Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8044,2,Mod(1,8044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8044, 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("8044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8044 = 2^{2} \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8044.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: | \(64.2316633859\) |
Analytic rank: | \(1\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8044.1 |
$q$-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 | ||||||||
\(3\) | −1.85715 | −1.07222 | −0.536112 | − | 0.844147i | \(-0.680108\pi\) | ||||
−0.536112 | + | 0.844147i | \(0.680108\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.680485 | 0.304322 | 0.152161 | − | 0.988356i | \(-0.451377\pi\) | ||||
0.152161 | + | 0.988356i | \(0.451377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30245 | 0.870243 | 0.435121 | − | 0.900372i | \(-0.356705\pi\) | ||||
0.435121 | + | 0.900372i | \(0.356705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.448994 | 0.149665 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.56658 | 1.97990 | 0.989949 | − | 0.141423i | \(-0.0451679\pi\) | ||||
0.989949 | + | 0.141423i | \(0.0451679\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.89757 | −1.63569 | −0.817846 | − | 0.575438i | \(-0.804832\pi\) | ||||
−0.817846 | + | 0.575438i | \(0.804832\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26376 | −0.326302 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.370174 | 0.0897804 | 0.0448902 | − | 0.998992i | \(-0.485706\pi\) | ||||
0.0448902 | + | 0.998992i | \(0.485706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59564 | 0.366066 | 0.183033 | − | 0.983107i | \(-0.441409\pi\) | ||||
0.183033 | + | 0.983107i | \(0.441409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.27598 | −0.933095 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.231612 | −0.0482944 | −0.0241472 | − | 0.999708i | \(-0.507687\pi\) | ||||
−0.0241472 | + | 0.999708i | \(0.507687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53694 | −0.907388 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.73759 | 0.911750 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.10755 | −0.577057 | −0.288528 | − | 0.957471i | \(-0.593166\pi\) | ||||
−0.288528 | + | 0.957471i | \(0.593166\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97669 | −0.534630 | −0.267315 | − | 0.963609i | \(-0.586136\pi\) | ||||
−0.267315 | + | 0.963609i | \(0.586136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.1951 | −2.12290 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.56678 | 0.264834 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.82043 | 0.628075 | 0.314037 | − | 0.949411i | \(-0.398318\pi\) | ||||
0.314037 | + | 0.949411i | \(0.398318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.9527 | 1.75383 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.44060 | 0.224984 | 0.112492 | − | 0.993653i | \(-0.464117\pi\) | ||||
0.112492 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.08724 | −0.775797 | −0.387899 | − | 0.921702i | \(-0.626799\pi\) | ||||
−0.387899 | + | 0.921702i | \(0.626799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.305534 | 0.0455463 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.35498 | 0.926969 | 0.463484 | − | 0.886105i | \(-0.346599\pi\) | ||||
0.463484 | + | 0.886105i | \(0.346599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.69874 | −0.242677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.687468 | −0.0962648 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6276 | −1.59718 | −0.798590 | − | 0.601876i | \(-0.794420\pi\) | ||||
−0.798590 | + | 0.601876i | \(0.794420\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.46846 | 0.602527 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.96334 | −0.392504 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.42038 | 0.705673 | 0.352837 | − | 0.935685i | \(-0.385217\pi\) | ||||
0.352837 | + | 0.935685i | \(0.385217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.39493 | −1.20290 | −0.601449 | − | 0.798912i | \(-0.705410\pi\) | ||||
−0.601449 | + | 0.798912i | \(0.705410\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03379 | 0.130245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.01321 | −0.497777 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.61423 | −0.563718 | −0.281859 | − | 0.959456i | \(-0.590951\pi\) | ||||
−0.281859 | + | 0.959456i | \(0.590951\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.430137 | 0.0517824 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.561887 | −0.0666837 | −0.0333419 | − | 0.999444i | \(-0.510615\pi\) | ||||
−0.0333419 | + | 0.999444i | \(0.510615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4642 | −1.22474 | −0.612371 | − | 0.790570i | \(-0.709784\pi\) | ||||
−0.612371 | + | 0.790570i | \(0.709784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.42576 | 0.972923 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.1192 | 1.72299 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.8746 | −1.56101 | −0.780505 | − | 0.625150i | \(-0.785038\pi\) | ||||
−0.780505 | + | 0.625150i | \(0.785038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1454 | −1.12727 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.72702 | 0.628622 | 0.314311 | − | 0.949320i | \(-0.398227\pi\) | ||||
0.314311 | + | 0.949320i | \(0.398227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.251898 | 0.0273222 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.77117 | 0.618734 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.14834 | −0.227724 | −0.113862 | − | 0.993497i | \(-0.536322\pi\) | ||||
−0.113862 | + | 0.993497i | \(0.536322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.5788 | −1.42345 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.52815 | 0.573243 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.08581 | 0.111402 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7070 | −1.59481 | −0.797404 | − | 0.603446i | \(-0.793794\pi\) | ||||
−0.797404 | + | 0.603446i | \(0.793794\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.94836 | 0.296321 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.40968 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.13508 | 0.604507 | 0.302254 | − | 0.953228i | \(-0.402261\pi\) | ||||
