Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1509.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1932) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.551929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.551929 | −0.246830 | −0.123415 | − | 0.992355i | \(-0.539385\pi\) | ||||
−0.123415 | + | 0.992355i | \(0.539385\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.103859 | 0.0313146 | 0.0156573 | − | 0.999877i | \(-0.495016\pi\) | ||||
0.0156573 | + | 0.999877i | \(0.495016\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.69537 | 1.57961 | 0.789806 | − | 0.613356i | \(-0.210181\pi\) | ||||
0.789806 | + | 0.613356i | \(0.210181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.551929 | −0.142508 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24730 | −1.03012 | −0.515061 | − | 0.857153i | \(-0.672231\pi\) | ||||
−0.515061 | + | 0.857153i | \(0.672231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69537 | −0.939075 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.14344 | 0.212332 | 0.106166 | − | 0.994348i | \(-0.466142\pi\) | ||||
0.106166 | + | 0.994348i | \(0.466142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.24730 | −1.12205 | −0.561024 | − | 0.827799i | \(-0.689593\pi\) | ||||
−0.561024 | + | 0.827799i | \(0.689593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.103859 | 0.0180795 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.551929 | 0.0932931 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.35116 | 0.550928 | 0.275464 | − | 0.961311i | \(-0.411169\pi\) | ||||
0.275464 | + | 0.961311i | \(0.411169\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.69537 | 0.911990 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.28689 | −1.45037 | −0.725184 | − | 0.688555i | \(-0.758245\pi\) | ||||
−0.725184 | + | 0.688555i | \(0.758245\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.799233 | 0.121882 | 0.0609409 | − | 0.998141i | \(-0.480590\pi\) | ||||
0.0609409 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.551929 | −0.0822768 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.14344 | −1.18784 | −0.593922 | − | 0.804523i | \(-0.702421\pi\) | ||||
−0.593922 | + | 0.804523i | \(0.702421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.24730 | −0.594741 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.695374 | 0.0955170 | 0.0477585 | − | 0.998859i | \(-0.484792\pi\) | ||||
0.0477585 | + | 0.998859i | \(0.484792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0573228 | −0.00772940 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.695374 | 0.0905300 | 0.0452650 | − | 0.998975i | \(-0.485587\pi\) | ||||
0.0452650 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.55193 | 0.966925 | 0.483463 | − | 0.875365i | \(-0.339379\pi\) | ||||
0.483463 | + | 0.875365i | \(0.339379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.14344 | −0.389896 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.551929 | 0.0674289 | 0.0337145 | − | 0.999432i | \(-0.489266\pi\) | ||||
0.0337145 | + | 0.999432i | \(0.489266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1900 | −1.44668 | −0.723342 | − | 0.690490i | \(-0.757395\pi\) | ||||
−0.723342 | + | 0.690490i | \(0.757395\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.14344 | −0.367912 | −0.183956 | − | 0.982934i | \(-0.558890\pi\) | ||||
−0.183956 | + | 0.982934i | \(0.558890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.69537 | −0.542175 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.103859 | −0.0118358 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.45502 | −0.951264 | −0.475632 | − | 0.879644i | \(-0.657781\pi\) | ||||
−0.475632 | + | 0.879644i | \(0.657781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.14344 | 0.125509 | 0.0627547 | − | 0.998029i | \(-0.480011\pi\) | ||||
0.0627547 | + | 0.998029i | \(0.480011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.34421 | 0.254265 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.14344 | 0.122590 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.69537 | 1.02771 | 0.513854 | − | 0.857878i | \(-0.328217\pi\) | ||||
0.513854 | + | 0.857878i | \(0.328217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.69537 | −0.597037 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.24730 | −0.647815 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.551929 | 0.0566268 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6381 | 1.79087 | 0.895436 | − | 0.445189i | \(-0.146864\pi\) | ||||
0.895436 | + | 0.445189i | \(0.146864\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.103859 | 0.0104382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2938 | 1.02428 | 0.512138 | − | 0.858903i | \(-0.328854\pi\) | ||||
0.512138 | + | 0.858903i | \(0.328854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2473 | −1.50236 | −0.751181 | − | 0.660097i | \(-0.770515\pi\) | ||||
−0.751181 | + | 0.660097i | \(0.770515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.551929 | 0.0538628 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.7992 | −1.23735 | −0.618674 | − | 0.785648i | \(-0.712330\pi\) | ||||
−0.618674 | + | 0.785648i | \(0.712330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.94268 | −0.760771 | −0.380385 | − | 0.924828i | \(-0.624209\pi\) | ||||
−0.380385 | + | 0.924828i | \(0.624209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.35116 | 0.318078 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.15039 | −0.766725 | −0.383362 | − | 0.923598i | \(-0.625234\pi\) | ||||
−0.383362 | + | 0.923598i | \(0.625234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.551929 | 0.0514677 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.69537 | 0.526538 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.24730 | 0.389350 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9892 | −0.999019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.28689 | −0.837371 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.35116 | 0.478622 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.73496 | 0.597631 | 0.298816 | − | 0.954311i | \(-0.403408\pi\) | ||||
