Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1765.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.48079\) 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 | ||||||||
\(7\) | 24.7900 | 1.33853 | 0.669267 | − | 0.743022i | \(-0.266608\pi\) | ||||
0.669267 | + | 0.743022i | \(0.266608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.16892 | 0.223911 | 0.111956 | − | 0.993713i | \(-0.464289\pi\) | ||||
0.111956 | + | 0.993713i | \(0.464289\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.7694 | −0.997808 | −0.498904 | − | 0.866657i | \(-0.666264\pi\) | ||||
−0.498904 | + | 0.866657i | \(0.666264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −60.3173 | −0.860535 | −0.430267 | − | 0.902701i | \(-0.641581\pi\) | ||||
−0.430267 | + | 0.902701i | \(0.641581\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −111.802 | −1.34995 | −0.674975 | − | 0.737841i | \(-0.735845\pi\) | ||||
−0.674975 | + | 0.737841i | \(0.735845\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.9268 | −0.334772 | −0.167386 | − | 0.985891i | \(-0.553533\pi\) | ||||
−0.167386 | + | 0.985891i | \(0.553533\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.2627 | −0.212991 | −0.106495 | − | 0.994313i | \(-0.533963\pi\) | ||||
−0.106495 | + | 0.994313i | \(0.533963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −124.274 | −0.720010 | −0.360005 | − | 0.932950i | \(-0.617225\pi\) | ||||
−0.360005 | + | 0.932950i | \(0.617225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 123.950 | 0.598610 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −438.610 | −1.94884 | −0.974419 | − | 0.224741i | \(-0.927846\pi\) | ||||
−0.974419 | + | 0.224741i | \(0.927846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −508.071 | −1.93530 | −0.967651 | − | 0.252291i | \(-0.918816\pi\) | ||||
−0.967651 | + | 0.252291i | \(0.918816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.5247 | −0.172092 | −0.0860459 | − | 0.996291i | \(-0.527423\pi\) | ||||
−0.0860459 | + | 0.996291i | \(0.527423\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 248.030 | 0.769763 | 0.384881 | − | 0.922966i | \(-0.374242\pi\) | ||||
0.384881 | + | 0.922966i | \(0.374242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 271.543 | 0.791672 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 320.404 | 0.830394 | 0.415197 | − | 0.909732i | \(-0.363713\pi\) | ||||
0.415197 | + | 0.909732i | \(0.363713\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.8446 | 0.100136 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 652.268 | 1.43929 | 0.719645 | − | 0.694343i | \(-0.244305\pi\) | ||||
0.719645 | + | 0.694343i | \(0.244305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 693.019 | 1.45462 | 0.727311 | − | 0.686308i | \(-0.240770\pi\) | ||||
0.727311 | + | 0.686308i | \(0.240770\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −233.847 | −0.446233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0308 | −0.0219373 | −0.0109686 | − | 0.999940i | \(-0.503491\pi\) | ||||
−0.0109686 | + | 0.999940i | \(0.503491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1168.30 | −1.95284 | −0.976421 | − | 0.215877i | \(-0.930739\pi\) | ||||
−0.976421 | + | 0.215877i | \(0.930739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −122.195 | −0.195915 | −0.0979575 | − | 0.995191i | \(-0.531231\pi\) | ||||
−0.0979575 | + | 0.995191i | \(0.531231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 202.507 | 0.299712 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −441.669 | −0.629008 | −0.314504 | − | 0.949256i | \(-0.601838\pi\) | ||||
−0.314504 | + | 0.949256i | \(0.601838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −428.581 | −0.566782 | −0.283391 | − | 0.959004i | \(-0.591459\pi\) | ||||
−0.283391 | + | 0.959004i | \(0.591459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −301.586 | −0.384843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1549.24 | 1.84515 | 0.922577 | − | 0.385813i | \(-0.126079\pi\) | ||||
0.922577 | + | 0.385813i | \(0.126079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1159.41 | −1.33560 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −559.008 | −0.603716 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −500.136 | −0.523516 | −0.261758 | − | 0.965134i | \(-0.584302\pi\) | ||||
−0.261758 | + | 0.965134i | \(0.584302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 535.936 | 0.527997 | 0.263998 | − | 0.964523i | \(-0.414959\pi\) | ||||
0.263998 | + | 0.964523i | \(0.414959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134.905 | −0.129055 | −0.0645273 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645273 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 808.631 | 0.730592 | 0.365296 | − | 0.930891i | \(-0.380968\pi\) | ||||