0.302254 | + | 0.953228i | \(0.402261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.90974 | −0.283962 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.996732 | −0.0963577 | −0.0481788 | − | 0.998839i | \(-0.515342\pi\) | ||||
−0.0481788 | + | 0.998839i | \(0.515342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14263 | −0.396792 | −0.198396 | − | 0.980122i | \(-0.563573\pi\) | ||||
−0.198396 | + | 0.980122i | \(0.563573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.09510 | −0.673437 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3207 | 1.34718 | 0.673590 | − | 0.739105i | \(-0.264751\pi\) | ||||
0.673590 | + | 0.739105i | \(0.264751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.157608 | −0.0146971 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.64798 | −0.244805 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.852306 | 0.0781308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.1200 | 2.92000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.67541 | −0.241234 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.48975 | −0.580461 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.40137 | −0.745501 | −0.372751 | − | 0.927932i | \(-0.621585\pi\) | ||||
−0.372751 | + | 0.927932i | \(0.621585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.44776 | 0.831829 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.33641 | −0.640985 | −0.320492 | − | 0.947251i | \(-0.603848\pi\) | ||||
−0.320492 | + | 0.947251i | \(0.603848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.67388 | 0.318566 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.22386 | 0.277466 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4111 | 1.74384 | 0.871921 | − | 0.489647i | \(-0.162874\pi\) | ||||
0.871921 | + | 0.489647i | \(0.162874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.2116 | −1.54469 | −0.772345 | − | 0.635204i | \(-0.780916\pi\) | ||||
−0.772345 | + | 0.635204i | \(0.780916\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.8021 | −0.993918 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −38.7269 | −3.23850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.11464 | −0.175611 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.15481 | 0.260205 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.17332 | 0.669585 | 0.334792 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334792 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.22683 | 0.750869 | 0.375434 | − | 0.926849i | \(-0.377494\pi\) | ||||
0.375434 | + | 0.926849i | \(0.377494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.166206 | 0.0134370 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02560 | −0.162700 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3721 | 1.30663 | 0.653316 | − | 0.757085i | \(-0.273377\pi\) | ||||
0.653316 | + | 0.757085i | \(0.273377\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.5942 | 1.71253 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.533273 | −0.0420278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1020 | 1.49619 | 0.748093 | − | 0.663594i | \(-0.230970\pi\) | ||||
0.748093 | + | 0.663594i | \(0.230970\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.29859 | −0.646044 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.3483 | 1.72936 | 0.864681 | − | 0.502321i | \(-0.167521\pi\) | ||||
0.864681 | + | 0.502321i | \(0.167521\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.7813 | 1.67549 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.716435 | 0.0547871 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.08784 | 0.310793 | 0.155396 | − | 0.987852i | \(-0.450334\pi\) | ||||
0.155396 | + | 0.987852i | \(0.450334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4461 | −0.789648 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0664 | −0.756640 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.82379 | −0.285803 | −0.142902 | − | 0.989737i | \(-0.545643\pi\) | ||||
−0.142902 | + | 0.989737i | \(0.545643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4569 | −1.29756 | −0.648782 | − | 0.760975i | \(-0.724721\pi\) | ||||
−0.648782 | + | 0.760975i | \(0.724721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.4478 | 1.28978 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.59975 | 0.191137 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.43078 | 0.177756 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.9081 | 0.793444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9404 | −1.58755 | −0.793775 | − | 0.608212i | \(-0.791887\pi\) | ||||
−0.793775 | + | 0.608212i | \(0.791887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.666760 | −0.0479944 | −0.0239972 | − | 0.999712i | \(-0.507639\pi\) | ||||
−0.0239972 | + | 0.999712i | \(0.507639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.45312 | 0.533729 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.54021 | −0.608465 | −0.304232 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304232 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.18802 | −0.509545 | −0.254773 | − | 0.967001i | \(-0.582001\pi\) | ||||
−0.254773 | + | 0.967001i | \(0.582001\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.56930 | 0.604432 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.15496 | −0.502180 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.980309 | 0.0684678 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.103992 | −0.00722797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.4779 | 0.724773 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.66359 | −0.252212 | −0.126106 | − | 0.992017i | \(-0.540248\pi\) | ||||
−0.126106 | + | 0.992017i | \(0.540248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.04351 | 0.0714999 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46180 | −0.236093 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.85367 | −0.465258 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.4336 | 1.31320 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.18313 | −0.146853 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.5793 | 1.71291 | 0.856457 | − | 0.516218i | \(-0.172660\pi\) | ||||
0.856457 | + | 0.516218i | \(0.172660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.03706 | −0.135804 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.62910 | 0.572733 | 0.286367 | − | 0.958120i | \(-0.407552\pi\) | ||||
