Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.887456 | −0.627526 | −0.313763 | − | 0.949501i | \(-0.601590\pi\) | ||||
−0.313763 | + | 0.949501i | \(0.601590\pi\) | |||||||
\(3\) | −2.66181 | −1.53680 | −0.768399 | − | 0.639971i | \(-0.778946\pi\) | ||||
−0.768399 | + | 0.639971i | \(0.778946\pi\) | |||||||
\(4\) | −1.21242 | −0.606211 | ||||||||
\(5\) | −0.744827 | −0.333097 | −0.166548 | − | 0.986033i | \(-0.553262\pi\) | ||||
−0.166548 | + | 0.986033i | \(0.553262\pi\) | |||||||
\(6\) | 2.36224 | 0.964382 | ||||||||
\(7\) | −0.702395 | −0.265480 | −0.132740 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132740 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(8\) | 2.85088 | 1.00794 | ||||||||
\(9\) | 4.08525 | 1.36175 | ||||||||
\(10\) | 0.661001 | 0.209027 | ||||||||
\(11\) | 1.89013 | 0.569896 | 0.284948 | − | 0.958543i | \(-0.408024\pi\) | ||||
0.284948 | + | 0.958543i | \(0.408024\pi\) | |||||||
\(12\) | 3.22724 | 0.931624 | ||||||||
\(13\) | 5.87931 | 1.63063 | 0.815314 | − | 0.579020i | \(-0.196565\pi\) | ||||
0.815314 | + | 0.579020i | \(0.196565\pi\) | |||||||
\(14\) | 0.623345 | 0.166596 | ||||||||
\(15\) | 1.98259 | 0.511903 | ||||||||
\(16\) | −0.105192 | −0.0262980 | ||||||||
\(17\) | −6.29540 | −1.52686 | −0.763429 | − | 0.645892i | \(-0.776486\pi\) | ||||
−0.763429 | + | 0.645892i | \(0.776486\pi\) | |||||||
\(18\) | −3.62548 | −0.854534 | ||||||||
\(19\) | −0.340965 | −0.0782227 | −0.0391114 | − | 0.999235i | \(-0.512453\pi\) | ||||
−0.0391114 | + | 0.999235i | \(0.512453\pi\) | |||||||
\(20\) | 0.903044 | 0.201927 | ||||||||
\(21\) | 1.86964 | 0.407990 | ||||||||
\(22\) | −1.67741 | −0.357625 | ||||||||
\(23\) | 4.82124 | 1.00530 | 0.502649 | − | 0.864491i | \(-0.332359\pi\) | ||||
0.502649 | + | 0.864491i | \(0.332359\pi\) | |||||||
\(24\) | −7.58852 | −1.54900 | ||||||||
\(25\) | −4.44523 | −0.889047 | ||||||||
\(26\) | −5.21763 | −1.02326 | ||||||||
\(27\) | −2.88873 | −0.555937 | ||||||||
\(28\) | 0.851598 | 0.160937 | ||||||||
\(29\) | −3.65200 | −0.678160 | −0.339080 | − | 0.940758i | \(-0.610116\pi\) | ||||
−0.339080 | + | 0.940758i | \(0.610116\pi\) | |||||||
\(30\) | −1.75946 | −0.321232 | ||||||||
\(31\) | −1.90470 | −0.342094 | −0.171047 | − | 0.985263i | \(-0.554715\pi\) | ||||
−0.171047 | + | 0.985263i | \(0.554715\pi\) | |||||||
\(32\) | −5.60841 | −0.991437 | ||||||||
\(33\) | −5.03118 | −0.875816 | ||||||||
\(34\) | 5.58689 | 0.958144 | ||||||||
\(35\) | 0.523162 | 0.0884306 | ||||||||
\(36\) | −4.95305 | −0.825508 | ||||||||
\(37\) | −3.11217 | −0.511638 | −0.255819 | − | 0.966725i | \(-0.582345\pi\) | ||||
−0.255819 | + | 0.966725i | \(0.582345\pi\) | |||||||
\(38\) | 0.302591 | 0.0490868 | ||||||||
\(39\) | −15.6496 | −2.50595 | ||||||||
\(40\) | −2.12341 | −0.335741 | ||||||||
\(41\) | −3.21126 | −0.501515 | −0.250757 | − | 0.968050i | \(-0.580680\pi\) | ||||
−0.250757 | + | 0.968050i | \(0.580680\pi\) | |||||||
\(42\) | −1.65923 | −0.256024 | ||||||||
\(43\) | 7.84913 | 1.19698 | 0.598491 | − | 0.801130i | \(-0.295767\pi\) | ||||
0.598491 | + | 0.801130i | \(0.295767\pi\) | |||||||
\(44\) | −2.29164 | −0.345477 | ||||||||
\(45\) | −3.04280 | −0.453595 | ||||||||
\(46\) | −4.27864 | −0.630851 | ||||||||
\(47\) | 12.3713 | 1.80453 | 0.902267 | − | 0.431177i | \(-0.141902\pi\) | ||||
0.902267 | + | 0.431177i | \(0.141902\pi\) | |||||||
\(48\) | 0.280001 | 0.0404147 | ||||||||
\(49\) | −6.50664 | −0.929520 | ||||||||
\(50\) | 3.94495 | 0.557900 | ||||||||
\(51\) | 16.7572 | 2.34647 | ||||||||
\(52\) | −7.12820 | −0.988504 | ||||||||
\(53\) | −11.6789 | −1.60423 | −0.802113 | − | 0.597172i | \(-0.796291\pi\) | ||||
−0.802113 | + | 0.597172i | \(0.796291\pi\) | |||||||
\(54\) | 2.56363 | 0.348865 | ||||||||
\(55\) | −1.40782 | −0.189830 | ||||||||
\(56\) | −2.00245 | −0.267588 | ||||||||
\(57\) | 0.907585 | 0.120213 | ||||||||
\(58\) | 3.24099 | 0.425563 | ||||||||
\(59\) | 6.85518 | 0.892468 | 0.446234 | − | 0.894916i | \(-0.352765\pi\) | ||||
0.446234 | + | 0.894916i | \(0.352765\pi\) | |||||||
\(60\) | −2.40373 | −0.310321 | ||||||||
\(61\) | −9.12686 | −1.16858 | −0.584288 | − | 0.811547i | \(-0.698626\pi\) | ||||
−0.584288 | + | 0.811547i | \(0.698626\pi\) | |||||||
\(62\) | 1.69034 | 0.214673 | ||||||||
\(63\) | −2.86946 | −0.361518 | ||||||||
\(64\) | 5.18761 | 0.648451 | ||||||||
\(65\) | −4.37907 | −0.543157 | ||||||||
\(66\) | 4.46495 | 0.549597 | ||||||||
\(67\) | −5.99837 | −0.732817 | −0.366409 | − | 0.930454i | \(-0.619413\pi\) | ||||
−0.366409 | + | 0.930454i | \(0.619413\pi\) | |||||||
\(68\) | 7.63268 | 0.925598 | ||||||||
\(69\) | −12.8332 | −1.54494 | ||||||||
\(70\) | −0.464284 | −0.0554925 | ||||||||
\(71\) | −9.17613 | −1.08901 | −0.544503 | − | 0.838759i | \(-0.683282\pi\) | ||||
−0.544503 | + | 0.838759i | \(0.683282\pi\) | |||||||
\(72\) | 11.6466 | 1.37256 | ||||||||
\(73\) | 7.10331 | 0.831380 | 0.415690 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415690 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(74\) | 2.76192 | 0.321066 | ||||||||
\(75\) | 11.8324 | 1.36629 | ||||||||
\(76\) | 0.413393 | 0.0474194 | ||||||||
\(77\) | −1.32762 | −0.151296 | ||||||||
\(78\) | 13.8884 | 1.57255 | ||||||||
\(79\) | −3.80975 | −0.428631 | −0.214315 | − | 0.976765i | \(-0.568752\pi\) | ||||
−0.214315 | + | 0.976765i | \(0.568752\pi\) | |||||||
\(80\) | 0.0783497 | 0.00875976 | ||||||||
\(81\) | −4.56648 | −0.507387 | ||||||||
\(82\) | 2.84985 | 0.314714 | ||||||||
\(83\) | −16.5815 | −1.82006 | −0.910031 | − | 0.414541i | \(-0.863942\pi\) | ||||
−0.910031 | + | 0.414541i | \(0.863942\pi\) | |||||||
\(84\) | −2.26680 | −0.247328 | ||||||||
\(85\) | 4.68898 | 0.508592 | ||||||||
\(86\) | −6.96576 | −0.751137 | ||||||||
\(87\) | 9.72095 | 1.04219 | ||||||||
\(88\) | 5.38854 | 0.574421 | ||||||||
\(89\) | −1.94358 | −0.206019 | −0.103010 | − | 0.994680i | \(-0.532847\pi\) | ||||
−0.103010 | + | 0.994680i | \(0.532847\pi\) | |||||||
\(90\) | 2.70036 | 0.284643 | ||||||||
\(91\) | −4.12960 | −0.432899 | ||||||||
\(92\) | −5.84537 | −0.609422 | ||||||||
\(93\) | 5.06995 | 0.525729 | ||||||||
\(94\) | −10.9790 | −1.13239 | ||||||||
\(95\) | 0.253960 | 0.0260557 | ||||||||
\(96\) | 14.9286 | 1.52364 | ||||||||
\(97\) | 9.71119 | 0.986022 | 0.493011 | − | 0.870023i | \(-0.335896\pi\) | ||||
0.493011 | + | 0.870023i | \(0.335896\pi\) | |||||||
\(98\) | 5.77436 | 0.583298 | ||||||||
\(99\) | 7.72166 | 0.776056 | ||||||||
\(100\) | 5.38950 | 0.538950 | ||||||||
\(101\) | −2.16605 | −0.215530 | −0.107765 | − | 0.994176i | \(-0.534369\pi\) | ||||
−0.107765 | + | 0.994176i | \(0.534369\pi\) | |||||||
\(102\) | −14.8713 | −1.47247 | ||||||||
\(103\) | 16.4622 | 1.62207 | 0.811037 | − | 0.584995i | \(-0.198904\pi\) | ||||
0.811037 | + | 0.584995i | \(0.198904\pi\) | |||||||
\(104\) | 16.7612 | 1.64357 | ||||||||
\(105\) | −1.39256 | −0.135900 | ||||||||
\(106\) | 10.3645 | 1.00669 | ||||||||
\(107\) | −15.2236 | −1.47173 | −0.735863 | − | 0.677131i | \(-0.763223\pi\) | ||||
−0.735863 | + | 0.677131i | \(0.763223\pi\) | |||||||
\(108\) | 3.50236 | 0.337015 | ||||||||
\(109\) | 13.4044 | 1.28391 | 0.641956 | − | 0.766741i | \(-0.278123\pi\) | ||||
0.641956 | + | 0.766741i | \(0.278123\pi\) | |||||||
