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: | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.07016 | −1.79257 | −0.896287 | − | 0.443475i | \(-0.853746\pi\) | ||||
−0.896287 | + | 0.443475i | \(0.853746\pi\) | |||||||
\(3\) | 5.26544 | 1.01333 | 0.506667 | − | 0.862142i | \(-0.330877\pi\) | ||||
0.506667 | + | 0.862142i | \(0.330877\pi\) | |||||||
\(4\) | 17.7066 | 2.21332 | ||||||||
\(5\) | 3.42027 | 0.305918 | 0.152959 | − | 0.988233i | \(-0.451120\pi\) | ||||
0.152959 | + | 0.988233i | \(0.451120\pi\) | |||||||
\(6\) | −26.6966 | −1.81648 | ||||||||
\(7\) | −25.1802 | −1.35960 | −0.679801 | − | 0.733397i | \(-0.737934\pi\) | ||||
−0.679801 | + | 0.733397i | \(0.737934\pi\) | |||||||
\(8\) | −49.2138 | −2.17497 | ||||||||
\(9\) | 0.724844 | 0.0268461 | ||||||||
\(10\) | −17.3413 | −0.548380 | ||||||||
\(11\) | 69.6830 | 1.91002 | 0.955009 | − | 0.296576i | \(-0.0958449\pi\) | ||||
0.955009 | + | 0.296576i | \(0.0958449\pi\) | |||||||
\(12\) | 93.2328 | 2.24283 | ||||||||
\(13\) | 26.4992 | 0.565350 | 0.282675 | − | 0.959216i | \(-0.408778\pi\) | ||||
0.282675 | + | 0.959216i | \(0.408778\pi\) | |||||||
\(14\) | 127.668 | 2.43719 | ||||||||
\(15\) | 18.0092 | 0.309997 | ||||||||
\(16\) | 107.870 | 1.68547 | ||||||||
\(17\) | 87.9096 | 1.25419 | 0.627095 | − | 0.778943i | \(-0.284244\pi\) | ||||
0.627095 | + | 0.778943i | \(0.284244\pi\) | |||||||
\(18\) | −3.67508 | −0.0481236 | ||||||||
\(19\) | −15.6070 | −0.188447 | −0.0942234 | − | 0.995551i | \(-0.530037\pi\) | ||||
−0.0942234 | + | 0.995551i | \(0.530037\pi\) | |||||||
\(20\) | 60.5611 | 0.677094 | ||||||||
\(21\) | −132.585 | −1.37773 | ||||||||
\(22\) | −353.304 | −3.42385 | ||||||||
\(23\) | −0.430477 | −0.00390263 | −0.00195132 | − | 0.999998i | \(-0.500621\pi\) | ||||
−0.00195132 | + | 0.999998i | \(0.500621\pi\) | |||||||
\(24\) | −259.133 | −2.20397 | ||||||||
\(25\) | −113.302 | −0.906414 | ||||||||
\(26\) | −134.355 | −1.01343 | ||||||||
\(27\) | −138.350 | −0.986130 | ||||||||
\(28\) | −445.854 | −3.00923 | ||||||||
\(29\) | 68.9739 | 0.441660 | 0.220830 | − | 0.975312i | \(-0.429123\pi\) | ||||
0.220830 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(30\) | −91.3096 | −0.555692 | ||||||||
\(31\) | −228.219 | −1.32223 | −0.661117 | − | 0.750283i | \(-0.729917\pi\) | ||||
−0.661117 | + | 0.750283i | \(0.729917\pi\) | |||||||
\(32\) | −153.207 | −0.846355 | ||||||||
\(33\) | 366.911 | 1.93549 | ||||||||
\(34\) | −445.716 | −2.24823 | ||||||||
\(35\) | −86.1229 | −0.415926 | ||||||||
\(36\) | 12.8345 | 0.0594189 | ||||||||
\(37\) | −276.114 | −1.22683 | −0.613417 | − | 0.789759i | \(-0.710206\pi\) | ||||
−0.613417 | + | 0.789759i | \(0.710206\pi\) | |||||||
\(38\) | 79.1300 | 0.337805 | ||||||||
