Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 216) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1 |
$q$-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 | ||||||||
\(5\) | 21.2337 | 1.89920 | 0.949599 | − | 0.313466i | \(-0.101490\pi\) | ||||
0.949599 | + | 0.313466i | \(0.101490\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.2337 | 1.57847 | 0.789235 | − | 0.614091i | \(-0.210477\pi\) | ||||
0.789235 | + | 0.614091i | \(0.210477\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.0274101 | 0.0137051 | − | 0.999906i | \(-0.495637\pi\) | ||||
0.0137051 | + | 0.999906i | \(0.495637\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9348 | 1.12934 | 0.564671 | − | 0.825316i | \(-0.309003\pi\) | ||||
0.564671 | + | 0.825316i | \(0.309003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 96.9348 | 1.38295 | 0.691474 | − | 0.722401i | \(-0.256961\pi\) | ||||
0.691474 | + | 0.722401i | \(0.256961\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −126.467 | −1.52703 | −0.763516 | − | 0.645789i | \(-0.776529\pi\) | ||||
−0.763516 | + | 0.645789i | \(0.776529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.9348 | 0.207923 | 0.103961 | − | 0.994581i | \(-0.466848\pi\) | ||||
0.103961 | + | 0.994581i | \(0.466848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 325.870 | 2.60696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −133.533 | −0.855048 | −0.427524 | − | 0.904004i | \(-0.640614\pi\) | ||||
−0.427524 | + | 0.904004i | \(0.640614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 101.832 | 0.589983 | 0.294992 | − | 0.955500i | \(-0.404683\pi\) | ||||
0.294992 | + | 0.955500i | \(0.404683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 620.739 | 2.99783 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −105.065 | −0.466828 | −0.233414 | − | 0.972378i | \(-0.574990\pi\) | ||||
−0.233414 | + | 0.972378i | \(0.574990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −16.3369 | −0.0622291 | −0.0311145 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311145 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 201.272 | 0.713805 | 0.356903 | − | 0.934142i | \(-0.383833\pi\) | ||||
0.356903 | + | 0.934142i | \(0.383833\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 251.870 | 0.781680 | 0.390840 | − | 0.920459i | \(-0.372185\pi\) | ||||
0.390840 | + | 0.920459i | \(0.372185\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 511.609 | 1.49157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −148.038 | −0.383671 | −0.191836 | − | 0.981427i | \(-0.561444\pi\) | ||||
−0.191836 | + | 0.981427i | \(0.561444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.2337 | 0.0520573 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −73.6085 | −0.162424 | −0.0812120 | − | 0.996697i | \(-0.525879\pi\) | ||||
−0.0812120 | + | 0.996697i | \(0.525879\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 607.478 | 1.27508 | 0.637538 | − | 0.770419i | \(-0.279953\pi\) | ||||
0.637538 | + | 0.770419i | \(0.279953\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1124.00 | 2.14485 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −761.945 | −1.38935 | −0.694675 | − | 0.719324i | \(-0.744452\pi\) | ||||
−0.694675 | + | 0.719324i | \(0.744452\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −701.196 | −1.17207 | −0.586033 | − | 0.810287i | \(-0.699311\pi\) | ||||
−0.586033 | + | 0.810287i | \(0.699311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −287.000 | −0.460148 | −0.230074 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230074 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.2337 | 0.0432661 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −128.522 | −0.183036 | −0.0915181 | − | 0.995803i | \(-0.529172\pi\) | ||||
−0.0915181 | + | 0.995803i | \(0.529172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 160.478 | 0.212226 | 0.106113 | − | 0.994354i | \(-0.466159\pi\) | ||||
0.106113 | + | 0.994354i | \(0.466159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2058.28 | 2.62649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −430.206 | −0.512380 | −0.256190 | − | 0.966626i | \(-0.582467\pi\) | ||||
−0.256190 | + | 0.966626i | \(0.582467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1547.48 | 1.78263 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2685.37 | −2.90014 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −31.1305 | −0.0325858 | −0.0162929 | − | 0.999867i | \(-0.505186\pi\) | ||||
−0.0162929 | + | 0.999867i | \(0.505186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −983.103 | −0.968539 | −0.484269 | − | 0.874919i | \(-0.660915\pi\) | ||||
−0.484269 | + | 0.874919i | \(0.660915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −952.152 | −0.910857 | −0.455429 | − | 0.890272i | \(-0.650514\pi\) | ||||
−0.455429 | + | 0.890272i | \(0.650514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −272.087 | −0.245828 | −0.122914 | − | 0.992417i | \(-0.539224\pi\) | ||||
