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: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 141x^{2} + 200x + 3500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.73555\) 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 | ||||||||
\(7\) | 11.2995 | 0.610114 | 0.305057 | − | 0.952334i | \(-0.401325\pi\) | ||||
0.305057 | + | 0.952334i | \(0.401325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −61.3933 | −1.68280 | −0.841399 | − | 0.540414i | \(-0.818268\pi\) | ||||
−0.841399 | + | 0.540414i | \(0.818268\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −75.7226 | −1.61551 | −0.807757 | − | 0.589516i | \(-0.799319\pi\) | ||||
−0.807757 | + | 0.589516i | \(0.799319\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.1657 | −0.159298 | −0.0796491 | − | 0.996823i | \(-0.525380\pi\) | ||||
−0.0796491 | + | 0.996823i | \(0.525380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 71.5271 | 0.863655 | 0.431828 | − | 0.901956i | \(-0.357869\pi\) | ||||
0.431828 | + | 0.901956i | \(0.357869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −126.156 | −1.14371 | −0.571855 | − | 0.820355i | \(-0.693776\pi\) | ||||
−0.571855 | + | 0.820355i | \(0.693776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 235.502 | 1.50798 | 0.753992 | − | 0.656883i | \(-0.228126\pi\) | ||||
0.753992 | + | 0.656883i | \(0.228126\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 110.923 | 0.642654 | 0.321327 | − | 0.946968i | \(-0.395871\pi\) | ||||
0.321327 | + | 0.946968i | \(0.395871\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −56.4973 | −0.272851 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 434.358 | 1.92995 | 0.964973 | − | 0.262349i | \(-0.0844971\pi\) | ||||
0.964973 | + | 0.262349i | \(0.0844971\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.15792 | 0.00441066 | 0.00220533 | − | 0.999998i | \(-0.499298\pi\) | ||||
0.00220533 | + | 0.999998i | \(0.499298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −77.6254 | −0.275297 | −0.137648 | − | 0.990481i | \(-0.543954\pi\) | ||||
−0.137648 | + | 0.990481i | \(0.543954\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 231.442 | 0.718282 | 0.359141 | − | 0.933283i | \(-0.383070\pi\) | ||||
0.359141 | + | 0.933283i | \(0.383070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −215.322 | −0.627761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −500.296 | −1.29662 | −0.648310 | − | 0.761376i | \(-0.724524\pi\) | ||||
−0.648310 | + | 0.761376i | \(0.724524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 306.967 | 0.752571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 334.718 | 0.738587 | 0.369293 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369293 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 147.171 | 0.308906 | 0.154453 | − | 0.988000i | \(-0.450638\pi\) | ||||
0.154453 | + | 0.988000i | \(0.450638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 378.613 | 0.722480 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 84.9722 | 0.154940 | 0.0774702 | − | 0.996995i | \(-0.475316\pi\) | ||||
0.0774702 | + | 0.996995i | \(0.475316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 101.308 | 0.169339 | 0.0846695 | − | 0.996409i | \(-0.473017\pi\) | ||||
0.0846695 | + | 0.996409i | \(0.473017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.4773 | −0.0809304 | −0.0404652 | − | 0.999181i | \(-0.512884\pi\) | ||||
−0.0404652 | + | 0.999181i | \(0.512884\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −693.712 | −1.02670 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −818.225 | −1.16528 | −0.582642 | − | 0.812729i | \(-0.697981\pi\) | ||||
−0.582642 | + | 0.812729i | \(0.697981\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −206.044 | −0.272486 | −0.136243 | − | 0.990675i | \(-0.543503\pi\) | ||||
−0.136243 | + | 0.990675i | \(0.543503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 55.8283 | 0.0712403 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 648.508 | 0.772379 | 0.386189 | − | 0.922420i | \(-0.373791\pi\) | ||||
0.386189 | + | 0.922420i | \(0.373791\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −855.625 | −0.985647 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −357.636 | −0.386238 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1885.00 | 1.97313 | 0.986563 | − | 0.163381i | \(-0.0522399\pi\) | ||||
0.986563 | + | 0.163381i | \(0.0522399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1923.79 | −1.89529 | −0.947647 | − | 0.319321i | \(-0.896545\pi\) | ||||
−0.947647 | + | 0.319321i | \(0.896545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1808.72 | 1.73028 | 0.865139 | − | 0.501531i | \(-0.167230\pi\) | ||||
0.865139 | + | 0.501531i | \(0.167230\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1342.31 | 1.21277 | 0.606385 | − | 0.795171i | \(-0.292619\pi\) | ||||