0.365296 | + | 0.930891i | \(0.380968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1073.96 | −0.943730 | −0.471865 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471865 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −523.376 | −0.435709 | −0.217854 | − | 0.975981i | \(-0.569906\pi\) | ||||
−0.217854 | + | 0.975981i | \(0.569906\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −184.634 | −0.149715 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1495.26 | −1.15185 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1264.27 | −0.949864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −114.730 | −0.0801622 | −0.0400811 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400811 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 499.073 | 0.332857 | 0.166428 | − | 0.986054i | \(-0.446777\pi\) | ||||
0.166428 | + | 0.986054i | \(0.446777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2771.56 | −1.80695 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1887.38 | 1.17701 | 0.588504 | − | 0.808495i | \(-0.299717\pi\) | ||||
0.588504 | + | 0.808495i | \(0.299717\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1784.90 | −1.08916 | −0.544580 | − | 0.838709i | \(-0.683311\pi\) | ||||
−0.544580 | + | 0.838709i | \(0.683311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −382.056 | −0.223420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −166.313 | −0.0952522 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 996.321 | 0.547797 | 0.273899 | − | 0.961759i | \(-0.411687\pi\) | ||||
0.273899 | + | 0.961759i | \(0.411687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3487.14 | −1.87933 | −0.939666 | − | 0.342093i | \(-0.888864\pi\) | ||||
−0.939666 | + | 0.342093i | \(0.888864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −621.371 | −0.321998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1785.99 | −0.907880 | −0.453940 | − | 0.891032i | \(-0.649982\pi\) | ||||
−0.453940 | + | 0.891032i | \(0.649982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −915.415 | −0.448104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −396.237 | −0.190403 | −0.0952014 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952014 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1749.48 | −0.810654 | −0.405327 | − | 0.914172i | \(-0.632842\pi\) | ||||
−0.405327 | + | 0.914172i | \(0.632842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.61953 | −0.00437849 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2998.95 | 1.31796 | 0.658978 | − | 0.752162i | \(-0.270989\pi\) | ||||
0.658978 | + | 0.752162i | \(0.270989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 619.750 | 0.267707 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −682.749 | −0.285090 | −0.142545 | − | 0.989788i | \(-0.545529\pi\) | ||||
−0.142545 | + | 0.989788i | \(0.545529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 59.3943 | 0.0243909 | 0.0121954 | − | 0.999926i | \(-0.496118\pi\) | ||||
0.0121954 | + | 0.999926i | \(0.496118\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2193.05 | −0.871546 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −492.727 | −0.192683 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3618.13 | −1.37067 | −0.685336 | − | 0.728227i | \(-0.740345\pi\) | ||||
−0.685336 | + | 0.728227i | \(0.740345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1536.37 | 0.573007 | 0.286504 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286504 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −136.471 | −0.0493561 | −0.0246780 | − | 0.999695i | \(-0.507856\pi\) | ||||
−0.0246780 | + | 0.999695i | \(0.507856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −123.255 | −0.0439061 | −0.0219531 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219531 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −824.581 | −0.285095 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2540.36 | −0.865494 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −913.298 | −0.302269 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4128.55 | 1.34702 | 0.673509 | − | 0.739179i | \(-0.264786\pi\) | ||||
0.673509 | + | 0.739179i | \(0.264786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −242.624 | −0.0769618 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3080.76 | −0.963758 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2821.01 | 0.858649 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3094.00 | −0.929102 | −0.464551 | − | 0.885546i | \(-0.653784\pi\) | ||||
−0.464551 | + | 0.885546i | \(0.653784\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1399.26 | −0.409128 | −0.204564 | − | 0.978853i | \(-0.565578\pi\) | ||||
−0.204564 | + | 0.978853i | \(0.565578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4787.68 | 1.38157 | 0.690784 | − | 0.723061i | \(-0.257265\pi\) | ||||
0.690784 | + | 0.723061i | \(0.257265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5117.74 | 1.43894 | 0.719472 | − | 0.694521i | \(-0.244384\pi\) | ||||
