Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.68360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 1.90549 | 0.366712 | 0.183356 | − | 0.983047i | \(-0.441304\pi\) | ||||
0.183356 | + | 0.983047i | \(0.441304\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.52855 | 0.583931 | 0.291966 | − | 0.956429i | \(-0.405691\pi\) | ||||
0.291966 | + | 0.956429i | \(0.405691\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.22706 | 0.282235 | 0.141117 | − | 0.989993i | \(-0.454930\pi\) | ||||
0.141117 | + | 0.989993i | \(0.454930\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.3691 | −0.865523 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.1299 | 0.579173 | 0.289586 | − | 0.957152i | \(-0.406482\pi\) | ||||
0.289586 | + | 0.957152i | \(0.406482\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −83.4615 | −1.78062 | −0.890310 | − | 0.455355i | \(-0.849512\pi\) | ||||
−0.890310 | + | 0.455355i | \(0.849512\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.4401 | 0.214134 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.3273 | 0.161604 | 0.0808020 | − | 0.996730i | \(-0.474252\pi\) | ||||
0.0808020 | + | 0.996730i | \(0.474252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.68096 | 0.0927438 | 0.0463719 | − | 0.998924i | \(-0.485234\pi\) | ||||
0.0463719 | + | 0.998924i | \(0.485234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.96011 | 0.103499 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 153.169 | 1.38861 | 0.694303 | − | 0.719683i | \(-0.255713\pi\) | ||||
0.694303 | + | 0.719683i | \(0.255713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −82.3780 | −0.659024 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −95.9778 | −0.684109 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 270.530 | 1.56737 | 0.783687 | − | 0.621156i | \(-0.213337\pi\) | ||||
0.783687 | + | 0.621156i | \(0.213337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 40.2628 | 0.212389 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 34.1251 | 0.164806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 298.404 | 1.32587 | 0.662936 | − | 0.748676i | \(-0.269310\pi\) | ||||
0.662936 | + | 0.748676i | \(0.269310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −159.035 | −0.652974 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −184.710 | −0.703584 | −0.351792 | − | 0.936078i | \(-0.614427\pi\) | ||||
−0.351792 | + | 0.936078i | \(0.614427\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −208.337 | −0.738861 | −0.369430 | − | 0.929258i | \(-0.620447\pi\) | ||||
−0.369430 | + | 0.929258i | \(0.620447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −152.566 | −0.505406 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −553.098 | −1.71654 | −0.858272 | − | 0.513194i | \(-0.828462\pi\) | ||||
−0.858272 | + | 0.513194i | \(0.828462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −315.678 | −0.920344 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.5840 | 0.0592620 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 321.465 | 0.833144 | 0.416572 | − | 0.909103i | \(-0.363231\pi\) | ||||
0.416572 | + | 0.909103i | \(0.363231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 137.948 | 0.338197 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.6360 | 0.0340102 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −104.930 | −0.231538 | −0.115769 | − | 0.993276i | \(-0.536933\pi\) | ||||
−0.115769 | + | 0.993276i | \(0.536933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −464.230 | −0.974403 | −0.487201 | − | 0.873290i | \(-0.661982\pi\) | ||||
−0.487201 | + | 0.873290i | \(0.661982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −122.152 | −0.244281 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −544.883 | −1.03976 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −745.813 | −1.35993 | −0.679967 | − | 0.733243i | \(-0.738006\pi\) | ||||
−0.679967 | + | 0.733243i | \(0.738006\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 291.862 | 0.509218 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −509.252 | −0.851227 | −0.425613 | − | 0.904905i | \(-0.639942\pi\) | ||||
−0.425613 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.374979 | −0.000601205 0 | −0.000300603 | − | 1.00000i | \(-0.500096\pi\) | ||||
−0.000300603 | 1.00000i | \(0.500096\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −156.970 | −0.241672 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 110.447 | 0.163463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 610.912 | 0.870037 | 0.435018 | − | 0.900422i | \(-0.356742\pi\) | ||||
0.435018 | + | 0.900422i | \(0.356742\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 448.081 | 0.614652 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −791.431 | −1.04664 | −0.523319 | − | 0.852137i | \(-0.675306\pi\) | ||||
−0.523319 | + | 0.852137i | \(0.675306\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 73.9507 | 0.0943656 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 55.2592 | 0.0680966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −342.011 | −0.407338 | −0.203669 | − | 0.979040i | \(-0.565287\pi\) | ||||
−0.203669 | + | 0.979040i | \(0.565287\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −436.258 | −0.502553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 515.491 | 0.574774 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 50.1455 | 0.0541560 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 601.476 | 0.629594 | 0.314797 | − | 0.949159i | \(-0.398063\pi\) | ||||
0.314797 | + | 0.949159i | \(0.398063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −493.787 | −0.501287 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −402.327 | −0.396367 | −0.198183 | − | 0.980165i | \(-0.563504\pi\) | ||||
−0.198183 | + | 0.980165i | \(0.563504\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1338.38 | −1.28033 | −0.640166 | − | 0.768236i | \(-0.721134\pi\) | ||||
−0.640166 | + | 0.768236i | \(0.721134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 65.0251 | 0.0604362 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −500.501 | −0.452199 | −0.226099 | − | 0.974104i | \(-0.572597\pi\) | ||||
−0.226099 | + | 0.974104i | \(0.572597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1274.80 | −1.12022 | −0.560108 | − | 0.828420i | \(-0.689240\pi\) | ||||
