Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73865 | −1.93652 | −0.968260 | − | 0.249946i | \(-0.919587\pi\) | ||||
−0.968260 | + | 0.249946i | \(0.919587\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.50022 | 2.75011 | ||||||||
\(5\) | −2.48832 | −1.11281 | −0.556404 | − | 0.830912i | \(-0.687819\pi\) | ||||
−0.556404 | + | 0.830912i | \(0.687819\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.47965 | 0.937220 | 0.468610 | − | 0.883405i | \(-0.344755\pi\) | ||||
0.468610 | + | 0.883405i | \(0.344755\pi\) | |||||||
\(8\) | −9.58588 | −3.38912 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.81463 | 2.15498 | ||||||||
\(11\) | 3.17008 | 0.955815 | 0.477907 | − | 0.878410i | \(-0.341395\pi\) | ||||
0.477907 | + | 0.878410i | \(0.341395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.77948 | 1.88029 | 0.940145 | − | 0.340775i | \(-0.110689\pi\) | ||||
0.940145 | + | 0.340775i | \(0.110689\pi\) | |||||||
\(14\) | −6.79090 | −1.81494 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.2520 | 3.81299 | ||||||||
\(17\) | 3.00920 | 0.729839 | 0.364920 | − | 0.931039i | \(-0.381096\pi\) | ||||
0.364920 | + | 0.931039i | \(0.381096\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.29624 | −1.44446 | −0.722228 | − | 0.691655i | \(-0.756882\pi\) | ||||
−0.722228 | + | 0.691655i | \(0.756882\pi\) | |||||||
\(20\) | −13.6863 | −3.06034 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.68174 | −1.85095 | ||||||||
\(23\) | 2.42607 | 0.505871 | 0.252935 | − | 0.967483i | \(-0.418604\pi\) | ||||
0.252935 | + | 0.967483i | \(0.418604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.19172 | 0.238343 | ||||||||
\(26\) | −18.5666 | −3.64122 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.6386 | 2.57746 | ||||||||
\(29\) | −0.314777 | −0.0584526 | −0.0292263 | − | 0.999573i | \(-0.509304\pi\) | ||||
−0.0292263 | + | 0.999573i | \(0.509304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.36807 | −1.32334 | −0.661672 | − | 0.749793i | \(-0.730153\pi\) | ||||
−0.661672 | + | 0.749793i | \(0.730153\pi\) | |||||||
\(32\) | −22.5981 | −3.99481 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.24116 | −1.41335 | ||||||||
\(35\) | −6.17015 | −1.04295 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4814 | −1.72313 | −0.861567 | − | 0.507643i | \(-0.830517\pi\) | ||||
−0.861567 | + | 0.507643i | \(0.830517\pi\) | |||||||
\(38\) | 17.2432 | 2.79722 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 23.8527 | 3.77144 | ||||||||
\(41\) | −6.72800 | −1.05074 | −0.525369 | − | 0.850875i | \(-0.676073\pi\) | ||||
−0.525369 | + | 0.850875i | \(0.676073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.53813 | −1.14955 | −0.574777 | − | 0.818310i | \(-0.694911\pi\) | ||||
−0.574777 | + | 0.818310i | \(0.694911\pi\) | |||||||
\(44\) | 17.4361 | 2.62859 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.64416 | −0.979628 | ||||||||
\(47\) | −8.67317 | −1.26511 | −0.632556 | − | 0.774515i | \(-0.717994\pi\) | ||||
−0.632556 | + | 0.774515i | \(0.717994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.851331 | −0.121619 | ||||||||
\(50\) | −3.26369 | −0.461556 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 37.2886 | 5.17100 | ||||||||
\(53\) | 4.75661 | 0.653371 | 0.326685 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326685 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.88816 | −1.06364 | ||||||||
\(56\) | −23.7696 | −3.17635 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.862065 | 0.113195 | ||||||||
\(59\) | 6.54400 | 0.851956 | 0.425978 | − | 0.904733i | \(-0.359930\pi\) | ||||
0.425978 | + | 0.904733i | \(0.359930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.08687 | −1.03542 | −0.517709 | − | 0.855557i | \(-0.673215\pi\) | ||||
−0.517709 | + | 0.855557i | \(0.673215\pi\) | |||||||
\(62\) | 20.1786 | 2.56268 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31.3843 | 3.92304 | ||||||||
\(65\) | −16.8695 | −2.09240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.75384 | −0.947283 | −0.473641 | − | 0.880718i | \(-0.657061\pi\) | ||||
−0.473641 | + | 0.880718i | \(0.657061\pi\) | |||||||
\(68\) | 16.5513 | 2.00714 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 16.8979 | 2.01969 | ||||||||
\(71\) | 5.97566 | 0.709181 | 0.354590 | − | 0.935022i | \(-0.384620\pi\) | ||||
0.354590 | + | 0.935022i | \(0.384620\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.31360 | 0.153745 | 0.0768726 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768726 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(74\) | 28.7050 | 3.33688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34.6307 | −3.97241 | ||||||||
\(77\) | 7.86069 | 0.895808 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3076 | 1.60973 | 0.804867 | − | 0.593455i | \(-0.202237\pi\) | ||||
0.804867 | + | 0.593455i | \(0.202237\pi\) | |||||||
\(80\) | −37.9517 | −4.24313 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.4257 | 2.03477 | ||||||||
\(83\) | −4.52789 | −0.497001 | −0.248500 | − | 0.968632i | \(-0.579938\pi\) | ||||
−0.248500 | + | 0.968632i | \(0.579938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.48785 | −0.812171 | ||||||||
\(86\) | 20.6443 | 2.22613 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30.3880 | −3.23937 | ||||||||
\(89\) | 4.07376 | 0.431817 | 0.215909 | − | 0.976414i | \(-0.430729\pi\) | ||||
0.215909 | + | 0.976414i | \(0.430729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.8107 | 1.76225 | ||||||||
\(92\) | 13.3439 | 1.39120 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 23.7528 | 2.44991 | ||||||||
\(95\) | 15.6670 | 1.60740 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.45212 | 0.858183 | 0.429091 | − | 0.903261i | \(-0.358834\pi\) | ||||
0.429091 | + | 0.903261i | \(0.358834\pi\) | |||||||
\(98\) | 2.33150 | 0.235517 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.55469 | 0.655469 | ||||||||
\(101\) | −13.2721 | −1.32062 | −0.660311 | − | 0.750992i | \(-0.729576\pi\) | ||||
−0.660311 | + | 0.750992i | \(0.729576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.97594 | −0.982959 | −0.491479 | − | 0.870889i | \(-0.663544\pi\) | ||||
−0.491479 | + | 0.870889i | \(0.663544\pi\) | |||||||
\(104\) | −64.9873 | −6.37253 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.0267 | −1.26527 | ||||||||
\(107\) | −0.379534 | −0.0366909 | −0.0183455 | − | 0.999832i | \(-0.505840\pi\) | ||||
−0.0183455 | + | 0.999832i | \(0.505840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.55120 | −0.244360 | −0.122180 | − | 0.992508i | \(-0.538989\pi\) | ||||
