Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 1.66428 | 0.960873 | 0.480436 | − | 0.877030i | \(-0.340478\pi\) | ||||
0.480436 | + | 0.877030i | \(0.340478\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.44274 | −1.53964 | −0.769819 | − | 0.638262i | \(-0.779654\pi\) | ||||
−0.769819 | + | 0.638262i | \(0.779654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.43077 | 1.67467 | 0.837336 | − | 0.546689i | \(-0.184112\pi\) | ||||
0.837336 | + | 0.546689i | \(0.184112\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.230172 | −0.0767239 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.18904 | 0.358509 | 0.179255 | − | 0.983803i | \(-0.442631\pi\) | ||||
0.179255 | + | 0.983803i | \(0.442631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.49702 | −0.969900 | −0.484950 | − | 0.874542i | \(-0.661162\pi\) | ||||
−0.484950 | + | 0.874542i | \(0.661162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.72968 | −1.47940 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.17128 | −0.526612 | −0.263306 | − | 0.964712i | \(-0.584813\pi\) | ||||
−0.263306 | + | 0.964712i | \(0.584813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.57445 | 1.27887 | 0.639433 | − | 0.768847i | \(-0.279169\pi\) | ||||
0.639433 | + | 0.768847i | \(0.279169\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.37404 | 1.60915 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.37514 | −1.53782 | −0.768911 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768911 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.85244 | 1.37049 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.37591 | −1.03459 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.21812 | −0.783284 | −0.391642 | − | 0.920118i | \(-0.628093\pi\) | ||||
−0.391642 | + | 0.920118i | \(0.628093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.45326 | −1.33864 | −0.669322 | − | 0.742972i | \(-0.733415\pi\) | ||||
−0.669322 | + | 0.742972i | \(0.733415\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97890 | 0.344482 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.2540 | −2.57839 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.18844 | −0.852975 | −0.426488 | − | 0.904493i | \(-0.640249\pi\) | ||||
−0.426488 | + | 0.904493i | \(0.640249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.82003 | −0.931950 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.01920 | −0.159172 | −0.0795861 | − | 0.996828i | \(-0.525360\pi\) | ||||
−0.0795861 | + | 0.996828i | \(0.525360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.120646 | −0.0183983 | −0.00919914 | − | 0.999958i | \(-0.502928\pi\) | ||||
−0.00919914 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.792421 | 0.118127 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.07754 | 0.448906 | 0.224453 | − | 0.974485i | \(-0.427941\pi\) | ||||
0.224453 | + | 0.974485i | \(0.427941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.6317 | 1.80453 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.61361 | −0.506007 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.80462 | −0.385245 | −0.192622 | − | 0.981273i | \(-0.561699\pi\) | ||||
−0.192622 | + | 0.981273i | \(0.561699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.09355 | −0.551975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.27745 | 1.22883 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.74850 | 0.357825 | 0.178912 | − | 0.983865i | \(-0.442742\pi\) | ||||
0.178912 | + | 0.983865i | \(0.442742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9165 | 1.39771 | 0.698855 | − | 0.715263i | \(-0.253693\pi\) | ||||
0.698855 | + | 0.715263i | \(0.253693\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.01984 | −0.128487 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0393 | 1.49330 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.55806 | −0.556855 | −0.278428 | − | 0.960457i | \(-0.589813\pi\) | ||||
−0.278428 | + | 0.960457i | \(0.589813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.2743 | −1.47765 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.710487 | −0.0843193 | −0.0421597 | − | 0.999111i | \(-0.513424\pi\) | ||||
−0.0421597 | + | 0.999111i | \(0.513424\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.34683 | −0.391717 | −0.195859 | − | 0.980632i | \(-0.562749\pi\) | ||||
−0.195859 | + | 0.980632i | \(0.562749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.4044 | 1.31686 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.26836 | 0.600385 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.35019 | −0.714452 | −0.357226 | − | 0.934018i | \(-0.616277\pi\) | ||||
−0.357226 | + | 0.934018i | \(0.616277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.25651 | −0.917390 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4018 | −1.47104 | −0.735520 | − | 0.677503i | \(-0.763062\pi\) | ||||
−0.735520 | + | 0.677503i | \(0.763062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.47514 | 0.810792 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.02013 | −0.752636 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.71069 | 1.02933 | 0.514665 | − | 0.857391i | \(-0.327916\pi\) | ||||
0.514665 | + | 0.857391i | \(0.327916\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4945 | −1.62426 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.4043 | −1.28627 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.1914 | −1.96899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.58484 | 0.770124 | 0.385062 | − | 0.922891i | \(-0.374180\pi\) | ||||
0.385062 | + | 0.922891i | \(0.374180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.273683 | −0.0275062 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3257 | −1.32595 | −0.662977 | − | 0.748640i | \(-0.730707\pi\) | ||||
−0.662977 | + | 0.748640i | \(0.730707\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.24375 | 0.615215 | 0.307607 | − | 0.951513i | \(-0.400472\pi\) | ||||
0.307607 | + | 0.951513i | \(0.400472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.3869 | −2.47750 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.29616 | 0.318652 | 0.159326 | − | 0.987226i | \(-0.449068\pi\) | ||||
0.159326 | + | 0.987226i | \(0.449068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.636565 | 0.0609719 | 0.0304860 | − | 0.999535i | \(-0.490295\pi\) | ||||