0.286367 | + | 0.958120i | \(0.407552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.95696 | 0.459729 | 0.229865 | − | 0.973223i | \(-0.426172\pi\) | ||||
0.229865 | + | 0.973223i | \(0.426172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.0786 | −1.84743 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.80201 | −0.249078 | −0.124539 | − | 0.992215i | \(-0.539745\pi\) | ||||
−0.124539 | + | 0.992215i | \(0.539745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.32447 | 0.282097 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.7671 | 1.67375 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9650 | 1.09737 | 0.548687 | − | 0.836028i | \(-0.315128\pi\) | ||||
0.548687 | + | 0.836028i | \(0.315128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.9314 | −1.79922 | −0.899608 | − | 0.436698i | \(-0.856148\pi\) | ||||
−0.899608 | + | 0.436698i | \(0.856148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.62870 | 0.296931 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.15597 | −0.0738521 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.41041 | −0.598770 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6359 | −0.674023 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.7637 | −1.81555 | −0.907775 | − | 0.419457i | \(-0.862221\pi\) | ||||
−0.907775 | + | 0.419457i | \(0.862221\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.52090 | −0.0956180 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.467812 | −0.0292955 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.5868 | −1.15941 | −0.579707 | − | 0.814825i | \(-0.696833\pi\) | ||||
−0.579707 | + | 0.814825i | \(0.696833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.79633 | 0.546578 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.39527 | −0.0863651 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.4319 | −1.56820 | −0.784099 | − | 0.620636i | \(-0.786874\pi\) | ||||
−0.784099 | + | 0.620636i | \(0.786874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.91244 | −0.486057 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.98978 | 0.244171 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2960 | 1.60329 | 0.801647 | − | 0.597797i | \(-0.203957\pi\) | ||||
0.801647 | + | 0.597797i | \(0.203957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.1101 | 1.10011 | 0.550056 | − | 0.835127i | \(-0.314606\pi\) | ||||
0.550056 | + | 0.835127i | \(0.314606\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.2179 | 1.52626 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.7922 | −1.79654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.12392 | −0.247782 | −0.123891 | − | 0.992296i | \(-0.539537\pi\) | ||||
−0.123891 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.33652 | −0.0800152 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0638 | −0.600357 | −0.300178 | − | 0.953883i | \(-0.597046\pi\) | ||||
−0.300178 | + | 0.953883i | \(0.597046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.8096 | −1.35589 | −0.677945 | − | 0.735113i | \(-0.737129\pi\) | ||||
−0.677945 | + | 0.735113i | \(0.737129\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.01651 | −0.119448 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.31691 | 0.195791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8630 | −0.991939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.1703 | 1.70999 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4199 | −1.07610 | −0.538050 | − | 0.842913i | \(-0.680839\pi\) | ||||
−0.538050 | + | 0.842913i | \(0.680839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.68849 | 0.214752 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.1098 | 1.80517 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.36595 | 0.0789947 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7131 | −0.675132 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.33228 | 0.363780 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.39311 | −0.366069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0224 | −1.31396 | −0.656979 | − | 0.753909i | \(-0.728166\pi\) | ||||
−0.656979 | + | 0.753909i | \(0.728166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.3937 | −0.648167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.97607 | 0.225462 | 0.112731 | − | 0.993626i | \(-0.464040\pi\) | ||||
0.112731 | + | 0.993626i | \(0.464040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.87697 | 0.388710 | 0.194355 | − | 0.980931i | \(-0.437739\pi\) | ||||
0.194355 | + | 0.980931i | \(0.437739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.703476 | 0.0396364 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9062 | 1.23038 | 0.615188 | − | 0.788381i | \(-0.289080\pi\) | ||||
0.615188 | + | 0.788381i | \(0.289080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4059 | −1.14251 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.85108 | 0.103317 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.590666 | 0.0328655 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.7569 | 1.48421 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.69348 | 0.425450 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6320 | 0.806688 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8035 | −1.36333 | −0.681663 | − | 0.731667i | \(-0.738743\pi\) | ||||
−0.681663 | + | 0.731667i | \(0.738743\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.71535 | 0.0940007 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.13992 | −0.171552 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4053 | −1.16602 | −0.583010 | − | 0.812465i | \(-0.698125\pi\) | ||||
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.5957 | −1.44448 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.5467 | −1.05851 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0284 | −1.08143 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.292702 | 0.0157585 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.2149 | 1.46097 | 0.730485 | − | 0.682928i | \(-0.239294\pi\) | ||||
0.730485 | + | 0.682928i | \(0.239294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.3301 | 0.820603 | 0.410302 | − | 0.911950i | \(-0.365423\pi\) | ||||
0.410302 | + | 0.911950i | \(0.365423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.9403 | −1.49134 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.47905 | −0.238396 | −0.119198 | − | 0.992871i | \(-0.538032\pi\) | ||||