0.606385 | + | 0.795171i | \(0.292619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1173.14 | 1.03088 | 0.515442 | − | 0.856924i | \(-0.327628\pi\) | ||||
0.515442 | + | 0.856924i | \(0.327628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 284.667 | 0.236984 | 0.118492 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118492 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 630.779 | 0.511483 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −126.166 | −0.0971900 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2438.14 | 1.83181 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2413.23 | 1.68614 | 0.843068 | − | 0.537807i | \(-0.180747\pi\) | ||||
0.843068 | + | 0.537807i | \(0.180747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118.912 | 0.0793085 | 0.0396543 | − | 0.999213i | \(-0.487374\pi\) | ||||
0.0396543 | + | 0.999213i | \(0.487374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 808.218 | 0.526928 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1097.16 | 0.684212 | 0.342106 | − | 0.939661i | \(-0.388860\pi\) | ||||
0.342106 | + | 0.939661i | \(0.388860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −355.233 | −0.216766 | −0.108383 | − | 0.994109i | \(-0.534567\pi\) | ||||
−0.108383 | + | 0.994109i | \(0.534567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4648.86 | 2.71858 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1177.51 | −0.674391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2001.55 | 1.10049 | 0.550246 | − | 0.835002i | \(-0.314534\pi\) | ||||
0.550246 | + | 0.835002i | \(0.314534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2652.70 | 1.42963 | 0.714813 | − | 0.699316i | \(-0.246512\pi\) | ||||
0.714813 | + | 0.699316i | \(0.246512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −554.613 | −0.287404 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3087.09 | −1.56928 | −0.784640 | − | 0.619952i | \(-0.787152\pi\) | ||||
−0.784640 | + | 0.619952i | \(0.787152\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1425.49 | −0.697793 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1139.42 | 0.547523 | 0.273761 | − | 0.961798i | \(-0.411732\pi\) | ||||
0.273761 | + | 0.961798i | \(0.411732\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2531.03 | −1.17280 | −0.586398 | − | 0.810023i | \(-0.699455\pi\) | ||||
−0.586398 | + | 0.810023i | \(0.699455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3536.92 | 1.60988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2872.89 | −1.26255 | −0.631277 | − | 0.775557i | \(-0.717469\pi\) | ||||
−0.631277 | + | 0.775557i | \(0.717469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 282.487 | 0.122023 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3827.16 | −1.59807 | −0.799036 | − | 0.601283i | \(-0.794657\pi\) | ||||
−0.799036 | + | 0.601283i | \(0.794657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −659.781 | −0.270946 | −0.135473 | − | 0.990781i | \(-0.543255\pi\) | ||||
−0.135473 | + | 0.990781i | \(0.543255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2171.79 | −0.863098 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 685.497 | 0.268067 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4376.11 | 1.65782 | 0.828911 | − | 0.559380i | \(-0.188961\pi\) | ||||
0.828911 | + | 0.559380i | \(0.188961\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3802.02 | −1.41801 | −0.709004 | − | 0.705204i | \(-0.750855\pi\) | ||||
−0.709004 | + | 0.705204i | \(0.750855\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3340.27 | −1.20804 | −0.604021 | − | 0.796968i | \(-0.706436\pi\) | ||||
−0.604021 | + | 0.796968i | \(0.706436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4274.83 | 1.52279 | 0.761393 | − | 0.648290i | \(-0.224516\pi\) | ||||
0.761393 | + | 0.648290i | \(0.224516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2661.04 | 0.920042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.78960 | −0.00197251 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4391.29 | −1.45336 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −126.348 | −0.0412233 | −0.0206117 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206117 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 388.127 | 0.123117 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1253.36 | 0.392092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 845.493 | 0.257348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3423.31 | 1.02799 | 0.513996 | − | 0.857793i | \(-0.328165\pi\) | ||||
0.513996 | + | 0.857793i | \(0.328165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2145.09 | 0.627200 | 0.313600 | − | 0.949555i | \(-0.398465\pi\) | ||||
0.313600 | + | 0.949555i | \(0.398465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3524.09 | 1.01694 | 0.508468 | − | 0.861081i | \(-0.330212\pi\) | ||||
