Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.95333 | −1.75127 | −0.875634 | − | 0.482975i | \(-0.839556\pi\) | ||||
−0.875634 | + | 0.482975i | \(0.839556\pi\) | |||||||
\(3\) | −0.318435 | −0.0612828 | −0.0306414 | − | 0.999530i | \(-0.509755\pi\) | ||||
−0.0306414 | + | 0.999530i | \(0.509755\pi\) | |||||||
\(4\) | 16.5355 | 2.06694 | ||||||||
\(5\) | 12.4187 | 1.11077 | 0.555383 | − | 0.831595i | \(-0.312572\pi\) | ||||
0.555383 | + | 0.831595i | \(0.312572\pi\) | |||||||
\(6\) | 1.57731 | 0.107323 | ||||||||
\(7\) | 3.53619 | 0.190936 | 0.0954681 | − | 0.995432i | \(-0.469565\pi\) | ||||
0.0954681 | + | 0.995432i | \(0.469565\pi\) | |||||||
\(8\) | −42.2793 | −1.86850 | ||||||||
\(9\) | −26.8986 | −0.996244 | ||||||||
\(10\) | −61.5142 | −1.94525 | ||||||||
\(11\) | 9.73366 | 0.266801 | 0.133400 | − | 0.991062i | \(-0.457410\pi\) | ||||
0.133400 | + | 0.991062i | \(0.457410\pi\) | |||||||
\(12\) | −5.26549 | −0.126668 | ||||||||
\(13\) | 58.2480 | 1.24270 | 0.621350 | − | 0.783533i | \(-0.286585\pi\) | ||||
0.621350 | + | 0.783533i | \(0.286585\pi\) | |||||||
\(14\) | −17.5159 | −0.334380 | ||||||||
\(15\) | −3.95456 | −0.0680709 | ||||||||
\(16\) | 77.1391 | 1.20530 | ||||||||
\(17\) | 96.5329 | 1.37722 | 0.688608 | − | 0.725134i | \(-0.258222\pi\) | ||||
0.688608 | + | 0.725134i | \(0.258222\pi\) | |||||||
\(18\) | 133.238 | 1.74469 | ||||||||
\(19\) | 130.512 | 1.57587 | 0.787933 | − | 0.615761i | \(-0.211151\pi\) | ||||
0.787933 | + | 0.615761i | \(0.211151\pi\) | |||||||
\(20\) | 205.350 | 2.29589 | ||||||||
\(21\) | −1.12605 | −0.0117011 | ||||||||
\(22\) | −48.2140 | −0.467239 | ||||||||
\(23\) | 86.1983 | 0.781460 | 0.390730 | − | 0.920505i | \(-0.372223\pi\) | ||||
0.390730 | + | 0.920505i | \(0.372223\pi\) | |||||||
\(24\) | 13.4632 | 0.114507 | ||||||||
\(25\) | 29.2253 | 0.233802 | ||||||||
\(26\) | −288.522 | −2.17630 | ||||||||
\(27\) | 17.1632 | 0.122336 | ||||||||
\(28\) | 58.4727 | 0.394653 | ||||||||
\(29\) | 78.0061 | 0.499495 | 0.249748 | − | 0.968311i | \(-0.419652\pi\) | ||||
0.249748 | + | 0.968311i | \(0.419652\pi\) | |||||||
\(30\) | 19.5883 | 0.119210 | ||||||||
\(31\) | −103.809 | −0.601439 | −0.300719 | − | 0.953713i | \(-0.597227\pi\) | ||||
−0.300719 | + | 0.953713i | \(0.597227\pi\) | |||||||
\(32\) | −43.8618 | −0.242305 | ||||||||
\(33\) | −3.09954 | −0.0163503 | ||||||||
\(34\) | −478.160 | −2.41187 | ||||||||
\(35\) | 43.9150 | 0.212085 | ||||||||
\(36\) | −444.782 | −2.05918 | ||||||||
\(37\) | 433.942 | 1.92810 | 0.964050 | − | 0.265721i | \(-0.0856100\pi\) | ||||
0.964050 | + | 0.265721i | \(0.0856100\pi\) | |||||||
\(38\) | −646.468 | −2.75976 | ||||||||
\(39\) | −18.5482 | −0.0761562 | ||||||||
\(40\) | −525.055 | −2.07546 | ||||||||
\(41\) | −265.176 | −1.01009 | −0.505043 | − | 0.863094i | \(-0.668523\pi\) | ||||
−0.505043 | + | 0.863094i | \(0.668523\pi\) | |||||||
\(42\) | 5.57768 | 0.0204918 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 160.951 | 0.551461 | ||||||||
\(45\) | −334.047 | −1.10659 | ||||||||
\(46\) | −426.969 | −1.36855 | ||||||||
\(47\) | 515.826 | 1.60087 | 0.800435 | − | 0.599419i | \(-0.204602\pi\) | ||||
0.800435 | + | 0.599419i | \(0.204602\pi\) | |||||||
\(48\) | −24.5638 | −0.0738641 | ||||||||
\(49\) | −330.495 | −0.963543 | ||||||||
\(50\) | −144.763 | −0.409450 | ||||||||
\(51\) | −30.7395 | −0.0843997 | ||||||||
\(52\) | 963.161 | 2.56858 | ||||||||
\(53\) | −142.256 | −0.368687 | −0.184343 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184343 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(54\) | −85.0151 | −0.214242 | ||||||||
\(55\) | 120.880 | 0.296353 | ||||||||
\(56\) | −149.507 | −0.356764 | ||||||||
\(57\) | −41.5595 | −0.0965735 | ||||||||
\(58\) | −386.390 | −0.874750 | ||||||||
\(59\) | −441.215 | −0.973582 | −0.486791 | − | 0.873518i | \(-0.661833\pi\) | ||||
−0.486791 | + | 0.873518i | \(0.661833\pi\) | |||||||
\(60\) | −65.3908 | −0.140698 | ||||||||
\(61\) | 465.998 | 0.978115 | 0.489057 | − | 0.872252i | \(-0.337341\pi\) | ||||
0.489057 | + | 0.872252i | \(0.337341\pi\) | |||||||
\(62\) | 514.199 | 1.05328 | ||||||||
\(63\) | −95.1185 | −0.190219 | ||||||||
\(64\) | −399.851 | −0.780959 | ||||||||
\(65\) | 723.367 | 1.38035 | ||||||||
\(66\) | 15.3530 | 0.0286338 | ||||||||
\(67\) | 445.362 | 0.812084 | 0.406042 | − | 0.913854i | \(-0.366909\pi\) | ||||
0.406042 | + | 0.913854i | \(0.366909\pi\) | |||||||
\(68\) | 1596.22 | 2.84662 | ||||||||
\(69\) | −27.4486 | −0.0478901 | ||||||||
\(70\) | −217.526 | −0.371418 | ||||||||
\(71\) | 978.896 | 1.63625 | 0.818124 | − | 0.575042i | \(-0.195014\pi\) | ||||
0.818124 | + | 0.575042i | \(0.195014\pi\) | |||||||
\(72\) | 1137.25 | 1.86148 | ||||||||
\(73\) | −28.4218 | −0.0455688 | −0.0227844 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227844 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(74\) | −2149.46 | −3.37662 | ||||||||
\(75\) | −9.30635 | −0.0143281 | ||||||||
\(76\) | 2158.08 | 3.25722 | ||||||||
\(77\) | 34.4200 | 0.0509419 | ||||||||
\(78\) | 91.8755 | 0.133370 | ||||||||
\(79\) | 6.16526 | 0.00878033 | 0.00439017 | − | 0.999990i | \(-0.498603\pi\) | ||||
0.00439017 | + | 0.999990i | \(0.498603\pi\) | |||||||
\(80\) | 957.971 | 1.33881 | ||||||||
\(81\) | 720.797 | 0.988747 | ||||||||
\(82\) | 1313.51 | 1.76893 | ||||||||
\(83\) | −773.485 | −1.02290 | −0.511452 | − | 0.859312i | \(-0.670892\pi\) | ||||
−0.511452 | + | 0.859312i | \(0.670892\pi\) | |||||||
\(84\) | −18.6197 | −0.0241855 | ||||||||
\(85\) | 1198.82 | 1.52977 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.8399 | −0.0306105 | ||||||||
\(88\) | −411.532 | −0.498516 | ||||||||
\(89\) | −18.0364 | −0.0214815 | −0.0107408 | − | 0.999942i | \(-0.503419\pi\) | ||||
−0.0107408 | + | 0.999942i | \(0.503419\pi\) | |||||||
\(90\) | 1654.65 | 1.93794 | ||||||||
\(91\) | 205.976 | 0.237276 | ||||||||
\(92\) | 1425.33 | 1.61523 | ||||||||
\(93\) | 33.0563 | 0.0368579 | ||||||||
\(94\) | −2555.06 | −2.80355 | ||||||||
\(95\) | 1620.79 | 1.75042 | ||||||||
\(96\) | 13.9671 | 0.0148491 | ||||||||
\(97\) | 1468.04 | 1.53667 | 0.768336 | − | 0.640047i | \(-0.221085\pi\) | ||||
0.768336 | + | 0.640047i | \(0.221085\pi\) | |||||||
\(98\) | 1637.05 | 1.68742 | ||||||||
\(99\) | −261.822 | −0.265799 | ||||||||
\(100\) | 483.255 | 0.483255 | ||||||||
\(101\) | 457.985 | 0.451200 | 0.225600 | − | 0.974220i | \(-0.427566\pi\) | ||||
0.225600 | + | 0.974220i | \(0.427566\pi\) | |||||||
\(102\) | 152.263 | 0.147807 | ||||||||
\(103\) | −1738.76 | −1.66335 | −0.831674 | − | 0.555265i | \(-0.812617\pi\) | ||||
−0.831674 | + | 0.555265i | \(0.812617\pi\) | |||||||
\(104\) | −2462.68 | −2.32198 | ||||||||
\(105\) | −13.9841 | −0.0129972 | ||||||||
\(106\) | 704.643 | 0.645669 | ||||||||
\(107\) | −13.2007 | −0.0119267 | −0.00596337 | − | 0.999982i | \(-0.501898\pi\) | ||||
−0.00596337 | + | 0.999982i | \(0.501898\pi\) | |||||||
\(108\) | 283.802 | 0.252860 | ||||||||
\(109\) | −1087.36 | −0.955504 | −0.477752 | − | 0.878495i | \(-0.658548\pi\) | ||||
−0.477752 | + | 0.878495i | \(0.658548\pi\) | |||||||
\(110\) | −598.758 | −0.518994 | ||||||||
\(111\) | −138.182 | −0.118159 | ||||||||