−0.119198 | + | 0.992871i | \(0.538032\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.382356 | −0.0202933 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.58286 | −0.0837737 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.0703 | −0.742604 | −0.371302 | − | 0.928512i | \(-0.621089\pi\) | ||||
−0.371302 | + | 0.928512i | \(0.621089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4539 | −0.865996 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −59.6515 | −3.13089 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.12074 | −0.372717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.68527 | 0.348968 | 0.174484 | − | 0.984660i | \(-0.444174\pi\) | ||||
0.174484 | + | 0.984660i | \(0.444174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.646822 | 0.0336722 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.7720 | −1.38993 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4728 | −0.594037 | −0.297018 | − | 0.954872i | \(-0.595992\pi\) | ||||
−0.297018 | + | 0.954872i | \(0.595992\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0524 | 0.622384 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.3270 | 0.943887 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.46940 | 0.435044 | 0.217522 | − | 0.976055i | \(-0.430203\pi\) | ||||
0.217522 | + | 0.976055i | \(0.430203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.6026 | 0.799345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.4392 | 1.24879 | 0.624393 | − | 0.781110i | \(-0.285346\pi\) | ||||
0.624393 | + | 0.781110i | \(0.285346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.2884 | 0.524345 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.28414 | −0.116110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4081 | 1.23754 | 0.618770 | − | 0.785572i | \(-0.287631\pi\) | ||||
0.618770 | + | 0.785572i | \(0.287631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0857367 | −0.00433589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.6248 | 0.687279 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.44143 | −0.475050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.5542 | −1.23234 | −0.616171 | − | 0.787612i | \(-0.711317\pi\) | ||||
−0.616171 | + | 0.787612i | \(0.711317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.82294 | −0.341574 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.6890 | −0.883347 | −0.441673 | − | 0.897176i | \(-0.645615\pi\) | ||||
−0.441673 | + | 0.897176i | \(0.645615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5552 | 0.874489 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.90379 | −0.343052 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.0872 | 1.24352 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4483 | −1.70336 | −0.851678 | − | 0.524065i | \(-0.824415\pi\) | ||||
−0.851678 | + | 0.524065i | \(0.824415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.9065 | −1.86979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.4801 | 0.614107 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.89715 | 0.191304 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.8217 | 1.65625 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.2710 | −0.794891 | −0.397446 | − | 0.917626i | \(-0.630103\pi\) | ||||
−0.397446 | + | 0.917626i | \(0.630103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8845 | 1.45648 | 0.728240 | − | 0.685323i | \(-0.240339\pi\) | ||||
0.728240 | + | 0.685323i | \(0.240339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.85335 | 0.138735 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.67946 | −0.0814657 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.6313 | −1.04681 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 71.9215 | 3.47240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3046 | −0.929871 | −0.464936 | − | 0.885344i | \(-0.653923\pi\) | ||||
−0.464936 | + | 0.885344i | \(0.653923\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.36408 | 0.305838 | 0.152919 | − | 0.988239i | \(-0.451133\pi\) | ||||
0.152919 | + | 0.988239i | \(0.451133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.92720 | 0.188295 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.369570 | −0.0176789 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.21387 | −0.344299 | −0.172150 | − | 0.985071i | \(-0.555071\pi\) | ||||
−0.172150 | + | 0.985071i | \(0.555071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.762725 | −0.0363203 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.7885 | 1.51032 | 0.755160 | − | 0.655541i | \(-0.227559\pi\) | ||||
0.755160 | + | 0.655541i | \(0.227559\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.46191 | −0.0693014 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.1791 | −0.717945 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.93673 | −0.280172 | −0.140086 | − | 0.990139i | \(-0.544738\pi\) | ||||
−0.140086 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.45983 | 0.445446 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.1356 | −0.805100 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.24020 | −0.433187 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.1069 | −0.519558 | −0.259779 | − | 0.965668i | \(-0.583650\pi\) | ||||
−0.259779 | + | 0.965668i | \(0.583650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.75373 | 0.0818573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.2598 | 1.73536 | 0.867681 | − | 0.497122i | \(-0.165610\pi\) | ||||
0.867681 | + | 0.497122i | \(0.165610\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.96776 | −0.0914493 | −0.0457247 | − | 0.998954i | \(-0.514560\pi\) | ||||
−0.0457247 | + | 0.998954i | \(0.514560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.76183 | 0.174451 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.78113 | 0.174970 | 0.0874849 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874849 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6240 | −0.490571 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.4053 | −1.40100 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.4058 | −1.53600 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.23934 | −0.332163 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.22075 | −0.239042 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6119 | −0.896089 | −0.448045 | − | 0.894011i | \(-0.647879\pi\) | ||||