\(110\) | 1.24938 | 0.119124 | ||||||||
\(111\) | 8.28402 | 0.786285 | ||||||||
\(112\) | 0.0738862 | 0.00698159 | ||||||||
\(113\) | −8.18271 | −0.769764 | −0.384882 | − | 0.922966i | \(-0.625758\pi\) | ||||
−0.384882 | + | 0.922966i | \(0.625758\pi\) | |||||||
\(114\) | −0.805442 | −0.0754366 | ||||||||
\(115\) | −3.59099 | −0.334861 | ||||||||
\(116\) | 4.42776 | 0.411108 | ||||||||
\(117\) | 24.0185 | 2.22051 | ||||||||
\(118\) | −6.08367 | −0.560047 | ||||||||
\(119\) | 4.42185 | 0.405351 | ||||||||
\(120\) | 5.65213 | 0.515967 | ||||||||
\(121\) | −7.42740 | −0.675218 | ||||||||
\(122\) | 8.09969 | 0.733312 | ||||||||
\(123\) | 8.54778 | 0.770727 | ||||||||
\(124\) | 2.30930 | 0.207381 | ||||||||
\(125\) | 7.03506 | 0.629235 | ||||||||
\(126\) | 2.54652 | 0.226862 | ||||||||
\(127\) | 5.96470 | 0.529281 | 0.264641 | − | 0.964347i | \(-0.414747\pi\) | ||||
0.264641 | + | 0.964347i | \(0.414747\pi\) | |||||||
\(128\) | 6.61305 | 0.584517 | ||||||||
\(129\) | −20.8929 | −1.83952 | ||||||||
\(130\) | 3.88623 | 0.340845 | ||||||||
\(131\) | −19.4936 | −1.70316 | −0.851580 | − | 0.524224i | \(-0.824355\pi\) | ||||
−0.851580 | + | 0.524224i | \(0.824355\pi\) | |||||||
\(132\) | 6.09991 | 0.530929 | ||||||||
\(133\) | 0.239492 | 0.0207666 | ||||||||
\(134\) | 5.32329 | 0.459862 | ||||||||
\(135\) | 2.15161 | 0.185181 | ||||||||
\(136\) | −17.9474 | −1.53898 | ||||||||
\(137\) | −11.6564 | −0.995875 | −0.497938 | − | 0.867213i | \(-0.665909\pi\) | ||||
−0.497938 | + | 0.867213i | \(0.665909\pi\) | |||||||
\(138\) | 11.3889 | 0.969491 | ||||||||
\(139\) | −9.44498 | −0.801113 | −0.400557 | − | 0.916272i | \(-0.631183\pi\) | ||||
−0.400557 | + | 0.916272i | \(0.631183\pi\) | |||||||
\(140\) | −0.634293 | −0.0536076 | ||||||||
\(141\) | −32.9300 | −2.77321 | ||||||||
\(142\) | 8.14341 | 0.683380 | ||||||||
\(143\) | 11.1127 | 0.929288 | ||||||||
\(144\) | −0.429735 | −0.0358113 | ||||||||
\(145\) | 2.72011 | 0.225893 | ||||||||
\(146\) | −6.30388 | −0.521713 | ||||||||
\(147\) | 17.3195 | 1.42849 | ||||||||
\(148\) | 3.77326 | 0.310160 | ||||||||
\(149\) | −12.7368 | −1.04344 | −0.521718 | − | 0.853118i | \(-0.674709\pi\) | ||||
−0.521718 | + | 0.853118i | \(0.674709\pi\) | |||||||
\(150\) | −10.5007 | −0.857380 | ||||||||
\(151\) | −11.1386 | −0.906448 | −0.453224 | − | 0.891397i | \(-0.649726\pi\) | ||||
−0.453224 | + | 0.891397i | \(0.649726\pi\) | |||||||
\(152\) | −0.972051 | −0.0788438 | ||||||||
\(153\) | −25.7183 | −2.07920 | ||||||||
\(154\) | 1.17820 | 0.0949423 | ||||||||
\(155\) | 1.41867 | 0.113950 | ||||||||
\(156\) | 18.9739 | 1.51913 | ||||||||
\(157\) | 14.5199 | 1.15881 | 0.579405 | − | 0.815040i | \(-0.303285\pi\) | ||||
0.579405 | + | 0.815040i | \(0.303285\pi\) | |||||||
\(158\) | 3.38099 | 0.268977 | ||||||||
\(159\) | 31.0872 | 2.46537 | ||||||||
\(160\) | 4.17730 | 0.330244 | ||||||||
\(161\) | −3.38641 | −0.266887 | ||||||||
\(162\) | 4.05255 | 0.318398 | ||||||||
\(163\) | −6.98817 | −0.547356 | −0.273678 | − | 0.961821i | \(-0.588240\pi\) | ||||
−0.273678 | + | 0.961821i | \(0.588240\pi\) | |||||||
\(164\) | 3.89340 | 0.304024 | ||||||||
\(165\) | 3.74736 | 0.291731 | ||||||||
\(166\) | 14.7154 | 1.14214 | ||||||||
\(167\) | −7.52881 | −0.582596 | −0.291298 | − | 0.956632i | \(-0.594087\pi\) | ||||
−0.291298 | + | 0.956632i | \(0.594087\pi\) | |||||||
\(168\) | 5.33014 | 0.411229 | ||||||||
\(169\) | 21.5663 | 1.65895 | ||||||||
\(170\) | −4.16127 | −0.319155 | ||||||||
\(171\) | −1.39293 | −0.106520 | ||||||||
\(172\) | −9.51645 | −0.725623 | ||||||||
\(173\) | −6.03121 | −0.458545 | −0.229272 | − | 0.973362i | \(-0.573635\pi\) | ||||
−0.229272 | + | 0.973362i | \(0.573635\pi\) | |||||||
\(174\) | −8.62691 | −0.654005 | ||||||||
\(175\) | 3.12231 | 0.236024 | ||||||||
\(176\) | −0.198826 | −0.0149871 | ||||||||
\(177\) | −18.2472 | −1.37154 | ||||||||
\(178\) | 1.72484 | 0.129282 | ||||||||
\(179\) | 12.2546 | 0.915952 | 0.457976 | − | 0.888965i | \(-0.348575\pi\) | ||||
0.457976 | + | 0.888965i | \(0.348575\pi\) | |||||||
\(180\) | 3.68916 | 0.274974 | ||||||||
\(181\) | 2.64714 | 0.196760 | 0.0983800 | − | 0.995149i | \(-0.468634\pi\) | ||||
0.0983800 | + | 0.995149i | \(0.468634\pi\) | |||||||
\(182\) | 3.66484 | 0.271656 | ||||||||
\(183\) | 24.2940 | 1.79587 | ||||||||
\(184\) | 13.7448 | 1.01328 | ||||||||
\(185\) | 2.31803 | 0.170425 | ||||||||
\(186\) | −4.49936 | −0.329909 | ||||||||
\(187\) | −11.8991 | −0.870151 | ||||||||
\(188\) | −14.9992 | −1.09393 | ||||||||
\(189\) | 2.02903 | 0.147590 | ||||||||
\(190\) | −0.225378 | −0.0163507 | ||||||||
\(191\) | −8.59383 | −0.621828 | −0.310914 | − | 0.950438i | \(-0.600635\pi\) | ||||
−0.310914 | + | 0.950438i | \(0.600635\pi\) | |||||||
\(192\) | −13.8084 | −0.996538 | ||||||||
\(193\) | 2.19690 | 0.158137 | 0.0790683 | − | 0.996869i | \(-0.474805\pi\) | ||||
0.0790683 | + | 0.996869i | \(0.474805\pi\) | |||||||
\(194\) | −8.61826 | −0.618755 | ||||||||
\(195\) | 11.6563 | 0.834722 | ||||||||
\(196\) | 7.88879 | 0.563485 | ||||||||
\(197\) | −5.74909 | −0.409606 | −0.204803 | − | 0.978803i | \(-0.565655\pi\) | ||||
−0.204803 | + | 0.978803i | \(0.565655\pi\) | |||||||
\(198\) | −6.85264 | −0.486996 | ||||||||
\(199\) | 0.107419 | 0.00761471 | 0.00380736 | − | 0.999993i | \(-0.498788\pi\) | ||||
0.00380736 | + | 0.999993i | \(0.498788\pi\) | |||||||
\(200\) | −12.6728 | −0.896105 | ||||||||
\(201\) | 15.9665 | 1.12619 | ||||||||
\(202\) | 1.92227 | 0.135251 | ||||||||
\(203\) | 2.56515 | 0.180038 | ||||||||
\(204\) | −20.3168 | −1.42246 | ||||||||
\(205\) | 2.39183 | 0.167053 | ||||||||
\(206\) | −14.6095 | −1.01789 | ||||||||
\(207\) | 19.6960 | 1.36896 | ||||||||
\(208\) | −0.618455 | −0.0428822 | ||||||||
\(209\) | −0.644468 | −0.0445788 | ||||||||
\(210\) | 1.23584 | 0.0852808 | ||||||||
\(211\) | −25.1728 | −1.73297 | −0.866483 | − | 0.499206i | \(-0.833625\pi\) | ||||
−0.866483 | + | 0.499206i | \(0.833625\pi\) | |||||||
\(212\) | 14.1598 | 0.972499 | ||||||||
\(213\) | 24.4251 | 1.67358 | ||||||||
\(214\) | 13.5103 | 0.923547 | ||||||||
\(215\) | −5.84624 | −0.398711 | ||||||||
\(216\) | −8.23545 | −0.560351 | ||||||||
\(217\) | 1.33785 | 0.0908191 | ||||||||
\(218\) | −11.8959 | −0.805689 | ||||||||
\(219\) | −18.9077 | −1.27766 | ||||||||
\(220\) | 1.70687 | 0.115077 | ||||||||
\(221\) | −37.0126 | −2.48974 | ||||||||
\(222\) | −7.35171 | −0.493414 | ||||||||
\(223\) | 19.7309 | 1.32128 | 0.660639 | − | 0.750704i | \(-0.270286\pi\) | ||||
0.660639 | + | 0.750704i | \(0.270286\pi\) | |||||||
\(224\) | 3.93932 | 0.263207 | ||||||||
\(225\) | −18.1599 | −1.21066 | ||||||||
\(226\) | 7.26180 | 0.483047 | ||||||||
\(227\) | −10.9814 | −0.728862 | −0.364431 | − | 0.931230i | \(-0.618737\pi\) | ||||
−0.364431 | + | 0.931230i | \(0.618737\pi\) | |||||||
\(228\) | −1.10038 | −0.0728741 | ||||||||
\(229\) | −16.6925 | −1.10307 | −0.551537 | − | 0.834151i | \(-0.685958\pi\) | ||||
−0.551537 | + | 0.834151i | \(0.685958\pi\) | |||||||
\(230\) | 3.18684 | 0.210134 | ||||||||
\(231\) | 3.53387 | 0.232512 | ||||||||
\(232\) | −10.4114 | −0.683544 | ||||||||
\(233\) | 6.27483 | 0.411077 | 0.205539 | − | 0.978649i | \(-0.434105\pi\) | ||||
0.205539 | + | 0.978649i | \(0.434105\pi\) | |||||||
