Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68347 | −1.89750 | −0.948750 | − | 0.316029i | \(-0.897650\pi\) | ||||
−0.948750 | + | 0.316029i | \(0.897650\pi\) | |||||||
\(3\) | 3.12668 | 1.80519 | 0.902594 | − | 0.430492i | \(-0.141660\pi\) | ||||
0.902594 | + | 0.430492i | \(0.141660\pi\) | |||||||
\(4\) | 5.20101 | 2.60050 | ||||||||
\(5\) | 2.33476 | 1.04414 | 0.522069 | − | 0.852903i | \(-0.325160\pi\) | ||||
0.522069 | + | 0.852903i | \(0.325160\pi\) | |||||||
\(6\) | −8.39034 | −3.42534 | ||||||||
\(7\) | 0.266736 | 0.100817 | 0.0504083 | − | 0.998729i | \(-0.483948\pi\) | ||||
0.0504083 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(8\) | −8.58980 | −3.03695 | ||||||||
\(9\) | 6.77612 | 2.25871 | ||||||||
\(10\) | −6.26526 | −1.98125 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 16.2619 | 4.69440 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.715776 | −0.191299 | ||||||||
\(15\) | 7.30005 | 1.88487 | ||||||||
\(16\) | 12.6484 | 3.16211 | ||||||||
\(17\) | −1.53629 | −0.372605 | −0.186303 | − | 0.982492i | \(-0.559650\pi\) | ||||
−0.186303 | + | 0.982492i | \(0.559650\pi\) | |||||||
\(18\) | −18.1835 | −4.28589 | ||||||||
\(19\) | 7.55923 | 1.73421 | 0.867103 | − | 0.498129i | \(-0.165979\pi\) | ||||
0.867103 | + | 0.498129i | \(0.165979\pi\) | |||||||
\(20\) | 12.1431 | 2.71528 | ||||||||
\(21\) | 0.833996 | 0.181993 | ||||||||
\(22\) | −2.68347 | −0.572118 | ||||||||
\(23\) | −3.95510 | −0.824696 | −0.412348 | − | 0.911026i | \(-0.635291\pi\) | ||||
−0.412348 | + | 0.911026i | \(0.635291\pi\) | |||||||
\(24\) | −26.8575 | −5.48227 | ||||||||
\(25\) | 0.451118 | 0.0902236 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.8067 | 2.27220 | ||||||||
\(28\) | 1.38729 | 0.262174 | ||||||||
\(29\) | 1.08736 | 0.201919 | 0.100959 | − | 0.994891i | \(-0.467809\pi\) | ||||
0.100959 | + | 0.994891i | \(0.467809\pi\) | |||||||
\(30\) | −19.5895 | −3.57653 | ||||||||
\(31\) | −3.25139 | −0.583967 | −0.291984 | − | 0.956423i | \(-0.594315\pi\) | ||||
−0.291984 | + | 0.956423i | \(0.594315\pi\) | |||||||
\(32\) | −16.7621 | −2.96315 | ||||||||
\(33\) | 3.12668 | 0.544285 | ||||||||
\(34\) | 4.12259 | 0.707018 | ||||||||
\(35\) | 0.622764 | 0.105266 | ||||||||
\(36\) | 35.2426 | 5.87377 | ||||||||
\(37\) | 3.44806 | 0.566857 | 0.283429 | − | 0.958993i | \(-0.408528\pi\) | ||||
0.283429 | + | 0.958993i | \(0.408528\pi\) | |||||||
\(38\) | −20.2850 | −3.29066 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.0551 | −3.17100 | ||||||||
\(41\) | −6.30467 | −0.984624 | −0.492312 | − | 0.870419i | \(-0.663848\pi\) | ||||
−0.492312 | + | 0.870419i | \(0.663848\pi\) | |||||||
\(42\) | −2.23800 | −0.345331 | ||||||||
\(43\) | 2.45816 | 0.374866 | 0.187433 | − | 0.982277i | \(-0.439983\pi\) | ||||
0.187433 | + | 0.982277i | \(0.439983\pi\) | |||||||
\(44\) | 5.20101 | 0.784081 | ||||||||
\(45\) | 15.8206 | 2.35840 | ||||||||
\(46\) | 10.6134 | 1.56486 | ||||||||
\(47\) | −6.48085 | −0.945329 | −0.472664 | − | 0.881243i | \(-0.656708\pi\) | ||||
−0.472664 | + | 0.881243i | \(0.656708\pi\) | |||||||
\(48\) | 39.5476 | 5.70821 | ||||||||
\(49\) | −6.92885 | −0.989836 | ||||||||
\(50\) | −1.21056 | −0.171199 | ||||||||
\(51\) | −4.80349 | −0.672623 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.06393 | 0.695584 | 0.347792 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347792 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(54\) | −31.6829 | −4.31150 | ||||||||
\(55\) | 2.33476 | 0.314819 | ||||||||
\(56\) | −2.29120 | −0.306175 | ||||||||
\(57\) | 23.6353 | 3.13057 | ||||||||
\(58\) | −2.91791 | −0.383140 | ||||||||
\(59\) | 10.8892 | 1.41766 | 0.708828 | − | 0.705381i | \(-0.249224\pi\) | ||||
0.708828 | + | 0.705381i | \(0.249224\pi\) | |||||||
\(60\) | 37.9676 | 4.90160 | ||||||||
\(61\) | 9.66466 | 1.23743 | 0.618716 | − | 0.785614i | \(-0.287653\pi\) | ||||
0.618716 | + | 0.785614i | \(0.287653\pi\) | |||||||
\(62\) | 8.72501 | 1.10808 | ||||||||
\(63\) | 1.80743 | 0.227715 | ||||||||
\(64\) | 19.6837 | 2.46047 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.39034 | −1.03278 | ||||||||
\(67\) | 6.41989 | 0.784314 | 0.392157 | − | 0.919898i | \(-0.371729\pi\) | ||||
0.392157 | + | 0.919898i | \(0.371729\pi\) | |||||||
\(68\) | −7.99026 | −0.968961 | ||||||||
\(69\) | −12.3663 | −1.48873 | ||||||||
\(70\) | −1.67117 | −0.199743 | ||||||||
\(71\) | 13.0818 | 1.55252 | 0.776262 | − | 0.630411i | \(-0.217114\pi\) | ||||
0.776262 | + | 0.630411i | \(0.217114\pi\) | |||||||
\(72\) | −58.2055 | −6.85958 | ||||||||
\(73\) | −1.49954 | −0.175508 | −0.0877540 | − | 0.996142i | \(-0.527969\pi\) | ||||
−0.0877540 | + | 0.996142i | \(0.527969\pi\) | |||||||
\(74\) | −9.25276 | −1.07561 | ||||||||
\(75\) | 1.41050 | 0.162871 | ||||||||
\(76\) | 39.3156 | 4.50981 | ||||||||
\(77\) | 0.266736 | 0.0303973 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.63953 | −0.409479 | −0.204739 | − | 0.978817i | \(-0.565635\pi\) | ||||
−0.204739 | + | 0.978817i | \(0.565635\pi\) | |||||||
\(80\) | 29.5311 | 3.30168 | ||||||||
\(81\) | 16.5874 | 1.84304 | ||||||||
\(82\) | 16.9184 | 1.86832 | ||||||||
\(83\) | −9.17706 | −1.00731 | −0.503657 | − | 0.863904i | \(-0.668012\pi\) | ||||
−0.503657 | + | 0.863904i | \(0.668012\pi\) | |||||||
\(84\) | 4.33762 | 0.473273 | ||||||||
\(85\) | −3.58688 | −0.389051 | ||||||||
\(86\) | −6.59640 | −0.711308 | ||||||||
\(87\) | 3.39984 | 0.364501 | ||||||||
\(88\) | −8.58980 | −0.915676 | ||||||||
\(89\) | −8.10322 | −0.858939 | −0.429470 | − | 0.903081i | \(-0.641299\pi\) | ||||
−0.429470 | + | 0.903081i | \(0.641299\pi\) | |||||||
\(90\) | −42.4542 | −4.47506 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.5705 | −2.14462 | ||||||||
\(93\) | −10.1661 | −1.05417 | ||||||||
\(94\) | 17.3912 | 1.79376 | ||||||||
\(95\) | 17.6490 | 1.81075 | ||||||||
\(96\) | −52.4097 | −5.34905 | ||||||||
\(97\) | −12.7243 | −1.29195 | −0.645977 | − | 0.763357i | \(-0.723550\pi\) | ||||
−0.645977 | + | 0.763357i | \(0.723550\pi\) | |||||||
\(98\) | 18.5934 | 1.87821 | ||||||||
\(99\) | 6.77612 | 0.681025 | ||||||||
\(100\) | 2.34627 | 0.234627 | ||||||||
\(101\) | 12.5430 | 1.24807 | 0.624037 | − | 0.781395i | \(-0.285492\pi\) | ||||
0.624037 | + | 0.781395i | \(0.285492\pi\) | |||||||
\(102\) | 12.8900 | 1.27630 | ||||||||
\(103\) | −4.78743 | −0.471719 | −0.235860 | − | 0.971787i | \(-0.575791\pi\) | ||||
−0.235860 | + | 0.971787i | \(0.575791\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.94718 | 0.190026 | ||||||||
\(106\) | −13.5889 | −1.31987 | ||||||||
\(107\) | −20.0718 | −1.94041 | −0.970206 | − | 0.242283i | \(-0.922104\pi\) | ||||
−0.970206 | + | 0.242283i | \(0.922104\pi\) | |||||||
\(108\) | 61.4067 | 5.90886 | ||||||||
\(109\) | −5.37319 | −0.514658 | −0.257329 | − | 0.966324i | \(-0.582842\pi\) | ||||
−0.257329 | + | 0.966324i | \(0.582842\pi\) | |||||||
\(110\) | −6.26526 | −0.597369 | ||||||||
\(111\) | 10.7810 | 1.02328 | ||||||||
\(112\) | 3.37379 | 0.318793 | ||||||||