\(112\) | 272.778 | 0.230135 | ||||||||
\(113\) | 399.977 | 0.332979 | 0.166490 | − | 0.986043i | \(-0.446757\pi\) | ||||
0.166490 | + | 0.986043i | \(0.446757\pi\) | |||||||
\(114\) | 205.858 | 0.169126 | ||||||||
\(115\) | 1070.47 | 0.868020 | ||||||||
\(116\) | 1289.87 | 1.03243 | ||||||||
\(117\) | −1566.79 | −1.23803 | ||||||||
\(118\) | 2185.49 | 1.70500 | ||||||||
\(119\) | 341.358 | 0.262960 | ||||||||
\(120\) | 167.196 | 0.127190 | ||||||||
\(121\) | −1236.26 | −0.928817 | ||||||||
\(122\) | −2308.25 | −1.71294 | ||||||||
\(123\) | 84.4413 | 0.0619010 | ||||||||
\(124\) | −1716.53 | −1.24314 | ||||||||
\(125\) | −1189.40 | −0.851067 | ||||||||
\(126\) | 471.154 | 0.333125 | ||||||||
\(127\) | −935.559 | −0.653680 | −0.326840 | − | 0.945080i | \(-0.605984\pi\) | ||||
−0.326840 | + | 0.945080i | \(0.605984\pi\) | |||||||
\(128\) | 2331.49 | 1.60997 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3583.08 | −2.41736 | ||||||||
\(131\) | 133.188 | 0.0888297 | 0.0444149 | − | 0.999013i | \(-0.485858\pi\) | ||||
0.0444149 | + | 0.999013i | \(0.485858\pi\) | |||||||
\(132\) | −51.2524 | −0.0337951 | ||||||||
\(133\) | 461.514 | 0.300890 | ||||||||
\(134\) | −2206.03 | −1.42218 | ||||||||
\(135\) | 213.145 | 0.135886 | ||||||||
\(136\) | −4081.34 | −2.57332 | ||||||||
\(137\) | 520.757 | 0.324754 | 0.162377 | − | 0.986729i | \(-0.448084\pi\) | ||||
0.162377 | + | 0.986729i | \(0.448084\pi\) | |||||||
\(138\) | 135.962 | 0.0838684 | ||||||||
\(139\) | 1806.24 | 1.10218 | 0.551090 | − | 0.834446i | \(-0.314212\pi\) | ||||
0.551090 | + | 0.834446i | \(0.314212\pi\) | |||||||
\(140\) | 726.157 | 0.438368 | ||||||||
\(141\) | −164.257 | −0.0981059 | ||||||||
\(142\) | −4848.80 | −2.86551 | ||||||||
\(143\) | 566.966 | 0.331553 | ||||||||
\(144\) | −2074.93 | −1.20077 | ||||||||
\(145\) | 968.738 | 0.554823 | ||||||||
\(146\) | 140.783 | 0.0798032 | ||||||||
\(147\) | 105.241 | 0.0590487 | ||||||||
\(148\) | 7175.46 | 3.98527 | ||||||||
\(149\) | −1327.42 | −0.729841 | −0.364920 | − | 0.931039i | \(-0.618904\pi\) | ||||
−0.364920 | + | 0.931039i | \(0.618904\pi\) | |||||||
\(150\) | 46.0975 | 0.0250923 | ||||||||
\(151\) | −1591.44 | −0.857681 | −0.428841 | − | 0.903380i | \(-0.641078\pi\) | ||||
−0.428841 | + | 0.903380i | \(0.641078\pi\) | |||||||
\(152\) | −5517.94 | −2.94450 | ||||||||
\(153\) | −2596.60 | −1.37204 | ||||||||
\(154\) | −170.494 | −0.0892129 | ||||||||
\(155\) | −1289.17 | −0.668058 | ||||||||
\(156\) | −306.704 | −0.157410 | ||||||||
\(157\) | 694.025 | 0.352798 | 0.176399 | − | 0.984319i | \(-0.443555\pi\) | ||||
0.176399 | + | 0.984319i | \(0.443555\pi\) | |||||||
\(158\) | −30.5386 | −0.0153767 | ||||||||
\(159\) | 45.2994 | 0.0225942 | ||||||||
\(160\) | −544.709 | −0.269144 | ||||||||
\(161\) | 304.813 | 0.149209 | ||||||||
\(162\) | −3570.35 | −1.73156 | ||||||||
\(163\) | −2263.22 | −1.08754 | −0.543769 | − | 0.839235i | \(-0.683003\pi\) | ||||
−0.543769 | + | 0.839235i | \(0.683003\pi\) | |||||||
\(164\) | −4384.82 | −2.08779 | ||||||||
\(165\) | −38.4924 | −0.0181614 | ||||||||
\(166\) | 3831.33 | 1.79138 | ||||||||
\(167\) | 866.676 | 0.401589 | 0.200795 | − | 0.979633i | \(-0.435648\pi\) | ||||
0.200795 | + | 0.979633i | \(0.435648\pi\) | |||||||
\(168\) | 47.6084 | 0.0218635 | ||||||||
\(169\) | 1195.83 | 0.544301 | ||||||||
\(170\) | −5938.15 | −2.67903 | ||||||||
\(171\) | −3510.58 | −1.56995 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2626.97 | −1.15448 | −0.577240 | − | 0.816575i | \(-0.695870\pi\) | ||||
−0.577240 | + | 0.816575i | \(0.695870\pi\) | |||||||
\(174\) | 123.040 | 0.0536072 | ||||||||
\(175\) | 103.346 | 0.0446413 | ||||||||
\(176\) | 750.846 | 0.321575 | ||||||||
\(177\) | 140.498 | 0.0596639 | ||||||||
\(178\) | 89.3403 | 0.0376199 | ||||||||
\(179\) | 609.964 | 0.254698 | 0.127349 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127349 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(180\) | −5523.64 | −2.28726 | ||||||||
\(181\) | −1467.02 | −0.602446 | −0.301223 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301223 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(182\) | −1020.27 | −0.415534 | ||||||||
\(183\) | −148.390 | −0.0599416 | ||||||||
\(184\) | −3644.40 | −1.46016 | ||||||||
\(185\) | 5389.02 | 2.14167 | ||||||||
\(186\) | −163.739 | −0.0645480 | ||||||||
\(187\) | 939.618 | 0.367442 | ||||||||
\(188\) | 8529.45 | 3.30890 | ||||||||
\(189\) | 60.6923 | 0.0233583 | ||||||||
\(190\) | −8028.33 | −3.06545 | ||||||||
\(191\) | 640.656 | 0.242703 | 0.121351 | − | 0.992610i | \(-0.461277\pi\) | ||||
0.121351 | + | 0.992610i | \(0.461277\pi\) | |||||||
\(192\) | 127.327 | 0.0478594 | ||||||||
\(193\) | 205.292 | 0.0765660 | 0.0382830 | − | 0.999267i | \(-0.487811\pi\) | ||||
0.0382830 | + | 0.999267i | \(0.487811\pi\) | |||||||
\(194\) | −7271.70 | −2.69112 | ||||||||
\(195\) | −230.345 | −0.0845917 | ||||||||
\(196\) | −5464.91 | −1.99159 | ||||||||
\(197\) | 3746.36 | 1.35491 | 0.677454 | − | 0.735565i | \(-0.263083\pi\) | ||||
0.677454 | + | 0.735565i | \(0.263083\pi\) | |||||||
\(198\) | 1296.89 | 0.465485 | ||||||||
\(199\) | 166.688 | 0.0593779 | 0.0296890 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296890 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(200\) | −1235.62 | −0.436859 | ||||||||
\(201\) | −141.819 | −0.0497668 | ||||||||
\(202\) | −2268.55 | −0.790173 | ||||||||
\(203\) | 275.844 | 0.0953717 | ||||||||
\(204\) | −508.293 | −0.174449 | ||||||||
\(205\) | −3293.15 | −1.12197 | ||||||||
\(206\) | 8612.64 | 2.91297 | ||||||||
\(207\) | −2318.61 | −0.778525 | ||||||||
\(208\) | 4493.20 | 1.49782 | ||||||||
\(209\) | 1270.36 | 0.420442 | ||||||||
\(210\) | 69.2678 | 0.0227616 | ||||||||
\(211\) | −4969.17 | −1.62129 | −0.810644 | − | 0.585539i | \(-0.800883\pi\) | ||||
−0.810644 | + | 0.585539i | \(0.800883\pi\) | |||||||
\(212\) | −2352.28 | −0.762053 | ||||||||
\(213\) | −311.715 | −0.100274 | ||||||||
\(214\) | 65.3875 | 0.0208869 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −725.647 | −0.228584 | ||||||||
\(217\) | −367.087 | −0.114836 | ||||||||
\(218\) | 5386.04 | 1.67334 | ||||||||
\(219\) | 9.05050 | 0.00279259 | ||||||||
\(220\) | 1998.81 | 0.612544 | ||||||||
\(221\) | 5622.85 | 1.71147 | ||||||||
\(222\) | 684.464 | 0.206929 | ||||||||
\(223\) | 4304.44 | 1.29259 | 0.646293 | − | 0.763090i | \(-0.276319\pi\) | ||||
0.646293 | + | 0.763090i | \(0.276319\pi\) | |||||||
\(224\) | −155.104 | −0.0462647 | ||||||||
\(225\) | −786.119 | −0.232924 | ||||||||
\(226\) | −1981.22 | −0.583136 | ||||||||
\(227\) | 1141.43 | 0.333742 | 0.166871 | − | 0.985979i | \(-0.446634\pi\) | ||||
0.166871 | + | 0.985979i | \(0.446634\pi\) | |||||||
\(228\) | −687.208 | −0.199612 | ||||||||
\(229\) | 2198.56 | 0.634433 | 0.317216 | − | 0.948353i | \(-0.397252\pi\) | ||||
0.317216 | + | 0.948353i | \(0.397252\pi\) | |||||||
\(230\) | −5302.42 | −1.52014 | ||||||||
\(231\) | −10.9605 | −0.00312186 | ||||||||
\(232\) | −3298.04 | −0.933305 | ||||||||
\(233\) | −2798.50 | −0.786849 | −0.393424 | − | 0.919357i | \(-0.628710\pi\) | ||||
−0.393424 | + | 0.919357i | \(0.628710\pi\) | |||||||
\(234\) | 7760.83 | 2.16813 | ||||||||
