Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,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, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30249 | −0.814052 | −0.407026 | − | 0.913416i | \(-0.633434\pi\) | ||||
−0.407026 | + | 0.913416i | \(0.633434\pi\) | |||||||
\(3\) | 4.54839 | 0.875339 | 0.437669 | − | 0.899136i | \(-0.355804\pi\) | ||||
0.437669 | + | 0.899136i | \(0.355804\pi\) | |||||||
\(4\) | −2.69855 | −0.337319 | ||||||||
\(5\) | −4.16672 | −0.372683 | −0.186341 | − | 0.982485i | \(-0.559663\pi\) | ||||
−0.186341 | + | 0.982485i | \(0.559663\pi\) | |||||||
\(6\) | −10.4726 | −0.712571 | ||||||||
\(7\) | −17.3608 | −0.937394 | −0.468697 | − | 0.883359i | \(-0.655276\pi\) | ||||
−0.468697 | + | 0.883359i | \(0.655276\pi\) | |||||||
\(8\) | 24.6333 | 1.08865 | ||||||||
\(9\) | −6.31212 | −0.233782 | ||||||||
\(10\) | 9.59382 | 0.303383 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −12.2741 | −0.295268 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 39.9730 | 0.763088 | ||||||||
\(15\) | −18.9519 | −0.326223 | ||||||||
\(16\) | −35.1294 | −0.548897 | ||||||||
\(17\) | 1.39107 | 0.0198462 | 0.00992308 | − | 0.999951i | \(-0.496841\pi\) | ||||
0.00992308 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(18\) | 14.5336 | 0.190311 | ||||||||
\(19\) | 58.9335 | 0.711593 | 0.355797 | − | 0.934563i | \(-0.384210\pi\) | ||||
0.355797 | + | 0.934563i | \(0.384210\pi\) | |||||||
\(20\) | 11.2441 | 0.125713 | ||||||||
\(21\) | −78.9636 | −0.820537 | ||||||||
\(22\) | −25.3274 | −0.245446 | ||||||||
\(23\) | 46.6310 | 0.422749 | 0.211375 | − | 0.977405i | \(-0.432206\pi\) | ||||
0.211375 | + | 0.977405i | \(0.432206\pi\) | |||||||
\(24\) | 112.042 | 0.952935 | ||||||||
\(25\) | −107.638 | −0.861108 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −151.517 | −1.07998 | ||||||||
\(28\) | 46.8489 | 0.316200 | ||||||||
\(29\) | 175.166 | 1.12164 | 0.560818 | − | 0.827939i | \(-0.310487\pi\) | ||||
0.560818 | + | 0.827939i | \(0.310487\pi\) | |||||||
\(30\) | 43.6364 | 0.265563 | ||||||||
\(31\) | −33.3275 | −0.193090 | −0.0965452 | − | 0.995329i | \(-0.530779\pi\) | ||||
−0.0965452 | + | 0.995329i | \(0.530779\pi\) | |||||||
\(32\) | −116.181 | −0.641816 | ||||||||
\(33\) | 50.0323 | 0.263925 | ||||||||
\(34\) | −3.20293 | −0.0161558 | ||||||||
\(35\) | 72.3375 | 0.349350 | ||||||||
\(36\) | 17.0336 | 0.0788592 | ||||||||
\(37\) | 376.578 | 1.67322 | 0.836610 | − | 0.547799i | \(-0.184534\pi\) | ||||
0.836610 | + | 0.547799i | \(0.184534\pi\) | |||||||
\(38\) | −135.694 | −0.579274 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −102.640 | −0.405720 | ||||||||
\(41\) | −270.238 | −1.02937 | −0.514683 | − | 0.857380i | \(-0.672090\pi\) | ||||
−0.514683 | + | 0.857380i | \(0.672090\pi\) | |||||||
\(42\) | 181.813 | 0.667960 | ||||||||
\(43\) | −125.758 | −0.445997 | −0.222998 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222998 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(44\) | −29.6840 | −0.101705 | ||||||||
\(45\) | 26.3008 | 0.0871266 | ||||||||
\(46\) | −107.367 | −0.344140 | ||||||||
\(47\) | 562.550 | 1.74588 | 0.872940 | − | 0.487828i | \(-0.162211\pi\) | ||||
0.872940 | + | 0.487828i | \(0.162211\pi\) | |||||||
\(48\) | −159.782 | −0.480471 | ||||||||
\(49\) | −41.6034 | −0.121293 | ||||||||
\(50\) | 247.836 | 0.700987 | ||||||||
\(51\) | 6.32715 | 0.0173721 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −356.005 | −0.922662 | −0.461331 | − | 0.887228i | \(-0.652628\pi\) | ||||
−0.461331 | + | 0.887228i | \(0.652628\pi\) | |||||||
\(54\) | 348.865 | 0.879158 | ||||||||
\(55\) | −45.8339 | −0.112368 | ||||||||
\(56\) | −427.653 | −1.02049 | ||||||||
\(57\) | 268.053 | 0.622885 | ||||||||
\(58\) | −403.317 | −0.913070 | ||||||||
\(59\) | 138.690 | 0.306032 | 0.153016 | − | 0.988224i | \(-0.451101\pi\) | ||||
0.153016 | + | 0.988224i | \(0.451101\pi\) | |||||||
\(60\) | 51.1426 | 0.110041 | ||||||||
\(61\) | 358.274 | 0.752006 | 0.376003 | − | 0.926619i | \(-0.377298\pi\) | ||||
0.376003 | + | 0.926619i | \(0.377298\pi\) | |||||||
\(62\) | 76.7362 | 0.157186 | ||||||||
\(63\) | 109.583 | 0.219146 | ||||||||
\(64\) | 548.541 | 1.07137 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −115.199 | −0.214848 | ||||||||
\(67\) | 291.047 | 0.530703 | 0.265351 | − | 0.964152i | \(-0.414512\pi\) | ||||
0.265351 | + | 0.964152i | \(0.414512\pi\) | |||||||
\(68\) | −3.75388 | −0.00669448 | ||||||||
\(69\) | 212.096 | 0.370049 | ||||||||
\(70\) | −166.556 | −0.284389 | ||||||||
\(71\) | 90.2883 | 0.150919 | 0.0754595 | − | 0.997149i | \(-0.475958\pi\) | ||||
0.0754595 | + | 0.997149i | \(0.475958\pi\) | |||||||
\(72\) | −155.488 | −0.254507 | ||||||||
\(73\) | 366.526 | 0.587652 | 0.293826 | − | 0.955859i | \(-0.405071\pi\) | ||||
0.293826 | + | 0.955859i | \(0.405071\pi\) | |||||||
\(74\) | −867.067 | −1.36209 | ||||||||
\(75\) | −489.582 | −0.753761 | ||||||||
\(76\) | −159.035 | −0.240034 | ||||||||
\(77\) | −190.969 | −0.282635 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 270.365 | 0.385044 | 0.192522 | − | 0.981293i | \(-0.438333\pi\) | ||||
0.192522 | + | 0.981293i | \(0.438333\pi\) | |||||||
\(80\) | 146.374 | 0.204564 | ||||||||
\(81\) | −518.730 | −0.711563 | ||||||||
\(82\) | 622.219 | 0.837958 | ||||||||
\(83\) | −746.776 | −0.987583 | −0.493791 | − | 0.869580i | \(-0.664389\pi\) | ||||
−0.493791 | + | 0.869580i | \(0.664389\pi\) | |||||||
\(84\) | 213.087 | 0.276782 | ||||||||
\(85\) | −5.79621 | −0.00739632 | ||||||||
\(86\) | 289.556 | 0.363065 | ||||||||
\(87\) | 796.722 | 0.981811 | ||||||||
\(88\) | 270.966 | 0.328240 | ||||||||
\(89\) | 1485.51 | 1.76926 | 0.884628 | − | 0.466297i | \(-0.154412\pi\) | ||||
0.884628 | + | 0.466297i | \(0.154412\pi\) | |||||||
\(90\) | −60.5574 | −0.0709256 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −125.836 | −0.142601 | ||||||||
\(93\) | −151.587 | −0.169019 | ||||||||
\(94\) | −1295.26 | −1.42124 | ||||||||
\(95\) | −245.559 | −0.265198 | ||||||||
\(96\) | −528.438 | −0.561807 | ||||||||
\(97\) | 869.043 | 0.909670 | 0.454835 | − | 0.890576i | \(-0.349698\pi\) | ||||
0.454835 | + | 0.890576i | \(0.349698\pi\) | |||||||
\(98\) | 95.7913 | 0.0987386 | ||||||||
\(99\) | −69.4334 | −0.0704880 | ||||||||
\(100\) | 290.468 | 0.290468 | ||||||||
\(101\) | −676.974 | −0.666945 | −0.333472 | − | 0.942760i | \(-0.608220\pi\) | ||||
−0.333472 | + | 0.942760i | \(0.608220\pi\) | |||||||
\(102\) | −14.5682 | −0.0141418 | ||||||||
\(103\) | −145.684 | −0.139365 | −0.0696827 | − | 0.997569i | \(-0.522199\pi\) | ||||
−0.0696827 | + | 0.997569i | \(0.522199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 329.019 | 0.305800 | ||||||||
\(106\) | 819.698 | 0.751095 | ||||||||
\(107\) | −1759.90 | −1.59005 | −0.795027 | − | 0.606574i | \(-0.792543\pi\) | ||||
−0.795027 | + | 0.606574i | \(0.792543\pi\) | |||||||
\(108\) | 408.875 | 0.364297 | ||||||||
\(109\) | −1586.57 | −1.39418 | −0.697090 | − | 0.716984i | \(-0.745522\pi\) | ||||
−0.697090 | + | 0.716984i | \(0.745522\pi\) | |||||||
\(110\) | 105.532 | 0.0914735 | ||||||||