−0.122180 | + | 0.992508i | \(0.538989\pi\) | |||||||
\(110\) | 21.6029 | 2.05976 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 37.8195 | 3.57361 | ||||||||
\(113\) | −19.1068 | −1.79742 | −0.898709 | − | 0.438545i | \(-0.855494\pi\) | ||||
−0.898709 | + | 0.438545i | \(0.855494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.03683 | −0.562937 | ||||||||
\(116\) | −1.73134 | −0.160751 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.9217 | −1.64983 | ||||||||
\(119\) | 7.46178 | 0.684020 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.950605 | −0.0864186 | ||||||||
\(122\) | 22.1471 | 2.00511 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −40.5260 | −3.63934 | ||||||||
\(125\) | 9.47621 | 0.847578 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.06679 | 0.804547 | 0.402274 | − | 0.915520i | \(-0.368220\pi\) | ||||
0.402274 | + | 0.915520i | \(0.368220\pi\) | |||||||
\(128\) | −40.7546 | −3.60223 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 46.1997 | 4.05198 | ||||||||
\(131\) | −3.91774 | −0.342295 | −0.171147 | − | 0.985245i | \(-0.554747\pi\) | ||||
−0.171147 | + | 0.985245i | \(0.554747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.6125 | −1.35377 | ||||||||
\(134\) | 21.2351 | 1.83443 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −28.8459 | −2.47351 | ||||||||
\(137\) | −22.7783 | −1.94608 | −0.973040 | − | 0.230637i | \(-0.925919\pi\) | ||||
−0.973040 | + | 0.230637i | \(0.925919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.47254 | −0.294537 | −0.147268 | − | 0.989097i | \(-0.547048\pi\) | ||||
−0.147268 | + | 0.989097i | \(0.547048\pi\) | |||||||
\(140\) | −33.9372 | −2.86822 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.3653 | −1.37334 | ||||||||
\(143\) | 21.4915 | 1.79721 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.783264 | 0.0650466 | ||||||||
\(146\) | −3.59749 | −0.297731 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −57.6501 | −4.73881 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.0059 | −1.22116 | −0.610581 | − | 0.791953i | \(-0.709064\pi\) | ||||
−0.610581 | + | 0.791953i | \(0.709064\pi\) | |||||||
\(152\) | 60.3550 | 4.89543 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.5277 | −1.73475 | ||||||||
\(155\) | 18.3341 | 1.47263 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.35510 | 0.347575 | 0.173788 | − | 0.984783i | \(-0.444399\pi\) | ||||
0.173788 | + | 0.984783i | \(0.444399\pi\) | |||||||
\(158\) | −39.1836 | −3.11728 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 56.2311 | 4.44546 | ||||||||
\(161\) | 6.01581 | 0.474112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3238 | 1.12193 | 0.560965 | − | 0.827840i | \(-0.310430\pi\) | ||||
0.560965 | + | 0.827840i | \(0.310430\pi\) | |||||||
\(164\) | −37.0055 | −2.88964 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4003 | 0.962452 | ||||||||
\(167\) | −25.4508 | −1.96944 | −0.984722 | − | 0.174137i | \(-0.944287\pi\) | ||||
−0.984722 | + | 0.174137i | \(0.944287\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.9614 | 2.53549 | ||||||||
\(170\) | 20.5066 | 1.57279 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −41.4614 | −3.16140 | ||||||||
\(173\) | −0.602157 | −0.0457812 | −0.0228906 | − | 0.999738i | \(-0.507287\pi\) | ||||
−0.0228906 | + | 0.999738i | \(0.507287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.95504 | 0.223380 | ||||||||
\(176\) | 48.3499 | 3.64451 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.1566 | −0.836223 | ||||||||
\(179\) | 10.6481 | 0.795880 | 0.397940 | − | 0.917411i | \(-0.369725\pi\) | ||||
0.397940 | + | 0.917411i | \(0.369725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00089 | 0.297383 | 0.148692 | − | 0.988884i | \(-0.452494\pi\) | ||||
0.148692 | + | 0.988884i | \(0.452494\pi\) | |||||||
\(182\) | −46.0388 | −3.41262 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −23.2560 | −1.71446 | ||||||||
\(185\) | 26.0811 | 1.91752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.53941 | 0.697591 | ||||||||
\(188\) | −47.7043 | −3.47920 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −42.9065 | −3.11277 | ||||||||
\(191\) | −0.911105 | −0.0659252 | −0.0329626 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329626 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.52960 | −0.254066 | −0.127033 | − | 0.991899i | \(-0.540545\pi\) | ||||
−0.127033 | + | 0.991899i | \(0.540545\pi\) | |||||||
\(194\) | −23.1474 | −1.66189 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.68251 | −0.334465 | ||||||||
\(197\) | −14.8739 | −1.05972 | −0.529862 | − | 0.848084i | \(-0.677756\pi\) | ||||
−0.529862 | + | 0.848084i | \(0.677756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2759 | 0.870213 | 0.435107 | − | 0.900379i | \(-0.356711\pi\) | ||||
0.435107 | + | 0.900379i | \(0.356711\pi\) | |||||||
\(200\) | −11.4236 | −0.807773 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 36.3476 | 2.55741 | ||||||||
\(203\) | −0.780537 | −0.0547829 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.7414 | 1.16927 | ||||||||
\(206\) | 27.3206 | 1.90352 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 103.400 | 7.16953 | ||||||||
\(209\) | −19.9596 | −1.38063 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0371 | 0.828671 | 0.414335 | − | 0.910124i | \(-0.364014\pi\) | ||||
0.414335 | + | 0.910124i | \(0.364014\pi\) | |||||||
\(212\) | 26.1624 | 1.79684 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.03941 | 0.0710527 | ||||||||
\(215\) | 18.7572 | 1.27923 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.2702 | −1.24026 | ||||||||
\(218\) | 6.98684 | 0.473208 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −43.3866 | −2.92512 | ||||||||
\(221\) | 20.4008 | 1.37231 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9425 | −0.866697 | −0.433348 | − | 0.901226i | \(-0.642668\pi\) | ||||
−0.433348 | + | 0.901226i | \(0.642668\pi\) | |||||||
\(224\) | −56.0353 | −3.74402 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 52.3269 | 3.48074 | ||||||||
\(227\) | 23.4952 | 1.55943 | 0.779715 | − | 0.626135i | \(-0.215364\pi\) | ||||
0.779715 | + | 0.626135i | \(0.215364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0115 | 0.925909 | 0.462954 | − | 0.886382i | \(-0.346789\pi\) | ||||
0.462954 | + | 0.886382i | \(0.346789\pi\) | |||||||
\(230\) | 16.5328 | 1.09014 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.01741 | 0.198103 | ||||||||
\(233\) | −0.283778 | −0.0185909 | −0.00929545 | − | 0.999957i | \(-0.502959\pi\) | ||||
−0.00929545 | + | 0.999957i | \(0.502959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.5816 | 1.40783 | ||||||||
