Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2112,4,Mod(1,2112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2112, 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("2112.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.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: | \(124.612033932\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2112.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0000 | 1.72784 | 0.863919 | − | 0.503631i | \(-0.168003\pi\) | ||||
0.863919 | + | 0.503631i | \(0.168003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000 | 0.810716 | 0.405358 | − | 0.914158i | \(-0.367147\pi\) | ||||
0.405358 | + | 0.914158i | \(0.367147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 42.0000 | 0.722957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.0285336 | −0.0142668 | − | 0.999898i | \(-0.504541\pi\) | ||||
−0.0142668 | + | 0.999898i | \(0.504541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72.0000 | 0.869365 | 0.434682 | − | 0.900584i | \(-0.356861\pi\) | ||||
0.434682 | + | 0.900584i | \(0.356861\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.0000 | 0.997567 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −68.0000 | −0.616477 | −0.308239 | − | 0.951309i | \(-0.599740\pi\) | ||||
−0.308239 | + | 0.951309i | \(0.599740\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.000 | 0.880645 | 0.440323 | − | 0.897840i | \(-0.354864\pi\) | ||||
0.440323 | + | 0.897840i | \(0.354864\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 448.000 | 2.16359 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −174.000 | −0.773120 | −0.386560 | − | 0.922264i | \(-0.626337\pi\) | ||||
−0.386560 | + | 0.922264i | \(0.626337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 114.000 | 0.468067 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94.0000 | 0.358057 | 0.179028 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179028 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −528.000 | −1.87254 | −0.936270 | − | 0.351280i | \(-0.885746\pi\) | ||||
−0.936270 | + | 0.351280i | \(0.885746\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 126.000 | 0.417399 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 340.000 | 1.05519 | 0.527597 | − | 0.849495i | \(-0.323093\pi\) | ||||
0.527597 | + | 0.849495i | \(0.323093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 681.000 | 1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | −0.0164739 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 438.000 | 1.13517 | 0.567584 | − | 0.823315i | \(-0.307878\pi\) | ||||
0.567584 | + | 0.823315i | \(0.307878\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −154.000 | −0.377552 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 216.000 | 0.501928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20.0000 | 0.0441318 | 0.0220659 | − | 0.999757i | \(-0.492976\pi\) | ||||
0.0220659 | + | 0.999757i | \(0.492976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −570.000 | −1.19641 | −0.598205 | − | 0.801343i | \(-0.704119\pi\) | ||||
−0.598205 | + | 0.801343i | \(0.704119\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 288.000 | 0.575946 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 532.000 | 1.01518 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −460.000 | −0.838775 | −0.419388 | − | 0.907807i | \(-0.637755\pi\) | ||||
−0.419388 | + | 0.907807i | \(0.637755\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −204.000 | −0.355923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1092.00 | 1.82530 | 0.912652 | − | 0.408738i | \(-0.134031\pi\) | ||||
0.912652 | + | 0.408738i | \(0.134031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 562.000 | 0.901057 | 0.450528 | − | 0.892762i | \(-0.351236\pi\) | ||||
0.450528 | + | 0.892762i | \(0.351236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 213.000 | 0.327935 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −352.000 | −0.520963 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.0000 | 0.0227866 | 0.0113933 | − | 0.999935i | \(-0.496373\pi\) | ||||
0.0113933 | + | 0.999935i | \(0.496373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 372.000 | 0.491955 | 0.245978 | − | 0.969275i | \(-0.420891\pi\) | ||||
0.245978 | + | 0.969275i | \(0.420891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.0000 | −0.0357297 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 162.000 | 0.199635 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −966.000 | −1.15051 | −0.575257 | − | 0.817973i | \(-0.695098\pi\) | ||||
−0.575257 | + | 0.817973i | \(0.695098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1216.00 | 1.40079 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 456.000 | 0.508441 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1008.00 | 1.08862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −526.000 | −0.550590 | −0.275295 | − | 0.961360i | \(-0.588775\pi\) | ||||
−0.275295 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −50.0000 | −0.0492593 | −0.0246296 | − | 0.999697i | \(-0.507841\pi\) | ||||
−0.0246296 | + | 0.999697i | \(0.507841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −944.000 | −0.903059 | −0.451530 | − | 0.892256i | \(-0.649121\pi\) | ||||
−0.451530 | + | 0.892256i | \(0.649121\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1344.00 | 1.24915 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 468.000 | 0.422834 | 0.211417 | − | 0.977396i | \(-0.432192\pi\) | ||||
0.211417 | + | 0.977396i | \(0.432192\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −154.000 | −0.135326 | −0.0676630 | − | 0.997708i | \(-0.521554\pi\) | ||||
−0.0676630 | + | 0.997708i | \(0.521554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −522.000 | −0.446361 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −54.0000 | −0.0449548 | −0.0224774 | − | 0.999747i | \(-0.507155\pi\) | ||||
−0.0224774 | + | 0.999747i | \(0.507155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −952.000 | −0.771952 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 342.000 | 0.270239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −64.0000 | −0.0493014 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 282.000 | 0.206724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2224.00 | 1.55392 | 0.776961 | − | 0.629549i | \(-0.216760\pi\) | ||||