0.0304860 | + | 0.999535i | \(0.490295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.63503 | −0.819600 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.76089 | −0.824156 | −0.412078 | − | 0.911149i | \(-0.635197\pi\) | ||||
−0.412078 | + | 0.911149i | \(0.635197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.3907 | 2.36769 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.804916 | 0.0744145 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.62042 | −0.881902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.58618 | −0.871471 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.69623 | −0.152944 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.37746 | −0.570418 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2731 | 0.911589 | 0.455795 | − | 0.890085i | \(-0.349355\pi\) | ||||
0.455795 | + | 0.890085i | \(0.349355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.200788 | −0.0176784 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7673 | −1.63970 | −0.819852 | − | 0.572576i | \(-0.805944\pi\) | ||||
−0.819852 | + | 0.572576i | \(0.805944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.6991 | 2.14168 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.5078 | 1.59290 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.56580 | −0.646390 | −0.323195 | − | 0.946332i | \(-0.604757\pi\) | ||||
−0.323195 | + | 0.946332i | \(0.604757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6960 | −0.907222 | −0.453611 | − | 0.891200i | \(-0.649864\pi\) | ||||
−0.453611 | + | 0.891200i | \(0.649864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.12189 | 0.431341 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.15810 | −0.347718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.5219 | 1.20598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.0227 | 1.73392 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.548032 | −0.0448966 | −0.0224483 | − | 0.999748i | \(-0.507146\pi\) | ||||
−0.0224483 | + | 0.999748i | \(0.507146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.3768 | −1.00721 | −0.503605 | − | 0.863934i | \(-0.667993\pi\) | ||||
−0.503605 | + | 0.863934i | \(0.667993\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.499766 | 0.0404037 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.6596 | 2.06103 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4613 | −1.39356 | −0.696782 | − | 0.717283i | \(-0.745386\pi\) | ||||
−0.696782 | + | 0.717283i | \(0.745386\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.66768 | −0.370171 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −32.6775 | −2.57535 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.7025 | 1.38657 | 0.693285 | − | 0.720664i | \(-0.256163\pi\) | ||||
0.693285 | + | 0.720664i | \(0.256163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.81282 | −0.530377 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.39101 | −0.649316 | −0.324658 | − | 0.945832i | \(-0.605249\pi\) | ||||
−0.324658 | + | 0.945832i | \(0.605249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.770825 | −0.0592942 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.28308 | −0.0981196 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.47941 | 0.340563 | 0.170282 | − | 0.985395i | \(-0.445532\pi\) | ||||
0.170282 | + | 0.985395i | \(0.445532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.3616 | 2.29512 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.57428 | 0.343824 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6765 | 0.797997 | 0.398999 | − | 0.916951i | \(-0.369358\pi\) | ||||
0.398999 | + | 0.916951i | \(0.369358\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.00808 | −0.595236 | −0.297618 | − | 0.954685i | \(-0.596192\pi\) | ||||
−0.297618 | + | 0.954685i | \(0.596192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.1681 | 1.34302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.8625 | 1.31327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58174 | −0.188795 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.8194 | −1.73261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.844203 | 0.0610844 | 0.0305422 | − | 0.999533i | \(-0.490277\pi\) | ||||
0.0305422 | + | 0.999533i | \(0.490277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4651 | 1.32915 | 0.664573 | − | 0.747223i | \(-0.268614\pi\) | ||||
0.664573 | + | 0.747223i | \(0.268614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0368 | 1.43487 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.91364 | −0.706318 | −0.353159 | − | 0.935563i | \(-0.614892\pi\) | ||||
−0.353159 | + | 0.935563i | \(0.614892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2198 | −1.22068 | −0.610341 | − | 0.792139i | \(-0.708968\pi\) | ||||
−0.610341 | + | 0.792139i | \(0.708968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.58588 | −0.535067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.6895 | −1.31174 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.50883 | 0.245068 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.69755 | 0.117988 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.62824 | 0.458485 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4567 | −0.719867 | −0.359933 | − | 0.932978i | \(-0.617201\pi\) | ||||
−0.359933 | + | 0.932978i | \(0.617201\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.18245 | −0.0810201 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.415351 | 0.0283267 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.0236 | −2.24179 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.57007 | −0.376390 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.59301 | 0.510761 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.52993 | −0.169417 | −0.0847083 | − | 0.996406i | \(-0.526996\pi\) | ||||
−0.0847083 | + | 0.996406i | \(0.526996\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.57724 | −0.105149 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.9881 | −1.79126 | −0.895632 | − | 0.444795i | \(-0.853277\pi\) | ||||
−0.895632 | + | 0.444795i | \(0.853277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.6989 | −1.16958 | −0.584789 | − | 0.811185i | \(-0.698823\pi\) | ||||
