(0.557664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14477.7 | −1.51159 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2607.87 | 0.268700 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18647.8 | 1.90877 | 0.954384 | − | 0.298583i | \(-0.0965141\pi\) | ||||
0.954384 | + | 0.298583i | \(0.0965141\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −144.345 | −0.0145831 | −0.00729157 | − | 0.999973i | \(-0.502321\pi\) | ||||
−0.00729157 | + | 0.999973i | \(0.502321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3418.69 | 0.343154 | 0.171577 | − | 0.985171i | \(-0.445114\pi\) | ||||
0.171577 | + | 0.985171i | \(0.445114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9571.86 | 0.948465 | 0.474232 | − | 0.880400i | \(-0.342726\pi\) | ||||
0.474232 | + | 0.880400i | \(0.342726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1325.22 | −0.130475 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18749.8 | 1.82265 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −784.384 | −0.0757685 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17144.0 | 1.63534 | 0.817670 | − | 0.575687i | \(-0.195265\pi\) | ||||
0.817670 | + | 0.575687i | \(0.195265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4133.46 | −0.391829 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3333.93 | 0.312136 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16588.4 | −1.54351 | −0.771757 | − | 0.635917i | \(-0.780622\pi\) | ||||
−0.771757 | + | 0.635917i | \(0.780622\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5835.61 | 0.536369 | 0.268185 | − | 0.963368i | \(-0.413576\pi\) | ||||
0.268185 | + | 0.963368i | \(0.413576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3939.42 | 0.359883 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −272.722 | −0.0246142 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9028.41 | 0.809954 | 0.404977 | − | 0.914327i | \(-0.367280\pi\) | ||||
0.404977 | + | 0.914327i | \(0.367280\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8169.36 | −0.724163 | −0.362081 | − | 0.932147i | \(-0.617934\pi\) | ||||
−0.362081 | + | 0.932147i | \(0.617934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6092.80 | 0.536884 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7955.70 | 0.692791 | 0.346395 | − | 0.938089i | \(-0.387406\pi\) | ||||
0.346395 | + | 0.938089i | \(0.387406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1515.90 | −0.131232 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1158.94 | 0.0991634 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20085.9 | 1.70866 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5276.52 | 0.443701 | 0.221851 | − | 0.975081i | \(-0.428790\pi\) | ||||
0.221851 | + | 0.975081i | \(0.428790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17227.2 | −1.44033 | −0.720167 | − | 0.693801i | \(-0.755935\pi\) | ||||
−0.720167 | + | 0.693801i | \(0.755935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3396.44 | −0.280742 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6371.28 | −0.523653 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16599.3 | 1.34896 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9899.80 | 0.800011 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10557.3 | −0.843663 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4830.69 | 0.383895 | 0.191948 | − | 0.981405i | \(-0.438520\pi\) | ||||
0.191948 | + | 0.981405i | \(0.438520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5377.04 | −0.422619 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16766.0 | 1.31053 | 0.655267 | − | 0.755398i | \(-0.272556\pi\) | ||||
0.655267 | + | 0.755398i | \(0.272556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4894.80 | 0.378449 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11162.9 | −0.858398 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17819.2 | 1.35552 | 0.677758 | − | 0.735285i | \(-0.262952\pi\) | ||||
0.677758 | + | 0.735285i | \(0.262952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21497.4 | −1.62655 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13031.8 | −0.975534 | −0.487767 | − | 0.872974i | \(-0.662189\pi\) | ||||
−0.487767 | + | 0.872974i | \(0.662189\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3467.05 | 0.258159 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7591.83 | 0.559342 | 0.279671 | − | 0.960096i | \(-0.409775\pi\) | ||||
0.279671 | + | 0.960096i | \(0.409775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9344.83 | 0.684884 | 0.342442 | − | 0.939539i | \(-0.388746\pi\) | ||||
0.342442 | + | 0.939539i | \(0.388746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1903.24 | −0.138036 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20553.5 | −1.48294 | −0.741469 | − | 0.670987i | \(-0.765870\pi\) | ||||
−0.741469 | + | 0.670987i | \(0.765870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6095.61 | −0.435264 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4353.69 | −0.309282 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4842.95 | 0.340528 | 0.170264 | − | 0.985398i | \(-0.445538\pi\) | ||||
0.170264 | + | 0.985398i | \(0.445538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4220.14 | −0.295226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15403.8 | 1.06671 | 0.533355 | − | 0.845891i | \(-0.320931\pi\) | ||||