0.719472 | + | 0.694521i | \(0.244384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1240.15 | 0.344248 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2813.92 | 0.761580 | 0.380790 | − | 0.924662i | \(-0.375652\pi\) | ||||
0.380790 | + | 0.924662i | \(0.375652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3543.20 | −0.947045 | −0.473522 | − | 0.880782i | \(-0.657018\pi\) | ||||
−0.473522 | + | 0.880782i | \(0.657018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1357.72 | 0.354046 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5228.90 | 1.34699 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3446.10 | −0.866597 | −0.433299 | − | 0.901250i | \(-0.642650\pi\) | ||||
−0.433299 | + | 0.901250i | \(0.642650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −301.652 | −0.0749593 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1354.83 | −0.328841 | −0.164421 | − | 0.986390i | \(-0.552575\pi\) | ||||
−0.164421 | + | 0.986390i | \(0.552575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10873.1 | −2.60858 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 344.218 | 0.0807050 | 0.0403525 | − | 0.999186i | \(-0.487152\pi\) | ||||
0.0403525 | + | 0.999186i | \(0.487152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1602.02 | 0.371363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −203.341 | −0.0460889 | −0.0230445 | − | 0.999734i | \(-0.507336\pi\) | ||||
−0.0230445 | + | 0.999734i | \(0.507336\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1586.34 | −0.355584 | −0.177792 | − | 0.984068i | \(-0.556895\pi\) | ||||
−0.177792 | + | 0.984068i | \(0.556895\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 204.223 | 0.0447822 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4330.18 | −0.939260 | −0.469630 | − | 0.882863i | \(-0.655613\pi\) | ||||
−0.469630 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6569.00 | 1.39457 | 0.697284 | − | 0.716795i | \(-0.254391\pi\) | ||||
0.697284 | + | 0.716795i | \(0.254391\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −997.534 | −0.209531 | −0.104765 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104765 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12595.1 | −2.59047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1274.82 | −0.259480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −182.221 | −0.0363326 | −0.0181663 | − | 0.999835i | \(-0.505783\pi\) | ||||
−0.0181663 | + | 0.999835i | \(0.505783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3261.34 | 0.643670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1727.05 | 0.334039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1202.93 | −0.230351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3465.09 | 0.650527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1671.12 | 0.310670 | 0.155335 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155335 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9271.81 | 1.69053 | 0.845267 | − | 0.534345i | \(-0.179442\pi\) | ||||
0.845267 | + | 0.534345i | \(0.179442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −572.410 | −0.103369 | −0.0516845 | − | 0.998663i | \(-0.516459\pi\) | ||||
−0.0516845 | + | 0.998663i | \(0.516459\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6048.37 | −1.07164 | −0.535820 | − | 0.844332i | \(-0.679998\pi\) | ||||
−0.535820 | + | 0.844332i | \(0.679998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −271.720 | −0.0476909 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6743.57 | 1.16168 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1169.24 | −0.199562 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6148.65 | 1.03035 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8537.53 | 1.41772 | 0.708860 | − | 0.705350i | \(-0.249210\pi\) | ||||
0.708860 | + | 0.705350i | \(0.249210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −60.1541 | −0.00981065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3638.91 | 0.588202 | 0.294101 | − | 0.955774i | \(-0.404980\pi\) | ||||
0.294101 | + | 0.955774i | \(0.404980\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1015.19 | −0.161218 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1771.41 | −0.278854 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7965.23 | −1.23226 | −0.616132 | − | 0.787643i | \(-0.711301\pi\) | ||||
−0.616132 | + | 0.787643i | \(0.711301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7699.35 | 1.18091 | 0.590454 | − | 0.807072i | \(-0.298949\pi\) | ||||
0.590454 | + | 0.807072i | \(0.298949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11674.7 | −1.76029 | −0.880144 | − | 0.474706i | \(-0.842554\pi\) | ||||
−0.880144 | + | 0.474706i | \(0.842554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5841.50 | −0.873337 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2547.12 | −0.374463 | −0.187231 | − | 0.982316i | \(-0.559951\pi\) | ||||