−0.584789 | + | 0.811185i | \(0.698823\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.76802 | 0.576894 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.68990 | 0.110709 | 0.0553544 | − | 0.998467i | \(-0.482371\pi\) | ||||
0.0553544 | + | 0.998467i | \(0.482371\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5952 | −0.691152 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.5685 | −0.686498 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8826 | 1.67421 | 0.837103 | − | 0.547045i | \(-0.184247\pi\) | ||||
0.837103 | + | 0.547045i | \(0.184247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9079 | 1.60446 | 0.802229 | − | 0.597016i | \(-0.203647\pi\) | ||||
0.802229 | + | 0.597016i | \(0.203647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.38659 | 0.153100 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −43.4876 | −2.77832 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.4940 | −1.24037 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.3044 | −1.41348 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.5831 | −1.55167 | −0.775837 | − | 0.630933i | \(-0.782672\pi\) | ||||
−0.775837 | + | 0.630933i | \(0.782672\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.76933 | −0.551323 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.4407 | 0.779068 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1488 | 0.633068 | 0.316534 | − | 0.948581i | \(-0.397481\pi\) | ||||
0.316534 | + | 0.948581i | \(0.397481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.9888 | −1.42845 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.970891 | 0.0600966 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1732 | 0.688972 | 0.344486 | − | 0.938791i | \(-0.388053\pi\) | ||||
0.344486 | + | 0.938791i | \(0.388053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.65558 | 0.593138 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.1613 | 0.989056 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.4053 | −1.18316 | −0.591581 | − | 0.806245i | \(-0.701496\pi\) | ||||
−0.591581 | + | 0.806245i | \(0.701496\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6613 | −0.769117 | −0.384559 | − | 0.923101i | \(-0.625646\pi\) | ||||
−0.384559 | + | 0.923101i | \(0.625646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.7872 | −1.56071 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.14783 | 0.491332 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6562 | −0.700351 | −0.350175 | − | 0.936684i | \(-0.613878\pi\) | ||||
−0.350175 | + | 0.936684i | \(0.613878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.71553 | 0.102706 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2193 | 1.08687 | 0.543437 | − | 0.839450i | \(-0.317123\pi\) | ||||
0.543437 | + | 0.839450i | \(0.317123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4899 | 1.15855 | 0.579276 | − | 0.815132i | \(-0.303335\pi\) | ||||
0.579276 | + | 0.815132i | \(0.303335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.9398 | −1.89195 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.51583 | −0.266561 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2856 | −0.722680 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.6233 | 0.739991 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.98593 | −0.232860 | −0.116430 | − | 0.993199i | \(-0.537145\pi\) | ||||
−0.116430 | + | 0.993199i | \(0.537145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.46237 | −0.550921 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.39217 | −0.370912 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.7910 | 1.49153 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.534552 | −0.0308111 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.1776 | −1.27407 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −37.5825 | −2.15197 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.14719 | −0.122546 | −0.0612732 | − | 0.998121i | \(-0.519516\pi\) | ||||
−0.0612732 | + | 0.998121i | \(0.519516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3913 | 0.591143 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.36490 | 0.0773963 | 0.0386981 | − | 0.999251i | \(-0.487679\pi\) | ||||
0.0386981 | + | 0.999251i | \(0.487679\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.1919 | 0.915222 | 0.457611 | − | 0.889153i | \(-0.348705\pi\) | ||||
0.457611 | + | 0.889153i | \(0.348705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.51103 | 0.197824 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.3104 | 1.14075 | 0.570374 | − | 0.821385i | \(-0.306798\pi\) | ||||
0.570374 | + | 0.821385i | \(0.306798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.01551 | −0.280815 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.48574 | 0.306184 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1037 | −0.673466 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.9631 | −1.32924 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.05942 | 0.0585862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6359 | 0.751770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.23075 | −0.507368 | −0.253684 | − | 0.967287i | \(-0.581642\pi\) | ||||
−0.253684 | + | 0.967287i | \(0.581642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.19423 | 0.0654436 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.6922 | 0.857356 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1199 | 0.932580 | 0.466290 | − | 0.884632i | \(-0.345590\pi\) | ||||
0.466290 | + | 0.884632i | \(0.345590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.5806 | −0.791908 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.86222 | −0.479916 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.9527 | 1.34732 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 42.2572 | 2.27505 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7339 | 0.576226 | 0.288113 | − | 0.957596i | \(-0.406972\pi\) | ||||
0.288113 | + | 0.957596i | \(0.406972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3070 | 0.765838 | 0.382919 | − | 0.923782i | \(-0.374919\pi\) | ||||
0.382919 | + | 0.923782i | \(0.374919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7997 | 1.00345 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.3791 | 0.765320 | 0.382660 | − | 0.923889i | \(-0.375008\pi\) | ||||