\(234\) | −21.3153 | −1.39343 | ||||||||
\(235\) | −9.21445 | −0.601085 | ||||||||
\(236\) | −8.31136 | −0.541024 | ||||||||
\(237\) | 10.1409 | 0.658719 | ||||||||
\(238\) | −3.92420 | −0.254368 | ||||||||
\(239\) | −14.7364 | −0.953217 | −0.476608 | − | 0.879116i | \(-0.658134\pi\) | ||||
−0.476608 | + | 0.879116i | \(0.658134\pi\) | |||||||
\(240\) | −0.208552 | −0.0134620 | ||||||||
\(241\) | 14.0484 | 0.904940 | 0.452470 | − | 0.891780i | \(-0.350543\pi\) | ||||
0.452470 | + | 0.891780i | \(0.350543\pi\) | |||||||
\(242\) | 6.59150 | 0.423717 | ||||||||
\(243\) | 20.8213 | 1.33569 | ||||||||
\(244\) | 11.0656 | 0.708403 | ||||||||
\(245\) | 4.84632 | 0.309620 | ||||||||
\(246\) | −7.58578 | −0.483652 | ||||||||
\(247\) | −2.00464 | −0.127552 | ||||||||
\(248\) | −5.43007 | −0.344810 | ||||||||
\(249\) | 44.1370 | 2.79707 | ||||||||
\(250\) | −6.24331 | −0.394862 | ||||||||
\(251\) | 9.94157 | 0.627506 | 0.313753 | − | 0.949505i | \(-0.398414\pi\) | ||||
0.313753 | + | 0.949505i | \(0.398414\pi\) | |||||||
\(252\) | 3.47899 | 0.219156 | ||||||||
\(253\) | 9.11277 | 0.572915 | ||||||||
\(254\) | −5.29341 | −0.332138 | ||||||||
\(255\) | −12.4812 | −0.781603 | ||||||||
\(256\) | −16.2440 | −1.01525 | ||||||||
\(257\) | −29.6057 | −1.84675 | −0.923376 | − | 0.383896i | \(-0.874582\pi\) | ||||
−0.923376 | + | 0.383896i | \(0.874582\pi\) | |||||||
\(258\) | 18.5416 | 1.15435 | ||||||||
\(259\) | 2.18597 | 0.135830 | ||||||||
\(260\) | 5.30928 | 0.329267 | ||||||||
\(261\) | −14.9193 | −0.923484 | ||||||||
\(262\) | 17.2997 | 1.06878 | ||||||||
\(263\) | 1.35298 | 0.0834280 | 0.0417140 | − | 0.999130i | \(-0.486718\pi\) | ||||
0.0417140 | + | 0.999130i | \(0.486718\pi\) | |||||||
\(264\) | −14.3433 | −0.882769 | ||||||||
\(265\) | 8.69879 | 0.534362 | ||||||||
\(266\) | −0.212539 | −0.0130316 | ||||||||
\(267\) | 5.17345 | 0.316610 | ||||||||
\(268\) | 7.27255 | 0.444242 | ||||||||
\(269\) | −11.0204 | −0.671926 | −0.335963 | − | 0.941875i | \(-0.609062\pi\) | ||||
−0.335963 | + | 0.941875i | \(0.609062\pi\) | |||||||
\(270\) | −1.90946 | −0.116206 | ||||||||
\(271\) | 18.9404 | 1.15055 | 0.575275 | − | 0.817960i | \(-0.304895\pi\) | ||||
0.575275 | + | 0.817960i | \(0.304895\pi\) | |||||||
\(272\) | 0.662225 | 0.0401533 | ||||||||
\(273\) | 10.9922 | 0.665279 | ||||||||
\(274\) | 10.3446 | 0.624938 | ||||||||
\(275\) | −8.40207 | −0.506664 | ||||||||
\(276\) | 15.5593 | 0.936559 | ||||||||
\(277\) | −11.5489 | −0.693908 | −0.346954 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346954 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(278\) | 8.38201 | 0.502720 | ||||||||
\(279\) | −7.78117 | −0.465846 | ||||||||
\(280\) | 1.49148 | 0.0891327 | ||||||||
\(281\) | 0.553133 | 0.0329971 | 0.0164986 | − | 0.999864i | \(-0.494748\pi\) | ||||
0.0164986 | + | 0.999864i | \(0.494748\pi\) | |||||||
\(282\) | 29.2239 | 1.74026 | ||||||||
\(283\) | −26.5908 | −1.58066 | −0.790330 | − | 0.612681i | \(-0.790091\pi\) | ||||
−0.790330 | + | 0.612681i | \(0.790091\pi\) | |||||||
\(284\) | 11.1253 | 0.660167 | ||||||||
\(285\) | −0.675994 | −0.0400424 | ||||||||
\(286\) | −9.86201 | −0.583153 | ||||||||
\(287\) | 2.25557 | 0.133142 | ||||||||
\(288\) | −22.9118 | −1.35009 | ||||||||
\(289\) | 22.6320 | 1.33130 | ||||||||
\(290\) | −2.41398 | −0.141754 | ||||||||
\(291\) | −25.8494 | −1.51532 | ||||||||
\(292\) | −8.61220 | −0.503991 | ||||||||
\(293\) | 10.8142 | 0.631773 | 0.315886 | − | 0.948797i | \(-0.397698\pi\) | ||||
0.315886 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(294\) | −15.3703 | −0.896412 | ||||||||
\(295\) | −5.10592 | −0.297278 | ||||||||
\(296\) | −8.87244 | −0.515700 | ||||||||
\(297\) | −5.46009 | −0.316826 | ||||||||
\(298\) | 11.3033 | 0.654784 | ||||||||
\(299\) | 28.3456 | 1.63927 | ||||||||
\(300\) | −14.3458 | −0.828257 | ||||||||
\(301\) | −5.51319 | −0.317775 | ||||||||
\(302\) | 9.88504 | 0.568820 | ||||||||
\(303\) | 5.76561 | 0.331226 | ||||||||
\(304\) | 0.0358667 | 0.00205710 | ||||||||
\(305\) | 6.79793 | 0.389249 | ||||||||
\(306\) | 22.8239 | 1.30475 | ||||||||
\(307\) | 4.14390 | 0.236505 | 0.118252 | − | 0.992984i | \(-0.462271\pi\) | ||||
0.118252 | + | 0.992984i | \(0.462271\pi\) | |||||||
\(308\) | 1.60963 | 0.0917173 | ||||||||
\(309\) | −43.8194 | −2.49280 | ||||||||
\(310\) | −1.25901 | −0.0715068 | ||||||||
\(311\) | −17.2875 | −0.980283 | −0.490141 | − | 0.871643i | \(-0.663055\pi\) | ||||
−0.490141 | + | 0.871643i | \(0.663055\pi\) | |||||||
\(312\) | −44.6153 | −2.52584 | ||||||||
\(313\) | −1.70690 | −0.0964795 | −0.0482397 | − | 0.998836i | \(-0.515361\pi\) | ||||
−0.0482397 | + | 0.998836i | \(0.515361\pi\) | |||||||
\(314\) | −12.8857 | −0.727184 | ||||||||
\(315\) | 2.13725 | 0.120420 | ||||||||
\(316\) | 4.61903 | 0.259841 | ||||||||
\(317\) | 5.39482 | 0.303003 | 0.151502 | − | 0.988457i | \(-0.451589\pi\) | ||||
0.151502 | + | 0.988457i | \(0.451589\pi\) | |||||||
\(318\) | −27.5885 | −1.54709 | ||||||||
\(319\) | −6.90276 | −0.386480 | ||||||||
\(320\) | −3.86387 | −0.215997 | ||||||||
\(321\) | 40.5225 | 2.26175 | ||||||||
\(322\) | 3.00529 | 0.167478 | ||||||||
\(323\) | 2.14651 | 0.119435 | ||||||||
\(324\) | 5.53650 | 0.307583 | ||||||||
\(325\) | −26.1349 | −1.44970 | ||||||||
\(326\) | 6.20170 | 0.343480 | ||||||||
\(327\) | −35.6801 | −1.97312 | ||||||||
\(328\) | −9.15493 | −0.505497 | ||||||||
\(329\) | −8.68951 | −0.479068 | ||||||||
\(330\) | −3.32561 | −0.183069 | ||||||||
\(331\) | −25.3872 | −1.39541 | −0.697703 | − | 0.716387i | \(-0.745795\pi\) | ||||
−0.697703 | + | 0.716387i | \(0.745795\pi\) | |||||||
\(332\) | 20.1038 | 1.10334 | ||||||||
\(333\) | −12.7140 | −0.696723 | ||||||||
\(334\) | 6.68149 | 0.365595 | ||||||||
\(335\) | 4.46775 | 0.244099 | ||||||||
\(336\) | −0.196671 | −0.0107293 | ||||||||
\(337\) | 16.3438 | 0.890306 | 0.445153 | − | 0.895455i | \(-0.353149\pi\) | ||||
0.445153 | + | 0.895455i | \(0.353149\pi\) | |||||||
\(338\) | −19.1391 | −1.04103 | ||||||||
\(339\) | 21.7808 | 1.18297 | ||||||||
\(340\) | −5.68502 | −0.308314 | ||||||||
\(341\) | −3.60013 | −0.194958 | ||||||||
\(342\) | 1.23616 | 0.0668440 | ||||||||
\(343\) | 9.48699 | 0.512249 | ||||||||
\(344\) | 22.3770 | 1.20648 | ||||||||
\(345\) | 9.55854 | 0.514615 | ||||||||
\(346\) | 5.35244 | 0.287749 | ||||||||
\(347\) | 21.5466 | 1.15668 | 0.578341 | − | 0.815795i | \(-0.303700\pi\) | ||||
0.578341 | + | 0.815795i | \(0.303700\pi\) | |||||||
\(348\) | −11.7859 | −0.631790 | ||||||||
\(349\) | −3.97176 | −0.212603 | −0.106302 | − | 0.994334i | \(-0.533901\pi\) | ||||
−0.106302 | + | 0.994334i | \(0.533901\pi\) | |||||||
\(350\) | −2.77091 | −0.148111 | ||||||||
\(351\) | −16.9838 | −0.906526 | ||||||||
\(352\) | −10.6006 | −0.565016 | ||||||||
\(353\) | 11.5765 | 0.616152 | 0.308076 | − | 0.951362i | \(-0.400315\pi\) | ||||
0.308076 | + | 0.951362i | \(0.400315\pi\) | |||||||
\(354\) | 16.1936 | 0.860680 | ||||||||
\(355\) | 6.83463 | 0.362744 | ||||||||
\(356\) | 2.35644 | 0.124891 | ||||||||
\(357\) | −11.7702 | −0.622942 | ||||||||
\(358\) | −10.8754 | −0.574784 | ||||||||
\(359\) | 20.0579 | 1.05862 | 0.529308 | − | 0.848430i | \(-0.322452\pi\) | ||||