−0.122914 | + | 0.992417i | \(0.539224\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1355.76 | −1.19136 | −0.595680 | − | 0.803222i | \(-0.703117\pi\) | ||||
−0.595680 | + | 0.803222i | \(0.703117\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1938.36 | 1.61368 | 0.806838 | − | 0.590773i | \(-0.201177\pi\) | ||||
0.806838 | + | 0.590773i | \(0.201177\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 486.989 | 0.394887 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2833.76 | 2.18294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.00 | −0.999249 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4265.20 | 3.05193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 232.375 | 0.162362 | 0.0811808 | − | 0.996699i | \(-0.474131\pi\) | ||||
0.0811808 | + | 0.996699i | \(0.474131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2795.30 | −1.86433 | −0.932163 | − | 0.362038i | \(-0.882081\pi\) | ||||
−0.932163 | + | 0.362038i | \(0.882081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3697.11 | −2.41038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1261.53 | 0.786715 | 0.393358 | − | 0.919386i | \(-0.371313\pi\) | ||||
0.393358 | + | 0.919386i | \(0.371313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 307.369 | 0.187559 | 0.0937794 | − | 0.995593i | \(-0.470105\pi\) | ||||
0.0937794 | + | 0.995593i | \(0.470105\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 52.9348 | 0.0309554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2835.39 | −1.62391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1597.76 | 0.878478 | 0.439239 | − | 0.898370i | \(-0.355248\pi\) | ||||
0.439239 | + | 0.898370i | \(0.355248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3415.41 | −1.84067 | −0.920337 | − | 0.391126i | \(-0.872086\pi\) | ||||
−0.920337 | + | 0.391126i | \(0.872086\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2162.26 | 1.12050 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −476.826 | −0.242387 | −0.121194 | − | 0.992629i | \(-0.538672\pi\) | ||||
−0.121194 | + | 0.992629i | \(0.538672\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 670.467 | 0.328200 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3304.04 | −1.58768 | −0.793842 | − | 0.608124i | \(-0.791922\pi\) | ||||
−0.793842 | + | 0.608124i | \(0.791922\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2091.65 | −0.969203 | −0.484601 | − | 0.874735i | \(-0.661035\pi\) | ||||
−0.484601 | + | 0.874735i | \(0.661035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 605.088 | 0.275416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2924.56 | 1.28526 | 0.642631 | − | 0.766176i | \(-0.277843\pi\) | ||||
0.642631 | + | 0.766176i | \(0.277843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9526.37 | 4.11500 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −231.913 | −0.0968381 | −0.0484191 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484191 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2291.74 | −0.941125 | −0.470562 | − | 0.882367i | \(-0.655949\pi\) | ||||
−0.470562 | + | 0.882367i | \(0.655949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2230.92 | −0.886598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 96.9348 | 0.0379068 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4217.80 | 1.59785 | 0.798925 | − | 0.601430i | \(-0.205402\pi\) | ||||
0.798925 | + | 0.601430i | \(0.205402\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1188.35 | −0.443208 | −0.221604 | − | 0.975137i | \(-0.571129\pi\) | ||||
−0.221604 | + | 0.975137i | \(0.571129\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3130.25 | −1.13209 | −0.566044 | − | 0.824375i | \(-0.691527\pi\) | ||||
−0.566044 | + | 0.824375i | \(0.691527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −659.146 | −0.234802 | −0.117401 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117401 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3903.65 | −1.34967 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −346.892 | −0.118185 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −126.467 | −0.0418561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3613.95 | −1.17912 | −0.589560 | − | 0.807725i | \(-0.700699\pi\) | ||||
−0.589560 | + | 0.807725i | \(0.700699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4273.74 | 1.35566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2976.91 | 0.931272 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5131.22 | 1.56182 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2054.13 | −0.616837 | −0.308419 | − | 0.951251i | \(-0.599800\pi\) | ||||
−0.308419 | + | 0.951251i | \(0.599800\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2153.61 | 0.629692 | 0.314846 | − | 0.949143i | \(-0.398047\pi\) | ||||
0.314846 | + | 0.949143i | \(0.398047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1819.87 | 0.525154 | 0.262577 | − | 0.964911i | \(-0.415428\pi\) | ||||
0.262577 | + | 0.964911i | \(0.415428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3989.68 | 1.12177 | 0.560886 | − | 0.827893i | \(-0.310461\pi\) | ||||