0.298816 | + | 0.954311i | \(0.403408\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.799233 | 0.0703685 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.49461 | 0.305325 | 0.152663 | − | 0.988278i | \(-0.451215\pi\) | ||||
0.152663 | + | 0.988278i | \(0.451215\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.551929 | −0.0475025 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.39075 | 0.375127 | 0.187563 | − | 0.982252i | \(-0.439941\pi\) | ||||
0.187563 | + | 0.982252i | \(0.439941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.34421 | −0.538109 | −0.269055 | − | 0.963125i | \(-0.586711\pi\) | ||||
−0.269055 | + | 0.963125i | \(0.586711\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.14344 | −0.685802 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.591515 | 0.0494650 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.631101 | −0.0524101 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.93573 | −0.486274 | −0.243137 | − | 0.969992i | \(-0.578176\pi\) | ||||
−0.243137 | + | 0.969992i | \(0.578176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.64884 | −0.134181 | −0.0670903 | − | 0.997747i | \(-0.521372\pi\) | ||||
−0.0670903 | + | 0.997747i | \(0.521372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24730 | −0.343374 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.44807 | 0.276956 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.14344 | 0.171065 | 0.0855327 | − | 0.996335i | \(-0.472741\pi\) | ||||
0.0855327 | + | 0.996335i | \(0.472741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.695374 | 0.0551467 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29384 | 0.492972 | 0.246486 | − | 0.969146i | \(-0.420724\pi\) | ||||
0.246486 | + | 0.969146i | \(0.420724\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0573228 | −0.00446257 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.00000 | −0.696441 | −0.348220 | − | 0.937413i | \(-0.613214\pi\) | ||||
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.4373 | 1.49518 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.0288 | −1.29468 | −0.647338 | − | 0.762203i | \(-0.724118\pi\) | ||||
−0.647338 | + | 0.762203i | \(0.724118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.69537 | 0.354937 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.695374 | 0.0522675 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.24035 | 0.0927083 | 0.0463542 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463542 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4303 | 1.44425 | 0.722123 | − | 0.691765i | \(-0.243167\pi\) | ||||
0.722123 | + | 0.691765i | \(0.243167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.55193 | 0.558255 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.84961 | −0.135986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.441120 | −0.0322579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4303 | −1.18886 | −0.594429 | − | 0.804148i | \(-0.702622\pi\) | ||||
−0.594429 | + | 0.804148i | \(0.702622\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6381 | 1.19763 | 0.598817 | − | 0.800886i | \(-0.295638\pi\) | ||||
0.598817 | + | 0.800886i | \(0.295638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.14344 | −0.225107 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7992 | −0.769413 | −0.384707 | − | 0.923039i | \(-0.625697\pi\) | ||||
−0.384707 | + | 0.923039i | \(0.625697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5016 | −1.16976 | −0.584882 | − | 0.811118i | \(-0.698859\pi\) | ||||
−0.584882 | + | 0.811118i | \(0.698859\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.551929 | 0.0389301 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.14344 | −0.0802541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.12571 | 0.357995 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.103859 | −0.00718407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8961 | 0.818964 | 0.409482 | − | 0.912318i | \(-0.365709\pi\) | ||||
0.409482 | + | 0.912318i | \(0.365709\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.1900 | −0.835244 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.441120 | −0.0300841 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.24730 | 0.424095 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.14344 | −0.212414 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.1900 | −1.62719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4234 | −0.831931 | −0.415966 | − | 0.909380i | \(-0.636556\pi\) | ||||
−0.415966 | + | 0.909380i | \(0.636556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.69537 | −0.313025 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.44807 | 0.0961118 | 0.0480559 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480559 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.87840 | −0.652783 | −0.326392 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326392 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.103859 | −0.00683341 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.04654 | −0.592658 | −0.296329 | − | 0.955086i | \(-0.595763\pi\) | ||||
−0.296329 | + | 0.955086i | \(0.595763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.49461 | 0.293196 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.45502 | −0.549213 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.6203 | 1.91598 | 0.957989 | − | 0.286804i | \(-0.0925927\pi\) | ||||
0.957989 | + | 0.286804i | \(0.0925927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3907 | −0.669327 | −0.334663 | − | 0.942338i | \(-0.608623\pi\) | ||||
−0.334663 | + | 0.942338i | \(0.608623\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.551929 | −0.0352615 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.69537 | −0.362388 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.14344 | 0.0724628 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.59847 | −0.479611 | −0.239805 | − | 0.970821i | \(-0.577084\pi\) | ||||
