Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(5\) | −1.79097 | −0.800944 | −0.400472 | − | 0.916309i | \(-0.631154\pi\) | ||||
−0.400472 | + | 0.916309i | \(0.631154\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.44185 | −1.67886 | −0.839431 | − | 0.543466i | \(-0.817112\pi\) | ||||
−0.839431 | + | 0.543466i | \(0.817112\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81330 | −0.546732 | −0.273366 | − | 0.961910i | \(-0.588137\pi\) | ||||
−0.273366 | + | 0.961910i | \(0.588137\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.51558 | −0.697696 | −0.348848 | − | 0.937179i | \(-0.613427\pi\) | ||||
−0.348848 | + | 0.937179i | \(0.613427\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.79097 | 0.462425 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.41675 | 0.586148 | 0.293074 | − | 0.956090i | \(-0.405322\pi\) | ||||
0.293074 | + | 0.956090i | \(0.405322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.57055 | −0.819141 | −0.409571 | − | 0.912278i | \(-0.634322\pi\) | ||||
−0.409571 | + | 0.912278i | \(0.634322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.44185 | 0.969291 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.16993 | −1.07801 | −0.539003 | − | 0.842304i | \(-0.681199\pi\) | ||||
−0.539003 | + | 0.842304i | \(0.681199\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79244 | −0.358488 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.45747 | 1.38482 | 0.692408 | − | 0.721506i | \(-0.256550\pi\) | ||||
0.692408 | + | 0.721506i | \(0.256550\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.28896 | −0.231504 | −0.115752 | − | 0.993278i | \(-0.536928\pi\) | ||||
−0.115752 | + | 0.993278i | \(0.536928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.81330 | 0.315656 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.95521 | 1.34468 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.97766 | −1.64032 | −0.820158 | − | 0.572137i | \(-0.806115\pi\) | ||||
−0.820158 | + | 0.572137i | \(0.806115\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.51558 | 0.402815 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2535 | −1.60133 | −0.800667 | − | 0.599110i | \(-0.795521\pi\) | ||||
−0.800667 | + | 0.599110i | \(0.795521\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.0743 | −1.68881 | −0.844406 | − | 0.535703i | \(-0.820047\pi\) | ||||
−0.844406 | + | 0.535703i | \(0.820047\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.79097 | −0.266981 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6910 | −1.55945 | −0.779725 | − | 0.626122i | \(-0.784641\pi\) | ||||
−0.779725 | + | 0.626122i | \(0.784641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.7300 | 1.81858 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41675 | −0.338413 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.98775 | −0.822481 | −0.411241 | − | 0.911527i | \(-0.634904\pi\) | ||||
−0.411241 | + | 0.911527i | \(0.634904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.24757 | 0.437902 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.57055 | 0.472932 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0586743 | −0.00763874 | −0.00381937 | − | 0.999993i | \(-0.501216\pi\) | ||||
−0.00381937 | + | 0.999993i | \(0.501216\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.61631 | −0.591057 | −0.295529 | − | 0.955334i | \(-0.595496\pi\) | ||||
−0.295529 | + | 0.955334i | \(0.595496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.44185 | −0.559621 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.50531 | 0.558816 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96605 | −0.484530 | −0.242265 | − | 0.970210i | \(-0.577890\pi\) | ||||
−0.242265 | + | 0.970210i | \(0.577890\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.16993 | 0.622387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.41945 | 0.761849 | 0.380924 | − | 0.924606i | \(-0.375606\pi\) | ||||
0.380924 | + | 0.924606i | \(0.375606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.78184 | 0.442631 | 0.221315 | − | 0.975202i | \(-0.428965\pi\) | ||||
0.221315 | + | 0.975202i | \(0.428965\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.79244 | 0.206973 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.05443 | 0.917887 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.8661 | −1.56006 | −0.780029 | − | 0.625743i | \(-0.784796\pi\) | ||||
−0.780029 | + | 0.625743i | \(0.784796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.9798 | −1.64424 | −0.822122 | − | 0.569311i | \(-0.807210\pi\) | ||||
−0.822122 | + | 0.569311i | \(0.807210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.32832 | −0.469472 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.45747 | −0.799524 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.96709 | −0.420510 | −0.210255 | − | 0.977647i | \(-0.567429\pi\) | ||||
−0.210255 | + | 0.977647i | \(0.567429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1738 | 1.17134 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.28896 | 0.133659 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.39474 | 0.656087 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.68234 | −0.780023 | −0.390012 | − | 0.920810i | \(-0.627529\pi\) | ||||
−0.390012 | + | 0.920810i | \(0.627529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.81330 | −0.182244 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3196 | 1.52436 | 0.762179 | − | 0.647366i | \(-0.224130\pi\) | ||||
0.762179 | + | 0.647366i | \(0.224130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.87011 | 0.578399 | 0.289200 | − | 0.957269i | \(-0.406611\pi\) | ||||
0.289200 | + | 0.957269i | \(0.406611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.95521 | −0.776349 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.35078 | 0.613954 | 0.306977 | − | 0.951717i | \(-0.400683\pi\) | ||||
0.306977 | + | 0.951717i | \(0.400683\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8531 | 1.23110 | 0.615551 | − | 0.788097i | \(-0.288933\pi\) | ||||
0.615551 | + | 0.788097i | \(0.288933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.97766 | 0.947037 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2890 | −1.34419 | −0.672096 | − | 0.740464i | \(-0.734606\pi\) | ||||