0.533355 | + | 0.845891i | \(0.320931\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1294.31 | 0.0891793 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3971.66 | −0.270914 | −0.135457 | − | 0.990783i | \(-0.543250\pi\) | ||||
−0.135457 | + | 0.990783i | \(0.543250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20636.8 | −1.40065 | −0.700326 | − | 0.713824i | \(-0.746962\pi\) | ||||
−0.700326 | + | 0.713824i | \(0.746962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3190.87 | −0.214425 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18039.1 | 1.20624 | 0.603118 | − | 0.797652i | \(-0.293925\pi\) | ||||
0.603118 | + | 0.797652i | \(0.293925\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23029.3 | −1.52482 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14654.4 | −0.965559 | −0.482779 | − | 0.875742i | \(-0.660373\pi\) | ||||
−0.482779 | + | 0.875742i | \(0.660373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19933.8 | −1.30066 | −0.650329 | − | 0.759653i | \(-0.725369\pi\) | ||||
−0.650329 | + | 0.759653i | \(0.725369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10548.9 | −0.684969 | −0.342485 | − | 0.939523i | \(-0.611268\pi\) | ||||
−0.342485 | + | 0.939523i | \(0.611268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6071.18 | −0.390428 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2051.48 | −0.130044 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23088.8 | 1.45666 | 0.728330 | − | 0.685227i | \(-0.240297\pi\) | ||||
0.728330 | + | 0.685227i | \(0.240297\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4167.89 | 0.260469 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12104.4 | 0.752892 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −711.767 | −0.0438582 | −0.0219291 | − | 0.999760i | \(-0.506981\pi\) | ||||
−0.0219291 | + | 0.999760i | \(0.506981\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6867.64 | −0.421203 | −0.210601 | − | 0.977572i | \(-0.567542\pi\) | ||||
−0.210601 | + | 0.977572i | \(0.567542\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1122.52 | −0.0682086 | −0.0341043 | − | 0.999418i | \(-0.510858\pi\) | ||||
−0.0341043 | + | 0.999418i | \(0.510858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23967.9 | −1.44965 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5153.57 | 0.308843 | 0.154422 | − | 0.988005i | \(-0.450649\pi\) | ||||
0.154422 | + | 0.988005i | \(0.450649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1768.60 | 0.105504 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28258.6 | 1.67041 | 0.835205 | − | 0.549939i | \(-0.185349\pi\) | ||||
0.835205 | + | 0.549939i | \(0.185349\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2401.89 | 0.141335 | 0.0706676 | − | 0.997500i | \(-0.477487\pi\) | ||||
0.0706676 | + | 0.997500i | \(0.477487\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1608.21 | 0.0937800 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11876.8 | 0.689463 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23176.9 | 1.33343 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21090.9 | −1.20801 | −0.604007 | − | 0.796979i | \(-0.706430\pi\) | ||||
−0.604007 | + | 0.796979i | \(0.706430\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9098.10 | −0.516497 | −0.258249 | − | 0.966079i | \(-0.583145\pi\) | ||||
−0.258249 | + | 0.966079i | \(0.583145\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6835.50 | −0.386336 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9488.98 | −0.531604 | −0.265802 | − | 0.964028i | \(-0.585637\pi\) | ||||
−0.265802 | + | 0.964028i | \(0.585637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7549.49 | 0.421097 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4991.69 | 0.276006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21798.7 | −1.20009 | −0.600043 | − | 0.799967i | \(-0.704850\pi\) | ||||
−0.600043 | + | 0.799967i | \(0.704850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3092.42 | 0.168780 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8238.42 | 0.447708 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13799.3 | 0.743499 | 0.371750 | − | 0.928333i | \(-0.378758\pi\) | ||||
0.371750 | + | 0.928333i | \(0.378758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2549.01 | −0.136753 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12492.0 | −0.664510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1561.32 | 0.0827030 | 0.0413515 | − | 0.999145i | \(-0.486834\pi\) | ||||
0.0413515 | + | 0.999145i | \(0.486834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10239.8 | −0.537846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11288.7 | 0.590452 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14008.2 | 0.726590 | 0.363295 | − | 0.931674i | \(-0.381652\pi\) | ||||
0.363295 | + | 0.931674i | \(0.381652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2376.16 | −0.122736 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3900.19 | −0.199793 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20977.4 | 1.07016 | 0.535081 | − | 0.844801i | \(-0.320281\pi\) | ||||