\(113\) | −15.1793 | −1.42795 | −0.713976 | − | 0.700170i | \(-0.753108\pi\) | ||||
−0.713976 | + | 0.700170i | \(0.753108\pi\) | |||||||
\(114\) | −63.4245 | −5.94025 | ||||||||
\(115\) | −9.23423 | −0.861096 | ||||||||
\(116\) | 5.65539 | 0.525090 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.2209 | −2.69000 | ||||||||
\(119\) | −0.409783 | −0.0375648 | ||||||||
\(120\) | −62.7060 | −5.72425 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −25.9348 | −2.34803 | ||||||||
\(123\) | −19.7127 | −1.77743 | ||||||||
\(124\) | −16.9105 | −1.51861 | ||||||||
\(125\) | −10.6206 | −0.949932 | ||||||||
\(126\) | −4.85018 | −0.432089 | ||||||||
\(127\) | 21.0600 | 1.86877 | 0.934387 | − | 0.356260i | \(-0.115948\pi\) | ||||
0.934387 | + | 0.356260i | \(0.115948\pi\) | |||||||
\(128\) | −19.2964 | −1.70558 | ||||||||
\(129\) | 7.68588 | 0.676704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.77616 | 0.329925 | 0.164962 | − | 0.986300i | \(-0.447250\pi\) | ||||
0.164962 | + | 0.986300i | \(0.447250\pi\) | |||||||
\(132\) | 16.2619 | 1.41541 | ||||||||
\(133\) | 2.01632 | 0.174837 | ||||||||
\(134\) | −17.2276 | −1.48824 | ||||||||
\(135\) | 27.5658 | 2.37249 | ||||||||
\(136\) | 13.1964 | 1.13158 | ||||||||
\(137\) | 2.81943 | 0.240880 | 0.120440 | − | 0.992721i | \(-0.461569\pi\) | ||||
0.120440 | + | 0.992721i | \(0.461569\pi\) | |||||||
\(138\) | 33.1847 | 2.82487 | ||||||||
\(139\) | −1.84271 | −0.156296 | −0.0781482 | − | 0.996942i | \(-0.524901\pi\) | ||||
−0.0781482 | + | 0.996942i | \(0.524901\pi\) | |||||||
\(140\) | 3.23900 | 0.273745 | ||||||||
\(141\) | −20.2635 | −1.70650 | ||||||||
\(142\) | −35.1046 | −2.94591 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 85.7074 | 7.14228 | ||||||||
\(145\) | 2.53874 | 0.210831 | ||||||||
\(146\) | 4.02397 | 0.333026 | ||||||||
\(147\) | −21.6643 | −1.78684 | ||||||||
\(148\) | 17.9334 | 1.47411 | ||||||||
\(149\) | −5.43166 | −0.444979 | −0.222490 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222490 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(150\) | −3.78504 | −0.309047 | ||||||||
\(151\) | 6.87113 | 0.559165 | 0.279582 | − | 0.960122i | \(-0.409804\pi\) | ||||
0.279582 | + | 0.960122i | \(0.409804\pi\) | |||||||
\(152\) | −64.9323 | −5.26670 | ||||||||
\(153\) | −10.4101 | −0.841606 | ||||||||
\(154\) | −0.715776 | −0.0576789 | ||||||||
\(155\) | −7.59123 | −0.609742 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.36679 | 0.428317 | 0.214158 | − | 0.976799i | \(-0.431299\pi\) | ||||
0.214158 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(158\) | 9.76656 | 0.776985 | ||||||||
\(159\) | 15.8333 | 1.25566 | ||||||||
\(160\) | −39.1356 | −3.09394 | ||||||||
\(161\) | −1.05497 | −0.0831430 | ||||||||
\(162\) | −44.5118 | −3.49718 | ||||||||
\(163\) | −4.34355 | −0.340213 | −0.170106 | − | 0.985426i | \(-0.554411\pi\) | ||||
−0.170106 | + | 0.985426i | \(0.554411\pi\) | |||||||
\(164\) | −32.7906 | −2.56052 | ||||||||
\(165\) | 7.30005 | 0.568308 | ||||||||
\(166\) | 24.6264 | 1.91138 | ||||||||
\(167\) | −16.6380 | −1.28749 | −0.643745 | − | 0.765240i | \(-0.722620\pi\) | ||||
−0.643745 | + | 0.765240i | \(0.722620\pi\) | |||||||
\(168\) | −7.16386 | −0.552704 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.62527 | 0.738224 | ||||||||
\(171\) | 51.2222 | 3.91706 | ||||||||
\(172\) | 12.7849 | 0.974840 | ||||||||
\(173\) | −2.66992 | −0.202990 | −0.101495 | − | 0.994836i | \(-0.532363\pi\) | ||||
−0.101495 | + | 0.994836i | \(0.532363\pi\) | |||||||
\(174\) | −9.12336 | −0.691640 | ||||||||
\(175\) | 0.120329 | 0.00909604 | ||||||||
\(176\) | 12.6484 | 0.953413 | ||||||||
\(177\) | 34.0471 | 2.55914 | ||||||||
\(178\) | 21.7447 | 1.62984 | ||||||||
\(179\) | −22.7448 | −1.70002 | −0.850011 | − | 0.526764i | \(-0.823405\pi\) | ||||
−0.850011 | + | 0.526764i | \(0.823405\pi\) | |||||||
\(180\) | 82.2832 | 6.13302 | ||||||||
\(181\) | 20.4550 | 1.52041 | 0.760203 | − | 0.649685i | \(-0.225099\pi\) | ||||
0.760203 | + | 0.649685i | \(0.225099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.2183 | 2.23380 | ||||||||
\(184\) | 33.9735 | 2.50456 | ||||||||
\(185\) | 8.05040 | 0.591877 | ||||||||
\(186\) | 27.2803 | 2.00029 | ||||||||
\(187\) | −1.53629 | −0.112345 | ||||||||
\(188\) | −33.7069 | −2.45833 | ||||||||
\(189\) | 3.14927 | 0.229075 | ||||||||
\(190\) | −47.3606 | −3.43590 | ||||||||
\(191\) | −7.69998 | −0.557151 | −0.278575 | − | 0.960414i | \(-0.589862\pi\) | ||||
−0.278575 | + | 0.960414i | \(0.589862\pi\) | |||||||
\(192\) | 61.5447 | 4.44161 | ||||||||
\(193\) | 7.54943 | 0.543420 | 0.271710 | − | 0.962379i | \(-0.412411\pi\) | ||||
0.271710 | + | 0.962379i | \(0.412411\pi\) | |||||||
\(194\) | 34.1452 | 2.45148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −36.0370 | −2.57407 | ||||||||
\(197\) | −18.8155 | −1.34055 | −0.670275 | − | 0.742113i | \(-0.733824\pi\) | ||||
−0.670275 | + | 0.742113i | \(0.733824\pi\) | |||||||
\(198\) | −18.1835 | −1.29224 | ||||||||
\(199\) | 9.03481 | 0.640461 | 0.320230 | − | 0.947340i | \(-0.396240\pi\) | ||||
0.320230 | + | 0.947340i | \(0.396240\pi\) | |||||||
\(200\) | −3.87501 | −0.274005 | ||||||||
\(201\) | 20.0729 | 1.41584 | ||||||||
\(202\) | −33.6587 | −2.36822 | ||||||||
\(203\) | 0.290039 | 0.0203567 | ||||||||
\(204\) | −24.9830 | −1.74916 | ||||||||
\(205\) | −14.7199 | −1.02808 | ||||||||
\(206\) | 12.8469 | 0.895087 | ||||||||
\(207\) | −26.8002 | −1.86275 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.55923 | 0.522883 | ||||||||
\(210\) | −5.22521 | −0.360573 | ||||||||
\(211\) | −11.2951 | −0.777585 | −0.388793 | − | 0.921325i | \(-0.627108\pi\) | ||||
−0.388793 | + | 0.921325i | \(0.627108\pi\) | |||||||
\(212\) | 26.3375 | 1.80887 | ||||||||
\(213\) | 40.9026 | 2.80260 | ||||||||
\(214\) | 53.8620 | 3.68193 | ||||||||
\(215\) | 5.73922 | 0.391412 | ||||||||
\(216\) | −101.417 | −6.90057 | ||||||||
\(217\) | −0.867262 | −0.0588736 | ||||||||
\(218\) | 14.4188 | 0.976563 | ||||||||
\(219\) | −4.68858 | −0.316825 | ||||||||
\(220\) | 12.1431 | 0.818689 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −28.9304 | −1.94168 | ||||||||
\(223\) | 25.9591 | 1.73835 | 0.869176 | − | 0.494503i | \(-0.164650\pi\) | ||||
0.869176 | + | 0.494503i | \(0.164650\pi\) | |||||||
\(224\) | −4.47105 | −0.298735 | ||||||||
\(225\) | 3.05683 | 0.203789 | ||||||||
\(226\) | 40.7333 | 2.70954 | ||||||||
\(227\) | −10.0343 | −0.665999 | −0.332999 | − | 0.942927i | \(-0.608061\pi\) | ||||
−0.332999 | + | 0.942927i | \(0.608061\pi\) | |||||||
\(228\) | 122.927 | 8.14105 | ||||||||
\(229\) | −2.98115 | −0.197000 | −0.0985001 | − | 0.995137i | \(-0.531404\pi\) | ||||
−0.0985001 | + | 0.995137i | \(0.531404\pi\) | |||||||
\(230\) | 24.7798 | 1.63393 | ||||||||
\(231\) | 0.833996 | 0.0548729 | ||||||||
\(232\) | −9.34024 | −0.613217 | ||||||||
\(233\) | −3.75063 | −0.245712 | −0.122856 | − | 0.992425i | \(-0.539205\pi\) | ||||
−0.122856 | + | 0.992425i | \(0.539205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.1312 | −0.987053 | ||||||||