0.529308 | + | 0.848430i | \(0.322452\pi\) | |||||||
\(360\) | −8.67468 | −0.457196 | ||||||||
\(361\) | −18.8837 | −0.993881 | ||||||||
\(362\) | −2.34922 | −0.123472 | ||||||||
\(363\) | 19.7704 | 1.03767 | ||||||||
\(364\) | 5.00681 | 0.262428 | ||||||||
\(365\) | −5.29074 | −0.276930 | ||||||||
\(366\) | −21.5599 | −1.12695 | ||||||||
\(367\) | −4.02946 | −0.210336 | −0.105168 | − | 0.994454i | \(-0.533538\pi\) | ||||
−0.105168 | + | 0.994454i | \(0.533538\pi\) | |||||||
\(368\) | −0.507155 | −0.0264373 | ||||||||
\(369\) | −13.1188 | −0.682938 | ||||||||
\(370\) | −2.05715 | −0.106946 | ||||||||
\(371\) | 8.20322 | 0.425890 | ||||||||
\(372\) | −6.14691 | −0.318703 | ||||||||
\(373\) | −10.2886 | −0.532725 | −0.266362 | − | 0.963873i | \(-0.585822\pi\) | ||||
−0.266362 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(374\) | 10.5600 | 0.546042 | ||||||||
\(375\) | −18.7260 | −0.967008 | ||||||||
\(376\) | 35.2690 | 1.81886 | ||||||||
\(377\) | −21.4712 | −1.10583 | ||||||||
\(378\) | −1.80068 | −0.0926168 | ||||||||
\(379\) | 15.1331 | 0.777335 | 0.388667 | − | 0.921378i | \(-0.372935\pi\) | ||||
0.388667 | + | 0.921378i | \(0.372935\pi\) | |||||||
\(380\) | −0.307906 | −0.0157953 | ||||||||
\(381\) | −15.8769 | −0.813399 | ||||||||
\(382\) | 7.62665 | 0.390213 | ||||||||
\(383\) | 15.1141 | 0.772292 | 0.386146 | − | 0.922438i | \(-0.373806\pi\) | ||||
0.386146 | + | 0.922438i | \(0.373806\pi\) | |||||||
\(384\) | −17.6027 | −0.898285 | ||||||||
\(385\) | 0.988846 | 0.0503962 | ||||||||
\(386\) | −1.94966 | −0.0992349 | ||||||||
\(387\) | 32.0657 | 1.62999 | ||||||||
\(388\) | −11.7741 | −0.597737 | ||||||||
\(389\) | −21.8318 | −1.10692 | −0.553459 | − | 0.832876i | \(-0.686693\pi\) | ||||
−0.553459 | + | 0.832876i | \(0.686693\pi\) | |||||||
\(390\) | −10.3444 | −0.523810 | ||||||||
\(391\) | −30.3516 | −1.53495 | ||||||||
\(392\) | −18.5497 | −0.936900 | ||||||||
\(393\) | 51.8882 | 2.61741 | ||||||||
\(394\) | 5.10206 | 0.257038 | ||||||||
\(395\) | 2.83761 | 0.142776 | ||||||||
\(396\) | −9.36191 | −0.470453 | ||||||||
\(397\) | 6.59713 | 0.331101 | 0.165550 | − | 0.986201i | \(-0.447060\pi\) | ||||
0.165550 | + | 0.986201i | \(0.447060\pi\) | |||||||
\(398\) | −0.0953294 | −0.00477843 | ||||||||
\(399\) | −0.637483 | −0.0319141 | ||||||||
\(400\) | 0.467602 | 0.0233801 | ||||||||
\(401\) | −3.00932 | −0.150278 | −0.0751391 | − | 0.997173i | \(-0.523940\pi\) | ||||
−0.0751391 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(402\) | −14.1696 | −0.706716 | ||||||||
\(403\) | −11.1983 | −0.557827 | ||||||||
\(404\) | 2.62616 | 0.130656 | ||||||||
\(405\) | 3.40124 | 0.169009 | ||||||||
\(406\) | −2.27645 | −0.112979 | ||||||||
\(407\) | −5.88242 | −0.291580 | ||||||||
\(408\) | 47.7728 | 2.36510 | ||||||||
\(409\) | −28.4495 | −1.40674 | −0.703370 | − | 0.710824i | \(-0.748322\pi\) | ||||
−0.703370 | + | 0.710824i | \(0.748322\pi\) | |||||||
\(410\) | −2.12265 | −0.104830 | ||||||||
\(411\) | 31.0272 | 1.53046 | ||||||||
\(412\) | −19.9592 | −0.983318 | ||||||||
\(413\) | −4.81504 | −0.236933 | ||||||||
\(414\) | −17.4793 | −0.859061 | ||||||||
\(415\) | 12.3504 | 0.606256 | ||||||||
\(416\) | −32.9736 | −1.61666 | ||||||||
\(417\) | 25.1408 | 1.23115 | ||||||||
\(418\) | 0.571938 | 0.0279744 | ||||||||
\(419\) | −17.2544 | −0.842930 | −0.421465 | − | 0.906845i | \(-0.638484\pi\) | ||||
−0.421465 | + | 0.906845i | \(0.638484\pi\) | |||||||
\(420\) | 1.68837 | 0.0823840 | ||||||||
\(421\) | −12.2245 | −0.595786 | −0.297893 | − | 0.954599i | \(-0.596284\pi\) | ||||
−0.297893 | + | 0.954599i | \(0.596284\pi\) | |||||||
\(422\) | 22.3398 | 1.08748 | ||||||||
\(423\) | 50.5397 | 2.45733 | ||||||||
\(424\) | −33.2953 | −1.61696 | ||||||||
\(425\) | 27.9845 | 1.35745 | ||||||||
\(426\) | −21.6762 | −1.05022 | ||||||||
\(427\) | 6.41066 | 0.310234 | ||||||||
\(428\) | 18.4575 | 0.892176 | ||||||||
\(429\) | −29.5798 | −1.42813 | ||||||||
\(430\) | 5.18829 | 0.250201 | ||||||||
\(431\) | 37.6535 | 1.81370 | 0.906852 | − | 0.421448i | \(-0.138478\pi\) | ||||
0.906852 | + | 0.421448i | \(0.138478\pi\) | |||||||
\(432\) | 0.303871 | 0.0146200 | ||||||||
\(433\) | −16.3693 | −0.786659 | −0.393329 | − | 0.919398i | \(-0.628677\pi\) | ||||
−0.393329 | + | 0.919398i | \(0.628677\pi\) | |||||||
\(434\) | −1.18728 | −0.0569914 | ||||||||
\(435\) | −7.24042 | −0.347152 | ||||||||
\(436\) | −16.2518 | −0.778322 | ||||||||
\(437\) | −1.64387 | −0.0786371 | ||||||||
\(438\) | 16.7797 | 0.801767 | ||||||||
\(439\) | 40.1000 | 1.91387 | 0.956935 | − | 0.290302i | \(-0.0937556\pi\) | ||||
0.956935 | + | 0.290302i | \(0.0937556\pi\) | |||||||
\(440\) | −4.01353 | −0.191338 | ||||||||
\(441\) | −26.5813 | −1.26577 | ||||||||
\(442\) | 32.8471 | 1.56238 | ||||||||
\(443\) | 22.2005 | 1.05478 | 0.527389 | − | 0.849624i | \(-0.323171\pi\) | ||||
0.527389 | + | 0.849624i | \(0.323171\pi\) | |||||||
\(444\) | −10.0437 | −0.476654 | ||||||||
\(445\) | 1.44763 | 0.0686243 | ||||||||
\(446\) | −17.5103 | −0.829137 | ||||||||
\(447\) | 33.9029 | 1.60355 | ||||||||
\(448\) | −3.64375 | −0.172151 | ||||||||
\(449\) | −31.0197 | −1.46391 | −0.731955 | − | 0.681353i | \(-0.761392\pi\) | ||||
−0.731955 | + | 0.681353i | \(0.761392\pi\) | |||||||
\(450\) | 16.1161 | 0.759721 | ||||||||
\(451\) | −6.06971 | −0.285811 | ||||||||
\(452\) | 9.92089 | 0.466639 | ||||||||
\(453\) | 29.6489 | 1.39303 | ||||||||
\(454\) | 9.74553 | 0.457380 | ||||||||
\(455\) | 3.07583 | 0.144197 | ||||||||
\(456\) | 2.58742 | 0.121167 | ||||||||
\(457\) | 36.3469 | 1.70024 | 0.850118 | − | 0.526593i | \(-0.176531\pi\) | ||||
0.850118 | + | 0.526593i | \(0.176531\pi\) | |||||||
\(458\) | 14.8139 | 0.692208 | ||||||||
\(459\) | 18.1857 | 0.848838 | ||||||||
\(460\) | 4.35379 | 0.202997 | ||||||||
\(461\) | 6.97833 | 0.325013 | 0.162507 | − | 0.986707i | \(-0.448042\pi\) | ||||
0.162507 | + | 0.986707i | \(0.448042\pi\) | |||||||
\(462\) | −3.13616 | −0.145907 | ||||||||
\(463\) | −6.18167 | −0.287287 | −0.143643 | − | 0.989630i | \(-0.545882\pi\) | ||||
−0.143643 | + | 0.989630i | \(0.545882\pi\) | |||||||
\(464\) | 0.384161 | 0.0178342 | ||||||||
\(465\) | −3.77623 | −0.175119 | ||||||||
\(466\) | −5.56863 | −0.257962 | ||||||||
\(467\) | −14.4609 | −0.669171 | −0.334585 | − | 0.942365i | \(-0.608596\pi\) | ||||
−0.334585 | + | 0.942365i | \(0.608596\pi\) | |||||||
\(468\) | −29.1205 | −1.34610 | ||||||||
\(469\) | 4.21322 | 0.194549 | ||||||||
\(470\) | 8.17742 | 0.377196 | ||||||||
\(471\) | −38.6491 | −1.78086 | ||||||||
\(472\) | 19.5433 | 0.899554 | ||||||||
\(473\) | 14.8359 | 0.682155 | ||||||||
\(474\) | −8.99957 | −0.413364 | ||||||||
\(475\) | 1.51567 | 0.0695436 | ||||||||
\(476\) | −5.36115 | −0.245728 | ||||||||
\(477\) | −47.7114 | −2.18455 | ||||||||
\(478\) | 13.0779 | 0.598169 | ||||||||
\(479\) | −28.0812 | −1.28306 | −0.641531 | − | 0.767097i | \(-0.721701\pi\) | ||||
−0.641531 | + | 0.767097i | \(0.721701\pi\) | |||||||
\(480\) | −11.1192 | −0.507519 | ||||||||
\(481\) | −18.2974 | −0.834291 | ||||||||
\(482\) | −12.4674 | −0.567874 | ||||||||
\(483\) | 9.01400 | 0.410151 | ||||||||
\(484\) | 9.00514 | 0.409325 | ||||||||
\(485\) | −7.23316 | −0.328441 | ||||||||
\(486\) | −18.4780 | −0.838180 | ||||||||