0.382660 | + | 0.923889i | \(0.375008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.44602 | 0.129821 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.0111 | −0.847396 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.5958 | 1.19256 | 0.596281 | − | 0.802776i | \(-0.296645\pi\) | ||||
0.596281 | + | 0.802776i | \(0.296645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0745 | 0.635499 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.9541 | −0.837373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5223 | 0.603103 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.8333 | 1.76609 | 0.883043 | − | 0.469292i | \(-0.155491\pi\) | ||||
0.883043 | + | 0.469292i | \(0.155491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.234591 | 0.0122123 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4266 | −0.645159 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.1865 | −0.527438 | −0.263719 | − | 0.964600i | \(-0.584949\pi\) | ||||
−0.263719 | + | 0.964600i | \(0.584949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.6139 | −0.548099 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.7508 | 0.759707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.6614 | −0.547641 | −0.273821 | − | 0.961781i | \(-0.588287\pi\) | ||||
−0.273821 | + | 0.961781i | \(0.588287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.0973 | 0.875921 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.1930 | −1.49169 | −0.745846 | − | 0.666119i | \(-0.767954\pi\) | ||||
−0.745846 | + | 0.666119i | \(0.767954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.1376 | −0.924376 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0277692 | 0.00141159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.9539 | −1.31591 | −0.657957 | − | 0.753056i | \(-0.728579\pi\) | ||||
−0.657957 | + | 0.753056i | \(0.728579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0135 | 0.809836 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.2340 | −1.57555 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.8620 | 1.10000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.93633 | 0.147370 | 0.0736852 | − | 0.997282i | \(-0.476524\pi\) | ||||
0.0736852 | + | 0.997282i | \(0.476524\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 41.1062 | 2.05788 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.7042 | −0.834167 | −0.417084 | − | 0.908868i | \(-0.636948\pi\) | ||||
−0.417084 | + | 0.908868i | \(0.636948\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.0642 | 1.29835 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.4250 | 1.41245 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.16927 | −0.305799 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.7034 | 1.51819 | 0.759093 | − | 0.650982i | \(-0.225643\pi\) | ||||
0.759093 | + | 0.650982i | \(0.225643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5916 | −0.621099 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.1780 | 0.599239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 46.1389 | 2.26487 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.8011 | −0.871725 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.56186 | −0.0763018 | −0.0381509 | − | 0.999272i | \(-0.512147\pi\) | ||||
−0.0381509 | + | 0.999272i | \(0.512147\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.04875 | 0.392272 | 0.196136 | − | 0.980577i | \(-0.437161\pi\) | ||||
0.196136 | + | 0.980577i | \(0.437161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.708363 | −0.0344418 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.8785 | −0.721715 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.3683 | 2.34071 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.92025 | −0.334113 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.5999 | 1.13677 | 0.568383 | − | 0.822764i | \(-0.307569\pi\) | ||||
0.568383 | + | 0.822764i | \(0.307569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.33138 | 0.448438 | 0.224219 | − | 0.974539i | \(-0.428017\pi\) | ||||
0.224219 | + | 0.974539i | \(0.428017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.1684 | 1.15879 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −41.1123 | −1.96667 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0237 | 1.14659 | 0.573295 | − | 0.819349i | \(-0.305665\pi\) | ||||
0.573295 | + | 0.819349i | \(0.305665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.90746 | −0.138450 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.08695 | 0.0991539 | 0.0495769 | − | 0.998770i | \(-0.484213\pi\) | ||||
0.0495769 | + | 0.998770i | \(0.484213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.4313 | −1.58480 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.912079 | −0.0431399 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.51869 | 0.260443 | 0.130221 | − | 0.991485i | \(-0.458431\pi\) | ||||
0.130221 | + | 0.991485i | \(0.458431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.21187 | −0.0570647 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.5985 | −0.967800 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 53.3435 | 2.50078 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9386 | −0.885912 | −0.442956 | − | 0.896543i | \(-0.646070\pi\) | ||||
−0.442956 | + | 0.896543i | \(0.646070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.6726 | 0.544830 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.9924 | 1.21059 | 0.605293 | − | 0.796003i | \(-0.293056\pi\) | ||||
0.605293 | + | 0.796003i | \(0.293056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.9190 | 1.66930 | 0.834650 | − | 0.550781i | \(-0.185670\pi\) | ||||
0.834650 | + | 0.550781i | \(0.185670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.7048 | 1.98039 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.83647 | −0.455177 | −0.227589 | − | 0.973757i | \(-0.573084\pi\) | ||||
−0.227589 | + | 0.973757i | \(0.573084\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.1957 | −0.932550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.0605 | −1.33904 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.143452 | −0.00659595 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.1986 | 1.75267 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.645545 | 0.0295575 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.2528 | 0.559843 | 0.279922 | − | 0.960023i | \(-0.409692\pi\) | ||||