0.508468 | + | 0.861081i | \(0.330212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1479.58 | −0.416011 | −0.208005 | − | 0.978128i | \(-0.566697\pi\) | ||||
−0.208005 | + | 0.978128i | \(0.566697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1157.21 | −0.321226 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3075.33 | 0.832328 | 0.416164 | − | 0.909290i | \(-0.363374\pi\) | ||||
0.416164 | + | 0.909290i | \(0.363374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2600.22 | 0.694998 | 0.347499 | − | 0.937680i | \(-0.387031\pi\) | ||||
0.347499 | + | 0.937680i | \(0.387031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1076.61 | 0.280743 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5416.22 | −1.39525 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1186.65 | −0.298410 | −0.149205 | − | 0.988806i | \(-0.547671\pi\) | ||||
−0.149205 | + | 0.988806i | \(0.547671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7745.13 | 1.92463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3364.26 | −0.816562 | −0.408281 | − | 0.912856i | \(-0.633872\pi\) | ||||
−0.408281 | + | 0.912856i | \(0.633872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4908.01 | 1.17749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1655.19 | 0.388074 | 0.194037 | − | 0.980994i | \(-0.437842\pi\) | ||||
0.194037 | + | 0.980994i | \(0.437842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2501.48 | 0.579867 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2646.65 | 0.599886 | 0.299943 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3798.31 | −0.851405 | −0.425703 | − | 0.904863i | \(-0.639973\pi\) | ||||
−0.425703 | + | 0.904863i | \(0.639973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1534.83 | −0.336560 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5471.39 | −1.18680 | −0.593400 | − | 0.804908i | \(-0.702215\pi\) | ||||
−0.593400 | + | 0.804908i | \(0.702215\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3611.68 | 0.766743 | 0.383371 | − | 0.923594i | \(-0.374763\pi\) | ||||
0.383371 | + | 0.923594i | \(0.374763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1914.83 | −0.402208 | −0.201104 | − | 0.979570i | \(-0.564453\pi\) | ||||
−0.201104 | + | 0.979570i | \(0.564453\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.0839 | 0.00269100 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4788.33 | −0.974624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1706.82 | −0.340319 | −0.170159 | − | 0.985417i | \(-0.554428\pi\) | ||||
−0.170159 | + | 0.985417i | \(0.554428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1673.59 | −0.330306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9552.85 | 1.84768 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −877.126 | −0.167962 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −735.853 | −0.138147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5888.56 | 1.09472 | 0.547358 | − | 0.836898i | \(-0.315634\pi\) | ||||
0.547358 | + | 0.836898i | \(0.315634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4902.98 | 0.893962 | 0.446981 | − | 0.894543i | \(-0.352499\pi\) | ||||
0.446981 | + | 0.894543i | \(0.352499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6209.11 | 1.12128 | 0.560638 | − | 0.828061i | \(-0.310556\pi\) | ||||
0.560638 | + | 0.828061i | \(0.310556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2427.25 | −0.430056 | −0.215028 | − | 0.976608i | \(-0.568984\pi\) | ||||
−0.215028 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14458.2 | −2.53763 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −798.648 | −0.137579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1893.07 | −0.323103 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2615.17 | 0.438234 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6058.23 | 1.00601 | 0.503006 | − | 0.864283i | \(-0.332227\pi\) | ||||
0.503006 | + | 0.864283i | \(0.332227\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −424.861 | −0.0692915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 117.584 | 0.0190065 | 0.00950326 | − | 0.999955i | \(-0.496975\pi\) | ||||
0.00950326 | + | 0.999955i | \(0.496975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6809.90 | −1.08146 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6308.74 | −0.993119 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1596.08 | 0.246922 | 0.123461 | − | 0.992349i | \(-0.460601\pi\) | ||||
0.123461 | + | 0.992349i | \(0.460601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3555.89 | 0.545394 | 0.272697 | − | 0.962100i | \(-0.412084\pi\) | ||||
0.272697 | + | 0.962100i | \(0.412084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2973.17 | 0.448289 | 0.224145 | − | 0.974556i | \(-0.428041\pi\) | ||||
0.224145 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −506.541 | −0.0757307 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12834.7 | 1.88688 | 0.943442 | − | 0.331537i | \(-0.107567\pi\) | ||||