\(39\) | 139.530 | 0.572888 | ||||||||
\(40\) | −168.324 | −0.665361 | ||||||||
\(41\) | −379.952 | −1.44728 | −0.723641 | − | 0.690176i | \(-0.757533\pi\) | ||||
−0.723641 | + | 0.690176i | \(0.757533\pi\) | |||||||
\(42\) | 672.226 | 2.46968 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 1233.85 | 4.22748 | ||||||||
\(45\) | 2.47916 | 0.00821269 | ||||||||
\(46\) | 2.18259 | 0.00699576 | ||||||||
\(47\) | −59.2069 | −0.183749 | −0.0918747 | − | 0.995771i | \(-0.529286\pi\) | ||||
−0.0918747 | + | 0.995771i | \(0.529286\pi\) | |||||||
\(48\) | 567.982 | 1.70794 | ||||||||
\(49\) | 291.041 | 0.848516 | ||||||||
\(50\) | 574.459 | 1.62481 | ||||||||
\(51\) | 462.883 | 1.27091 | ||||||||
\(52\) | 469.209 | 1.25130 | ||||||||
\(53\) | −263.990 | −0.684185 | −0.342093 | − | 0.939666i | \(-0.611136\pi\) | ||||
−0.342093 | + | 0.939666i | \(0.611136\pi\) | |||||||
\(54\) | 701.458 | 1.76771 | ||||||||
\(55\) | 238.334 | 0.584309 | ||||||||
\(56\) | 1239.21 | 2.95709 | ||||||||
\(57\) | −82.1776 | −0.190959 | ||||||||
\(58\) | −349.709 | −0.791708 | ||||||||
\(59\) | 697.350 | 1.53877 | 0.769383 | − | 0.638788i | \(-0.220564\pi\) | ||||
0.769383 | + | 0.638788i | \(0.220564\pi\) | |||||||
\(60\) | 318.881 | 0.686123 | ||||||||
\(61\) | −782.784 | −1.64304 | −0.821518 | − | 0.570182i | \(-0.806873\pi\) | ||||
−0.821518 | + | 0.570182i | \(0.806873\pi\) | |||||||
\(62\) | 1157.11 | 2.37020 | ||||||||
\(63\) | −18.2517 | −0.0365000 | ||||||||
\(64\) | −86.1752 | −0.168311 | ||||||||
\(65\) | 90.6342 | 0.172951 | ||||||||
\(66\) | −1860.30 | −3.46950 | ||||||||
\(67\) | 546.386 | 0.996294 | 0.498147 | − | 0.867093i | \(-0.334014\pi\) | ||||
0.498147 | + | 0.867093i | \(0.334014\pi\) | |||||||
\(68\) | 1556.58 | 2.77592 | ||||||||
\(69\) | −2.26665 | −0.00395467 | ||||||||
\(70\) | 436.657 | 0.745579 | ||||||||
\(71\) | 400.262 | 0.669048 | 0.334524 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334524 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(72\) | −35.6724 | −0.0583893 | ||||||||
\(73\) | 79.9453 | 0.128177 | 0.0640883 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640883 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(74\) | 1399.94 | 2.19919 | ||||||||
\(75\) | −596.584 | −0.918501 | ||||||||
\(76\) | −276.346 | −0.417093 | ||||||||
\(77\) | −1754.63 | −2.59686 | ||||||||
\(78\) | −707.439 | −1.02694 | ||||||||
\(79\) | −155.448 | −0.221383 | −0.110692 | − | 0.993855i | \(-0.535307\pi\) | ||||
−0.110692 | + | 0.993855i | \(0.535307\pi\) | |||||||
\(80\) | 368.943 | 0.515614 | ||||||||
\(81\) | −748.045 | −1.02613 | ||||||||
\(82\) | 1926.42 | 2.59436 | ||||||||
\(83\) | 92.2738 | 0.122028 | 0.0610142 | − | 0.998137i | \(-0.480566\pi\) | ||||