−0.448045 | + | 0.894011i | \(0.647879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5312 | −1.02734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.990367 | 0.0450633 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.6884 | −0.485336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.49717 | −0.385043 | −0.192522 | − | 0.981293i | \(-0.561667\pi\) | ||||
−0.192522 | + | 0.981293i | \(0.561667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.4752 | −1.60425 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.6851 | 0.843248 | 0.421624 | − | 0.906771i | \(-0.361460\pi\) | ||||
0.421624 | + | 0.906771i | \(0.361460\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.15033 | −0.0518084 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00631 | 0.0901771 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.29371 | −0.0580310 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.4084 | −1.45080 | −0.725400 | − | 0.688328i | \(-0.758345\pi\) | ||||
−0.725400 | + | 0.688328i | \(0.758345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.5040 | −1.85426 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.6379 | −1.81195 | −0.905977 | − | 0.423327i | \(-0.860862\pi\) | ||||
−0.905977 | + | 0.423327i | \(0.860862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.32024 | −0.103249 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.4511 | −1.79650 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.08830 | −0.269859 | −0.134930 | − | 0.990855i | \(-0.543081\pi\) | ||||
−0.134930 | + | 0.990855i | \(0.543081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0933 | −1.06582 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.55950 | 0.333760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.17483 | 0.183965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.7305 | 1.83530 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.59172 | −0.333240 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.3649 | −1.94366 | −0.971830 | − | 0.235683i | \(-0.924267\pi\) | ||||
−0.971830 | + | 0.235683i | \(0.924267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.58390 | −0.200440 | −0.100220 | − | 0.994965i | \(-0.531955\pi\) | ||||
−0.100220 | + | 0.994965i | \(0.531955\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.3999 | 0.846680 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.10189 | −0.0479993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9464 | −0.997668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.43372 | 0.105614 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.49605 | −0.368005 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.678261 | −0.0293238 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.10133 | 0.306445 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.1549 | −0.480477 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1671 | −0.566098 | −0.283049 | − | 0.959105i | \(-0.591346\pi\) | ||||
−0.283049 | + | 0.959105i | \(0.591346\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.4201 | 1.39128 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.81900 | −0.120753 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.77647 | 0.161470 | 0.0807350 | − | 0.996736i | \(-0.474273\pi\) | ||||
0.0807350 | + | 0.996736i | \(0.474273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.21827 | −0.180031 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.95853 | −0.211241 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.9454 | −1.35846 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.82811 | −0.204942 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.7815 | 1.47374 | 0.736869 | − | 0.676036i | \(-0.236304\pi\) | ||||
0.736869 | + | 0.676036i | \(0.236304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.0024 | 1.26897 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.51431 | −0.190594 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.6239 | −0.953485 | −0.476743 | − | 0.879043i | \(-0.658183\pi\) | ||||
−0.476743 | + | 0.879043i | \(0.658183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.74505 | 0.409977 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3592 | −0.980995 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2911 | −1.18603 | −0.593013 | − | 0.805193i | \(-0.702062\pi\) | ||||
−0.593013 | + | 0.805193i | \(0.702062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9319 | −0.834123 | −0.417061 | − | 0.908878i | \(-0.636940\pi\) | ||||
−0.417061 | + | 0.908878i | \(0.636940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.7465 | 1.70221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.05081 | 0.0438217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.2836 | −1.38561 | −0.692807 | − | 0.721123i | \(-0.743626\pi\) | ||||
−0.692807 | + | 0.721123i | \(0.743626\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.23827 | 0.0514608 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.1861 | 0.547054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −76.3538 | −3.16225 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.80191 | −0.0744998 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.7714 | 0.692232 | 0.346116 | − | 0.938192i | \(-0.387500\pi\) | ||||
0.346116 | + | 0.938192i | \(0.387500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.74974 | −0.195709 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8604 | 0.652411 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.36743 | 0.302544 | 0.151272 | − | 0.988492i | \(-0.451663\pi\) | ||||
0.151272 | + | 0.988492i | \(0.451663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.579982 | 0.0237769 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.3492 | 0.546347 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.8462 | 1.58721 | 0.793607 | − | 0.608431i | \(-0.208201\pi\) | ||||
0.793607 | + | 0.608431i | \(0.208201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3522 | 0.422276 | 0.211138 | − | 0.977456i | \(-0.432283\pi\) | ||||
0.211138 | + | 0.977456i | \(0.432283\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.07176 | −0.0843687 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.8572 | 0.888621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.50840 | 0.264168 | 0.132084 | − | 0.991239i | \(-0.457833\pi\) | ||||