−0.239805 | + | 0.970821i | \(0.577084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.103859 | −0.00652955 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.34421 | 0.146800 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1327 | 0.819193 | 0.409596 | − | 0.912267i | \(-0.365670\pi\) | ||||
0.409596 | + | 0.912267i | \(0.365670\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.35116 | −0.208231 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14344 | 0.0707774 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.7023 | −0.721596 | −0.360798 | − | 0.932644i | \(-0.617496\pi\) | ||||
−0.360798 | + | 0.932644i | \(0.617496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.383797 | −0.0235765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.69537 | 0.593347 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7093 | −1.44558 | −0.722790 | − | 0.691068i | \(-0.757141\pi\) | ||||
−0.722790 | + | 0.691068i | \(0.757141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.9249 | −1.57483 | −0.787414 | − | 0.616425i | \(-0.788581\pi\) | ||||
−0.787414 | + | 0.616425i | \(0.788581\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.69537 | −0.344700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.487656 | −0.0294068 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.16118 | −0.129853 | −0.0649264 | − | 0.997890i | \(-0.520681\pi\) | ||||
−0.0649264 | + | 0.997890i | \(0.520681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.24730 | −0.374016 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6093 | −0.871515 | −0.435757 | − | 0.900064i | \(-0.643519\pi\) | ||||
−0.435757 | + | 0.900064i | \(0.643519\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.04654 | −0.537761 | −0.268880 | − | 0.963174i | \(-0.586654\pi\) | ||||
−0.268880 | + | 0.963174i | \(0.586654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.551929 | 0.0326935 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.28689 | 0.548188 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.03959 | 0.0611521 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.6381 | 1.03396 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9892 | 0.758838 | 0.379419 | − | 0.925225i | \(-0.376124\pi\) | ||||
0.379419 | + | 0.925225i | \(0.376124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.383797 | −0.0223455 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.103859 | 0.00602650 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.69537 | −0.329372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.799233 | −0.0460670 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2938 | 0.591366 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.16813 | −0.238667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.53419 | 0.144634 | 0.0723170 | − | 0.997382i | \(-0.476961\pi\) | ||||
0.0723170 | + | 0.997382i | \(0.476961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.2473 | −0.867389 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.94268 | −0.393683 | −0.196842 | − | 0.980435i | \(-0.563068\pi\) | ||||
−0.196842 | + | 0.980435i | \(0.563068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.53419 | −0.425858 | −0.212929 | − | 0.977068i | \(-0.568300\pi\) | ||||
−0.212929 | + | 0.977068i | \(0.568300\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.551929 | 0.0310977 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2404 | −0.631321 | −0.315661 | − | 0.948872i | \(-0.602226\pi\) | ||||
−0.315661 | + | 0.948872i | \(0.602226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.118757 | 0.00664911 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7992 | −0.714384 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.24730 | 0.236326 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.7419 | −1.48337 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.94268 | −0.439231 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.14344 | 0.448963 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24730 | 0.0685580 | 0.0342790 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342790 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.35116 | 0.183643 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.304626 | −0.0166435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.20077 | 0.283304 | 0.141652 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.15039 | −0.442669 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.648838 | −0.0351365 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.551929 | 0.0297149 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.62415 | 0.409286 | 0.204643 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204643 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.0357 | −1.71483 | −0.857417 | − | 0.514622i | \(-0.827932\pi\) | ||||
−0.857417 | + | 0.514622i | \(0.827932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.69537 | 0.303997 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.7419 | −1.42333 | −0.711664 | − | 0.702520i | \(-0.752058\pi\) | ||||
−0.711664 | + | 0.702520i | \(0.752058\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.72801 | 0.357086 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.24730 | 0.224791 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.63110 | 0.455532 | 0.227766 | − | 0.973716i | \(-0.426858\pi\) | ||||
0.227766 | + | 0.973716i | \(0.426858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9892 | −0.576784 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.73496 | 0.0908119 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.1257 | 1.88575 | 0.942873 | − | 0.333152i | \(-0.108112\pi\) | ||||
0.942873 | + | 0.333152i | \(0.108112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.28689 | −0.483456 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.695374 | −0.0361020 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6381 | −0.706152 | −0.353076 | − | 0.935595i | \(-0.614864\pi\) | ||||
−0.353076 | + | 0.935595i | \(0.614864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.35116 | 0.276333 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.51234 | 0.335403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.702324 | −0.0360760 | −0.0180380 | − | 0.999837i | \(-0.505742\pi\) | ||||