0.0610142 | + | 0.998137i | \(0.480566\pi\) | |||||||
\(84\) | −2347.62 | −3.04936 | ||||||||
\(85\) | 300.674 | 0.383679 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 363.178 | 0.447549 | ||||||||
\(88\) | −3429.37 | −4.15422 | ||||||||
\(89\) | −924.441 | −1.10102 | −0.550509 | − | 0.834830i | \(-0.685566\pi\) | ||||
−0.550509 | + | 0.834830i | \(0.685566\pi\) | |||||||
\(90\) | −12.5697 | −0.0147219 | ||||||||
\(91\) | −667.254 | −0.768650 | ||||||||
\(92\) | −7.62226 | −0.00863778 | ||||||||
\(93\) | −1201.67 | −1.33987 | ||||||||
\(94\) | 300.189 | 0.329384 | ||||||||
\(95\) | −53.3800 | −0.0576492 | ||||||||
\(96\) | −806.701 | −0.857641 | ||||||||
\(97\) | 190.938 | 0.199864 | 0.0999321 | − | 0.994994i | \(-0.468137\pi\) | ||||
0.0999321 | + | 0.994994i | \(0.468137\pi\) | |||||||
\(98\) | −1475.62 | −1.52103 | ||||||||
\(99\) | 50.5093 | 0.0512765 | ||||||||
\(100\) | −2006.18 | −2.00618 | ||||||||
\(101\) | −19.3893 | −0.0191021 | −0.00955105 | − | 0.999954i | \(-0.503040\pi\) | ||||
−0.00955105 | + | 0.999954i | \(0.503040\pi\) | |||||||
\(102\) | −2346.89 | −2.27821 | ||||||||
\(103\) | 614.919 | 0.588250 | 0.294125 | − | 0.955767i | \(-0.404972\pi\) | ||||
0.294125 | + | 0.955767i | \(0.404972\pi\) | |||||||
\(104\) | −1304.13 | −1.22962 | ||||||||
\(105\) | −453.475 | −0.421472 | ||||||||
\(106\) | 1338.47 | 1.22645 | ||||||||
\(107\) | 1143.39 | 1.03304 | 0.516520 | − | 0.856275i | \(-0.327227\pi\) | ||||
0.516520 | + | 0.856275i | \(0.327227\pi\) | |||||||
\(108\) | −2449.71 | −2.18262 | ||||||||
\(109\) | 399.428 | 0.350993 | 0.175496 | − | 0.984480i | \(-0.443847\pi\) | ||||
0.175496 | + | 0.984480i | \(0.443847\pi\) | |||||||
\(110\) | −1208.39 | −1.04742 | ||||||||
\(111\) | −1453.86 | −1.24319 | ||||||||
\(112\) | −2716.18 | −2.29156 | ||||||||
\(113\) | 836.348 | 0.696257 | 0.348129 | − | 0.937447i | \(-0.386817\pi\) | ||||
0.348129 | + | 0.937447i | \(0.386817\pi\) | |||||||
\(114\) | 416.654 | 0.342309 | ||||||||
\(115\) | −1.47234 | −0.00119389 | ||||||||
\(116\) | 1221.29 | 0.977535 | ||||||||
\(117\) | 19.2078 | 0.0151774 | ||||||||
\(118\) | −3535.68 | −2.75835 | ||||||||
\(119\) | −2213.58 | −1.70520 | ||||||||
\(120\) | −886.302 | −0.674233 | ||||||||
\(121\) | 3524.71 | 2.64817 | ||||||||
\(122\) | 3968.84 | 2.94526 | ||||||||
\(123\) | −2000.62 | −1.46658 | ||||||||
\(124\) | −4040.97 | −2.92653 | ||||||||
\(125\) | −815.055 | −0.583206 | ||||||||
\(126\) | 92.5391 | 0.0654289 | ||||||||
\(127\) | −1742.03 | −1.21716 | −0.608582 | − | 0.793491i | \(-0.708261\pi\) | ||||
−0.608582 | + | 0.793491i | \(0.708261\pi\) | |||||||
\(128\) | 1662.58 | 1.14807 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −459.530 | −0.310027 | ||||||||