\(235\) | 6405.91 | 1.77819 | ||||||||
\(236\) | −7295.72 | −2.01234 | ||||||||
\(237\) | −1.96324 | −0.000538084 0 | ||||||||
\(238\) | −1690.86 | −0.460514 | ||||||||
\(239\) | 1924.99 | 0.520992 | 0.260496 | − | 0.965475i | \(-0.416114\pi\) | ||||
0.260496 | + | 0.965475i | \(0.416114\pi\) | |||||||
\(240\) | −305.052 | −0.0820458 | ||||||||
\(241\) | 299.388 | 0.0800218 | 0.0400109 | − | 0.999199i | \(-0.487261\pi\) | ||||
0.0400109 | + | 0.999199i | \(0.487261\pi\) | |||||||
\(242\) | 6123.59 | 1.62661 | ||||||||
\(243\) | −692.933 | −0.182929 | ||||||||
\(244\) | 7705.52 | 2.02170 | ||||||||
\(245\) | −4104.34 | −1.07027 | ||||||||
\(246\) | −418.266 | −0.108405 | ||||||||
\(247\) | 7602.05 | 1.95833 | ||||||||
\(248\) | 4388.95 | 1.12379 | ||||||||
\(249\) | 246.305 | 0.0626864 | ||||||||
\(250\) | 5891.51 | 1.49045 | ||||||||
\(251\) | 4016.43 | 1.01002 | 0.505010 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505010 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(252\) | −1572.83 | −0.393171 | ||||||||
\(253\) | 839.024 | 0.208494 | ||||||||
\(254\) | 4634.13 | 1.14477 | ||||||||
\(255\) | −381.746 | −0.0937484 | ||||||||
\(256\) | −8349.84 | −2.03853 | ||||||||
\(257\) | −3740.00 | −0.907762 | −0.453881 | − | 0.891062i | \(-0.649961\pi\) | ||||
−0.453881 | + | 0.891062i | \(0.649961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1534.50 | 0.368144 | ||||||||
\(260\) | 11961.3 | 2.85310 | ||||||||
\(261\) | −2098.25 | −0.497619 | ||||||||
\(262\) | −659.725 | −0.155565 | ||||||||
\(263\) | −5952.87 | −1.39570 | −0.697851 | − | 0.716243i | \(-0.745860\pi\) | ||||
−0.697851 | + | 0.716243i | \(0.745860\pi\) | |||||||
\(264\) | 131.046 | 0.0305505 | ||||||||
\(265\) | −1766.64 | −0.409525 | ||||||||
\(266\) | −2286.03 | −0.526939 | ||||||||
\(267\) | 5.74342 | 0.00131645 | ||||||||
\(268\) | 7364.29 | 1.67853 | ||||||||
\(269\) | 887.028 | 0.201052 | 0.100526 | − | 0.994934i | \(-0.467947\pi\) | ||||
0.100526 | + | 0.994934i | \(0.467947\pi\) | |||||||
\(270\) | −1055.78 | −0.237973 | ||||||||
\(271\) | −8634.54 | −1.93546 | −0.967732 | − | 0.251981i | \(-0.918918\pi\) | ||||
−0.967732 | + | 0.251981i | \(0.918918\pi\) | |||||||
\(272\) | 7446.47 | 1.65996 | ||||||||
\(273\) | −65.5899 | −0.0145410 | ||||||||
\(274\) | −2579.48 | −0.568731 | ||||||||
\(275\) | 284.469 | 0.0623786 | ||||||||
\(276\) | −453.876 | −0.0989860 | ||||||||
\(277\) | −7032.45 | −1.52541 | −0.762705 | − | 0.646746i | \(-0.776129\pi\) | ||||
−0.762705 | + | 0.646746i | \(0.776129\pi\) | |||||||
\(278\) | −8946.89 | −1.93021 | ||||||||
\(279\) | 2792.31 | 0.599180 | ||||||||
\(280\) | −1856.69 | −0.396281 | ||||||||
\(281\) | −6538.48 | −1.38809 | −0.694045 | − | 0.719932i | \(-0.744173\pi\) | ||||
−0.694045 | + | 0.719932i | \(0.744173\pi\) | |||||||
\(282\) | 813.620 | 0.171810 | ||||||||
\(283\) | −5321.63 | −1.11780 | −0.558901 | − | 0.829235i | \(-0.688777\pi\) | ||||
−0.558901 | + | 0.829235i | \(0.688777\pi\) | |||||||
\(284\) | 16186.5 | 3.38202 | ||||||||
\(285\) | −516.117 | −0.107271 | ||||||||
\(286\) | −2808.37 | −0.580638 | ||||||||
\(287\) | −937.712 | −0.192862 | ||||||||
\(288\) | 1179.82 | 0.241395 | ||||||||
\(289\) | 4405.61 | 0.896725 | ||||||||
\(290\) | −4798.48 | −0.971643 | ||||||||
\(291\) | −467.476 | −0.0941716 | ||||||||
\(292\) | −469.969 | −0.0941879 | ||||||||
\(293\) | 9700.76 | 1.93421 | 0.967106 | − | 0.254373i | \(-0.0818689\pi\) | ||||
0.967106 | + | 0.254373i | \(0.0818689\pi\) | |||||||
\(294\) | −521.295 | −0.103410 | ||||||||
\(295\) | −5479.34 | −1.08142 | ||||||||
\(296\) | −18346.8 | −3.60265 | ||||||||
\(297\) | 167.061 | 0.0326392 | ||||||||
\(298\) | 6575.14 | 1.27815 | ||||||||
\(299\) | 5020.88 | 0.971120 | ||||||||
\(300\) | −153.885 | −0.0296152 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7882.95 | 1.50203 | ||||||||
\(303\) | −145.839 | −0.0276508 | ||||||||
\(304\) | 10067.6 | 1.89939 | ||||||||
\(305\) | 5787.12 | 1.08646 | ||||||||
\(306\) | 12861.8 | 2.40282 | ||||||||
\(307\) | 917.394 | 0.170549 | 0.0852743 | − | 0.996358i | \(-0.472823\pi\) | ||||
0.0852743 | + | 0.996358i | \(0.472823\pi\) | |||||||
\(308\) | 569.153 | 0.105294 | ||||||||
\(309\) | 553.681 | 0.101935 | ||||||||
\(310\) | 6385.71 | 1.16995 | ||||||||
\(311\) | 2039.76 | 0.371911 | 0.185956 | − | 0.982558i | \(-0.440462\pi\) | ||||
0.185956 | + | 0.982558i | \(0.440462\pi\) | |||||||
\(312\) | 784.204 | 0.142298 | ||||||||
\(313\) | 1019.23 | 0.184058 | 0.0920290 | − | 0.995756i | \(-0.470665\pi\) | ||||
0.0920290 | + | 0.995756i | \(0.470665\pi\) | |||||||
\(314\) | −3437.74 | −0.617844 | ||||||||
\(315\) | −1181.25 | −0.211289 | ||||||||
\(316\) | 101.946 | 0.0181484 | ||||||||
\(317\) | −200.716 | −0.0355626 | −0.0177813 | − | 0.999842i | \(-0.505660\pi\) | ||||
−0.0177813 | + | 0.999842i | \(0.505660\pi\) | |||||||
\(318\) | −224.383 | −0.0395685 | ||||||||
\(319\) | 759.284 | 0.133266 | ||||||||
\(320\) | −4965.65 | −0.867463 | ||||||||
\(321\) | 4.20357 | 0.000730904 0 | ||||||||
\(322\) | −1509.84 | −0.261305 | ||||||||
\(323\) | 12598.7 | 2.17031 | ||||||||
\(324\) | 11918.7 | 2.04368 | ||||||||
\(325\) | 1702.31 | 0.290546 | ||||||||
\(326\) | 11210.5 | 1.90457 | ||||||||
\(327\) | 346.253 | 0.0585560 | ||||||||
\(328\) | 11211.4 | 1.88734 | ||||||||
\(329\) | 1824.06 | 0.305664 | ||||||||
\(330\) | 190.666 | 0.0318054 | ||||||||
\(331\) | 11939.2 | 1.98259 | 0.991297 | − | 0.131641i | \(-0.0420247\pi\) | ||||
0.991297 | + | 0.131641i | \(0.0420247\pi\) | |||||||
\(332\) | −12790.0 | −2.11428 | ||||||||
\(333\) | −11672.4 | −1.92086 | ||||||||
\(334\) | −4292.93 | −0.703290 | ||||||||
\(335\) | 5530.84 | 0.902036 | ||||||||
\(336\) | −86.8622 | −0.0141033 | ||||||||
\(337\) | −9933.49 | −1.60567 | −0.802837 | − | 0.596199i | \(-0.796677\pi\) | ||||
−0.802837 | + | 0.596199i | \(0.796677\pi\) | |||||||
\(338\) | −5923.35 | −0.953218 | ||||||||
\(339\) | −127.367 | −0.0204059 | ||||||||
\(340\) | 19823.1 | 3.16193 | ||||||||
\(341\) | −1010.44 | −0.160464 | ||||||||
\(342\) | 17389.1 | 2.74940 | ||||||||
\(343\) | −2381.61 | −0.374911 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −340.877 | −0.0531947 | ||||||||
\(346\) | 13012.3 | 2.02180 | ||||||||
\(347\) | −3888.13 | −0.601515 | −0.300757 | − | 0.953701i | \(-0.597239\pi\) | ||||
−0.300757 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(348\) | −410.740 | −0.0632700 | ||||||||
\(349\) | −1958.57 | −0.300401 | −0.150201 | − | 0.988656i | \(-0.547992\pi\) | ||||
−0.150201 | + | 0.988656i | \(0.547992\pi\) | |||||||
\(350\) | −511.908 | −0.0781789 | ||||||||
\(351\) | 999.722 | 0.152026 | ||||||||
\(352\) | −426.936 | −0.0646470 | ||||||||
\(353\) | −2805.65 | −0.423030 | −0.211515 | − | 0.977375i | \(-0.567840\pi\) | ||||
−0.211515 | + | 0.977375i | \(0.567840\pi\) | |||||||
\(354\) | −695.936 | −0.104487 | ||||||||
\(355\) | 12156.7 | 1.81749 | ||||||||
\(356\) | −298.241 | −0.0444010 | ||||||||
\(357\) | −108.701 | −0.0161150 | ||||||||
\(358\) | −3021.36 | −0.446044 | ||||||||
\(359\) | 5817.68 | 0.855279 | 0.427639 | − | 0.903949i | \(-0.359345\pi\) | ||||
0.427639 | + | 0.903949i | \(0.359345\pi\) | |||||||