−0.0180380 | + | 0.999837i | \(0.505742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.73496 | 0.345042 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.3512 | −1.60197 | −0.800985 | − | 0.598685i | \(-0.795690\pi\) | ||||
−0.800985 | + | 0.598685i | \(0.795690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0573228 | 0.00292144 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.799233 | 0.0406273 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.2473 | −1.53360 | −0.766800 | − | 0.641887i | \(-0.778152\pi\) | ||||
−0.766800 | + | 0.641887i | \(0.778152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.24730 | 0.214795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.49461 | 0.176280 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.66657 | 0.234801 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.0931 | 0.807688 | 0.403844 | − | 0.914828i | \(-0.367674\pi\) | ||||
0.403844 | + | 0.914828i | \(0.367674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00000 | 0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.00000 | 0.349563 | 0.174782 | − | 0.984607i | \(-0.444078\pi\) | ||||
0.174782 | + | 0.984607i | \(0.444078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.5807 | −1.77240 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.551929 | −0.0274256 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.348048 | 0.0172521 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5342 | −1.01535 | −0.507675 | − | 0.861549i | \(-0.669495\pi\) | ||||
−0.507675 | + | 0.861549i | \(0.669495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.39075 | 0.216580 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.695374 | −0.0342171 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.631101 | −0.0309795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.34421 | −0.310677 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.86351 | −0.0910382 | −0.0455191 | − | 0.998963i | \(-0.514494\pi\) | ||||
−0.0455191 | + | 0.998963i | \(0.514494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9823 | −0.681454 | −0.340727 | − | 0.940162i | \(-0.610673\pi\) | ||||
−0.340727 | + | 0.940162i | \(0.610673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.14344 | −0.395948 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.9427 | 0.967362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.55193 | −0.365463 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.591515 | 0.0285586 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.83882 | 0.281246 | 0.140623 | − | 0.990063i | \(-0.455089\pi\) | ||||
0.140623 | + | 0.990063i | \(0.455089\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0535 | 1.58845 | 0.794225 | − | 0.607624i | \(-0.207877\pi\) | ||||
0.794225 | + | 0.607624i | \(0.207877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.631101 | −0.0302590 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000 | 0.0478365 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.3265 | −0.970130 | −0.485065 | − | 0.874478i | \(-0.661204\pi\) | ||||
−0.485065 | + | 0.874478i | \(0.661204\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4154 | −0.779921 | −0.389960 | − | 0.920832i | \(-0.627511\pi\) | ||||
−0.389960 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.35116 | −0.253669 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.93573 | −0.280750 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.33343 | 0.0629282 | 0.0314641 | − | 0.999505i | \(-0.489983\pi\) | ||||
0.0314641 | + | 0.999505i | \(0.489983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.964526 | −0.0454177 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.64884 | −0.0774692 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.14344 | 0.147367 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2404 | 0.525802 | 0.262901 | − | 0.964823i | \(-0.415321\pi\) | ||||
0.262901 | + | 0.964823i | \(0.415321\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.24730 | −0.198247 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.9427 | −1.58087 | −0.790434 | − | 0.612547i | \(-0.790145\pi\) | ||||
−0.790434 | + | 0.612547i | \(0.790145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8607 | −1.20185 | −0.600924 | − | 0.799306i | \(-0.705200\pi\) | ||||
−0.600924 | + | 0.799306i | \(0.705200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.44807 | 0.159900 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.8350 | 1.51942 | 0.759711 | − | 0.650261i | \(-0.225340\pi\) | ||||
0.759711 | + | 0.650261i | \(0.225340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.551929 | −0.0254857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.14344 | 0.0987647 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0830074 | 0.00381668 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.69537 | 0.215439 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.695374 | 0.0318390 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.3651 | 1.25034 | 0.625171 | − | 0.780488i | \(-0.285029\pi\) | ||||
0.625171 | + | 0.780488i | \(0.285029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0861 | 0.870252 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.73496 | −0.442042 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.24730 | 0.373721 | 0.186860 | − | 0.982386i | \(-0.440169\pi\) | ||||
0.186860 | + | 0.982386i | \(0.440169\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.29384 | 0.284617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3730 | 1.59636 | 0.798181 | − | 0.602418i | \(-0.205796\pi\) | ||||
0.798181 | + | 0.602418i | \(0.205796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.85656 | −0.218728 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0573228 | −0.00257647 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1900 | 0.546795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6311 | 0.923575 | 0.461787 | − | 0.886991i | \(-0.347208\pi\) | ||||