0.560886 | + | 0.827893i | \(0.310461\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5348.12 | 1.48457 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5704.32 | 1.54386 | 0.771929 | − | 0.635709i | \(-0.219292\pi\) | ||||
0.771929 | + | 0.635709i | \(0.219292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6223.95 | 1.66357 | 0.831785 | − | 0.555099i | \(-0.187319\pi\) | ||||
0.831785 | + | 0.555099i | \(0.187319\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10863.3 | 2.83279 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6694.52 | −1.72454 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4622.52 | 1.16243 | 0.581217 | − | 0.813749i | \(-0.302577\pi\) | ||||
0.581217 | + | 0.813749i | \(0.302577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.9348 | 0.00569919 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4905.09 | 1.19055 | 0.595274 | − | 0.803523i | \(-0.297043\pi\) | ||||
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3071.44 | −0.736874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4432.85 | −1.03932 | −0.519660 | − | 0.854373i | \(-0.673941\pi\) | ||||
−0.519660 | + | 0.854373i | \(0.673941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3143.39 | −0.728668 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4454.81 | 1.00972 | 0.504860 | − | 0.863201i | \(-0.331544\pi\) | ||||
0.504860 | + | 0.863201i | \(0.331544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3256.23 | 0.729897 | 0.364948 | − | 0.931028i | \(-0.381087\pi\) | ||||
0.364948 | + | 0.931028i | \(0.381087\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 325.870 | 0.0714570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3421.61 | 0.742182 | 0.371091 | − | 0.928596i | \(-0.378984\pi\) | ||||
0.371091 | + | 0.928596i | \(0.378984\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1715.11 | 0.364109 | 0.182055 | − | 0.983288i | \(-0.441725\pi\) | ||||
0.182055 | + | 0.983288i | \(0.441725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4487.60 | 0.942615 | 0.471307 | − | 0.881969i | \(-0.343782\pi\) | ||||
0.471307 | + | 0.881969i | \(0.343782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −477.587 | −0.0982268 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4483.35 | 0.912548 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1685.31 | 0.336031 | 0.168016 | − | 0.985784i | \(-0.446264\pi\) | ||||
0.168016 | + | 0.985784i | \(0.446264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1562.98 | −0.308475 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1214.05 | 0.234816 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5883.91 | 1.12672 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12899.0 | 2.42162 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8079.07 | 1.50194 | 0.750972 | − | 0.660334i | \(-0.229585\pi\) | ||||
0.750972 | + | 0.660334i | \(0.229585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2557.63 | −0.466334 | −0.233167 | − | 0.972437i | \(-0.574909\pi\) | ||||
−0.233167 | + | 0.972437i | \(0.574909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4081.43 | −0.737049 | −0.368524 | − | 0.929618i | \(-0.620137\pi\) | ||||
−0.368524 | + | 0.929618i | \(0.620137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7701.93 | −1.36462 | −0.682308 | − | 0.731065i | \(-0.739024\pi\) | ||||
−0.682308 | + | 0.731065i | \(0.739024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −133.533 | −0.0234370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12259.1 | −2.11181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17249.8 | 2.94415 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7363.07 | 1.23386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 357.314 | 0.0593346 | 0.0296673 | − | 0.999560i | \(-0.490555\pi\) | ||||
0.0296673 | + | 0.999560i | \(0.490555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16178.9 | −2.63865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6659.09 | −1.07639 | −0.538195 | − | 0.842820i | \(-0.680894\pi\) | ||||
−0.538195 | + | 0.842820i | \(0.680894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 101.832 | 0.0161715 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4929.05 | 0.775929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7894.04 | 1.22125 | 0.610626 | − | 0.791919i | \(-0.290918\pi\) | ||||
0.610626 | + | 0.791919i | \(0.290918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1254.46 | 0.192405 | 0.0962027 | − | 0.995362i | \(-0.469330\pi\) | ||||
0.0962027 | + | 0.995362i | \(0.469330\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8604.92 | −1.29743 | −0.648716 | − | 0.761030i | \(-0.724694\pi\) | ||||
−0.648716 | + | 0.761030i | \(0.724694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14889.0 | −2.22598 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3875.61 | 0.569768 | 0.284884 | − | 0.958562i | \(-0.408045\pi\) | ||||