−0.672096 | + | 0.740464i | \(0.734606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.25917 | 0.863422 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.51558 | −0.232565 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.7349 | −0.984062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.71193 | −0.701085 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2535 | 0.924530 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1650 | 1.08807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1129 | 1.16358 | 0.581791 | − | 0.813338i | \(-0.302352\pi\) | ||||
0.581791 | + | 0.813338i | \(0.302352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0743 | 0.975037 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2950 | −0.899475 | −0.449738 | − | 0.893161i | \(-0.648482\pi\) | ||||
−0.449738 | + | 0.893161i | \(0.648482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8599 | 1.37523 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.79097 | 0.154142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1710 | 0.868968 | 0.434484 | − | 0.900680i | \(-0.356931\pi\) | ||||
0.434484 | + | 0.900680i | \(0.356931\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.72509 | 0.315958 | 0.157979 | − | 0.987442i | \(-0.449502\pi\) | ||||
0.157979 | + | 0.987442i | \(0.449502\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6910 | 0.900349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.56151 | 0.381452 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.3561 | −1.10916 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.7300 | −1.04996 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.87390 | −0.153516 | −0.0767579 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767579 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8972 | 1.29370 | 0.646849 | − | 0.762618i | \(-0.276086\pi\) | ||||
0.646849 | + | 0.762618i | \(0.276086\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.41675 | 0.195383 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.30849 | 0.185422 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9023 | 1.42876 | 0.714378 | − | 0.699760i | \(-0.246710\pi\) | ||||
0.714378 | + | 0.699760i | \(0.246710\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.98775 | 0.474860 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.9641 | 1.80982 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2246 | −0.879177 | −0.439588 | − | 0.898199i | \(-0.644876\pi\) | ||||
−0.439588 | + | 0.898199i | \(0.644876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.24757 | −0.252823 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.50349 | 0.425873 | 0.212937 | − | 0.977066i | \(-0.431697\pi\) | ||||
0.212937 | + | 0.977066i | \(0.431697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.67187 | −0.513221 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.57055 | −0.273047 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6287 | −0.960144 | −0.480072 | − | 0.877229i | \(-0.659390\pi\) | ||||
−0.480072 | + | 0.877229i | \(0.659390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.96176 | 0.601852 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0586743 | 0.00441023 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.4659 | −1.30547 | −0.652733 | − | 0.757588i | \(-0.726378\pi\) | ||||
−0.652733 | + | 0.757588i | \(0.726378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.96334 | 0.740569 | 0.370284 | − | 0.928918i | \(-0.379260\pi\) | ||||
0.370284 | + | 0.928918i | \(0.379260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.61631 | 0.341247 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.8696 | 1.31380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.38230 | −0.320466 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.44185 | 0.323097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00549 | 0.289827 | 0.144914 | − | 0.989444i | \(-0.453710\pi\) | ||||
0.144914 | + | 0.989444i | \(0.453710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.2439 | 1.38521 | 0.692604 | − | 0.721318i | \(-0.256463\pi\) | ||||
0.692604 | + | 0.721318i | \(0.256463\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.50531 | −0.322632 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.0976 | −1.78813 | −0.894063 | − | 0.447941i | \(-0.852158\pi\) | ||||
−0.894063 | + | 0.447941i | \(0.852158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1127 | 0.716867 | 0.358434 | − | 0.933555i | \(-0.383311\pi\) | ||||
0.358434 | + | 0.933555i | \(0.383311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.96605 | 0.279744 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −33.1250 | −2.32492 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.3637 | 1.28258 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.16993 | −0.359335 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.47450 | 0.447851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0164 | −0.827240 | −0.413620 | − | 0.910450i | \(-0.635736\pi\) | ||||
−0.413620 | + | 0.910450i | \(0.635736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.41945 | −0.439853 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.8337 | 1.35265 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.72538 | 0.388664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.78184 | −0.255553 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.07953 | −0.408953 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.8248 | −1.39453 | −0.697265 | − | 0.716813i | \(-0.745600\pi\) | ||||
−0.697265 | + | 0.716813i | \(0.745600\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.79244 | −0.119496 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.9517 | 1.25787 | 0.628935 | − | 0.777458i | \(-0.283491\pi\) | ||||
0.628935 | + | 0.777458i | \(0.283491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4258 | 1.41585 | 0.707927 | − | 0.706285i | \(-0.249630\pi\) | ||||
0.707927 | + | 0.706285i | \(0.249630\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.05443 | −0.529942 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0637 | 0.790320 | 0.395160 | − | 0.918612i | \(-0.370689\pi\) | ||||