\(236\) | 56.6349 | 3.68662 | ||||||||
\(237\) | −11.3796 | −0.739186 | ||||||||
\(238\) | 1.09964 | 0.0712791 | ||||||||
\(239\) | 8.17311 | 0.528675 | 0.264337 | − | 0.964430i | \(-0.414847\pi\) | ||||
0.264337 | + | 0.964430i | \(0.414847\pi\) | |||||||
\(240\) | 92.3343 | 5.96016 | ||||||||
\(241\) | 4.62614 | 0.297996 | 0.148998 | − | 0.988838i | \(-0.452395\pi\) | ||||
0.148998 | + | 0.988838i | \(0.452395\pi\) | |||||||
\(242\) | −2.68347 | −0.172500 | ||||||||
\(243\) | 16.4434 | 1.05484 | ||||||||
\(244\) | 50.2660 | 3.21795 | ||||||||
\(245\) | −16.1772 | −1.03353 | ||||||||
\(246\) | 52.8984 | 3.37268 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 27.9288 | 1.77348 | ||||||||
\(249\) | −28.6937 | −1.81839 | ||||||||
\(250\) | 28.4999 | 1.80249 | ||||||||
\(251\) | −12.9557 | −0.817758 | −0.408879 | − | 0.912589i | \(-0.634080\pi\) | ||||
−0.408879 | + | 0.912589i | \(0.634080\pi\) | |||||||
\(252\) | 9.40046 | 0.592173 | ||||||||
\(253\) | −3.95510 | −0.248655 | ||||||||
\(254\) | −56.5139 | −3.54600 | ||||||||
\(255\) | −11.2150 | −0.702311 | ||||||||
\(256\) | 12.4139 | 0.775871 | ||||||||
\(257\) | −0.638721 | −0.0398423 | −0.0199211 | − | 0.999802i | \(-0.506342\pi\) | ||||
−0.0199211 | + | 0.999802i | \(0.506342\pi\) | |||||||
\(258\) | −20.6248 | −1.28405 | ||||||||
\(259\) | 0.919719 | 0.0571486 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.36811 | 0.456074 | ||||||||
\(262\) | −10.1332 | −0.626032 | ||||||||
\(263\) | 14.5476 | 0.897046 | 0.448523 | − | 0.893771i | \(-0.351950\pi\) | ||||
0.448523 | + | 0.893771i | \(0.351950\pi\) | |||||||
\(264\) | −26.8575 | −1.65297 | ||||||||
\(265\) | 11.8231 | 0.726285 | ||||||||
\(266\) | −5.41072 | −0.331752 | ||||||||
\(267\) | −25.3362 | −1.55055 | ||||||||
\(268\) | 33.3899 | 2.03961 | ||||||||
\(269\) | −14.9672 | −0.912564 | −0.456282 | − | 0.889835i | \(-0.650819\pi\) | ||||
−0.456282 | + | 0.889835i | \(0.650819\pi\) | |||||||
\(270\) | −73.9721 | −4.50180 | ||||||||
\(271\) | −21.3675 | −1.29799 | −0.648993 | − | 0.760795i | \(-0.724809\pi\) | ||||
−0.648993 | + | 0.760795i | \(0.724809\pi\) | |||||||
\(272\) | −19.4317 | −1.17822 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.56586 | −0.457070 | ||||||||
\(275\) | 0.451118 | 0.0272035 | ||||||||
\(276\) | −64.3174 | −3.87145 | ||||||||
\(277\) | 23.9016 | 1.43611 | 0.718055 | − | 0.695986i | \(-0.245032\pi\) | ||||
0.718055 | + | 0.695986i | \(0.245032\pi\) | |||||||
\(278\) | 4.94485 | 0.296572 | ||||||||
\(279\) | −22.0318 | −1.31901 | ||||||||
\(280\) | −5.34942 | −0.319689 | ||||||||
\(281\) | 19.5972 | 1.16907 | 0.584535 | − | 0.811368i | \(-0.301277\pi\) | ||||
0.584535 | + | 0.811368i | \(0.301277\pi\) | |||||||
\(282\) | 54.3765 | 3.23808 | ||||||||
\(283\) | −1.39789 | −0.0830957 | −0.0415479 | − | 0.999137i | \(-0.513229\pi\) | ||||
−0.0415479 | + | 0.999137i | \(0.513229\pi\) | |||||||
\(284\) | 68.0385 | 4.03734 | ||||||||
\(285\) | 55.1828 | 3.26875 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.68168 | −0.0992664 | ||||||||
\(288\) | −113.582 | −6.69289 | ||||||||
\(289\) | −14.6398 | −0.861165 | ||||||||
\(290\) | −6.81263 | −0.400051 | ||||||||
\(291\) | −39.7847 | −2.33222 | ||||||||
\(292\) | −7.79912 | −0.456409 | ||||||||
\(293\) | 20.0795 | 1.17306 | 0.586529 | − | 0.809928i | \(-0.300494\pi\) | ||||
0.586529 | + | 0.809928i | \(0.300494\pi\) | |||||||
\(294\) | 58.1355 | 3.39053 | ||||||||
\(295\) | 25.4238 | 1.48023 | ||||||||
\(296\) | −29.6181 | −1.72152 | ||||||||
\(297\) | 11.8067 | 0.685094 | ||||||||
\(298\) | 14.5757 | 0.844347 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.33603 | 0.423546 | ||||||||
\(301\) | 0.655679 | 0.0377927 | ||||||||
\(302\) | −18.4385 | −1.06101 | ||||||||
\(303\) | 39.2179 | 2.25301 | ||||||||
\(304\) | 95.6125 | 5.48375 | ||||||||
\(305\) | 22.5647 | 1.29205 | ||||||||
\(306\) | 27.9351 | 1.59695 | ||||||||
\(307\) | 4.32372 | 0.246768 | 0.123384 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123384 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(308\) | 1.38729 | 0.0790483 | ||||||||
\(309\) | −14.9687 | −0.851542 | ||||||||
\(310\) | 20.3708 | 1.15699 | ||||||||
\(311\) | −25.3775 | −1.43902 | −0.719512 | − | 0.694480i | \(-0.755634\pi\) | ||||
−0.719512 | + | 0.694480i | \(0.755634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1230 | 1.19394 | 0.596972 | − | 0.802262i | \(-0.296370\pi\) | ||||
0.596972 | + | 0.802262i | \(0.296370\pi\) | |||||||
\(314\) | −14.4016 | −0.812731 | ||||||||
\(315\) | 4.21992 | 0.237766 | ||||||||
\(316\) | −18.9292 | −1.06485 | ||||||||
\(317\) | 21.0836 | 1.18417 | 0.592087 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592087 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(318\) | −42.4881 | −2.38261 | ||||||||
\(319\) | 1.08736 | 0.0608807 | ||||||||
\(320\) | 45.9568 | 2.56907 | ||||||||
\(321\) | −62.7580 | −3.50281 | ||||||||
\(322\) | 2.83097 | 0.157764 | ||||||||
\(323\) | −11.6132 | −0.646175 | ||||||||
\(324\) | 86.2712 | 4.79284 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.6558 | 0.645553 | ||||||||
\(327\) | −16.8002 | −0.929055 | ||||||||
\(328\) | 54.1559 | 2.99026 | ||||||||
\(329\) | −1.72867 | −0.0953048 | ||||||||
\(330\) | −19.5895 | −1.07836 | ||||||||
\(331\) | −28.2148 | −1.55083 | −0.775413 | − | 0.631454i | \(-0.782458\pi\) | ||||
−0.775413 | + | 0.631454i | \(0.782458\pi\) | |||||||
\(332\) | −47.7300 | −2.61952 | ||||||||
\(333\) | 23.3644 | 1.28036 | ||||||||
\(334\) | 44.6477 | 2.44301 | ||||||||
\(335\) | 14.9889 | 0.818932 | ||||||||
\(336\) | 10.5488 | 0.575482 | ||||||||
\(337\) | −7.49761 | −0.408421 | −0.204211 | − | 0.978927i | \(-0.565463\pi\) | ||||
−0.204211 | + | 0.978927i | \(0.565463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −47.4609 | −2.57772 | ||||||||
\(340\) | −18.6554 | −1.01173 | ||||||||
\(341\) | −3.25139 | −0.176073 | ||||||||
\(342\) | −137.453 | −7.43262 | ||||||||
\(343\) | −3.71532 | −0.200608 | ||||||||
\(344\) | −21.1151 | −1.13845 | ||||||||
\(345\) | −28.8725 | −1.55444 | ||||||||
\(346\) | 7.16464 | 0.385174 | ||||||||
\(347\) | 22.1568 | 1.18944 | 0.594720 | − | 0.803933i | \(-0.297263\pi\) | ||||
0.594720 | + | 0.803933i | \(0.297263\pi\) | |||||||
\(348\) | 17.6826 | 0.947886 | ||||||||
\(349\) | −32.7247 | −1.75171 | −0.875856 | − | 0.482573i | \(-0.839702\pi\) | ||||
−0.875856 | + | 0.482573i | \(0.839702\pi\) | |||||||
\(350\) | −0.322900 | −0.0172597 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.7621 | −0.893424 | ||||||||
\(353\) | −8.19679 | −0.436271 | −0.218135 | − | 0.975919i | \(-0.569997\pi\) | ||||
−0.218135 | + | 0.975919i | \(0.569997\pi\) | |||||||
\(354\) | −91.3644 | −4.85596 | ||||||||
\(355\) | 30.5429 | 1.62105 | ||||||||
\(356\) | −42.1449 | −2.23367 | ||||||||
\(357\) | −1.28126 | −0.0678115 | ||||||||
\(358\) | 61.0348 | 3.22579 | ||||||||
\(359\) | 15.1960 | 0.802017 | 0.401008 | − | 0.916074i | \(-0.368660\pi\) | ||||