\(487\) | −1.25353 | −0.0568031 | −0.0284015 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284015 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(488\) | −26.0196 | −1.17785 | ||||||||
\(489\) | 18.6012 | 0.841176 | ||||||||
\(490\) | −4.30090 | −0.194295 | ||||||||
\(491\) | 27.8138 | 1.25522 | 0.627610 | − | 0.778528i | \(-0.284033\pi\) | ||||
0.627610 | + | 0.778528i | \(0.284033\pi\) | |||||||
\(492\) | −10.3635 | −0.467223 | ||||||||
\(493\) | 22.9908 | 1.03545 | ||||||||
\(494\) | 1.77903 | 0.0800423 | ||||||||
\(495\) | −5.75130 | −0.258502 | ||||||||
\(496\) | 0.200359 | 0.00899637 | ||||||||
\(497\) | 6.44526 | 0.289110 | ||||||||
\(498\) | −39.1696 | −1.75523 | ||||||||
\(499\) | 15.5317 | 0.695294 | 0.347647 | − | 0.937626i | \(-0.386981\pi\) | ||||
0.347647 | + | 0.937626i | \(0.386981\pi\) | |||||||
\(500\) | −8.52946 | −0.381449 | ||||||||
\(501\) | 20.0403 | 0.895334 | ||||||||
\(502\) | −8.82271 | −0.393777 | ||||||||
\(503\) | 5.79797 | 0.258519 | 0.129259 | − | 0.991611i | \(-0.458740\pi\) | ||||
0.129259 | + | 0.991611i | \(0.458740\pi\) | |||||||
\(504\) | −8.18049 | −0.364388 | ||||||||
\(505\) | 1.61333 | 0.0717922 | ||||||||
\(506\) | −8.08719 | −0.359519 | ||||||||
\(507\) | −57.4054 | −2.54946 | ||||||||
\(508\) | −7.23173 | −0.320856 | ||||||||
\(509\) | 27.8607 | 1.23491 | 0.617453 | − | 0.786608i | \(-0.288165\pi\) | ||||
0.617453 | + | 0.786608i | \(0.288165\pi\) | |||||||
\(510\) | 11.0765 | 0.490476 | ||||||||
\(511\) | −4.98933 | −0.220715 | ||||||||
\(512\) | 1.18974 | 0.0525795 | ||||||||
\(513\) | 0.984957 | 0.0434869 | ||||||||
\(514\) | 26.2738 | 1.15889 | ||||||||
\(515\) | −12.2615 | −0.540307 | ||||||||
\(516\) | 25.3310 | 1.11514 | ||||||||
\(517\) | 23.3833 | 1.02840 | ||||||||
\(518\) | −1.93996 | −0.0852368 | ||||||||
\(519\) | 16.0540 | 0.704691 | ||||||||
\(520\) | −12.4842 | −0.547469 | ||||||||
\(521\) | 43.8886 | 1.92279 | 0.961397 | − | 0.275165i | \(-0.0887325\pi\) | ||||
0.961397 | + | 0.275165i | \(0.0887325\pi\) | |||||||
\(522\) | 13.2403 | 0.579511 | ||||||||
\(523\) | 34.5381 | 1.51025 | 0.755123 | − | 0.655583i | \(-0.227577\pi\) | ||||
0.755123 | + | 0.655583i | \(0.227577\pi\) | |||||||
\(524\) | 23.6344 | 1.03247 | ||||||||
\(525\) | −8.31100 | −0.362722 | ||||||||
\(526\) | −1.20071 | −0.0523533 | ||||||||
\(527\) | 11.9908 | 0.522329 | ||||||||
\(528\) | 0.529239 | 0.0230322 | ||||||||
\(529\) | 0.244341 | 0.0106235 | ||||||||
\(530\) | −7.71979 | −0.335326 | ||||||||
\(531\) | 28.0051 | 1.21532 | ||||||||
\(532\) | −0.290365 | −0.0125889 | ||||||||
\(533\) | −18.8800 | −0.817784 | ||||||||
\(534\) | −4.59121 | −0.198681 | ||||||||
\(535\) | 11.3390 | 0.490227 | ||||||||
\(536\) | −17.1007 | −0.738636 | ||||||||
\(537\) | −32.6195 | −1.40763 | ||||||||
\(538\) | 9.78013 | 0.421651 | ||||||||
\(539\) | −12.2984 | −0.529730 | ||||||||
\(540\) | −2.60865 | −0.112259 | ||||||||
\(541\) | −18.2238 | −0.783501 | −0.391751 | − | 0.920071i | \(-0.628130\pi\) | ||||
−0.391751 | + | 0.920071i | \(0.628130\pi\) | |||||||
\(542\) | −16.8088 | −0.722000 | ||||||||
\(543\) | −7.04618 | −0.302381 | ||||||||
\(544\) | 35.3072 | 1.51378 | ||||||||
\(545\) | −9.98399 | −0.427667 | ||||||||
\(546\) | −9.75511 | −0.417480 | ||||||||
\(547\) | −45.4436 | −1.94303 | −0.971514 | − | 0.236982i | \(-0.923842\pi\) | ||||
−0.971514 | + | 0.236982i | \(0.923842\pi\) | |||||||
\(548\) | 14.1325 | 0.603710 | ||||||||
\(549\) | −37.2855 | −1.59131 | ||||||||
\(550\) | 7.45647 | 0.317945 | ||||||||
\(551\) | 1.24520 | 0.0530475 | ||||||||
\(552\) | −36.5861 | −1.55721 | ||||||||
\(553\) | 2.67595 | 0.113793 | ||||||||
\(554\) | 10.2492 | 0.435446 | ||||||||
\(555\) | −6.17016 | −0.261909 | ||||||||
\(556\) | 11.4513 | 0.485643 | ||||||||
\(557\) | 30.7625 | 1.30345 | 0.651725 | − | 0.758455i | \(-0.274046\pi\) | ||||
0.651725 | + | 0.758455i | \(0.274046\pi\) | |||||||
\(558\) | 6.90544 | 0.292331 | ||||||||
\(559\) | 46.1475 | 1.95183 | ||||||||
\(560\) | −0.0550324 | −0.00232554 | ||||||||
\(561\) | 31.6733 | 1.33725 | ||||||||
\(562\) | −0.490881 | −0.0207066 | ||||||||
\(563\) | −38.5265 | −1.62370 | −0.811849 | − | 0.583867i | \(-0.801539\pi\) | ||||
−0.811849 | + | 0.583867i | \(0.801539\pi\) | |||||||
\(564\) | 39.9250 | 1.68115 | ||||||||
\(565\) | 6.09470 | 0.256406 | ||||||||
\(566\) | 23.5982 | 0.991906 | ||||||||
\(567\) | 3.20747 | 0.134701 | ||||||||
\(568\) | −26.1601 | −1.09765 | ||||||||
\(569\) | −38.2664 | −1.60421 | −0.802105 | − | 0.597183i | \(-0.796287\pi\) | ||||
−0.802105 | + | 0.597183i | \(0.796287\pi\) | |||||||
\(570\) | 0.599915 | 0.0251277 | ||||||||
\(571\) | −4.57864 | −0.191610 | −0.0958051 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958051 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(572\) | −13.4732 | −0.563344 | ||||||||
\(573\) | 22.8752 | 0.955624 | ||||||||
\(574\) | −2.00172 | −0.0835503 | ||||||||
\(575\) | −21.4315 | −0.893757 | ||||||||
\(576\) | 21.1927 | 0.883028 | ||||||||
\(577\) | 40.3948 | 1.68166 | 0.840828 | − | 0.541302i | \(-0.182068\pi\) | ||||
0.840828 | + | 0.541302i | \(0.182068\pi\) | |||||||
\(578\) | −20.0849 | −0.835424 | ||||||||
\(579\) | −5.84775 | −0.243024 | ||||||||
\(580\) | −3.29792 | −0.136939 | ||||||||
\(581\) | 11.6468 | 0.483190 | ||||||||
\(582\) | 22.9402 | 0.950902 | ||||||||
\(583\) | −22.0747 | −0.914242 | ||||||||
\(584\) | 20.2507 | 0.837980 | ||||||||
\(585\) | −17.8896 | −0.739644 | ||||||||
\(586\) | −9.59714 | −0.396454 | ||||||||
\(587\) | 7.39675 | 0.305296 | 0.152648 | − | 0.988281i | \(-0.451220\pi\) | ||||
0.152648 | + | 0.988281i | \(0.451220\pi\) | |||||||
\(588\) | −20.9985 | −0.865963 | ||||||||
\(589\) | 0.649435 | 0.0267595 | ||||||||
\(590\) | 4.53128 | 0.186550 | ||||||||
\(591\) | 15.3030 | 0.629481 | ||||||||
\(592\) | 0.327375 | 0.0134550 | ||||||||
\(593\) | −1.30863 | −0.0537390 | −0.0268695 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268695 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(594\) | 4.84559 | 0.198817 | ||||||||
\(595\) | −3.29352 | −0.135021 | ||||||||
\(596\) | 15.4423 | 0.632542 | ||||||||
\(597\) | −0.285929 | −0.0117023 | ||||||||
\(598\) | −25.1554 | −1.02868 | ||||||||
\(599\) | 27.8919 | 1.13963 | 0.569816 | − | 0.821773i | \(-0.307015\pi\) | ||||
0.569816 | + | 0.821773i | \(0.307015\pi\) | |||||||
\(600\) | 33.7327 | 1.37713 | ||||||||
\(601\) | −12.3512 | −0.503817 | −0.251908 | − | 0.967751i | \(-0.581058\pi\) | ||||
−0.251908 | + | 0.967751i | \(0.581058\pi\) | |||||||
\(602\) | 4.89271 | 0.199412 | ||||||||
\(603\) | −24.5048 | −0.997914 | ||||||||
\(604\) | 13.5047 | 0.549498 | ||||||||
\(605\) | 5.53213 | 0.224913 | ||||||||
\(606\) | −5.11673 | −0.207853 | ||||||||
\(607\) | 37.5057 | 1.52231 | 0.761154 | − | 0.648571i | \(-0.224633\pi\) | ||||
0.761154 | + | 0.648571i | \(0.224633\pi\) | |||||||
\(608\) | 1.91227 | 0.0775529 | ||||||||
\(609\) | −6.82794 | −0.276682 | ||||||||
\(610\) | −6.03287 | −0.244264 | ||||||||
\(611\) | 72.7345 | 2.94252 | ||||||||
\(612\) | 31.1814 | 1.26043 | ||||||||
\(613\) | 38.7247 | 1.56407 | 0.782037 | − | 0.623232i | \(-0.214181\pi\) | ||||
0.782037 | + | 0.623232i | \(0.214181\pi\) | |||||||