0.395160 | + | 0.918612i | \(0.370689\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.1473 | 1.24903 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8661 | 0.900700 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.05208 | −0.326792 | −0.163396 | − | 0.986561i | \(-0.552245\pi\) | ||||
−0.163396 | + | 0.986561i | \(0.552245\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.1868 | −1.36476 | −0.682382 | − | 0.730996i | \(-0.739056\pi\) | ||||
−0.682382 | + | 0.730996i | \(0.739056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.7991 | −1.45658 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.98201 | 0.571512 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.9798 | 0.949305 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5889 | −0.731482 | −0.365741 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365741 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.37466 | 0.589380 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.32832 | 0.271050 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.593402 | 0.0370154 | 0.0185077 | − | 0.999829i | \(-0.494108\pi\) | ||||
0.0185077 | + | 0.999829i | \(0.494108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 44.3193 | 2.75387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.45747 | 0.461606 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.07853 | 0.498143 | 0.249072 | − | 0.968485i | \(-0.419875\pi\) | ||||
0.249072 | + | 0.968485i | \(0.419875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7239 | 0.658762 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.96709 | 0.242782 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.59074 | 0.279903 | 0.139951 | − | 0.990158i | \(-0.455305\pi\) | ||||
0.139951 | + | 0.990158i | \(0.455305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0274 | 1.15583 | 0.577915 | − | 0.816097i | \(-0.303867\pi\) | ||||
0.577915 | + | 0.816097i | \(0.303867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.1738 | −0.676271 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.25024 | 0.195997 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.5295 | −1.95451 | −0.977254 | − | 0.212072i | \(-0.931979\pi\) | ||||
−0.977254 | + | 0.212072i | \(0.931979\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.28896 | −0.0771681 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3406 | 1.51169 | 0.755847 | − | 0.654748i | \(-0.227225\pi\) | ||||
0.755847 | + | 0.654748i | \(0.227225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.181596 | 0.0107948 | 0.00539738 | − | 0.999985i | \(-0.498282\pi\) | ||||
0.00539738 | + | 0.999985i | \(0.498282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.39474 | −0.378792 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.5447 | 2.68842 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1593 | −0.656430 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.68234 | 0.450347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5225 | −1.14051 | −0.570257 | − | 0.821466i | \(-0.693156\pi\) | ||||
−0.570257 | + | 0.821466i | \(0.693156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.105084 | 0.00611820 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.81330 | 0.105219 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.0054 | 0.752120 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 49.1903 | 2.83528 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.3196 | −0.880089 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.26765 | 0.473404 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.67738 | −0.438171 | −0.219086 | − | 0.975706i | \(-0.570307\pi\) | ||||
−0.219086 | + | 0.975706i | \(0.570307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.87011 | −0.333939 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8409 | 1.29519 | 0.647594 | − | 0.761985i | \(-0.275775\pi\) | ||||
0.647594 | + | 0.761985i | \(0.275775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.51047 | −0.254947 | −0.127473 | − | 0.991842i | \(-0.540687\pi\) | ||||
−0.127473 | + | 0.991842i | \(0.540687\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.95521 | 0.448225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.22120 | −0.461748 | −0.230874 | − | 0.972984i | \(-0.574159\pi\) | ||||
−0.230874 | + | 0.972984i | \(0.574159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5226 | −0.757123 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.35078 | −0.354466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.62914 | −0.480138 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.50903 | 0.250116 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.8531 | −0.710777 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 47.4881 | 2.61810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5035 | 1.40180 | 0.700898 | − | 0.713261i | \(-0.252783\pi\) | ||||
0.700898 | + | 0.713261i | \(0.252783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.97766 | −0.546772 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.10306 | 0.388082 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.14378 | 0.0623056 | 0.0311528 | − | 0.999515i | \(-0.490082\pi\) | ||||
0.0311528 | + | 0.999515i | \(0.490082\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.2890 | 0.776070 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.33728 | 0.126571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −25.4520 | −1.37428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.25917 | −0.498497 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.5902 | −1.85690 | −0.928450 | − | 0.371458i | \(-0.878858\pi\) | ||||
−0.928450 | + | 0.371458i | \(0.878858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3435 | −0.767790 | −0.383895 | − | 0.923377i | \(-0.625417\pi\) | ||||
−0.383895 | + | 0.923377i | \(0.625417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.51558 | 0.134272 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.480704 | −0.0255853 | −0.0127926 | − | 0.999918i | \(-0.504072\pi\) | ||||
−0.0127926 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4970 | −0.610198 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.7349 | 0.568149 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.57158 | −0.346835 | −0.173417 | − | 0.984848i | \(-0.555481\pi\) | ||||