0.943442 | + | 0.331537i | \(0.107567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1742.87 | −0.254099 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 252.386 | 0.0361932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7503.89 | 1.06730 | 0.533651 | − | 0.845705i | \(-0.320819\pi\) | ||||
0.533651 | + | 0.845705i | \(0.320819\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5653.07 | −0.791086 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10834.1 | −1.50394 | −0.751970 | − | 0.659197i | \(-0.770896\pi\) | ||||
−0.751970 | + | 0.659197i | \(0.770896\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17832.8 | −2.43617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1526.64 | 0.206909 | 0.103454 | − | 0.994634i | \(-0.467010\pi\) | ||||
0.103454 | + | 0.994634i | \(0.467010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8794.30 | −1.17328 | −0.586642 | − | 0.809846i | \(-0.699550\pi\) | ||||
−0.586642 | + | 0.809846i | \(0.699550\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3468.56 | 0.459154 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7955.47 | −1.03691 | −0.518456 | − | 0.855104i | \(-0.673493\pi\) | ||||
−0.518456 | + | 0.855104i | \(0.673493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1408.61 | 0.182191 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4091.12 | 0.521131 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3359.28 | −0.424679 | −0.212339 | − | 0.977196i | \(-0.568108\pi\) | ||||
−0.212339 | + | 0.977196i | \(0.568108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3387.77 | 0.421888 | 0.210944 | − | 0.977498i | \(-0.432346\pi\) | ||||
0.210944 | + | 0.977498i | \(0.432346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8399.34 | −1.03822 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26666.7 | −3.24771 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7919.60 | −0.957454 | −0.478727 | − | 0.877964i | \(-0.658902\pi\) | ||||
−0.478727 | + | 0.877964i | \(0.658902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3782.14 | 0.450622 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1030.22 | 0.121859 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10671.6 | 1.24425 | 0.622127 | − | 0.782917i | \(-0.286269\pi\) | ||||
0.622127 | + | 0.782917i | \(0.286269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8445.59 | −0.977703 | −0.488852 | − | 0.872367i | \(-0.662584\pi\) | ||||
−0.488852 | + | 0.872367i | \(0.662584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −279.141 | −0.0318596 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1662.95 | 0.188468 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11206.9 | 1.25248 | 0.626241 | − | 0.779630i | \(-0.284593\pi\) | ||||
0.626241 | + | 0.779630i | \(0.284593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5119.10 | −0.568148 | −0.284074 | − | 0.958802i | \(-0.591686\pi\) | ||||
−0.284074 | + | 0.958802i | \(0.591686\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9023.57 | −0.987771 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14018.6 | −1.52408 | −0.762039 | − | 0.647531i | \(-0.775802\pi\) | ||||
−0.762039 | + | 0.647531i | \(0.775802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10393.3 | 1.11468 | 0.557338 | − | 0.830286i | \(-0.311823\pi\) | ||||
0.557338 | + | 0.830286i | \(0.311823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3242.54 | −0.345418 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2522.28 | 0.265108 | 0.132554 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132554 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −71.0886 | −0.00742225 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4278.13 | 0.440795 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10879.1 | 1.11357 | 0.556785 | − | 0.830657i | \(-0.312035\pi\) | ||||
0.556785 | + | 0.830657i | \(0.312035\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 288.174 | 0.0291141 | 0.0145570 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145570 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3397.84 | −0.341060 | −0.170530 | − | 0.985352i | \(-0.554548\pi\) | ||||
−0.170530 | + | 0.985352i | \(0.554548\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16484.3 | 1.63341 | 0.816703 | − | 0.577058i | \(-0.195799\pi\) | ||||
0.816703 | + | 0.577058i | \(0.195799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 960.140 | 0.0945313 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4765.68 | 0.463269 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1788.18 | 0.172731 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8583.18 | 0.818738 | 0.409369 | − | 0.912369i | \(-0.365749\pi\) | ||||
0.409369 | + | 0.912369i | \(0.365749\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32890.7 | −3.11785 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9425.02 | −0.882409 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6076.49 | −0.565404 | −0.282702 | − | 0.959208i | \(-0.591231\pi\) | ||||