\(111\) | 1712.83 | 1.46463 | ||||||||
\(112\) | 609.874 | 0.514533 | ||||||||
\(113\) | −1328.52 | −1.10599 | −0.552995 | − | 0.833185i | \(-0.686515\pi\) | ||||
−0.552995 | + | 0.833185i | \(0.686515\pi\) | |||||||
\(114\) | −617.188 | −0.507061 | ||||||||
\(115\) | −194.298 | −0.157551 | ||||||||
\(116\) | −472.693 | −0.378349 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −319.332 | −0.249126 | ||||||||
\(119\) | −24.1501 | −0.0186037 | ||||||||
\(120\) | −466.847 | −0.355142 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −824.923 | −0.612172 | ||||||||
\(123\) | −1229.15 | −0.901044 | ||||||||
\(124\) | 89.9360 | 0.0651330 | ||||||||
\(125\) | 969.339 | 0.693602 | ||||||||
\(126\) | −252.314 | −0.178396 | ||||||||
\(127\) | 587.994 | 0.410835 | 0.205417 | − | 0.978674i | \(-0.434145\pi\) | ||||
0.205417 | + | 0.978674i | \(0.434145\pi\) | |||||||
\(128\) | −333.560 | −0.230335 | ||||||||
\(129\) | −571.995 | −0.390398 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −579.068 | −0.386209 | −0.193104 | − | 0.981178i | \(-0.561856\pi\) | ||||
−0.193104 | + | 0.981178i | \(0.561856\pi\) | |||||||
\(132\) | −135.015 | −0.0890267 | ||||||||
\(133\) | −1023.13 | −0.667043 | ||||||||
\(134\) | −670.133 | −0.432020 | ||||||||
\(135\) | 631.327 | 0.402489 | ||||||||
\(136\) | 34.2667 | 0.0216055 | ||||||||
\(137\) | −1413.01 | −0.881178 | −0.440589 | − | 0.897709i | \(-0.645230\pi\) | ||||
−0.440589 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(138\) | −488.348 | −0.301239 | ||||||||
\(139\) | 1506.31 | 0.919162 | 0.459581 | − | 0.888136i | \(-0.348000\pi\) | ||||
0.459581 | + | 0.888136i | \(0.348000\pi\) | |||||||
\(140\) | −195.206 | −0.117842 | ||||||||
\(141\) | 2558.70 | 1.52824 | ||||||||
\(142\) | −207.888 | −0.122856 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 221.741 | 0.128323 | ||||||||
\(145\) | −729.866 | −0.418014 | ||||||||
\(146\) | −843.921 | −0.478379 | ||||||||
\(147\) | −189.229 | −0.106172 | ||||||||
\(148\) | −1016.22 | −0.564408 | ||||||||
\(149\) | −592.565 | −0.325804 | −0.162902 | − | 0.986642i | \(-0.552085\pi\) | ||||
−0.162902 | + | 0.986642i | \(0.552085\pi\) | |||||||
\(150\) | 1127.26 | 0.613601 | ||||||||
\(151\) | −687.583 | −0.370561 | −0.185281 | − | 0.982686i | \(-0.559319\pi\) | ||||
−0.185281 | + | 0.982686i | \(0.559319\pi\) | |||||||
\(152\) | 1451.73 | 0.774674 | ||||||||
\(153\) | −8.78063 | −0.00463968 | ||||||||
\(154\) | 439.703 | 0.230080 | ||||||||
\(155\) | 138.866 | 0.0719614 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −304.141 | −0.154606 | −0.0773029 | − | 0.997008i | \(-0.524631\pi\) | ||||
−0.0773029 | + | 0.997008i | \(0.524631\pi\) | |||||||
\(158\) | −622.513 | −0.313446 | ||||||||
\(159\) | −1619.25 | −0.807642 | ||||||||
\(160\) | 484.094 | 0.239194 | ||||||||
\(161\) | −809.550 | −0.396282 | ||||||||
\(162\) | 1194.37 | 0.579250 | ||||||||
\(163\) | −3724.50 | −1.78972 | −0.894862 | − | 0.446343i | \(-0.852726\pi\) | ||||
−0.894862 | + | 0.446343i | \(0.852726\pi\) | |||||||
\(164\) | 729.250 | 0.347225 | ||||||||
\(165\) | −208.471 | −0.0983601 | ||||||||
\(166\) | 1719.44 | 0.803944 | ||||||||
\(167\) | 1404.56 | 0.650826 | 0.325413 | − | 0.945572i | \(-0.394497\pi\) | ||||
0.325413 | + | 0.945572i | \(0.394497\pi\) | |||||||
\(168\) | −1945.13 | −0.893276 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.3457 | 0.00602099 | ||||||||
\(171\) | −371.996 | −0.166358 | ||||||||
\(172\) | 339.363 | 0.150443 | ||||||||
\(173\) | 1353.10 | 0.594650 | 0.297325 | − | 0.954776i | \(-0.403906\pi\) | ||||
0.297325 | + | 0.954776i | \(0.403906\pi\) | |||||||
\(174\) | −1834.44 | −0.799246 | ||||||||
\(175\) | 1868.69 | 0.807197 | ||||||||
\(176\) | −386.424 | −0.165499 | ||||||||
\(177\) | 630.816 | 0.267882 | ||||||||
\(178\) | −3420.37 | −1.44027 | ||||||||
\(179\) | −3628.19 | −1.51499 | −0.757496 | − | 0.652840i | \(-0.773577\pi\) | ||||
−0.757496 | + | 0.652840i | \(0.773577\pi\) | |||||||
\(180\) | −70.9741 | −0.0293894 | ||||||||
\(181\) | −2868.20 | −1.17785 | −0.588927 | − | 0.808186i | \(-0.700450\pi\) | ||||
−0.588927 | + | 0.808186i | \(0.700450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1629.57 | 0.658260 | ||||||||
\(184\) | 1148.67 | 0.460225 | ||||||||
\(185\) | −1569.10 | −0.623580 | ||||||||
\(186\) | 349.027 | 0.137591 | ||||||||
\(187\) | 15.3018 | 0.00598384 | ||||||||
\(188\) | −1518.07 | −0.588918 | ||||||||
\(189\) | 2630.45 | 1.01236 | ||||||||
\(190\) | 565.397 | 0.215885 | ||||||||
\(191\) | 563.116 | 0.213328 | 0.106664 | − | 0.994295i | \(-0.465983\pi\) | ||||
0.106664 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(192\) | 2494.98 | 0.937811 | ||||||||
\(193\) | −713.977 | −0.266286 | −0.133143 | − | 0.991097i | \(-0.542507\pi\) | ||||
−0.133143 | + | 0.991097i | \(0.542507\pi\) | |||||||
\(194\) | −2000.96 | −0.740519 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 112.269 | 0.0409143 | ||||||||
\(197\) | −1436.96 | −0.519692 | −0.259846 | − | 0.965650i | \(-0.583672\pi\) | ||||
−0.259846 | + | 0.965650i | \(0.583672\pi\) | |||||||
\(198\) | 159.869 | 0.0573810 | ||||||||
\(199\) | −1614.93 | −0.575273 | −0.287637 | − | 0.957740i | \(-0.592870\pi\) | ||||
−0.287637 | + | 0.957740i | \(0.592870\pi\) | |||||||
\(200\) | −2651.49 | −0.937443 | ||||||||
\(201\) | 1323.80 | 0.464545 | ||||||||
\(202\) | 1558.72 | 0.542928 | ||||||||
\(203\) | −3041.01 | −1.05141 | ||||||||
\(204\) | −17.0741 | −0.00585994 | ||||||||
\(205\) | 1126.00 | 0.383627 | ||||||||
\(206\) | 335.435 | 0.113451 | ||||||||
\(207\) | −294.340 | −0.0988313 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 648.268 | 0.214553 | ||||||||
\(210\) | −757.563 | −0.248937 | ||||||||
\(211\) | −1856.32 | −0.605660 | −0.302830 | − | 0.953045i | \(-0.597931\pi\) | ||||
−0.302830 | + | 0.953045i | \(0.597931\pi\) | |||||||
\(212\) | 960.698 | 0.311231 | ||||||||
\(213\) | 410.666 | 0.132105 | ||||||||
\(214\) | 4052.14 | 1.29439 | ||||||||
\(215\) | 523.997 | 0.166215 | ||||||||
\(216\) | −3732.35 | −1.17571 | ||||||||
\(217\) | 578.592 | 0.181002 | ||||||||
\(218\) | 3653.05 | 1.13494 | ||||||||
\(219\) | 1667.10 | 0.514394 | ||||||||
\(220\) | 123.685 | 0.0379038 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3943.76 | −1.19229 | ||||||||
\(223\) | 323.796 | 0.0972332 | 0.0486166 | − | 0.998818i | \(-0.484519\pi\) | ||||
0.0486166 | + | 0.998818i | \(0.484519\pi\) | |||||||
\(224\) | 2017.00 | 0.601635 | ||||||||
\(225\) | 679.427 | 0.201312 | ||||||||
\(226\) | 3058.90 | 0.900333 | ||||||||
\(227\) | 1514.68 | 0.442875 | 0.221438 | − | 0.975175i | \(-0.428925\pi\) | ||||
0.221438 | + | 0.975175i | \(0.428925\pi\) | |||||||
\(228\) | −723.353 | −0.210111 | ||||||||
\(229\) | −3454.15 | −0.996755 | −0.498378 | − | 0.866960i | \(-0.666071\pi\) | ||||
−0.498378 | + | 0.866960i | \(0.666071\pi\) | |||||||
\(230\) | 447.369 | 0.128255 | ||||||||
\(231\) | −868.600 | −0.247401 | ||||||||
\(232\) | 4314.90 | 1.22107 | ||||||||
\(233\) | −6965.84 | −1.95857 | −0.979287 | − | 0.202479i | \(-0.935100\pi\) | ||||