0.279922 | + | 0.960023i | \(0.409692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.1441 | 0.827300 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −54.3845 | −2.47458 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.1126 | −1.18571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5386 | −1.42915 | −0.714576 | − | 0.699558i | \(-0.753380\pi\) | ||||
−0.714576 | + | 0.699558i | \(0.753380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.4620 | 1.33232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.4460 | −1.37401 | −0.687004 | − | 0.726654i | \(-0.741074\pi\) | ||||
−0.687004 | + | 0.726654i | \(0.741074\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.15870 | 0.412487 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.942220 | 0.0423496 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.14800 | −0.141207 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.7996 | 0.931117 | 0.465558 | − | 0.885017i | \(-0.345854\pi\) | ||||
0.465558 | + | 0.885017i | \(0.345854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9650 | −0.623910 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.8768 | 2.04149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.28287 | −0.0569742 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.3203 | −1.03365 | −0.516826 | − | 0.856090i | \(-0.672887\pi\) | ||||
−0.516826 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8290 | −0.655998 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.9677 | −1.32311 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.4956 | −0.947208 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.65932 | 0.160937 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.45499 | 0.327238 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.4086 | −1.11317 | −0.556586 | − | 0.830790i | \(-0.687889\pi\) | ||||
−0.556586 | + | 0.830790i | \(0.687889\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6210 | −1.33896 | −0.669480 | − | 0.742830i | \(-0.733483\pi\) | ||||
−0.669480 | + | 0.742830i | \(0.733483\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 50.5301 | 2.20532 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.1831 | 0.704946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3926 | 1.36490 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.632627 | −0.0274537 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.56416 | 0.154381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3478 | −0.490609 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.7686 | 0.766774 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0196 | 0.646939 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1009 | 0.520257 | 0.260129 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260129 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.3277 | −0.571946 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.19153 | −0.0938747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3069 | 1.42410 | 0.712050 | − | 0.702129i | \(-0.247767\pi\) | ||||
0.712050 | + | 0.702129i | \(0.247767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.51266 | −0.107238 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.5137 | −1.00172 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.1362 | −1.19647 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.7281 | 1.26189 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7330 | 1.34457 | 0.672285 | − | 0.740292i | \(-0.265313\pi\) | ||||
0.672285 | + | 0.740292i | \(0.265313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.421900 | 0.0178445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.29673 | −0.181408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.9937 | 1.55910 | 0.779550 | − | 0.626341i | \(-0.215448\pi\) | ||||
0.779550 | + | 0.626341i | \(0.215448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.1615 | 1.26890 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.5826 | −1.53633 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.61211 | 0.402961 | 0.201480 | − | 0.979493i | \(-0.435425\pi\) | ||||
0.201480 | + | 0.979493i | \(0.435425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.49307 | −0.271727 | −0.135863 | − | 0.990728i | \(-0.543381\pi\) | ||||
−0.135863 | + | 0.990728i | \(0.543381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.40499 | 0.0586943 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −50.5377 | −2.10757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.2064 | 1.96523 | 0.982614 | − | 0.185659i | \(-0.0594419\pi\) | ||||
0.982614 | + | 0.185659i | \(0.0594419\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.7311 | 1.27714 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −59.3803 | −2.46351 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.33481 | −0.138114 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.77111 | −0.114571 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.61084 | 0.231584 | 0.115792 | − | 0.993273i | \(-0.463059\pi\) | ||||
0.115792 | + | 0.993273i | \(0.463059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.5478 | −1.71195 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.4991 | −0.678681 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0721 | 1.02959 | 0.514793 | − | 0.857314i | \(-0.327869\pi\) | ||||
0.514793 | + | 0.857314i | \(0.327869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33.1206 | 1.35781 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.6586 | −1.17292 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.1633 | −1.15072 | −0.575361 | − | 0.817900i | \(-0.695138\pi\) | ||||
−0.575361 | + | 0.817900i | \(0.695138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.8480 | −1.09515 | −0.547576 | − | 0.836756i | \(-0.684449\pi\) | ||||
−0.547576 | + | 0.836756i | \(0.684449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.04914 | 0.0427241 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.0027 | 1.34175 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.2396 | −1.71445 | −0.857225 | − | 0.514942i | \(-0.827814\pi\) | ||||
−0.857225 | + | 0.514942i | \(0.827814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.1045 | −1.26042 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7622 | −0.435393 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3212 | −1.30544 | −0.652721 | − | 0.757598i | \(-0.726373\pi\) | ||||