\(614\) | −3.67753 | −0.148413 | ||||||||
\(615\) | −6.36661 | −0.256727 | ||||||||
\(616\) | −3.78488 | −0.152497 | ||||||||
\(617\) | −1.44876 | −0.0583247 | −0.0291623 | − | 0.999575i | \(-0.509284\pi\) | ||||
−0.0291623 | + | 0.999575i | \(0.509284\pi\) | |||||||
\(618\) | 38.8878 | 1.56430 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | −1.72003 | −0.0690779 | ||||||||
\(621\) | −13.9273 | −0.558882 | ||||||||
\(622\) | 15.3419 | 0.615153 | ||||||||
\(623\) | 1.36516 | 0.0546940 | ||||||||
\(624\) | 1.64621 | 0.0659013 | ||||||||
\(625\) | 16.9863 | 0.679450 | ||||||||
\(626\) | 1.51480 | 0.0605434 | ||||||||
\(627\) | 1.71545 | 0.0685087 | ||||||||
\(628\) | −17.6042 | −0.702483 | ||||||||
\(629\) | 19.5924 | 0.781199 | ||||||||
\(630\) | −1.89672 | −0.0755670 | ||||||||
\(631\) | −3.22709 | −0.128469 | −0.0642343 | − | 0.997935i | \(-0.520460\pi\) | ||||
−0.0642343 | + | 0.997935i | \(0.520460\pi\) | |||||||
\(632\) | −10.8612 | −0.432034 | ||||||||
\(633\) | 67.0053 | 2.66322 | ||||||||
\(634\) | −4.78767 | −0.190143 | ||||||||
\(635\) | −4.44267 | −0.176302 | ||||||||
\(636\) | −37.6907 | −1.49453 | ||||||||
\(637\) | −38.2546 | −1.51570 | ||||||||
\(638\) | 6.12590 | 0.242527 | ||||||||
\(639\) | −37.4868 | −1.48295 | ||||||||
\(640\) | −4.92558 | −0.194701 | ||||||||
\(641\) | 33.9282 | 1.34008 | 0.670042 | − | 0.742323i | \(-0.266276\pi\) | ||||
0.670042 | + | 0.742323i | \(0.266276\pi\) | |||||||
\(642\) | −35.9620 | −1.41931 | ||||||||
\(643\) | −1.59209 | −0.0627860 | −0.0313930 | − | 0.999507i | \(-0.509994\pi\) | ||||
−0.0313930 | + | 0.999507i | \(0.509994\pi\) | |||||||
\(644\) | 4.10576 | 0.161790 | ||||||||
\(645\) | 15.5616 | 0.612738 | ||||||||
\(646\) | −1.90493 | −0.0749486 | ||||||||
\(647\) | −0.934541 | −0.0367406 | −0.0183703 | − | 0.999831i | \(-0.505848\pi\) | ||||
−0.0183703 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(648\) | −13.0185 | −0.511415 | ||||||||
\(649\) | 12.9572 | 0.508614 | ||||||||
\(650\) | 23.1936 | 0.909727 | ||||||||
\(651\) | −3.56110 | −0.139571 | ||||||||
\(652\) | 8.47261 | 0.331813 | ||||||||
\(653\) | −25.8591 | −1.01195 | −0.505973 | − | 0.862549i | \(-0.668866\pi\) | ||||
−0.505973 | + | 0.862549i | \(0.668866\pi\) | |||||||
\(654\) | 31.6646 | 1.23818 | ||||||||
\(655\) | 14.5193 | 0.567317 | ||||||||
\(656\) | 0.337798 | 0.0131888 | ||||||||
\(657\) | 29.0188 | 1.13213 | ||||||||
\(658\) | 7.71156 | 0.300628 | ||||||||
\(659\) | −3.49910 | −0.136306 | −0.0681528 | − | 0.997675i | \(-0.521711\pi\) | ||||
−0.0681528 | + | 0.997675i | \(0.521711\pi\) | |||||||
\(660\) | −4.54337 | −0.176851 | ||||||||
\(661\) | 31.4489 | 1.22322 | 0.611611 | − | 0.791159i | \(-0.290522\pi\) | ||||
0.611611 | + | 0.791159i | \(0.290522\pi\) | |||||||
\(662\) | 22.5300 | 0.875654 | ||||||||
\(663\) | 98.5206 | 3.82622 | ||||||||
\(664\) | −47.2721 | −1.83451 | ||||||||
\(665\) | −0.178380 | −0.00691728 | ||||||||
\(666\) | 11.2831 | 0.437212 | ||||||||
\(667\) | −17.6072 | −0.681752 | ||||||||
\(668\) | 9.12808 | 0.353176 | ||||||||
\(669\) | −52.5199 | −2.03054 | ||||||||
\(670\) | −3.96493 | −0.153179 | ||||||||
\(671\) | −17.2510 | −0.665966 | ||||||||
\(672\) | −10.4857 | −0.404496 | ||||||||
\(673\) | −7.73543 | −0.298179 | −0.149089 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149089 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(674\) | −14.5044 | −0.558690 | ||||||||
\(675\) | 12.8411 | 0.494254 | ||||||||
\(676\) | −26.1474 | −1.00567 | ||||||||
\(677\) | −27.4352 | −1.05442 | −0.527210 | − | 0.849735i | \(-0.676762\pi\) | ||||
−0.527210 | + | 0.849735i | \(0.676762\pi\) | |||||||
\(678\) | −19.3295 | −0.742347 | ||||||||
\(679\) | −6.82109 | −0.261769 | ||||||||
\(680\) | 13.3677 | 0.512629 | ||||||||
\(681\) | 29.2305 | 1.12011 | ||||||||
\(682\) | 3.19496 | 0.122341 | ||||||||
\(683\) | −13.9103 | −0.532261 | −0.266131 | − | 0.963937i | \(-0.585745\pi\) | ||||
−0.266131 | + | 0.963937i | \(0.585745\pi\) | |||||||
\(684\) | 1.68881 | 0.0645734 | ||||||||
\(685\) | 8.68202 | 0.331723 | ||||||||
\(686\) | −8.41929 | −0.321450 | ||||||||
\(687\) | 44.4324 | 1.69520 | ||||||||
\(688\) | −0.825665 | −0.0314782 | ||||||||
\(689\) | −68.6641 | −2.61589 | ||||||||
\(690\) | −8.48279 | −0.322934 | ||||||||
\(691\) | 3.45766 | 0.131536 | 0.0657678 | − | 0.997835i | \(-0.479050\pi\) | ||||
0.0657678 | + | 0.997835i | \(0.479050\pi\) | |||||||
\(692\) | 7.31237 | 0.277975 | ||||||||
\(693\) | −5.42365 | −0.206028 | ||||||||
\(694\) | −19.1217 | −0.725848 | ||||||||
\(695\) | 7.03488 | 0.266848 | ||||||||
\(696\) | 27.7133 | 1.05047 | ||||||||
\(697\) | 20.2162 | 0.765742 | ||||||||
\(698\) | 3.52476 | 0.133414 | ||||||||
\(699\) | −16.7024 | −0.631743 | ||||||||
\(700\) | −3.78555 | −0.143080 | ||||||||
\(701\) | −5.79713 | −0.218955 | −0.109477 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109477 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(702\) | 15.0724 | 0.568869 | ||||||||
\(703\) | 1.06114 | 0.0400217 | ||||||||
\(704\) | 9.80526 | 0.369550 | ||||||||
\(705\) | 24.5272 | 0.923746 | ||||||||
\(706\) | −10.2736 | −0.386652 | ||||||||
\(707\) | 1.52142 | 0.0572189 | ||||||||
\(708\) | 22.1233 | 0.831445 | ||||||||
\(709\) | −30.0393 | −1.12815 | −0.564075 | − | 0.825724i | \(-0.690767\pi\) | ||||
−0.564075 | + | 0.825724i | \(0.690767\pi\) | |||||||
\(710\) | −6.06543 | −0.227632 | ||||||||
\(711\) | −15.5638 | −0.583688 | ||||||||
\(712\) | −5.54092 | −0.207655 | ||||||||
\(713\) | −9.18300 | −0.343906 | ||||||||
\(714\) | 10.4455 | 0.390913 | ||||||||
\(715\) | −8.27701 | −0.309543 | ||||||||
\(716\) | −14.8577 | −0.555260 | ||||||||
\(717\) | 39.2255 | 1.46490 | ||||||||
\(718\) | −17.8005 | −0.664310 | ||||||||
\(719\) | 1.18923 | 0.0443507 | 0.0221754 | − | 0.999754i | \(-0.492941\pi\) | ||||
0.0221754 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(720\) | 0.320078 | 0.0119286 | ||||||||
\(721\) | −11.5630 | −0.430628 | ||||||||
\(722\) | 16.7585 | 0.623687 | ||||||||
\(723\) | −37.3944 | −1.39071 | ||||||||
\(724\) | −3.20944 | −0.119278 | ||||||||
\(725\) | 16.2340 | 0.602915 | ||||||||
\(726\) | −17.5453 | −0.651168 | ||||||||
\(727\) | −10.3813 | −0.385021 | −0.192511 | − | 0.981295i | \(-0.561663\pi\) | ||||
−0.192511 | + | 0.981295i | \(0.561663\pi\) | |||||||
\(728\) | −11.7730 | −0.436336 | ||||||||
\(729\) | −41.7230 | −1.54530 | ||||||||
\(730\) | 4.69530 | 0.173781 | ||||||||
\(731\) | −49.4134 | −1.82762 | ||||||||
\(732\) | −29.4546 | −1.08867 | ||||||||
\(733\) | −8.96405 | −0.331095 | −0.165547 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165547 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(734\) | 3.57597 | 0.131991 | ||||||||
\(735\) | −12.9000 | −0.475824 | ||||||||
\(736\) | −27.0395 | −0.996689 | ||||||||
\(737\) | −11.3377 | −0.417630 | ||||||||
\(738\) | 11.6424 | 0.428561 | ||||||||
\(739\) | −16.7451 | −0.615979 | −0.307989 | − | 0.951390i | \(-0.599656\pi\) | ||||
−0.307989 | + | 0.951390i | \(0.599656\pi\) | |||||||
\(740\) | −2.81043 | −0.103313 | ||||||||
\(741\) | 5.33597 | 0.196022 | ||||||||
\(742\) | −7.28000 | −0.267257 | ||||||||
\(743\) | −25.6229 | −0.940011 | −0.470006 | − | 0.882663i | \(-0.655748\pi\) | ||||