−0.187231 | + | 0.982316i | \(0.559951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5640.59 | 0.822363 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −610.973 | −0.0876158 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11020.0 | −1.56742 | −0.783708 | − | 0.621130i | \(-0.786674\pi\) | ||||
−0.783708 | + | 0.621130i | \(0.786674\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7942.81 | 1.11151 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8430.05 | 1.17022 | 0.585109 | − | 0.810955i | \(-0.301052\pi\) | ||||
0.585109 | + | 0.810955i | \(0.301052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1555.68 | 0.212524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1675.32 | 0.227059 | 0.113529 | − | 0.993535i | \(-0.463784\pi\) | ||||
0.113529 | + | 0.993535i | \(0.463784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12124.4 | −1.61757 | −0.808783 | − | 0.588108i | \(-0.799873\pi\) | ||||
−0.808783 | + | 0.588108i | \(0.799873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1012.54 | 0.134035 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15159.1 | 1.97583 | 0.987916 | − | 0.154992i | \(-0.0495351\pi\) | ||||
0.987916 | + | 0.154992i | \(0.0495351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2227.32 | 0.288083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2208.34 | −0.281301 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3884.64 | −0.491095 | −0.245547 | − | 0.969385i | \(-0.578968\pi\) | ||||
−0.245547 | + | 0.969385i | \(0.578968\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7056.99 | 0.878825 | 0.439413 | − | 0.898285i | \(-0.355187\pi\) | ||||
0.439413 | + | 0.898285i | \(0.355187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5812.24 | 0.718432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3582.97 | −0.436366 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7034.26 | 0.850420 | 0.425210 | − | 0.905095i | \(-0.360200\pi\) | ||||
0.425210 | + | 0.905095i | \(0.360200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16169.7 | 1.92654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2142.91 | −0.253473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6153.56 | −0.717473 | −0.358737 | − | 0.933439i | \(-0.616792\pi\) | ||||
−0.358737 | + | 0.933439i | \(0.616792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13024.0 | −1.50772 | −0.753862 | − | 0.657033i | \(-0.771811\pi\) | ||||
−0.753862 | + | 0.657033i | \(0.771811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1507.93 | −0.172107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17179.9 | 1.94706 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11614.6 | −1.29805 | −0.649023 | − | 0.760769i | \(-0.724822\pi\) | ||||
−0.649023 | + | 0.760769i | \(0.724822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1245.75 | 0.138260 | 0.0691301 | − | 0.997608i | \(-0.477978\pi\) | ||||
0.0691301 | + | 0.997608i | \(0.477978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4128.47 | 0.451926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7984.30 | 0.868041 | 0.434020 | − | 0.900903i | \(-0.357095\pi\) | ||||
0.434020 | + | 0.900903i | \(0.357095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13840.8 | −1.48442 | −0.742210 | − | 0.670167i | \(-0.766222\pi\) | ||||
−0.742210 | + | 0.670167i | \(0.766222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7746.18 | 0.825178 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7756.38 | 0.815247 | 0.407624 | − | 0.913150i | \(-0.366358\pi\) | ||||
0.407624 | + | 0.913150i | \(0.366358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4150.39 | −0.433336 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5797.07 | −0.597298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16107.6 | 1.64875 | 0.824377 | − | 0.566041i | \(-0.191526\pi\) | ||||
0.824377 | + | 0.566041i | \(0.191526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6272.71 | 0.633730 | 0.316865 | − | 0.948471i | \(-0.397370\pi\) | ||||
0.316865 | + | 0.948471i | \(0.397370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18657.9 | 1.87280 | 0.936399 | − | 0.350937i | \(-0.114137\pi\) | ||||
0.936399 | + | 0.350937i | \(0.114137\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16289.5 | −1.61411 | −0.807054 | − | 0.590478i | \(-0.798939\pi\) | ||||
−0.807054 | + | 0.590478i | \(0.798939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −298.244 | −0.0293638 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −396.394 | −0.0385333 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2795.04 | −0.269990 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11328.9 | 1.08065 | 0.540324 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540324 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20513.5 | 1.94457 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2500.68 | −0.234124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14122.4 | 1.31406 | 0.657029 | − | 0.753866i | \(-0.271813\pi\) | ||||