0.461787 | + | 0.886991i | \(0.347208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | −0.402090 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.05732 | −0.359258 | −0.179629 | − | 0.983734i | \(-0.557490\pi\) | ||||
−0.179629 | + | 0.983734i | \(0.557490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.68147 | −0.252822 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.4373 | 0.863240 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.7064 | 1.49401 | 0.747006 | − | 0.664818i | \(-0.231491\pi\) | ||||
0.747006 | + | 0.664818i | \(0.231491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.14344 | 0.139058 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.41544 | 0.370828 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.845769 | −0.0371969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0288 | −0.747481 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7815 | 1.43618 | 0.718092 | − | 0.695948i | \(-0.245016\pi\) | ||||
0.718092 | + | 0.695948i | \(0.245016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.53419 | 0.416901 | 0.208451 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208451 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.69537 | 0.204923 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.5342 | 1.15585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.695374 | 0.0301767 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.8923 | −2.29102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.06427 | 0.305415 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.24035 | 0.0535252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.103859 | 0.00447352 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0149 | 1.20445 | 0.602227 | − | 0.798325i | \(-0.294280\pi\) | ||||
0.602227 | + | 0.798325i | \(0.294280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.4303 | 0.833835 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.38380 | 0.187781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2543 | 0.994280 | 0.497140 | − | 0.867670i | \(-0.334384\pi\) | ||||
0.497140 | + | 0.867670i | \(0.334384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.55193 | 0.322308 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.14344 | −0.0487124 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.45502 | 0.359544 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.84961 | −0.0785114 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.8062 | −1.60190 | −0.800950 | − | 0.598732i | \(-0.795672\pi\) | ||||
−0.800950 | + | 0.598732i | \(0.795672\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.55193 | 0.192526 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.441120 | −0.0186241 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.18998 | 0.345167 | 0.172583 | − | 0.984995i | \(-0.444789\pi\) | ||||
0.172583 | + | 0.984995i | \(0.444789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.49844 | 0.189251 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0288 | 0.588118 | 0.294059 | − | 0.955787i | \(-0.404994\pi\) | ||||
0.294059 | + | 0.955787i | \(0.404994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.6627 | −0.697314 | −0.348657 | − | 0.937250i | \(-0.613362\pi\) | ||||
−0.348657 | + | 0.937250i | \(0.613362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.4303 | −0.686387 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.69537 | 0.195811 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1969 | −0.882440 | −0.441220 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441220 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.6381 | 0.691454 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.14344 | −0.0474381 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0722207 | 0.00299108 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.14344 | −0.129965 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.368899 | −0.0152261 | −0.00761305 | − | 0.999971i | \(-0.502423\pi\) | ||||
−0.00761305 | + | 0.999971i | \(0.502423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.24730 | 0.257416 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.7992 | −0.444221 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.39075 | −0.0571112 | −0.0285556 | − | 0.999592i | \(-0.509091\pi\) | ||||
−0.0285556 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34421 | −0.0961033 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.5016 | −0.675364 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.5560 | −1.65707 | −0.828537 | − | 0.559934i | \(-0.810827\pi\) | ||||
−0.828537 | + | 0.559934i | \(0.810827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.47276 | 0.345611 | 0.172806 | − | 0.984956i | \(-0.444717\pi\) | ||||
0.172806 | + | 0.984956i | \(0.444717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.551929 | 0.0224763 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.06527 | 0.246588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.51234 | 0.101973 | 0.0509864 | − | 0.998699i | \(-0.483763\pi\) | ||||
0.0509864 | + | 0.998699i | \(0.483763\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.14344 | −0.0463347 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.3800 | −1.87633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.32647 | −0.255524 | −0.127762 | − | 0.991805i | \(-0.540779\pi\) | ||||
−0.127762 | + | 0.991805i | \(0.540779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.12571 | 0.206688 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.2584 | −1.09738 | −0.548690 | − | 0.836026i | \(-0.684873\pi\) | ||||
−0.548690 | + | 0.836026i | \(0.684873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.5016 | 1.58770 | 0.793851 | − | 0.608113i | \(-0.208073\pi\) | ||||
0.793851 | + | 0.608113i | \(0.208073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.69537 | −0.388437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.5234 | 0.820936 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.103859 | −0.00414772 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.2334 | −0.567523 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.2118 | 1.52119 | 0.760594 | − | 0.649227i | \(-0.224908\pi\) | ||||