−0.560108 | + | 0.828420i | \(0.689240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 568.605 | 0.486212 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 335.278 | 0.279118 | 0.139559 | − | 0.990214i | \(-0.455432\pi\) | ||||
0.139559 | + | 0.990214i | \(0.455432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 999.972 | 0.810851 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1950.42 | 1.54117 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 59.2083 | 0.0456103 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −884.528 | −0.664559 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −351.964 | −0.258012 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1353.88 | −0.968756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 755.312 | 0.527741 | 0.263870 | − | 0.964558i | \(-0.415001\pi\) | ||||
0.263870 | + | 0.964558i | \(0.415001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −396.983 | −0.270949 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 253.351 | 0.168973 | 0.0844863 | − | 0.996425i | \(-0.473075\pi\) | ||||
0.0844863 | + | 0.996425i | \(0.473075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.1488 | 0.0261755 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −626.596 | −0.399473 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2477.49 | −1.54501 | −0.772504 | − | 0.635010i | \(-0.780996\pi\) | ||||
−0.772504 | + | 0.635010i | \(0.780996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −423.114 | −0.258187 | −0.129094 | − | 0.991632i | \(-0.541207\pi\) | ||||
−0.129094 | + | 0.991632i | \(0.541207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1053.92 | −0.629477 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1763.53 | −1.03129 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 189.328 | 0.108433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −601.521 | −0.337501 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1263.82 | 0.694873 | 0.347437 | − | 0.937703i | \(-0.387052\pi\) | ||||
0.347437 | + | 0.937703i | \(0.387052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3369.67 | 1.81603 | 0.908013 | − | 0.418943i | \(-0.137599\pi\) | ||||
0.908013 | + | 0.418943i | \(0.137599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −264.708 | −0.139872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1766.17 | 0.915238 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3688.61 | 1.87505 | 0.937527 | − | 0.347914i | \(-0.113110\pi\) | ||||
0.937527 | + | 0.347914i | \(0.113110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 612.548 | 0.305523 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 800.624 | 0.391913 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1975.81 | 0.949432 | 0.474716 | − | 0.880139i | \(-0.342551\pi\) | ||||
0.474716 | + | 0.880139i | \(0.342551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 262.857 | 0.124021 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1608.44 | −0.745297 | −0.372649 | − | 0.927973i | \(-0.621550\pi\) | ||||
−0.372649 | + | 0.927973i | \(0.621550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4768.82 | 2.17061 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −179.497 | −0.0802719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4445.71 | −1.95376 | −0.976881 | − | 0.213784i | \(-0.931421\pi\) | ||||
−0.976881 | + | 0.213784i | \(0.931421\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −430.595 | −0.186000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −199.944 | −0.0849078 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1461.35 | −0.610203 | −0.305101 | − | 0.952320i | \(-0.598690\pi\) | ||||
−0.305101 | + | 0.952320i | \(0.598690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3789.62 | −1.55624 | −0.778122 | − | 0.628113i | \(-0.783828\pi\) | ||||
−0.778122 | + | 0.628113i | \(0.783828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −884.585 | −0.357325 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1948.14 | 0.774218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 239.344 | 0.0935966 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −501.682 | −0.193079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4782.10 | −1.81163 | −0.905813 | − | 0.423678i | \(-0.860739\pi\) | ||||
−0.905813 | + | 0.423678i | \(0.860739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3557.27 | −1.32673 | −0.663363 | − | 0.748298i | \(-0.730871\pi\) | ||||
−0.663363 | + | 0.748298i | \(0.730871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1038.27 | −0.381292 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2290.24 | 0.828290 | 0.414145 | − | 0.910211i | \(-0.364081\pi\) | ||||
0.414145 | + | 0.910211i | \(0.364081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2788.00 | −0.993146 | −0.496573 | − | 0.867995i | \(-0.665409\pi\) | ||||
−0.496573 | + | 0.867995i | \(0.665409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1421.14 | −0.498703 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 151.585 | 0.0524097 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1205.89 | −0.410845 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3579.42 | −1.20187 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 162.298 | 0.0537147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −628.449 | −0.205044 | −0.102522 | − | 0.994731i | \(-0.532691\pi\) | ||||
−0.102522 | + | 0.994731i | \(0.532691\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −970.374 | −0.312155 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1360.14 | −0.431444 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1414.08 | 0.442367 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.714519 | −0.000220469 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −945.391 | −0.287755 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 136.439 | 0.0409714 | 0.0204857 | − | 0.999790i | \(-0.493479\pi\) | ||||
0.0204857 | + | 0.999790i | \(0.493479\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1925.10 | 0.570400 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4180.45 | −1.22232 | −0.611159 | − | 0.791508i | \(-0.709296\pi\) | ||||
−0.611159 | + | 0.791508i | \(0.709296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1352.95 | 0.390417 | 0.195209 | − | 0.980762i | \(-0.437462\pi\) | ||||
0.195209 | + | 0.980762i | \(0.437462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 210.456 | 0.0599436 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2175.34 | 0.611635 | 0.305818 | − | 0.952090i | \(-0.401070\pi\) | ||||