0.657029 | + | 0.753866i | \(0.271813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5220.81 | −0.479861 | −0.239931 | − | 0.970790i | \(-0.577125\pi\) | ||||
−0.239931 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2006.31 | 0.183286 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28962.1 | −2.61394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17934.3 | 1.60892 | 0.804459 | − | 0.594008i | \(-0.202455\pi\) | ||||
0.804459 | + | 0.594008i | \(0.202455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7305.37 | 0.647576 | 0.323788 | − | 0.946130i | \(-0.395044\pi\) | ||||
0.323788 | + | 0.946130i | \(0.395044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2679.68 | 0.236127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6083.17 | 0.529728 | 0.264864 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264864 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3029.20 | −0.262239 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −674.527 | −0.0577150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2026.13 | 0.172358 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10005.0 | 0.841316 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12931.9 | −1.08121 | −0.540607 | − | 0.841276i | \(-0.681805\pi\) | ||||
−0.540607 | + | 0.841276i | \(0.681805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7495.89 | 0.619594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10803.4 | −0.887927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23762.2 | 1.93106 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4043.15 | 0.326730 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2218.22 | 0.177264 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13088.9 | 1.04017 | 0.520087 | − | 0.854113i | \(-0.325900\pi\) | ||||
0.520087 | + | 0.854113i | \(0.325900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5369.79 | −0.422049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4522.72 | −0.353524 | −0.176762 | − | 0.984254i | \(-0.556562\pi\) | ||||
−0.176762 | + | 0.984254i | \(0.556562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3718.82 | 0.287526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10949.0 | −0.841948 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5477.36 | −0.416667 | −0.208333 | − | 0.978058i | \(-0.566804\pi\) | ||||
−0.208333 | + | 0.978058i | \(0.566804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2269.47 | 0.171715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17369.7 | 1.30026 | 0.650129 | − | 0.759824i | \(-0.274715\pi\) | ||||
0.650129 | + | 0.759824i | \(0.274715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2616.88 | −0.194855 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7997.66 | −0.589243 | −0.294622 | − | 0.955614i | \(-0.595194\pi\) | ||||
−0.294622 | + | 0.955614i | \(0.595194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14623.1 | 1.07173 | 0.535864 | − | 0.844305i | \(-0.319986\pi\) | ||||
0.535864 | + | 0.844305i | \(0.319986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −923.170 | −0.0669545 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3818.29 | −0.275490 | −0.137745 | − | 0.990468i | \(-0.543985\pi\) | ||||
−0.137745 | + | 0.990468i | \(0.543985\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10624.5 | −0.758657 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2617.35 | 0.185934 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19568.8 | −1.37597 | −0.687983 | − | 0.725726i | \(-0.741504\pi\) | ||||
−0.687983 | + | 0.725726i | \(0.741504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13894.1 | 0.971977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5170.99 | 0.358090 | 0.179045 | − | 0.983841i | \(-0.442699\pi\) | ||||
0.179045 | + | 0.983841i | \(0.442699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7476.32 | −0.515125 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10252.3 | 0.699327 | 0.349663 | − | 0.936875i | \(-0.386296\pi\) | ||||
0.349663 | + | 0.936875i | \(0.386296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21251.0 | −1.44234 | −0.721168 | − | 0.692760i | \(-0.756395\pi\) | ||||
−0.721168 | + | 0.692760i | \(0.756395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6321.34 | −0.424792 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18653.8 | −1.24734 | −0.623669 | − | 0.781689i | \(-0.714359\pi\) | ||||
−0.623669 | + | 0.781689i | \(0.714359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11600.2 | −0.768076 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6156.56 | 0.405646 | 0.202823 | − | 0.979215i | \(-0.434988\pi\) | ||||