\(360\) | 14123.3 | 2.06767 | ||||||||
\(361\) | 10174.3 | 1.48335 | ||||||||
\(362\) | 7266.64 | 1.05504 | ||||||||
\(363\) | 393.667 | 0.0569206 | ||||||||
\(364\) | 3405.92 | 0.490436 | ||||||||
\(365\) | −352.963 | −0.0506163 | ||||||||
\(366\) | 735.026 | 0.104974 | ||||||||
\(367\) | 1916.69 | 0.272617 | 0.136308 | − | 0.990666i | \(-0.456476\pi\) | ||||
0.136308 | + | 0.990666i | \(0.456476\pi\) | |||||||
\(368\) | 6649.26 | 0.941893 | ||||||||
\(369\) | 7132.86 | 1.00629 | ||||||||
\(370\) | −26693.6 | −3.75064 | ||||||||
\(371\) | −503.045 | −0.0703956 | ||||||||
\(372\) | 546.603 | 0.0761830 | ||||||||
\(373\) | 6773.49 | 0.940263 | 0.470132 | − | 0.882596i | \(-0.344206\pi\) | ||||
0.470132 | + | 0.882596i | \(0.344206\pi\) | |||||||
\(374\) | −4654.24 | −0.643490 | ||||||||
\(375\) | 378.747 | 0.0521558 | ||||||||
\(376\) | −21808.7 | −2.99122 | ||||||||
\(377\) | 4543.70 | 0.620722 | ||||||||
\(378\) | −300.629 | −0.0409066 | ||||||||
\(379\) | 7501.32 | 1.01667 | 0.508333 | − | 0.861160i | \(-0.330262\pi\) | ||||
0.508333 | + | 0.861160i | \(0.330262\pi\) | |||||||
\(380\) | 26800.6 | 3.61801 | ||||||||
\(381\) | 297.915 | 0.0400594 | ||||||||
\(382\) | −3173.38 | −0.425037 | ||||||||
\(383\) | 3690.85 | 0.492411 | 0.246206 | − | 0.969218i | \(-0.420816\pi\) | ||||
0.246206 | + | 0.969218i | \(0.420816\pi\) | |||||||
\(384\) | −742.428 | −0.0986637 | ||||||||
\(385\) | 427.454 | 0.0565845 | ||||||||
\(386\) | −1016.88 | −0.134088 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24274.8 | 3.17621 | ||||||||
\(389\) | 3452.25 | 0.449964 | 0.224982 | − | 0.974363i | \(-0.427768\pi\) | ||||
0.224982 | + | 0.974363i | \(0.427768\pi\) | |||||||
\(390\) | 1140.98 | 0.148143 | ||||||||
\(391\) | 8320.97 | 1.07624 | ||||||||
\(392\) | 13973.1 | 1.80038 | ||||||||
\(393\) | −42.4117 | −0.00544374 | ||||||||
\(394\) | −18557.0 | −2.37281 | ||||||||
\(395\) | 76.5648 | 0.00975290 | ||||||||
\(396\) | −4329.36 | −0.549390 | ||||||||
\(397\) | −5704.24 | −0.721128 | −0.360564 | − | 0.932734i | \(-0.617416\pi\) | ||||
−0.360564 | + | 0.932734i | \(0.617416\pi\) | |||||||
\(398\) | −825.662 | −0.103987 | ||||||||
\(399\) | −146.962 | −0.0184394 | ||||||||
\(400\) | 2254.41 | 0.281802 | ||||||||
\(401\) | −10612.3 | −1.32158 | −0.660788 | − | 0.750573i | \(-0.729778\pi\) | ||||
−0.660788 | + | 0.750573i | \(0.729778\pi\) | |||||||
\(402\) | 702.476 | 0.0871551 | ||||||||
\(403\) | −6046.65 | −0.747407 | ||||||||
\(404\) | 7573.02 | 0.932604 | ||||||||
\(405\) | 8951.39 | 1.09827 | ||||||||
\(406\) | −1366.35 | −0.167021 | ||||||||
\(407\) | 4223.85 | 0.514418 | ||||||||
\(408\) | 1299.64 | 0.157701 | ||||||||
\(409\) | 9169.13 | 1.10852 | 0.554260 | − | 0.832344i | \(-0.313001\pi\) | ||||
0.554260 | + | 0.832344i | \(0.313001\pi\) | |||||||
\(410\) | 16312.1 | 1.96487 | ||||||||
\(411\) | −165.827 | −0.0199018 | ||||||||
\(412\) | −28751.2 | −3.43804 | ||||||||
\(413\) | −1560.22 | −0.185892 | ||||||||
\(414\) | 11484.9 | 1.36341 | ||||||||
\(415\) | −9605.71 | −1.13621 | ||||||||
\(416\) | −2554.86 | −0.301112 | ||||||||
\(417\) | −575.169 | −0.0675447 | ||||||||
\(418\) | −6292.50 | −0.736307 | ||||||||
\(419\) | 9637.63 | 1.12370 | 0.561849 | − | 0.827240i | \(-0.310090\pi\) | ||||
0.561849 | + | 0.827240i | \(0.310090\pi\) | |||||||
\(420\) | −231.234 | −0.0268644 | ||||||||
\(421\) | −7920.50 | −0.916916 | −0.458458 | − | 0.888716i | \(-0.651598\pi\) | ||||
−0.458458 | + | 0.888716i | \(0.651598\pi\) | |||||||
\(422\) | 24614.0 | 2.83931 | ||||||||
\(423\) | −13875.0 | −1.59486 | ||||||||
\(424\) | 6014.49 | 0.688890 | ||||||||
\(425\) | 2821.20 | 0.321996 | ||||||||
\(426\) | 1544.03 | 0.175606 | ||||||||
\(427\) | 1647.86 | 0.186757 | ||||||||
\(428\) | −218.280 | −0.0246518 | ||||||||
\(429\) | −180.542 | −0.0203185 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11681.4 | 1.30550 | 0.652751 | − | 0.757572i | \(-0.273615\pi\) | ||||
0.652751 | + | 0.757572i | \(0.273615\pi\) | |||||||
\(432\) | 1323.95 | 0.147451 | ||||||||
\(433\) | 1330.29 | 0.147644 | 0.0738219 | − | 0.997271i | \(-0.476480\pi\) | ||||
0.0738219 | + | 0.997271i | \(0.476480\pi\) | |||||||
\(434\) | 1818.30 | 0.201109 | ||||||||
\(435\) | −308.480 | −0.0340011 | ||||||||
\(436\) | −17980.0 | −1.97497 | ||||||||
\(437\) | 11249.9 | 1.23148 | ||||||||
\(438\) | −44.8302 | −0.00489057 | ||||||||
\(439\) | −9593.16 | −1.04295 | −0.521477 | − | 0.853266i | \(-0.674619\pi\) | ||||
−0.521477 | + | 0.853266i | \(0.674619\pi\) | |||||||
\(440\) | −5110.71 | −0.553735 | ||||||||
\(441\) | 8889.86 | 0.959925 | ||||||||
\(442\) | −27851.9 | −2.99723 | ||||||||
\(443\) | 8919.62 | 0.956623 | 0.478311 | − | 0.878190i | \(-0.341249\pi\) | ||||
0.478311 | + | 0.878190i | \(0.341249\pi\) | |||||||
\(444\) | −2284.92 | −0.244228 | ||||||||
\(445\) | −223.989 | −0.0238609 | ||||||||
\(446\) | −21321.3 | −2.26366 | ||||||||
\(447\) | 422.696 | 0.0447267 | ||||||||
\(448\) | −1413.95 | −0.149113 | ||||||||
\(449\) | −14843.4 | −1.56014 | −0.780068 | − | 0.625694i | \(-0.784816\pi\) | ||||
−0.780068 | + | 0.625694i | \(0.784816\pi\) | |||||||
\(450\) | 3893.91 | 0.407913 | ||||||||
\(451\) | −2581.13 | −0.269492 | ||||||||
\(452\) | 6613.82 | 0.688248 | ||||||||
\(453\) | 506.772 | 0.0525612 | ||||||||
\(454\) | −5653.88 | −0.584471 | ||||||||
\(455\) | 2557.96 | 0.263558 | ||||||||
\(456\) | 1757.11 | 0.180447 | ||||||||
\(457\) | 13541.6 | 1.38610 | 0.693051 | − | 0.720889i | \(-0.256266\pi\) | ||||
0.693051 | + | 0.720889i | \(0.256266\pi\) | |||||||
\(458\) | −10890.2 | −1.11106 | ||||||||
\(459\) | 1656.81 | 0.168483 | ||||||||
\(460\) | 17700.9 | 1.79414 | ||||||||
\(461\) | 12039.0 | 1.21629 | 0.608146 | − | 0.793825i | \(-0.291914\pi\) | ||||
0.608146 | + | 0.793825i | \(0.291914\pi\) | |||||||
\(462\) | 54.2912 | 0.00546722 | ||||||||
\(463\) | −13045.9 | −1.30949 | −0.654745 | − | 0.755850i | \(-0.727224\pi\) | ||||
−0.654745 | + | 0.755850i | \(0.727224\pi\) | |||||||
\(464\) | 6017.32 | 0.602041 | ||||||||
\(465\) | 410.518 | 0.0409405 | ||||||||
\(466\) | 13861.9 | 1.37798 | ||||||||
\(467\) | 8743.50 | 0.866383 | 0.433192 | − | 0.901302i | \(-0.357387\pi\) | ||||
0.433192 | + | 0.901302i | \(0.357387\pi\) | |||||||
\(468\) | −25907.7 | −2.55894 | ||||||||
\(469\) | 1574.88 | 0.155056 | ||||||||
\(470\) | −31730.6 | −3.11409 | ||||||||
\(471\) | −221.002 | −0.0216205 | ||||||||
\(472\) | 18654.3 | 1.81913 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.72456 | 0.000942329 0 | ||||||||
\(475\) | 3814.24 | 0.368441 | ||||||||
\(476\) | 5644.54 | 0.543523 | ||||||||
\(477\) | 3826.49 | 0.367302 | ||||||||
\(478\) | −9535.11 | −0.912397 | ||||||||
\(479\) | −1878.47 | −0.179185 | −0.0895924 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895924 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(480\) | 173.454 | 0.0164939 | ||||||||
\(481\) | 25276.3 | 2.39605 | ||||||||
\(482\) | −1482.97 | −0.140140 | ||||||||
\(483\) | −97.0632 | −0.00914395 | ||||||||
\(484\) | −20442.1 | −1.91981 | ||||||||
\(485\) | 18231.2 | 1.70688 | ||||||||
\(486\) | 3432.33 | 0.320357 | ||||||||
\(487\) | −10129.4 | −0.942520 | −0.471260 | − | 0.881994i | \(-0.656201\pi\) | ||||