0.535081 | + | 0.844801i | \(0.320281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10669.4 | −0.539838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20802.8 | 1.04825 | 0.524126 | − | 0.851641i | \(-0.324392\pi\) | ||||
0.524126 | + | 0.851641i | \(0.324392\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5736.49 | −0.286711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3111.47 | 0.154881 | 0.0774407 | − | 0.996997i | \(-0.475325\pi\) | ||||
0.0774407 | + | 0.996997i | \(0.475325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5449.19 | −0.269060 | −0.134530 | − | 0.990910i | \(-0.542952\pi\) | ||||
−0.134530 | + | 0.990910i | \(0.542952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12027.0 | 0.591459 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20297.4 | −0.990188 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28975.5 | 1.40790 | 0.703949 | − | 0.710251i | \(-0.251419\pi\) | ||||
0.703949 | + | 0.710251i | \(0.251419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8005.64 | −0.385901 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20654.2 | 0.991666 | 0.495833 | − | 0.868418i | \(-0.334863\pi\) | ||||
0.495833 | + | 0.868418i | \(0.334863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13619.4 | 0.648757 | 0.324378 | − | 0.945927i | \(-0.394845\pi\) | ||||
0.324378 | + | 0.945927i | \(0.394845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11024.5 | 0.523083 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27480.2 | 1.29368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15267.8 | −0.715959 | −0.357980 | − | 0.933729i | \(-0.616534\pi\) | ||||
−0.357980 | + | 0.933729i | \(0.616534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16108.3 | 0.749514 | 0.374757 | − | 0.927123i | \(-0.377726\pi\) | ||||
0.374757 | + | 0.927123i | \(0.377726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3362.62 | 0.155857 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10236.4 | 0.470805 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1180.54 | −0.0540882 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16042.0 | −0.729379 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25511.0 | 1.15549 | 0.577743 | − | 0.816219i | \(-0.303933\pi\) | ||||
0.577743 | + | 0.816219i | \(0.303933\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7108.43 | −0.319528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26573.3 | −1.18997 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26626.1 | −1.18337 | −0.591685 | − | 0.806169i | \(-0.701537\pi\) | ||||
−0.591685 | + | 0.806169i | \(0.701537\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11429.7 | −0.506074 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6561.90 | −0.288374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3902.18 | 0.170849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18935.5 | 0.822911 | 0.411456 | − | 0.911430i | \(-0.365020\pi\) | ||||
0.411456 | + | 0.911430i | \(0.365020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18366.2 | −0.795220 | −0.397610 | − | 0.917554i | \(-0.630160\pi\) | ||||
−0.397610 | + | 0.917554i | \(0.630160\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1962.41 | 0.0843437 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13256.9 | −0.567688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32495.2 | −1.38135 | −0.690675 | − | 0.723165i | \(-0.742687\pi\) | ||||
−0.690675 | + | 0.723165i | \(0.742687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11442.4 | −0.484637 | −0.242318 | − | 0.970197i | \(-0.577908\pi\) | ||||
−0.242318 | + | 0.970197i | \(0.577908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32378.4 | −1.36143 | −0.680717 | − | 0.732546i | \(-0.738332\pi\) | ||||
−0.680717 | + | 0.732546i | \(0.738332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35365.1 | −1.48164 | −0.740821 | − | 0.671702i | \(-0.765563\pi\) | ||||
−0.740821 | + | 0.671702i | \(0.765563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6007.53 | 0.249878 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1304.09 | −0.0540477 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6335.06 | −0.260680 | −0.130340 | − | 0.991469i | \(-0.541607\pi\) | ||||
−0.130340 | + | 0.991469i | \(0.541607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.5692 | −0.00207344 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1957.95 | −0.0797107 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6542.18 | 0.265398 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6184.94 | −0.249139 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4491.51 | 0.180289 | 0.0901445 | − | 0.995929i | \(-0.471267\pi\) | ||||
0.0901445 | + | 0.995929i | \(0.471267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10823.8 | −0.431430 | −0.215715 | − | 0.976456i | \(-0.569208\pi\) | ||||
−0.215715 | + | 0.976456i | \(0.569208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45625.9 | −1.81226 | −0.906132 | − | 0.422995i | \(-0.860979\pi\) | ||||
−0.906132 | + | 0.422995i | \(0.860979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29567.9 | −1.16629 | −0.583143 | − | 0.812370i | \(-0.698177\pi\) | ||||