\(131\) | −592.422 | −0.395116 | −0.197558 | − | 0.980291i | \(-0.563301\pi\) | ||||
−0.197558 | + | 0.980291i | \(0.563301\pi\) | |||||||
\(132\) | 6496.74 | 4.28385 | ||||||||
\(133\) | 392.986 | 0.256212 | ||||||||
\(134\) | −2770.27 | −1.78593 | ||||||||
\(135\) | −473.195 | −0.301675 | ||||||||
\(136\) | −4326.37 | −2.72782 | ||||||||
\(137\) | −1517.58 | −0.946394 | −0.473197 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473197 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(138\) | 11.4923 | 0.00708904 | ||||||||
\(139\) | −1161.08 | −0.708502 | −0.354251 | − | 0.935150i | \(-0.615264\pi\) | ||||
−0.354251 | + | 0.935150i | \(0.615264\pi\) | |||||||
\(140\) | −1524.94 | −0.920578 | ||||||||
\(141\) | −311.751 | −0.186200 | ||||||||
\(142\) | −2029.40 | −1.19932 | ||||||||
\(143\) | 1846.54 | 1.07983 | ||||||||
\(144\) | 78.1888 | 0.0452481 | ||||||||
\(145\) | 235.909 | 0.135112 | ||||||||
\(146\) | −405.336 | −0.229766 | ||||||||
\(147\) | 1532.46 | 0.859830 | ||||||||
\(148\) | −4889.03 | −2.71538 | ||||||||
\(149\) | −485.816 | −0.267111 | −0.133556 | − | 0.991041i | \(-0.542639\pi\) | ||||
−0.133556 | + | 0.991041i | \(0.542639\pi\) | |||||||
\(150\) | 3024.78 | 1.64648 | ||||||||
\(151\) | 2216.13 | 1.19434 | 0.597172 | − | 0.802113i | \(-0.296291\pi\) | ||||
0.597172 | + | 0.802113i | \(0.296291\pi\) | |||||||
\(152\) | 768.080 | 0.409865 | ||||||||
\(153\) | 63.7208 | 0.0336701 | ||||||||
\(154\) | 8896.25 | 4.65507 | ||||||||
\(155\) | −780.568 | −0.404495 | ||||||||
\(156\) | 2470.59 | 1.26799 | ||||||||
\(157\) | −432.876 | −0.220046 | −0.110023 | − | 0.993929i | \(-0.535092\pi\) | ||||
−0.110023 | + | 0.993929i | \(0.535092\pi\) | |||||||
\(158\) | 788.147 | 0.396846 | ||||||||
\(159\) | −1390.02 | −0.693308 | ||||||||
\(160\) | −524.008 | −0.258915 | ||||||||
\(161\) | 10.8395 | 0.00530603 | ||||||||
\(162\) | 3792.71 | 1.83941 | ||||||||
\(163\) | 1441.60 | 0.692727 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(164\) | −6727.65 | −3.20330 | ||||||||
\(165\) | 1254.93 | 0.592100 | ||||||||
\(166\) | −467.843 | −0.218745 | ||||||||
\(167\) | −1815.41 | −0.841201 | −0.420601 | − | 0.907246i | \(-0.638181\pi\) | ||||
−0.420601 | + | 0.907246i | \(0.638181\pi\) | |||||||
\(168\) | 6525.00 | 2.99652 | ||||||||
\(169\) | −1494.79 | −0.680380 | ||||||||
\(170\) | −1524.47 | −0.687773 | ||||||||
\(171\) | −11.3126 | −0.00505905 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1459.79 | 0.641534 | 0.320767 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320767 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(174\) | −1841.37 | −0.802265 | ||||||||
\(175\) | 2852.96 | 1.23236 | ||||||||
\(176\) | 7516.69 | 3.21927 | ||||||||