0.401008 | + | 0.916074i | \(0.368660\pi\) | |||||||
\(360\) | −135.896 | −7.16235 | ||||||||
\(361\) | 38.1420 | 2.00747 | ||||||||
\(362\) | −54.8903 | −2.88497 | ||||||||
\(363\) | 3.12668 | 0.164108 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.50107 | −0.183254 | ||||||||
\(366\) | −81.0898 | −4.23863 | ||||||||
\(367\) | 11.8602 | 0.619099 | 0.309549 | − | 0.950883i | \(-0.399822\pi\) | ||||
0.309549 | + | 0.950883i | \(0.399822\pi\) | |||||||
\(368\) | −50.0259 | −2.60778 | ||||||||
\(369\) | −42.7212 | −2.22398 | ||||||||
\(370\) | −21.6030 | −1.12309 | ||||||||
\(371\) | 1.35073 | 0.0701264 | ||||||||
\(372\) | −52.8737 | −2.74137 | ||||||||
\(373\) | −31.4345 | −1.62762 | −0.813810 | − | 0.581132i | \(-0.802610\pi\) | ||||
−0.813810 | + | 0.581132i | \(0.802610\pi\) | |||||||
\(374\) | 4.12259 | 0.213174 | ||||||||
\(375\) | −33.2071 | −1.71481 | ||||||||
\(376\) | 55.6692 | 2.87092 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8.45096 | −0.434670 | ||||||||
\(379\) | −27.8846 | −1.43233 | −0.716167 | − | 0.697929i | \(-0.754105\pi\) | ||||
−0.716167 | + | 0.697929i | \(0.754105\pi\) | |||||||
\(380\) | 91.7926 | 4.70886 | ||||||||
\(381\) | 65.8479 | 3.37349 | ||||||||
\(382\) | 20.6626 | 1.05719 | ||||||||
\(383\) | −20.0951 | −1.02681 | −0.513406 | − | 0.858146i | \(-0.671617\pi\) | ||||
−0.513406 | + | 0.858146i | \(0.671617\pi\) | |||||||
\(384\) | −60.3338 | −3.07889 | ||||||||
\(385\) | 0.622764 | 0.0317390 | ||||||||
\(386\) | −20.2587 | −1.03114 | ||||||||
\(387\) | 16.6568 | 0.846712 | ||||||||
\(388\) | −66.1790 | −3.35973 | ||||||||
\(389\) | −1.80049 | −0.0912883 | −0.0456441 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456441 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.07619 | 0.307286 | ||||||||
\(392\) | 59.5174 | 3.00609 | ||||||||
\(393\) | 11.8068 | 0.595576 | ||||||||
\(394\) | 50.4908 | 2.54369 | ||||||||
\(395\) | −8.49743 | −0.427552 | ||||||||
\(396\) | 35.2426 | 1.77101 | ||||||||
\(397\) | −4.76541 | −0.239169 | −0.119584 | − | 0.992824i | \(-0.538156\pi\) | ||||
−0.119584 | + | 0.992824i | \(0.538156\pi\) | |||||||
\(398\) | −24.2446 | −1.21527 | ||||||||
\(399\) | 6.30437 | 0.315613 | ||||||||
\(400\) | 5.70594 | 0.285297 | ||||||||
\(401\) | 29.3417 | 1.46526 | 0.732628 | − | 0.680629i | \(-0.238294\pi\) | ||||
0.732628 | + | 0.680629i | \(0.238294\pi\) | |||||||
\(402\) | −53.8651 | −2.68655 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 65.2361 | 3.24562 | ||||||||
\(405\) | 38.7277 | 1.92439 | ||||||||
\(406\) | −0.778310 | −0.0386269 | ||||||||
\(407\) | 3.44806 | 0.170914 | ||||||||
\(408\) | 41.2610 | 2.04272 | ||||||||
\(409\) | 12.2591 | 0.606172 | 0.303086 | − | 0.952963i | \(-0.401983\pi\) | ||||
0.303086 | + | 0.952963i | \(0.401983\pi\) | |||||||
\(410\) | 39.5004 | 1.95079 | ||||||||
\(411\) | 8.81546 | 0.434834 | ||||||||
\(412\) | −24.8994 | −1.22671 | ||||||||
\(413\) | 2.90454 | 0.142923 | ||||||||
\(414\) | 71.9176 | 3.53456 | ||||||||
\(415\) | −21.4263 | −1.05177 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.76155 | −0.282144 | ||||||||
\(418\) | −20.2850 | −0.992170 | ||||||||
\(419\) | 36.1583 | 1.76645 | 0.883224 | − | 0.468951i | \(-0.155368\pi\) | ||||
0.883224 | + | 0.468951i | \(0.155368\pi\) | |||||||
\(420\) | 10.1273 | 0.494162 | ||||||||
\(421\) | 1.38467 | 0.0674849 | 0.0337424 | − | 0.999431i | \(-0.489257\pi\) | ||||
0.0337424 | + | 0.999431i | \(0.489257\pi\) | |||||||
\(422\) | 30.3100 | 1.47547 | ||||||||
\(423\) | −43.9150 | −2.13522 | ||||||||
\(424\) | −43.4981 | −2.11245 | ||||||||
\(425\) | −0.693049 | −0.0336178 | ||||||||
\(426\) | −109.761 | −5.31792 | ||||||||
\(427\) | 2.57791 | 0.124754 | ||||||||
\(428\) | −104.393 | −5.04604 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.4010 | −0.742704 | ||||||||
\(431\) | −0.0306402 | −0.00147589 | −0.000737943 | − | 1.00000i | \(-0.500235\pi\) | ||||
−0.000737943 | 1.00000i | \(0.500235\pi\) | ||||||||
\(432\) | 149.336 | 7.18495 | ||||||||
\(433\) | 13.5388 | 0.650631 | 0.325315 | − | 0.945606i | \(-0.394530\pi\) | ||||
0.325315 | + | 0.945606i | \(0.394530\pi\) | |||||||
\(434\) | 2.32727 | 0.111713 | ||||||||
\(435\) | 7.93782 | 0.380589 | ||||||||
\(436\) | −27.9460 | −1.33837 | ||||||||
\(437\) | −29.8975 | −1.43019 | ||||||||
\(438\) | 12.5817 | 0.601175 | ||||||||
\(439\) | 15.5973 | 0.744417 | 0.372208 | − | 0.928149i | \(-0.378601\pi\) | ||||
0.372208 | + | 0.928149i | \(0.378601\pi\) | |||||||
\(440\) | −20.0551 | −0.956092 | ||||||||
\(441\) | −46.9507 | −2.23575 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3311 | 0.775914 | 0.387957 | − | 0.921677i | \(-0.373181\pi\) | ||||
0.387957 | + | 0.921677i | \(0.373181\pi\) | |||||||
\(444\) | 56.0719 | 2.66105 | ||||||||
\(445\) | −18.9191 | −0.896851 | ||||||||
\(446\) | −69.6605 | −3.29852 | ||||||||
\(447\) | −16.9831 | −0.803271 | ||||||||
\(448\) | 5.25035 | 0.248056 | ||||||||
\(449\) | −2.94124 | −0.138806 | −0.0694029 | − | 0.997589i | \(-0.522109\pi\) | ||||
−0.0694029 | + | 0.997589i | \(0.522109\pi\) | |||||||
\(450\) | −8.20291 | −0.386689 | ||||||||
\(451\) | −6.30467 | −0.296875 | ||||||||
\(452\) | −78.9479 | −3.71340 | ||||||||
\(453\) | 21.4838 | 1.00940 | ||||||||
\(454\) | 26.9267 | 1.26373 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −203.022 | −9.50739 | ||||||||
\(457\) | −25.6418 | −1.19947 | −0.599735 | − | 0.800199i | \(-0.704727\pi\) | ||||
−0.599735 | + | 0.800199i | \(0.704727\pi\) | |||||||
\(458\) | 7.99983 | 0.373808 | ||||||||
\(459\) | −18.1385 | −0.846634 | ||||||||
\(460\) | −48.0273 | −2.23928 | ||||||||
\(461\) | 25.4408 | 1.18490 | 0.592449 | − | 0.805608i | \(-0.298161\pi\) | ||||
0.592449 | + | 0.805608i | \(0.298161\pi\) | |||||||
\(462\) | −2.23800 | −0.104121 | ||||||||
\(463\) | −10.6067 | −0.492934 | −0.246467 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246467 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(464\) | 13.7535 | 0.638489 | ||||||||
\(465\) | −23.7353 | −1.10070 | ||||||||
\(466\) | 10.0647 | 0.466238 | ||||||||
\(467\) | −5.17505 | −0.239473 | −0.119736 | − | 0.992806i | \(-0.538205\pi\) | ||||
−0.119736 | + | 0.992806i | \(0.538205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71241 | 0.0790719 | ||||||||
\(470\) | 40.6042 | 1.87293 | ||||||||
\(471\) | 16.7802 | 0.773193 | ||||||||
\(472\) | −93.5363 | −4.30536 | ||||||||
\(473\) | 2.45816 | 0.113026 | ||||||||
\(474\) | 30.5369 | 1.40261 | ||||||||
\(475\) | 3.41011 | 0.156466 | ||||||||
\(476\) | −2.13129 | −0.0976873 | ||||||||
\(477\) | 34.3138 | 1.57112 | ||||||||
\(478\) | −21.9323 | −1.00316 | ||||||||
\(479\) | 17.9210 | 0.818829 | 0.409415 | − | 0.912348i | \(-0.365733\pi\) | ||||
0.409415 | + | 0.912348i | \(0.365733\pi\) | |||||||
\(480\) | −122.364 | −5.58514 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.4141 | −0.565447 | ||||||||
\(483\) | −3.29854 | −0.150089 | ||||||||
\(484\) | 5.20101 | 0.236409 | ||||||||
\(485\) | −29.7081 | −1.34898 | ||||||||