−0.173417 | + | 0.984848i | \(0.555481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.25114 | −0.329007 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.71193 | 0.404771 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.77315 | −0.354523 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3002 | 0.903063 | 0.451532 | − | 0.892255i | \(-0.350878\pi\) | ||||
0.451532 | + | 0.892255i | \(0.350878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.2535 | −0.533778 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.5967 | 1.38083 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.3387 | 1.88155 | 0.940773 | − | 0.339036i | \(-0.110101\pi\) | ||||
0.940773 | + | 0.339036i | \(0.110101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.1650 | −0.628199 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.7598 | −0.966181 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.4654 | −1.25670 | −0.628350 | − | 0.777930i | \(-0.716270\pi\) | ||||
−0.628350 | + | 0.777930i | \(0.716270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1129 | −0.671795 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.1310 | −0.977547 | −0.488773 | − | 0.872411i | \(-0.662555\pi\) | ||||
−0.488773 | + | 0.872411i | \(0.662555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.4252 | −0.735176 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.0743 | −0.562938 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.2551 | −0.722762 | −0.361381 | − | 0.932418i | \(-0.617695\pi\) | ||||
−0.361381 | + | 0.932418i | \(0.617695\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4944 | −0.631871 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2950 | 0.519312 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.8337 | 1.24952 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.3027 | 1.16953 | 0.584764 | − | 0.811203i | \(-0.301187\pi\) | ||||
0.584764 | + | 0.811203i | \(0.301187\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.8599 | −0.793987 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.67183 | −0.333175 | −0.166588 | − | 0.986027i | \(-0.553275\pi\) | ||||
−0.166588 | + | 0.986027i | \(0.553275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.24248 | 0.161520 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.79097 | −0.0889938 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0925 | 0.896813 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9559 | −0.541736 | −0.270868 | − | 0.962617i | \(-0.587311\pi\) | ||||
−0.270868 | + | 0.962617i | \(0.587311\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1710 | −0.501699 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.260622 | 0.0128244 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.8283 | 1.31695 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.72509 | −0.182418 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0127 | −0.831127 | −0.415564 | − | 0.909564i | \(-0.636416\pi\) | ||||
−0.415564 | + | 0.909564i | \(0.636416\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.3469 | −1.62523 | −0.812613 | − | 0.582803i | \(-0.801956\pi\) | ||||
−0.812613 | + | 0.582803i | \(0.801956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.6910 | −0.519817 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.33188 | −0.210127 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.5049 | 0.992304 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.56151 | −0.220232 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.5757 | −1.85813 | −0.929063 | − | 0.369921i | \(-0.879385\pi\) | ||||
−0.929063 | + | 0.369921i | \(0.879385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.3071 | 0.783671 | 0.391836 | − | 0.920035i | \(-0.371840\pi\) | ||||
0.391836 | + | 0.920035i | \(0.371840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.3561 | 0.640374 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.4595 | 0.883039 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7738 | 1.03921 | 0.519603 | − | 0.854408i | \(-0.326080\pi\) | ||||
0.519603 | + | 0.854408i | \(0.326080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.7300 | 0.606193 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.04240 | 0.287083 | 0.143541 | − | 0.989644i | \(-0.454151\pi\) | ||||
0.143541 | + | 0.989644i | \(0.454151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.10492 | 0.336805 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.87390 | 0.0886323 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.44696 | 0.115479 | 0.0577395 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577395 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.5928 | 0.875500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.8972 | −0.746917 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.0119 | −0.938174 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.29158 | −0.107195 | −0.0535977 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535977 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41675 | −0.112804 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.40370 | 0.298250 | 0.149125 | − | 0.988818i | \(-0.452354\pi\) | ||||
0.149125 | + | 0.988818i | \(0.452354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.72070 | 0.0799677 | 0.0399838 | − | 0.999200i | \(-0.487269\pi\) | ||||
0.0399838 | + | 0.999200i | \(0.487269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.30849 | −0.107054 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.5008 | −1.31886 | −0.659429 | − | 0.751767i | \(-0.729202\pi\) | ||||
−0.659429 | + | 0.751767i | \(0.729202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.6166 | 0.813459 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.9023 | −0.824893 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0810 | 0.923327 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.40001 | 0.293653 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.98775 | −0.274160 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.4969 | −1.71328 | −0.856638 | − | 0.515919i | \(-0.827451\pi\) | ||||