−0.471260 | + | 0.881994i | \(0.656201\pi\) | |||||||
\(488\) | −19702.1 | −1.82760 | ||||||||
\(489\) | 720.687 | 0.0666474 | ||||||||
\(490\) | 20330.2 | 1.87433 | ||||||||
\(491\) | 9039.71 | 0.830868 | 0.415434 | − | 0.909623i | \(-0.363630\pi\) | ||||
0.415434 | + | 0.909623i | \(0.363630\pi\) | |||||||
\(492\) | 1396.28 | 0.127946 | ||||||||
\(493\) | 7530.16 | 0.687913 | ||||||||
\(494\) | −37655.5 | −3.42956 | ||||||||
\(495\) | −3251.50 | −0.295240 | ||||||||
\(496\) | −8007.71 | −0.724913 | ||||||||
\(497\) | 3461.56 | 0.312419 | ||||||||
\(498\) | −1220.03 | −0.109781 | ||||||||
\(499\) | −11297.8 | −1.01354 | −0.506771 | − | 0.862081i | \(-0.669161\pi\) | ||||
−0.506771 | + | 0.862081i | \(0.669161\pi\) | |||||||
\(500\) | −19667.4 | −1.75910 | ||||||||
\(501\) | −275.980 | −0.0246105 | ||||||||
\(502\) | −19894.7 | −1.76881 | ||||||||
\(503\) | −8507.23 | −0.754113 | −0.377056 | − | 0.926190i | \(-0.623064\pi\) | ||||
−0.377056 | + | 0.926190i | \(0.623064\pi\) | |||||||
\(504\) | 4021.54 | 0.355424 | ||||||||
\(505\) | 5687.60 | 0.501178 | ||||||||
\(506\) | −4155.97 | −0.365129 | ||||||||
\(507\) | −380.794 | −0.0333563 | ||||||||
\(508\) | −15469.9 | −1.35112 | ||||||||
\(509\) | 963.852 | 0.0839332 | 0.0419666 | − | 0.999119i | \(-0.486638\pi\) | ||||
0.0419666 | + | 0.999119i | \(0.486638\pi\) | |||||||
\(510\) | 1890.91 | 0.164179 | ||||||||
\(511\) | −100.505 | −0.00870073 | ||||||||
\(512\) | 22707.6 | 1.96005 | ||||||||
\(513\) | 2240.00 | 0.192784 | ||||||||
\(514\) | 18525.5 | 1.58973 | ||||||||
\(515\) | −21593.2 | −1.84759 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5020.87 | 0.427113 | ||||||||
\(518\) | −7600.90 | −0.644719 | ||||||||
\(519\) | 836.520 | 0.0707498 | ||||||||
\(520\) | −30583.4 | −2.57918 | ||||||||
\(521\) | 2246.41 | 0.188900 | 0.0944500 | − | 0.995530i | \(-0.469891\pi\) | ||||
0.0944500 | + | 0.995530i | \(0.469891\pi\) | |||||||
\(522\) | 10393.4 | 0.871465 | ||||||||
\(523\) | 5441.13 | 0.454921 | 0.227461 | − | 0.973787i | \(-0.426958\pi\) | ||||
0.227461 | + | 0.973787i | \(0.426958\pi\) | |||||||
\(524\) | 2202.33 | 0.183606 | ||||||||
\(525\) | −32.9090 | −0.00273575 | ||||||||
\(526\) | 29486.5 | 2.44425 | ||||||||
\(527\) | −10021.0 | −0.828311 | ||||||||
\(528\) | −239.096 | −0.0197070 | ||||||||
\(529\) | −4736.85 | −0.389320 | ||||||||
\(530\) | 8750.78 | 0.717188 | ||||||||
\(531\) | 11868.1 | 0.969926 | ||||||||
\(532\) | 7631.37 | 0.621921 | ||||||||
\(533\) | −15446.0 | −1.25523 | ||||||||
\(534\) | −28.4491 | −0.00230545 | ||||||||
\(535\) | −163.936 | −0.0132478 | ||||||||
\(536\) | −18829.6 | −1.51738 | ||||||||
\(537\) | −194.234 | −0.0156086 | ||||||||
\(538\) | −4393.74 | −0.352096 | ||||||||
\(539\) | −3216.93 | −0.257074 | ||||||||
\(540\) | 3524.47 | 0.280869 | ||||||||
\(541\) | 8047.68 | 0.639550 | 0.319775 | − | 0.947493i | \(-0.396393\pi\) | ||||
0.319775 | + | 0.947493i | \(0.396393\pi\) | |||||||
\(542\) | 42769.8 | 3.38952 | ||||||||
\(543\) | 467.150 | 0.0369196 | ||||||||
\(544\) | −4234.11 | −0.333706 | ||||||||
\(545\) | −13503.6 | −1.06134 | ||||||||
\(546\) | 324.889 | 0.0254651 | ||||||||
\(547\) | −5703.27 | −0.445803 | −0.222902 | − | 0.974841i | \(-0.571553\pi\) | ||||
−0.222902 | + | 0.974841i | \(0.571553\pi\) | |||||||
\(548\) | 8610.99 | 0.671247 | ||||||||
\(549\) | −12534.7 | −0.974441 | ||||||||
\(550\) | −1409.07 | −0.109242 | ||||||||
\(551\) | 10180.7 | 0.787138 | ||||||||
\(552\) | 1160.50 | 0.0894825 | ||||||||
\(553\) | 21.8015 | 0.00167648 | ||||||||
\(554\) | 34834.1 | 2.67140 | ||||||||
\(555\) | −1716.05 | −0.131248 | ||||||||
\(556\) | 29867.0 | 2.27814 | ||||||||
\(557\) | −20648.4 | −1.57074 | −0.785369 | − | 0.619027i | \(-0.787527\pi\) | ||||
−0.785369 | + | 0.619027i | \(0.787527\pi\) | |||||||
\(558\) | −13831.2 | −1.04932 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3387.57 | 0.255626 | ||||||||
\(561\) | −299.207 | −0.0225179 | ||||||||
\(562\) | 32387.3 | 2.43092 | ||||||||
\(563\) | 12005.8 | 0.898728 | 0.449364 | − | 0.893349i | \(-0.351651\pi\) | ||||
0.449364 | + | 0.893349i | \(0.351651\pi\) | |||||||
\(564\) | −2716.07 | −0.202779 | ||||||||
\(565\) | 4967.21 | 0.369862 | ||||||||
\(566\) | 26359.8 | 1.95757 | ||||||||
\(567\) | 2548.87 | 0.188788 | ||||||||
\(568\) | −41387.0 | −3.05732 | ||||||||
\(569\) | 12384.5 | 0.912450 | 0.456225 | − | 0.889864i | \(-0.349201\pi\) | ||||
0.456225 | + | 0.889864i | \(0.349201\pi\) | |||||||
\(570\) | 2556.50 | 0.187860 | ||||||||
\(571\) | 5347.17 | 0.391895 | 0.195948 | − | 0.980614i | \(-0.437222\pi\) | ||||
0.195948 | + | 0.980614i | \(0.437222\pi\) | |||||||
\(572\) | 9375.08 | 0.685300 | ||||||||
\(573\) | −204.007 | −0.0148735 | ||||||||
\(574\) | 4644.80 | 0.337753 | ||||||||
\(575\) | 2519.17 | 0.182707 | ||||||||
\(576\) | 10755.4 | 0.778026 | ||||||||
\(577\) | −14667.0 | −1.05822 | −0.529112 | − | 0.848552i | \(-0.677475\pi\) | ||||
−0.529112 | + | 0.848552i | \(0.677475\pi\) | |||||||
\(578\) | −21822.4 | −1.57041 | ||||||||
\(579\) | −65.3721 | −0.00469218 | ||||||||
\(580\) | 16018.6 | 1.14678 | ||||||||
\(581\) | −2735.19 | −0.195309 | ||||||||
\(582\) | 2315.57 | 0.164920 | ||||||||
\(583\) | −1384.67 | −0.0983659 | ||||||||
\(584\) | 1201.65 | 0.0851451 | ||||||||
\(585\) | −19457.6 | −1.37516 | ||||||||
\(586\) | −48051.1 | −3.38732 | ||||||||
\(587\) | 10701.6 | 0.752472 | 0.376236 | − | 0.926524i | \(-0.377218\pi\) | ||||
0.376236 | + | 0.926524i | \(0.377218\pi\) | |||||||
\(588\) | 1740.22 | 0.122050 | ||||||||
\(589\) | −13548.3 | −0.947786 | ||||||||
\(590\) | 27141.0 | 1.89386 | ||||||||
\(591\) | −1192.97 | −0.0830326 | ||||||||
\(592\) | 33473.9 | 2.32394 | ||||||||
\(593\) | 26097.6 | 1.80725 | 0.903627 | − | 0.428320i | \(-0.140894\pi\) | ||||
0.903627 | + | 0.428320i | \(0.140894\pi\) | |||||||
\(594\) | −827.507 | −0.0571600 | ||||||||
\(595\) | 4239.24 | 0.292088 | ||||||||
\(596\) | −21949.5 | −1.50854 | ||||||||
\(597\) | −53.0793 | −0.00363885 | ||||||||
\(598\) | −24870.1 | −1.70069 | ||||||||
\(599\) | 21865.5 | 1.49149 | 0.745743 | − | 0.666234i | \(-0.232095\pi\) | ||||
0.745743 | + | 0.666234i | \(0.232095\pi\) | |||||||
\(600\) | 393.466 | 0.0267719 | ||||||||
\(601\) | 20916.6 | 1.41965 | 0.709823 | − | 0.704380i | \(-0.248775\pi\) | ||||
0.709823 | + | 0.704380i | \(0.248775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11979.6 | −0.809035 | ||||||||
\(604\) | −26315.3 | −1.77278 | ||||||||
\(605\) | −15352.8 | −1.03170 | ||||||||
\(606\) | 722.387 | 0.0484240 | ||||||||
\(607\) | 5440.14 | 0.363770 | 0.181885 | − | 0.983320i | \(-0.441780\pi\) | ||||
0.181885 | + | 0.983320i | \(0.441780\pi\) | |||||||
\(608\) | −5724.48 | −0.381839 | ||||||||
\(609\) | −87.8384 | −0.00584465 | ||||||||
\(610\) | −28665.5 | −1.90268 | ||||||||
\(611\) | 30045.8 | 1.98940 | ||||||||
\(612\) | −42936.1 | −2.83593 | ||||||||
\(613\) | 20121.1 | 1.32575 | 0.662875 | − | 0.748730i | \(-0.269336\pi\) | ||||
0.662875 | + | 0.748730i | \(0.269336\pi\) | |||||||
\(614\) | −4544.16 | −0.298676 | ||||||||
\(615\) | 1048.66 | 0.0687575 | ||||||||
\(616\) | −1455.25 | −0.0951848 | ||||||||