\(236\) | 35.9934 | 2.34297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −20.4352 | −1.32462 | ||||||||
\(239\) | −27.1056 | −1.75331 | −0.876657 | − | 0.481115i | \(-0.840232\pi\) | ||||
−0.876657 | + | 0.481115i | \(0.840232\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6800 | 1.39653 | 0.698265 | − | 0.715839i | \(-0.253956\pi\) | ||||
0.698265 | + | 0.715839i | \(0.253956\pi\) | |||||||
\(242\) | 2.60338 | 0.167351 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −44.4795 | −2.84751 | ||||||||
\(245\) | 2.11838 | 0.135338 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.6852 | −2.71599 | ||||||||
\(248\) | 70.6294 | 4.48497 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.9521 | −1.64135 | ||||||||
\(251\) | 19.3183 | 1.21936 | 0.609681 | − | 0.792647i | \(-0.291298\pi\) | ||||
0.609681 | + | 0.792647i | \(0.291298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.69083 | 0.483518 | ||||||||
\(254\) | −24.8308 | −1.55802 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 48.8441 | 3.05276 | ||||||||
\(257\) | 1.23987 | 0.0773407 | 0.0386703 | − | 0.999252i | \(-0.487688\pi\) | ||||
0.0386703 | + | 0.999252i | \(0.487688\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.9903 | −1.61496 | ||||||||
\(260\) | −92.7859 | −5.75434 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7293 | 0.662861 | ||||||||
\(263\) | −27.1610 | −1.67482 | −0.837409 | − | 0.546577i | \(-0.815930\pi\) | ||||
−0.837409 | + | 0.546577i | \(0.815930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.8360 | −0.727077 | ||||||||
\(266\) | 42.7571 | 2.62161 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −42.6478 | −2.60513 | ||||||||
\(269\) | −4.77174 | −0.290938 | −0.145469 | − | 0.989363i | \(-0.546469\pi\) | ||||
−0.145469 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7670 | 1.14002 | 0.570008 | − | 0.821639i | \(-0.306940\pi\) | ||||
0.570008 | + | 0.821639i | \(0.306940\pi\) | |||||||
\(272\) | 45.8963 | 2.78287 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 62.3818 | 3.76862 | ||||||||
\(275\) | 3.77783 | 0.227812 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.49008 | −0.209699 | −0.104849 | − | 0.994488i | \(-0.533436\pi\) | ||||
−0.104849 | + | 0.994488i | \(0.533436\pi\) | |||||||
\(278\) | 9.51007 | 0.570376 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 59.1464 | 3.53467 | ||||||||
\(281\) | −21.0452 | −1.25545 | −0.627727 | − | 0.778434i | \(-0.716015\pi\) | ||||
−0.627727 | + | 0.778434i | \(0.716015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.35846 | 0.259084 | 0.129542 | − | 0.991574i | \(-0.458649\pi\) | ||||
0.129542 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(284\) | 32.8675 | 1.95032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −58.8577 | −3.48033 | ||||||||
\(287\) | −16.6831 | −0.984772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.94469 | −0.467335 | ||||||||
\(290\) | −2.14509 | −0.125964 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.22509 | 0.422816 | ||||||||
\(293\) | −25.5865 | −1.49478 | −0.747390 | − | 0.664385i | \(-0.768693\pi\) | ||||
−0.747390 | + | 0.664385i | \(0.768693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.2835 | −0.948064 | ||||||||
\(296\) | 100.474 | 5.83991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.73865 | 0.158646 | ||||||||
\(299\) | 16.4475 | 0.951183 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6919 | −1.07738 | ||||||||
\(302\) | 41.0959 | 2.36481 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −96.0299 | −5.50769 | ||||||||
\(305\) | 20.1227 | 1.15222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.4103 | −0.936584 | −0.468292 | − | 0.883574i | \(-0.655131\pi\) | ||||
−0.468292 | + | 0.883574i | \(0.655131\pi\) | |||||||
\(308\) | 43.2355 | 2.46357 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −50.2107 | −2.85178 | ||||||||
\(311\) | 13.3945 | 0.759533 | 0.379767 | − | 0.925082i | \(-0.376004\pi\) | ||||
0.379767 | + | 0.925082i | \(0.376004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.20881 | 0.124850 | 0.0624248 | − | 0.998050i | \(-0.480117\pi\) | ||||
0.0624248 | + | 0.998050i | \(0.480117\pi\) | |||||||
\(314\) | −11.9271 | −0.673086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 78.6951 | 4.42694 | ||||||||
\(317\) | 15.5054 | 0.870872 | 0.435436 | − | 0.900220i | \(-0.356594\pi\) | ||||
0.435436 | + | 0.900220i | \(0.356594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.997867 | −0.0558698 | ||||||||
\(320\) | −78.0941 | −4.36559 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.4752 | −0.918127 | ||||||||
\(323\) | −18.9467 | −1.05422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.07921 | 0.448154 | ||||||||
\(326\) | −39.2280 | −2.17264 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 64.4938 | 3.56107 | ||||||||
\(329\) | −21.5064 | −1.18569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.7541 | −1.30564 | −0.652822 | − | 0.757511i | \(-0.726415\pi\) | ||||
−0.652822 | + | 0.757511i | \(0.726415\pi\) | |||||||
\(332\) | −24.9044 | −1.36681 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 69.7009 | 3.81387 | ||||||||
\(335\) | 19.2940 | 1.05414 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.8512 | 1.19031 | 0.595156 | − | 0.803610i | \(-0.297090\pi\) | ||||
0.595156 | + | 0.803610i | \(0.297090\pi\) | |||||||
\(338\) | −90.2697 | −4.91003 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −41.1848 | −2.23356 | ||||||||
\(341\) | −23.3574 | −1.26487 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4686 | −1.05120 | ||||||||
\(344\) | 72.2596 | 3.89598 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.64910 | 0.0886562 | ||||||||
\(347\) | 9.38008 | 0.503549 | 0.251775 | − | 0.967786i | \(-0.418986\pi\) | ||||
0.251775 | + | 0.967786i | \(0.418986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.67456 | −0.357281 | −0.178640 | − | 0.983914i | \(-0.557170\pi\) | ||||
−0.178640 | + | 0.983914i | \(0.557170\pi\) | |||||||
\(350\) | −8.09282 | −0.432580 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −71.6376 | −3.81830 | ||||||||
\(353\) | 8.47972 | 0.451330 | 0.225665 | − | 0.974205i | \(-0.427545\pi\) | ||||
0.225665 | + | 0.974205i | \(0.427545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8693 | −0.789183 | ||||||||
\(356\) | 22.4066 | 1.18754 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.1616 | −1.54124 | ||||||||
\(359\) | −23.1074 | −1.21956 | −0.609782 | − | 0.792569i | \(-0.708743\pi\) | ||||