0.760594 | + | 0.649227i | \(0.224908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8961 | 0.472829 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.71722 | −0.147513 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.69537 | 0.225659 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.1900 | −0.482228 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.8141 | −0.743113 | −0.371557 | − | 0.928410i | \(-0.621176\pi\) | ||||
−0.371557 | + | 0.928410i | \(0.621176\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.3581 | −0.763409 | −0.381705 | − | 0.924284i | \(-0.624663\pi\) | ||||
−0.381705 | + | 0.924284i | \(0.624663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.441120 | −0.0173691 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.43728 | 0.331704 | 0.165852 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165852 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0722207 | 0.00283491 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.24730 | 0.244851 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.1396 | 1.84472 | 0.922358 | − | 0.386337i | \(-0.126260\pi\) | ||||
0.922358 | + | 0.386337i | \(0.126260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.92878 | −0.0753635 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.14344 | −0.122637 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.64884 | 0.103184 | 0.0515920 | − | 0.998668i | \(-0.483570\pi\) | ||||
0.0515920 | + | 0.998668i | \(0.483570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.37996 | 0.131465 | 0.0657326 | − | 0.997837i | \(-0.479062\pi\) | ||||
0.0657326 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.1900 | −0.939461 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.551929 | −0.0214029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.14344 | −0.0442743 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.4234 | −0.480316 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.784335 | 0.0302789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.2077 | 0.740403 | 0.370202 | − | 0.928951i | \(-0.379289\pi\) | ||||
0.370202 | + | 0.928951i | \(0.379289\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.69537 | −0.180725 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.0506 | −1.80830 | −0.904152 | − | 0.427212i | \(-0.859496\pi\) | ||||
−0.904152 | + | 0.427212i | \(0.859496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.6381 | −0.676886 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.44807 | 0.0554902 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3651 | −0.894039 | −0.447020 | − | 0.894524i | \(-0.647515\pi\) | ||||
−0.447020 | + | 0.894524i | \(0.647515\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.42338 | −0.0925927 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.87840 | −0.376885 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.96041 | 0.150880 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.1000 | 1.56352 | 0.781759 | − | 0.623580i | \(-0.214323\pi\) | ||||
0.781759 | + | 0.623580i | \(0.214323\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.103859 | −0.00394527 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.50156 | 0.132822 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.4442 | 1.49406 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.04654 | −0.342171 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.2039 | 1.48071 | 0.740355 | − | 0.672216i | \(-0.234657\pi\) | ||||
0.740355 | + | 0.672216i | \(0.234657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.35116 | −0.126391 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.49461 | 0.169277 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.2938 | −0.387140 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.03164 | 0.0762998 | 0.0381499 | − | 0.999272i | \(-0.487854\pi\) | ||||
0.0381499 | + | 0.999272i | \(0.487854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.45502 | −0.317088 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.24730 | 0.233963 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.326475 | −0.0122095 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.6203 | 1.10619 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.4303 | −1.24674 | −0.623371 | − | 0.781927i | \(-0.714237\pi\) | ||||
−0.623371 | + | 0.781927i | \(0.714237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2473 | 0.567839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3907 | −0.386436 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.36890 | −0.199396 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.2185 | 0.378983 | 0.189492 | − | 0.981882i | \(-0.439316\pi\) | ||||
0.189492 | + | 0.981882i | \(0.439316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.39458 | −0.125553 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.3800 | 1.56534 | 0.782670 | − | 0.622437i | \(-0.213857\pi\) | ||||
0.782670 | + | 0.622437i | \(0.213857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.551929 | −0.0203582 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0573228 | 0.00211151 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.4303 | −1.37690 | −0.688449 | − | 0.725285i | \(-0.741708\pi\) | ||||
−0.688449 | + | 0.725285i | \(0.741708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.69537 | −0.209225 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.5123 | 0.642466 | 0.321233 | − | 0.947000i | \(-0.395903\pi\) | ||||
0.321233 | + | 0.947000i | \(0.395903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27610 | 0.120027 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.14344 | 0.0418364 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7992 | 0.467674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7242 | 0.683255 | 0.341627 | − | 0.939835i | \(-0.389022\pi\) | ||||