0.776961 | + | 0.629549i | \(0.216760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1584.00 | −1.08111 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2772.00 | −1.84878 | −0.924392 | − | 0.381443i | \(-0.875427\pi\) | ||||
−0.924392 | + | 0.381443i | \(0.875427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2304.00 | 1.50212 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 378.000 | 0.240986 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1130.00 | 0.704689 | 0.352345 | − | 0.935870i | \(-0.385385\pi\) | ||||
0.352345 | + | 0.935870i | \(0.385385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1616.00 | −0.986096 | −0.493048 | − | 0.870002i | \(-0.664117\pi\) | ||||
−0.493048 | + | 0.870002i | \(0.664117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1020.00 | 0.609216 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −418.000 | −0.244440 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 756.000 | 0.432982 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2043.00 | 1.14628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2066.00 | −1.13593 | −0.567964 | − | 0.823053i | \(-0.692269\pi\) | ||||
−0.567964 | + | 0.823053i | \(0.692269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −248.000 | −0.133655 | −0.0668277 | − | 0.997765i | \(-0.521288\pi\) | ||||
−0.0668277 | + | 0.997765i | \(0.521288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.0000 | −0.00951120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2128.00 | 1.10274 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2366.00 | −1.20272 | −0.601361 | − | 0.798977i | \(-0.705375\pi\) | ||||
−0.601361 | + | 0.798977i | \(0.705375\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1314.00 | 0.655390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2176.00 | −1.06517 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −284.000 | −0.136470 | −0.0682350 | − | 0.997669i | \(-0.521737\pi\) | ||||
−0.0682350 | + | 0.997669i | \(0.521737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −462.000 | −0.217980 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −600.000 | −0.278020 | −0.139010 | − | 0.990291i | \(-0.544392\pi\) | ||||
−0.139010 | + | 0.990291i | \(0.544392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.000 | −0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 648.000 | 0.289788 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −138.000 | −0.0606471 | −0.0303235 | − | 0.999540i | \(-0.509654\pi\) | ||||
−0.0303235 | + | 0.999540i | \(0.509654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2272.00 | 0.981412 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 60.0000 | 0.0254795 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3972.00 | 1.65855 | 0.829277 | − | 0.558838i | \(-0.188752\pi\) | ||||
0.829277 | + | 0.558838i | \(0.188752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2230.00 | −0.915771 | −0.457886 | − | 0.889011i | \(-0.651393\pi\) | ||||
−0.457886 | + | 0.889011i | \(0.651393\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1710.00 | −0.690748 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2436.00 | −0.968099 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.0000 | 0.00860320 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 772.000 | 0.292461 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 394.000 | 0.146947 | 0.0734734 | − | 0.997297i | \(-0.476592\pi\) | ||||
0.0734734 | + | 0.997297i | \(0.476592\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1596.00 | 0.586112 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3058.00 | −1.10596 | −0.552978 | − | 0.833196i | \(-0.686509\pi\) | ||||
−0.552978 | + | 0.833196i | \(0.686509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2664.00 | −0.948975 | −0.474487 | − | 0.880262i | \(-0.657367\pi\) | ||||
−0.474487 | + | 0.880262i | \(0.657367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1380.00 | −0.484267 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1728.00 | 0.597447 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1316.00 | 0.448358 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −612.000 | −0.205492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −792.000 | −0.262123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6000.00 | −1.95762 | −0.978808 | − | 0.204779i | \(-0.934352\pi\) | ||||
−0.978808 | + | 0.204779i | \(0.934352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3276.00 | 1.05384 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7392.00 | −2.34479 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4864.00 | 1.52161 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1686.00 | 0.520225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −76.0000 | −0.0231326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 560.000 | 0.168163 | 0.0840816 | − | 0.996459i | \(-0.473204\pi\) | ||||
0.0840816 | + | 0.996459i | \(0.473204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 639.000 | 0.189333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5292.00 | 1.54732 | 0.773662 | − | 0.633599i | \(-0.218423\pi\) | ||||
0.773662 | + | 0.633599i | \(0.218423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5322.00 | 1.53575 | 0.767877 | − | 0.640597i | \(-0.221313\pi\) | ||||
0.767877 | + | 0.640597i | \(0.221313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1056.00 | −0.300778 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3954.00 | −1.11174 | −0.555869 | − | 0.831270i | \(-0.687615\pi\) | ||||
−0.555869 | + | 0.831270i | \(0.687615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4760.00 | 1.32131 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 48.0000 | 0.0131558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3360.00 | 0.909374 | 0.454687 | − | 0.890651i | \(-0.349751\pi\) | ||||
0.454687 | + | 0.890651i | \(0.349751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3278.00 | −0.876160 | −0.438080 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438080 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9534.00 | 2.48614 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2736.00 | 0.704808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1116.00 | 0.284031 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2092.00 | 0.526079 | 0.263040 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263040 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 748.000 | 0.185875 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −84.0000 | −0.0206286 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 658.000 | 0.159708 | 0.0798539 | − | 0.996807i | \(-0.474555\pi\) | ||||