\(177\) | 3671.85 | 1.55928 | ||||||||
\(178\) | 4687.07 | 1.97365 | ||||||||
\(179\) | 4162.49 | 1.73810 | 0.869048 | − | 0.494728i | \(-0.164732\pi\) | ||||
0.869048 | + | 0.494728i | \(0.164732\pi\) | |||||||
\(180\) | 43.8974 | 0.0181773 | ||||||||
\(181\) | 408.845 | 0.167896 | 0.0839481 | − | 0.996470i | \(-0.473247\pi\) | ||||
0.0839481 | + | 0.996470i | \(0.473247\pi\) | |||||||
\(182\) | 3383.08 | 1.37786 | ||||||||
\(183\) | −4121.70 | −1.66495 | ||||||||
\(184\) | 21.1854 | 0.00848810 | ||||||||
\(185\) | −944.384 | −0.375311 | ||||||||
\(186\) | 6092.67 | 2.40181 | ||||||||
\(187\) | 6125.80 | 2.39552 | ||||||||
\(188\) | −1048.35 | −0.406696 | ||||||||
\(189\) | 3483.68 | 1.34074 | ||||||||
\(190\) | 270.645 | 0.103340 | ||||||||
\(191\) | −3385.99 | −1.28273 | −0.641366 | − | 0.767235i | \(-0.721632\pi\) | ||||
−0.641366 | + | 0.767235i | \(0.721632\pi\) | |||||||
\(192\) | −453.750 | −0.170555 | ||||||||
\(193\) | −198.605 | −0.0740722 | −0.0370361 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370361 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(194\) | −968.087 | −0.358271 | ||||||||
\(195\) | 477.229 | 0.175257 | ||||||||
\(196\) | 5153.33 | 1.87804 | ||||||||
\(197\) | −800.217 | −0.289407 | −0.144703 | − | 0.989475i | \(-0.546223\pi\) | ||||
−0.144703 | + | 0.989475i | \(0.546223\pi\) | |||||||
\(198\) | −256.090 | −0.0919169 | ||||||||
\(199\) | −3022.75 | −1.07677 | −0.538384 | − | 0.842699i | \(-0.680965\pi\) | ||||
−0.538384 | + | 0.842699i | \(0.680965\pi\) | |||||||
\(200\) | 5576.02 | 1.97142 | ||||||||
\(201\) | 2876.96 | 1.00958 | ||||||||
\(202\) | 98.3071 | 0.0342419 | ||||||||
\(203\) | −1736.78 | −0.600481 | ||||||||
\(204\) | 8196.06 | 2.81294 | ||||||||
\(205\) | −1299.54 | −0.442750 | ||||||||
\(206\) | −3117.74 | −1.05448 | ||||||||
\(207\) | −0.312028 | −0.000104770 0 | ||||||||
\(208\) | 2858.46 | 0.952878 | ||||||||
\(209\) | −1087.54 | −0.359937 | ||||||||
\(210\) | 2299.19 | 0.755520 | ||||||||
\(211\) | −581.734 | −0.189802 | −0.0949011 | − | 0.995487i | \(-0.530253\pi\) | ||||
−0.0949011 | + | 0.995487i | \(0.530253\pi\) | |||||||
\(212\) | −4674.35 | −1.51432 | ||||||||
\(213\) | 2107.56 | 0.677969 | ||||||||
\(214\) | −5797.15 | −1.85180 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6808.75 | 2.14480 | ||||||||
\(217\) | 5746.58 | 1.79771 | ||||||||
\(218\) | −2025.16 | −0.629181 | ||||||||
\(219\) | 420.947 | 0.129886 | ||||||||
\(220\) | 4220.08 | 1.29326 | ||||||||
\(221\) | 2329.53 | 0.709056 | ||||||||
\(222\) | 7371.32 | 2.22852 | ||||||||
\(223\) | −2267.15 | −0.680805 | −0.340403 | − | 0.940280i | \(-0.610563\pi\) | ||||
−0.340403 | + | 0.940280i | \(0.610563\pi\) | |||||||
\(224\) | 3857.77 | 1.15071 | ||||||||