0.341627 | + | 0.939835i | \(0.389022\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.59847 | −0.276903 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.910042 | 0.0331198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.85656 | −0.176515 | −0.0882573 | − | 0.996098i | \(-0.528130\pi\) | ||||
−0.0882573 | + | 0.996098i | \(0.528130\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.103859 | −0.00376984 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.46581 | 0.306885 | 0.153443 | − | 0.988158i | \(-0.450964\pi\) | ||||
0.153443 | + | 0.988158i | \(0.450964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.94268 | 0.287544 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.34421 | 0.0847552 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.96041 | 0.143002 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.58768 | −0.165436 | −0.0827180 | − | 0.996573i | \(-0.526360\pi\) | ||||
−0.0827180 | + | 0.996573i | \(0.526360\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1327 | 0.472961 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.3404 | 1.52288 | 0.761439 | − | 0.648237i | \(-0.224493\pi\) | ||||
0.761439 | + | 0.648237i | \(0.224493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3334 | 1.05369 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.35116 | −0.120222 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.28689 | 0.332737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.26604 | −0.0453024 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.14344 | 0.0408634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.18303 | −0.0422242 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.5668 | 1.08959 | 0.544795 | − | 0.838569i | \(-0.316608\pi\) | ||||
0.544795 | + | 0.838569i | \(0.316608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7023 | −0.416614 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.15039 | 0.289795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.0111 | 1.52737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.383797 | −0.0136119 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.6884 | 0.945352 | 0.472676 | − | 0.881236i | \(-0.343288\pi\) | ||||
0.472676 | + | 0.881236i | \(0.343288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5877 | 1.22362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.69537 | 0.342569 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.326475 | −0.0115210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.551929 | −0.0194530 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.7093 | −0.834606 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.6846 | −1.64134 | −0.820671 | − | 0.571401i | \(-0.806400\pi\) | ||||
−0.820671 | + | 0.571401i | \(0.806400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.80718 | 0.168803 | 0.0844015 | − | 0.996432i | \(-0.473102\pi\) | ||||
0.0844015 | + | 0.996432i | \(0.473102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.9249 | −0.909227 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.47376 | −0.121680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.799233 | −0.0279616 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.69537 | −0.199012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.96453 | −0.277964 | −0.138982 | − | 0.990295i | \(-0.544383\pi\) | ||||
−0.138982 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0070 | −0.697398 | −0.348699 | − | 0.937235i | \(-0.613377\pi\) | ||||
−0.348699 | + | 0.937235i | \(0.613377\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.487656 | −0.0169780 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.9715 | −1.38994 | −0.694972 | − | 0.719037i | \(-0.744583\pi\) | ||||
−0.694972 | + | 0.719037i | \(0.744583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.8103 | −1.38267 | −0.691334 | − | 0.722535i | \(-0.742977\pi\) | ||||
−0.691334 | + | 0.722535i | \(0.742977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.16118 | −0.0749706 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.24730 | −0.147160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.96736 | 0.171903 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.24730 | −0.215938 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.7499 | −0.854460 | −0.427230 | − | 0.904143i | \(-0.640511\pi\) | ||||
−0.427230 | + | 0.904143i | \(0.640511\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6925 | −0.954915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.6093 | −0.503169 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.7280 | −0.369055 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9892 | 0.377594 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.04654 | −0.310476 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.35116 | −0.114876 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.2514 | 1.72058 | 0.860288 | − | 0.509809i | \(-0.170284\pi\) | ||||
0.860288 | + | 0.509809i | \(0.170284\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.551929 | 0.0188756 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.31257 | −0.318111 | −0.159056 | − | 0.987270i | \(-0.550845\pi\) | ||||
−0.159056 | + | 0.987270i | \(0.550845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.6637 | 0.807396 | 0.403698 | − | 0.914892i | \(-0.367725\pi\) | ||||
0.403698 | + | 0.914892i | \(0.367725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.28689 | 0.316496 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.5985 | −1.07562 | −0.537812 | − | 0.843065i | \(-0.680749\pi\) | ||||
−0.537812 | + | 0.843065i | \(0.680749\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.39870 | 0.319565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.03959 | 0.0353062 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.878129 | −0.0297885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14344 | 0.106512 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.6381 | 0.596958 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.35116 | −0.180902 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.9388 | −0.977195 | −0.488598 | − | 0.872509i | \(-0.662491\pi\) | ||||