\(486\) | −44.1253 | −2.00156 | ||||||||
\(487\) | 6.46395 | 0.292910 | 0.146455 | − | 0.989217i | \(-0.453214\pi\) | ||||
0.146455 | + | 0.989217i | \(0.453214\pi\) | |||||||
\(488\) | −83.0175 | −3.75803 | ||||||||
\(489\) | −13.5809 | −0.614148 | ||||||||
\(490\) | 43.4111 | 1.96111 | ||||||||
\(491\) | 16.7077 | 0.754007 | 0.377004 | − | 0.926212i | \(-0.376954\pi\) | ||||
0.377004 | + | 0.926212i | \(0.376954\pi\) | |||||||
\(492\) | −102.526 | −4.62222 | ||||||||
\(493\) | −1.67051 | −0.0752359 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.8206 | 0.711084 | ||||||||
\(496\) | −41.1251 | −1.84657 | ||||||||
\(497\) | 3.48938 | 0.156520 | ||||||||
\(498\) | 76.9987 | 3.45040 | ||||||||
\(499\) | −18.7254 | −0.838264 | −0.419132 | − | 0.907925i | \(-0.637665\pi\) | ||||
−0.419132 | + | 0.907925i | \(0.637665\pi\) | |||||||
\(500\) | −55.2376 | −2.47030 | ||||||||
\(501\) | −52.0218 | −2.32416 | ||||||||
\(502\) | 34.7663 | 1.55169 | ||||||||
\(503\) | −38.7263 | −1.72672 | −0.863359 | − | 0.504590i | \(-0.831644\pi\) | ||||
−0.863359 | + | 0.504590i | \(0.831644\pi\) | |||||||
\(504\) | −15.5255 | −0.691559 | ||||||||
\(505\) | 29.2849 | 1.30316 | ||||||||
\(506\) | 10.6134 | 0.471823 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 109.533 | 4.85975 | ||||||||
\(509\) | 10.4846 | 0.464721 | 0.232360 | − | 0.972630i | \(-0.425355\pi\) | ||||
0.232360 | + | 0.972630i | \(0.425355\pi\) | |||||||
\(510\) | 30.0951 | 1.33263 | ||||||||
\(511\) | −0.399981 | −0.0176941 | ||||||||
\(512\) | 5.28047 | 0.233366 | ||||||||
\(513\) | 89.2496 | 3.94046 | ||||||||
\(514\) | 1.71399 | 0.0756007 | ||||||||
\(515\) | −11.1775 | −0.492540 | ||||||||
\(516\) | 39.9743 | 1.75977 | ||||||||
\(517\) | −6.48085 | −0.285027 | ||||||||
\(518\) | −2.46804 | −0.108439 | ||||||||
\(519\) | −8.34797 | −0.366435 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.86293 | −0.388292 | −0.194146 | − | 0.980973i | \(-0.562194\pi\) | ||||
−0.194146 | + | 0.980973i | \(0.562194\pi\) | |||||||
\(522\) | −19.7721 | −0.865401 | ||||||||
\(523\) | −38.3068 | −1.67504 | −0.837520 | − | 0.546407i | \(-0.815995\pi\) | ||||
−0.837520 | + | 0.546407i | \(0.815995\pi\) | |||||||
\(524\) | 19.6398 | 0.857970 | ||||||||
\(525\) | 0.376231 | 0.0164201 | ||||||||
\(526\) | −39.0382 | −1.70214 | ||||||||
\(527\) | 4.99508 | 0.217589 | ||||||||
\(528\) | 39.5476 | 1.72109 | ||||||||
\(529\) | −7.35715 | −0.319876 | ||||||||
\(530\) | −31.7268 | −1.37813 | ||||||||
\(531\) | 73.7867 | 3.20207 | ||||||||
\(532\) | 10.4869 | 0.454663 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 67.9888 | 2.94216 | ||||||||
\(535\) | −46.8628 | −2.02606 | ||||||||
\(536\) | −55.1456 | −2.38193 | ||||||||
\(537\) | −71.1155 | −3.06886 | ||||||||
\(538\) | 40.1639 | 1.73159 | ||||||||
\(539\) | −6.92885 | −0.298447 | ||||||||
\(540\) | 143.370 | 6.16967 | ||||||||
\(541\) | −18.3574 | −0.789245 | −0.394623 | − | 0.918843i | \(-0.629125\pi\) | ||||
−0.394623 | + | 0.918843i | \(0.629125\pi\) | |||||||
\(542\) | 57.3391 | 2.46293 | ||||||||
\(543\) | 63.9561 | 2.74462 | ||||||||
\(544\) | 25.7515 | 1.10409 | ||||||||
\(545\) | −12.5451 | −0.537374 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.64398 | −0.0702916 | −0.0351458 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351458 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(548\) | 14.6639 | 0.626410 | ||||||||
\(549\) | 65.4889 | 2.79500 | ||||||||
\(550\) | −1.21056 | −0.0516185 | ||||||||
\(551\) | 8.21964 | 0.350168 | ||||||||
\(552\) | 106.224 | 4.52121 | ||||||||
\(553\) | −0.970791 | −0.0412822 | ||||||||
\(554\) | −64.1393 | −2.72502 | ||||||||
\(555\) | 25.1710 | 1.06845 | ||||||||
\(556\) | −9.58393 | −0.406449 | ||||||||
\(557\) | 7.76685 | 0.329092 | 0.164546 | − | 0.986369i | \(-0.447384\pi\) | ||||
0.164546 | + | 0.986369i | \(0.447384\pi\) | |||||||
\(558\) | 59.1217 | 2.50282 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.87700 | 0.332864 | ||||||||
\(561\) | −4.80349 | −0.202803 | ||||||||
\(562\) | −52.5885 | −2.21831 | ||||||||
\(563\) | −45.9808 | −1.93786 | −0.968930 | − | 0.247333i | \(-0.920446\pi\) | ||||
−0.968930 | + | 0.247333i | \(0.920446\pi\) | |||||||
\(564\) | −105.391 | −4.43775 | ||||||||
\(565\) | −35.4402 | −1.49098 | ||||||||
\(566\) | 3.75119 | 0.157674 | ||||||||
\(567\) | 4.42445 | 0.185809 | ||||||||
\(568\) | −112.370 | −4.71494 | ||||||||
\(569\) | 29.8201 | 1.25012 | 0.625061 | − | 0.780576i | \(-0.285074\pi\) | ||||
0.625061 | + | 0.780576i | \(0.285074\pi\) | |||||||
\(570\) | −148.081 | −6.20244 | ||||||||
\(571\) | 27.3401 | 1.14415 | 0.572075 | − | 0.820202i | \(-0.306139\pi\) | ||||
0.572075 | + | 0.820202i | \(0.306139\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.0753 | −1.00576 | ||||||||
\(574\) | 4.51273 | 0.188358 | ||||||||
\(575\) | −1.78422 | −0.0744071 | ||||||||
\(576\) | 133.379 | 5.55747 | ||||||||
\(577\) | −40.3312 | −1.67901 | −0.839504 | − | 0.543353i | \(-0.817154\pi\) | ||||
−0.839504 | + | 0.543353i | \(0.817154\pi\) | |||||||
\(578\) | 39.2855 | 1.63406 | ||||||||
\(579\) | 23.6046 | 0.980975 | ||||||||
\(580\) | 13.2040 | 0.548266 | ||||||||
\(581\) | −2.44785 | −0.101554 | ||||||||
\(582\) | 106.761 | 4.42538 | ||||||||
\(583\) | 5.06393 | 0.209726 | ||||||||
\(584\) | 12.8807 | 0.533009 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −53.8827 | −2.22588 | ||||||||
\(587\) | 6.46283 | 0.266750 | 0.133375 | − | 0.991066i | \(-0.457419\pi\) | ||||
0.133375 | + | 0.991066i | \(0.457419\pi\) | |||||||
\(588\) | −112.676 | −4.64668 | ||||||||
\(589\) | −24.5780 | −1.01272 | ||||||||
\(590\) | −68.2239 | −2.80873 | ||||||||
\(591\) | −58.8300 | −2.41994 | ||||||||
\(592\) | 43.6126 | 1.79247 | ||||||||
\(593\) | 18.4337 | 0.756983 | 0.378492 | − | 0.925605i | \(-0.376443\pi\) | ||||
0.378492 | + | 0.925605i | \(0.376443\pi\) | |||||||
\(594\) | −31.6829 | −1.29997 | ||||||||
\(595\) | −0.956747 | −0.0392228 | ||||||||
\(596\) | −28.2501 | −1.15717 | ||||||||
\(597\) | 28.2490 | 1.15615 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.81967 | −0.401221 | −0.200610 | − | 0.979671i | \(-0.564293\pi\) | ||||
−0.200610 | + | 0.979671i | \(0.564293\pi\) | |||||||
\(600\) | −12.1159 | −0.494631 | ||||||||
\(601\) | 15.7357 | 0.641872 | 0.320936 | − | 0.947101i | \(-0.396003\pi\) | ||||
0.320936 | + | 0.947101i | \(0.396003\pi\) | |||||||
\(602\) | −1.75949 | −0.0717116 | ||||||||
\(603\) | 43.5019 | 1.77153 | ||||||||
\(604\) | 35.7368 | 1.45411 | ||||||||
\(605\) | 2.33476 | 0.0949216 | ||||||||
\(606\) | −105.240 | −4.27508 | ||||||||
\(607\) | 20.9871 | 0.851839 | 0.425919 | − | 0.904761i | \(-0.359951\pi\) | ||||
0.425919 | + | 0.904761i | \(0.359951\pi\) | |||||||
\(608\) | −126.709 | −5.13872 | ||||||||
\(609\) | 0.906858 | 0.0367477 | ||||||||
\(610\) | −60.5516 | −2.45166 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −54.1429 | −2.18860 | ||||||||
\(613\) | −1.66482 | −0.0672413 | −0.0336206 | − | 0.999435i | \(-0.510704\pi\) | ||||