−0.470006 | + | 0.882663i | \(0.655748\pi\) | |||||||
\(744\) | 14.4538 | 0.529903 | ||||||||
\(745\) | 9.48669 | 0.347565 | ||||||||
\(746\) | 9.13071 | 0.334299 | ||||||||
\(747\) | −67.7398 | −2.47847 | ||||||||
\(748\) | 14.4268 | 0.527495 | ||||||||
\(749\) | 10.6930 | 0.390714 | ||||||||
\(750\) | 16.6185 | 0.606823 | ||||||||
\(751\) | −36.6073 | −1.33582 | −0.667910 | − | 0.744242i | \(-0.732811\pi\) | ||||
−0.667910 | + | 0.744242i | \(0.732811\pi\) | |||||||
\(752\) | −1.30136 | −0.0474556 | ||||||||
\(753\) | −26.4626 | −0.964351 | ||||||||
\(754\) | 19.0548 | 0.693935 | ||||||||
\(755\) | 8.29634 | 0.301935 | ||||||||
\(756\) | −2.46004 | −0.0894708 | ||||||||
\(757\) | 5.69461 | 0.206974 | 0.103487 | − | 0.994631i | \(-0.467000\pi\) | ||||
0.103487 | + | 0.994631i | \(0.467000\pi\) | |||||||
\(758\) | −13.4300 | −0.487798 | ||||||||
\(759\) | −24.2565 | −0.880455 | ||||||||
\(760\) | 0.724010 | 0.0262626 | ||||||||
\(761\) | 22.4126 | 0.812457 | 0.406228 | − | 0.913772i | \(-0.366844\pi\) | ||||
0.406228 | + | 0.913772i | \(0.366844\pi\) | |||||||
\(762\) | 14.0901 | 0.510429 | ||||||||
\(763\) | −9.41521 | −0.340853 | ||||||||
\(764\) | 10.4193 | 0.376959 | ||||||||
\(765\) | 19.1557 | 0.692575 | ||||||||
\(766\) | −13.4131 | −0.484634 | ||||||||
\(767\) | 40.3037 | 1.45528 | ||||||||
\(768\) | 43.2385 | 1.56024 | ||||||||
\(769\) | 15.8950 | 0.573187 | 0.286594 | − | 0.958052i | \(-0.407477\pi\) | ||||
0.286594 | + | 0.958052i | \(0.407477\pi\) | |||||||
\(770\) | −0.877557 | −0.0316250 | ||||||||
\(771\) | 78.8048 | 2.83809 | ||||||||
\(772\) | −2.66357 | −0.0958641 | ||||||||
\(773\) | −53.8368 | −1.93637 | −0.968187 | − | 0.250228i | \(-0.919494\pi\) | ||||
−0.968187 | + | 0.250228i | \(0.919494\pi\) | |||||||
\(774\) | −28.4569 | −1.02286 | ||||||||
\(775\) | 8.46682 | 0.304137 | ||||||||
\(776\) | 27.6855 | 0.993851 | ||||||||
\(777\) | −5.81865 | −0.208743 | ||||||||
\(778\) | 19.3748 | 0.694620 | ||||||||
\(779\) | 1.09493 | 0.0392298 | ||||||||
\(780\) | −14.1323 | −0.506018 | ||||||||
\(781\) | −17.3441 | −0.620620 | ||||||||
\(782\) | 26.9357 | 0.963220 | ||||||||
\(783\) | 10.5497 | 0.377014 | ||||||||
\(784\) | 0.684446 | 0.0244445 | ||||||||
\(785\) | −10.8148 | −0.385996 | ||||||||
\(786\) | −46.0485 | −1.64250 | ||||||||
\(787\) | −24.9789 | −0.890401 | −0.445200 | − | 0.895431i | \(-0.646868\pi\) | ||||
−0.445200 | + | 0.895431i | \(0.646868\pi\) | |||||||
\(788\) | 6.97032 | 0.248307 | ||||||||
\(789\) | −3.60137 | −0.128212 | ||||||||
\(790\) | −2.51825 | −0.0895954 | ||||||||
\(791\) | 5.74749 | 0.204357 | ||||||||
\(792\) | 22.0136 | 0.782218 | ||||||||
\(793\) | −53.6597 | −1.90551 | ||||||||
\(794\) | −5.85467 | −0.207774 | ||||||||
\(795\) | −23.1546 | −0.821207 | ||||||||
\(796\) | −0.130237 | −0.00461612 | ||||||||
\(797\) | −44.5255 | −1.57717 | −0.788587 | − | 0.614923i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614923i | \(0.789187\pi\) | |||||||
\(798\) | 0.565738 | 0.0200269 | ||||||||
\(799\) | −77.8821 | −2.75527 | ||||||||
\(800\) | 24.9307 | 0.881434 | ||||||||
\(801\) | −7.94001 | −0.280547 | ||||||||
\(802\) | 2.67064 | 0.0943035 | ||||||||
\(803\) | 13.4262 | 0.473800 | ||||||||
\(804\) | −19.3582 | −0.682710 | ||||||||
\(805\) | 2.52229 | 0.0888991 | ||||||||
\(806\) | 9.93801 | 0.350051 | ||||||||
\(807\) | 29.3343 | 1.03262 | ||||||||
\(808\) | −6.17515 | −0.217241 | ||||||||
\(809\) | −14.4853 | −0.509276 | −0.254638 | − | 0.967037i | \(-0.581956\pi\) | ||||
−0.254638 | + | 0.967037i | \(0.581956\pi\) | |||||||
\(810\) | −3.01845 | −0.106057 | ||||||||
\(811\) | 47.9375 | 1.68331 | 0.841657 | − | 0.540012i | \(-0.181580\pi\) | ||||
0.841657 | + | 0.540012i | \(0.181580\pi\) | |||||||
\(812\) | −3.11004 | −0.109141 | ||||||||
\(813\) | −50.4159 | −1.76816 | ||||||||
\(814\) | 5.22039 | 0.182974 | ||||||||
\(815\) | 5.20498 | 0.182322 | ||||||||
\(816\) | −1.76272 | −0.0617075 | ||||||||
\(817\) | −2.67628 | −0.0936311 | ||||||||
\(818\) | 25.2477 | 0.882766 | ||||||||
\(819\) | −16.8704 | −0.589501 | ||||||||
\(820\) | −2.89991 | −0.101269 | ||||||||
\(821\) | 25.2123 | 0.879916 | 0.439958 | − | 0.898018i | \(-0.354993\pi\) | ||||
0.439958 | + | 0.898018i | \(0.354993\pi\) | |||||||
\(822\) | −27.5353 | −0.960404 | ||||||||
\(823\) | −18.1629 | −0.633117 | −0.316559 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316559 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(824\) | 46.9319 | 1.63495 | ||||||||
\(825\) | 22.3648 | 0.778641 | ||||||||
\(826\) | 4.27314 | 0.148681 | ||||||||
\(827\) | −24.1281 | −0.839015 | −0.419508 | − | 0.907752i | \(-0.637797\pi\) | ||||
−0.419508 | + | 0.907752i | \(0.637797\pi\) | |||||||
\(828\) | −23.8798 | −0.829881 | ||||||||
\(829\) | −30.8815 | −1.07256 | −0.536280 | − | 0.844040i | \(-0.680171\pi\) | ||||
−0.536280 | + | 0.844040i | \(0.680171\pi\) | |||||||
\(830\) | −10.9604 | −0.380442 | ||||||||
\(831\) | 30.7411 | 1.06640 | ||||||||
\(832\) | 30.4995 | 1.05738 | ||||||||
\(833\) | 40.9619 | 1.41925 | ||||||||
\(834\) | −22.3113 | −0.772579 | ||||||||
\(835\) | 5.60766 | 0.194061 | ||||||||
\(836\) | 0.781367 | 0.0270242 | ||||||||
\(837\) | 5.50217 | 0.190183 | ||||||||
\(838\) | 15.3125 | 0.528961 | ||||||||
\(839\) | 6.41671 | 0.221529 | 0.110765 | − | 0.993847i | \(-0.464670\pi\) | ||||
0.110765 | + | 0.993847i | \(0.464670\pi\) | |||||||
\(840\) | −3.97003 | −0.136979 | ||||||||
\(841\) | −15.6629 | −0.540100 | ||||||||
\(842\) | 10.8487 | 0.373871 | ||||||||
\(843\) | −1.47234 | −0.0507100 | ||||||||
\(844\) | 30.5200 | 1.05054 | ||||||||
\(845\) | −16.0631 | −0.552589 | ||||||||
\(846\) | −44.8518 | −1.54204 | ||||||||
\(847\) | 5.21697 | 0.179257 | ||||||||
\(848\) | 1.22853 | 0.0421879 | ||||||||
\(849\) | 70.7798 | 2.42916 | ||||||||
\(850\) | −24.8350 | −0.851835 | ||||||||
\(851\) | −15.0045 | −0.514349 | ||||||||
\(852\) | −29.6136 | −1.01454 | ||||||||
\(853\) | −10.6345 | −0.364119 | −0.182060 | − | 0.983288i | \(-0.558276\pi\) | ||||
−0.182060 | + | 0.983288i | \(0.558276\pi\) | |||||||
\(854\) | −5.68918 | −0.194680 | ||||||||
\(855\) | 1.03749 | 0.0354814 | ||||||||
\(856\) | −43.4008 | −1.48341 | ||||||||
\(857\) | 4.45614 | 0.152219 | 0.0761095 | − | 0.997099i | \(-0.475750\pi\) | ||||
0.0761095 | + | 0.997099i | \(0.475750\pi\) | |||||||
\(858\) | 26.2508 | 0.896188 | ||||||||
\(859\) | 5.10952 | 0.174335 | 0.0871673 | − | 0.996194i | \(-0.472219\pi\) | ||||
0.0871673 | + | 0.996194i | \(0.472219\pi\) | |||||||
\(860\) | 7.08811 | 0.241703 | ||||||||
\(861\) | −6.00391 | −0.204613 | ||||||||
\(862\) | −33.4158 | −1.13815 | ||||||||
\(863\) | −17.1442 | −0.583597 | −0.291798 | − | 0.956480i | \(-0.594254\pi\) | ||||
−0.291798 | + | 0.956480i | \(0.594254\pi\) | |||||||
\(864\) | 16.2012 | 0.551177 | ||||||||
\(865\) | 4.49221 | 0.152740 | ||||||||
\(866\) | 14.5270 | 0.493649 | ||||||||
\(867\) | −60.2423 | −2.04593 | ||||||||
\(868\) | −1.62204 | −0.0550555 | ||||||||
\(869\) | −7.20094 | −0.244275 | ||||||||
\(870\) | 6.42556 | 0.217847 | ||||||||
\(871\) | −35.2663 | −1.19495 | ||||||||
\(872\) | 38.2145 | 1.29411 | ||||||||
\(873\) | 39.6727 | 1.34272 | ||||||||
\(874\) | 1.45887 | 0.0493469 | ||||||||