−0.282702 | + | 0.959208i | \(0.591231\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1652.84 | −0.151918 | −0.0759589 | − | 0.997111i | \(-0.524202\pi\) | ||||
−0.0759589 | + | 0.997111i | \(0.524202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2629.53 | −0.240219 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1144.73 | 0.103316 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18468.0 | −1.65680 | −0.828400 | − | 0.560137i | \(-0.810748\pi\) | ||||
−0.828400 | + | 0.560137i | \(0.810748\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3044.06 | 0.269837 | 0.134918 | − | 0.990857i | \(-0.456923\pi\) | ||||
0.134918 | + | 0.990857i | \(0.456923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9618.97 | 0.847601 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8238.76 | −0.717440 | −0.358720 | − | 0.933445i | \(-0.616787\pi\) | ||||
−0.358720 | + | 0.933445i | \(0.616787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −570.366 | −0.0493767 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9043.61 | −0.773804 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14209.0 | −1.20872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11609.7 | −0.976261 | −0.488131 | − | 0.872771i | \(-0.662321\pi\) | ||||
−0.488131 | + | 0.872771i | \(0.662321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10413.6 | −0.870662 | −0.435331 | − | 0.900270i | \(-0.643369\pi\) | ||||
−0.435331 | + | 0.900270i | \(0.643369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1238.52 | −0.102374 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3748.31 | 0.308072 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −87.6808 | −0.00712547 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6711.57 | −0.542367 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13219.3 | 1.05640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15045.2 | 1.19565 | 0.597823 | − | 0.801628i | \(-0.296032\pi\) | ||||
0.597823 | + | 0.801628i | \(0.296032\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5865.70 | −0.461026 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8132.94 | −0.635721 | −0.317860 | − | 0.948138i | \(-0.602964\pi\) | ||||
−0.317860 | + | 0.948138i | \(0.602964\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16844.8 | 1.30238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9245.50 | −0.710956 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19419.4 | −1.47725 | −0.738623 | − | 0.674118i | \(-0.764524\pi\) | ||||
−0.738623 | + | 0.674118i | \(0.764524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5878.00 | 0.444746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5696.48 | −0.426426 | −0.213213 | − | 0.977006i | \(-0.568393\pi\) | ||||
−0.213213 | + | 0.977006i | \(0.568393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1423.33 | −0.105982 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18615.2 | 1.37151 | 0.685754 | − | 0.727833i | \(-0.259473\pi\) | ||||
0.685754 | + | 0.727833i | \(0.259473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11250.1 | −0.824521 | −0.412260 | − | 0.911066i | \(-0.635261\pi\) | ||||
−0.412260 | + | 0.911066i | \(0.635261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3153.90 | −0.228742 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2336.40 | 0.168571 | 0.0842856 | − | 0.996442i | \(-0.473139\pi\) | ||||
0.0842856 | + | 0.996442i | \(0.473139\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2328.19 | −0.166247 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30714.8 | 2.18195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20277.2 | −1.42578 | −0.712889 | − | 0.701277i | \(-0.752614\pi\) | ||||
−0.712889 | + | 0.701277i | \(0.752614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7933.97 | 0.555031 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25051.8 | 1.73483 | 0.867414 | − | 0.497587i | \(-0.165780\pi\) | ||||
0.867414 | + | 0.497587i | \(0.165780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 630.830 | 0.0434647 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26572.3 | −1.81254 | −0.906271 | − | 0.422697i | \(-0.861084\pi\) | ||||
−0.906271 | + | 0.422697i | \(0.861084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4224.74 | 0.286740 | 0.143370 | − | 0.989669i | \(-0.454206\pi\) | ||||
0.143370 | + | 0.989669i | \(0.454206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12190.7 | −0.819211 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17428.2 | −1.16539 | −0.582693 | − | 0.812692i | \(-0.698001\pi\) | ||||
−0.582693 | + | 0.812692i | \(0.698001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17525.4 | −1.16039 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7100.27 | −0.467826 | −0.233913 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233913 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26045.2 | 1.69941 | 0.849707 | − | 0.527255i | \(-0.176779\pi\) | ||||