0.0798539 | + | 0.996807i | \(0.474555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5568.00 | −1.33583 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 486.000 | 0.115259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5104.00 | 1.19668 | 0.598339 | − | 0.801243i | \(-0.295828\pi\) | ||||
0.598339 | + | 0.801243i | \(0.295828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6132.00 | 1.42146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2898.00 | −0.664250 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4238.00 | 0.960578 | 0.480289 | − | 0.877110i | \(-0.340532\pi\) | ||||
0.480289 | + | 0.877110i | \(0.340532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3376.00 | 0.756743 | 0.378372 | − | 0.925654i | \(-0.376484\pi\) | ||||
0.378372 | + | 0.925654i | \(0.376484\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3648.00 | 0.808744 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −781.000 | −0.171258 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2074.00 | −0.449872 | −0.224936 | − | 0.974374i | \(-0.572217\pi\) | ||||
−0.224936 | + | 0.974374i | \(0.572217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1368.00 | 0.293548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 702.000 | 0.149031 | 0.0745157 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745157 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4912.00 | 1.03176 | 0.515880 | − | 0.856661i | \(-0.327465\pi\) | ||||
0.515880 | + | 0.856661i | \(0.327465\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3024.00 | 0.628513 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3008.00 | 0.618664 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4909.00 | −0.999186 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1578.00 | −0.317883 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3486.00 | 0.695066 | 0.347533 | − | 0.937668i | \(-0.387019\pi\) | ||||
0.347533 | + | 0.937668i | \(0.387019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 280.000 | 0.0552618 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2584.00 | −0.499788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16896.0 | −3.23545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −150.000 | −0.0284399 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7980.00 | −1.49814 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8360.00 | 1.55417 | 0.777085 | − | 0.629395i | \(-0.216697\pi\) | ||||
0.777085 | + | 0.629395i | \(0.216697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2832.00 | −0.521381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5532.00 | 1.00865 | 0.504326 | − | 0.863513i | \(-0.331741\pi\) | ||||
0.504326 | + | 0.863513i | \(0.331741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4826.00 | 0.871507 | 0.435753 | − | 0.900066i | \(-0.356482\pi\) | ||||
0.435753 | + | 0.900066i | \(0.356482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4032.00 | 0.721198 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7570.00 | −1.34124 | −0.670621 | − | 0.741800i | \(-0.733972\pi\) | ||||
−0.670621 | + | 0.741800i | \(0.733972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −594.000 | −0.104256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1404.00 | 0.244123 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −144.000 | −0.0248061 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2698.00 | 0.460487 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −462.000 | −0.0781305 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10880.0 | 1.82320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3676.00 | 0.610427 | 0.305213 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305213 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1566.00 | −0.257707 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6440.00 | −1.05031 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5686.00 | −0.919098 | −0.459549 | − | 0.888152i | \(-0.651989\pi\) | ||||
−0.459549 | + | 0.888152i | \(0.651989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −162.000 | −0.0259547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1672.00 | −0.265525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10816.0 | 1.70265 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2856.00 | −0.445687 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1652.00 | −0.255574 | −0.127787 | − | 0.991802i | \(-0.540787\pi\) | ||||
−0.127787 | + | 0.991802i | \(0.540787\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6990.00 | 1.07211 | 0.536055 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536055 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1026.00 | 0.156022 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8094.00 | −1.22040 | −0.610199 | − | 0.792249i | \(-0.708910\pi\) | ||||
−0.610199 | + | 0.792249i | \(0.708910\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15288.0 | 2.28564 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −192.000 | −0.0284642 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1024.00 | −0.150542 | −0.0752711 | − | 0.997163i | \(-0.523982\pi\) | ||||
−0.0752711 | + | 0.997163i | \(0.523982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1675.00 | −0.244205 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7868.00 | 1.12830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13664.0 | 1.94347 | 0.971737 | − | 0.236066i | \(-0.0758581\pi\) | ||||
0.971737 | + | 0.236066i | \(0.0758581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 846.000 | 0.119352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14016.0 | 1.96139 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1958.00 | 0.271800 | 0.135900 | − | 0.990723i | \(-0.456607\pi\) | ||||
0.135900 | + | 0.990723i | \(0.456607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2268.00 | −0.312317 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2052.00 | 0.280327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6124.00 | 0.829997 | 0.414998 | − | 0.909822i | \(-0.363782\pi\) | ||||