−0.0336206 | + | 0.999435i | \(0.510704\pi\) | |||||||
\(614\) | −11.6026 | −0.468241 | ||||||||
\(615\) | −46.0244 | −1.85588 | ||||||||
\(616\) | −2.29120 | −0.0923153 | ||||||||
\(617\) | −10.5682 | −0.425462 | −0.212731 | − | 0.977111i | \(-0.568236\pi\) | ||||
−0.212731 | + | 0.977111i | \(0.568236\pi\) | |||||||
\(618\) | 40.1682 | 1.61580 | ||||||||
\(619\) | 28.5798 | 1.14872 | 0.574359 | − | 0.818603i | \(-0.305251\pi\) | ||||
0.574359 | + | 0.818603i | \(0.305251\pi\) | |||||||
\(620\) | −39.4820 | −1.58564 | ||||||||
\(621\) | −46.6967 | −1.87388 | ||||||||
\(622\) | 68.0996 | 2.73055 | ||||||||
\(623\) | −2.16142 | −0.0865953 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.0521 | −1.08208 | ||||||||
\(626\) | −56.6830 | −2.26551 | ||||||||
\(627\) | 23.6353 | 0.943902 | ||||||||
\(628\) | 27.9127 | 1.11384 | ||||||||
\(629\) | −5.29722 | −0.211214 | ||||||||
\(630\) | −11.3240 | −0.451160 | ||||||||
\(631\) | 22.7451 | 0.905469 | 0.452735 | − | 0.891645i | \(-0.350448\pi\) | ||||
0.452735 | + | 0.891645i | \(0.350448\pi\) | |||||||
\(632\) | 31.2628 | 1.24357 | ||||||||
\(633\) | −35.3161 | −1.40369 | ||||||||
\(634\) | −56.5772 | −2.24697 | ||||||||
\(635\) | 49.1701 | 1.95126 | ||||||||
\(636\) | 82.3489 | 3.26535 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.91791 | −0.115521 | ||||||||
\(639\) | 88.6437 | 3.50669 | ||||||||
\(640\) | −45.0526 | −1.78086 | ||||||||
\(641\) | −10.4900 | −0.414329 | −0.207165 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207165 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(642\) | 168.409 | 6.64658 | ||||||||
\(643\) | 35.6282 | 1.40504 | 0.702520 | − | 0.711664i | \(-0.252058\pi\) | ||||
0.702520 | + | 0.711664i | \(0.252058\pi\) | |||||||
\(644\) | −5.48689 | −0.216214 | ||||||||
\(645\) | 17.9447 | 0.706572 | ||||||||
\(646\) | 31.1636 | 1.22612 | ||||||||
\(647\) | 4.37246 | 0.171899 | 0.0859495 | − | 0.996299i | \(-0.472608\pi\) | ||||
0.0859495 | + | 0.996299i | \(0.472608\pi\) | |||||||
\(648\) | −142.482 | −5.59724 | ||||||||
\(649\) | 10.8892 | 0.427440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.71165 | −0.106278 | ||||||||
\(652\) | −22.5908 | −0.884724 | ||||||||
\(653\) | −23.0934 | −0.903716 | −0.451858 | − | 0.892090i | \(-0.649239\pi\) | ||||
−0.451858 | + | 0.892090i | \(0.649239\pi\) | |||||||
\(654\) | 45.0829 | 1.76288 | ||||||||
\(655\) | 8.81644 | 0.344487 | ||||||||
\(656\) | −79.7443 | −3.11349 | ||||||||
\(657\) | −10.1611 | −0.396421 | ||||||||
\(658\) | 4.63884 | 0.180841 | ||||||||
\(659\) | 30.0102 | 1.16903 | 0.584516 | − | 0.811383i | \(-0.301285\pi\) | ||||
0.584516 | + | 0.811383i | \(0.301285\pi\) | |||||||
\(660\) | 37.9676 | 1.47789 | ||||||||
\(661\) | −35.0403 | −1.36291 | −0.681455 | − | 0.731860i | \(-0.738653\pi\) | ||||
−0.681455 | + | 0.731860i | \(0.738653\pi\) | |||||||
\(662\) | 75.7136 | 2.94269 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 78.8291 | 3.05916 | ||||||||
\(665\) | 4.70762 | 0.182554 | ||||||||
\(666\) | −62.6977 | −2.42949 | ||||||||
\(667\) | −4.30064 | −0.166521 | ||||||||
\(668\) | −86.5346 | −3.34812 | ||||||||
\(669\) | 81.1659 | 3.13805 | ||||||||
\(670\) | −40.2223 | −1.55392 | ||||||||
\(671\) | 9.66466 | 0.373100 | ||||||||
\(672\) | −13.9795 | −0.539273 | ||||||||
\(673\) | −12.4420 | −0.479606 | −0.239803 | − | 0.970822i | \(-0.577083\pi\) | ||||
−0.239803 | + | 0.970822i | \(0.577083\pi\) | |||||||
\(674\) | 20.1196 | 0.774978 | ||||||||
\(675\) | 5.32622 | 0.205006 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5713 | 1.13652 | 0.568259 | − | 0.822849i | \(-0.307617\pi\) | ||||
0.568259 | + | 0.822849i | \(0.307617\pi\) | |||||||
\(678\) | 127.360 | 4.89123 | ||||||||
\(679\) | −3.39401 | −0.130250 | ||||||||
\(680\) | 30.8105 | 1.18153 | ||||||||
\(681\) | −31.3740 | −1.20225 | ||||||||
\(682\) | 8.72501 | 0.334098 | ||||||||
\(683\) | 13.5278 | 0.517628 | 0.258814 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258814 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(684\) | 266.407 | 10.1863 | ||||||||
\(685\) | 6.58271 | 0.251512 | ||||||||
\(686\) | 9.96994 | 0.380654 | ||||||||
\(687\) | −9.32111 | −0.355622 | ||||||||
\(688\) | 31.0919 | 1.18537 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 77.4784 | 2.94955 | ||||||||
\(691\) | 5.92854 | 0.225532 | 0.112766 | − | 0.993622i | \(-0.464029\pi\) | ||||
0.112766 | + | 0.993622i | \(0.464029\pi\) | |||||||
\(692\) | −13.8863 | −0.527876 | ||||||||
\(693\) | 1.80743 | 0.0686586 | ||||||||
\(694\) | −59.4571 | −2.25696 | ||||||||
\(695\) | −4.30229 | −0.163195 | ||||||||
\(696\) | −29.2039 | −1.10697 | ||||||||
\(697\) | 9.68581 | 0.366876 | ||||||||
\(698\) | 87.8156 | 3.32387 | ||||||||
\(699\) | −11.7270 | −0.443556 | ||||||||
\(700\) | 0.625833 | 0.0236543 | ||||||||
\(701\) | 0.404230 | 0.0152675 | 0.00763377 | − | 0.999971i | \(-0.497570\pi\) | ||||
0.00763377 | + | 0.999971i | \(0.497570\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.0647 | 0.983047 | ||||||||
\(704\) | 19.6837 | 0.741858 | ||||||||
\(705\) | −47.3105 | −1.78182 | ||||||||
\(706\) | 21.9958 | 0.827824 | ||||||||
\(707\) | 3.34566 | 0.125826 | ||||||||
\(708\) | 177.079 | 6.65505 | ||||||||
\(709\) | 22.1763 | 0.832849 | 0.416425 | − | 0.909170i | \(-0.363283\pi\) | ||||
0.416425 | + | 0.909170i | \(0.363283\pi\) | |||||||
\(710\) | −81.9609 | −3.07594 | ||||||||
\(711\) | −24.6619 | −0.924892 | ||||||||
\(712\) | 69.6050 | 2.60856 | ||||||||
\(713\) | 12.8596 | 0.481596 | ||||||||
\(714\) | 3.43822 | 0.128672 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −118.296 | −4.42091 | ||||||||
\(717\) | 25.5547 | 0.954358 | ||||||||
\(718\) | −40.7781 | −1.52183 | ||||||||
\(719\) | 8.69164 | 0.324144 | 0.162072 | − | 0.986779i | \(-0.448182\pi\) | ||||
0.162072 | + | 0.986779i | \(0.448182\pi\) | |||||||
\(720\) | 200.106 | 7.45752 | ||||||||
\(721\) | −1.27698 | −0.0475571 | ||||||||
\(722\) | −102.353 | −3.80918 | ||||||||
\(723\) | 14.4645 | 0.537939 | ||||||||
\(724\) | 106.386 | 3.95382 | ||||||||
\(725\) | 0.490530 | 0.0182178 | ||||||||
\(726\) | −8.39034 | −0.311395 | ||||||||
\(727\) | −24.2296 | −0.898627 | −0.449314 | − | 0.893374i | \(-0.648331\pi\) | ||||
−0.449314 | + | 0.893374i | \(0.648331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.65092 | 0.0611451 | ||||||||
\(730\) | 9.39502 | 0.347725 | ||||||||
\(731\) | −3.77645 | −0.139677 | ||||||||
\(732\) | 157.165 | 5.80900 | ||||||||
\(733\) | 6.69006 | 0.247103 | 0.123552 | − | 0.992338i | \(-0.460572\pi\) | ||||
0.123552 | + | 0.992338i | \(0.460572\pi\) | |||||||
\(734\) | −31.8266 | −1.17474 | ||||||||
\(735\) | −50.5810 | −1.86571 | ||||||||
\(736\) | 66.2959 | 2.44370 | ||||||||
\(737\) | 6.41989 | 0.236480 | ||||||||
\(738\) | 114.641 | 4.21999 | ||||||||
\(739\) | −32.0479 | −1.17890 | −0.589450 | − | 0.807805i | \(-0.700655\pi\) | ||||
−0.589450 | + | 0.807805i | \(0.700655\pi\) | |||||||
\(740\) | 41.8702 | 1.53918 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.62464 | −0.133065 | ||||||||