0.132084 | + | 0.991239i | \(0.457833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.2878 | 0.538449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.4789 | −1.51623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.1002 | −0.529113 | −0.264557 | − | 0.964370i | \(-0.585226\pi\) | ||||
−0.264557 | + | 0.964370i | \(0.585226\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.82058 | −0.0734128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2219 | 0.773843 | 0.386921 | − | 0.922113i | \(-0.373539\pi\) | ||||
0.386921 | + | 0.922113i | \(0.373539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.34390 | 0.174596 | 0.0872981 | − | 0.996182i | \(-0.472177\pi\) | ||||
0.0872981 | + | 0.996182i | \(0.472177\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.09728 | −0.0440324 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.94644 | −0.198175 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.2685 | 0.730741 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.4590 | −0.777119 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.41422 | 0.0563888 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.5364 | 1.13601 | 0.568007 | − | 0.823023i | \(-0.307714\pi\) | ||||
0.568007 | + | 0.823023i | \(0.307714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.80383 | 0.270428 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.71701 | −0.226873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0184 | 0.396945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.252284 | −0.00998021 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.6773 | −1.92264 | −0.961320 | − | 0.275435i | \(-0.911178\pi\) | ||||
−0.961320 | + | 0.275435i | \(0.911178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.55293 | 0.218986 | 0.109493 | − | 0.993988i | \(-0.465077\pi\) | ||||
0.109493 | + | 0.993988i | \(0.465077\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.42906 | 0.253144 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.1567 | −0.674500 | −0.337250 | − | 0.941415i | \(-0.609497\pi\) | ||||
−0.337250 | + | 0.941415i | \(0.609497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.5934 | 1.39716 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.7283 | 0.498860 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.7365 | −1.08541 | −0.542706 | − | 0.839923i | \(-0.682600\pi\) | ||||
−0.542706 | + | 0.839923i | \(0.682600\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.99232 | −0.195066 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.69837 | −0.183301 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9429 | −0.893728 | −0.446864 | − | 0.894602i | \(-0.647459\pi\) | ||||
−0.446864 | + | 0.894602i | \(0.647459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5574 | −0.994068 | −0.497034 | − | 0.867731i | \(-0.665578\pi\) | ||||
−0.497034 | + | 0.867731i | \(0.665578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.05439 | 0.157459 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.50002 | 0.0969467 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.719744 | 0.0278686 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −47.5045 | −1.83663 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −61.6925 | −2.38161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.3533 | 1.43986 | 0.719932 | − | 0.694045i | \(-0.244173\pi\) | ||||
0.719932 | + | 0.694045i | \(0.244173\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.4942 | −0.827311 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.1483 | −1.27399 | −0.636997 | − | 0.770866i | \(-0.719824\pi\) | ||||
−0.636997 | + | 0.770866i | \(0.719824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.1646 | −1.38787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.0255 | −0.614099 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.7875 | 1.17805 | 0.589025 | − | 0.808114i | \(-0.299512\pi\) | ||||
0.589025 | + | 0.808114i | \(0.299512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8895 | 0.530690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.9201 | −0.492933 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 68.5748 | 2.61249 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7468 | −1.16966 | −0.584831 | − | 0.811155i | \(-0.698839\pi\) | ||||
−0.584831 | + | 0.811155i | \(0.698839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.78844 | 0.257871 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.3927 | −0.470084 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.533274 | 0.0201992 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.06089 | 0.267067 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.1719 | −0.610804 | −0.305402 | − | 0.952223i | \(-0.598791\pi\) | ||||
−0.305402 | + | 0.952223i | \(0.598791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.09604 | 0.229917 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.03118 | −0.302472 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.85061 | −0.295253 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.2127 | 0.871770 | 0.435885 | − | 0.900002i | \(-0.356436\pi\) | ||||
0.435885 | + | 0.900002i | \(0.356436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.22960 | −0.233628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.689436 | 0.0258196 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.3531 | −0.985549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.5065 | −1.17663 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.0358 | −0.933678 | −0.466839 | − | 0.884342i | \(-0.654607\pi\) | ||||
−0.466839 | + | 0.884342i | \(0.654607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1257 | 0.526068 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.8726 | 1.92916 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.0987 | 0.523614 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.7280 | 1.36217 | 0.681083 | − | 0.732207i | \(-0.261509\pi\) | ||||
0.681083 | + | 0.732207i | \(0.261509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8400 | 0.808889 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.88317 | −0.0696514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.1539 | 1.26150 | 0.630751 | − | 0.775985i | \(-0.282747\pi\) | ||||
0.630751 | + | 0.775985i | \(0.282747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.14680 | 0.0791861 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.2997 | −1.11610 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.4174 | −1.33964 | −0.669818 | − | 0.742525i | \(-0.733628\pi\) | ||||