0.284884 | + | 0.958562i | \(0.408045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9135.00 | 1.33183 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6094.07 | −0.873913 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11890.1 | −1.69117 | −0.845583 | − | 0.533843i | \(-0.820747\pi\) | ||||
−0.845583 | + | 0.533843i | \(0.820747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4327.70 | −0.605614 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12384.5 | −1.71916 | −0.859578 | − | 0.511005i | \(-0.829273\pi\) | ||||
−0.859578 | + | 0.511005i | \(0.829273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7068.52 | −0.965642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2062.80 | −0.279576 | −0.139788 | − | 0.990181i | \(-0.544642\pi\) | ||||
−0.139788 | + | 0.990181i | \(0.544642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11905.2 | −1.58833 | −0.794164 | − | 0.607704i | \(-0.792091\pi\) | ||||
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 620.739 | 0.0821709 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12716.6 | 1.65747 | 0.828735 | − | 0.559641i | \(-0.189061\pi\) | ||||
0.828735 | + | 0.559641i | \(0.189061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2223.17 | 0.287547 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2729.00 | −0.347622 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4531.59 | 0.572881 | 0.286441 | − | 0.958098i | \(-0.407528\pi\) | ||||
0.286441 | + | 0.958098i | \(0.407528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4829.15 | 0.601388 | 0.300694 | − | 0.953721i | \(-0.402782\pi\) | ||||
0.300694 | + | 0.953721i | \(0.402782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5390.43 | 0.666294 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −105.065 | −0.0127958 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11484.9 | 1.38849 | 0.694245 | − | 0.719739i | \(-0.255738\pi\) | ||||
0.694245 | + | 0.719739i | \(0.255738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2151.85 | −0.256381 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3407.54 | 0.403059 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8211.65 | 0.957435 | 0.478718 | − | 0.877969i | \(-0.341102\pi\) | ||||
0.478718 | + | 0.877969i | \(0.341102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9788.13 | −1.13312 | −0.566561 | − | 0.824020i | \(-0.691726\pi\) | ||||
−0.566561 | + | 0.824020i | \(0.691726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31588.1 | 3.60529 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17758.8 | 2.01267 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11206.3 | −1.25241 | −0.626207 | − | 0.779657i | \(-0.715394\pi\) | ||||
−0.626207 | + | 0.779657i | \(0.715394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 719.306 | 0.0798329 | 0.0399165 | − | 0.999203i | \(-0.487291\pi\) | ||||
0.0399165 | + | 0.999203i | \(0.487291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2900.50 | −0.317505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8795.00 | 0.956179 | 0.478090 | − | 0.878311i | \(-0.341329\pi\) | ||||
0.478090 | + | 0.878311i | \(0.341329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3023.65 | 0.324285 | 0.162142 | − | 0.986767i | \(-0.448160\pi\) | ||||
0.162142 | + | 0.986767i | \(0.448160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9134.87 | −0.973111 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3137.67 | −0.329790 | −0.164895 | − | 0.986311i | \(-0.552728\pi\) | ||||
−0.164895 | + | 0.986311i | \(0.552728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.3369 | −0.00170571 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32858.7 | 3.38558 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9015.74 | −0.922841 | −0.461421 | − | 0.887182i | \(-0.652660\pi\) | ||||
−0.461421 | + | 0.887182i | \(0.652660\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12262.6 | −1.23888 | −0.619442 | − | 0.785042i | \(-0.712641\pi\) | ||||
−0.619442 | + | 0.785042i | \(0.712641\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3472.30 | 0.348534 | 0.174267 | − | 0.984698i | \(-0.444244\pi\) | ||||
0.174267 | + | 0.984698i | \(0.444244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11825.0 | 1.17172 | 0.585860 | − | 0.810412i | \(-0.300757\pi\) | ||||
0.585860 | + | 0.810412i | \(0.300757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22274.5 | −2.19305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 201.272 | 0.0195655 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41211.9 | −3.98090 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1703.96 | 0.162538 | 0.0812692 | − | 0.996692i | \(-0.474103\pi\) | ||||
0.0812692 | + | 0.996692i | \(0.474103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5561.60 | −0.527208 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −661.015 | −0.0618869 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7721.95 | 0.718512 | 0.359256 | − | 0.933239i | \(-0.383031\pi\) | ||||
0.359256 | + | 0.933239i | \(0.383031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20223.6 | 1.85882 | 0.929410 | − | 0.369049i | \(-0.120317\pi\) | ||||