−0.488598 | + | 0.872509i | \(0.662491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.9892 | 0.438115 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9753 | 0.841440 | 0.420720 | − | 0.907191i | \(-0.361778\pi\) | ||||
0.420720 | + | 0.907191i | \(0.361778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.92778 | 0.233138 | 0.116569 | − | 0.993183i | \(-0.462810\pi\) | ||||
0.116569 | + | 0.993183i | \(0.462810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.383797 | −0.0129012 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.9139 | −0.836526 | −0.418263 | − | 0.908326i | \(-0.637361\pi\) | ||||
−0.418263 | + | 0.908326i | \(0.637361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.73496 | −0.225883 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.103859 | 0.00347940 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.14344 | 0.272510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.684587 | −0.0228832 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.69537 | −0.190163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.14344 | −0.238247 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.95346 | −0.0983941 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.799233 | −0.0265968 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.7242 | −0.356484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2435 | −0.937809 | −0.468904 | − | 0.883249i | \(-0.655351\pi\) | ||||
−0.468904 | + | 0.883249i | \(0.655351\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.2938 | 0.341425 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.9645 | 1.19156 | 0.595779 | − | 0.803148i | \(-0.296843\pi\) | ||||
0.595779 | + | 0.803148i | \(0.296843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.118757 | 0.00393028 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.16813 | −0.137794 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.49461 | −0.115402 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.8566 | 1.54566 | 0.772828 | − | 0.634616i | \(-0.218842\pi\) | ||||
0.772828 | + | 0.634616i | \(0.218842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.53419 | 0.0835045 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −69.4265 | −2.28520 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.7350 | −0.517362 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.2473 | −0.500787 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.5304 | −1.46099 | −0.730497 | − | 0.682916i | \(-0.760711\pi\) | ||||
−0.730497 | + | 0.682916i | \(0.760711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.94268 | −0.227293 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.243467 | 0.00796223 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.3661 | 1.41671 | 0.708354 | − | 0.705858i | \(-0.249438\pi\) | ||||
0.708354 | + | 0.705858i | \(0.249438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.53419 | −0.245869 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3661 | −0.468320 | −0.234160 | − | 0.972198i | \(-0.575234\pi\) | ||||
−0.234160 | + | 0.972198i | \(0.575234\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.28689 | 0.302423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.551929 | 0.0179543 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.50539 | 0.243893 | 0.121946 | − | 0.992537i | \(-0.461086\pi\) | ||||
0.121946 | + | 0.992537i | \(0.461086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9031 | −0.581159 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.2404 | −0.364493 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.4918 | 1.31166 | 0.655829 | − | 0.754910i | \(-0.272319\pi\) | ||||
0.655829 | + | 0.754910i | \(0.272319\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.06838 | 0.293446 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.118757 | 0.00383886 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.39075 | −0.141785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.02880 | 0.258994 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.7992 | −0.412450 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.18303 | −0.295612 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.88224 | 0.157002 | 0.0785011 | − | 0.996914i | \(-0.474987\pi\) | ||||
0.0785011 | + | 0.996914i | \(0.474987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.24730 | 0.136443 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.50156 | 0.0481873 | 0.0240936 | − | 0.999710i | \(-0.492330\pi\) | ||||
0.0240936 | + | 0.999710i | \(0.492330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.34421 | 0.203386 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.7419 | −0.856427 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.47276 | 0.303060 | 0.151530 | − | 0.988453i | \(-0.451580\pi\) | ||||
0.151530 | + | 0.988453i | \(0.451580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00695 | 0.0321823 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.94268 | −0.253590 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.3404 | −0.393597 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.96041 | 0.189915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.14344 | 0.259209 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.799233 | −0.0254141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.6064 | −0.591052 | −0.295526 | − | 0.955335i | \(-0.595495\pi\) | ||||
−0.295526 | + | 0.955335i | \(0.595495\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.24730 | 0.0395820 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.10770 | 0.288733 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0288 | 0.349286 | 0.174643 | − | 0.984632i | \(-0.444123\pi\) | ||||
0.174643 | + | 0.984632i | \(0.444123\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35116 | 0.106026 |
(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 | 7728.2.a.bv.1.2 | 3 | ||
4.3 | odd | 2 | 1932.2.a.i.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 5796.2.a.p.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.i.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
5796.2.a.p.1.2 | 3 | 12.11 | even | 2 | |||
7728.2.a.bv.1.2 | 3 | 1.1 | even | 1 | trivial |