0.849707 | + | 0.527255i | \(0.176779\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8865.32 | 0.575650 | 0.287825 | − | 0.957683i | \(-0.407068\pi\) | ||||
0.287825 | + | 0.957683i | \(0.407068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7327.79 | 0.471239 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4849.89 | −0.307437 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 177.883 | 0.0112225 | 0.00561126 | − | 0.999984i | \(-0.498214\pi\) | ||||
0.00561126 | + | 0.999984i | \(0.498214\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12066.1 | −0.754063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16304.8 | 1.01416 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27742.7 | 1.70947 | 0.854736 | − | 0.519064i | \(-0.173719\pi\) | ||||
0.854736 | + | 0.519064i | \(0.173719\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9182.34 | 0.563166 | 0.281583 | − | 0.959537i | \(-0.409140\pi\) | ||||
0.281583 | + | 0.959537i | \(0.409140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16429.9 | −0.998341 | −0.499171 | − | 0.866504i | \(-0.666362\pi\) | ||||
−0.499171 | + | 0.866504i | \(0.666362\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20549.5 | −1.24289 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10965.8 | 0.657158 | 0.328579 | − | 0.944477i | \(-0.393430\pi\) | ||||
0.328579 | + | 0.944477i | \(0.393430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −594.561 | −0.0354678 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23252.7 | 1.37450 | 0.687250 | − | 0.726421i | \(-0.258818\pi\) | ||||
0.687250 | + | 0.726421i | \(0.258818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2215.22 | −0.130351 | −0.0651755 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651755 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4041.09 | −0.235649 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29709.9 | −1.72470 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9035.30 | −0.519827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20009.1 | −1.14605 | −0.573026 | − | 0.819537i | \(-0.694230\pi\) | ||||
−0.573026 | + | 0.819537i | \(0.694230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18842.2 | −1.06967 | −0.534834 | − | 0.844957i | \(-0.679626\pi\) | ||||
−0.534834 | + | 0.844957i | \(0.679626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21299.5 | 1.20383 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20258.1 | 1.13493 | 0.567463 | − | 0.823399i | \(-0.307925\pi\) | ||||
0.567463 | + | 0.823399i | \(0.307925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5485.82 | −0.305989 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37883.7 | 2.09471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22738.2 | 1.25181 | 0.625905 | − | 0.779899i | \(-0.284730\pi\) | ||||
0.625905 | + | 0.779899i | \(0.284730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1776.17 | 0.0969407 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9289 | −0.000702610 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8306.55 | 0.447552 | 0.223776 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223776 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31068.4 | 1.66681 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21737.8 | −1.15634 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24716.6 | 1.30924 | 0.654620 | − | 0.755958i | \(-0.272829\pi\) | ||||
0.654620 | + | 0.755958i | \(0.272829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13993.5 | −0.735009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23244.3 | −1.21579 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9888.23 | 0.512891 | 0.256446 | − | 0.966559i | \(-0.417449\pi\) | ||||
0.256446 | + | 0.966559i | \(0.417449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20437.6 | 1.05567 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5887.54 | 0.301597 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6335.29 | 0.323195 | 0.161598 | − | 0.986857i | \(-0.448335\pi\) | ||||
0.161598 | + | 0.986857i | \(0.448335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 866.739 | 0.0438543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13170.9 | −0.663680 | −0.331840 | − | 0.943336i | \(-0.607669\pi\) | ||||
−0.331840 | + | 0.943336i | \(0.607669\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5216.73 | −0.260734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31361.7 | −1.56111 | −0.780554 | − | 0.625088i | \(-0.785063\pi\) | ||||
−0.780554 | + | 0.625088i | \(0.785063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20002.1 | 0.987624 | 0.493812 | − | 0.869569i | \(-0.335603\pi\) | ||||