−0.979287 | + | 0.202479i | \(0.935100\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2343.99 | −0.650659 | ||||||||
\(236\) | −374.262 | −0.103230 | ||||||||
\(237\) | 1229.73 | 0.337044 | ||||||||
\(238\) | 55.6053 | 0.0151444 | ||||||||
\(239\) | −2194.92 | −0.594048 | −0.297024 | − | 0.954870i | \(-0.595994\pi\) | ||||
−0.297024 | + | 0.954870i | \(0.595994\pi\) | |||||||
\(240\) | 665.768 | 0.179063 | ||||||||
\(241\) | 6112.18 | 1.63369 | 0.816847 | − | 0.576855i | \(-0.195720\pi\) | ||||
0.816847 | + | 0.576855i | \(0.195720\pi\) | |||||||
\(242\) | −278.601 | −0.0740048 | ||||||||
\(243\) | 1731.56 | 0.457118 | ||||||||
\(244\) | −966.821 | −0.253666 | ||||||||
\(245\) | 173.350 | 0.0452037 | ||||||||
\(246\) | 2830.10 | 0.733497 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −820.967 | −0.210207 | ||||||||
\(249\) | −3396.63 | −0.864469 | ||||||||
\(250\) | −2231.89 | −0.564629 | ||||||||
\(251\) | −3005.30 | −0.755749 | −0.377874 | − | 0.925857i | \(-0.623345\pi\) | ||||
−0.377874 | + | 0.925857i | \(0.623345\pi\) | |||||||
\(252\) | −295.716 | −0.0739221 | ||||||||
\(253\) | 512.941 | 0.127464 | ||||||||
\(254\) | −1353.85 | −0.334441 | ||||||||
\(255\) | −26.3634 | −0.00647428 | ||||||||
\(256\) | −3620.31 | −0.883865 | ||||||||
\(257\) | 3397.11 | 0.824537 | 0.412269 | − | 0.911062i | \(-0.364737\pi\) | ||||
0.412269 | + | 0.911062i | \(0.364737\pi\) | |||||||
\(258\) | 1317.01 | 0.317805 | ||||||||
\(259\) | −6537.69 | −1.56847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1105.67 | −0.262219 | ||||||||
\(262\) | 1333.30 | 0.314394 | ||||||||
\(263\) | 103.229 | 0.0242028 | 0.0121014 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121014 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(264\) | 1232.46 | 0.287321 | ||||||||
\(265\) | 1483.37 | 0.343860 | ||||||||
\(266\) | 2355.75 | 0.543008 | ||||||||
\(267\) | 6756.69 | 1.54870 | ||||||||
\(268\) | −785.406 | −0.179016 | ||||||||
\(269\) | −64.7352 | −0.0146728 | −0.00733638 | − | 0.999973i | \(-0.502335\pi\) | ||||
−0.00733638 | + | 0.999973i | \(0.502335\pi\) | |||||||
\(270\) | −1453.62 | −0.327647 | ||||||||
\(271\) | 2540.69 | 0.569506 | 0.284753 | − | 0.958601i | \(-0.408088\pi\) | ||||
0.284753 | + | 0.958601i | \(0.408088\pi\) | |||||||
\(272\) | −48.8676 | −0.0108935 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3253.43 | 0.717325 | ||||||||
\(275\) | −1184.02 | −0.259634 | ||||||||
\(276\) | −572.351 | −0.124824 | ||||||||
\(277\) | 563.954 | 0.122327 | 0.0611637 | − | 0.998128i | \(-0.480519\pi\) | ||||
0.0611637 | + | 0.998128i | \(0.480519\pi\) | |||||||
\(278\) | −3468.26 | −0.748246 | ||||||||
\(279\) | 210.368 | 0.0451411 | ||||||||
\(280\) | 1781.91 | 0.380319 | ||||||||
\(281\) | 1398.31 | 0.296855 | 0.148427 | − | 0.988923i | \(-0.452579\pi\) | ||||
0.148427 | + | 0.988923i | \(0.452579\pi\) | |||||||
\(282\) | −5891.37 | −1.24406 | ||||||||
\(283\) | 6039.06 | 1.26850 | 0.634249 | − | 0.773129i | \(-0.281310\pi\) | ||||
0.634249 | + | 0.773129i | \(0.281310\pi\) | |||||||
\(284\) | −243.647 | −0.0509078 | ||||||||
\(285\) | −1116.90 | −0.232138 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4691.53 | 0.964922 | ||||||||
\(288\) | 733.350 | 0.150045 | ||||||||
\(289\) | −4911.06 | −0.999606 | ||||||||
\(290\) | 1680.51 | 0.340285 | ||||||||
\(291\) | 3952.75 | 0.796269 | ||||||||
\(292\) | −989.088 | −0.198226 | ||||||||
\(293\) | 4006.30 | 0.798807 | 0.399404 | − | 0.916775i | \(-0.369217\pi\) | ||||
0.399404 | + | 0.916775i | \(0.369217\pi\) | |||||||
\(294\) | 435.697 | 0.0864297 | ||||||||
\(295\) | −577.882 | −0.114053 | ||||||||
\(296\) | 9276.36 | 1.82155 | ||||||||
\(297\) | −1666.68 | −0.325625 | ||||||||
\(298\) | 1364.37 | 0.265222 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1321.16 | 0.254258 | ||||||||
\(301\) | 2183.25 | 0.418075 | ||||||||
\(302\) | 1583.15 | 0.301656 | ||||||||
\(303\) | −3079.14 | −0.583803 | ||||||||
\(304\) | −2070.30 | −0.390592 | ||||||||
\(305\) | −1492.83 | −0.280259 | ||||||||
\(306\) | 20.2173 | 0.00377695 | ||||||||
\(307\) | −3450.64 | −0.641492 | −0.320746 | − | 0.947165i | \(-0.603934\pi\) | ||||
−0.320746 | + | 0.947165i | \(0.603934\pi\) | |||||||
\(308\) | 515.338 | 0.0953380 | ||||||||
\(309\) | −662.626 | −0.121992 | ||||||||
\(310\) | −319.738 | −0.0585804 | ||||||||
\(311\) | −928.020 | −0.169206 | −0.0846032 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846032 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8253.90 | 1.49054 | 0.745268 | − | 0.666765i | \(-0.232321\pi\) | ||||
0.745268 | + | 0.666765i | \(0.232321\pi\) | |||||||
\(314\) | 700.281 | 0.125857 | ||||||||
\(315\) | −456.603 | −0.0816720 | ||||||||
\(316\) | −729.594 | −0.129883 | ||||||||
\(317\) | −8757.50 | −1.55164 | −0.775820 | − | 0.630954i | \(-0.782664\pi\) | ||||
−0.775820 | + | 0.630954i | \(0.782664\pi\) | |||||||
\(318\) | 3728.31 | 0.657463 | ||||||||
\(319\) | 1926.82 | 0.338186 | ||||||||
\(320\) | −2285.62 | −0.399281 | ||||||||
\(321\) | −8004.71 | −1.39184 | ||||||||
\(322\) | 1863.98 | 0.322595 | ||||||||
\(323\) | 81.9808 | 0.0141224 | ||||||||
\(324\) | 1399.82 | 0.240024 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8575.60 | 1.45693 | ||||||||
\(327\) | −7216.33 | −1.22038 | ||||||||
\(328\) | −6656.84 | −1.12062 | ||||||||
\(329\) | −9766.30 | −1.63658 | ||||||||
\(330\) | 480.001 | 0.0800702 | ||||||||
\(331\) | −884.985 | −0.146958 | −0.0734791 | − | 0.997297i | \(-0.523410\pi\) | ||||
−0.0734791 | + | 0.997297i | \(0.523410\pi\) | |||||||
\(332\) | 2015.21 | 0.333130 | ||||||||
\(333\) | −2377.01 | −0.391169 | ||||||||
\(334\) | −3233.98 | −0.529807 | ||||||||
\(335\) | −1212.71 | −0.197784 | ||||||||
\(336\) | 2773.95 | 0.450391 | ||||||||
\(337\) | 1403.28 | 0.226829 | 0.113414 | − | 0.993548i | \(-0.463821\pi\) | ||||
0.113414 | + | 0.993548i | \(0.463821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6042.64 | −0.968115 | ||||||||
\(340\) | 15.6414 | 0.00249492 | ||||||||
\(341\) | −366.603 | −0.0582189 | ||||||||
\(342\) | 856.515 | 0.135424 | ||||||||
\(343\) | 6677.01 | 1.05109 | ||||||||
\(344\) | −3097.82 | −0.485533 | ||||||||
\(345\) | −883.744 | −0.137911 | ||||||||
\(346\) | −3115.50 | −0.484076 | ||||||||
\(347\) | −5649.13 | −0.873952 | −0.436976 | − | 0.899473i | \(-0.643951\pi\) | ||||
−0.436976 | + | 0.899473i | \(0.643951\pi\) | |||||||
\(348\) | −2149.99 | −0.331183 | ||||||||
\(349\) | −9445.14 | −1.44867 | −0.724336 | − | 0.689447i | \(-0.757854\pi\) | ||||
−0.724336 | + | 0.689447i | \(0.757854\pi\) | |||||||
\(350\) | −4302.63 | −0.657101 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1277.99 | −0.193515 | ||||||||
\(353\) | 8070.52 | 1.21686 | 0.608429 | − | 0.793609i | \(-0.291800\pi\) | ||||
0.608429 | + | 0.793609i | \(0.291800\pi\) | |||||||
\(354\) | −1452.45 | −0.218070 | ||||||||
\(355\) | −376.206 | −0.0562449 | ||||||||
\(356\) | −4008.72 | −0.596803 | ||||||||
\(357\) | −109.844 | −0.0162845 | ||||||||
\(358\) | 8353.86 | 1.23328 | ||||||||
\(359\) | −13277.5 | −1.95198 | −0.975989 | − | 0.217820i | \(-0.930106\pi\) | ||||