\(225\) | −82.1261 | −0.0243337 | ||||||||
\(226\) | −4240.42 | −1.24809 | ||||||||
\(227\) | −3026.65 | −0.884958 | −0.442479 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442479 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(228\) | −1455.08 | −0.422654 | ||||||||
\(229\) | −1509.02 | −0.435454 | −0.217727 | − | 0.976010i | \(-0.569864\pi\) | ||||
−0.217727 | + | 0.976010i | \(0.569864\pi\) | |||||||
\(230\) | 7.46503 | 0.00214013 | ||||||||
\(231\) | −9238.89 | −2.63149 | ||||||||
\(232\) | −3394.47 | −0.960595 | ||||||||
\(233\) | −2927.26 | −0.823051 | −0.411525 | − | 0.911398i | \(-0.635004\pi\) | ||||
−0.411525 | + | 0.911398i | \(0.635004\pi\) | |||||||
\(234\) | −97.3865 | −0.0272066 | ||||||||
\(235\) | −202.503 | −0.0562122 | ||||||||
\(236\) | 12347.7 | 3.40578 | ||||||||
\(237\) | −818.503 | −0.224335 | ||||||||
\(238\) | 11223.2 | 3.05669 | ||||||||
\(239\) | −3687.79 | −0.998089 | −0.499044 | − | 0.866576i | \(-0.666316\pi\) | ||||
−0.499044 | + | 0.866576i | \(0.666316\pi\) | |||||||
\(240\) | 1942.65 | 0.522489 | ||||||||
\(241\) | −2219.41 | −0.593216 | −0.296608 | − | 0.954999i | \(-0.595855\pi\) | ||||
−0.296608 | + | 0.954999i | \(0.595855\pi\) | |||||||
\(242\) | −17870.9 | −4.74704 | ||||||||
\(243\) | −203.331 | −0.0536778 | ||||||||
\(244\) | −13860.4 | −3.63657 | ||||||||
\(245\) | 995.437 | 0.259576 | ||||||||
\(246\) | 10143.4 | 2.62895 | ||||||||
\(247\) | −413.572 | −0.106538 | ||||||||
\(248\) | 11231.5 | 2.87581 | ||||||||
\(249\) | 485.862 | 0.123656 | ||||||||
\(250\) | 4132.46 | 1.04544 | ||||||||
\(251\) | −3749.36 | −0.942859 | −0.471430 | − | 0.881904i | \(-0.656262\pi\) | ||||
−0.471430 | + | 0.881904i | \(0.656262\pi\) | |||||||
\(252\) | −323.175 | −0.0807861 | ||||||||
\(253\) | −29.9969 | −0.00745410 | ||||||||
\(254\) | 8832.36 | 2.18186 | ||||||||
\(255\) | 1583.18 | 0.388795 | ||||||||
\(256\) | −7740.13 | −1.88968 | ||||||||
\(257\) | 3129.98 | 0.759698 | 0.379849 | − | 0.925048i | \(-0.375976\pi\) | ||||
0.379849 | + | 0.925048i | \(0.375976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6952.60 | 1.66801 | ||||||||
\(260\) | 1604.82 | 0.382795 | ||||||||
\(261\) | 49.9953 | 0.0118568 | ||||||||
\(262\) | 3003.68 | 0.708274 | ||||||||
\(263\) | −2025.82 | −0.474971 | −0.237485 | − | 0.971391i | \(-0.576323\pi\) | ||||
−0.237485 | + | 0.971391i | \(0.576323\pi\) | |||||||
\(264\) | −18057.1 | −4.20962 | ||||||||
\(265\) | −902.916 | −0.209304 | ||||||||
\(266\) | −1992.51 | −0.459280 | ||||||||
\(267\) | −4867.59 | −1.11570 | ||||||||
\(268\) | 9674.62 | 2.20512 | ||||||||
\(269\) | 4608.81 | 1.04462 | 0.522312 | − | 0.852754i | \(-0.325070\pi\) | ||||
0.522312 | + | 0.852754i | \(0.325070\pi\) | |||||||