−0.609782 | + | 0.792569i | \(0.708743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.6426 | 1.08645 | ||||||||
\(362\) | −10.9570 | −0.575889 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 92.4628 | 4.84637 | ||||||||
\(365\) | −3.26865 | −0.171089 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.6452 | −1.49527 | −0.747633 | − | 0.664112i | \(-0.768810\pi\) | ||||
−0.747633 | + | 0.664112i | \(0.768810\pi\) | |||||||
\(368\) | 37.0023 | 1.92888 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −71.4270 | −3.71331 | ||||||||
\(371\) | 11.7947 | 0.612352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5542 | 1.01248 | 0.506238 | − | 0.862394i | \(-0.331036\pi\) | ||||
0.506238 | + | 0.862394i | \(0.331036\pi\) | |||||||
\(374\) | −26.1251 | −1.35090 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 83.1400 | 4.28762 | ||||||||
\(377\) | −2.13402 | −0.109908 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.63031 | 0.237843 | 0.118922 | − | 0.992904i | \(-0.462056\pi\) | ||||
0.118922 | + | 0.992904i | \(0.462056\pi\) | |||||||
\(380\) | 86.1720 | 4.42053 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.49520 | 0.127666 | ||||||||
\(383\) | 2.09803 | 0.107204 | 0.0536021 | − | 0.998562i | \(-0.482930\pi\) | ||||
0.0536021 | + | 0.998562i | \(0.482930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.5599 | −0.996863 | ||||||||
\(386\) | 9.66634 | 0.492004 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 46.4885 | 2.36010 | ||||||||
\(389\) | 17.4299 | 0.883729 | 0.441864 | − | 0.897082i | \(-0.354317\pi\) | ||||
0.441864 | + | 0.897082i | \(0.354317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.30054 | 0.369204 | ||||||||
\(392\) | 8.16076 | 0.412181 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 40.7345 | 2.05217 | ||||||||
\(395\) | −35.6019 | −1.79133 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4745 | 1.22834 | 0.614169 | − | 0.789175i | \(-0.289491\pi\) | ||||
0.614169 | + | 0.789175i | \(0.289491\pi\) | |||||||
\(398\) | −33.6193 | −1.68519 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.1760 | 0.908800 | ||||||||
\(401\) | 36.3412 | 1.81479 | 0.907396 | − | 0.420276i | \(-0.138067\pi\) | ||||
0.907396 | + | 0.420276i | \(0.138067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.9517 | −2.48827 | ||||||||
\(404\) | −72.9994 | −3.63185 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.13762 | 0.106088 | ||||||||
\(407\) | −33.2269 | −1.64700 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.706028 | 0.0349108 | 0.0174554 | − | 0.999848i | \(-0.494443\pi\) | ||||
0.0174554 | + | 0.999848i | \(0.494443\pi\) | |||||||
\(410\) | −45.8488 | −2.26431 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −54.8698 | −2.70324 | ||||||||
\(413\) | 16.2268 | 0.798471 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2668 | 0.553067 | ||||||||
\(416\) | −153.203 | −7.51140 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 54.6623 | 2.67362 | ||||||||
\(419\) | −18.2145 | −0.889835 | −0.444918 | − | 0.895571i | \(-0.646767\pi\) | ||||
−0.444918 | + | 0.895571i | \(0.646767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6571 | −1.44540 | −0.722699 | − | 0.691163i | \(-0.757099\pi\) | ||||
−0.722699 | + | 0.691163i | \(0.757099\pi\) | |||||||
\(422\) | −32.9655 | −1.60474 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −45.5963 | −2.21435 | ||||||||
\(425\) | 3.58611 | 0.173952 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0526 | −0.970414 | ||||||||
\(428\) | −2.08752 | −0.100904 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −51.3696 | −2.47726 | ||||||||
\(431\) | −5.95610 | −0.286895 | −0.143448 | − | 0.989658i | \(-0.545819\pi\) | ||||
−0.143448 | + | 0.989658i | \(0.545819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.6458 | −1.32857 | −0.664285 | − | 0.747479i | \(-0.731264\pi\) | ||||
−0.664285 | + | 0.747479i | \(0.731264\pi\) | |||||||
\(434\) | 50.0358 | 2.40180 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0321 | −0.672017 | ||||||||
\(437\) | −15.2751 | −0.730708 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.8197 | 1.85276 | 0.926381 | − | 0.376587i | \(-0.122902\pi\) | ||||
0.926381 | + | 0.376587i | \(0.122902\pi\) | |||||||
\(440\) | 75.6149 | 3.60480 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −55.8708 | −2.65750 | ||||||||
\(443\) | −17.2197 | −0.818133 | −0.409067 | − | 0.912505i | \(-0.634146\pi\) | ||||
−0.409067 | + | 0.912505i | \(0.634146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1368 | −0.480530 | ||||||||
\(446\) | 35.4451 | 1.67838 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 77.8221 | 3.67675 | ||||||||
\(449\) | −14.6566 | −0.691687 | −0.345843 | − | 0.938292i | \(-0.612407\pi\) | ||||
−0.345843 | + | 0.938292i | \(0.612407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.3283 | −1.00431 | ||||||||
\(452\) | −105.092 | −4.94310 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −64.3451 | −3.01987 | ||||||||
\(455\) | −41.8304 | −1.96104 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.8089 | −1.72185 | −0.860925 | − | 0.508732i | \(-0.830114\pi\) | ||||
−0.860925 | + | 0.508732i | \(0.830114\pi\) | |||||||
\(458\) | −38.3727 | −1.79304 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −33.2039 | −1.54814 | ||||||||
\(461\) | −3.08406 | −0.143639 | −0.0718194 | − | 0.997418i | \(-0.522881\pi\) | ||||
−0.0718194 | + | 0.997418i | \(0.522881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.7752 | −1.61614 | −0.808071 | − | 0.589086i | \(-0.799488\pi\) | ||||
−0.808071 | + | 0.589086i | \(0.799488\pi\) | |||||||
\(464\) | −4.80096 | −0.222879 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.777169 | 0.0360017 | ||||||||
\(467\) | −4.65470 | −0.215394 | −0.107697 | − | 0.994184i | \(-0.534348\pi\) | ||||
−0.107697 | + | 0.994184i | \(0.534348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.2268 | −0.887812 | ||||||||
\(470\) | −59.1045 | −2.72629 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −62.7300 | −2.88738 | ||||||||
\(473\) | −23.8965 | −1.09876 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.50332 | −0.344276 | ||||||||
\(476\) | 41.0414 | 1.88113 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 74.2328 | 3.39533 | ||||||||
\(479\) | 32.7789 | 1.49770 | 0.748852 | − | 0.662737i | \(-0.230605\pi\) | ||||
0.748852 | + | 0.662737i | \(0.230605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −71.0586 | −3.23999 | ||||||||
\(482\) | −59.3739 | −2.70441 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.22853 | −0.237661 | ||||||||