0.202823 | + | 0.979215i | \(0.434988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16106.4 | −1.05092 | −0.525461 | − | 0.850818i | \(-0.676107\pi\) | ||||
−0.525461 | + | 0.850818i | \(0.676107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27462.5 | −1.78322 | −0.891608 | − | 0.452807i | \(-0.850423\pi\) | ||||
−0.891608 | + | 0.452807i | \(0.850423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38405.6 | 2.46980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26455.7 | 1.67704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9282.80 | −0.585646 | −0.292823 | − | 0.956167i | \(-0.594595\pi\) | ||||
−0.292823 | + | 0.956167i | \(0.594595\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −573.648 | −0.0358496 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12699.9 | −0.789937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22076.4 | −1.36032 | −0.680160 | − | 0.733064i | \(-0.738090\pi\) | ||||
−0.680160 | + | 0.733064i | \(0.738090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25416.1 | 1.55881 | 0.779403 | − | 0.626523i | \(-0.215522\pi\) | ||||
0.779403 | + | 0.626523i | \(0.215522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15054.7 | 0.914777 | 0.457389 | − | 0.889267i | \(-0.348785\pi\) | ||||
0.457389 | + | 0.889267i | \(0.348785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5328.32 | 0.322273 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14629.6 | −0.876726 | −0.438363 | − | 0.898798i | \(-0.644442\pi\) | ||||
−0.438363 | + | 0.898798i | \(0.644442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2495.37 | 0.148858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5302.96 | 0.313466 | 0.156733 | − | 0.987641i | \(-0.449904\pi\) | ||||
0.156733 | + | 0.987641i | \(0.449904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7326.18 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13857.8 | −0.808094 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1228.28 | 0.0713034 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5661.22 | 0.325706 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27965.1 | −1.60174 | −0.800872 | − | 0.598836i | \(-0.795630\pi\) | ||||
−0.800872 | + | 0.598836i | \(0.795630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17423.1 | 0.989103 | 0.494551 | − | 0.869148i | \(-0.335332\pi\) | ||||
0.494551 | + | 0.869148i | \(0.335332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12398.4 | −0.700744 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18318.0 | −1.02624 | −0.513118 | − | 0.858318i | \(-0.671510\pi\) | ||||
−0.513118 | + | 0.858318i | \(0.671510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9436.91 | 0.526374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14985.1 | −0.828574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27603.8 | 1.51968 | 0.759838 | − | 0.650112i | \(-0.225278\pi\) | ||||
0.759838 | + | 0.650112i | \(0.225278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8924.50 | −0.487087 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30645.5 | 1.66540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8448.22 | −0.455185 | −0.227593 | − | 0.973756i | \(-0.573085\pi\) | ||||
−0.227593 | + | 0.973756i | \(0.573085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49037.2 | 2.63083 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13285.9 | 0.706741 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14440.0 | 0.764889 | 0.382444 | − | 0.923979i | \(-0.375082\pi\) | ||||
0.382444 | + | 0.923979i | \(0.375082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4589.05 | 0.241040 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1910.28 | −0.0999166 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24213.5 | 1.25593 | 0.627964 | − | 0.778242i | \(-0.283888\pi\) | ||||
0.627964 | + | 0.778242i | \(0.283888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3344.31 | −0.172744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −831.567 | −0.0425981 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10688.4 | −0.545271 | −0.272636 | − | 0.962117i | \(-0.587895\pi\) | ||||
−0.272636 | + | 0.962117i | \(0.587895\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2926.88 | 0.148091 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18715.7 | −0.943085 | −0.471542 | − | 0.881843i | \(-0.656303\pi\) | ||||
−0.471542 | + | 0.881843i | \(0.656303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −98.2788 | −0.00491200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13155.2 | 0.654832 | 0.327416 | − | 0.944880i | \(-0.393822\pi\) | ||||
0.327416 | + | 0.944880i | \(0.393822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20680.3 | 1.02111 | 0.510557 | − | 0.859844i | \(-0.329439\pi\) | ||||