−0.856638 | + | 0.515919i | \(0.827451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.0996 | 1.14444 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.9641 | −1.04490 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.7588 | 0.624755 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5097 | 0.566866 | 0.283433 | − | 0.958992i | \(-0.408527\pi\) | ||||
0.283433 | + | 0.958992i | \(0.408527\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.2246 | 0.507593 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3268 | −0.511172 | −0.255586 | − | 0.966786i | \(-0.582268\pi\) | ||||
−0.255586 | + | 0.966786i | \(0.582268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0228 | 0.811708 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.24757 | 0.145967 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.5142 | −1.27904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.6999 | 1.32955 | 0.664774 | − | 0.747044i | \(-0.268528\pi\) | ||||
0.664774 | + | 0.747044i | \(0.268528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.50349 | −0.245878 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.4369 | −1.22093 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.67187 | 0.296308 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6491 | 0.782281 | 0.391141 | − | 0.920331i | \(-0.372081\pi\) | ||||
0.391141 | + | 0.920331i | \(0.372081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.7984 | −0.743116 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.57055 | 0.157644 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5132 | −0.463266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3861 | 0.852600 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.6287 | 0.554340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.6893 | −0.906414 | −0.453207 | − | 0.891405i | \(-0.649720\pi\) | ||||
−0.453207 | + | 0.891405i | \(0.649720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0143 | 0.612803 | 0.306401 | − | 0.951902i | \(-0.400875\pi\) | ||||
0.306401 | + | 0.951902i | \(0.400875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.96176 | −0.347480 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.11510 | −0.135696 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.72820 | 0.162096 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0586743 | −0.00254625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.7936 | 1.11724 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3740 | −0.491743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4659 | 0.753711 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.0834 | −0.994274 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1304 | 0.478531 | 0.239266 | − | 0.970954i | \(-0.423093\pi\) | ||||
0.239266 | + | 0.970954i | \(0.423093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.96334 | −0.427568 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.0194 | −0.986045 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.91069 | 0.167209 | 0.0836046 | − | 0.996499i | \(-0.473357\pi\) | ||||
0.0836046 | + | 0.996499i | \(0.473357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.61631 | −0.197019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.6273 | −1.13436 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.5912 | 2.61912 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.8696 | −0.758524 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0319 | 0.891152 | 0.445576 | − | 0.895244i | \(-0.352999\pi\) | ||||
0.445576 | + | 0.895244i | \(0.352999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.8582 | 1.17828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.38230 | 0.185021 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.87046 | 0.120976 | 0.0604878 | − | 0.998169i | \(-0.480734\pi\) | ||||
0.0604878 | + | 0.998169i | \(0.480734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.5910 | 1.07662 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.44185 | −0.186540 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4112 | −0.729916 | −0.364958 | − | 0.931024i | \(-0.618917\pi\) | ||||
−0.364958 | + | 0.931024i | \(0.618917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.3984 | −1.81616 | −0.908082 | − | 0.418791i | \(-0.862454\pi\) | ||||
−0.908082 | + | 0.418791i | \(0.862454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.00549 | −0.167332 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.26680 | 0.386452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.7678 | −1.07273 | −0.536364 | − | 0.843987i | \(-0.680203\pi\) | ||||
−0.536364 | + | 0.843987i | \(0.680203\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2439 | −0.799750 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 66.5379 | 2.76046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8576 | 0.449677 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.50531 | 0.186272 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.4582 | −1.33969 | −0.669847 | − | 0.742499i | \(-0.733640\pi\) | ||||
−0.669847 | + | 0.742499i | \(0.733640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.60231 | 0.189635 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.0976 | 1.03238 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.9474 | 0.860206 | 0.430103 | − | 0.902780i | \(-0.358477\pi\) | ||||
0.430103 | + | 0.902780i | \(0.358477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.2258 | 0.788179 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.1127 | −0.413884 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.7101 | −0.478463 | −0.239232 | − | 0.970962i | \(-0.576896\pi\) | ||||
−0.239232 | + | 0.970962i | \(0.576896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.5160 | −0.877658 | −0.438829 | − | 0.898571i | \(-0.644607\pi\) | ||||
−0.438829 | + | 0.898571i | \(0.644607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.96605 | −0.161510 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.8118 | 0.561530 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1856 | 0.859898 | 0.429949 | − | 0.902853i | \(-0.358532\pi\) | ||||
0.429949 | + | 0.902853i | \(0.358532\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.1250 | 1.34229 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.8942 | 1.08802 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5879 | −0.508419 | −0.254209 | − | 0.967149i | \(-0.581815\pi\) | ||||