−0.975989 | + | 0.217820i | \(0.930106\pi\) | |||||||
\(360\) | 647.876 | 0.0948502 | ||||||||
\(361\) | −3385.84 | −0.493635 | ||||||||
\(362\) | 6604.00 | 0.958835 | ||||||||
\(363\) | 550.356 | 0.0795762 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1527.21 | −0.219008 | ||||||||
\(366\) | −3752.07 | −0.535858 | ||||||||
\(367\) | −13420.1 | −1.90878 | −0.954390 | − | 0.298562i | \(-0.903493\pi\) | ||||
−0.954390 | + | 0.298562i | \(0.903493\pi\) | |||||||
\(368\) | −1638.12 | −0.232046 | ||||||||
\(369\) | 1705.77 | 0.240648 | ||||||||
\(370\) | 3612.82 | 0.507627 | ||||||||
\(371\) | 6180.53 | 0.864898 | ||||||||
\(372\) | 409.064 | 0.0570134 | ||||||||
\(373\) | 5921.20 | 0.821951 | 0.410976 | − | 0.911646i | \(-0.365188\pi\) | ||||
0.410976 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(374\) | −35.2322 | −0.00487116 | ||||||||
\(375\) | 4408.93 | 0.607137 | ||||||||
\(376\) | 13857.5 | 1.90065 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −6056.57 | −0.824117 | ||||||||
\(379\) | 7455.99 | 1.01052 | 0.505262 | − | 0.862966i | \(-0.331396\pi\) | ||||
0.505262 | + | 0.862966i | \(0.331396\pi\) | |||||||
\(380\) | 662.654 | 0.0894564 | ||||||||
\(381\) | 2674.43 | 0.359620 | ||||||||
\(382\) | −1296.57 | −0.173660 | ||||||||
\(383\) | −9968.01 | −1.32987 | −0.664937 | − | 0.746900i | \(-0.731542\pi\) | ||||
−0.664937 | + | 0.746900i | \(0.731542\pi\) | |||||||
\(384\) | −1517.16 | −0.201621 | ||||||||
\(385\) | 795.712 | 0.105333 | ||||||||
\(386\) | 1643.92 | 0.216771 | ||||||||
\(387\) | 793.798 | 0.104266 | ||||||||
\(388\) | −2345.16 | −0.306849 | ||||||||
\(389\) | 5260.84 | 0.685694 | 0.342847 | − | 0.939391i | \(-0.388609\pi\) | ||||
0.342847 | + | 0.939391i | \(0.388609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.8671 | 0.00838995 | ||||||||
\(392\) | −1024.83 | −0.132045 | ||||||||
\(393\) | −2633.83 | −0.338064 | ||||||||
\(394\) | 3308.59 | 0.423057 | ||||||||
\(395\) | −1126.54 | −0.143499 | ||||||||
\(396\) | 187.369 | 0.0237769 | ||||||||
\(397\) | −14345.3 | −1.81352 | −0.906761 | − | 0.421644i | \(-0.861453\pi\) | ||||
−0.906761 | + | 0.421644i | \(0.861453\pi\) | |||||||
\(398\) | 3718.36 | 0.468302 | ||||||||
\(399\) | −4653.60 | −0.583889 | ||||||||
\(400\) | 3781.28 | 0.472660 | ||||||||
\(401\) | −3703.40 | −0.461195 | −0.230597 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230597 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(402\) | −3048.03 | −0.378164 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1826.85 | 0.224973 | ||||||||
\(405\) | 2161.40 | 0.265187 | ||||||||
\(406\) | 7001.89 | 0.855907 | ||||||||
\(407\) | 4142.36 | 0.504495 | ||||||||
\(408\) | 155.858 | 0.0189121 | ||||||||
\(409\) | −8793.65 | −1.06312 | −0.531562 | − | 0.847019i | \(-0.678395\pi\) | ||||
−0.531562 | + | 0.847019i | \(0.678395\pi\) | |||||||
\(410\) | −2592.61 | −0.312292 | ||||||||
\(411\) | −6426.91 | −0.771329 | ||||||||
\(412\) | 393.134 | 0.0470105 | ||||||||
\(413\) | −2407.77 | −0.286873 | ||||||||
\(414\) | 677.715 | 0.0804538 | ||||||||
\(415\) | 3111.61 | 0.368055 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6851.29 | 0.804578 | ||||||||
\(418\) | −1492.63 | −0.174658 | ||||||||
\(419\) | −1247.40 | −0.145440 | −0.0727201 | − | 0.997352i | \(-0.523168\pi\) | ||||
−0.0727201 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(420\) | −887.875 | −0.103152 | ||||||||
\(421\) | 1060.57 | 0.122776 | 0.0613881 | − | 0.998114i | \(-0.480447\pi\) | ||||
0.0613881 | + | 0.998114i | \(0.480447\pi\) | |||||||
\(422\) | 4274.15 | 0.493039 | ||||||||
\(423\) | −3550.89 | −0.408156 | ||||||||
\(424\) | −8769.58 | −1.00445 | ||||||||
\(425\) | −149.733 | −0.0170897 | ||||||||
\(426\) | −945.555 | −0.107541 | ||||||||
\(427\) | −6219.92 | −0.704925 | ||||||||
\(428\) | 4749.17 | 0.536355 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1206.50 | −0.135308 | ||||||||
\(431\) | −15286.8 | −1.70844 | −0.854222 | − | 0.519909i | \(-0.825966\pi\) | ||||
−0.854222 | + | 0.519909i | \(0.825966\pi\) | |||||||
\(432\) | 5322.69 | 0.592797 | ||||||||
\(433\) | −8781.08 | −0.974577 | −0.487288 | − | 0.873241i | \(-0.662014\pi\) | ||||
−0.487288 | + | 0.873241i | \(0.662014\pi\) | |||||||
\(434\) | −1332.20 | −0.147345 | ||||||||
\(435\) | −3319.72 | −0.365904 | ||||||||
\(436\) | 4281.43 | 0.470283 | ||||||||
\(437\) | 2748.13 | 0.300825 | ||||||||
\(438\) | −3838.48 | −0.418744 | ||||||||
\(439\) | −1906.09 | −0.207227 | −0.103614 | − | 0.994618i | \(-0.533041\pi\) | ||||
−0.103614 | + | 0.994618i | \(0.533041\pi\) | |||||||
\(440\) | −1129.04 | −0.122329 | ||||||||
\(441\) | 262.606 | 0.0283561 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4620.37 | −0.495532 | −0.247766 | − | 0.968820i | \(-0.579696\pi\) | ||||
−0.247766 | + | 0.968820i | \(0.579696\pi\) | |||||||
\(444\) | −4622.15 | −0.494048 | ||||||||
\(445\) | −6189.70 | −0.659371 | ||||||||
\(446\) | −745.537 | −0.0791529 | ||||||||
\(447\) | −2695.22 | −0.285189 | ||||||||
\(448\) | −9523.10 | −1.00430 | ||||||||
\(449\) | −8833.44 | −0.928454 | −0.464227 | − | 0.885716i | \(-0.653668\pi\) | ||||
−0.464227 | + | 0.885716i | \(0.653668\pi\) | |||||||
\(450\) | −1564.37 | −0.163878 | ||||||||
\(451\) | −2972.61 | −0.310366 | ||||||||
\(452\) | 3585.08 | 0.373071 | ||||||||
\(453\) | −3127.40 | −0.324366 | ||||||||
\(454\) | −3487.53 | −0.360524 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6603.02 | 0.678102 | ||||||||
\(457\) | −9240.25 | −0.945822 | −0.472911 | − | 0.881110i | \(-0.656797\pi\) | ||||
−0.472911 | + | 0.881110i | \(0.656797\pi\) | |||||||
\(458\) | 7953.15 | 0.811411 | ||||||||
\(459\) | −210.771 | −0.0214334 | ||||||||
\(460\) | 524.323 | 0.0531450 | ||||||||
\(461\) | 9390.04 | 0.948672 | 0.474336 | − | 0.880344i | \(-0.342688\pi\) | ||||
0.474336 | + | 0.880344i | \(0.342688\pi\) | |||||||
\(462\) | 1999.94 | 0.201398 | ||||||||
\(463\) | −7817.84 | −0.784721 | −0.392360 | − | 0.919812i | \(-0.628341\pi\) | ||||
−0.392360 | + | 0.919812i | \(0.628341\pi\) | |||||||
\(464\) | −6153.47 | −0.615663 | ||||||||
\(465\) | 631.619 | 0.0629906 | ||||||||
\(466\) | 16038.8 | 1.59438 | ||||||||
\(467\) | −16645.0 | −1.64933 | −0.824666 | − | 0.565620i | \(-0.808637\pi\) | ||||
−0.824666 | + | 0.565620i | \(0.808637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5052.81 | −0.497478 | ||||||||
\(470\) | 5397.00 | 0.529670 | ||||||||
\(471\) | −1383.35 | −0.135332 | ||||||||
\(472\) | 3416.39 | 0.333161 | ||||||||
\(473\) | −1383.33 | −0.134473 | ||||||||
\(474\) | −2831.43 | −0.274371 | ||||||||
\(475\) | −6343.51 | −0.612758 | ||||||||
\(476\) | 65.1703 | 0.00627537 | ||||||||
\(477\) | 2247.15 | 0.215702 | ||||||||
\(478\) | 5053.77 | 0.483586 | ||||||||
\(479\) | 245.962 | 0.0234620 | 0.0117310 | − | 0.999931i | \(-0.496266\pi\) | ||||
0.0117310 | + | 0.999931i | \(0.496266\pi\) | |||||||
\(480\) | 2201.85 | 0.209375 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14073.2 | −1.32991 | ||||||||
\(483\) | −3682.15 | −0.346881 | ||||||||
\(484\) | −326.525 | −0.0306653 | ||||||||