0.414998 | + | 0.909822i | \(0.363782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6672.00 | 0.897157 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5612.00 | −0.748720 | −0.374360 | − | 0.927283i | \(-0.622138\pi\) | ||||
−0.374360 | + | 0.927283i | \(0.622138\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4928.00 | −0.652348 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4752.00 | −0.624180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12450.0 | −1.62273 | −0.811363 | − | 0.584543i | \(-0.801274\pi\) | ||||
−0.811363 | + | 0.584543i | \(0.801274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 136.000 | 0.0175903 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8316.00 | −1.06740 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 224.000 | 0.0285333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14830.0 | −1.87480 | −0.937401 | − | 0.348252i | \(-0.886775\pi\) | ||||
−0.937401 | + | 0.348252i | \(0.886775\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6912.00 | 0.867250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3358.00 | −0.418181 | −0.209090 | − | 0.977896i | \(-0.567050\pi\) | ||||
−0.209090 | + | 0.977896i | \(0.567050\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5776.00 | 0.713953 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1134.00 | 0.139133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1914.00 | 0.233104 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10698.0 | 1.29335 | 0.646677 | − | 0.762764i | \(-0.276158\pi\) | ||||
0.646677 | + | 0.762764i | \(0.276158\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3390.00 | 0.406852 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 640.000 | 0.0762526 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5208.00 | 0.616026 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4848.00 | −0.569323 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2044.00 | −0.238320 | −0.119160 | − | 0.992875i | \(-0.538020\pi\) | ||||
−0.119160 | + | 0.992875i | \(0.538020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3070.00 | −0.355398 | −0.177699 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177699 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3060.00 | 0.351731 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −142.000 | −0.0162071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18240.0 | −2.06720 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1254.00 | −0.141127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12600.0 | 1.40817 | 0.704084 | − | 0.710116i | \(-0.251358\pi\) | ||||
0.704084 | + | 0.710116i | \(0.251358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9902.00 | −1.09898 | −0.549492 | − | 0.835499i | \(-0.685179\pi\) | ||||
−0.549492 | + | 0.835499i | \(0.685179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2268.00 | 0.249982 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4896.00 | −0.535944 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11440.0 | −1.24374 | −0.621869 | − | 0.783121i | \(-0.713627\pi\) | ||||
−0.621869 | + | 0.783121i | \(0.713627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5180.00 | −0.555551 | −0.277776 | − | 0.960646i | \(-0.589597\pi\) | ||||
−0.277776 | + | 0.960646i | \(0.589597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13524.0 | −1.44067 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6198.00 | −0.655829 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10826.0 | 1.13789 | 0.568943 | − | 0.822377i | \(-0.307353\pi\) | ||||
0.568943 | + | 0.822377i | \(0.307353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1034.00 | −0.107958 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −744.000 | −0.0771659 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17024.0 | 1.75406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15798.0 | −1.61707 | −0.808533 | − | 0.588451i | \(-0.799738\pi\) | ||||
−0.808533 | + | 0.588451i | \(0.799738\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −54.0000 | −0.00549129 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3894.00 | 0.393409 | 0.196705 | − | 0.980463i | \(-0.436976\pi\) | ||||
0.196705 | + | 0.980463i | \(0.436976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15992.0 | 1.60521 | 0.802604 | − | 0.596512i | \(-0.203447\pi\) | ||||
0.802604 | + | 0.596512i | \(0.203447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6384.00 | 0.636669 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11844.0 | 1.17361 | 0.586804 | − | 0.809729i | \(-0.300386\pi\) | ||||
0.586804 | + | 0.809729i | \(0.300386\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14720.0 | −1.44927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7098.00 | −0.694392 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5808.00 | 0.564592 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5112.00 | 0.493799 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3942.00 | 0.378389 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14936.0 | −1.42472 | −0.712362 | − | 0.701812i | \(-0.752375\pi\) | ||||
−0.712362 | + | 0.701812i | \(0.752375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6612.00 | −0.626780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6528.00 | −0.614978 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7364.00 | −0.689447 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2056.00 | 0.191306 | 0.0956532 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956532 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −852.000 | −0.0787909 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17852.0 | −1.64083 | −0.820417 | − | 0.571766i | \(-0.806259\pi\) | ||||
−0.820417 | + | 0.571766i | \(0.806259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −108.000 | −0.00986628 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1386.00 | −0.125851 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34944.0 | 3.15383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4508.00 | 0.404420 | 0.202210 | − | 0.979342i | \(-0.435188\pi\) | ||||
0.202210 | + | 0.979342i | \(0.435188\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1800.00 | −0.160515 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5912.00 | 0.524062 | 0.262031 | − | 0.965059i | \(-0.415608\pi\) | ||||