−0.669818 | + | 0.742525i | \(0.733628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.4765 | 0.642016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.1337 | 0.518517 | 0.259258 | − | 0.965808i | \(-0.416522\pi\) | ||||
0.259258 | + | 0.965808i | \(0.416522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.56183 | 0.203770 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.57140 | 0.0940826 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.29492 | −0.0838546 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.48411 | 0.163627 | 0.0818137 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818137 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 53.4185 | 1.94668 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.27873 | 0.228506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.9372 | 1.96038 | 0.980191 | − | 0.198053i | \(-0.0634618\pi\) | ||||
0.980191 | + | 0.198053i | \(0.0634618\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.82453 | 0.102524 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7104 | 1.18575 | 0.592876 | − | 0.805294i | \(-0.297992\pi\) | ||||
0.592876 | + | 0.805294i | \(0.297992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.53819 | −0.345306 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.113101 | 0.00408917 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.9671 | −1.15426 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.04603 | 0.109843 | 0.0549213 | − | 0.998491i | \(-0.482509\pi\) | ||||
0.0549213 | + | 0.998491i | \(0.482509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.5185 | 1.24315 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6985 | 0.384799 | 0.192400 | − | 0.981317i | \(-0.438373\pi\) | ||||
0.192400 | + | 0.981317i | \(0.438373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.5051 | 0.485116 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3361 | −0.586054 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.29869 | 0.0823590 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.68968 | −0.132027 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.7223 | −0.526132 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.1409 | 0.397637 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.3092 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702322\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702322\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 47.2308 | 1.68146 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.9727 | 1.17237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.4072 | 1.96757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.6946 | 0.521162 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.5569 | −0.551054 | −0.275527 | − | 0.961293i | \(-0.588852\pi\) | ||||
−0.275527 | + | 0.961293i | \(0.588852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.35245 | 0.0832237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.964593 | −0.0340822 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −68.7141 | −2.42487 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.362885 | −0.0127900 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.8355 | −1.71909 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.7581 | −0.975923 | −0.487961 | − | 0.872865i | \(-0.662259\pi\) | ||||
−0.487961 | + | 0.872865i | \(0.662259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.38201 | 0.294332 | 0.147166 | − | 0.989112i | \(-0.452985\pi\) | ||||
0.147166 | + | 0.989112i | \(0.452985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.6332 | −1.17957 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.9986 | 0.455323 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.11742 | −0.283993 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.09682 | −0.213040 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2785 | −0.882224 | −0.441112 | − | 0.897452i | \(-0.645416\pi\) | ||||
−0.441112 | + | 0.897452i | \(0.645416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.5385 | 0.959933 | 0.479966 | − | 0.877287i | \(-0.340649\pi\) | ||||
0.479966 | + | 0.877287i | \(0.340649\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 55.3284 | 1.92629 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.85259 | 0.0644209 | 0.0322104 | − | 0.999481i | \(-0.489745\pi\) | ||||
0.0322104 | + | 0.999481i | \(0.489745\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4656 | 1.30123 | 0.650617 | − | 0.759406i | \(-0.274510\pi\) | ||||
0.650617 | + | 0.759406i | \(0.274510\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.65872 | 0.265678 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.628830 | −0.0217877 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.2077 | 0.526284 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.1023 | −0.487448 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.1728 | −0.765490 | −0.382745 | − | 0.923854i | \(-0.625021\pi\) | ||||
−0.382745 | + | 0.923854i | \(0.625021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.3432 | −0.667005 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.6900 | 0.643717 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.8219 | 0.509888 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 73.9545 | 2.54111 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 42.3608 | 1.45382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.884856 | −0.0303325 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4261 | −0.870573 | −0.435287 | − | 0.900292i | \(-0.643353\pi\) | ||||
−0.435287 | + | 0.900292i | \(0.643353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.487523 | 0.0166730 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.2101 | −0.963639 | −0.481820 | − | 0.876270i | \(-0.660024\pi\) | ||||
−0.481820 | + | 0.876270i | \(0.660024\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.20655 | −0.177645 | −0.0888226 | − | 0.996047i | \(-0.528310\pi\) | ||||
−0.0888226 | + | 0.996047i | \(0.528310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.15999 | −0.209932 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.1135 | 1.39952 | 0.699761 | − | 0.714377i | \(-0.253290\pi\) | ||||