\(485\) | −3621.06 | −0.339018 | ||||||||
\(486\) | −3986.90 | −0.372118 | ||||||||
\(487\) | −240.346 | −0.0223637 | −0.0111818 | − | 0.999937i | \(-0.503559\pi\) | ||||
−0.0111818 | + | 0.999937i | \(0.503559\pi\) | |||||||
\(488\) | 8825.48 | 0.818669 | ||||||||
\(489\) | −16940.5 | −1.56661 | ||||||||
\(490\) | −399.135 | −0.0367982 | ||||||||
\(491\) | 5208.20 | 0.478702 | 0.239351 | − | 0.970933i | \(-0.423065\pi\) | ||||
0.239351 | + | 0.970933i | \(0.423065\pi\) | |||||||
\(492\) | 3316.91 | 0.303939 | ||||||||
\(493\) | 243.668 | 0.0222602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 289.309 | 0.0262697 | ||||||||
\(496\) | 1170.78 | 0.105987 | ||||||||
\(497\) | −1567.47 | −0.141471 | ||||||||
\(498\) | 7820.70 | 0.703723 | ||||||||
\(499\) | −13603.3 | −1.22037 | −0.610186 | − | 0.792258i | \(-0.708905\pi\) | ||||
−0.610186 | + | 0.792258i | \(0.708905\pi\) | |||||||
\(500\) | −2615.81 | −0.233965 | ||||||||
\(501\) | 6388.48 | 0.569693 | ||||||||
\(502\) | 6919.67 | 0.615219 | ||||||||
\(503\) | 9041.72 | 0.801491 | 0.400746 | − | 0.916189i | \(-0.368751\pi\) | ||||
0.400746 | + | 0.916189i | \(0.368751\pi\) | |||||||
\(504\) | 2699.40 | 0.238573 | ||||||||
\(505\) | 2820.76 | 0.248559 | ||||||||
\(506\) | −1181.04 | −0.103762 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1586.73 | −0.138582 | ||||||||
\(509\) | 8952.50 | 0.779593 | 0.389796 | − | 0.920901i | \(-0.372545\pi\) | ||||
0.389796 | + | 0.920901i | \(0.372545\pi\) | |||||||
\(510\) | 60.7015 | 0.00527041 | ||||||||
\(511\) | −6363.17 | −0.550861 | ||||||||
\(512\) | 11004.2 | 0.949847 | ||||||||
\(513\) | −8929.40 | −0.768505 | ||||||||
\(514\) | −7821.81 | −0.671216 | ||||||||
\(515\) | 607.022 | 0.0519390 | ||||||||
\(516\) | 1543.56 | 0.131689 | ||||||||
\(517\) | 6188.05 | 0.526402 | ||||||||
\(518\) | 15053.0 | 1.27681 | ||||||||
\(519\) | 6154.44 | 0.520520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8131.19 | −0.683751 | −0.341875 | − | 0.939745i | \(-0.611062\pi\) | ||||
−0.341875 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(522\) | 2545.79 | 0.213460 | ||||||||
\(523\) | −13541.4 | −1.13217 | −0.566084 | − | 0.824347i | \(-0.691542\pi\) | ||||
−0.566084 | + | 0.824347i | \(0.691542\pi\) | |||||||
\(524\) | 1562.64 | 0.130276 | ||||||||
\(525\) | 8499.52 | 0.706571 | ||||||||
\(526\) | −237.683 | −0.0197024 | ||||||||
\(527\) | −46.3610 | −0.00383210 | ||||||||
\(528\) | −1757.61 | −0.144867 | ||||||||
\(529\) | −9992.55 | −0.821283 | ||||||||
\(530\) | −3415.45 | −0.279920 | ||||||||
\(531\) | −875.428 | −0.0715449 | ||||||||
\(532\) | 2760.97 | 0.225006 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −15557.2 | −1.26072 | ||||||||
\(535\) | 7333.00 | 0.592585 | ||||||||
\(536\) | 7169.45 | 0.577748 | ||||||||
\(537\) | −16502.4 | −1.32613 | ||||||||
\(538\) | 149.052 | 0.0119444 | ||||||||
\(539\) | −457.637 | −0.0365711 | ||||||||
\(540\) | −1703.67 | −0.135767 | ||||||||
\(541\) | 20393.5 | 1.62068 | 0.810338 | − | 0.585963i | \(-0.199283\pi\) | ||||
0.810338 | + | 0.585963i | \(0.199283\pi\) | |||||||
\(542\) | −5849.91 | −0.463607 | ||||||||
\(543\) | −13045.7 | −1.03102 | ||||||||
\(544\) | −161.616 | −0.0127376 | ||||||||
\(545\) | 6610.78 | 0.519586 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14378.3 | −1.12390 | −0.561949 | − | 0.827172i | \(-0.689948\pi\) | ||||
−0.561949 | + | 0.827172i | \(0.689948\pi\) | |||||||
\(548\) | 3813.07 | 0.297238 | ||||||||
\(549\) | −2261.47 | −0.175806 | ||||||||
\(550\) | 2726.20 | 0.211355 | ||||||||
\(551\) | 10323.1 | 0.798148 | ||||||||
\(552\) | 5224.62 | 0.402852 | ||||||||
\(553\) | −4693.75 | −0.360938 | ||||||||
\(554\) | −1298.50 | −0.0995809 | ||||||||
\(555\) | −7136.86 | −0.545843 | ||||||||
\(556\) | −4064.85 | −0.310050 | ||||||||
\(557\) | −17107.4 | −1.30137 | −0.650686 | − | 0.759347i | \(-0.725519\pi\) | ||||
−0.650686 | + | 0.759347i | \(0.725519\pi\) | |||||||
\(558\) | −484.369 | −0.0367472 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2541.17 | −0.191757 | ||||||||
\(561\) | 69.5986 | 0.00523789 | ||||||||
\(562\) | −3219.59 | −0.241655 | ||||||||
\(563\) | 5524.08 | 0.413521 | 0.206760 | − | 0.978392i | \(-0.433708\pi\) | ||||
0.206760 | + | 0.978392i | \(0.433708\pi\) | |||||||
\(564\) | −6904.77 | −0.515503 | ||||||||
\(565\) | 5535.57 | 0.412183 | ||||||||
\(566\) | −13904.9 | −1.03262 | ||||||||
\(567\) | 9005.55 | 0.667015 | ||||||||
\(568\) | 2224.10 | 0.164298 | ||||||||
\(569\) | 18693.4 | 1.37727 | 0.688635 | − | 0.725108i | \(-0.258210\pi\) | ||||
0.688635 | + | 0.725108i | \(0.258210\pi\) | |||||||
\(570\) | 2571.65 | 0.188973 | ||||||||
\(571\) | 23031.5 | 1.68798 | 0.843992 | − | 0.536355i | \(-0.180199\pi\) | ||||
0.843992 | + | 0.536355i | \(0.180199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2561.27 | 0.186734 | ||||||||
\(574\) | −10802.2 | −0.785497 | ||||||||
\(575\) | −5019.29 | −0.364033 | ||||||||
\(576\) | −3462.46 | −0.250467 | ||||||||
\(577\) | 8356.41 | 0.602915 | 0.301458 | − | 0.953480i | \(-0.402527\pi\) | ||||
0.301458 | + | 0.953480i | \(0.402527\pi\) | |||||||
\(578\) | 11307.7 | 0.813732 | ||||||||
\(579\) | −3247.45 | −0.233090 | ||||||||
\(580\) | 1969.58 | 0.141004 | ||||||||
\(581\) | 12964.6 | 0.925754 | ||||||||
\(582\) | −9101.16 | −0.648205 | ||||||||
\(583\) | −3916.06 | −0.278193 | ||||||||
\(584\) | 9028.73 | 0.639746 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9224.46 | −0.650271 | ||||||||
\(587\) | 14373.2 | 1.01064 | 0.505321 | − | 0.862932i | \(-0.331374\pi\) | ||||
0.505321 | + | 0.862932i | \(0.331374\pi\) | |||||||
\(588\) | 510.643 | 0.0358139 | ||||||||
\(589\) | −1964.11 | −0.137402 | ||||||||
\(590\) | 1330.57 | 0.0928450 | ||||||||
\(591\) | −6535.87 | −0.454907 | ||||||||
\(592\) | −13229.0 | −0.918426 | ||||||||
\(593\) | 5370.38 | 0.371898 | 0.185949 | − | 0.982559i | \(-0.440464\pi\) | ||||
0.185949 | + | 0.982559i | \(0.440464\pi\) | |||||||
\(594\) | 3837.52 | 0.265076 | ||||||||
\(595\) | 100.627 | 0.00693326 | ||||||||
\(596\) | 1599.07 | 0.109900 | ||||||||
\(597\) | −7345.34 | −0.503559 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6427.64 | 0.438441 | 0.219220 | − | 0.975675i | \(-0.429649\pi\) | ||||
0.219220 | + | 0.975675i | \(0.429649\pi\) | |||||||
\(600\) | −12060.0 | −0.820580 | ||||||||
\(601\) | 20326.7 | 1.37961 | 0.689804 | − | 0.723996i | \(-0.257696\pi\) | ||||
0.689804 | + | 0.723996i | \(0.257696\pi\) | |||||||
\(602\) | −5026.91 | −0.340335 | ||||||||
\(603\) | −1837.13 | −0.124069 | ||||||||
\(604\) | 1855.48 | 0.124997 | ||||||||
\(605\) | −504.173 | −0.0338802 | ||||||||
\(606\) | 7089.69 | 0.475246 | ||||||||
\(607\) | 2402.92 | 0.160678 | 0.0803390 | − | 0.996768i | \(-0.474400\pi\) | ||||
0.0803390 | + | 0.996768i | \(0.474400\pi\) | |||||||
\(608\) | −6846.96 | −0.456712 | ||||||||
\(609\) | −13831.7 | −0.920344 | ||||||||
\(610\) | 3437.22 | 0.228146 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 23.6950 | 0.00156505 | ||||||||
\(613\) | 3076.49 | 0.202705 | 0.101352 | − | 0.994851i | \(-0.467683\pi\) | ||||