0.262031 | + | 0.965059i | \(0.415608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −700.000 | −0.0616824 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2259.00 | −0.197881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11406.0 | 0.993246 | 0.496623 | − | 0.867966i | \(-0.334573\pi\) | ||||
0.496623 | + | 0.867966i | \(0.334573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17984.0 | 1.55688 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1944.00 | 0.167309 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13216.0 | −1.13081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3740.00 | −0.318153 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −414.000 | −0.0350146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1542.00 | −0.129667 | −0.0648333 | − | 0.997896i | \(-0.520652\pi\) | ||||
−0.0648333 | + | 0.997896i | \(0.520652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7504.00 | −0.627394 | −0.313697 | − | 0.949523i | \(-0.601568\pi\) | ||||
−0.313697 | + | 0.949523i | \(0.601568\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6816.00 | 0.566618 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −304.000 | −0.0251280 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7543.00 | −0.619956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 180.000 | 0.0147106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3572.00 | 0.290282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6552.00 | 0.529472 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11916.0 | 0.957567 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7491.00 | −0.598627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1018.00 | −0.0809006 | −0.0404503 | − | 0.999182i | \(-0.512879\pi\) | ||||
−0.0404503 | + | 0.999182i | \(0.512879\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6690.00 | −0.528721 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2156.00 | −0.169455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7904.00 | 0.617826 | 0.308913 | − | 0.951090i | \(-0.400035\pi\) | ||||
0.308913 | + | 0.951090i | \(0.400035\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5130.00 | −0.398803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3888.00 | 0.300607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 512.000 | 0.0393715 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7308.00 | −0.558932 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22934.0 | 1.74460 | 0.872302 | − | 0.488967i | \(-0.162626\pi\) | ||||
0.872302 | + | 0.488967i | \(0.162626\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20064.0 | −1.51810 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 66.0000 | 0.00496706 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14020.0 | 1.04951 | 0.524754 | − | 0.851254i | \(-0.324157\pi\) | ||||
0.524754 | + | 0.851254i | \(0.324157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −756.000 | −0.0562923 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2592.00 | 0.191982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4230.00 | 0.311653 | 0.155827 | − | 0.987784i | \(-0.450196\pi\) | ||||
0.155827 | + | 0.987784i | \(0.450196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8536.00 | −0.625605 | −0.312803 | − | 0.949818i | \(-0.601268\pi\) | ||||
−0.312803 | + | 0.949818i | \(0.601268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2316.00 | 0.168852 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4828.00 | −0.350159 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11982.0 | −0.864501 | −0.432251 | − | 0.901754i | \(-0.642280\pi\) | ||||
−0.432251 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1182.00 | 0.0848398 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11904.0 | 0.850019 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4818.00 | −0.342266 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4788.00 | 0.338392 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20396.0 | −1.43413 | −0.717064 | − | 0.697007i | \(-0.754514\pi\) | ||||
−0.717064 | + | 0.697007i | \(0.754514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10944.0 | 0.765602 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9174.00 | −0.638524 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12518.0 | 0.866868 | 0.433434 | − | 0.901185i | \(-0.357302\pi\) | ||||
0.433434 | + | 0.901185i | \(0.357302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −896.000 | −0.0617352 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7992.00 | −0.547891 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25292.0 | 1.72521 | 0.862607 | − | 0.505875i | \(-0.168830\pi\) | ||||
0.862607 | + | 0.505875i | \(0.168830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15962.0 | 1.08337 | 0.541683 | − | 0.840583i | \(-0.317787\pi\) | ||||
0.541683 | + | 0.840583i | \(0.317787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4140.00 | −0.279592 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1694.00 | 0.113836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1600.00 | 0.106988 | 0.0534942 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534942 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5184.00 | 0.344936 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12920.0 | 0.855462 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2162.00 | −0.142451 | −0.0712254 | − | 0.997460i | \(-0.522691\pi\) | ||||
−0.0712254 | + | 0.997460i | \(0.522691\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3948.00 | 0.258860 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18126.0 | −1.18270 | −0.591350 | − | 0.806415i | \(-0.701405\pi\) | ||||
−0.591350 | + | 0.806415i | \(0.701405\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17348.0 | 1.12645 | 0.563227 | − | 0.826302i | \(-0.309560\pi\) | ||||
0.563227 | + | 0.826302i | \(0.309560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1836.00 | −0.118641 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30912.0 | −1.98790 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2376.00 | −0.151337 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 348.000 | 0.0220599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10096.0 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18000.0 | −1.13023 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31136.0 | 1.94582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25878.0 | 1.60961 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9828.00 | 0.608435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8922.00 | 0.549763 | 0.274881 | − | 0.961478i | \(-0.411361\pi\) | ||||