\(875\) | −4.94139 | −0.167049 | ||||||||
\(876\) | 22.9241 | 0.774533 | ||||||||
\(877\) | −39.8771 | −1.34655 | −0.673277 | − | 0.739391i | \(-0.735114\pi\) | ||||
−0.673277 | + | 0.739391i | \(0.735114\pi\) | |||||||
\(878\) | −35.5870 | −1.20100 | ||||||||
\(879\) | −28.7854 | −0.970907 | ||||||||
\(880\) | 0.148091 | 0.00499216 | ||||||||
\(881\) | −6.42351 | −0.216413 | −0.108207 | − | 0.994128i | \(-0.534511\pi\) | ||||
−0.108207 | + | 0.994128i | \(0.534511\pi\) | |||||||
\(882\) | 23.5897 | 0.794307 | ||||||||
\(883\) | 40.3184 | 1.35682 | 0.678410 | − | 0.734683i | \(-0.262669\pi\) | ||||
0.678410 | + | 0.734683i | \(0.262669\pi\) | |||||||
\(884\) | 44.8749 | 1.50931 | ||||||||
\(885\) | 13.5910 | 0.456857 | ||||||||
\(886\) | −19.7020 | −0.661900 | ||||||||
\(887\) | −19.3059 | −0.648230 | −0.324115 | − | 0.946018i | \(-0.605066\pi\) | ||||
−0.324115 | + | 0.946018i | \(0.605066\pi\) | |||||||
\(888\) | 23.6168 | 0.792527 | ||||||||
\(889\) | −4.18957 | −0.140514 | ||||||||
\(890\) | −1.28471 | −0.0430635 | ||||||||
\(891\) | −8.63124 | −0.289158 | ||||||||
\(892\) | −23.9221 | −0.800973 | ||||||||
\(893\) | −4.21817 | −0.141156 | ||||||||
\(894\) | −30.0873 | −1.00627 | ||||||||
\(895\) | −9.12756 | −0.305101 | ||||||||
\(896\) | −4.64497 | −0.155178 | ||||||||
\(897\) | −75.4506 | −2.51922 | ||||||||
\(898\) | 27.5286 | 0.918642 | ||||||||
\(899\) | 6.95596 | 0.231994 | ||||||||
\(900\) | 22.0174 | 0.733915 | ||||||||
\(901\) | 73.5236 | 2.44943 | ||||||||
\(902\) | 5.38660 | 0.179354 | ||||||||
\(903\) | 14.6751 | 0.488356 | ||||||||
\(904\) | −23.3279 | −0.775876 | ||||||||
\(905\) | −1.97166 | −0.0655401 | ||||||||
\(906\) | −26.3121 | −0.874162 | ||||||||
\(907\) | −15.5038 | −0.514794 | −0.257397 | − | 0.966306i | \(-0.582865\pi\) | ||||
−0.257397 | + | 0.966306i | \(0.582865\pi\) | |||||||
\(908\) | 13.3141 | 0.441844 | ||||||||
\(909\) | −8.84885 | −0.293498 | ||||||||
\(910\) | −2.72967 | −0.0904876 | ||||||||
\(911\) | 43.5095 | 1.44154 | 0.720768 | − | 0.693177i | \(-0.243789\pi\) | ||||
0.720768 | + | 0.693177i | \(0.243789\pi\) | |||||||
\(912\) | −0.0954705 | −0.00316135 | ||||||||
\(913\) | −31.3413 | −1.03725 | ||||||||
\(914\) | −32.2563 | −1.06694 | ||||||||
\(915\) | −18.0948 | −0.598197 | ||||||||
\(916\) | 20.2384 | 0.668695 | ||||||||
\(917\) | 13.6922 | 0.452155 | ||||||||
\(918\) | −16.1390 | −0.532668 | ||||||||
\(919\) | −12.4316 | −0.410081 | −0.205040 | − | 0.978754i | \(-0.565733\pi\) | ||||
−0.205040 | + | 0.978754i | \(0.565733\pi\) | |||||||
\(920\) | −10.2375 | −0.337520 | ||||||||
\(921\) | −11.0303 | −0.363460 | ||||||||
\(922\) | −6.19296 | −0.203954 | ||||||||
\(923\) | −53.9493 | −1.77576 | ||||||||
\(924\) | −4.28454 | −0.140951 | ||||||||
\(925\) | 13.8343 | 0.454870 | ||||||||
\(926\) | 5.48596 | 0.180280 | ||||||||
\(927\) | 67.2524 | 2.20886 | ||||||||
\(928\) | 20.4819 | 0.672352 | ||||||||
\(929\) | −8.03582 | −0.263647 | −0.131823 | − | 0.991273i | \(-0.542083\pi\) | ||||
−0.131823 | + | 0.991273i | \(0.542083\pi\) | |||||||
\(930\) | 3.35124 | 0.109892 | ||||||||
\(931\) | 2.21854 | 0.0727096 | ||||||||
\(932\) | −7.60773 | −0.249200 | ||||||||
\(933\) | 46.0160 | 1.50650 | ||||||||
\(934\) | 12.8334 | 0.419922 | ||||||||
\(935\) | 8.86279 | 0.289844 | ||||||||
\(936\) | 68.4738 | 2.23814 | ||||||||
\(937\) | 48.8183 | 1.59483 | 0.797413 | − | 0.603434i | \(-0.206201\pi\) | ||||
0.797413 | + | 0.603434i | \(0.206201\pi\) | |||||||
\(938\) | −3.73905 | −0.122084 | ||||||||
\(939\) | 4.54344 | 0.148270 | ||||||||
\(940\) | 11.1718 | 0.364384 | ||||||||
\(941\) | −39.8127 | −1.29786 | −0.648928 | − | 0.760850i | \(-0.724782\pi\) | ||||
−0.648928 | + | 0.760850i | \(0.724782\pi\) | |||||||
\(942\) | 34.2994 | 1.11754 | ||||||||
\(943\) | −15.4823 | −0.504172 | ||||||||
\(944\) | −0.721109 | −0.0234701 | ||||||||
\(945\) | −1.51128 | −0.0491619 | ||||||||
\(946\) | −13.1662 | −0.428070 | ||||||||
\(947\) | −58.4316 | −1.89877 | −0.949386 | − | 0.314111i | \(-0.898294\pi\) | ||||
−0.949386 | + | 0.314111i | \(0.898294\pi\) | |||||||
\(948\) | −12.2950 | −0.399323 | ||||||||
\(949\) | 41.7626 | 1.35567 | ||||||||
\(950\) | −1.34509 | −0.0436405 | ||||||||
\(951\) | −14.3600 | −0.465655 | ||||||||
\(952\) | 12.6062 | 0.408569 | ||||||||
\(953\) | 15.4235 | 0.499616 | 0.249808 | − | 0.968295i | \(-0.419633\pi\) | ||||
0.249808 | + | 0.968295i | \(0.419633\pi\) | |||||||
\(954\) | 42.3418 | 1.37087 | ||||||||
\(955\) | 6.40092 | 0.207129 | ||||||||
\(956\) | 17.8667 | 0.577850 | ||||||||
\(957\) | 18.3739 | 0.593943 | ||||||||
\(958\) | 24.9208 | 0.805156 | ||||||||
\(959\) | 8.18741 | 0.264385 | ||||||||
\(960\) | 10.2849 | 0.331944 | ||||||||
\(961\) | −27.3721 | −0.882972 | ||||||||
\(962\) | 16.2382 | 0.523540 | ||||||||
\(963\) | −62.1924 | −2.00412 | ||||||||
\(964\) | −17.0326 | −0.548584 | ||||||||
\(965\) | −1.63631 | −0.0526748 | ||||||||
\(966\) | −7.99953 | −0.257381 | ||||||||
\(967\) | −26.6967 | −0.858508 | −0.429254 | − | 0.903184i | \(-0.641224\pi\) | ||||
−0.429254 | + | 0.903184i | \(0.641224\pi\) | |||||||
\(968\) | −21.1747 | −0.680579 | ||||||||
\(969\) | −5.71361 | −0.183548 | ||||||||
\(970\) | 6.41911 | 0.206105 | ||||||||
\(971\) | −14.7951 | −0.474798 | −0.237399 | − | 0.971412i | \(-0.576295\pi\) | ||||
−0.237399 | + | 0.971412i | \(0.576295\pi\) | |||||||
\(972\) | −25.2442 | −0.809708 | ||||||||
\(973\) | 6.63411 | 0.212680 | ||||||||
\(974\) | 1.11246 | 0.0356454 | ||||||||
\(975\) | 69.5662 | 2.22790 | ||||||||
\(976\) | 0.960072 | 0.0307311 | ||||||||
\(977\) | 0.662748 | 0.0212032 | 0.0106016 | − | 0.999944i | \(-0.496625\pi\) | ||||
0.0106016 | + | 0.999944i | \(0.496625\pi\) | |||||||
\(978\) | −16.5078 | −0.527860 | ||||||||
\(979\) | −3.67362 | −0.117409 | ||||||||
\(980\) | −5.87578 | −0.187695 | ||||||||
\(981\) | 54.7605 | 1.74837 | ||||||||
\(982\) | −24.6836 | −0.787684 | ||||||||
\(983\) | −11.3042 | −0.360548 | −0.180274 | − | 0.983616i | \(-0.557698\pi\) | ||||
−0.180274 | + | 0.983616i | \(0.557698\pi\) | |||||||
\(984\) | 24.3687 | 0.776846 | ||||||||
\(985\) | 4.28207 | 0.136438 | ||||||||
\(986\) | −20.4033 | −0.649774 | ||||||||
\(987\) | 23.1299 | 0.736232 | ||||||||
\(988\) | 2.43047 | 0.0773234 | ||||||||
\(989\) | 37.8425 | 1.20332 | ||||||||
\(990\) | 5.10403 | 0.162217 | ||||||||
\(991\) | 1.44897 | 0.0460281 | 0.0230140 | − | 0.999735i | \(-0.492674\pi\) | ||||
0.0230140 | + | 0.999735i | \(0.492674\pi\) | |||||||
\(992\) | 10.6823 | 0.339164 | ||||||||
\(993\) | 67.5760 | 2.14446 | ||||||||
\(994\) | −5.71989 | −0.181424 | ||||||||
\(995\) | −0.0800084 | −0.00253644 | ||||||||
\(996\) | −53.5126 | −1.69561 | ||||||||
\(997\) | −37.0709 | −1.17405 | −0.587024 | − | 0.809570i | \(-0.699701\pi\) | ||||
−0.587024 | + | 0.809570i | \(0.699701\pi\) | |||||||
\(998\) | −13.7837 | −0.436315 | ||||||||
\(999\) | 8.99024 | 0.284439 |
(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 | 619.2.a.a.1.9 | ✓ | 21 | |
3.2 | odd | 2 | 5571.2.a.e.1.13 | 21 | |||
4.3 | odd | 2 | 9904.2.a.j.1.19 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.a.1.9 | ✓ | 21 | 1.1 | even | 1 | trivial | |
5571.2.a.e.1.13 | 21 | 3.2 | odd | 2 | |||
9904.2.a.j.1.19 | 21 | 4.3 | odd | 2 |