−0.254209 | + | 0.967149i | \(0.581815\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.3637 | −0.740497 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.35448 | 0.175305 | 0.0876524 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876524 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.8826 | 1.40205 | 0.701025 | − | 0.713136i | \(-0.252726\pi\) | ||||
0.701025 | + | 0.713136i | \(0.252726\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.16993 | 0.207462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.6212 | 0.705979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8250 | −0.512998 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.47450 | −0.258567 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.1135 | −0.961469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6950 | 0.983092 | 0.491546 | − | 0.870852i | \(-0.336432\pi\) | ||||
0.491546 | + | 0.870852i | \(0.336432\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.0164 | 0.477607 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.4848 | −0.931965 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.0234 | −1.26881 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.41945 | 0.253950 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.85763 | 0.389353 | 0.194676 | − | 0.980868i | \(-0.437634\pi\) | ||||
0.194676 | + | 0.980868i | \(0.437634\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9394 | 0.786335 | 0.393167 | − | 0.919467i | \(-0.371379\pi\) | ||||
0.393167 | + | 0.919467i | \(0.371379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.8337 | −0.780950 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2156 | −0.676813 | −0.338407 | − | 0.941000i | \(-0.609888\pi\) | ||||
−0.338407 | + | 0.941000i | \(0.609888\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.106394 | 0.00417634 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.72538 | −0.224395 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.8272 | 1.12810 | 0.564049 | − | 0.825742i | \(-0.309243\pi\) | ||||
0.564049 | + | 0.825742i | \(0.309243\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4379 | 0.720429 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.78184 | 0.147544 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0092 | 0.428858 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.6456 | −1.07529 | −0.537644 | − | 0.843172i | \(-0.680686\pi\) | ||||
−0.537644 | + | 0.843172i | \(0.680686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.07953 | 0.236109 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.4045 | −1.10148 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.5546 | −1.49284 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8248 | 0.805132 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.37077 | 0.323150 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.2899 | −0.550835 | −0.275418 | − | 0.961325i | \(-0.588816\pi\) | ||||
−0.275418 | + | 0.961325i | \(0.588816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.79244 | 0.0689911 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.7177 | −0.949979 | −0.474990 | − | 0.879991i | \(-0.657548\pi\) | ||||
−0.474990 | + | 0.879991i | \(0.657548\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.1238 | 1.30955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.9517 | −0.726231 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.6300 | −1.09550 | −0.547748 | − | 0.836644i | \(-0.684515\pi\) | ||||
−0.547748 | + | 0.836644i | \(0.684515\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2159 | −0.695995 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.4258 | −0.817444 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0627 | 0.573842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3159 | −0.430477 | −0.215238 | − | 0.976562i | \(-0.569053\pi\) | ||||
−0.215238 | + | 0.976562i | \(0.569053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.05443 | 0.305962 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.67151 | −0.253065 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.7803 | −0.938619 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0637 | −0.456292 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8584 | 0.447886 | 0.223943 | − | 0.974602i | \(-0.428107\pi\) | ||||
0.223943 | + | 0.974602i | \(0.428107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.6258 | 1.34365 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.1473 | −0.721129 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −68.0474 | −2.55919 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.79744 | −0.180172 | −0.0900858 | − | 0.995934i | \(-0.528714\pi\) | ||||
−0.0900858 | + | 0.995934i | \(0.528714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8661 | −0.520019 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.66385 | 0.249563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.16950 | −0.305522 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.05208 | 0.188673 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.1635 | −0.528209 | −0.264105 | − | 0.964494i | \(-0.585076\pi\) | ||||
−0.264105 | + | 0.964494i | \(0.585076\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.0742 | −0.971053 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.1868 | 0.787946 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.3671 | −0.496440 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5322 | 0.576059 | 0.288029 | − | 0.957622i | \(-0.407000\pi\) | ||||
0.288029 | + | 0.957622i | \(0.407000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.7638 | −0.989895 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.35869 | −0.0501843 | −0.0250922 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250922 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.7991 | 0.840957 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.19165 | 0.264908 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.0815 | −1.32728 | −0.663640 | − | 0.748052i | \(-0.730989\pi\) | ||||