\(617\) | −2560.72 | −0.167084 | −0.0835419 | − | 0.996504i | \(-0.526623\pi\) | ||||
−0.0835419 | + | 0.996504i | \(0.526623\pi\) | |||||||
\(618\) | −2742.57 | −0.178515 | ||||||||
\(619\) | −5669.37 | −0.368128 | −0.184064 | − | 0.982914i | \(-0.558925\pi\) | ||||
−0.184064 | + | 0.982914i | \(0.558925\pi\) | |||||||
\(620\) | −21317.2 | −1.38083 | ||||||||
\(621\) | 1479.44 | 0.0956004 | ||||||||
\(622\) | −10103.6 | −0.651316 | ||||||||
\(623\) | −63.7801 | −0.00410160 | ||||||||
\(624\) | −1430.79 | −0.0917909 | ||||||||
\(625\) | −18424.0 | −1.17914 | ||||||||
\(626\) | −5048.57 | −0.322335 | ||||||||
\(627\) | −404.526 | −0.0257659 | ||||||||
\(628\) | 11476.1 | 0.729212 | ||||||||
\(629\) | 41889.7 | 2.65541 | ||||||||
\(630\) | 5851.14 | 0.370024 | ||||||||
\(631\) | −7445.04 | −0.469703 | −0.234851 | − | 0.972031i | \(-0.575460\pi\) | ||||
−0.234851 | + | 0.972031i | \(0.575460\pi\) | |||||||
\(632\) | −260.663 | −0.0164060 | ||||||||
\(633\) | 1582.36 | 0.0993571 | ||||||||
\(634\) | 994.213 | 0.0622796 | ||||||||
\(635\) | −11618.5 | −0.726086 | ||||||||
\(636\) | 749.048 | 0.0467008 | ||||||||
\(637\) | −19250.7 | −1.19739 | ||||||||
\(638\) | −3760.99 | −0.233384 | ||||||||
\(639\) | −26330.9 | −1.63010 | ||||||||
\(640\) | 28954.2 | 1.78830 | ||||||||
\(641\) | −10314.8 | −0.635585 | −0.317792 | − | 0.948160i | \(-0.602942\pi\) | ||||
−0.317792 | + | 0.948160i | \(0.602942\pi\) | |||||||
\(642\) | −20.8217 | −0.00128001 | ||||||||
\(643\) | −1904.97 | −0.116835 | −0.0584175 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584175 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(644\) | 5040.24 | 0.308406 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −62405.5 | −3.80079 | ||||||||
\(647\) | 21967.1 | 1.33480 | 0.667399 | − | 0.744700i | \(-0.267407\pi\) | ||||
0.667399 | + | 0.744700i | \(0.267407\pi\) | |||||||
\(648\) | −30474.7 | −1.84747 | ||||||||
\(649\) | −4294.64 | −0.259752 | ||||||||
\(650\) | −8432.13 | −0.508824 | ||||||||
\(651\) | 116.893 | 0.00703750 | ||||||||
\(652\) | −37423.4 | −2.24788 | ||||||||
\(653\) | 19436.1 | 1.16477 | 0.582383 | − | 0.812914i | \(-0.302120\pi\) | ||||
0.582383 | + | 0.812914i | \(0.302120\pi\) | |||||||
\(654\) | −1715.11 | −0.102547 | ||||||||
\(655\) | 1654.03 | 0.0986691 | ||||||||
\(656\) | −20455.4 | −1.21746 | ||||||||
\(657\) | 764.507 | 0.0453977 | ||||||||
\(658\) | −9035.16 | −0.535300 | ||||||||
\(659\) | 22294.7 | 1.31787 | 0.658936 | − | 0.752199i | \(-0.271007\pi\) | ||||
0.658936 | + | 0.752199i | \(0.271007\pi\) | |||||||
\(660\) | −636.491 | −0.0375385 | ||||||||
\(661\) | 2771.21 | 0.163067 | 0.0815336 | − | 0.996671i | \(-0.474018\pi\) | ||||
0.0815336 | + | 0.996671i | \(0.474018\pi\) | |||||||
\(662\) | −59138.9 | −3.47205 | ||||||||
\(663\) | −1790.51 | −0.104883 | ||||||||
\(664\) | 32702.3 | 1.91129 | ||||||||
\(665\) | 5731.43 | 0.334218 | ||||||||
\(666\) | 57817.5 | 3.36394 | ||||||||
\(667\) | 6723.99 | 0.390336 | ||||||||
\(668\) | 14330.9 | 0.830060 | ||||||||
\(669\) | −1370.68 | −0.0792133 | ||||||||
\(670\) | −27396.1 | −1.57971 | ||||||||
\(671\) | 4535.87 | 0.260962 | ||||||||
\(672\) | 49.3904 | 0.00283523 | ||||||||
\(673\) | −2838.17 | −0.162561 | −0.0812803 | − | 0.996691i | \(-0.525901\pi\) | ||||
−0.0812803 | + | 0.996691i | \(0.525901\pi\) | |||||||
\(674\) | 49203.9 | 2.81196 | ||||||||
\(675\) | 501.599 | 0.0286023 | ||||||||
\(676\) | 19773.7 | 1.12504 | ||||||||
\(677\) | 19477.4 | 1.10573 | 0.552863 | − | 0.833272i | \(-0.313535\pi\) | ||||
0.552863 | + | 0.833272i | \(0.313535\pi\) | |||||||
\(678\) | 630.889 | 0.0357362 | ||||||||
\(679\) | 5191.27 | 0.293406 | ||||||||
\(680\) | −50685.1 | −2.85836 | ||||||||
\(681\) | −363.471 | −0.0204526 | ||||||||
\(682\) | 5005.04 | 0.281016 | ||||||||
\(683\) | 10684.6 | 0.598587 | 0.299294 | − | 0.954161i | \(-0.403249\pi\) | ||||
0.299294 | + | 0.954161i | \(0.403249\pi\) | |||||||
\(684\) | −58049.3 | −3.24499 | ||||||||
\(685\) | 6467.15 | 0.360726 | ||||||||
\(686\) | 11796.9 | 0.656570 | ||||||||
\(687\) | −700.099 | −0.0388798 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8286.14 | −0.458167 | ||||||||
\(690\) | 1688.48 | 0.0931582 | ||||||||
\(691\) | −18492.3 | −1.01806 | −0.509030 | − | 0.860749i | \(-0.669996\pi\) | ||||
−0.509030 | + | 0.860749i | \(0.669996\pi\) | |||||||
\(692\) | −43438.3 | −2.38624 | ||||||||
\(693\) | −925.850 | −0.0507506 | ||||||||
\(694\) | 19259.2 | 1.05341 | ||||||||
\(695\) | 22431.2 | 1.22426 | ||||||||
\(696\) | 1050.21 | 0.0571956 | ||||||||
\(697\) | −25598.2 | −1.39111 | ||||||||
\(698\) | 9701.47 | 0.526083 | ||||||||
\(699\) | 891.140 | 0.0482203 | ||||||||
\(700\) | 1708.88 | 0.0922709 | ||||||||
\(701\) | −26750.8 | −1.44132 | −0.720658 | − | 0.693291i | \(-0.756160\pi\) | ||||
−0.720658 | + | 0.693291i | \(0.756160\pi\) | |||||||
\(702\) | −4951.96 | −0.266239 | ||||||||
\(703\) | 56634.6 | 3.03843 | ||||||||
\(704\) | −3892.01 | −0.208360 | ||||||||
\(705\) | −2039.87 | −0.108973 | ||||||||
\(706\) | 13897.3 | 0.740839 | ||||||||
\(707\) | 1619.52 | 0.0861504 | ||||||||
\(708\) | 2323.21 | 0.123322 | ||||||||
\(709\) | 19220.7 | 1.01812 | 0.509060 | − | 0.860731i | \(-0.329993\pi\) | ||||
0.509060 | + | 0.860731i | \(0.329993\pi\) | |||||||
\(710\) | −60216.0 | −3.18291 | ||||||||
\(711\) | −165.837 | −0.00874736 | ||||||||
\(712\) | 762.565 | 0.0401381 | ||||||||
\(713\) | −8948.13 | −0.470000 | ||||||||
\(714\) | 538.430 | 0.0282216 | ||||||||
\(715\) | 7041.01 | 0.368278 | ||||||||
\(716\) | 10086.1 | 0.526445 | ||||||||
\(717\) | −612.983 | −0.0319279 | ||||||||
\(718\) | −28816.9 | −1.49782 | ||||||||
\(719\) | −15744.5 | −0.816647 | −0.408323 | − | 0.912837i | \(-0.633886\pi\) | ||||
−0.408323 | + | 0.912837i | \(0.633886\pi\) | |||||||
\(720\) | −25768.1 | −1.33378 | ||||||||
\(721\) | −6148.57 | −0.317593 | ||||||||
\(722\) | −50396.8 | −2.59775 | ||||||||
\(723\) | −95.3355 | −0.00490396 | ||||||||
\(724\) | −24257.9 | −1.24522 | ||||||||
\(725\) | 2279.75 | 0.116783 | ||||||||
\(726\) | −1949.96 | −0.0996832 | ||||||||
\(727\) | −23957.5 | −1.22219 | −0.611097 | − | 0.791556i | \(-0.709271\pi\) | ||||
−0.611097 | + | 0.791556i | \(0.709271\pi\) | |||||||
\(728\) | −8708.50 | −0.443350 | ||||||||
\(729\) | −19240.9 | −0.977537 | ||||||||
\(730\) | 1748.35 | 0.0886427 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2453.71 | −0.123896 | ||||||||
\(733\) | −2994.98 | −0.150917 | −0.0754586 | − | 0.997149i | \(-0.524042\pi\) | ||||
−0.0754586 | + | 0.997149i | \(0.524042\pi\) | |||||||
\(734\) | −9494.00 | −0.477425 | ||||||||
\(735\) | 1306.97 | 0.0655893 | ||||||||
\(736\) | −3780.81 | −0.189351 | ||||||||
\(737\) | 4335.00 | 0.216665 | ||||||||
\(738\) | −35331.5 | −1.76229 | ||||||||
\(739\) | −6010.04 | −0.299165 | −0.149582 | − | 0.988749i | \(-0.547793\pi\) | ||||
−0.149582 | + | 0.988749i | \(0.547793\pi\) | |||||||
\(740\) | 89110.2 | 4.42670 | ||||||||
\(741\) | −2420.76 | −0.120012 | ||||||||
\(742\) | 2491.75 | 0.123282 | ||||||||
\(743\) | 12435.1 | 0.613995 | 0.306998 | − | 0.951710i | \(-0.400676\pi\) | ||||
0.306998 | + | 0.951710i | \(0.400676\pi\) | |||||||
\(744\) | −1397.60 | −0.0688688 | ||||||||