0.510557 | + | 0.859844i | \(0.329439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4981.60 | 0.244982 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20045.9 | 0.977921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −76.2198 | −0.00370346 | −0.00185173 | − | 0.999998i | \(-0.500589\pi\) | ||||
−0.00185173 | + | 0.999998i | \(0.500589\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17435.7 | −0.840463 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15781.3 | 0.757701 | 0.378851 | − | 0.925458i | \(-0.376319\pi\) | ||||
0.378851 | + | 0.925458i | \(0.376319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32298.0 | −1.53851 | −0.769253 | − | 0.638944i | \(-0.779371\pi\) | ||||
−0.769253 | + | 0.638944i | \(0.779371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26623.4 | −1.26321 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30506.2 | −1.43613 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6530.51 | −0.306237 | −0.153119 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153119 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8952.60 | 0.416562 | 0.208281 | − | 0.978069i | \(-0.433213\pi\) | ||||
0.208281 | + | 0.978069i | \(0.433213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3106.86 | −0.144002 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 56803.2 | 2.61256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9543.75 | −0.437263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8929.93 | −0.406016 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15275.5 | −0.691886 | −0.345943 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345943 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12974.5 | −0.583211 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32412.1 | −1.45143 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42475.4 | −1.88777 | −0.943887 | − | 0.330267i | \(-0.892861\pi\) | ||||
−0.943887 | + | 0.330267i | \(0.892861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14960.5 | −0.662408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −998.197 | −0.0438675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4577.07 | −0.200398 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39893.7 | 1.73373 | 0.866864 | − | 0.498544i | \(-0.166132\pi\) | ||||
0.866864 | + | 0.498544i | \(0.166132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8645.69 | −0.374342 | −0.187171 | − | 0.982327i | \(-0.559932\pi\) | ||||
−0.187171 | + | 0.982327i | \(0.559932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1981.18 | −0.0851508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5425.14 | 0.232315 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42123.4 | 1.79064 | 0.895320 | − | 0.445424i | \(-0.146947\pi\) | ||||
0.895320 | + | 0.445424i | \(0.146947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17950.5 | 0.760287 | 0.380143 | − | 0.924928i | \(-0.375875\pi\) | ||||
0.380143 | + | 0.924928i | \(0.375875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19430.2 | −0.816994 | −0.408497 | − | 0.912760i | \(-0.633947\pi\) | ||||
−0.408497 | + | 0.912760i | \(0.633947\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23552.0 | −0.986724 | −0.493362 | − | 0.869824i | \(-0.664232\pi\) | ||||
−0.493362 | + | 0.869824i | \(0.664232\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16378.8 | −0.681261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8747.42 | −0.362535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15526.2 | −0.638883 | −0.319442 | − | 0.947606i | \(-0.603495\pi\) | ||||
−0.319442 | + | 0.947606i | \(0.603495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23282.6 | −0.954635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −48.0977 | −0.00195812 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31341.2 | −1.27142 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16196.4 | 0.652417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6582.11 | −0.264205 | −0.132103 | − | 0.991236i | \(-0.542173\pi\) | ||||
−0.132103 | + | 0.991236i | \(0.542173\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41261.8 | −1.64466 | −0.822332 | − | 0.569009i | \(-0.807327\pi\) | ||||
−0.822332 | + | 0.569009i | \(0.807327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2460.09 | −0.0977149 | −0.0488575 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488575 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38478.8 | −1.51777 | −0.758884 | − | 0.651226i | \(-0.774255\pi\) | ||||
−0.758884 | + | 0.651226i | \(0.774255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14994.8 | 0.589408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3607.95 | −0.140842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 562.675 | 0.0218892 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3098.75 | 0.119722 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28139.7 | 1.08348 | 0.541739 | − | 0.840547i | \(-0.317766\pi\) | ||||