0.305818 | + | 0.952090i | \(0.401070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3610.93 | −1.00234 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1164.09 | 0.319053 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4512.18 | −1.22121 | −0.610604 | − | 0.791936i | \(-0.709073\pi\) | ||||
−0.610604 | + | 0.791936i | \(0.709073\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1950.53 | 0.521346 | 0.260673 | − | 0.965427i | \(-0.416056\pi\) | ||||
0.260673 | + | 0.965427i | \(0.416056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3445.21 | 0.909509 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2060.92 | −0.537417 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −641.064 | −0.165141 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1508.06 | −0.383814 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.4143 | −0.00689393 | −0.00344696 | − | 0.999994i | \(-0.501097\pi\) | ||||
−0.00344696 | + | 0.999994i | \(0.501097\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3236.44 | 0.804243 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 140.912 | 0.0346050 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4458.31 | 1.08211 | 0.541053 | − | 0.840988i | \(-0.318026\pi\) | ||||
0.541053 | + | 0.840988i | \(0.318026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1559.77 | 0.374207 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −677.704 | −0.160724 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4641.08 | 1.08814 | 0.544071 | − | 0.839039i | \(-0.316882\pi\) | ||||
0.544071 | + | 0.839039i | \(0.316882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2098.70 | 0.486499 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −651.699 | −0.149376 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 235.021 | 0.0532694 | 0.0266347 | − | 0.999645i | \(-0.491521\pi\) | ||||
0.0266347 | + | 0.999645i | \(0.491521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3816.09 | 0.855392 | 0.427696 | − | 0.903923i | \(-0.359325\pi\) | ||||
0.427696 | + | 0.903923i | \(0.359325\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −831.286 | −0.184292 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1740.64 | −0.381689 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2024.79 | 0.439198 | 0.219599 | − | 0.975590i | \(-0.429525\pi\) | ||||
0.219599 | + | 0.975590i | \(0.429525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6322.04 | −1.35660 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5451.81 | 1.15739 | 0.578697 | − | 0.815543i | \(-0.303561\pi\) | ||||
0.578697 | + | 0.815543i | \(0.303561\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5026.80 | −1.05587 | −0.527937 | − | 0.849284i | \(-0.677034\pi\) | ||||
−0.527937 | + | 0.849284i | \(0.677034\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 95.5517 | 0.0198596 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −965.493 | −0.198576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4784.69 | −0.973884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1146.11 | 0.230880 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6160.34 | −1.22830 | −0.614148 | − | 0.789191i | \(-0.710500\pi\) | ||||
−0.614148 | + | 0.789191i | \(0.710500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −685.043 | −0.135203 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2028.00 | −0.396217 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12783.7 | −2.47258 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1088.99 | −0.208532 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −766.629 | −0.145352 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3030.75 | −0.568984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4329.54 | 0.804885 | 0.402443 | − | 0.915445i | \(-0.368161\pi\) | ||||
0.402443 | + | 0.915445i | \(0.368161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2550.26 | −0.469513 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6411.83 | −1.16907 | −0.584536 | − | 0.811368i | \(-0.698724\pi\) | ||||
−0.584536 | + | 0.811368i | \(0.698724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5263 | −0.00352617 | −0.00176309 | − | 0.999998i | \(-0.500561\pi\) | ||||
−0.00176309 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −797.474 | −0.142643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8198.11 | 1.45253 | 0.726265 | − | 0.687415i | \(-0.241255\pi\) | ||||
0.726265 | + | 0.687415i | \(0.241255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 612.767 | 0.107550 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −953.699 | −0.165826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 87.0043 | 0.0149878 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6875.39 | 1.17347 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2429.11 | −0.410796 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2891.08 | −0.484469 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2374.46 | −0.394297 | −0.197148 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197148 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6973.43 | −1.14757 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4869.08 | −0.794108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4985.34 | −0.805842 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 638.869 | 0.102356 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5716.26 | 0.907780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3442.95 | −0.541988 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1905.44 | 0.297348 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2023.98 | 0.313121 | 0.156560 | − | 0.987668i | \(-0.449959\pi\) | ||||
0.156560 | + | 0.987668i | \(0.449959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2651.99 | 0.406755 | 0.203378 | − | 0.979100i | \(-0.434808\pi\) | ||||
0.203378 | + | 0.979100i | \(0.434808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8010.45 | 1.21814 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1729.22 | −0.260729 | −0.130364 | − | 0.991466i | \(-0.541615\pi\) | ||||
−0.130364 | + | 0.991466i | \(0.541615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3324.68 | −0.497058 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 112.821 | 0.0167258 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6875.38 | 1.01078 | 0.505388 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505388 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6800.00 | −0.991399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1685.46 | −0.243701 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.44807 | −0.000351063 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7435.15 | −1.05753 | −0.528763 | − | 0.848770i | \(-0.677344\pi\) | ||||