0.274881 | + | 0.961478i | \(0.411361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14644.0 | −0.898138 | −0.449069 | − | 0.893497i | \(-0.648244\pi\) | ||||
−0.449069 | + | 0.893497i | \(0.648244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22176.0 | −1.35377 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6932.00 | −0.421213 | −0.210607 | − | 0.977571i | \(-0.567544\pi\) | ||||
−0.210607 | + | 0.977571i | \(0.567544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −220.000 | −0.0133062 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14592.0 | 0.878503 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5942.00 | 0.356093 | 0.178046 | − | 0.984022i | \(-0.443022\pi\) | ||||
0.178046 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38808.0 | −2.31504 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5058.00 | 0.300352 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 484.000 | 0.0286100 | 0.0143050 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143050 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17114.0 | 1.00705 | 0.503523 | − | 0.863982i | \(-0.332037\pi\) | ||||
0.503523 | + | 0.863982i | \(0.332037\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −228.000 | −0.0133556 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32256.0 | 1.88095 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3672.00 | −0.213164 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1680.00 | 0.0970890 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6270.00 | 0.360731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16154.0 | 0.925247 | 0.462623 | − | 0.886555i | \(-0.346908\pi\) | ||||
0.462623 | + | 0.886555i | \(0.346908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1917.00 | 0.109312 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3390.00 | 0.192449 | 0.0962247 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962247 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16832.0 | −0.951330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15876.0 | 0.893347 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25540.0 | −1.43084 | −0.715418 | − | 0.698697i | \(-0.753764\pi\) | ||||
−0.715418 | + | 0.698697i | \(0.753764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15820.0 | 0.882410 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15966.0 | 0.886668 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16644.0 | 0.920299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12476.0 | 0.686844 | 0.343422 | − | 0.939181i | \(-0.388414\pi\) | ||||
0.343422 | + | 0.939181i | \(0.388414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3168.00 | −0.173654 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22624.0 | −1.23479 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −188.000 | −0.0102167 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11862.0 | −0.641863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20806.0 | 1.12102 | 0.560508 | − | 0.828149i | \(-0.310606\pi\) | ||||
0.560508 | + | 0.828149i | \(0.310606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12528.0 | −0.672123 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14280.0 | 0.762859 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1600.00 | −0.0851120 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14198.0 | −0.752069 | −0.376035 | − | 0.926606i | \(-0.622713\pi\) | ||||
−0.376035 | + | 0.926606i | \(0.622713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 144.000 | 0.00759553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10336.0 | −0.542898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5852.00 | −0.306087 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10080.0 | 0.525027 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4596.00 | −0.238389 | −0.119195 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119195 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30208.0 | −1.56034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9834.00 | −0.505851 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3834.00 | 0.196402 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19560.0 | −0.997855 | −0.498927 | − | 0.866644i | \(-0.666273\pi\) | ||||
−0.498927 | + | 0.866644i | \(0.666273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1056.00 | 0.0534303 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1638.00 | 0.0825388 | 0.0412694 | − | 0.999148i | \(-0.486860\pi\) | ||||
0.0412694 | + | 0.999148i | \(0.486860\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28602.0 | 1.43538 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5060.00 | 0.252900 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15592.0 | −0.776131 | −0.388066 | − | 0.921632i | \(-0.626857\pi\) | ||||
−0.388066 | + | 0.921632i | \(0.626857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8208.00 | 0.406921 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −592.000 | −0.0292307 | −0.0146153 | − | 0.999893i | \(-0.504652\pi\) | ||||
−0.0146153 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28924.0 | −1.42241 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3348.00 | 0.163985 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14976.0 | 0.730589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39832.0 | −1.93541 | −0.967703 | − | 0.252092i | \(-0.918881\pi\) | ||||
−0.967703 | + | 0.252092i | \(0.918881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6276.00 | 0.303732 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3472.00 | −0.167363 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10958.0 | −0.526123 | −0.263062 | − | 0.964779i | \(-0.584732\pi\) | ||||