0.929410 | + | 0.369049i | \(0.120317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12944.0 | −1.18249 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20498.5 | −1.85007 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13702.4 | 1.22927 | 0.614633 | − | 0.788813i | \(-0.289304\pi\) | ||||
0.614633 | + | 0.788813i | \(0.289304\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13707.6 | −1.21509 | −0.607546 | − | 0.794285i | \(-0.707846\pi\) | ||||
−0.607546 | + | 0.794285i | \(0.707846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20874.9 | −1.83945 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12339.2 | 1.07451 | 0.537254 | − | 0.843421i | \(-0.319462\pi\) | ||||
0.537254 | + | 0.843421i | \(0.319462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8390.07 | −0.726330 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20217.7 | −1.72990 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 251.870 | 0.0214259 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1416.70 | −0.119130 | −0.0595649 | − | 0.998224i | \(-0.518971\pi\) | ||||
−0.0595649 | + | 0.998224i | \(0.518971\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6696.15 | −0.559851 | −0.279925 | − | 0.960022i | \(-0.590310\pi\) | ||||
−0.279925 | + | 0.960022i | \(0.590310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9871.02 | 0.815917 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11641.0 | −0.956768 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −864.789 | −0.0702780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5777.40 | −0.466876 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 511.609 | 0.0408841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7105.69 | −0.564691 | −0.282345 | − | 0.959313i | \(-0.591112\pi\) | ||||
−0.282345 | + | 0.959313i | \(0.591112\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28787.8 | −2.26263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12028.0 | −0.940185 | −0.470092 | − | 0.882617i | \(-0.655779\pi\) | ||||
−0.470092 | + | 0.882617i | \(0.655779\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16887.5 | 1.30569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3757.17 | −0.288917 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14529.5 | 1.10527 | 0.552634 | − | 0.833424i | \(-0.313623\pi\) | ||||
0.552634 | + | 0.833424i | \(0.313623\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10654.3 | 0.806131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10233.4 | −0.766053 | −0.383027 | − | 0.923737i | \(-0.625118\pi\) | ||||
−0.383027 | + | 0.923737i | \(0.625118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41158.5 | 3.06469 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −319.460 | −0.0235368 | −0.0117684 | − | 0.999931i | \(-0.503746\pi\) | ||||
−0.0117684 | + | 0.999931i | \(0.503746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6793.96 | 0.497931 | 0.248965 | − | 0.968512i | \(-0.419909\pi\) | ||||
0.248965 | + | 0.968512i | \(0.419909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7473.74 | 0.542046 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11145.6 | −0.804156 | −0.402078 | − | 0.915605i | \(-0.631712\pi\) | ||||
−0.402078 | + | 0.915605i | \(0.631712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4691.36 | 0.334992 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −148.038 | −0.0105165 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23817.6 | −1.67471 | −0.837356 | − | 0.546658i | \(-0.815900\pi\) | ||||
−0.837356 | + | 0.546658i | \(0.815900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12878.4 | −0.900924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16416.2 | 1.13682 | 0.568408 | − | 0.822747i | \(-0.307559\pi\) | ||||
0.568408 | + | 0.822747i | \(0.307559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60171.2 | 4.14585 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4801.70 | 0.327533 | 0.163766 | − | 0.986499i | \(-0.447636\pi\) | ||||
0.163766 | + | 0.986499i | \(0.447636\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4524.21 | 0.307066 | 0.153533 | − | 0.988144i | \(-0.450935\pi\) | ||||
0.153533 | + | 0.988144i | \(0.450935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28240.8 | −1.89777 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14978.3 | −1.00157 | −0.500783 | − | 0.865573i | \(-0.666955\pi\) | ||||
−0.500783 | + | 0.865573i | \(0.666955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13332.6 | 0.882784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11651.6 | −0.767709 | −0.383854 | − | 0.923394i | \(-0.625404\pi\) | ||||
−0.383854 | + | 0.923394i | \(0.625404\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 341.120 | 0.0222576 | 0.0111288 | − | 0.999938i | \(-0.496458\pi\) | ||||
0.0111288 | + | 0.999938i | \(0.496458\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18415.1 | −1.19575 | −0.597873 | − | 0.801591i | \(-0.703987\pi\) | ||||