\(270\) | 2399.17 | 0.540774 | ||||||||
\(271\) | −5970.94 | −1.33841 | −0.669204 | − | 0.743079i | \(-0.733365\pi\) | ||||
−0.669204 | + | 0.743079i | \(0.733365\pi\) | |||||||
\(272\) | 9482.80 | 2.11389 | ||||||||
\(273\) | −3513.38 | −0.778900 | ||||||||
\(274\) | 7694.40 | 1.69648 | ||||||||
\(275\) | −7895.20 | −1.73127 | ||||||||
\(276\) | −40.1346 | −0.00875296 | ||||||||
\(277\) | −2568.36 | −0.557104 | −0.278552 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278552 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(278\) | 5886.88 | 1.27004 | ||||||||
\(279\) | −165.423 | −0.0354968 | ||||||||
\(280\) | 4238.44 | 0.904625 | ||||||||
\(281\) | −4320.27 | −0.917174 | −0.458587 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458587 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(282\) | 1580.63 | 0.333776 | ||||||||
\(283\) | −7668.11 | −1.61068 | −0.805339 | − | 0.592814i | \(-0.798017\pi\) | ||||
−0.805339 | + | 0.592814i | \(0.798017\pi\) | |||||||
\(284\) | 7087.27 | 1.48082 | ||||||||
\(285\) | −281.069 | −0.0584179 | ||||||||
\(286\) | −9362.26 | −1.93567 | ||||||||
\(287\) | 9567.26 | 1.96773 | ||||||||
\(288\) | −111.051 | −0.0227213 | ||||||||
\(289\) | 2815.11 | 0.572991 | ||||||||
\(290\) | −1196.10 | −0.242198 | ||||||||
\(291\) | 1005.37 | 0.202529 | ||||||||
\(292\) | 1415.56 | 0.283696 | ||||||||
\(293\) | −3130.46 | −0.624176 | −0.312088 | − | 0.950053i | \(-0.601028\pi\) | ||||
−0.312088 | + | 0.950053i | \(0.601028\pi\) | |||||||
\(294\) | −7769.81 | −1.54131 | ||||||||
\(295\) | 2385.12 | 0.470736 | ||||||||
\(296\) | 13588.6 | 2.66832 | ||||||||
\(297\) | −9640.65 | −1.88353 | ||||||||
\(298\) | 2463.16 | 0.478816 | ||||||||
\(299\) | −11.4073 | −0.00220635 | ||||||||
\(300\) | −10563.4 | −2.03294 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11236.1 | −2.14095 | ||||||||
\(303\) | −102.093 | −0.0193568 | ||||||||
\(304\) | −1683.52 | −0.317620 | ||||||||
\(305\) | −2677.33 | −0.502634 | ||||||||
\(306\) | −323.075 | −0.0603561 | ||||||||
\(307\) | 4928.32 | 0.916202 | 0.458101 | − | 0.888900i | \(-0.348530\pi\) | ||||
0.458101 | + | 0.888900i | \(0.348530\pi\) | |||||||
\(308\) | −31068.4 | −5.74769 | ||||||||
\(309\) | 3237.82 | 0.596094 | ||||||||
\(310\) | 3957.61 | 0.725087 | ||||||||
\(311\) | −7959.42 | −1.45125 | −0.725623 | − | 0.688093i | \(-0.758448\pi\) | ||||
−0.725623 | + | 0.688093i | \(0.758448\pi\) | |||||||
\(312\) | −6866.80 | −1.24601 | ||||||||
\(313\) | −3887.39 | −0.702007 | −0.351004 | − | 0.936374i | \(-0.614159\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614159\pi\) | |||||||
\(314\) | 2194.75 | 0.394449 | ||||||||
\(315\) | −62.4256 | −0.0111660 | ||||||||
\(316\) | −2752.45 | −0.489992 | ||||||||