−0.663640 | + | 0.748052i | \(0.730989\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.98201 | −0.329962 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.48440 | 0.201203 | 0.100602 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100602 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.35609 | 0.122958 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.9798 | −0.548081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.2092 | −1.03074 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8666 | −1.16283 | −0.581414 | − | 0.813608i | \(-0.697500\pi\) | ||||
−0.581414 | + | 0.813608i | \(0.697500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5889 | 0.422322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.4714 | −1.03618 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4940 | −0.563138 | −0.281569 | − | 0.959541i | \(-0.590855\pi\) | ||||
−0.281569 | + | 0.959541i | \(0.590855\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.37466 | −0.340278 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.7765 | 0.499399 | 0.249700 | − | 0.968323i | \(-0.419668\pi\) | ||||
0.249700 | + | 0.968323i | \(0.419668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.0915 | −2.06685 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.32832 | −0.156491 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.147600 | 0.00532952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.7485 | 1.72185 | 0.860927 | − | 0.508728i | \(-0.169884\pi\) | ||||
0.860927 | + | 0.508728i | \(0.169884\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.593402 | −0.0213708 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.91160 | −0.284560 | −0.142280 | − | 0.989826i | \(-0.545443\pi\) | ||||
−0.142280 | + | 0.989826i | \(0.545443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.31039 | 0.0829916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.3193 | −1.58994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.6108 | 1.31172 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6404 | −0.416527 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.45747 | −0.266508 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.0624 | −1.14435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.04807 | 0.215590 | 0.107795 | − | 0.994173i | \(-0.465621\pi\) | ||||
0.107795 | + | 0.994173i | \(0.465621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.07853 | −0.287603 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.4694 | 2.25671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.6127 | 0.412378 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.7239 | −0.380336 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.3854 | 0.367870 | 0.183935 | − | 0.982938i | \(-0.441116\pi\) | ||||
0.183935 | + | 0.982938i | \(0.441116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.8376 | −0.914069 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.96709 | −0.140170 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.85762 | −0.242000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.1279 | −1.44957 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.59074 | −0.161602 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8024 | 1.04780 | 0.523899 | − | 0.851781i | \(-0.324477\pi\) | ||||
0.523899 | + | 0.851781i | \(0.324477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.7347 | −0.482291 | −0.241145 | − | 0.970489i | \(-0.577523\pi\) | ||||
−0.241145 | + | 0.970489i | \(0.577523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.0274 | −0.667318 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.1028 | 0.704172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.5413 | 1.38338 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.1738 | 0.390445 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.5908 | 0.893124 | 0.446562 | − | 0.894753i | \(-0.352648\pi\) | ||||
0.446562 | + | 0.894753i | \(0.352648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.5326 | −1.44774 | −0.723868 | − | 0.689939i | \(-0.757638\pi\) | ||||
−0.723868 | + | 0.689939i | \(0.757638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.25024 | −0.113159 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.5733 | −1.06314 | −0.531569 | − | 0.847015i | \(-0.678397\pi\) | ||||
−0.531569 | + | 0.847015i | \(0.678397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.1329 | 1.39387 | 0.696937 | − | 0.717132i | \(-0.254546\pi\) | ||||
0.696937 | + | 0.717132i | \(0.254546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.5295 | 1.12844 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.7654 | 1.06596 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.85657 | −0.341101 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.28896 | 0.0445530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.1065 | 1.03939 | 0.519695 | − | 0.854352i | \(-0.326046\pi\) | ||||
0.519695 | + | 0.854352i | \(0.326046\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6138 | 0.917717 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.3406 | −0.872777 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9491 | 0.411061 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.2552 | 1.17702 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.181596 | −0.00623235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.5838 | 1.76827 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.3786 | −0.663509 | −0.331755 | − | 0.943366i | \(-0.607641\pi\) | ||||
−0.331755 | + | 0.943366i | \(0.607641\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.39474 | 0.218696 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.55876 | 0.326521 | 0.163260 | − | 0.986583i | \(-0.447799\pi\) | ||||
0.163260 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.2422 | −0.758894 | −0.379447 | − | 0.925213i | \(-0.623886\pi\) | ||||
−0.379447 | + | 0.925213i | \(0.623886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −45.5447 | −1.55216 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.9012 | 1.86886 | 0.934430 | − | 0.356147i | \(-0.115910\pi\) | ||||
0.934430 | + | 0.356147i | \(0.115910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.6176 | 0.769022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.1593 | 0.378990 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.1435 | 0.852933 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.97691 | 0.338055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.68234 | −0.260008 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −54.0353 | −1.82673 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.61018 | −0.121907 | −0.0609536 | − | 0.998141i | \(-0.519414\pi\) | ||||