0.541739 | + | 0.840547i | \(0.317766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14885.8 | −0.569257 | −0.284629 | − | 0.958638i | \(-0.591870\pi\) | ||||
−0.284629 | + | 0.958638i | \(0.591870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22144.8 | −0.843979 | −0.421989 | − | 0.906601i | \(-0.638668\pi\) | ||||
−0.421989 | + | 0.906601i | \(0.638668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24626.1 | −0.932202 | −0.466101 | − | 0.884732i | \(-0.654342\pi\) | ||||
−0.466101 | + | 0.884732i | \(0.654342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2844.14 | −0.107300 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27730.1 | −1.03914 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3413.75 | −0.127496 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4133.69 | 0.153355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19325.9 | −0.714583 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 296.972 | 0.0109079 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18461.8 | −0.675871 | −0.337935 | − | 0.941169i | \(-0.609729\pi\) | ||||
−0.337935 | + | 0.941169i | \(0.609729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44797.5 | 1.62921 | 0.814603 | − | 0.580018i | \(-0.196955\pi\) | ||||
0.814603 | + | 0.580018i | \(0.196955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3501.05 | −0.126909 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12372.0 | 0.445540 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46730.6 | −1.67737 | −0.838684 | − | 0.544618i | \(-0.816675\pi\) | ||||
−0.838684 | + | 0.544618i | \(0.816675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54640.7 | 1.94856 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10965.2 | −0.389767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8092.99 | −0.285815 | −0.142908 | − | 0.989736i | \(-0.545645\pi\) | ||||
−0.142908 | + | 0.989736i | \(0.545645\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30359.0 | −1.06872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2463.64 | −0.0861706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40337.2 | −1.40636 | −0.703180 | − | 0.711012i | \(-0.748237\pi\) | ||||
−0.703180 | + | 0.711012i | \(0.748237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17800.7 | 0.616668 | 0.308334 | − | 0.951278i | \(-0.400229\pi\) | ||||
0.308334 | + | 0.951278i | \(0.400229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18761.4 | 0.647886 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3077.80 | −0.105612 | −0.0528062 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528062 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5714.97 | 0.195486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15297.9 | −0.519986 | −0.259993 | − | 0.965611i | \(-0.583720\pi\) | ||||
−0.259993 | + | 0.965611i | \(0.583720\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18090.6 | −0.612983 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46788.2 | 1.57546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14346.9 | −0.481585 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7681.85 | 0.256257 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22338.3 | −0.742865 | −0.371433 | − | 0.928460i | \(-0.621133\pi\) | ||||
−0.371433 | + | 0.928460i | \(0.621133\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14686.2 | 0.485378 | 0.242689 | − | 0.970104i | \(-0.421970\pi\) | ||||
0.242689 | + | 0.970104i | \(0.421970\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44247.6 | −1.45788 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31945.7 | −1.04609 | −0.523047 | − | 0.852304i | \(-0.675205\pi\) | ||||
−0.523047 | + | 0.852304i | \(0.675205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12655.6 | 0.413151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18534.7 | −0.601389 | −0.300694 | − | 0.953721i | \(-0.597218\pi\) | ||||
−0.300694 | + | 0.953721i | \(0.597218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −682.354 | −0.0220727 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1791.86 | 0.0576116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31869.1 | −1.02155 | −0.510775 | − | 0.859714i | \(-0.670641\pi\) | ||||
−0.510775 | + | 0.859714i | \(0.670641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −616.275 | −0.0196354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7832.72 | 0.248811 | 0.124406 | − | 0.992231i | \(-0.460298\pi\) | ||||
0.124406 | + | 0.992231i | \(0.460298\pi\) | |||||||
\(998\) | 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.l.1.3 | yes | 3 | |
3.2 | odd | 2 | 1080.4.a.f.1.3 | ✓ | 3 | ||
4.3 | odd | 2 | 2160.4.a.bp.1.1 | 3 | |||
12.11 | even | 2 | 2160.4.a.bh.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.f.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.4.a.l.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
2160.4.a.bh.1.1 | 3 | 12.11 | even | 2 | |||
2160.4.a.bp.1.1 | 3 | 4.3 | odd | 2 |