−0.652721 | + | 0.757598i | \(0.726373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.83968 | 0.235479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9580 | 0.883995 | 0.441997 | − | 0.897016i | \(-0.354270\pi\) | ||||
0.441997 | + | 0.897016i | \(0.354270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7735 | −0.473216 | −0.236608 | − | 0.971605i | \(-0.576036\pi\) | ||||
−0.236608 | + | 0.971605i | \(0.576036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.6481 | 1.59102 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.0258 | 1.72379 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.3063 | −0.492251 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0313 | 0.440546 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.2655 | 0.449187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3254 | 0.729523 | 0.364762 | − | 0.931101i | \(-0.381150\pi\) | ||||
0.364762 | + | 0.931101i | \(0.381150\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.4028 | −0.691700 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.3675 | −1.40352 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.1733 | −1.75021 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.163534 | 0.00646930 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.9149 | 0.786592 | 0.393296 | − | 0.919412i | \(-0.371335\pi\) | ||||
0.393296 | + | 0.919412i | \(0.371335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.73358 | 0.0683655 | 0.0341828 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341828 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.691260 | 0.0272183 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.9039 | −1.33290 | −0.666449 | − | 0.745551i | \(-0.732187\pi\) | ||||
−0.666449 | + | 0.745551i | \(0.732187\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.26808 | 0.128283 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −54.9606 | −2.15407 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.6760 | −0.613450 | −0.306725 | − | 0.951798i | \(-0.599233\pi\) | ||||
−0.306725 | + | 0.951798i | \(0.599233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.6108 | 2.52455 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.770346 | 0.0300541 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.2087 | −1.52736 | −0.763678 | − | 0.645598i | \(-0.776608\pi\) | ||||
−0.763678 | + | 0.645598i | \(0.776608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.444082 | 0.0172728 | 0.00863640 | − | 0.999963i | \(-0.497251\pi\) | ||||
0.00863640 | + | 0.999963i | \(0.497251\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.6369 | 0.490776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −85.0324 | −3.29742 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1092 | 1.20455 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.21051 | −0.162788 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.9801 | 0.501092 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.69877 | −0.296766 | −0.148383 | − | 0.988930i | \(-0.547407\pi\) | ||||
−0.148383 | + | 0.988930i | \(0.547407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −36.8381 | −1.41790 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.7491 | −0.912751 | −0.456376 | − | 0.889787i | \(-0.650853\pi\) | ||||
−0.456376 | + | 0.889787i | \(0.650853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.6067 | 1.28971 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −44.9158 | −1.72118 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.6013 | 1.93620 | 0.968102 | − | 0.250556i | \(-0.0806134\pi\) | ||||
0.968102 | + | 0.250556i | \(0.0806134\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.0471 | 0.995207 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.4560 | −1.12382 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.80784 | 0.373649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.7377 | −0.903025 | −0.451512 | − | 0.892265i | \(-0.649115\pi\) | ||||
−0.451512 | + | 0.892265i | \(0.649115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.21263 | −0.0460639 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.8235 | 1.39679 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.21296 | 0.0838220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.81246 | 0.106377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.6053 | 1.45810 | 0.729051 | − | 0.684460i | \(-0.239962\pi\) | ||||
0.729051 | + | 0.684460i | \(0.239962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.9227 | −1.09084 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.6333 | −0.664109 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −59.0429 | −2.22054 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7065 | −0.965426 | −0.482713 | − | 0.875779i | \(-0.660349\pi\) | ||||
−0.482713 | + | 0.875779i | \(0.660349\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.46163 | 0.0548156 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 54.9688 | 2.05860 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.3153 | 0.535360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.0759 | 1.60870 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9169 | −1.22759 | −0.613796 | − | 0.789465i | \(-0.710358\pi\) | ||||
−0.613796 | + | 0.789465i | \(0.710358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.6646 | 1.03028 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.4537 | 1.54168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.9044 | −1.07348 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5790 | 1.17120 | 0.585600 | − | 0.810600i | \(-0.300859\pi\) | ||||
0.585600 | + | 0.810600i | \(0.300859\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.7415 | 1.06450 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.261955 | 0.00968875 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.80843 | 0.140668 | 0.0703338 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703338 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −72.3755 | −2.66961 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.41971 | −0.199638 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.43646 | −0.0528411 | −0.0264205 | − | 0.999651i | \(-0.508411\pi\) | ||||
−0.0264205 | + | 0.999651i | \(0.508411\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.4434 | −1.19184 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.3477 | −0.966605 | −0.483302 | − | 0.875453i | \(-0.660563\pi\) | ||||