\(485\) | −21.0315 | −0.954993 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1514 | 1.18503 | 0.592517 | − | 0.805558i | \(-0.298134\pi\) | ||||
0.592517 | + | 0.805558i | \(0.298134\pi\) | |||||||
\(488\) | 77.5198 | 3.50915 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.80151 | −0.262085 | ||||||||
\(491\) | 7.84533 | 0.354055 | 0.177027 | − | 0.984206i | \(-0.443352\pi\) | ||||
0.177027 | + | 0.984206i | \(0.443352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.947228 | −0.0426610 | ||||||||
\(494\) | 116.900 | 5.25958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −112.378 | −5.04590 | ||||||||
\(497\) | 14.8176 | 0.664658 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.1048 | −0.855247 | −0.427623 | − | 0.903957i | \(-0.640649\pi\) | ||||
−0.427623 | + | 0.903957i | \(0.640649\pi\) | |||||||
\(500\) | 52.1212 | 2.33093 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.9062 | −2.36132 | ||||||||
\(503\) | 4.05590 | 0.180844 | 0.0904218 | − | 0.995904i | \(-0.471178\pi\) | ||||
0.0904218 | + | 0.995904i | \(0.471178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.0251 | 1.46960 | ||||||||
\(506\) | −21.0625 | −0.936343 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 49.8693 | 2.21259 | ||||||||
\(509\) | 8.75481 | 0.388050 | 0.194025 | − | 0.980997i | \(-0.437846\pi\) | ||||
0.194025 | + | 0.980997i | \(0.437846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.25727 | 0.144093 | ||||||||
\(512\) | −52.2578 | −2.30949 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.39556 | −0.149772 | ||||||||
\(515\) | 24.8233 | 1.09384 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.4946 | −1.20921 | ||||||||
\(518\) | 71.1783 | 3.12739 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 161.709 | 7.09140 | ||||||||
\(521\) | −28.4166 | −1.24496 | −0.622478 | − | 0.782637i | \(-0.713874\pi\) | ||||
−0.622478 | + | 0.782637i | \(0.713874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.3726 | −1.45928 | −0.729642 | − | 0.683830i | \(-0.760313\pi\) | ||||
−0.729642 | + | 0.683830i | \(0.760313\pi\) | |||||||
\(524\) | −21.5484 | −0.941348 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 74.3845 | 3.24332 | ||||||||
\(527\) | −22.1720 | −0.965829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.1142 | −0.744095 | ||||||||
\(530\) | 32.4146 | 1.40800 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −85.8720 | −3.72302 | ||||||||
\(533\) | −45.6123 | −1.97569 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.944400 | 0.0408300 | ||||||||
\(536\) | 74.3274 | 3.21045 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.0681 | 0.563407 | ||||||||
\(539\) | −2.69879 | −0.116245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8890 | 0.597134 | 0.298567 | − | 0.954389i | \(-0.403491\pi\) | ||||
0.298567 | + | 0.954389i | \(0.403491\pi\) | |||||||
\(542\) | −51.3963 | −2.20766 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −68.0022 | −2.91557 | ||||||||
\(545\) | 6.34818 | 0.271926 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.7903 | 1.31650 | 0.658248 | − | 0.752801i | \(-0.271298\pi\) | ||||
0.658248 | + | 0.752801i | \(0.271298\pi\) | |||||||
\(548\) | −125.285 | −5.35193 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.3462 | −0.441162 | ||||||||
\(551\) | 1.98191 | 0.0844322 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.4779 | 1.50867 | ||||||||
\(554\) | 9.55812 | 0.406086 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.0997 | −0.810008 | ||||||||
\(557\) | 9.45861 | 0.400774 | 0.200387 | − | 0.979717i | \(-0.435780\pi\) | ||||
0.200387 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.1046 | −2.16149 | ||||||||
\(560\) | −94.1070 | −3.97674 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 57.6356 | 2.43121 | ||||||||
\(563\) | 34.3037 | 1.44573 | 0.722864 | − | 0.690990i | \(-0.242825\pi\) | ||||
0.722864 | + | 0.690990i | \(0.242825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 47.5438 | 2.00018 | ||||||||
\(566\) | −11.9363 | −0.501721 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −57.2820 | −2.40350 | ||||||||
\(569\) | 44.1953 | 1.85276 | 0.926381 | − | 0.376587i | \(-0.122902\pi\) | ||||
0.926381 | + | 0.376587i | \(0.122902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1800 | 1.05375 | 0.526876 | − | 0.849942i | \(-0.323363\pi\) | ||||
0.526876 | + | 0.849942i | \(0.323363\pi\) | |||||||
\(572\) | 118.208 | 4.94252 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 45.6892 | 1.90703 | ||||||||
\(575\) | 2.89118 | 0.120571 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.75420 | −0.197920 | −0.0989600 | − | 0.995091i | \(-0.531552\pi\) | ||||
−0.0989600 | + | 0.995091i | \(0.531552\pi\) | |||||||
\(578\) | 21.7578 | 0.905003 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.30812 | 0.178885 | ||||||||
\(581\) | −11.2276 | −0.465799 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0788 | 0.624501 | ||||||||
\(584\) | −12.5920 | −0.521061 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.0726 | 2.89467 | ||||||||
\(587\) | 17.7706 | 0.733469 | 0.366735 | − | 0.930326i | \(-0.380476\pi\) | ||||
0.366735 | + | 0.930326i | \(0.380476\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 46.3911 | 1.91151 | ||||||||
\(590\) | 44.5950 | 1.83595 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −159.862 | −6.57030 | ||||||||
\(593\) | 15.6395 | 0.642239 | 0.321120 | − | 0.947039i | \(-0.395941\pi\) | ||||
0.321120 | + | 0.947039i | \(0.395941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.5673 | −0.761183 | ||||||||
\(596\) | −5.50022 | −0.225298 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −45.0440 | −1.84199 | ||||||||
\(599\) | −4.52110 | −0.184727 | −0.0923635 | − | 0.995725i | \(-0.529442\pi\) | ||||
−0.0923635 | + | 0.995725i | \(0.529442\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.15979 | 0.292054 | 0.146027 | − | 0.989281i | \(-0.453351\pi\) | ||||
0.146027 | + | 0.989281i | \(0.453351\pi\) | |||||||
\(602\) | 51.1907 | 2.08638 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −82.5357 | −3.35833 | ||||||||
\(605\) | 2.36540 | 0.0961674 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.2276 | −1.06455 | −0.532273 | − | 0.846573i | \(-0.678662\pi\) | ||||
−0.532273 | + | 0.846573i | \(0.678662\pi\) | |||||||
\(608\) | 142.283 | 5.77033 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −55.1090 | −2.23130 | ||||||||
\(611\) | −58.7996 | −2.37878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.252061 | 0.0101807 | 0.00509033 | − | 0.999987i | \(-0.498380\pi\) | ||||
0.00509033 | + | 0.999987i | \(0.498380\pi\) | |||||||