−0.528763 | + | 0.848770i | \(0.677344\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4316.52 | 0.608968 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1680.32 | 0.235142 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1397.48 | −0.193991 | −0.0969954 | − | 0.995285i | \(-0.530923\pi\) | ||||
−0.0969954 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2579.80 | −0.355254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2420.38 | −0.330653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7009.57 | −0.950020 | −0.475010 | − | 0.879980i | \(-0.657556\pi\) | ||||
−0.475010 | + | 0.879980i | \(0.657556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1439.24 | 0.193529 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11728.7 | −1.56477 | −0.782387 | − | 0.622792i | \(-0.785998\pi\) | ||||
−0.782387 | + | 0.622792i | \(0.785998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 721.060 | 0.0954510 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4868.64 | 0.639501 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4367.15 | 0.569212 | 0.284606 | − | 0.958645i | \(-0.408137\pi\) | ||||
0.284606 | + | 0.958645i | \(0.408137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1734.99 | 0.224404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 482.758 | 0.0619642 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3988.37 | 0.508042 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1632.74 | −0.206410 | −0.103205 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103205 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 76.5032 | 0.00959887 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5028.65 | 0.626232 | 0.313116 | − | 0.949715i | \(-0.398627\pi\) | ||||
0.313116 | + | 0.949715i | \(0.398627\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22578.8 | −2.79090 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2925.32 | 0.358915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6305.23 | 0.767908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2497.21 | −0.301904 | −0.150952 | − | 0.988541i | \(-0.548234\pi\) | ||||
−0.150952 | + | 0.988541i | \(0.548234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4720.82 | −0.566572 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −548.477 | −0.0653482 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5166.90 | −0.611164 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −806.239 | −0.0946803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12909.4 | −1.50517 | −0.752585 | − | 0.658496i | \(-0.771193\pi\) | ||||
−0.752585 | + | 0.658496i | \(0.771193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4019.30 | 0.465293 | 0.232647 | − | 0.972561i | \(-0.425261\pi\) | ||||
0.232647 | + | 0.972561i | \(0.425261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12925.4 | 1.48571 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −933.118 | −0.106501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2426.56 | −0.275010 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3360.39 | −0.378185 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8768.94 | 0.980012 | 0.490006 | − | 0.871719i | \(-0.336995\pi\) | ||||
0.490006 | + | 0.871719i | \(0.336995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4496.26 | 0.499021 | 0.249511 | − | 0.968372i | \(-0.419730\pi\) | ||||
0.249511 | + | 0.968372i | \(0.419730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 360.762 | 0.0397638 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1176.48 | 0.128785 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7316.62 | −0.795451 | −0.397725 | − | 0.917504i | \(-0.630200\pi\) | ||||
−0.397725 | + | 0.917504i | \(0.630200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7377.11 | 0.796578 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12801.1 | 1.37291 | 0.686454 | − | 0.727173i | \(-0.259166\pi\) | ||||
0.686454 | + | 0.727173i | \(0.259166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2232.84 | −0.237858 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2408.19 | 0.254818 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6412.22 | 0.673968 | 0.336984 | − | 0.941510i | \(-0.390593\pi\) | ||||
0.336984 | + | 0.941510i | \(0.390593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3902.91 | −0.407496 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6420.87 | 0.665957 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2848.14 | −0.293456 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2153.32 | −0.220412 | −0.110206 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110206 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1087.17 | −0.110555 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1850.55 | 0.186960 | 0.0934800 | − | 0.995621i | \(-0.470201\pi\) | ||||
0.0934800 | + | 0.995621i | \(0.470201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1892.04 | 0.189914 | 0.0949572 | − | 0.995481i | \(-0.469729\pi\) | ||||
0.0949572 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3365.41 | 0.335628 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3739.40 | 0.370533 | 0.185267 | − | 0.982688i | \(-0.440685\pi\) | ||||
0.185267 | + | 0.982688i | \(0.440685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3898.41 | −0.383821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7028.61 | 0.687604 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4402.13 | −0.427928 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −632.742 | −0.0611204 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7512.35 | −0.721105 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7260.30 | −0.692550 | −0.346275 | − | 0.938133i | \(-0.612554\pi\) | ||||
−0.346275 | + | 0.938133i | \(0.612554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24905.2 | −2.36087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1525.58 | 0.143719 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3926.77 | 0.367640 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4756.40 | 0.442573 | 0.221287 | − | 0.975209i | \(-0.428974\pi\) | ||||