−0.483302 | + | 0.875453i | \(0.660563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.88673 | 0.0691245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.08472 | 0.112864 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.6045 | 0.533638 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.72181 | 0.172301 | 0.0861506 | − | 0.996282i | \(-0.472543\pi\) | ||||
0.0861506 | + | 0.996282i | \(0.472543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −40.9132 | −1.49096 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.6101 | 1.55074 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.9298 | −1.45127 | −0.725637 | − | 0.688078i | \(-0.758455\pi\) | ||||
−0.725637 | + | 0.688078i | \(0.758455\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.5946 | −0.529751 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.2738 | 1.42367 | 0.711837 | − | 0.702344i | \(-0.247863\pi\) | ||||
0.711837 | + | 0.702344i | \(0.247863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.82047 | 0.102108 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.72056 | −0.0622071 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.61158 | −0.347054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.4607 | 1.53117 | 0.765586 | − | 0.643334i | \(-0.222449\pi\) | ||||
0.765586 | + | 0.643334i | \(0.222449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.8905 | 0.608297 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.8437 | 1.61292 | 0.806459 | − | 0.591291i | \(-0.201381\pi\) | ||||
0.806459 | + | 0.591291i | \(0.201381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −51.0730 | −1.83460 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −38.2598 | −1.37256 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.68147 | −0.203560 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.844798 | −0.0302292 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.6762 | 0.810382 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.1147 | 2.14559 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.7168 | 1.80786 | 0.903929 | − | 0.427682i | \(-0.140670\pi\) | ||||
0.903929 | + | 0.427682i | \(0.140670\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.5954 | 0.662014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.8175 | −1.38019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.1752 | −1.35564 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.0696 | 0.569930 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.2596 | 1.10727 | 0.553635 | − | 0.832759i | \(-0.313240\pi\) | ||||
0.553635 | + | 0.832759i | \(0.313240\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.68219 | −0.236399 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.23513 | −0.0789743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.97952 | −0.140434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 112.500 | 3.96511 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.2959 | −1.13687 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.92457 | −0.243455 | −0.121727 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121727 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0880 | 0.354236 | 0.177118 | − | 0.984190i | \(-0.443323\pi\) | ||||
0.177118 | + | 0.984190i | \(0.443323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.0719 | −0.739024 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.9452 | −2.13482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.672533 | −0.0235289 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.56639 | 0.124620 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.2386 | 1.75334 | 0.876669 | − | 0.481093i | \(-0.159760\pi\) | ||||
0.876669 | + | 0.481093i | \(0.159760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.8517 | 1.77258 | 0.886290 | − | 0.463131i | \(-0.153274\pi\) | ||||
0.886290 | + | 0.463131i | \(0.153274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5603 | 0.472108 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.04513 | −0.244983 | −0.122492 | − | 0.992470i | \(-0.539088\pi\) | ||||
−0.122492 | + | 0.992470i | \(0.539088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.8119 | −0.896483 | −0.448241 | − | 0.893913i | \(-0.647949\pi\) | ||||
−0.448241 | + | 0.893913i | \(0.647949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.3991 | −0.672948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.4269 | −0.950285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.8880 | 0.999712 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.0680 | 1.38495 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.6885 | 1.30115 | 0.650576 | − | 0.759441i | \(-0.274527\pi\) | ||||
0.650576 | + | 0.759441i | \(0.274527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2075 | −0.386466 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.3220 | 1.04435 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.65375 | 0.0912917 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.4741 | −1.45943 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.4366 | 1.11322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.2655 | 1.31172 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.3708 | −1.72466 | −0.862332 | − | 0.506342i | \(-0.830997\pi\) | ||||
−0.862332 | + | 0.506342i | \(0.830997\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.41731 | 0.151069 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.3295 | −1.68506 | −0.842532 | − | 0.538647i | \(-0.818936\pi\) | ||||
−0.842532 | + | 0.538647i | \(0.818936\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.9902 | 1.63740 | 0.818702 | − | 0.574219i | \(-0.194694\pi\) | ||||
0.818702 | + | 0.574219i | \(0.194694\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.51561 | −0.256131 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.1553 | −1.53710 | −0.768552 | − | 0.639788i | \(-0.779022\pi\) | ||||
−0.768552 | + | 0.639788i | \(0.779022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.4214 | −0.524344 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.4466 | −0.694403 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.55063 | −0.256138 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.9396 | 0.540094 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.74582 | −0.0590869 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.2571 | −0.955263 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.47313 | −0.319885 | −0.159942 | − | 0.987126i | \(-0.551131\pi\) | ||||