\(743\) | −27.7046 | −1.01638 | −0.508191 | − | 0.861244i | \(-0.669686\pi\) | ||||
−0.508191 | + | 0.861244i | \(0.669686\pi\) | |||||||
\(744\) | 87.3244 | 3.20147 | ||||||||
\(745\) | −12.6816 | −0.464619 | ||||||||
\(746\) | 84.3536 | 3.08841 | ||||||||
\(747\) | −62.1848 | −2.27522 | ||||||||
\(748\) | −7.99026 | −0.292153 | ||||||||
\(749\) | −5.35385 | −0.195626 | ||||||||
\(750\) | 89.1102 | 3.25384 | ||||||||
\(751\) | 30.0879 | 1.09792 | 0.548961 | − | 0.835848i | \(-0.315023\pi\) | ||||
0.548961 | + | 0.835848i | \(0.315023\pi\) | |||||||
\(752\) | −81.9727 | −2.98924 | ||||||||
\(753\) | −40.5084 | −1.47621 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0425 | 0.583845 | ||||||||
\(756\) | 16.3794 | 0.595711 | ||||||||
\(757\) | −18.0765 | −0.657003 | −0.328502 | − | 0.944503i | \(-0.606544\pi\) | ||||
−0.328502 | + | 0.944503i | \(0.606544\pi\) | |||||||
\(758\) | 74.8274 | 2.71785 | ||||||||
\(759\) | −12.3663 | −0.448870 | ||||||||
\(760\) | −151.601 | −5.49916 | ||||||||
\(761\) | 28.5069 | 1.03337 | 0.516687 | − | 0.856174i | \(-0.327165\pi\) | ||||
0.516687 | + | 0.856174i | \(0.327165\pi\) | |||||||
\(762\) | −176.701 | −6.40119 | ||||||||
\(763\) | −1.43322 | −0.0518861 | ||||||||
\(764\) | −40.0476 | −1.44887 | ||||||||
\(765\) | −24.3051 | −0.878752 | ||||||||
\(766\) | 53.9246 | 1.94838 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38.8144 | 1.40059 | ||||||||
\(769\) | 15.3331 | 0.552927 | 0.276464 | − | 0.961024i | \(-0.410837\pi\) | ||||
0.276464 | + | 0.961024i | \(0.410837\pi\) | |||||||
\(770\) | −1.67117 | −0.0602247 | ||||||||
\(771\) | −1.99707 | −0.0719228 | ||||||||
\(772\) | 39.2646 | 1.41316 | ||||||||
\(773\) | 22.6186 | 0.813536 | 0.406768 | − | 0.913532i | \(-0.366656\pi\) | ||||
0.406768 | + | 0.913532i | \(0.366656\pi\) | |||||||
\(774\) | −44.6980 | −1.60664 | ||||||||
\(775\) | −1.46676 | −0.0526877 | ||||||||
\(776\) | 109.299 | 3.92360 | ||||||||
\(777\) | 2.87567 | 0.103164 | ||||||||
\(778\) | 4.83155 | 0.173219 | ||||||||
\(779\) | −47.6585 | −1.70754 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0818 | 0.468103 | ||||||||
\(782\) | −16.3053 | −0.583075 | ||||||||
\(783\) | 12.8382 | 0.458799 | ||||||||
\(784\) | −87.6392 | −3.12997 | ||||||||
\(785\) | 12.5302 | 0.447222 | ||||||||
\(786\) | −31.6833 | −1.13011 | ||||||||
\(787\) | −13.6903 | −0.488008 | −0.244004 | − | 0.969774i | \(-0.578461\pi\) | ||||
−0.244004 | + | 0.969774i | \(0.578461\pi\) | |||||||
\(788\) | −97.8596 | −3.48610 | ||||||||
\(789\) | 45.4858 | 1.61934 | ||||||||
\(790\) | 22.8026 | 0.811280 | ||||||||
\(791\) | −4.04887 | −0.143961 | ||||||||
\(792\) | −58.2055 | −2.06824 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.7878 | 0.453823 | ||||||||
\(795\) | 36.9669 | 1.31108 | ||||||||
\(796\) | 46.9901 | 1.66552 | ||||||||
\(797\) | 33.7231 | 1.19453 | 0.597266 | − | 0.802043i | \(-0.296254\pi\) | ||||
0.597266 | + | 0.802043i | \(0.296254\pi\) | |||||||
\(798\) | −16.9176 | −0.598876 | ||||||||
\(799\) | 9.95647 | 0.352234 | ||||||||
\(800\) | −7.56170 | −0.267346 | ||||||||
\(801\) | −54.9083 | −1.94009 | ||||||||
\(802\) | −78.7376 | −2.78032 | ||||||||
\(803\) | −1.49954 | −0.0529176 | ||||||||
\(804\) | 104.399 | 3.68188 | ||||||||
\(805\) | −2.46310 | −0.0868128 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.7975 | −1.64735 | ||||||||
\(808\) | −107.742 | −3.79034 | ||||||||
\(809\) | −5.96962 | −0.209881 | −0.104940 | − | 0.994479i | \(-0.533465\pi\) | ||||
−0.104940 | + | 0.994479i | \(0.533465\pi\) | |||||||
\(810\) | −103.924 | −3.65153 | ||||||||
\(811\) | −34.4025 | −1.20803 | −0.604017 | − | 0.796971i | \(-0.706434\pi\) | ||||
−0.604017 | + | 0.796971i | \(0.706434\pi\) | |||||||
\(812\) | 1.50849 | 0.0529377 | ||||||||
\(813\) | −66.8094 | −2.34311 | ||||||||
\(814\) | −9.25276 | −0.324309 | ||||||||
\(815\) | −10.1411 | −0.355229 | ||||||||
\(816\) | −60.7567 | −2.12691 | ||||||||
\(817\) | 18.5818 | 0.650095 | ||||||||
\(818\) | −32.8968 | −1.15021 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −76.5583 | −2.67353 | ||||||||
\(821\) | −43.5132 | −1.51862 | −0.759311 | − | 0.650728i | \(-0.774464\pi\) | ||||
−0.759311 | + | 0.650728i | \(0.774464\pi\) | |||||||
\(822\) | −23.6560 | −0.825098 | ||||||||
\(823\) | −51.6931 | −1.80191 | −0.900953 | − | 0.433916i | \(-0.857132\pi\) | ||||
−0.900953 | + | 0.433916i | \(0.857132\pi\) | |||||||
\(824\) | 41.1231 | 1.43259 | ||||||||
\(825\) | 1.41050 | 0.0491074 | ||||||||
\(826\) | −7.79425 | −0.271197 | ||||||||
\(827\) | −48.9877 | −1.70347 | −0.851734 | − | 0.523974i | \(-0.824449\pi\) | ||||
−0.851734 | + | 0.523974i | \(0.824449\pi\) | |||||||
\(828\) | −139.388 | −4.84408 | ||||||||
\(829\) | 41.8011 | 1.45181 | 0.725906 | − | 0.687794i | \(-0.241421\pi\) | ||||
0.725906 | + | 0.687794i | \(0.241421\pi\) | |||||||
\(830\) | 57.4967 | 1.99574 | ||||||||
\(831\) | 74.7327 | 2.59245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6447 | 0.368818 | ||||||||
\(834\) | 15.4609 | 0.535369 | ||||||||
\(835\) | −38.8459 | −1.34432 | ||||||||
\(836\) | 39.3156 | 1.35976 | ||||||||
\(837\) | −38.3882 | −1.32689 | ||||||||
\(838\) | −97.0297 | −3.35183 | ||||||||
\(839\) | 30.6863 | 1.05941 | 0.529705 | − | 0.848182i | \(-0.322303\pi\) | ||||
0.529705 | + | 0.848182i | \(0.322303\pi\) | |||||||
\(840\) | −16.7259 | −0.577099 | ||||||||
\(841\) | −27.8176 | −0.959229 | ||||||||
\(842\) | −3.71573 | −0.128052 | ||||||||
\(843\) | 61.2741 | 2.11039 | ||||||||
\(844\) | −58.7458 | −2.02211 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 117.844 | 4.05158 | ||||||||
\(847\) | 0.266736 | 0.00916514 | ||||||||
\(848\) | 64.0508 | 2.19951 | ||||||||
\(849\) | −4.37074 | −0.150003 | ||||||||
\(850\) | 1.85978 | 0.0637898 | ||||||||
\(851\) | −13.6374 | −0.467485 | ||||||||
\(852\) | 212.734 | 7.28816 | ||||||||
\(853\) | −41.4726 | −1.42000 | −0.709998 | − | 0.704204i | \(-0.751304\pi\) | ||||
−0.709998 | + | 0.704204i | \(0.751304\pi\) | |||||||
\(854\) | −6.91774 | −0.236720 | ||||||||
\(855\) | 119.592 | 4.08995 | ||||||||
\(856\) | 172.412 | 5.89294 | ||||||||
\(857\) | −24.1190 | −0.823890 | −0.411945 | − | 0.911209i | \(-0.635150\pi\) | ||||
−0.411945 | + | 0.911209i | \(0.635150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.9287 | −1.63531 | −0.817653 | − | 0.575712i | \(-0.804725\pi\) | ||||
−0.817653 | + | 0.575712i | \(0.804725\pi\) | |||||||
\(860\) | 29.8497 | 1.01787 | ||||||||
\(861\) | −5.25807 | −0.179195 | ||||||||
\(862\) | 0.0822220 | 0.00280049 | ||||||||
\(863\) | −32.9887 | −1.12295 | −0.561474 | − | 0.827495i | \(-0.689765\pi\) | ||||
−0.561474 | + | 0.827495i | \(0.689765\pi\) | |||||||
\(864\) | −197.905 | −6.73288 | ||||||||
\(865\) | −6.23363 | −0.211950 | ||||||||
\(866\) | −36.3308 | −1.23457 | ||||||||
\(867\) | −45.7740 | −1.55457 | ||||||||
\(868\) | −4.51063 | −0.153101 | ||||||||
\(869\) | −3.63953 | −0.123462 | ||||||||