\(745\) | −16484.9 | −0.810683 | ||||||||
\(746\) | −33551.4 | −1.64665 | ||||||||
\(747\) | 20805.7 | 1.01906 | ||||||||
\(748\) | 15537.1 | 0.759481 | ||||||||
\(749\) | −46.6802 | −0.00227724 | ||||||||
\(750\) | −1876.06 | −0.0913388 | ||||||||
\(751\) | −33154.2 | −1.61094 | −0.805468 | − | 0.592640i | \(-0.798086\pi\) | ||||
−0.805468 | + | 0.592640i | \(0.798086\pi\) | |||||||
\(752\) | 39790.4 | 1.92953 | ||||||||
\(753\) | −1278.97 | −0.0618969 | ||||||||
\(754\) | −22506.5 | −1.08705 | ||||||||
\(755\) | −19763.7 | −0.952684 | ||||||||
\(756\) | 1003.58 | 0.0482801 | ||||||||
\(757\) | −2104.38 | −0.101037 | −0.0505185 | − | 0.998723i | \(-0.516087\pi\) | ||||
−0.0505185 | + | 0.998723i | \(0.516087\pi\) | |||||||
\(758\) | −37156.5 | −1.78046 | ||||||||
\(759\) | −267.175 | −0.0127771 | ||||||||
\(760\) | −68525.9 | −3.27065 | ||||||||
\(761\) | 7428.23 | 0.353841 | 0.176921 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176921 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(762\) | −1475.67 | −0.0701547 | ||||||||
\(763\) | −3845.10 | −0.182440 | ||||||||
\(764\) | 10593.6 | 0.501652 | ||||||||
\(765\) | −32246.5 | −1.52402 | ||||||||
\(766\) | −18282.0 | −0.862344 | ||||||||
\(767\) | −25699.9 | −1.20987 | ||||||||
\(768\) | 2658.88 | 0.124927 | ||||||||
\(769\) | 27269.3 | 1.27874 | 0.639372 | − | 0.768897i | \(-0.279194\pi\) | ||||
0.639372 | + | 0.768897i | \(0.279194\pi\) | |||||||
\(770\) | −2117.32 | −0.0990947 | ||||||||
\(771\) | 1190.95 | 0.0556302 | ||||||||
\(772\) | 3394.61 | 0.158257 | ||||||||
\(773\) | −21246.0 | −0.988571 | −0.494285 | − | 0.869300i | \(-0.664570\pi\) | ||||
−0.494285 | + | 0.869300i | \(0.664570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3033.84 | −0.140618 | ||||||||
\(776\) | −62067.7 | −2.87127 | ||||||||
\(777\) | −488.639 | −0.0225609 | ||||||||
\(778\) | −17100.2 | −0.788008 | ||||||||
\(779\) | −34608.6 | −1.59176 | ||||||||
\(780\) | −3808.88 | −0.174846 | ||||||||
\(781\) | 9528.23 | 0.436552 | ||||||||
\(782\) | −41216.6 | −1.88478 | ||||||||
\(783\) | 1338.83 | 0.0611060 | ||||||||
\(784\) | −25494.1 | −1.16136 | ||||||||
\(785\) | 8618.93 | 0.391876 | ||||||||
\(786\) | 210.080 | 0.00953345 | ||||||||
\(787\) | 36931.1 | 1.67275 | 0.836374 | − | 0.548159i | \(-0.184671\pi\) | ||||
0.836374 | + | 0.548159i | \(0.184671\pi\) | |||||||
\(788\) | 61947.9 | 2.80051 | ||||||||
\(789\) | 1895.60 | 0.0855326 | ||||||||
\(790\) | −379.251 | −0.0170799 | ||||||||
\(791\) | 1414.39 | 0.0635778 | ||||||||
\(792\) | 11069.6 | 0.496644 | ||||||||
\(793\) | 27143.5 | 1.21550 | ||||||||
\(794\) | 28255.0 | 1.26289 | ||||||||
\(795\) | 562.561 | 0.0250969 | ||||||||
\(796\) | 2756.27 | 0.122731 | ||||||||
\(797\) | 8617.90 | 0.383013 | 0.191507 | − | 0.981491i | \(-0.438663\pi\) | ||||
0.191507 | + | 0.981491i | \(0.438663\pi\) | |||||||
\(798\) | 727.953 | 0.0322923 | ||||||||
\(799\) | 49794.2 | 2.20475 | ||||||||
\(800\) | −1281.87 | −0.0566514 | ||||||||
\(801\) | 485.154 | 0.0214008 | ||||||||
\(802\) | 52566.2 | 2.31443 | ||||||||
\(803\) | −276.648 | −0.0121578 | ||||||||
\(804\) | −2345.05 | −0.102865 | ||||||||
\(805\) | 3785.40 | 0.165736 | ||||||||
\(806\) | 29951.1 | 1.30891 | ||||||||
\(807\) | −282.461 | −0.0123211 | ||||||||
\(808\) | −19363.3 | −0.843066 | ||||||||
\(809\) | −12821.8 | −0.557218 | −0.278609 | − | 0.960405i | \(-0.589873\pi\) | ||||
−0.278609 | + | 0.960405i | \(0.589873\pi\) | |||||||
\(810\) | −44339.2 | −1.92336 | ||||||||
\(811\) | 26275.3 | 1.13767 | 0.568835 | − | 0.822452i | \(-0.307394\pi\) | ||||
0.568835 | + | 0.822452i | \(0.307394\pi\) | |||||||
\(812\) | 4561.22 | 0.197128 | ||||||||
\(813\) | 2749.54 | 0.118611 | ||||||||
\(814\) | −20922.1 | −0.900884 | ||||||||
\(815\) | −28106.3 | −1.20800 | ||||||||
\(816\) | −2371.22 | −0.101727 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −45417.8 | −1.94131 | ||||||||
\(819\) | −5540.46 | −0.236385 | ||||||||
\(820\) | −54454.0 | −2.31904 | ||||||||
\(821\) | 41560.4 | 1.76671 | 0.883355 | − | 0.468704i | \(-0.155279\pi\) | ||||
0.883355 | + | 0.468704i | \(0.155279\pi\) | |||||||
\(822\) | 821.398 | 0.0348535 | ||||||||
\(823\) | −21443.6 | −0.908234 | −0.454117 | − | 0.890942i | \(-0.650045\pi\) | ||||
−0.454117 | + | 0.890942i | \(0.650045\pi\) | |||||||
\(824\) | 73513.3 | 3.10796 | ||||||||
\(825\) | −90.5848 | −0.00382274 | ||||||||
\(826\) | 7728.29 | 0.325547 | ||||||||
\(827\) | −39485.6 | −1.66028 | −0.830139 | − | 0.557557i | \(-0.811739\pi\) | ||||
−0.830139 | + | 0.557557i | \(0.811739\pi\) | |||||||
\(828\) | −38339.5 | −1.60916 | ||||||||
\(829\) | 9431.88 | 0.395154 | 0.197577 | − | 0.980287i | \(-0.436693\pi\) | ||||
0.197577 | + | 0.980287i | \(0.436693\pi\) | |||||||
\(830\) | 47580.3 | 1.98980 | ||||||||
\(831\) | 2239.38 | 0.0934815 | ||||||||
\(832\) | −23290.5 | −0.970497 | ||||||||
\(833\) | −31903.7 | −1.32701 | ||||||||
\(834\) | 2849.00 | 0.118289 | ||||||||
\(835\) | 10763.0 | 0.446072 | ||||||||
\(836\) | 21006.0 | 0.869028 | ||||||||
\(837\) | −1781.69 | −0.0735773 | ||||||||
\(838\) | −47738.4 | −1.96790 | ||||||||
\(839\) | 33753.5 | 1.38891 | 0.694457 | − | 0.719534i | \(-0.255644\pi\) | ||||
0.694457 | + | 0.719534i | \(0.255644\pi\) | |||||||
\(840\) | 591.236 | 0.0242852 | ||||||||
\(841\) | −18304.1 | −0.750504 | ||||||||
\(842\) | 39232.9 | 1.60577 | ||||||||
\(843\) | 2082.08 | 0.0850660 | ||||||||
\(844\) | −82167.8 | −3.35110 | ||||||||
\(845\) | 14850.7 | 0.604592 | ||||||||
\(846\) | 68727.5 | 2.79302 | ||||||||
\(847\) | −4371.63 | −0.177345 | ||||||||
\(848\) | −10973.5 | −0.444378 | ||||||||
\(849\) | 1694.59 | 0.0685021 | ||||||||
\(850\) | −13974.4 | −0.563902 | ||||||||
\(851\) | 37405.1 | 1.50673 | ||||||||
\(852\) | −5154.36 | −0.207260 | ||||||||
\(853\) | −4810.50 | −0.193093 | −0.0965466 | − | 0.995328i | \(-0.530780\pi\) | ||||
−0.0965466 | + | 0.995328i | \(0.530780\pi\) | |||||||
\(854\) | −8162.39 | −0.327062 | ||||||||
\(855\) | −43597.0 | −1.74385 | ||||||||
\(856\) | 558.116 | 0.0222851 | ||||||||
\(857\) | −18134.3 | −0.722821 | −0.361410 | − | 0.932407i | \(-0.617705\pi\) | ||||
−0.361410 | + | 0.932407i | \(0.617705\pi\) | |||||||
\(858\) | 894.284 | 0.0355832 | ||||||||
\(859\) | 3895.00 | 0.154710 | 0.0773549 | − | 0.997004i | \(-0.475353\pi\) | ||||
0.0773549 | + | 0.997004i | \(0.475353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 298.600 | 0.0118191 | ||||||||
\(862\) | −57861.7 | −2.28628 | ||||||||
\(863\) | 13915.3 | 0.548878 | 0.274439 | − | 0.961605i | \(-0.411508\pi\) | ||||
0.274439 | + | 0.961605i | \(0.411508\pi\) | |||||||
\(864\) | −752.809 | −0.0296425 | ||||||||
\(865\) | −32623.7 | −1.28236 | ||||||||
\(866\) | −6589.38 | −0.258564 | ||||||||
\(867\) | −1402.90 | −0.0549538 | ||||||||
\(868\) | −6069.97 | −0.237360 | ||||||||
\(869\) | 60.0105 | 0.00234260 | ||||||||
\(870\) | 1528.00 | 0.0595451 | ||||||||
\(871\) | 25941.5 | 1.00918 | ||||||||
\(872\) | 45972.7 | 1.78536 | ||||||||
\(873\) | −39488.3 | −1.53090 | ||||||||
\(874\) | −55724.5 | −2.15665 | ||||||||
\(875\) | −4205.95 | −0.162499 | ||||||||
\(876\) | 149.655 | 0.00577210 | ||||||||