0.101352 | + | 0.994851i | \(0.467683\pi\) | |||||||
\(614\) | 7945.05 | 0.522208 | ||||||||
\(615\) | 5121.51 | 0.335803 | ||||||||
\(616\) | −4704.18 | −0.307690 | ||||||||
\(617\) | −23027.3 | −1.50250 | −0.751251 | − | 0.660017i | \(-0.770549\pi\) | ||||
−0.751251 | + | 0.660017i | \(0.770549\pi\) | |||||||
\(618\) | 1525.69 | 0.0993078 | ||||||||
\(619\) | 10155.0 | 0.659391 | 0.329695 | − | 0.944087i | \(-0.393054\pi\) | ||||
0.329695 | + | 0.944087i | \(0.393054\pi\) | |||||||
\(620\) | −374.738 | −0.0242739 | ||||||||
\(621\) | −7065.37 | −0.456559 | ||||||||
\(622\) | 2136.76 | 0.137743 | ||||||||
\(623\) | −25789.6 | −1.65849 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9415.85 | 0.602614 | ||||||||
\(626\) | −19004.5 | −1.21338 | ||||||||
\(627\) | 2948.58 | 0.187807 | ||||||||
\(628\) | 820.740 | 0.0521514 | ||||||||
\(629\) | 523.848 | 0.0332070 | ||||||||
\(630\) | 1051.32 | 0.0664853 | ||||||||
\(631\) | −5762.78 | −0.363570 | −0.181785 | − | 0.983338i | \(-0.558188\pi\) | ||||
−0.181785 | + | 0.983338i | \(0.558188\pi\) | |||||||
\(632\) | 6659.99 | 0.419177 | ||||||||
\(633\) | −8443.26 | −0.530157 | ||||||||
\(634\) | 20164.0 | 1.26312 | ||||||||
\(635\) | −2450.00 | −0.153111 | ||||||||
\(636\) | 4369.63 | 0.272433 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4436.48 | −0.275301 | ||||||||
\(639\) | −569.911 | −0.0352822 | ||||||||
\(640\) | 1389.85 | 0.0858417 | ||||||||
\(641\) | −13564.2 | −0.835811 | −0.417906 | − | 0.908490i | \(-0.637236\pi\) | ||||
−0.417906 | + | 0.908490i | \(0.637236\pi\) | |||||||
\(642\) | 18430.7 | 1.13303 | ||||||||
\(643\) | 390.407 | 0.0239442 | 0.0119721 | − | 0.999928i | \(-0.496189\pi\) | ||||
0.0119721 | + | 0.999928i | \(0.496189\pi\) | |||||||
\(644\) | 2184.61 | 0.133673 | ||||||||
\(645\) | 2383.34 | 0.145495 | ||||||||
\(646\) | −188.760 | −0.0114964 | ||||||||
\(647\) | 14443.1 | 0.877612 | 0.438806 | − | 0.898582i | \(-0.355402\pi\) | ||||
0.438806 | + | 0.898582i | \(0.355402\pi\) | |||||||
\(648\) | −12778.0 | −0.774642 | ||||||||
\(649\) | 1525.59 | 0.0922721 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2631.66 | 0.158438 | ||||||||
\(652\) | 10050.7 | 0.603707 | ||||||||
\(653\) | 21664.2 | 1.29829 | 0.649147 | − | 0.760663i | \(-0.275126\pi\) | ||||
0.649147 | + | 0.760663i | \(0.275126\pi\) | |||||||
\(654\) | 16615.5 | 0.993453 | ||||||||
\(655\) | 2412.81 | 0.143933 | ||||||||
\(656\) | 9493.29 | 0.565017 | ||||||||
\(657\) | −2313.56 | −0.137383 | ||||||||
\(658\) | 22486.8 | 1.33226 | ||||||||
\(659\) | 2002.80 | 0.118389 | 0.0591943 | − | 0.998246i | \(-0.481147\pi\) | ||||
0.0591943 | + | 0.998246i | \(0.481147\pi\) | |||||||
\(660\) | 562.568 | 0.0331787 | ||||||||
\(661\) | 5664.78 | 0.333335 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(662\) | 2037.67 | 0.119632 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18395.6 | −1.07513 | ||||||||
\(665\) | 4263.10 | 0.248595 | ||||||||
\(666\) | 5473.04 | 0.318432 | ||||||||
\(667\) | 8168.14 | 0.474171 | ||||||||
\(668\) | −3790.27 | −0.219536 | ||||||||
\(669\) | 1472.75 | 0.0851120 | ||||||||
\(670\) | 2792.26 | 0.161006 | ||||||||
\(671\) | 3941.02 | 0.226738 | ||||||||
\(672\) | 9174.09 | 0.526634 | ||||||||
\(673\) | −25837.7 | −1.47989 | −0.739947 | − | 0.672665i | \(-0.765150\pi\) | ||||
−0.739947 | + | 0.672665i | \(0.765150\pi\) | |||||||
\(674\) | −3231.02 | −0.184650 | ||||||||
\(675\) | 16309.0 | 0.929977 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30528.7 | 1.73311 | 0.866553 | − | 0.499085i | \(-0.166330\pi\) | ||||
0.866553 | + | 0.499085i | \(0.166330\pi\) | |||||||
\(678\) | 13913.1 | 0.788096 | ||||||||
\(679\) | −15087.3 | −0.852719 | ||||||||
\(680\) | −142.780 | −0.00805198 | ||||||||
\(681\) | 6889.35 | 0.387666 | ||||||||
\(682\) | 844.099 | 0.0473933 | ||||||||
\(683\) | 15284.7 | 0.856298 | 0.428149 | − | 0.903708i | \(-0.359166\pi\) | ||||
0.428149 | + | 0.903708i | \(0.359166\pi\) | |||||||
\(684\) | 1003.85 | 0.0561157 | ||||||||
\(685\) | 5887.60 | 0.328399 | ||||||||
\(686\) | −15373.7 | −0.855645 | ||||||||
\(687\) | −15710.8 | −0.872498 | ||||||||
\(688\) | 4417.80 | 0.244807 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2034.81 | 0.112266 | ||||||||
\(691\) | 26541.3 | 1.46119 | 0.730593 | − | 0.682813i | \(-0.239244\pi\) | ||||
0.730593 | + | 0.682813i | \(0.239244\pi\) | |||||||
\(692\) | −3651.41 | −0.200587 | ||||||||
\(693\) | 1205.42 | 0.0660751 | ||||||||
\(694\) | 13007.1 | 0.711443 | ||||||||
\(695\) | −6276.36 | −0.342556 | ||||||||
\(696\) | 19625.9 | 1.06885 | ||||||||
\(697\) | −375.920 | −0.0204290 | ||||||||
\(698\) | 21747.3 | 1.17930 | ||||||||
\(699\) | −31683.4 | −1.71441 | ||||||||
\(700\) | −5042.75 | −0.272283 | ||||||||
\(701\) | −23167.2 | −1.24823 | −0.624117 | − | 0.781331i | \(-0.714541\pi\) | ||||
−0.624117 | + | 0.781331i | \(0.714541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22193.1 | 1.19065 | ||||||||
\(704\) | 6033.95 | 0.323030 | ||||||||
\(705\) | −10661.4 | −0.569547 | ||||||||
\(706\) | −18582.3 | −0.990586 | ||||||||
\(707\) | 11752.8 | 0.625190 | ||||||||
\(708\) | −1702.29 | −0.0903615 | ||||||||
\(709\) | −15225.3 | −0.806484 | −0.403242 | − | 0.915093i | \(-0.632117\pi\) | ||||
−0.403242 | + | 0.915093i | \(0.632117\pi\) | |||||||
\(710\) | 866.209 | 0.0457863 | ||||||||
\(711\) | −1706.58 | −0.0900165 | ||||||||
\(712\) | 36593.0 | 1.92610 | ||||||||
\(713\) | −1554.10 | −0.0816288 | ||||||||
\(714\) | 252.915 | 0.0132564 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9790.85 | 0.511035 | ||||||||
\(717\) | −9983.34 | −0.519993 | ||||||||
\(718\) | 30571.3 | 1.58901 | ||||||||
\(719\) | 711.358 | 0.0368973 | 0.0184487 | − | 0.999830i | \(-0.494127\pi\) | ||||
0.0184487 | + | 0.999830i | \(0.494127\pi\) | |||||||
\(720\) | −923.934 | −0.0478236 | ||||||||
\(721\) | 2529.18 | 0.130640 | ||||||||
\(722\) | 7795.86 | 0.401845 | ||||||||
\(723\) | 27800.6 | 1.43003 | ||||||||
\(724\) | 7739.98 | 0.397312 | ||||||||
\(725\) | −18854.6 | −0.965849 | ||||||||
\(726\) | −1267.19 | −0.0647792 | ||||||||
\(727\) | −7249.37 | −0.369827 | −0.184914 | − | 0.982755i | \(-0.559201\pi\) | ||||
−0.184914 | + | 0.982755i | \(0.559201\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21881.5 | 1.11170 | ||||||||
\(730\) | 3516.38 | 0.178284 | ||||||||
\(731\) | −174.938 | −0.00885133 | ||||||||
\(732\) | −4397.48 | −0.222043 | ||||||||
\(733\) | −20158.7 | −1.01579 | −0.507897 | − | 0.861418i | \(-0.669577\pi\) | ||||
−0.507897 | + | 0.861418i | \(0.669577\pi\) | |||||||
\(734\) | 30899.6 | 1.55385 | ||||||||
\(735\) | 788.462 | 0.0395685 | ||||||||
\(736\) | −5417.64 | −0.271327 | ||||||||
\(737\) | 3201.52 | 0.160013 | ||||||||
\(738\) | −3927.52 | −0.195900 | ||||||||
\(739\) | 20211.8 | 1.00610 | 0.503048 | − | 0.864259i | \(-0.332212\pi\) | ||||
0.503048 | + | 0.864259i | \(0.332212\pi\) | |||||||
\(740\) | 4234.28 | 0.210345 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14230.6 | −0.704072 | ||||||||
\(743\) | 30489.9 | 1.50547 | 0.752736 | − | 0.658322i | \(-0.228734\pi\) | ||||