0.221287 | + | 0.975209i | \(0.428974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3764.88 | 0.348168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2007.83 | 0.184546 | 0.0922730 | − | 0.995734i | \(-0.470587\pi\) | ||||
0.0922730 | + | 0.995734i | \(0.470587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 328.491 | 0.0300091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3223.71 | −0.292717 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2661.89 | −0.240246 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8952.55 | 0.803149 | 0.401574 | − | 0.915826i | \(-0.368463\pi\) | ||||
0.401574 | + | 0.915826i | \(0.368463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3064.86 | −0.273309 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20564.9 | 1.82295 | 0.911477 | − | 0.411351i | \(-0.134943\pi\) | ||||
0.911477 | + | 0.411351i | \(0.134943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2626.61 | −0.231451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9086.94 | 0.795987 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13321.9 | −1.16008 | −0.580041 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580041 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.96004 | −0.000169681 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −737.201 | −0.0634468 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8737.66 | −0.747626 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11686.9 | −0.994176 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8471.24 | −0.716467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13047.0 | −1.09712 | −0.548558 | − | 0.836113i | \(-0.684823\pi\) | ||||
−0.548558 | + | 0.836113i | \(0.684823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20207.4 | 1.68950 | 0.844750 | − | 0.535161i | \(-0.179749\pi\) | ||||
0.844750 | + | 0.535161i | \(0.179749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −820.494 | −0.0682082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3064.36 | 0.253294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11293.8 | 0.928228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2452.13 | 0.200402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15416.2 | 1.25281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3267.55 | −0.264053 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2784.58 | −0.223768 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6670.23 | −0.533038 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17866.0 | 1.41981 | 0.709906 | − | 0.704297i | \(-0.248737\pi\) | ||||
0.709906 | + | 0.704297i | \(0.248737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7221.08 | −0.570693 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8322.59 | −0.654129 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8027.79 | 0.627502 | 0.313751 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313751 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10848.6 | 0.843367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 222.748 | 0.0172221 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3193.27 | 0.245555 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3712.16 | 0.283915 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17357.6 | −1.32040 | −0.660201 | − | 0.751089i | \(-0.729529\pi\) | ||||
−0.660201 | + | 0.751089i | \(0.729529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17388.1 | 1.31563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 456.067 | 0.0343229 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6073.90 | 0.454679 | 0.227340 | − | 0.973816i | \(-0.426997\pi\) | ||||
0.227340 | + | 0.973816i | \(0.426997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2188.88 | 0.162986 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2342.15 | 0.173476 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5084.04 | 0.374577 | 0.187288 | − | 0.982305i | \(-0.440030\pi\) | ||||
0.187288 | + | 0.982305i | \(0.440030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15552.3 | −1.13983 | −0.569914 | − | 0.821704i | \(-0.693024\pi\) | ||||
−0.569914 | + | 0.821704i | \(0.693024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9112.24 | −0.664344 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12617.8 | −0.915125 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20714.3 | −1.49454 | −0.747269 | − | 0.664521i | \(-0.768635\pi\) | ||||
−0.747269 | + | 0.664521i | \(0.768635\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6778.34 | −0.486526 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4136.86 | −0.295397 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6792.52 | 0.482534 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12733.4 | 0.899936 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1015.03 | 0.0713711 | 0.0356856 | − | 0.999363i | \(-0.488639\pi\) | ||||
0.0356856 | + | 0.999363i | \(0.488639\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2077.93 | 0.145364 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4364.03 | 0.303744 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3831.39 | 0.265323 | 0.132661 | − | 0.991161i | \(-0.457648\pi\) | ||||
0.132661 | + | 0.991161i | \(0.457648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 386.545 | 0.0266333 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5312.50 | −0.364198 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16703.5 | −1.13938 | −0.569688 | − | 0.821861i | \(-0.692936\pi\) | ||||
−0.569688 | + | 0.821861i | \(0.692936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17781.6 | 1.20686 | 0.603432 | − | 0.797414i | \(-0.293799\pi\) | ||||
0.603432 | + | 0.797414i | \(0.293799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17429.0 | 1.17705 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5774.69 | −0.388057 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7610.08 | 0.508869 | 0.254435 | − | 0.967090i | \(-0.418111\pi\) | ||||
0.254435 | + | 0.967090i | \(0.418111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 288.843 | 0.0192192 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46162.4 | 3.05651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4207.29 | −0.277212 | −0.138606 | − | 0.990348i | \(-0.544262\pi\) | ||||
−0.138606 | + | 0.990348i | \(0.544262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2297.81 | −0.150661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28539.4 | 1.86216 | 0.931082 | − | 0.364810i | \(-0.118866\pi\) | ||||