\(614\) | 44.9421 | 1.81371 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −75.3516 | −3.03600 | ||||||||
\(617\) | 8.17449 | 0.329093 | 0.164546 | − | 0.986369i | \(-0.447384\pi\) | ||||
0.164546 | + | 0.986369i | \(0.447384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.4564 | 0.942791 | 0.471396 | − | 0.881922i | \(-0.343750\pi\) | ||||
0.471396 | + | 0.881922i | \(0.343750\pi\) | |||||||
\(620\) | 100.841 | 4.04989 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −36.6829 | −1.47085 | ||||||||
\(623\) | 10.1015 | 0.404708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5384 | −1.18154 | ||||||||
\(626\) | −6.04917 | −0.241774 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.9540 | 0.955869 | ||||||||
\(629\) | −31.5407 | −1.25761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6859 | 1.02254 | 0.511270 | − | 0.859420i | \(-0.329175\pi\) | ||||
0.511270 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(632\) | −137.151 | −5.45558 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42.4640 | −1.68646 | ||||||||
\(635\) | −22.5610 | −0.895307 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.77158 | −0.228678 | ||||||||
\(638\) | 2.73281 | 0.108193 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 101.410 | 4.00860 | ||||||||
\(641\) | −20.7646 | −0.820154 | −0.410077 | − | 0.912051i | \(-0.634498\pi\) | ||||
−0.410077 | + | 0.912051i | \(0.634498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.6968 | −1.84154 | −0.920771 | − | 0.390104i | \(-0.872439\pi\) | ||||
−0.920771 | + | 0.390104i | \(0.872439\pi\) | |||||||
\(644\) | 33.0882 | 1.30386 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 51.8883 | 2.04152 | ||||||||
\(647\) | 25.8031 | 1.01443 | 0.507213 | − | 0.861821i | \(-0.330676\pi\) | ||||
0.507213 | + | 0.861821i | \(0.330676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7450 | 0.814312 | ||||||||
\(650\) | −22.1262 | −0.867859 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 78.7842 | 3.08543 | ||||||||
\(653\) | −34.7608 | −1.36029 | −0.680147 | − | 0.733076i | \(-0.738084\pi\) | ||||
−0.680147 | + | 0.733076i | \(0.738084\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.74858 | 0.380909 | ||||||||
\(656\) | −102.615 | −4.00645 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 58.8987 | 2.29611 | ||||||||
\(659\) | −28.7064 | −1.11824 | −0.559122 | − | 0.829085i | \(-0.688862\pi\) | ||||
−0.559122 | + | 0.829085i | \(0.688862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5659 | 0.877711 | 0.438856 | − | 0.898558i | \(-0.355384\pi\) | ||||
0.438856 | + | 0.898558i | \(0.355384\pi\) | |||||||
\(662\) | 65.0543 | 2.52841 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 43.4038 | 1.68440 | ||||||||
\(665\) | 38.8487 | 1.50649 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.763671 | −0.0295695 | ||||||||
\(668\) | −139.985 | −5.41618 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −52.8396 | −2.04137 | ||||||||
\(671\) | −25.6360 | −0.989667 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.25388 | −0.163975 | −0.0819874 | − | 0.996633i | \(-0.526127\pi\) | ||||
−0.0819874 | + | 0.996633i | \(0.526127\pi\) | |||||||
\(674\) | −59.8430 | −2.30506 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 181.295 | 6.97287 | ||||||||
\(677\) | 38.8249 | 1.49216 | 0.746081 | − | 0.665855i | \(-0.231933\pi\) | ||||
0.746081 | + | 0.665855i | \(0.231933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.9583 | 0.804306 | ||||||||
\(680\) | 71.7776 | 2.75255 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 63.9677 | 2.44945 | ||||||||
\(683\) | −8.06370 | −0.308549 | −0.154274 | − | 0.988028i | \(-0.549304\pi\) | ||||
−0.154274 | + | 0.988028i | \(0.549304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.6795 | 2.16561 | ||||||||
\(686\) | 53.3176 | 2.03568 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −114.971 | −4.38324 | ||||||||
\(689\) | 32.2474 | 1.22853 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.24490 | −0.313651 | −0.156825 | − | 0.987626i | \(-0.550126\pi\) | ||||
−0.156825 | + | 0.987626i | \(0.550126\pi\) | |||||||
\(692\) | −3.31200 | −0.125903 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.6888 | −0.975133 | ||||||||
\(695\) | 8.64077 | 0.327763 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.2459 | −0.766869 | ||||||||
\(698\) | 18.2793 | 0.691881 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.2534 | 0.614319 | ||||||||
\(701\) | −35.0902 | −1.32534 | −0.662669 | − | 0.748913i | \(-0.730576\pi\) | ||||
−0.662669 | + | 0.748913i | \(0.730576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 65.9935 | 2.48899 | ||||||||
\(704\) | 99.4907 | 3.74970 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.2230 | −0.874010 | ||||||||
\(707\) | −32.9101 | −1.23771 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.80885 | 0.143044 | 0.0715221 | − | 0.997439i | \(-0.477214\pi\) | ||||
0.0715221 | + | 0.997439i | \(0.477214\pi\) | |||||||
\(710\) | 40.7220 | 1.52827 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.0505 | −1.46348 | ||||||||
\(713\) | −17.8755 | −0.669441 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53.4776 | −1.99995 | ||||||||
\(716\) | 58.5671 | 2.18876 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 63.2832 | 2.36171 | ||||||||
\(719\) | 2.73421 | 0.101969 | 0.0509844 | − | 0.998699i | \(-0.483764\pi\) | ||||
0.0509844 | + | 0.998699i | \(0.483764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.7369 | −0.921249 | ||||||||
\(722\) | −56.5329 | −2.10394 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.0057 | 0.817837 | ||||||||
\(725\) | −0.375124 | −0.0139318 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.03525 | 0.112571 | 0.0562856 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562856 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(728\) | −161.146 | −5.97246 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.95170 | 0.331317 | ||||||||
\(731\) | −22.6838 | −0.838989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.33373 | −0.197006 | −0.0985029 | − | 0.995137i | \(-0.531405\pi\) | ||||
−0.0985029 | + | 0.995137i | \(0.531405\pi\) | |||||||
\(734\) | 78.4492 | 2.89561 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.8245 | −2.02086 | ||||||||
\(737\) | −24.5803 | −0.905426 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4637 | 0.936697 | 0.468348 | − | 0.883544i | \(-0.344849\pi\) | ||||
0.468348 | + | 0.883544i | \(0.344849\pi\) | |||||||
\(740\) | 143.452 | 5.27339 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −32.3017 | −1.18583 | ||||||||