−0.159942 | + | 0.987126i | \(0.551131\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.63370 | −0.223749 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.9715 | −1.00976 | −0.504882 | − | 0.863188i | \(-0.668464\pi\) | ||||
−0.504882 | + | 0.863188i | \(0.668464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.0660 | −1.55024 | −0.775122 | − | 0.631811i | \(-0.782312\pi\) | ||||
−0.775122 | + | 0.631811i | \(0.782312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.7480 | −0.529365 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.4170 | 1.82715 | 0.913573 | − | 0.406675i | \(-0.133312\pi\) | ||||
0.913573 | + | 0.406675i | \(0.133312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.5176 | 1.52661 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.81732 | −0.328893 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.1556 | 0.574090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36.7563 | −1.22863 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.9235 | 1.43317 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.4387 | 1.04854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.08962 | 0.202875 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.889645 | −0.0296055 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.5697 | 0.916449 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.0368 | −0.997357 | −0.498678 | − | 0.866787i | \(-0.666181\pi\) | ||||
−0.498678 | + | 0.866787i | \(0.666181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.06719 | 0.101732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0040 | −1.39166 | −0.695828 | − | 0.718209i | \(-0.744962\pi\) | ||||
−0.695828 | + | 0.718209i | \(0.744962\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.9353 | −0.527381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −62.5479 | −2.06777 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −83.1534 | −2.74597 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.7108 | −1.14500 | −0.572502 | − | 0.819903i | \(-0.694027\pi\) | ||||
−0.572502 | + | 0.819903i | \(0.694027\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.57352 | −0.117751 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.48459 | 0.0817813 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.5535 | −1.16899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.43713 | −0.0472017 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.0708 | −1.15064 | −0.575318 | − | 0.817930i | \(-0.695122\pi\) | ||||
−0.575318 | + | 0.817930i | \(0.695122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70.4147 | 2.30775 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.27157 | 0.0743680 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.88824 | 0.290676 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.9508 | 0.945781 | 0.472890 | − | 0.881121i | \(-0.343211\pi\) | ||||
0.472890 | + | 0.881121i | \(0.343211\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.9479 | 0.879412 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.91056 | 0.160080 | 0.0800398 | − | 0.996792i | \(-0.474495\pi\) | ||||
0.0800398 | + | 0.996792i | \(0.474495\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.51673 | 0.244778 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 82.0039 | 2.66759 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.2429 | 0.527825 | 0.263912 | − | 0.964547i | \(-0.414987\pi\) | ||||
0.263912 | + | 0.964547i | \(0.414987\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.7040 | 0.379926 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.8023 | 1.09611 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.1190 | 0.360178 | 0.180089 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180089 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.90637 | −0.0940479 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.34721 | −0.269827 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.5223 | −1.08249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5510 | 0.791969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.758683 | −0.0244482 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −63.5704 | −2.04640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.8298 | 0.798473 | 0.399236 | − | 0.916848i | \(-0.369275\pi\) | ||||
0.399236 | + | 0.916848i | \(0.369275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.1439 | −0.647115 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.97994 | 0.0956309 | 0.0478154 | − | 0.998856i | \(-0.484774\pi\) | ||||
0.0478154 | + | 0.998856i | \(0.484774\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.3914 | −1.51930 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39.8814 | −1.27723 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.9009 | −1.53249 | −0.766243 | − | 0.642551i | \(-0.777876\pi\) | ||||
−0.766243 | + | 0.642551i | \(0.777876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5464 | 0.369025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.146519 | −0.00467800 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.3043 | −1.34930 | −0.674649 | − | 0.738139i | \(-0.735705\pi\) | ||||
−0.674649 | + | 0.738139i | \(0.735705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.1301 | 1.08747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.6939 | 0.722355 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.889777 | 0.0282933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4541 | 0.459151 | 0.229575 | − | 0.973291i | \(-0.426266\pi\) | ||||
0.229575 | + | 0.973291i | \(0.426266\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.3626 | −0.487516 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 59.2834 | 1.87941 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7728 | −0.626211 | −0.313105 | − | 0.949718i | \(-0.601369\pi\) | ||||
−0.313105 | + | 0.949718i | \(0.601369\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.8926 | 0.882483 |
(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 | 4024.2.a.d.1.21 | ✓ | 28 | |
4.3 | odd | 2 | 8048.2.a.v.1.8 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.21 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8048.2.a.v.1.8 | 28 | 4.3 | odd | 2 |