−0.263062 | + | 0.964779i | \(0.584732\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2244.00 | 0.107315 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8970.00 | −0.427283 | −0.213641 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213641 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4928.00 | −0.233821 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −252.000 | −0.0119099 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 760.000 | 0.0357784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10054.0 | −0.471465 | −0.235732 | − | 0.971818i | \(-0.575749\pi\) | ||||
−0.235732 | + | 0.971818i | \(0.575749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1974.00 | 0.0922074 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26346.0 | −1.22587 | −0.612936 | − | 0.790132i | \(-0.710012\pi\) | ||||
−0.612936 | + | 0.790132i | \(0.710012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10792.0 | 0.500207 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16704.0 | −0.771239 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6768.00 | 0.311282 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12012.0 | −0.550350 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1458.00 | 0.0665449 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33124.0 | −1.50605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16040.0 | −0.726511 | −0.363256 | − | 0.931690i | \(-0.618335\pi\) | ||||
−0.363256 | + | 0.931690i | \(0.618335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15312.0 | 0.690902 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1728.00 | −0.0776746 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21660.0 | −0.969948 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18396.0 | 0.820678 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32810.0 | −1.45821 | −0.729103 | − | 0.684404i | \(-0.760062\pi\) | ||||
−0.729103 | + | 0.684404i | \(0.760062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −680.000 | −0.0301085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8694.00 | −0.383505 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6182.00 | −0.271679 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30464.0 | −1.33381 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12714.0 | 0.554590 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18918.0 | 0.822153 | 0.411076 | − | 0.911601i | \(-0.365153\pi\) | ||||
0.411076 | + | 0.911601i | \(0.365153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8552.00 | −0.370285 | −0.185143 | − | 0.982712i | \(-0.559275\pi\) | ||||
−0.185143 | + | 0.982712i | \(0.559275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10128.0 | 0.436906 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3976.00 | −0.170887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38016.0 | −1.62792 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10944.0 | 0.466928 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46430.0 | 1.97371 | 0.986856 | − | 0.161600i | \(-0.0516654\pi\) | ||||
0.986856 | + | 0.161600i | \(0.0516654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16392.0 | −0.694276 | −0.347138 | − | 0.937814i | \(-0.612846\pi\) | ||||
−0.347138 | + | 0.937814i | \(0.612846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2343.00 | −0.0988761 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13876.0 | −0.583453 | −0.291727 | − | 0.956502i | \(-0.594230\pi\) | ||||
−0.291727 | + | 0.956502i | \(0.594230\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24554.0 | 1.02870 | 0.514352 | − | 0.857579i | \(-0.328032\pi\) | ||||
0.514352 | + | 0.857579i | \(0.328032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6222.00 | −0.259734 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1362.00 | −0.0566513 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8400.00 | −0.348137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4104.00 | 0.169480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19900.0 | −0.818861 | −0.409430 | − | 0.912341i | \(-0.634273\pi\) | ||||
−0.409430 | + | 0.912341i | \(0.634273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2106.00 | 0.0860433 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10542.0 | −0.429178 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3872.00 | 0.157076 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14736.0 | 0.595687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11832.0 | 0.476611 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41138.0 | −1.65128 | −0.825638 | − | 0.564200i | \(-0.809185\pi\) | ||||
−0.825638 | + | 0.564200i | \(0.809185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9072.00 | 0.362872 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19910.0 | 0.793597 | 0.396799 | − | 0.917906i | \(-0.370121\pi\) | ||||
0.396799 | + | 0.917906i | \(0.370121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42924.0 | 1.70495 | 0.852473 | − | 0.522772i | \(-0.175102\pi\) | ||||
0.852473 | + | 0.522772i | \(0.175102\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9024.00 | 0.357186 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46236.0 | 1.82374 | 0.911872 | − | 0.410474i | \(-0.134637\pi\) | ||||
0.911872 | + | 0.410474i | \(0.134637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1932.00 | −0.0759422 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14727.0 | −0.576880 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −176.000 | −0.00687042 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17480.0 | −0.680008 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4734.00 | −0.183530 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24192.0 | −0.934673 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25746.0 | −0.991312 | −0.495656 | − | 0.868519i | \(-0.665072\pi\) | ||||
−0.495656 | + | 0.868519i | \(0.665072\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10458.0 | 0.401296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24550.0 | −0.938831 | −0.469416 | − | 0.882977i | \(-0.655535\pi\) | ||||
−0.469416 | + | 0.882977i | \(0.655535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19436.0 | −0.740740 | −0.370370 | − | 0.928884i | \(-0.620769\pi\) | ||||
−0.370370 | + | 0.928884i | \(0.620769\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 840.000 | 0.0319054 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22912.0 | 0.867316 | 0.433658 | − | 0.901077i | \(-0.357223\pi\) | ||||