−0.583143 | + | 0.812370i | \(0.698177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1024.35 | −0.0402647 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48320.9 | −1.88628 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6577.12 | 0.255864 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1281.43 | −0.0495087 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1813.37 | −0.0698212 | −0.0349106 | − | 0.999390i | \(-0.511115\pi\) | ||||
−0.0349106 | + | 0.999390i | \(0.511115\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29307.8 | −1.12078 | −0.560390 | − | 0.828229i | \(-0.689349\pi\) | ||||
−0.560390 | + | 0.828229i | \(0.689349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48560.6 | 1.85073 | 0.925365 | − | 0.379077i | \(-0.123759\pi\) | ||||
0.925365 | + | 0.379077i | \(0.123759\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10983.5 | −0.415770 | −0.207885 | − | 0.978153i | \(-0.566658\pi\) | ||||
−0.207885 | + | 0.978153i | \(0.566658\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8545.36 | −0.322387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14201.6 | −0.532182 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9184.62 | −0.343026 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20983.8 | −0.778476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2477.43 | 0.0916039 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14403.4 | 0.529043 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41652.9 | 1.52488 | 0.762438 | − | 0.647061i | \(-0.224002\pi\) | ||||
0.762438 | + | 0.647061i | \(0.224002\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7771.00 | −0.282618 | −0.141309 | − | 0.989966i | \(-0.545131\pi\) | ||||
−0.141309 | + | 0.989966i | \(0.545131\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26386.1 | −0.956465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3626.14 | −0.130584 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11284.4 | −0.405045 | −0.202523 | − | 0.979278i | \(-0.564914\pi\) | ||||
−0.202523 | + | 0.979278i | \(0.564914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1353.53 | 0.0482688 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2031.06 | 0.0721954 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50206.4 | −1.77311 | −0.886555 | − | 0.462623i | \(-0.846908\pi\) | ||||
−0.886555 | + | 0.462623i | \(0.846908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7464.47 | 0.262769 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5602.70 | 0.195966 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16233.7 | 0.565988 | 0.282994 | − | 0.959122i | \(-0.408672\pi\) | ||||
0.282994 | + | 0.959122i | \(0.408672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33113.6 | 1.14715 | 0.573577 | − | 0.819152i | \(-0.305556\pi\) | ||||
0.573577 | + | 0.819152i | \(0.305556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24837.7 | 0.857717 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19025.7 | 0.652855 | 0.326427 | − | 0.945222i | \(-0.394155\pi\) | ||||
0.326427 | + | 0.945222i | \(0.394155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7523.49 | 0.257347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46547.9 | 1.58220 | 0.791098 | − | 0.611689i | \(-0.209510\pi\) | ||||
0.791098 | + | 0.611689i | \(0.209510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3741.21 | 0.126767 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15478.6 | −0.521199 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11699.4 | −0.392716 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3108.10 | −0.103682 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1793.49 | −0.0596430 | −0.0298215 | − | 0.999555i | \(-0.509494\pi\) | ||||
−0.0298215 | + | 0.999555i | \(0.509494\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34899.8 | −1.15344 | −0.576719 | − | 0.816942i | \(-0.695667\pi\) | ||||
−0.576719 | + | 0.816942i | \(0.695667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6340.34 | −0.208902 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31360.4 | 1.02693 | 0.513464 | − | 0.858111i | \(-0.328362\pi\) | ||||
0.513464 | + | 0.858111i | \(0.328362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26280.4 | −0.857941 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56392.0 | −1.82973 | −0.914866 | − | 0.403758i | \(-0.867704\pi\) | ||||
−0.914866 | + | 0.403758i | \(0.867704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2941.22 | 0.0951421 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32166.8 | −1.03422 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10086.0 | 0.323303 | 0.161652 | − | 0.986848i | \(-0.448318\pi\) | ||||
0.161652 | + | 0.986848i | \(0.448318\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20076.6 | 0.639668 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33875.2 | 1.07607 | 0.538033 | − | 0.842924i | \(-0.319168\pi\) | ||||
0.538033 | + | 0.842924i | \(0.319168\pi\) | |||||||
\(998\) | 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 | 1080.4.a.e.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.k.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bj.1.2 | 3 | |||
12.11 | even | 2 | 2160.4.a.br.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.k.1.2 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bj.1.2 | 3 | 4.3 | odd | 2 | |||
2160.4.a.br.1.2 | 3 | 12.11 | even | 2 |