0.931082 | + | 0.364810i | \(0.118866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16799.9 | −1.09086 | −0.545432 | − | 0.838155i | \(-0.683634\pi\) | ||||
−0.545432 | + | 0.838155i | \(0.683634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14700.8 | −0.949958 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1787.71 | −0.114965 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1458.39 | 0.0933369 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 309.256 | 0.0196978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3380.10 | 0.214266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16207.1 | −1.02249 | −0.511247 | − | 0.859434i | \(-0.670816\pi\) | ||||
−0.511247 | + | 0.859434i | \(0.670816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1197.50 | −0.0751919 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4931.09 | 0.308164 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26346.9 | 1.63878 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11900.8 | 0.736756 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10697.0 | 0.659133 | 0.329567 | − | 0.944132i | \(-0.393097\pi\) | ||||
0.329567 | + | 0.944132i | \(0.393097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7901.34 | −0.484601 | −0.242300 | − | 0.970201i | \(-0.577902\pi\) | ||||
−0.242300 | + | 0.970201i | \(0.577902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2591.72 | −0.158216 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −312.370 | −0.0189807 | −0.00949036 | − | 0.999955i | \(-0.503021\pi\) | ||||
−0.00949036 | + | 0.999955i | \(0.503021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2217.17 | −0.134101 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2694.50 | 0.162221 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13732.3 | −0.822950 | −0.411475 | − | 0.911421i | \(-0.634986\pi\) | ||||
−0.411475 | + | 0.911421i | \(0.634986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1654.02 | 0.0986684 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.76293 | 0.000520357 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19869.0 | −1.17449 | −0.587244 | − | 0.809410i | \(-0.699787\pi\) | ||||
−0.587244 | + | 0.809410i | \(0.699787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11047.2 | 0.650057 | 0.325029 | − | 0.945704i | \(-0.394626\pi\) | ||||
0.325029 | + | 0.945704i | \(0.394626\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1801.43 | −0.105523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 262.114 | 0.0152847 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4441.90 | 0.257858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 259.983 | 0.0150247 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9809.12 | −0.564347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25673.8 | −1.47051 | −0.735253 | − | 0.677793i | \(-0.762937\pi\) | ||||
−0.735253 | + | 0.677793i | \(0.762937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7906.46 | 0.450844 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4268.79 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3143.95 | 0.177693 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7965.79 | −0.448238 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7370.85 | −0.412940 | −0.206470 | − | 0.978453i | \(-0.566198\pi\) | ||||
−0.206470 | + | 0.978453i | \(0.566198\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16174.4 | −0.902178 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2578.04 | 0.143171 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26830.0 | −1.48351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2112.00 | −0.116272 | −0.0581361 | − | 0.998309i | \(-0.518516\pi\) | ||||
−0.0581361 | + | 0.998309i | \(0.518516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2581.05 | −0.141481 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2762.32 | −0.150764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2092.27 | −0.113702 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4145.08 | 0.224294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20945.5 | −1.12853 | −0.564266 | − | 0.825593i | \(-0.690841\pi\) | ||||
−0.564266 | + | 0.825593i | \(0.690841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2292.02 | 0.122966 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6880.58 | −0.367571 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2102.99 | −0.111868 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7826.11 | −0.414550 | −0.207275 | − | 0.978283i | \(-0.566459\pi\) | ||||
−0.207275 | + | 0.978283i | \(0.566459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14276.5 | −0.753037 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41436.8 | 2.17646 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11513.3 | −0.602200 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8597.91 | −0.447831 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23373.7 | 1.21237 | 0.606183 | − | 0.795325i | \(-0.292700\pi\) | ||||
0.606183 | + | 0.795325i | \(0.292700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6995.78 | −0.361354 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3716.71 | 0.191184 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2388.96 | −0.122378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31240.8 | 1.59375 | 0.796875 | − | 0.604145i | \(-0.206485\pi\) | ||||
0.796875 | + | 0.604145i | \(0.206485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5533.38 | −0.281125 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2359.88 | −0.119403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4426.59 | 0.223056 | 0.111528 | − | 0.993761i | \(-0.464426\pi\) | ||||
0.111528 | + | 0.993761i | \(0.464426\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3927.06 | −0.197077 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15758.9 | −0.787636 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32119.5 | 1.59883 | 0.799414 | − | 0.600781i | \(-0.205144\pi\) | ||||
0.799414 | + | 0.600781i | \(0.205144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1221.54 | −0.0605593 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19215.0 | −0.948763 | −0.474382 | − | 0.880319i | \(-0.657328\pi\) | ||||
−0.474382 | + | 0.880319i | \(0.657328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8250.91 | 0.405758 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18495.0 | 0.905888 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2616.15 | −0.127626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3593.57 | 0.174609 | 0.0873045 | − | 0.996182i | \(-0.472175\pi\) | ||||