0.752736 | + | 0.658322i | \(0.228734\pi\) | |||||||
\(744\) | −3734.08 | −0.184003 | ||||||||
\(745\) | 2469.05 | 0.121422 | ||||||||
\(746\) | −13633.5 | −0.669111 | ||||||||
\(747\) | 4713.75 | 0.230879 | ||||||||
\(748\) | −41.2927 | −0.00201846 | ||||||||
\(749\) | 30553.2 | 1.49051 | ||||||||
\(750\) | −10151.5 | −0.494241 | ||||||||
\(751\) | −13731.3 | −0.667193 | −0.333596 | − | 0.942716i | \(-0.608262\pi\) | ||||
−0.333596 | + | 0.942716i | \(0.608262\pi\) | |||||||
\(752\) | −19762.1 | −0.958309 | ||||||||
\(753\) | −13669.3 | −0.661536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2864.96 | 0.138102 | ||||||||
\(756\) | −7098.39 | −0.341489 | ||||||||
\(757\) | 17226.4 | 0.827085 | 0.413543 | − | 0.910485i | \(-0.364291\pi\) | ||||
0.413543 | + | 0.910485i | \(0.364291\pi\) | |||||||
\(758\) | −17167.3 | −0.822619 | ||||||||
\(759\) | 2333.06 | 0.111574 | ||||||||
\(760\) | −6048.93 | −0.288708 | ||||||||
\(761\) | −524.915 | −0.0250041 | −0.0125021 | − | 0.999922i | \(-0.503980\pi\) | ||||
−0.0125021 | + | 0.999922i | \(0.503980\pi\) | |||||||
\(762\) | −6157.84 | −0.292749 | ||||||||
\(763\) | 27544.0 | 1.30690 | ||||||||
\(764\) | −1519.60 | −0.0719596 | ||||||||
\(765\) | 36.5864 | 0.00172913 | ||||||||
\(766\) | 22951.2 | 1.08259 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16466.6 | −0.773681 | ||||||||
\(769\) | −23219.0 | −1.08882 | −0.544408 | − | 0.838821i | \(-0.683246\pi\) | ||||
−0.544408 | + | 0.838821i | \(0.683246\pi\) | |||||||
\(770\) | −1832.12 | −0.0857467 | ||||||||
\(771\) | 15451.4 | 0.721749 | ||||||||
\(772\) | 1926.70 | 0.0898232 | ||||||||
\(773\) | −20012.5 | −0.931175 | −0.465588 | − | 0.885002i | \(-0.654157\pi\) | ||||
−0.465588 | + | 0.885002i | \(0.654157\pi\) | |||||||
\(774\) | −1827.71 | −0.0848782 | ||||||||
\(775\) | 3587.32 | 0.166272 | ||||||||
\(776\) | 21407.4 | 0.990310 | ||||||||
\(777\) | −29736.0 | −1.37294 | ||||||||
\(778\) | −12113.0 | −0.558191 | ||||||||
\(779\) | −15926.0 | −0.732490 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 993.171 | 0.0455038 | ||||||||
\(782\) | −149.356 | −0.00682986 | ||||||||
\(783\) | −26540.5 | −1.21134 | ||||||||
\(784\) | 1461.50 | 0.0665773 | ||||||||
\(785\) | 1267.27 | 0.0576189 | ||||||||
\(786\) | 6064.36 | 0.275202 | ||||||||
\(787\) | −27618.3 | −1.25093 | −0.625467 | − | 0.780250i | \(-0.715092\pi\) | ||||
−0.625467 | + | 0.780250i | \(0.715092\pi\) | |||||||
\(788\) | 3877.72 | 0.175302 | ||||||||
\(789\) | 469.524 | 0.0211857 | ||||||||
\(790\) | 2593.84 | 0.116816 | ||||||||
\(791\) | 23064.2 | 1.03675 | ||||||||
\(792\) | −1710.37 | −0.0767366 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 33029.8 | 1.47630 | ||||||||
\(795\) | 6746.97 | 0.300994 | ||||||||
\(796\) | 4357.97 | 0.194050 | ||||||||
\(797\) | 29515.2 | 1.31177 | 0.655885 | − | 0.754861i | \(-0.272296\pi\) | ||||
0.655885 | + | 0.754861i | \(0.272296\pi\) | |||||||
\(798\) | 10714.9 | 0.475316 | ||||||||
\(799\) | 782.548 | 0.0346490 | ||||||||
\(800\) | 12505.6 | 0.552673 | ||||||||
\(801\) | −9376.73 | −0.413621 | ||||||||
\(802\) | 8527.03 | 0.375436 | ||||||||
\(803\) | 4031.78 | 0.177184 | ||||||||
\(804\) | −3572.33 | −0.156700 | ||||||||
\(805\) | 3373.17 | 0.147688 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −294.441 | −0.0128436 | ||||||||
\(808\) | −16676.1 | −0.726068 | ||||||||
\(809\) | 27669.7 | 1.20249 | 0.601246 | − | 0.799064i | \(-0.294671\pi\) | ||||
0.601246 | + | 0.799064i | \(0.294671\pi\) | |||||||
\(810\) | −4976.60 | −0.215876 | ||||||||
\(811\) | 11063.8 | 0.479040 | 0.239520 | − | 0.970891i | \(-0.423010\pi\) | ||||
0.239520 | + | 0.970891i | \(0.423010\pi\) | |||||||
\(812\) | 8206.32 | 0.354662 | ||||||||
\(813\) | 11556.1 | 0.498510 | ||||||||
\(814\) | −9537.74 | −0.410685 | ||||||||
\(815\) | 15518.9 | 0.666999 | ||||||||
\(816\) | −222.269 | −0.00953551 | ||||||||
\(817\) | −7411.34 | −0.317368 | ||||||||
\(818\) | 20247.3 | 0.865439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3038.58 | −0.129405 | ||||||||
\(821\) | 15354.0 | 0.652691 | 0.326346 | − | 0.945251i | \(-0.394183\pi\) | ||||
0.326346 | + | 0.945251i | \(0.394183\pi\) | |||||||
\(822\) | 14797.9 | 0.627902 | ||||||||
\(823\) | 16823.2 | 0.712539 | 0.356269 | − | 0.934383i | \(-0.384049\pi\) | ||||
0.356269 | + | 0.934383i | \(0.384049\pi\) | |||||||
\(824\) | −3588.66 | −0.151720 | ||||||||
\(825\) | −5385.40 | −0.227267 | ||||||||
\(826\) | 5543.85 | 0.233529 | ||||||||
\(827\) | −35426.2 | −1.48959 | −0.744795 | − | 0.667294i | \(-0.767453\pi\) | ||||
−0.744795 | + | 0.667294i | \(0.767453\pi\) | |||||||
\(828\) | 794.292 | 0.0333376 | ||||||||
\(829\) | −42315.2 | −1.77282 | −0.886410 | − | 0.462901i | \(-0.846809\pi\) | ||||
−0.886410 | + | 0.462901i | \(0.846809\pi\) | |||||||
\(830\) | −7164.44 | −0.299616 | ||||||||
\(831\) | 2565.08 | 0.107078 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −57.8734 | −0.00240719 | ||||||||
\(834\) | −15775.0 | −0.654968 | ||||||||
\(835\) | −5852.40 | −0.242552 | ||||||||
\(836\) | −1749.38 | −0.0723729 | ||||||||
\(837\) | 5049.68 | 0.208533 | ||||||||
\(838\) | 2872.12 | 0.118396 | ||||||||
\(839\) | −15519.4 | −0.638606 | −0.319303 | − | 0.947653i | \(-0.603449\pi\) | ||||
−0.319303 | + | 0.947653i | \(0.603449\pi\) | |||||||
\(840\) | 8104.82 | 0.332908 | ||||||||
\(841\) | 6294.00 | 0.258067 | ||||||||
\(842\) | −2441.94 | −0.0999463 | ||||||||
\(843\) | 6360.07 | 0.259848 | ||||||||
\(844\) | 5009.36 | 0.204300 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8175.87 | 0.332260 | ||||||||
\(847\) | −2100.65 | −0.0852176 | ||||||||
\(848\) | 12506.3 | 0.506447 | ||||||||
\(849\) | 27468.0 | 1.11036 | ||||||||
\(850\) | 344.758 | 0.0139119 | ||||||||
\(851\) | 17560.2 | 0.707352 | ||||||||
\(852\) | −1108.20 | −0.0445615 | ||||||||
\(853\) | −1499.09 | −0.0601732 | −0.0300866 | − | 0.999547i | \(-0.509578\pi\) | ||||
−0.0300866 | + | 0.999547i | \(0.509578\pi\) | |||||||
\(854\) | 14321.3 | 0.573846 | ||||||||
\(855\) | 1550.00 | 0.0619987 | ||||||||
\(856\) | −43352.1 | −1.73101 | ||||||||
\(857\) | 7709.00 | 0.307275 | 0.153637 | − | 0.988127i | \(-0.450901\pi\) | ||||
0.153637 | + | 0.988127i | \(0.450901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32493.2 | 1.29063 | 0.645316 | − | 0.763916i | \(-0.276726\pi\) | ||||
0.645316 | + | 0.763916i | \(0.276726\pi\) | |||||||
\(860\) | −1414.03 | −0.0560675 | ||||||||
\(861\) | 21338.9 | 0.844633 | ||||||||
\(862\) | 35197.7 | 1.39076 | ||||||||
\(863\) | 10257.0 | 0.404582 | 0.202291 | − | 0.979325i | \(-0.435161\pi\) | ||||
0.202291 | + | 0.979325i | \(0.435161\pi\) | |||||||
\(864\) | 17603.4 | 0.693147 | ||||||||
\(865\) | −5637.99 | −0.221616 | ||||||||
\(866\) | 20218.3 | 0.793356 | ||||||||
\(867\) | −22337.5 | −0.874994 | ||||||||
\(868\) | −1561.36 | −0.0610553 | ||||||||
\(869\) | 2974.02 | 0.116095 | ||||||||
\(870\) | 7643.61 | 0.297865 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −39082.4 | −1.51777 | ||||||||
\(873\) | −5485.51 | −0.212665 | ||||||||