−0.597873 | + | 0.801591i | \(0.703987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12576.5 | −0.808776 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49832.2 | 3.18926 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10184.5 | −0.645599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13557.6 | 0.855341 | 0.427671 | − | 0.903935i | \(-0.359334\pi\) | ||||
0.427671 | + | 0.903935i | \(0.359334\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4934.17 | 0.308357 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27081.9 | 1.68449 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9682.55 | −0.596627 | −0.298313 | − | 0.954468i | \(-0.596424\pi\) | ||||
−0.298313 | + | 0.954468i | \(0.596424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3259.50 | 0.199910 | 0.0999551 | − | 0.994992i | \(-0.468130\pi\) | ||||
0.0999551 | + | 0.994992i | \(0.468130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8115.35 | 0.493118 | 0.246559 | − | 0.969128i | \(-0.420700\pi\) | ||||
0.246559 | + | 0.969128i | \(0.420700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −73.6085 | −0.00445206 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3427.74 | −0.205418 | −0.102709 | − | 0.994711i | \(-0.532751\pi\) | ||||
−0.102709 | + | 0.994711i | \(0.532751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59354.6 | −3.54073 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13820.2 | −0.816934 | −0.408467 | − | 0.912773i | \(-0.633936\pi\) | ||||
−0.408467 | + | 0.912773i | \(0.633936\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22719.7 | 1.33690 | 0.668451 | − | 0.743756i | \(-0.266957\pi\) | ||||
0.668451 | + | 0.743756i | \(0.266957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −78503.2 | −4.57778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3062.54 | −0.177784 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 607.478 | 0.0349500 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5133.17 | −0.294011 | −0.147005 | − | 0.989136i | \(-0.546963\pi\) | ||||
−0.147005 | + | 0.989136i | \(0.546963\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9295.88 | 0.527725 | 0.263862 | − | 0.964560i | \(-0.415004\pi\) | ||||
0.263862 | + | 0.964560i | \(0.415004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −910.059 | −0.0514357 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13824.3 | 0.774486 | 0.387243 | − | 0.921978i | \(-0.373427\pi\) | ||||
0.387243 | + | 0.921978i | \(0.373427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26787.0 | 1.49413 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7836.35 | −0.433296 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11015.2 | 0.606424 | 0.303212 | − | 0.952923i | \(-0.401941\pi\) | ||||
0.303212 | + | 0.952923i | \(0.401941\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6526.57 | 0.356212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1583.61 | −0.0860596 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −460.523 | −0.0248127 | −0.0124064 | − | 0.999923i | \(-0.503949\pi\) | ||||
−0.0124064 | + | 0.999923i | \(0.503949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13287.3 | 0.712861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28739.7 | −1.52881 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26445.0 | −1.40080 | −0.700398 | − | 0.713752i | \(-0.746994\pi\) | ||||
−0.700398 | + | 0.713752i | \(0.746994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2335.48 | 0.122671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1124.00 | 0.0587905 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15524.4 | −0.805235 | −0.402617 | − | 0.915368i | \(-0.631899\pi\) | ||||
−0.402617 | + | 0.915368i | \(0.631899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27834.9 | −1.43776 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −43514.2 | −2.22907 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18934.0 | 0.965922 | 0.482961 | − | 0.875642i | \(-0.339561\pi\) | ||||
0.482961 | + | 0.875642i | \(0.339561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19510.2 | 0.987156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16779.9 | 0.845540 | 0.422770 | − | 0.906237i | \(-0.361058\pi\) | ||||
0.422770 | + | 0.906237i | \(0.361058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −761.945 | −0.0380823 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30309.0 | −1.50871 | −0.754353 | − | 0.656469i | \(-0.772049\pi\) | ||||
−0.754353 | + | 0.656469i | \(0.772049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32098.8 | −1.58492 | −0.792458 | − | 0.609927i | \(-0.791199\pi\) | ||||
−0.792458 | + | 0.609927i | \(0.791199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33926.2 | 1.66840 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7954.09 | −0.388032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9434.07 | 0.458394 | 0.229197 | − | 0.973380i | \(-0.426390\pi\) | ||||
0.229197 | + | 0.973380i | \(0.426390\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72521.7 | −3.49581 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1280.65 | −0.0614876 | −0.0307438 | − | 0.999527i | \(-0.509788\pi\) | ||||