\(743\) | −49.4663 | −1.81474 | −0.907372 | − | 0.420330i | \(-0.861914\pi\) | ||||
−0.907372 | + | 0.420330i | \(0.861914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.48832 | 0.0911648 | ||||||||
\(746\) | −53.5521 | −1.96068 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 52.4688 | 1.91845 | ||||||||
\(749\) | −0.941111 | −0.0343874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.14112 | 0.224093 | 0.112046 | − | 0.993703i | \(-0.464259\pi\) | ||||
0.112046 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(752\) | −132.283 | −4.82386 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.84435 | 0.212839 | ||||||||
\(755\) | 37.3394 | 1.35892 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.19697 | −0.116196 | −0.0580979 | − | 0.998311i | \(-0.518504\pi\) | ||||
−0.0580979 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(758\) | −12.6808 | −0.460588 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −150.182 | −5.44768 | ||||||||
\(761\) | 1.19046 | 0.0431540 | 0.0215770 | − | 0.999767i | \(-0.493131\pi\) | ||||
0.0215770 | + | 0.999767i | \(0.493131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.32607 | −0.229019 | ||||||||
\(764\) | −5.01127 | −0.181302 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.74577 | −0.207603 | ||||||||
\(767\) | 44.3649 | 1.60192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.1117 | −0.797367 | −0.398684 | − | 0.917088i | \(-0.630533\pi\) | ||||
−0.398684 | + | 0.917088i | \(0.630533\pi\) | |||||||
\(770\) | 53.5677 | 1.93045 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.4135 | −0.698709 | ||||||||
\(773\) | 51.8878 | 1.86628 | 0.933138 | − | 0.359519i | \(-0.117059\pi\) | ||||
0.933138 | + | 0.359519i | \(0.117059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.78064 | −0.315410 | ||||||||
\(776\) | −81.0210 | −2.90848 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47.7343 | −1.71136 | ||||||||
\(779\) | 42.3611 | 1.51774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.9433 | 0.677845 | ||||||||
\(782\) | −19.9936 | −0.714971 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.9845 | −0.463731 | ||||||||
\(785\) | −10.8369 | −0.386785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3399 | −1.01021 | −0.505104 | − | 0.863058i | \(-0.668546\pi\) | ||||
−0.505104 | + | 0.863058i | \(0.668546\pi\) | |||||||
\(788\) | −81.8098 | −2.91435 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 97.5012 | 3.46894 | ||||||||
\(791\) | −47.3782 | −1.68458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.8248 | −1.94689 | ||||||||
\(794\) | −67.0270 | −2.37870 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 67.5200 | 2.39318 | ||||||||
\(797\) | −49.6000 | −1.75692 | −0.878461 | − | 0.477814i | \(-0.841429\pi\) | ||||
−0.878461 | + | 0.477814i | \(0.841429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.0993 | −0.923328 | ||||||||
\(800\) | −26.9305 | −0.952135 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −99.5259 | −3.51438 | ||||||||
\(803\) | 4.16422 | 0.146952 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.9692 | −0.527596 | ||||||||
\(806\) | 136.800 | 4.81859 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 127.225 | 4.47575 | ||||||||
\(809\) | 38.3130 | 1.34701 | 0.673506 | − | 0.739182i | \(-0.264788\pi\) | ||||
0.673506 | + | 0.739182i | \(0.264788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4768 | 0.929727 | 0.464863 | − | 0.885382i | \(-0.346103\pi\) | ||||
0.464863 | + | 0.885382i | \(0.346103\pi\) | |||||||
\(812\) | −4.29312 | −0.150659 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 90.9970 | 3.18944 | ||||||||
\(815\) | −35.6422 | −1.24849 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.4618 | 1.66048 | ||||||||
\(818\) | −1.93356 | −0.0676055 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 92.0813 | 3.21562 | ||||||||
\(821\) | −7.34677 | −0.256404 | −0.128202 | − | 0.991748i | \(-0.540921\pi\) | ||||
−0.128202 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.73931 | −0.269776 | −0.134888 | − | 0.990861i | \(-0.543067\pi\) | ||||
−0.134888 | + | 0.990861i | \(0.543067\pi\) | |||||||
\(824\) | 95.6282 | 3.33137 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −44.4397 | −1.54625 | ||||||||
\(827\) | 34.0565 | 1.18426 | 0.592130 | − | 0.805842i | \(-0.298287\pi\) | ||||
0.592130 | + | 0.805842i | \(0.298287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.2306 | −1.32780 | −0.663901 | − | 0.747820i | \(-0.731101\pi\) | ||||
−0.663901 | + | 0.747820i | \(0.731101\pi\) | |||||||
\(830\) | −30.8559 | −1.07102 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 212.769 | 7.37645 | ||||||||
\(833\) | −2.56183 | −0.0887621 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.3297 | 2.19161 | ||||||||
\(836\) | −109.782 | −3.79689 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.8831 | 1.72318 | ||||||||
\(839\) | 44.7835 | 1.54610 | 0.773049 | − | 0.634346i | \(-0.218731\pi\) | ||||
0.773049 | + | 0.634346i | \(0.218731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9009 | −0.996583 | ||||||||
\(842\) | 81.2205 | 2.79904 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 66.2069 | 2.27894 | ||||||||
\(845\) | −82.0183 | −2.82151 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.35717 | −0.0809932 | ||||||||
\(848\) | 72.5477 | 2.49130 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.82112 | −0.336862 | ||||||||
\(851\) | −25.4287 | −0.871683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.17950 | −0.177343 | −0.0886713 | − | 0.996061i | \(-0.528262\pi\) | ||||
−0.0886713 | + | 0.996061i | \(0.528262\pi\) | |||||||
\(854\) | 54.9171 | 1.87923 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.63816 | 0.124350 | ||||||||
\(857\) | 2.43044 | 0.0830221 | 0.0415110 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415110 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.9715 | −0.954376 | −0.477188 | − | 0.878801i | \(-0.658344\pi\) | ||||
−0.477188 | + | 0.878801i | \(0.658344\pi\) | |||||||
\(860\) | 103.169 | 3.51803 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.3117 | 0.555578 | ||||||||
\(863\) | 33.4019 | 1.13701 | 0.568507 | − | 0.822678i | \(-0.307521\pi\) | ||||
0.568507 | + | 0.822678i | \(0.307521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.49836 | 0.0509457 | ||||||||
\(866\) | 75.7121 | 2.57280 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −100.490 | −3.41086 | ||||||||
\(869\) | 45.3563 | 1.53861 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.5670 | −1.78117 | ||||||||