\(877\) | 4738.08 | 0.182433 | 0.0912164 | − | 0.995831i | \(-0.470925\pi\) | ||||
0.0912164 | + | 0.995831i | \(0.470925\pi\) | |||||||
\(878\) | 47518.1 | 1.82649 | ||||||||
\(879\) | −3089.06 | −0.118534 | ||||||||
\(880\) | 9324.56 | 0.357194 | ||||||||
\(881\) | −26778.4 | −1.02405 | −0.512024 | − | 0.858971i | \(-0.671104\pi\) | ||||
−0.512024 | + | 0.858971i | \(0.671104\pi\) | |||||||
\(882\) | −44034.5 | −1.68109 | ||||||||
\(883\) | −24306.7 | −0.926372 | −0.463186 | − | 0.886261i | \(-0.653294\pi\) | ||||
−0.463186 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(884\) | 92976.7 | 3.53750 | ||||||||
\(885\) | 1744.81 | 0.0662726 | ||||||||
\(886\) | −44181.9 | −1.67530 | ||||||||
\(887\) | −26914.4 | −1.01882 | −0.509412 | − | 0.860523i | \(-0.670137\pi\) | ||||
−0.509412 | + | 0.860523i | \(0.670137\pi\) | |||||||
\(888\) | 5842.25 | 0.220781 | ||||||||
\(889\) | −3308.31 | −0.124811 | ||||||||
\(890\) | 1109.49 | 0.0417869 | ||||||||
\(891\) | 7015.99 | 0.263798 | ||||||||
\(892\) | 71176.1 | 2.67170 | ||||||||
\(893\) | 67321.3 | 2.52276 | ||||||||
\(894\) | −2093.76 | −0.0783285 | ||||||||
\(895\) | 7574.99 | 0.282910 | ||||||||
\(896\) | 8244.58 | 0.307402 | ||||||||
\(897\) | −1598.82 | −0.0595130 | ||||||||
\(898\) | 73524.1 | 2.73222 | ||||||||
\(899\) | −8097.71 | −0.300416 | ||||||||
\(900\) | −12998.9 | −0.481440 | ||||||||
\(901\) | −13732.4 | −0.507761 | ||||||||
\(902\) | 12785.2 | 0.471952 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16910.7 | −0.622171 | ||||||||
\(905\) | −18218.5 | −0.669177 | ||||||||
\(906\) | −2510.21 | −0.0920487 | ||||||||
\(907\) | 41966.5 | 1.53636 | 0.768178 | − | 0.640236i | \(-0.221163\pi\) | ||||
0.768178 | + | 0.640236i | \(0.221163\pi\) | |||||||
\(908\) | 18874.1 | 0.689824 | ||||||||
\(909\) | −12319.2 | −0.449506 | ||||||||
\(910\) | −12670.4 | −0.461561 | ||||||||
\(911\) | 26977.3 | 0.981117 | 0.490558 | − | 0.871408i | \(-0.336793\pi\) | ||||
0.490558 | + | 0.871408i | \(0.336793\pi\) | |||||||
\(912\) | −3205.86 | −0.116400 | ||||||||
\(913\) | −7528.83 | −0.272911 | ||||||||
\(914\) | −67076.0 | −2.42743 | ||||||||
\(915\) | −1842.82 | −0.0665812 | ||||||||
\(916\) | 36354.3 | 1.31133 | ||||||||
\(917\) | 470.978 | 0.0169608 | ||||||||
\(918\) | −8206.75 | −0.295058 | ||||||||
\(919\) | 16827.5 | 0.604014 | 0.302007 | − | 0.953306i | \(-0.402343\pi\) | ||||
0.302007 | + | 0.953306i | \(0.402343\pi\) | |||||||
\(920\) | −45258.9 | −1.62189 | ||||||||
\(921\) | −292.130 | −0.0104517 | ||||||||
\(922\) | −59633.0 | −2.13005 | ||||||||
\(923\) | 57018.7 | 2.03336 | ||||||||
\(924\) | −181.238 | −0.00645270 | ||||||||
\(925\) | 12682.1 | 0.450794 | ||||||||
\(926\) | 64620.7 | 2.29327 | ||||||||
\(927\) | 46770.1 | 1.65710 | ||||||||
\(928\) | −3421.49 | −0.121030 | ||||||||
\(929\) | −22663.1 | −0.800379 | −0.400190 | − | 0.916432i | \(-0.631056\pi\) | ||||
−0.400190 | + | 0.916432i | \(0.631056\pi\) | |||||||
\(930\) | −2033.43 | −0.0716978 | ||||||||
\(931\) | −43133.5 | −1.51842 | ||||||||
\(932\) | −46274.6 | −1.62637 | ||||||||
\(933\) | −649.532 | −0.0227918 | ||||||||
\(934\) | −43309.5 | −1.51727 | ||||||||
\(935\) | 11668.9 | 0.408143 | ||||||||
\(936\) | 66242.7 | 2.31326 | ||||||||
\(937\) | −38575.3 | −1.34493 | −0.672465 | − | 0.740129i | \(-0.734765\pi\) | ||||
−0.672465 | + | 0.740129i | \(0.734765\pi\) | |||||||
\(938\) | −7800.93 | −0.271545 | ||||||||
\(939\) | −324.558 | −0.0112796 | ||||||||
\(940\) | 105925. | 3.67542 | ||||||||
\(941\) | −22927.5 | −0.794278 | −0.397139 | − | 0.917758i | \(-0.629997\pi\) | ||||
−0.397139 | + | 0.917758i | \(0.629997\pi\) | |||||||
\(942\) | 1094.70 | 0.0378632 | ||||||||
\(943\) | −22857.7 | −0.789342 | ||||||||
\(944\) | −34035.0 | −1.17346 | ||||||||
\(945\) | 753.722 | 0.0259456 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54420.4 | 1.86740 | 0.933698 | − | 0.358060i | \(-0.116562\pi\) | ||||
0.933698 | + | 0.358060i | \(0.116562\pi\) | |||||||
\(948\) | −32.4631 | −0.00111219 | ||||||||
\(949\) | −1655.51 | −0.0566283 | ||||||||
\(950\) | −18893.2 | −0.645239 | ||||||||
\(951\) | 63.9150 | 0.00217937 | ||||||||
\(952\) | −14432.4 | −0.491341 | ||||||||
\(953\) | 14552.8 | 0.494661 | 0.247331 | − | 0.968931i | \(-0.420447\pi\) | ||||
0.247331 | + | 0.968931i | \(0.420447\pi\) | |||||||
\(954\) | −18953.9 | −0.643244 | ||||||||
\(955\) | 7956.14 | 0.269586 | ||||||||
\(956\) | 31830.7 | 1.07686 | ||||||||
\(957\) | −241.783 | −0.00816690 | ||||||||
\(958\) | 9304.69 | 0.313800 | ||||||||
\(959\) | 1841.49 | 0.0620073 | ||||||||
\(960\) | 1581.24 | 0.0531606 | ||||||||
\(961\) | −19014.8 | −0.638272 | ||||||||
\(962\) | −125202. | −4.19612 | ||||||||
\(963\) | 355.080 | 0.0118819 | ||||||||
\(964\) | 4950.53 | 0.165400 | ||||||||
\(965\) | 2549.47 | 0.0850469 | ||||||||
\(966\) | 480.787 | 0.0160135 | ||||||||
\(967\) | 21132.6 | 0.702771 | 0.351386 | − | 0.936231i | \(-0.385711\pi\) | ||||
0.351386 | + | 0.936231i | \(0.385711\pi\) | |||||||
\(968\) | 52268.0 | 1.73549 | ||||||||
\(969\) | −4011.86 | −0.133003 | ||||||||
\(970\) | −90305.5 | −2.98921 | ||||||||
\(971\) | −43710.7 | −1.44464 | −0.722319 | − | 0.691560i | \(-0.756924\pi\) | ||||
−0.722319 | + | 0.691560i | \(0.756924\pi\) | |||||||
\(972\) | −11458.0 | −0.378103 | ||||||||
\(973\) | 6387.19 | 0.210446 | ||||||||
\(974\) | 50174.4 | 1.65061 | ||||||||
\(975\) | −542.077 | −0.0178055 | ||||||||
\(976\) | 35946.7 | 1.17892 | ||||||||
\(977\) | 5105.55 | 0.167186 | 0.0835932 | − | 0.996500i | \(-0.473360\pi\) | ||||
0.0835932 | + | 0.996500i | \(0.473360\pi\) | |||||||
\(978\) | −3569.80 | −0.116717 | ||||||||
\(979\) | −175.560 | −0.00573128 | ||||||||
\(980\) | −67867.4 | −2.21219 | ||||||||
\(981\) | 29248.4 | 0.951916 | ||||||||
\(982\) | −44776.7 | −1.45507 | ||||||||
\(983\) | 31668.3 | 1.02753 | 0.513765 | − | 0.857931i | \(-0.328250\pi\) | ||||
0.513765 | + | 0.857931i | \(0.328250\pi\) | |||||||
\(984\) | −3570.12 | −0.115662 | ||||||||
\(985\) | 46525.0 | 1.50499 | ||||||||
\(986\) | −37299.4 | −1.20472 | ||||||||
\(987\) | −580.844 | −0.0187320 | ||||||||
\(988\) | 125704. | 4.04774 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 16105.8 | 0.517045 | ||||||||
\(991\) | −33652.0 | −1.07870 | −0.539350 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539350 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(992\) | 4553.24 | 0.145731 | ||||||||
\(993\) | −3801.87 | −0.121499 | ||||||||
\(994\) | −17146.3 | −0.547129 | ||||||||
\(995\) | 2070.06 | 0.0659550 | ||||||||
\(996\) | 4072.77 | 0.129569 | ||||||||
\(997\) | 8769.30 | 0.278562 | 0.139281 | − | 0.990253i | \(-0.455521\pi\) | ||||
0.139281 | + | 0.990253i | \(0.455521\pi\) | |||||||
\(998\) | 55961.6 | 1.77498 | ||||||||
\(999\) | 7447.84 | 0.235875 |
(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 | 1849.4.a.h.1.2 | 30 | ||
43.21 | even | 7 | 43.4.e.a.11.1 | yes | 60 | ||
43.41 | even | 7 | 43.4.e.a.4.1 | ✓ | 60 | ||
43.42 | odd | 2 | 1849.4.a.g.1.29 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.1 | ✓ | 60 | 43.41 | even | 7 | ||
43.4.e.a.11.1 | yes | 60 | 43.21 | even | 7 | ||
1849.4.a.g.1.29 | 30 | 43.42 | odd | 2 | |||
1849.4.a.h.1.2 | 30 | 1.1 | even | 1 | trivial |