0.0873045 | + | 0.996182i | \(0.472175\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.2377 | −0.00252808 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21999.1 | 1.06043 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32956.7 | 1.58234 | 0.791169 | − | 0.611598i | \(-0.209473\pi\) | ||||
0.791169 | + | 0.611598i | \(0.209473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6167.01 | 0.294925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15689.7 | 0.747373 | 0.373687 | − | 0.927555i | \(-0.378094\pi\) | ||||
0.373687 | + | 0.927555i | \(0.378094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6663.45 | −0.316164 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1728.16 | −0.0816756 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8757.64 | 0.412282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2134.77 | 0.100106 | 0.0500532 | − | 0.998747i | \(-0.484061\pi\) | ||||
0.0500532 | + | 0.998747i | \(0.484061\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8495.25 | 0.396821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14780.2 | −0.687721 | −0.343861 | − | 0.939021i | \(-0.611735\pi\) | ||||
−0.343861 | + | 0.939021i | \(0.611735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22285.7 | −1.03294 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2972.13 | 0.137226 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1418.75 | −0.0652530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10760.4 | −0.493007 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2783.36 | −0.127036 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24081.3 | 1.09490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35525.7 | −1.60909 | −0.804545 | − | 0.593892i | \(-0.797591\pi\) | ||||
−0.804545 | + | 0.593892i | \(0.797591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8843.53 | 0.399034 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1752.52 | 0.0787768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38745.3 | 1.73504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3999.05 | 0.178405 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2190.00 | −0.0973321 | −0.0486660 | − | 0.998815i | \(-0.515497\pi\) | ||||
−0.0486660 | + | 0.998815i | \(0.515497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6265.09 | −0.277400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7992.50 | 0.352561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.92326 | −0.000348202 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5226.91 | 0.228850 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 447.830 | 0.0195345 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21464.6 | 0.932824 | 0.466412 | − | 0.884568i | \(-0.345546\pi\) | ||||
0.466412 | + | 0.884568i | \(0.345546\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32288.8 | 1.39804 | 0.699021 | − | 0.715101i | \(-0.253620\pi\) | ||||
0.699021 | + | 0.715101i | \(0.253620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7271.52 | 0.313682 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12899.2 | 0.554403 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1600.22 | −0.0685248 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10195.0 | 0.434971 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40334.4 | 1.71459 | 0.857296 | − | 0.514825i | \(-0.172143\pi\) | ||||
0.857296 | + | 0.514825i | \(0.172143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8188.53 | 0.346822 | 0.173411 | − | 0.984850i | \(-0.444521\pi\) | ||||
0.173411 | + | 0.984850i | \(0.444521\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3316.77 | −0.139970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7630.74 | 0.320855 | 0.160427 | − | 0.987048i | \(-0.448713\pi\) | ||||
0.160427 | + | 0.987048i | \(0.448713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12637.7 | −0.529462 | −0.264731 | − | 0.964322i | \(-0.585283\pi\) | ||||
−0.264731 | + | 0.964322i | \(0.585283\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3858.21 | 0.161059 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3575.77 | −0.148731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10500.8 | −0.435203 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25964.8 | −1.07225 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24059.1 | 0.990005 | 0.495002 | − | 0.868892i | \(-0.335167\pi\) | ||||
0.495002 | + | 0.868892i | \(0.335167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10388.4 | 0.424430 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31133.5 | 1.26749 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4623.48 | −0.187562 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9578.51 | −0.387201 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45706.2 | 1.84111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18588.4 | 0.746138 | 0.373069 | − | 0.927804i | \(-0.378305\pi\) | ||||
0.373069 | + | 0.927804i | \(0.378305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1171.86 | −0.0468733 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28616.2 | 1.14062 | 0.570310 | − | 0.821430i | \(-0.306823\pi\) | ||||
0.570310 | + | 0.821430i | \(0.306823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31968.9 | 1.26981 | 0.634904 | − | 0.772591i | \(-0.281040\pi\) | ||||
0.634904 | + | 0.772591i | \(0.281040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1839.74 | −0.0728200 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15417.8 | 0.608145 | 0.304072 | − | 0.952649i | \(-0.401654\pi\) | ||||
0.304072 | + | 0.952649i | \(0.401654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29024.0 | −1.14086 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9117.18 | −0.357135 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12908.5 | 0.503902 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 62246.7 | 2.42153 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14056.0 | −0.544928 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7076.80 | −0.273417 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41961.0 | 1.61565 | 0.807824 | − | 0.589424i | \(-0.200645\pi\) | ||||
0.807824 | + | 0.589424i | \(0.200645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11738.5 | −0.450430 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22884.6 | −0.875145 | −0.437573 | − | 0.899183i | \(-0.644162\pi\) | ||||