\(872\) | 24.4555 | 0.828166 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 41.8332 | 1.41503 | ||||||||
\(875\) | 23.4977 | 0.794367 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2112 | 0.513645 | 0.256822 | − | 0.966459i | \(-0.417324\pi\) | ||||
0.256822 | + | 0.966459i | \(0.417324\pi\) | |||||||
\(878\) | −106.314 | −3.58791 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −120.310 | −4.05564 | ||||||||
\(881\) | 35.0040 | 1.17932 | 0.589658 | − | 0.807653i | \(-0.299263\pi\) | ||||
0.589658 | + | 0.807653i | \(0.299263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.7983 | −1.47393 | −0.736966 | − | 0.675930i | \(-0.763742\pi\) | ||||
−0.736966 | + | 0.675930i | \(0.763742\pi\) | |||||||
\(884\) | 112.209 | 3.77400 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47.1588 | 1.58433 | ||||||||
\(887\) | −13.5202 | −0.453965 | −0.226983 | − | 0.973899i | \(-0.572886\pi\) | ||||
−0.226983 | + | 0.973899i | \(0.572886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.4825 | 0.754038 | ||||||||
\(890\) | 27.7612 | 0.930556 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −71.1868 | −2.38351 | ||||||||
\(893\) | 54.6083 | 1.82740 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.4959 | −0.885662 | ||||||||
\(896\) | −101.057 | −3.37608 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.1393 | 1.33946 | ||||||||
\(899\) | 2.31930 | 0.0773529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3136 | 0.476856 | ||||||||
\(902\) | 58.4108 | 1.94487 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 183.156 | 6.09167 | ||||||||
\(905\) | −9.95547 | −0.330931 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.0600 | −1.19735 | −0.598676 | − | 0.800991i | \(-0.704306\pi\) | ||||
−0.598676 | + | 0.800991i | \(0.704306\pi\) | |||||||
\(908\) | 129.229 | 4.28860 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 114.559 | 3.79760 | ||||||||
\(911\) | 28.8375 | 0.955430 | 0.477715 | − | 0.878515i | \(-0.341465\pi\) | ||||
0.477715 | + | 0.878515i | \(0.341465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.3538 | −0.475041 | ||||||||
\(914\) | 100.807 | 3.33440 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 77.0665 | 2.54635 | ||||||||
\(917\) | −9.71464 | −0.320806 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1788 | 0.830572 | 0.415286 | − | 0.909691i | \(-0.363682\pi\) | ||||
0.415286 | + | 0.909691i | \(0.363682\pi\) | |||||||
\(920\) | 57.8683 | 1.90786 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.44616 | 0.278159 | ||||||||
\(923\) | 40.5119 | 1.33347 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.4909 | −0.410697 | ||||||||
\(926\) | 95.2372 | 3.12969 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.11335 | 0.233507 | ||||||||
\(929\) | −53.1220 | −1.74288 | −0.871439 | − | 0.490504i | \(-0.836813\pi\) | ||||
−0.871439 | + | 0.490504i | \(0.836813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.36018 | 0.175673 | ||||||||
\(932\) | −1.56084 | −0.0511270 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.7476 | 0.417114 | ||||||||
\(935\) | −23.7371 | −0.776285 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.0773 | −1.57062 | −0.785309 | − | 0.619104i | \(-0.787496\pi\) | ||||
−0.785309 | + | 0.619104i | \(0.787496\pi\) | |||||||
\(938\) | 52.6556 | 1.71927 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 118.703 | 3.87168 | ||||||||
\(941\) | 59.0197 | 1.92399 | 0.961994 | − | 0.273069i | \(-0.0880388\pi\) | ||||
0.961994 | + | 0.273069i | \(0.0880388\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3226 | −0.531537 | ||||||||
\(944\) | 99.8089 | 3.24850 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 65.4441 | 2.12777 | ||||||||
\(947\) | −14.7766 | −0.480176 | −0.240088 | − | 0.970751i | \(-0.577176\pi\) | ||||
−0.240088 | + | 0.970751i | \(0.577176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.90553 | 0.289086 | ||||||||
\(950\) | 20.5490 | 0.666697 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −71.5277 | −2.31823 | ||||||||
\(953\) | −10.8816 | −0.352489 | −0.176244 | − | 0.984346i | \(-0.556395\pi\) | ||||
−0.176244 | + | 0.984346i | \(0.556395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.26712 | 0.0733622 | ||||||||
\(956\) | −149.087 | −4.82181 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −89.7699 | −2.90033 | ||||||||
\(959\) | −56.4822 | −1.82390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.2885 | 0.751240 | ||||||||
\(962\) | 194.605 | 6.27431 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 119.245 | 3.84061 | ||||||||
\(965\) | 8.78275 | 0.282727 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0491 | −0.901998 | −0.450999 | − | 0.892524i | \(-0.648932\pi\) | ||||
−0.450999 | + | 0.892524i | \(0.648932\pi\) | |||||||
\(968\) | 9.11238 | 0.292883 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 57.5981 | 1.84936 | ||||||||
\(971\) | −0.970323 | −0.0311391 | −0.0155696 | − | 0.999879i | \(-0.504956\pi\) | ||||
−0.0155696 | + | 0.999879i | \(0.504956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.61068 | −0.276046 | ||||||||
\(974\) | −71.6197 | −2.29484 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −123.341 | −3.94804 | ||||||||
\(977\) | −11.2790 | −0.360847 | −0.180423 | − | 0.983589i | \(-0.557747\pi\) | ||||
−0.180423 | + | 0.983589i | \(0.557747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9141 | 0.412737 | ||||||||
\(980\) | 11.6516 | 0.372195 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.4856 | −0.685634 | ||||||||
\(983\) | −14.7779 | −0.471341 | −0.235671 | − | 0.971833i | \(-0.575729\pi\) | ||||
−0.235671 | + | 0.971833i | \(0.575729\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.0110 | 1.17927 | ||||||||
\(986\) | 2.59413 | 0.0826139 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −234.778 | −7.46928 | ||||||||
\(989\) | −18.2880 | −0.581526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4544 | 0.554457 | 0.277228 | − | 0.960804i | \(-0.410584\pi\) | ||||
0.277228 | + | 0.960804i | \(0.410584\pi\) | |||||||
\(992\) | 166.504 | 5.28651 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −40.5801 | −1.28712 | ||||||||
\(995\) | −30.5462 | −0.968381 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0910 | 0.446268 | 0.223134 | − | 0.974788i | \(-0.428371\pi\) | ||||
0.223134 | + | 0.974788i | \(0.428371\pi\) | |||||||
\(998\) | 52.3213 | 1.65620 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4023.2.a.e.1.2 | ✓ | 25 | |
3.2 | odd | 2 | 4023.2.a.f.1.24 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.2 | ✓ | 25 | 1.1 | even | 1 | trivial | |
4023.2.a.f.1.24 | yes | 25 | 3.2 | odd | 2 |