−0.0307438 | + | 0.999527i | \(0.509788\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19624.7 | −0.934818 | −0.467409 | − | 0.884041i | \(-0.654812\pi\) | ||||
−0.467409 | + | 0.884041i | \(0.654812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39633.9 | −1.88053 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3896.45 | −0.183432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17644.9 | 0.827426 | 0.413713 | − | 0.910407i | \(-0.364232\pi\) | ||||
0.413713 | + | 0.910407i | \(0.364232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22541.7 | −1.04886 | −0.524430 | − | 0.851454i | \(-0.675722\pi\) | ||||
−0.524430 | + | 0.851454i | \(0.675722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33183.8 | 1.53806 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2066.08 | 0.0950258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −701.196 | −0.0321264 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10124.8 | −0.460342 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39687.8 | 1.79761 | 0.898804 | − | 0.438350i | \(-0.144437\pi\) | ||||
0.898804 | + | 0.438350i | \(0.144437\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56665.4 | 2.54714 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32156.7 | 1.44000 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1991.97 | −0.0885309 | −0.0442654 | − | 0.999020i | \(-0.514095\pi\) | ||||
−0.0442654 | + | 0.999020i | \(0.514095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24414.9 | 1.08102 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −287.000 | −0.0126127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14236.5 | 0.623317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21679.4 | 0.942160 | 0.471080 | − | 0.882090i | \(-0.343864\pi\) | ||||
0.471080 | + | 0.882090i | \(0.343864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15099.7 | 0.653786 | 0.326893 | − | 0.945061i | \(-0.393998\pi\) | ||||
0.326893 | + | 0.945061i | \(0.393998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −70157.0 | −3.01533 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25454.3 | −1.09000 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9902.77 | 0.420961 | 0.210480 | − | 0.977598i | \(-0.432497\pi\) | ||||
0.210480 | + | 0.977598i | \(0.432497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11488.7 | 0.486600 | 0.243300 | − | 0.969951i | \(-0.421770\pi\) | ||||
0.243300 | + | 0.969951i | \(0.421770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36938.8 | 1.55319 | 0.776594 | − | 0.630001i | \(-0.216945\pi\) | ||||
0.776594 | + | 0.630001i | \(0.216945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3205.00 | −0.134275 | −0.0671376 | − | 0.997744i | \(-0.521387\pi\) | ||||
−0.0671376 | + | 0.997744i | \(0.521387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49592.6 | 2.06277 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44413.5 | −1.84071 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1126.63 | 0.0463594 | 0.0231797 | − | 0.999731i | \(-0.492621\pi\) | ||||
0.0231797 | + | 0.999731i | \(0.492621\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6558.04 | −0.268893 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12848.2 | 0.523069 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38880.8 | −1.57728 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2409.65 | −0.0970641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6254.66 | −0.251061 | −0.125531 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125531 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19069.4 | −0.760090 | −0.380045 | − | 0.924968i | \(-0.624092\pi\) | ||||
−0.380045 | + | 0.924968i | \(0.624092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26790.3 | −1.06411 | −0.532056 | − | 0.846709i | \(-0.678580\pi\) | ||||
−0.532056 | + | 0.846709i | \(0.678580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46056.3 | −1.81666 | −0.908329 | − | 0.418256i | \(-0.862641\pi\) | ||||
−0.908329 | + | 0.418256i | \(0.862641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 62099.2 | 2.44097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −128.522 | −0.00501704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40333.4 | −1.56905 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 124688. | 4.81738 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36490.2 | −1.40500 | −0.702500 | − | 0.711684i | \(-0.747933\pi\) | ||||
−0.702500 | + | 0.711684i | \(0.747933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38136.3 | 1.45839 | 0.729197 | − | 0.684303i | \(-0.239894\pi\) | ||||
0.729197 | + | 0.684303i | \(0.239894\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13336.1 | 0.508262 | 0.254131 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254131 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28027.2 | 1.06095 | 0.530474 | − | 0.847701i | \(-0.322014\pi\) | ||||