\(874\) | −6327.53 | −0.244888 | ||||||||
\(875\) | −16828.5 | −0.650179 | ||||||||
\(876\) | −4498.76 | −0.173515 | ||||||||
\(877\) | −45870.2 | −1.76616 | −0.883082 | − | 0.469219i | \(-0.844536\pi\) | ||||
−0.883082 | + | 0.469219i | \(0.844536\pi\) | |||||||
\(878\) | 4388.75 | 0.168694 | ||||||||
\(879\) | 18222.2 | 0.699227 | ||||||||
\(880\) | 1610.12 | 0.0616785 | ||||||||
\(881\) | −6836.28 | −0.261430 | −0.130715 | − | 0.991420i | \(-0.541727\pi\) | ||||
−0.130715 | + | 0.991420i | \(0.541727\pi\) | |||||||
\(882\) | −604.647 | −0.0230834 | ||||||||
\(883\) | −17094.1 | −0.651487 | −0.325744 | − | 0.945458i | \(-0.605615\pi\) | ||||
−0.325744 | + | 0.945458i | \(0.605615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2628.43 | −0.0998348 | ||||||||
\(886\) | 10638.4 | 0.403389 | ||||||||
\(887\) | 28116.2 | 1.06432 | 0.532159 | − | 0.846644i | \(-0.321381\pi\) | ||||
0.532159 | + | 0.846644i | \(0.321381\pi\) | |||||||
\(888\) | 42192.5 | 1.59447 | ||||||||
\(889\) | −10208.0 | −0.385114 | ||||||||
\(890\) | 14251.7 | 0.536763 | ||||||||
\(891\) | −5706.03 | −0.214544 | ||||||||
\(892\) | −873.781 | −0.0327986 | ||||||||
\(893\) | 33153.0 | 1.24236 | ||||||||
\(894\) | 6205.71 | 0.232159 | ||||||||
\(895\) | 15117.6 | 0.564611 | ||||||||
\(896\) | 5790.86 | 0.215914 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20338.9 | 0.755810 | ||||||||
\(899\) | −5837.84 | −0.216577 | ||||||||
\(900\) | −1833.47 | −0.0679062 | ||||||||
\(901\) | −495.230 | −0.0183113 | ||||||||
\(902\) | 6844.41 | 0.252654 | ||||||||
\(903\) | 9930.29 | 0.365957 | ||||||||
\(904\) | −32725.8 | −1.20403 | ||||||||
\(905\) | 11951.0 | 0.438966 | ||||||||
\(906\) | 7200.80 | 0.264051 | ||||||||
\(907\) | −23330.1 | −0.854095 | −0.427047 | − | 0.904229i | \(-0.640446\pi\) | ||||
−0.427047 | + | 0.904229i | \(0.640446\pi\) | |||||||
\(908\) | −4087.43 | −0.149390 | ||||||||
\(909\) | 4273.14 | 0.155920 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25834.6 | −0.939560 | −0.469780 | − | 0.882784i | \(-0.655667\pi\) | ||||
−0.469780 | + | 0.882784i | \(0.655667\pi\) | |||||||
\(912\) | −9416.54 | −0.341900 | ||||||||
\(913\) | −8214.54 | −0.297767 | ||||||||
\(914\) | 21275.6 | 0.769949 | ||||||||
\(915\) | −6789.97 | −0.245322 | ||||||||
\(916\) | 9321.21 | 0.336224 | ||||||||
\(917\) | 10053.1 | 0.362030 | ||||||||
\(918\) | 485.297 | 0.0174479 | ||||||||
\(919\) | 31228.6 | 1.12093 | 0.560466 | − | 0.828177i | \(-0.310622\pi\) | ||||
0.560466 | + | 0.828177i | \(0.310622\pi\) | |||||||
\(920\) | −4786.20 | −0.171518 | ||||||||
\(921\) | −15694.8 | −0.561523 | ||||||||
\(922\) | −21620.4 | −0.772268 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2343.96 | 0.0834531 | ||||||||
\(925\) | −40534.3 | −1.44082 | ||||||||
\(926\) | 18000.5 | 0.638804 | ||||||||
\(927\) | 919.573 | 0.0325812 | ||||||||
\(928\) | −20350.9 | −0.719884 | ||||||||
\(929\) | 4317.75 | 0.152487 | 0.0762437 | − | 0.997089i | \(-0.475707\pi\) | ||||
0.0762437 | + | 0.997089i | \(0.475707\pi\) | |||||||
\(930\) | −1454.30 | −0.0512777 | ||||||||
\(931\) | −2451.83 | −0.0863111 | ||||||||
\(932\) | 18797.7 | 0.660663 | ||||||||
\(933\) | −4221.00 | −0.148113 | ||||||||
\(934\) | 38324.9 | 1.34264 | ||||||||
\(935\) | −63.7583 | −0.00223007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40522.5 | 1.41282 | 0.706409 | − | 0.707804i | \(-0.250314\pi\) | ||||
0.706409 | + | 0.707804i | \(0.250314\pi\) | |||||||
\(938\) | 11634.0 | 0.404973 | ||||||||
\(939\) | 37542.0 | 1.30472 | ||||||||
\(940\) | 6325.36 | 0.219479 | ||||||||
\(941\) | 50791.1 | 1.75956 | 0.879778 | − | 0.475384i | \(-0.157691\pi\) | ||||
0.879778 | + | 0.475384i | \(0.157691\pi\) | |||||||
\(942\) | 3185.15 | 0.110168 | ||||||||
\(943\) | −12601.4 | −0.435164 | ||||||||
\(944\) | −4872.10 | −0.167980 | ||||||||
\(945\) | −10960.3 | −0.377290 | ||||||||
\(946\) | 3185.11 | 0.109468 | ||||||||
\(947\) | 16851.5 | 0.578248 | 0.289124 | − | 0.957292i | \(-0.406636\pi\) | ||||
0.289124 | + | 0.957292i | \(0.406636\pi\) | |||||||
\(948\) | −3318.48 | −0.113691 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14605.9 | 0.498817 | ||||||||
\(951\) | −39832.5 | −1.35821 | ||||||||
\(952\) | −594.896 | −0.0202528 | ||||||||
\(953\) | −19119.0 | −0.649868 | −0.324934 | − | 0.945737i | \(-0.605342\pi\) | ||||
−0.324934 | + | 0.945737i | \(0.605342\pi\) | |||||||
\(954\) | −5174.04 | −0.175593 | ||||||||
\(955\) | −2346.35 | −0.0795037 | ||||||||
\(956\) | 5923.09 | 0.200383 | ||||||||
\(957\) | 8763.94 | 0.296027 | ||||||||
\(958\) | −566.324 | −0.0190993 | ||||||||
\(959\) | 24530.9 | 0.826010 | ||||||||
\(960\) | −10395.9 | −0.349506 | ||||||||
\(961\) | −28680.3 | −0.962716 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11108.7 | 0.371727 | ||||||||
\(964\) | −16494.0 | −0.551075 | ||||||||
\(965\) | 2974.94 | 0.0992401 | ||||||||
\(966\) | 8478.11 | 0.282380 | ||||||||
\(967\) | 12584.8 | 0.418511 | 0.209256 | − | 0.977861i | \(-0.432896\pi\) | ||||
0.209256 | + | 0.977861i | \(0.432896\pi\) | |||||||
\(968\) | 2980.63 | 0.0989680 | ||||||||
\(969\) | 372.881 | 0.0123619 | ||||||||
\(970\) | 8337.44 | 0.275979 | ||||||||
\(971\) | −4243.01 | −0.140231 | −0.0701156 | − | 0.997539i | \(-0.522337\pi\) | ||||
−0.0701156 | + | 0.997539i | \(0.522337\pi\) | |||||||
\(972\) | −4672.71 | −0.154195 | ||||||||
\(973\) | −26150.7 | −0.861617 | ||||||||
\(974\) | 553.394 | 0.0182052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12586.0 | −0.412774 | ||||||||
\(977\) | 50395.4 | 1.65025 | 0.825123 | − | 0.564953i | \(-0.191106\pi\) | ||||
0.825123 | + | 0.564953i | \(0.191106\pi\) | |||||||
\(978\) | 39005.2 | 1.27531 | ||||||||
\(979\) | 16340.6 | 0.533451 | ||||||||
\(980\) | −467.793 | −0.0152480 | ||||||||
\(981\) | 10014.6 | 0.325935 | ||||||||
\(982\) | −11991.8 | −0.389689 | ||||||||
\(983\) | −31148.7 | −1.01067 | −0.505335 | − | 0.862923i | \(-0.668631\pi\) | ||||
−0.505335 | + | 0.862923i | \(0.668631\pi\) | |||||||
\(984\) | −30277.9 | −0.980919 | ||||||||
\(985\) | 5987.42 | 0.193680 | ||||||||
\(986\) | −561.043 | −0.0181209 | ||||||||
\(987\) | −44421.0 | −1.43256 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5864.20 | −0.188545 | ||||||||
\(990\) | −666.131 | −0.0213849 | ||||||||
\(991\) | 25818.0 | 0.827584 | 0.413792 | − | 0.910371i | \(-0.364204\pi\) | ||||
0.413792 | + | 0.910371i | \(0.364204\pi\) | |||||||
\(992\) | 3872.03 | 0.123929 | ||||||||
\(993\) | −4025.26 | −0.128638 | ||||||||
\(994\) | 3609.09 | 0.115164 | ||||||||
\(995\) | 6728.96 | 0.214394 | ||||||||
\(996\) | 9165.98 | 0.291602 | ||||||||
\(997\) | −25082.9 | −0.796773 | −0.398386 | − | 0.917218i | \(-0.630430\pi\) | ||||
−0.398386 | + | 0.917218i | \(0.630430\pi\) | |||||||
\(998\) | 31321.4 | 0.993448 | ||||||||
\(999\) | −57057.9 | −1.80704 |
(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 | 1859.4.a.n.1.13 | ✓ | 39 | |
13.12 | even | 2 | 1859.4.a.o.1.27 | yes | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.n.1.13 | ✓ | 39 | 1.1 | even | 1 | trivial | |
1859.4.a.o.1.27 | yes | 39 | 13.12 | even | 2 |