\(870\) | −21.3009 | −0.722168 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 46.1546 | 1.56299 | ||||||||
\(873\) | −86.2211 | −2.91814 | ||||||||
\(874\) | 80.2291 | 2.71379 | ||||||||
\(875\) | −2.83288 | −0.0957688 | ||||||||
\(876\) | −24.3853 | −0.823904 | ||||||||
\(877\) | −8.41464 | −0.284142 | −0.142071 | − | 0.989856i | \(-0.545376\pi\) | ||||
−0.142071 | + | 0.989856i | \(0.545376\pi\) | |||||||
\(878\) | −41.8548 | −1.41253 | ||||||||
\(879\) | 62.7822 | 2.11759 | ||||||||
\(880\) | 29.5311 | 0.995494 | ||||||||
\(881\) | −20.8178 | −0.701369 | −0.350684 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(882\) | 125.991 | 4.24233 | ||||||||
\(883\) | 42.2995 | 1.42349 | 0.711746 | − | 0.702437i | \(-0.247905\pi\) | ||||
0.711746 | + | 0.702437i | \(0.247905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 79.4919 | 2.67209 | ||||||||
\(886\) | −43.8240 | −1.47230 | ||||||||
\(887\) | −34.4350 | −1.15622 | −0.578108 | − | 0.815961i | \(-0.696209\pi\) | ||||
−0.578108 | + | 0.815961i | \(0.696209\pi\) | |||||||
\(888\) | −92.6063 | −3.10766 | ||||||||
\(889\) | 5.61745 | 0.188403 | ||||||||
\(890\) | 50.7688 | 1.70177 | ||||||||
\(891\) | 16.5874 | 0.555699 | ||||||||
\(892\) | 135.014 | 4.52059 | ||||||||
\(893\) | −48.9902 | −1.63940 | ||||||||
\(894\) | 45.5735 | 1.52421 | ||||||||
\(895\) | −53.1036 | −1.77506 | ||||||||
\(896\) | −5.14705 | −0.171951 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.89273 | 0.263384 | ||||||||
\(899\) | −3.53545 | −0.117914 | ||||||||
\(900\) | 15.8986 | 0.529953 | ||||||||
\(901\) | −7.77966 | −0.259178 | ||||||||
\(902\) | 16.9184 | 0.563321 | ||||||||
\(903\) | 2.05010 | 0.0682230 | ||||||||
\(904\) | 130.388 | 4.33663 | ||||||||
\(905\) | 47.7575 | 1.58751 | ||||||||
\(906\) | −57.6512 | −1.91533 | ||||||||
\(907\) | −8.62987 | −0.286550 | −0.143275 | − | 0.989683i | \(-0.545763\pi\) | ||||
−0.143275 | + | 0.989683i | \(0.545763\pi\) | |||||||
\(908\) | −52.1884 | −1.73193 | ||||||||
\(909\) | 84.9927 | 2.81903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.0264 | 1.42553 | 0.712763 | − | 0.701405i | \(-0.247443\pi\) | ||||
0.712763 | + | 0.701405i | \(0.247443\pi\) | |||||||
\(912\) | 298.950 | 9.89921 | ||||||||
\(913\) | −9.17706 | −0.303716 | ||||||||
\(914\) | 68.8088 | 2.27599 | ||||||||
\(915\) | 70.5525 | 2.33239 | ||||||||
\(916\) | −15.5050 | −0.512300 | ||||||||
\(917\) | 1.00724 | 0.0332619 | ||||||||
\(918\) | 48.6742 | 1.60649 | ||||||||
\(919\) | −39.5049 | −1.30315 | −0.651574 | − | 0.758585i | \(-0.725891\pi\) | ||||
−0.651574 | + | 0.758585i | \(0.725891\pi\) | |||||||
\(920\) | 79.3202 | 2.61511 | ||||||||
\(921\) | 13.5189 | 0.445462 | ||||||||
\(922\) | −68.2697 | −2.24834 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.33762 | 0.142697 | ||||||||
\(925\) | 1.55548 | 0.0511439 | ||||||||
\(926\) | 28.4627 | 0.935341 | ||||||||
\(927\) | −32.4402 | −1.06548 | ||||||||
\(928\) | −18.2265 | −0.598315 | ||||||||
\(929\) | 23.8514 | 0.782539 | 0.391269 | − | 0.920276i | \(-0.372036\pi\) | ||||
0.391269 | + | 0.920276i | \(0.372036\pi\) | |||||||
\(930\) | 63.6930 | 2.08858 | ||||||||
\(931\) | −52.3768 | −1.71658 | ||||||||
\(932\) | −19.5070 | −0.638974 | ||||||||
\(933\) | −79.3472 | −2.59771 | ||||||||
\(934\) | 13.8871 | 0.454399 | ||||||||
\(935\) | −3.58688 | −0.117303 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8554 | −0.713985 | −0.356993 | − | 0.934107i | \(-0.616198\pi\) | ||||
−0.356993 | + | 0.934107i | \(0.616198\pi\) | |||||||
\(938\) | −4.59521 | −0.150039 | ||||||||
\(939\) | 66.0449 | 2.15529 | ||||||||
\(940\) | −78.6977 | −2.56683 | ||||||||
\(941\) | −14.3904 | −0.469112 | −0.234556 | − | 0.972103i | \(-0.575364\pi\) | ||||
−0.234556 | + | 0.972103i | \(0.575364\pi\) | |||||||
\(942\) | −45.0292 | −1.46713 | ||||||||
\(943\) | 24.9356 | 0.812016 | ||||||||
\(944\) | 137.732 | 4.48279 | ||||||||
\(945\) | 7.35279 | 0.239186 | ||||||||
\(946\) | −6.59640 | −0.214467 | ||||||||
\(947\) | −18.5363 | −0.602349 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(948\) | −59.1855 | −1.92226 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.15091 | −0.296895 | ||||||||
\(951\) | 65.9216 | 2.13766 | ||||||||
\(952\) | 3.51996 | 0.114082 | ||||||||
\(953\) | 15.7252 | 0.509388 | 0.254694 | − | 0.967022i | \(-0.418025\pi\) | ||||
0.254694 | + | 0.967022i | \(0.418025\pi\) | |||||||
\(954\) | −92.0799 | −2.98120 | ||||||||
\(955\) | −17.9776 | −0.581742 | ||||||||
\(956\) | 42.5084 | 1.37482 | ||||||||
\(957\) | 3.39984 | 0.109901 | ||||||||
\(958\) | −48.0903 | −1.55373 | ||||||||
\(959\) | 0.752043 | 0.0242847 | ||||||||
\(960\) | 143.692 | 4.63765 | ||||||||
\(961\) | −20.4284 | −0.658982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −136.009 | −4.38282 | ||||||||
\(964\) | 24.0606 | 0.774939 | ||||||||
\(965\) | 17.6261 | 0.567405 | ||||||||
\(966\) | 8.85153 | 0.284793 | ||||||||
\(967\) | 40.7288 | 1.30975 | 0.654874 | − | 0.755738i | \(-0.272722\pi\) | ||||
0.654874 | + | 0.755738i | \(0.272722\pi\) | |||||||
\(968\) | −8.58980 | −0.276087 | ||||||||
\(969\) | −36.3107 | −1.16647 | ||||||||
\(970\) | 79.7209 | 2.55968 | ||||||||
\(971\) | 51.9398 | 1.66683 | 0.833414 | − | 0.552649i | \(-0.186383\pi\) | ||||
0.833414 | + | 0.552649i | \(0.186383\pi\) | |||||||
\(972\) | 85.5221 | 2.74312 | ||||||||
\(973\) | −0.491516 | −0.0157573 | ||||||||
\(974\) | −17.3458 | −0.555796 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 122.243 | 3.91290 | ||||||||
\(977\) | 6.50233 | 0.208028 | 0.104014 | − | 0.994576i | \(-0.466831\pi\) | ||||
0.104014 | + | 0.994576i | \(0.466831\pi\) | |||||||
\(978\) | 36.4438 | 1.16535 | ||||||||
\(979\) | −8.10322 | −0.258980 | ||||||||
\(980\) | −84.1379 | −2.68769 | ||||||||
\(981\) | −36.4093 | −1.16246 | ||||||||
\(982\) | −44.8345 | −1.43073 | ||||||||
\(983\) | −10.4399 | −0.332981 | −0.166491 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(984\) | 169.328 | 5.39798 | ||||||||
\(985\) | −43.9298 | −1.39972 | ||||||||
\(986\) | 4.48276 | 0.142760 | ||||||||
\(987\) | −5.40500 | −0.172043 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.72228 | −0.309151 | ||||||||
\(990\) | −42.4542 | −1.34928 | ||||||||
\(991\) | −25.3194 | −0.804296 | −0.402148 | − | 0.915575i | \(-0.631736\pi\) | ||||
−0.402148 | + | 0.915575i | \(0.631736\pi\) | |||||||
\(992\) | 54.5002 | 1.73038 | ||||||||
\(993\) | −88.2186 | −2.79953 | ||||||||
\(994\) | −9.36364 | −0.296997 | ||||||||
\(995\) | 21.0941 | 0.668729 | ||||||||
\(996\) | −149.236 | −4.72873 | ||||||||
\(997\) | −21.2428 | −0.672766 | −0.336383 | − | 0.941725i | \(-0.609204\pi\) | ||||
−0.336383 | + | 0.941725i | \(0.609204\pi\) | |||||||
\(998\) | 50.2490 | 1.59060 | ||||||||
\(999\) | 40.7102 | 1.28801 |
(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 | 1859.2.a.t.1.3 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.19 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.19 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.3 | yes | 21 | 1.1 | even | 1 | trivial |