0.530474 | + | 0.847701i | \(0.322014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6793.17 | 0.256283 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31853.3 | −1.19365 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4924.38 | −0.183915 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13597.8 | −0.504464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14350.0 | −0.530598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48662.1 | −1.78738 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45203.3 | 1.65485 | 0.827427 | − | 0.561573i | \(-0.189804\pi\) | ||||
0.827427 | + | 0.561573i | \(0.189804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29822.0 | 1.08457 | 0.542287 | − | 0.840194i | \(-0.317559\pi\) | ||||
0.542287 | + | 0.840194i | \(0.317559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 160.478 | 0.00581714 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −81717.0 | −2.94279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36967.7 | 1.32693 | 0.663467 | − | 0.748206i | \(-0.269084\pi\) | ||||
0.663467 | + | 0.748206i | \(0.269084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37117.6 | −1.32366 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34237.6 | −1.21700 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50409.4 | −1.78028 | −0.890139 | − | 0.455690i | \(-0.849393\pi\) | ||||
−0.890139 | + | 0.455690i | \(0.849393\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −64701.8 | −2.27767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2058.28 | 0.0719925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30156.5 | −1.05141 | −0.525705 | − | 0.850667i | \(-0.676198\pi\) | ||||
−0.525705 | + | 0.850667i | \(0.676198\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42221.1 | −1.46267 | −0.731333 | − | 0.682020i | \(-0.761102\pi\) | ||||
−0.731333 | + | 0.682020i | \(0.761102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −374.682 | −0.0129388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40164.6 | 1.37822 | 0.689111 | − | 0.724656i | \(-0.258001\pi\) | ||||
0.689111 | + | 0.724656i | \(0.258001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15192.3 | −0.519665 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7132.10 | −0.242425 | −0.121213 | − | 0.992627i | \(-0.538678\pi\) | ||||
−0.121213 | + | 0.992627i | \(0.538678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 89559.5 | 3.03464 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36879.3 | 1.24181 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19421.3 | −0.651919 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25233.0 | −0.841740 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −549.206 | −0.0182640 | −0.00913199 | − | 0.999958i | \(-0.502907\pi\) | ||||
−0.00913199 | + | 0.999958i | \(0.502907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31024.8 | 1.02537 | 0.512685 | − | 0.858577i | \(-0.328651\pi\) | ||||
0.512685 | + | 0.858577i | \(0.328651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8985.52 | 0.296056 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7827.03 | −0.256304 | −0.128152 | − | 0.991755i | \(-0.540904\pi\) | ||||
−0.128152 | + | 0.991755i | \(0.540904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −430.206 | −0.0140444 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47421.5 | 1.53867 | 0.769334 | − | 0.638847i | \(-0.220588\pi\) | ||||
0.769334 | + | 0.638847i | \(0.220588\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −66466.8 | −2.15006 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4616.11 | 0.148416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43260.0 | 1.38668 | 0.693339 | − | 0.720612i | \(-0.256139\pi\) | ||||
0.693339 | + | 0.720612i | \(0.256139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13996.1 | −0.445936 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40209.1 | 1.27727 | 0.638634 | − | 0.769511i | \(-0.279500\pi\) | ||||
0.638634 | + | 0.769511i | \(0.279500\pi\) | |||||||
\(998\) | 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 | 1728.4.a.bt.1.2 | 2 | ||
3.2 | odd | 2 | 1728.4.a.bh.1.1 | 2 | |||
4.3 | odd | 2 | 1728.4.a.bs.1.2 | 2 | |||
8.3 | odd | 2 | 432.4.a.o.1.1 | 2 | |||
8.5 | even | 2 | 216.4.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1728.4.a.bg.1.1 | 2 | |||
24.5 | odd | 2 | 216.4.a.h.1.2 | yes | 2 | ||
24.11 | even | 2 | 432.4.a.s.1.2 | 2 | |||
72.5 | odd | 6 | 648.4.i.m.217.1 | 4 | |||
72.13 | even | 6 | 648.4.i.s.217.2 | 4 | |||
72.29 | odd | 6 | 648.4.i.m.433.1 | 4 | |||
72.61 | even | 6 | 648.4.i.s.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.e.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
216.4.a.h.1.2 | yes | 2 | 24.5 | odd | 2 | ||
432.4.a.o.1.1 | 2 | 8.3 | odd | 2 | |||
432.4.a.s.1.2 | 2 | 24.11 | even | 2 | |||
648.4.i.m.217.1 | 4 | 72.5 | odd | 6 | |||
648.4.i.m.433.1 | 4 | 72.29 | odd | 6 | |||
648.4.i.s.217.2 | 4 | 72.13 | even | 6 | |||
648.4.i.s.433.2 | 4 | 72.61 | even | 6 | |||
1728.4.a.bg.1.1 | 2 | 12.11 | even | 2 | |||
1728.4.a.bh.1.1 | 2 | 3.2 | odd | 2 | |||
1728.4.a.bs.1.2 | 2 | 4.3 | odd | 2 | |||
1728.4.a.bt.1.2 | 2 | 1.1 | even | 1 | trivial |