0.699761 | + | 0.714377i | \(0.253290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.78172 | 0.0945812 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.3170 | 1.06358 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −91.1084 | −3.09064 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.2127 | 0.922068 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.05237 | −0.238687 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.9423 | −0.505142 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.2642 | 1.12325 | 0.561626 | − | 0.827391i | \(-0.310176\pi\) | ||||
0.561626 | + | 0.827391i | \(0.310176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.2084 | 1.15382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.99610 | 0.336777 | 0.168389 | − | 0.985721i | \(-0.446144\pi\) | ||||
0.168389 | + | 0.985721i | \(0.446144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1715 | 1.11631 | 0.558156 | − | 0.829736i | \(-0.311509\pi\) | ||||
0.558156 | + | 0.829736i | \(0.311509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.85007 | −0.230262 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.2150 | −1.65248 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.3437 | −0.648767 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −66.6205 | −2.23187 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1403 | 0.339331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.60203 | −0.0869763 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.53676 | −0.0847000 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.25020 | 0.308512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.30425 | −0.143395 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.7530 | 0.723893 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.8792 | −0.394877 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2825 | −0.706673 | −0.353336 | − | 0.935496i | \(-0.614953\pi\) | ||||
−0.353336 | + | 0.935496i | \(0.614953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.53093 | −0.0507777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.1420 | −0.799861 | −0.399931 | − | 0.916545i | \(-0.630966\pi\) | ||||
−0.399931 | + | 0.916545i | \(0.630966\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.6069 | 1.24461 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8729 | 0.392508 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8917 | −0.557812 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.0218 | −1.12228 | −0.561138 | − | 0.827722i | \(-0.689636\pi\) | ||||
−0.561138 | + | 0.827722i | \(0.689636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.7560 | 1.40886 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.31377 | 0.109074 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.3331 | −0.569907 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.75462 | 0.0904735 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4502 | 0.441288 | 0.220644 | − | 0.975354i | \(-0.429184\pi\) | ||||
0.220644 | + | 0.975354i | \(0.429184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.71058 | −0.0888358 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.38415 | −0.241746 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.65411 | 0.0540952 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6409 | −1.09900 | −0.549500 | − | 0.835494i | \(-0.685182\pi\) | ||||
−0.549500 | + | 0.835494i | \(0.685182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.7716 | −0.416784 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.2118 | −0.495889 | −0.247945 | − | 0.968774i | \(-0.579755\pi\) | ||||
−0.247945 | + | 0.968774i | \(0.579755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.333660 | −0.0108655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.42277 | 0.241463 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.8411 | 1.39215 | 0.696074 | − | 0.717970i | \(-0.254929\pi\) | ||||
0.696074 | + | 0.717970i | \(0.254929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.7134 | 2.00330 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.6830 | −1.31924 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7959 | −1.35390 | −0.676951 | − | 0.736028i | \(-0.736699\pi\) | ||||
−0.676951 | + | 0.736028i | \(0.736699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.9301 | −0.483127 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.8968 | 1.22503 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.9955 | 1.51757 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1393 | −0.714171 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.447527 | −0.0144214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.453720 | −0.0146058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9647 | 0.545547 | 0.272774 | − | 0.962078i | \(-0.412059\pi\) | ||||
0.272774 | + | 0.962078i | \(0.412059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.09695 | −0.0352392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.4192 | 0.847831 | 0.423915 | − | 0.905702i | \(-0.360655\pi\) | ||||
0.423915 | + | 0.905702i | \(0.360655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.9313 | −1.34425 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −49.6915 | −1.59140 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.2390 | 1.22337 | 0.611687 | − | 0.791100i | \(-0.290491\pi\) | ||||
0.611687 | + | 0.791100i | \(0.290491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1073 | −0.450870 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.86002 | −0.0593859 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.6524 | −1.23282 | −0.616410 | − | 0.787426i | \(-0.711413\pi\) | ||||
−0.616410 | + | 0.787426i | \(0.711413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.81149 | −0.185169 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.1738 | −0.864950 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17827 | 0.0374667 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.64624 | −0.147593 | −0.0737963 | − | 0.997273i | \(-0.523511\pi\) | ||||
−0.0737963 | + | 0.997273i | \(0.523511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.0638 | 1.46179 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.89134 | −0.155066 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.3137 | −0.706682 | −0.353341 | − | 0.935495i | \(-0.614955\pi\) | ||||
−0.353341 | + | 0.935495i | \(0.614955\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.0996 | 0.572647 |
(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 | 8044.2.a.a.1.20 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8044.2.a.a.1.20 | ✓ | 80 | 1.1 | even | 1 | trivial |