0.493812 | + | 0.869569i | \(0.335603\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10007.8 | −0.492155 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15167.4 | 0.739927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25698.3 | −1.24866 | −0.624331 | − | 0.781160i | \(-0.714628\pi\) | ||||
−0.624331 | + | 0.781160i | \(0.714628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13263.5 | −0.639348 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33958.5 | −1.63044 | −0.815219 | − | 0.579153i | \(-0.803384\pi\) | ||||
−0.815219 | + | 0.579153i | \(0.803384\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13216.4 | 0.629559 | 0.314780 | − | 0.949165i | \(-0.398069\pi\) | ||||
0.314780 | + | 0.949165i | \(0.398069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13255.9 | 0.628957 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25345.8 | −1.19320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3107.27 | 0.145710 | 0.0728551 | − | 0.997343i | \(-0.476789\pi\) | ||||
0.0728551 | + | 0.997343i | \(0.476789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20568.2 | −0.957034 | −0.478517 | − | 0.878078i | \(-0.658825\pi\) | ||||
−0.478517 | + | 0.878078i | \(0.658825\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2773.06 | 0.128531 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 82.8228 | 0.00380929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6219.65 | −0.284963 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15435.5 | 0.701803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19353.9 | 0.876609 | 0.438304 | − | 0.898827i | \(-0.355579\pi\) | ||||
0.438304 | + | 0.898827i | \(0.355579\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3216.58 | 0.144587 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11144.1 | −0.499042 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29243.9 | −1.29971 | −0.649856 | − | 0.760057i | \(-0.725171\pi\) | ||||
−0.649856 | + | 0.760057i | \(0.725171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2584.20 | −0.114421 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3098.97 | 0.136190 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7127.47 | 0.312063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31460.5 | 1.36723 | 0.683617 | − | 0.729841i | \(-0.260406\pi\) | ||||
0.683617 | + | 0.729841i | \(0.260406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22991.8 | 0.995503 | 0.497751 | − | 0.867320i | \(-0.334159\pi\) | ||||
0.497751 | + | 0.867320i | \(0.334159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5697.10 | −0.244860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5552.32 | −0.237762 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32144.1 | −1.36643 | −0.683214 | − | 0.730218i | \(-0.739419\pi\) | ||||
−0.683214 | + | 0.730218i | \(0.739419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 908.840 | 0.0384935 | 0.0192468 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192468 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23098.9 | 0.971255 | 0.485628 | − | 0.874166i | \(-0.338591\pi\) | ||||
0.485628 | + | 0.874166i | \(0.338591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42491.6 | 1.78021 | 0.890104 | − | 0.455757i | \(-0.150631\pi\) | ||||
0.890104 | + | 0.455757i | \(0.150631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2404.21 | 0.100001 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12655.2 | 0.524491 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12239.5 | −0.503642 | −0.251821 | − | 0.967774i | \(-0.581029\pi\) | ||||
−0.251821 | + | 0.967774i | \(0.581029\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31072.0 | 1.27402 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17684.6 | −0.719962 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27549.7 | 1.11761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54796.8 | −2.20730 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9020.23 | 0.362071 | 0.181036 | − | 0.983477i | \(-0.442055\pi\) | ||||
0.181036 | + | 0.983477i | \(0.442055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39913.4 | −1.59092 | −0.795459 | − | 0.606008i | \(-0.792770\pi\) | ||||
−0.795459 | + | 0.606008i | \(0.792770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26038.5 | 1.03425 | 0.517126 | − | 0.855910i | \(-0.327002\pi\) | ||||
0.517126 | + | 0.855910i | \(0.327002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6044.84 | −0.238434 | −0.119217 | − | 0.992868i | \(-0.538038\pi\) | ||||
−0.119217 | + | 0.992868i | \(0.538038\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14364.5 | 0.564631 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50233.5 | 1.96094 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6434.32 | −0.250308 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1412.43 | −0.0545702 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28918.4 | 1.11346 | 0.556731 | − | 0.830693i | \(-0.312055\pi\) | ||||