−0.437573 | + | 0.899183i | \(0.644162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29611.7 | −1.12855 | −0.564277 | − | 0.825585i | \(-0.690845\pi\) | ||||
−0.564277 | + | 0.825585i | \(0.690845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1305.34 | −0.0495803 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27117.7 | 1.02652 | 0.513259 | − | 0.858234i | \(-0.328438\pi\) | ||||
0.513259 | + | 0.858234i | \(0.328438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3948.06 | 0.148947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9467.91 | 0.355990 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4248.32 | −0.159199 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9540.48 | −0.356316 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24359.2 | −0.906724 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7845.36 | 0.291054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3641.32 | 0.134639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2075.05 | −0.0764712 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24740.7 | −0.908740 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10010.9 | −0.366491 | −0.183245 | − | 0.983067i | \(-0.558660\pi\) | ||||
−0.183245 | + | 0.983067i | \(0.558660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9402.02 | 0.343064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40394.1 | 1.46906 | 0.734532 | − | 0.678575i | \(-0.237402\pi\) | ||||
0.734532 | + | 0.678575i | \(0.237402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16722.8 | −0.606183 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5775.06 | −0.208653 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1324.28 | 0.0476899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2392.98 | 0.0858945 | 0.0429472 | − | 0.999077i | \(-0.486325\pi\) | ||||
0.0429472 | + | 0.999077i | \(0.486325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8249.89 | 0.295161 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42502.9 | 1.51571 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24581.9 | −0.873781 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31276.7 | 1.10816 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21920.3 | −0.774148 | −0.387074 | − | 0.922049i | \(-0.626514\pi\) | ||||
−0.387074 | + | 0.922049i | \(0.626514\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2424.71 | −0.0853562 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12217.7 | −0.428712 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1562.57 | 0.0546540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4891.90 | 0.170556 | 0.0852782 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852782 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.2072 | −0.00129309 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40152.3 | 1.39100 | 0.695499 | − | 0.718527i | \(-0.255183\pi\) | ||||
0.695499 | + | 0.718527i | \(0.255183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28291.9 | −0.977001 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3275.26 | −0.112745 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16057.5 | 0.551002 | 0.275501 | − | 0.961301i | \(-0.411156\pi\) | ||||
0.275501 | + | 0.961301i | \(0.411156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.2963 | 0.00107052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15621.4 | 0.532659 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21912.3 | −0.744815 | −0.372408 | − | 0.928069i | \(-0.621468\pi\) | ||||
−0.372408 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31220.2 | −1.05787 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1167.62 | 0.0394397 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12950.0 | −0.436055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43395.3 | 1.45666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11696.3 | 0.391388 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23223.8 | −0.774717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17618.1 | 0.585895 | 0.292948 | − | 0.956129i | \(-0.405364\pi\) | ||||
0.292948 | + | 0.956129i | \(0.405364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 165.786 | 0.00549619 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24152.9 | −0.798252 | −0.399126 | − | 0.916896i | \(-0.630686\pi\) | ||||
−0.399126 | + | 0.916896i | \(0.630686\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2211.64 | −0.0728694 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13101.0 | 0.430325 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43754.7 | −1.43279 | −0.716395 | − | 0.697695i | \(-0.754209\pi\) | ||||
−0.716395 | + | 0.697695i | \(0.754209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7226.66 | −0.235919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29790.9 | 0.969572 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51651.4 | −1.67591 | −0.837957 | − | 0.545736i | \(-0.816250\pi\) | ||||
−0.837957 | + | 0.545736i | \(0.816250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14952.0 | 0.483665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5508.91 | −0.177660 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31910.7 | −1.02599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23894.0 | 0.765911 | 0.382956 | − | 0.923767i | \(-0.374906\pi\) | ||||
0.382956 | + | 0.923767i | \(0.374906\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4524.51 | −0.144593 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18201.6 | −0.579929 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5951.47 | −0.189052 | −0.0945261 | − | 0.995522i | \(-0.530134\pi\) | ||||
−0.0945261 | + | 0.995522i | \(0.530134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28640.1 | −0.907040 |
(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 | 1856.4.a.y.1.4 | 5 | ||
4.3 | odd | 2 | 1856.4.a.bb.1.2 | 5 | |||
8.3 | odd | 2 | 464.4.a.l.1.4 | 5 | |||
8.5 | even | 2 | 29.4.a.b.1.5 | ✓ | 5 | ||
24.5 | odd | 2 | 261.4.a.f.1.1 | 5 | |||
40.29 | even | 2 | 725.4.a.c.1.1 | 5 | |||
56.13 | odd | 2 | 1421.4.a.e.1.5 | 5 | |||
232.173 | even | 2 | 841.4.a.b.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.5 | ✓ | 5 | 8.5 | even | 2 | ||
261.4.a.f.1.1 | 5 | 24.5 | odd | 2 | |||
464.4.a.l.1.4 | 5 | 8.3 | odd | 2 | |||
725.4.a.c.1.1 | 5 | 40.29 | even | 2 | |||
841.4.a.b.1.1 | 5 | 232.173 | even | 2 | |||
1421.4.a.e.1.5 | 5 | 56.13 | odd | 2 | |||
1856.4.a.y.1.4 | 5 | 1.1 | even | 1 | trivial | ||
1856.4.a.bb.1.2 | 5 | 4.3 | odd | 2 |