−0.0609536 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.5225 | 0.658476 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.6558 | 1.80771 | 0.903856 | − | 0.427838i | \(-0.140724\pi\) | ||||
0.903856 | + | 0.427838i | \(0.140724\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.4251 | 1.39407 | 0.697033 | − | 0.717039i | \(-0.254503\pi\) | ||||
0.697033 | + | 0.717039i | \(0.254503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.105084 | −0.00353235 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.8980 | 0.735263 | 0.367632 | − | 0.929971i | \(-0.380169\pi\) | ||||
0.367632 | + | 0.929971i | \(0.380169\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.2456 | −1.95349 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.81330 | −0.0607480 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.1730 | 1.27741 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.2809 | 1.04561 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.0054 | −0.434237 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.61239 | −0.320591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4709 | −0.482096 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −49.1903 | −1.63695 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.8440 | −0.593154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.1990 | 1.86606 | 0.933028 | − | 0.359803i | \(-0.117156\pi\) | ||||
0.933028 | + | 0.359803i | \(0.117156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.3196 | 0.508119 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.2043 | −1.69648 | −0.848238 | − | 0.529616i | \(-0.822336\pi\) | ||||
−0.848238 | + | 0.529616i | \(0.822336\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.1629 | 0.898960 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.26765 | −0.273320 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.7287 | 1.51009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.6079 | 0.679792 | 0.339896 | − | 0.940463i | \(-0.389608\pi\) | ||||
0.339896 | + | 0.940463i | \(0.389608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.67738 | 0.252978 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.1486 | −0.531539 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.8844 | 0.588034 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.87011 | 0.192800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.6208 | −0.840591 | −0.420295 | − | 0.907387i | \(-0.638074\pi\) | ||||
−0.420295 | + | 0.907387i | \(0.638074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.4533 | −1.48967 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.8409 | −0.747778 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.84856 | 0.256675 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.7353 | −0.514049 | −0.257025 | − | 0.966405i | \(-0.582742\pi\) | ||||
−0.257025 | + | 0.966405i | \(0.582742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.51047 | 0.147194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.0599 | −1.89270 | −0.946349 | − | 0.323145i | \(-0.895260\pi\) | ||||
−0.946349 | + | 0.323145i | \(0.895260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.0101 | 1.72625 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.95521 | −0.258783 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.5628 | −0.960661 | −0.480330 | − | 0.877088i | \(-0.659483\pi\) | ||||
−0.480330 | + | 0.877088i | \(0.659483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.51351 | −0.308822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.22120 | 0.266591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0784 | 1.16869 | 0.584347 | − | 0.811504i | \(-0.301351\pi\) | ||||
0.584347 | + | 0.811504i | \(0.301351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.17370 | −0.232136 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.5226 | 0.437125 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.1781 | −1.45888 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3386 | −0.946406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.35078 | 0.204651 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.4652 | −1.10947 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6440 | −0.406603 | −0.203302 | − | 0.979116i | \(-0.565167\pi\) | ||||
−0.203302 | + | 0.979116i | \(0.565167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.62914 | 0.277208 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.0916 | −0.869412 | −0.434706 | − | 0.900572i | \(-0.643148\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.5463 | −0.530450 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.50903 | −0.144404 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.89384 | −0.220554 | −0.110277 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110277 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.19353 | 0.229906 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8531 | 0.410367 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.8660 | −1.04826 | −0.524131 | − | 0.851637i | \(-0.675610\pi\) | ||||
−0.524131 | + | 0.851637i | \(0.675610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.9489 | 1.43219 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.4881 | −1.51156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.2533 | 1.82055 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.5094 | 0.937398 | 0.468699 | − | 0.883358i | \(-0.344723\pi\) | ||||
0.468699 | + | 0.883358i | \(0.344723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5035 | −0.809328 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.1114 | −0.574171 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5507 | −0.365815 | −0.182907 | − | 0.983130i | \(-0.558551\pi\) | ||||
−0.182907 | + | 0.983130i | \(0.558551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.97766 | 0.315679 |
(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 | 6036.2.a.i.1.8 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.8 | ✓ | 26 | 1.1 | even | 1 | trivial |