0.556731 | + | 0.830693i | \(0.312055\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25949.7 | −0.992359 | −0.496179 | − | 0.868220i | \(-0.665264\pi\) | ||||
−0.496179 | + | 0.868220i | \(0.665264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39784.1 | 1.51624 | 0.758121 | − | 0.652114i | \(-0.226118\pi\) | ||||
0.758121 | + | 0.652114i | \(0.226118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16227.6 | −0.614284 | −0.307142 | − | 0.951664i | \(-0.599373\pi\) | ||||
−0.307142 | + | 0.951664i | \(0.599373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27268.2 | 1.02873 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16554.4 | 0.620348 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19135.8 | 0.714680 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26122.4 | 0.969112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5586.13 | 0.206549 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3298.91 | 0.121171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2107.66 | −0.0771596 | −0.0385798 | − | 0.999256i | \(-0.512283\pi\) | ||||
−0.0385798 | + | 0.999256i | \(0.512283\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3471.16 | −0.126240 | −0.0631199 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631199 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12649.8 | 0.458538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1343.65 | 0.0483872 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7620.88 | −0.273547 | −0.136773 | − | 0.990602i | \(-0.543673\pi\) | ||||
−0.136773 | + | 0.990602i | \(0.543673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7671.32 | −0.273569 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10858.9 | 0.385989 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23396.4 | 0.826276 | 0.413138 | − | 0.910669i | \(-0.364433\pi\) | ||||
0.413138 | + | 0.910669i | \(0.364433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15401.4 | −0.542169 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3427.48 | −0.119883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23669.1 | 0.825226 | 0.412613 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412613 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15682.0 | 0.543272 | 0.271636 | − | 0.962400i | \(-0.412435\pi\) | ||||
0.271636 | + | 0.962400i | \(0.412435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −146.079 | −0.00504451 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28683.3 | −0.984247 | −0.492123 | − | 0.870526i | \(-0.663779\pi\) | ||||
−0.492123 | + | 0.870526i | \(0.663779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3822.27 | 0.130744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20850.6 | −0.708728 | −0.354364 | − | 0.935108i | \(-0.615303\pi\) | ||||
−0.354364 | + | 0.935108i | \(0.615303\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21880.5 | −0.741401 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12397.4 | 0.417447 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17487.2 | −0.586996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19010.1 | 0.634152 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5002.87 | −0.166372 | −0.0831858 | − | 0.996534i | \(-0.526509\pi\) | ||||
−0.0831858 | + | 0.996534i | \(0.526509\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39413.3 | 1.30261 | 0.651304 | − | 0.758817i | \(-0.274222\pi\) | ||||
0.651304 | + | 0.758817i | \(0.274222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4013.94 | −0.132252 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11631.3 | 0.380879 | 0.190439 | − | 0.981699i | \(-0.439009\pi\) | ||||
0.190439 | + | 0.981699i | \(0.439009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39814.1 | −1.29976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38605.2 | −1.25261 | −0.626304 | − | 0.779579i | \(-0.715433\pi\) | ||||
−0.626304 | + | 0.779579i | \(0.715433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16701.3 | 0.540253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9792.90 | 0.314860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 382.345 | 0.0122559 | 0.00612795 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612795 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21374.1 | −0.681011 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36072.1 | 1.14585 | 0.572926 | − | 0.819607i | \(-0.305808\pi\) | ||||
0.572926 | + | 0.819607i | \(0.305808\pi\) | |||||||
\(998\) | 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.o.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 1080.4.a.p.1.3 | yes | 4 | ||
4.3 | odd | 2 | 2160.4.a.bu.1.2 | 4 | |||
12.11 | even | 2 | 2160.4.a.bv.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.o.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1080.4.a.p.1.3 | yes | 4 | 3.2 | odd | 2 | ||
2160.4.a.bu.1.2 | 4 | 4.3 | odd | 2 | |||
2160.4.a.bv.1.2 | 4 | 12.11 | even | 2 |