0.433658 | + | 0.901077i | \(0.357223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 71168.0 | 2.68492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24480.0 | 0.917348 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55608.0 | 2.07684 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7752.00 | −0.288553 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8208.00 | 0.304507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −876.000 | −0.0323904 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −50688.0 | −1.86799 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31220.0 | −1.14673 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39900.0 | −1.46070 | −0.730352 | − | 0.683071i | \(-0.760644\pi\) | ||||
−0.730352 | + | 0.683071i | \(0.760644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −450.000 | −0.0164198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29460.0 | −1.07141 | −0.535704 | − | 0.844406i | \(-0.679954\pi\) | ||||
−0.535704 | + | 0.844406i | \(0.679954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4092.00 | −0.148330 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23940.0 | −0.864953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −88704.0 | −3.19440 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29368.0 | −1.05415 | −0.527073 | − | 0.849820i | \(-0.676711\pi\) | ||||
−0.527073 | + | 0.849820i | \(0.676711\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25080.0 | 0.897301 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41496.0 | 1.47980 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12354.0 | −0.439132 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8496.00 | −0.301020 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33954.0 | 1.19913 | 0.599567 | − | 0.800325i | \(-0.295340\pi\) | ||||
0.599567 | + | 0.800325i | \(0.295340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49032.0 | 1.72606 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16596.0 | 0.582346 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 308.000 | 0.0107729 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2854.00 | −0.0995049 | −0.0497525 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497525 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14478.0 | 0.503165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6294.00 | 0.218043 | 0.109022 | − | 0.994039i | \(-0.465228\pi\) | ||||
0.109022 | + | 0.994039i | \(0.465228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6392.00 | −0.220734 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12096.0 | 0.416384 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2268.00 | 0.0778248 | 0.0389124 | − | 0.999243i | \(-0.487611\pi\) | ||||
0.0389124 | + | 0.999243i | \(0.487611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21356.0 | 0.730501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22710.0 | −0.774366 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26566.0 | 0.902998 | 0.451499 | − | 0.892272i | \(-0.350889\pi\) | ||||
0.451499 | + | 0.892272i | \(0.350889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10808.0 | 0.366218 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1782.00 | −0.0601921 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36160.0 | 1.21759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6687.00 | −0.224464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4212.00 | 0.140945 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5516.00 | 0.184007 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11176.0 | −0.371661 | −0.185830 | − | 0.982582i | \(-0.559497\pi\) | ||||
−0.185830 | + | 0.982582i | \(0.559497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −432.000 | −0.0143218 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42316.0 | −1.39854 | −0.699271 | − | 0.714856i | \(-0.746492\pi\) | ||||
−0.699271 | + | 0.714856i | \(0.746492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51712.0 | −1.70381 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8094.00 | 0.265862 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45054.0 | −1.47534 | −0.737669 | − | 0.675163i | \(-0.764073\pi\) | ||||
−0.737669 | + | 0.675163i | \(0.764073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10626.0 | 0.346893 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1386.00 | −0.0451086 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12300.0 | 0.399094 | 0.199547 | − | 0.979888i | \(-0.436053\pi\) | ||||
0.199547 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42812.0 | −1.38488 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32640.0 | 1.05263 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35904.0 | 1.15438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36280.0 | −1.16294 | −0.581469 | − | 0.813568i | \(-0.697522\pi\) | ||||
−0.581469 | + | 0.813568i | \(0.697522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11028.0 | 0.352430 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −37296.0 | −1.18830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3290.00 | −0.104509 | −0.0522544 | − | 0.998634i | \(-0.516641\pi\) | ||||
−0.0522544 | + | 0.998634i | \(0.516641\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4698.00 | −0.148787 |
(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 | 2112.4.a.y.1.1 | 1 | ||
4.3 | odd | 2 | 2112.4.a.l.1.1 | 1 | |||
8.3 | odd | 2 | 33.4.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 528.4.a.a.1.1 | 1 | |||
24.5 | odd | 2 | 1584.4.a.t.1.1 | 1 | |||
24.11 | even | 2 | 99.4.a.b.1.1 | 1 | |||
40.3 | even | 4 | 825.4.c.a.199.2 | 2 | |||
40.19 | odd | 2 | 825.4.a.i.1.1 | 1 | |||
40.27 | even | 4 | 825.4.c.a.199.1 | 2 | |||
56.27 | even | 2 | 1617.4.a.a.1.1 | 1 | |||
88.43 | even | 2 | 363.4.a.h.1.1 | 1 | |||
120.59 | even | 2 | 2475.4.a.b.1.1 | 1 | |||
264.131 | odd | 2 | 1089.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
99.4.a.b.1.1 | 1 | 24.11 | even | 2 | |||
363.4.a.h.1.1 | 1 | 88.43 | even | 2 | |||
528.4.a.a.1.1 | 1 | 8.5 | even | 2 | |||
825.4.a.i.1.1 | 1 | 40.19 | odd | 2 | |||
825.4.c.a.199.1 | 2 | 40.27 | even | 4 | |||
825.4.c.a.199.2 | 2 | 40.3 | even | 4 | |||
1089.4.a.a.1.1 | 1 | 264.131 | odd | 2 | |||
1584.4.a.t.1.1 | 1 | 24.5 | odd | 2 | |||
1617.4.a.a.1.1 | 1 | 56.27 | even | 2 | |||
2112.4.a.l.1.1 | 1 | 4.3 | odd | 2 | |||
2112.4.a.y.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2475.4.a.b.1.1 | 1 | 120.59 | even | 2 |