\(317\) | 2937.52 | 0.520466 | 0.260233 | − | 0.965546i | \(-0.416201\pi\) | ||||
0.260233 | + | 0.965546i | \(0.416201\pi\) | |||||||
\(318\) | 7047.64 | 1.24281 | ||||||||
\(319\) | 4806.31 | 0.843579 | ||||||||
\(320\) | −294.742 | −0.0514893 | ||||||||
\(321\) | 6020.43 | 1.04681 | ||||||||
\(322\) | −54.9579 | −0.00951144 | ||||||||
\(323\) | −1372.00 | −0.236348 | ||||||||
\(324\) | −13245.3 | −2.27114 | ||||||||
\(325\) | −3002.40 | −0.512441 | ||||||||
\(326\) | −7309.13 | −1.24176 | ||||||||
\(327\) | 2103.16 | 0.355673 | ||||||||
\(328\) | 18698.9 | 3.14779 | ||||||||
\(329\) | 1490.84 | 0.249826 | ||||||||
\(330\) | −6362.72 | −1.06138 | ||||||||
\(331\) | 6056.24 | 1.00568 | 0.502841 | − | 0.864379i | \(-0.332288\pi\) | ||||
0.502841 | + | 0.864379i | \(0.332288\pi\) | |||||||
\(332\) | 1633.85 | 0.270088 | ||||||||
\(333\) | −200.140 | −0.0329357 | ||||||||
\(334\) | 9204.42 | 1.50792 | ||||||||
\(335\) | 1868.79 | 0.304784 | ||||||||
\(336\) | −14301.9 | −2.32212 | ||||||||
\(337\) | 706.610 | 0.114218 | 0.0571091 | − | 0.998368i | \(-0.481812\pi\) | ||||
0.0571091 | + | 0.998368i | \(0.481812\pi\) | |||||||
\(338\) | 7578.85 | 1.21963 | ||||||||
\(339\) | 4403.74 | 0.705541 | ||||||||
\(340\) | 5323.91 | 0.849204 | ||||||||
\(341\) | −15902.9 | −2.52549 | ||||||||
\(342\) | 57.3569 | 0.00906873 | ||||||||
\(343\) | 1308.34 | 0.205958 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.75254 | −0.00120981 | ||||||||
\(346\) | −7401.35 | −1.15000 | ||||||||
\(347\) | 343.739 | 0.0531783 | 0.0265892 | − | 0.999646i | \(-0.491535\pi\) | ||||
0.0265892 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(348\) | 6430.63 | 0.990569 | ||||||||
\(349\) | −7218.47 | −1.10715 | −0.553576 | − | 0.832799i | \(-0.686737\pi\) | ||||
−0.553576 | + | 0.832799i | \(0.686737\pi\) | |||||||
\(350\) | −14465.0 | −2.20910 | ||||||||
\(351\) | −3666.17 | −0.557508 | ||||||||
\(352\) | −10675.9 | −1.61655 | ||||||||
\(353\) | 3833.43 | 0.577997 | 0.288999 | − | 0.957329i | \(-0.406678\pi\) | ||||
0.288999 | + | 0.957329i | \(0.406678\pi\) | |||||||
\(354\) | −18616.9 | −2.79513 | ||||||||
\(355\) | 1369.00 | 0.204674 | ||||||||
\(356\) | −16368.7 | −2.43690 | ||||||||
\(357\) | −11655.5 | −1.72793 | ||||||||
\(358\) | −21104.5 | −3.11566 | ||||||||
\(359\) | −6085.37 | −0.894634 | −0.447317 | − | 0.894376i | \(-0.647620\pi\) | ||||
−0.447317 | + | 0.894376i | \(0.647620\pi\) | |||||||
\(360\) | −122.009 | −0.0178623 | ||||||||
\(361\) | −6615.42 | −0.964488 | ||||||||
\(362\) | −2072.91 | −0.300966 | ||||||||
\(363\) | 18559.2 | 2.68348 | ||||||||
\(364\) | −11814.8 | −1.70127 | ||||||||
\(365\) | 273.434 | 0.0392115 | ||||||||
\(366\) | 20897.7 | 2.98454 | ||||||||
\(367\) | 7608.08 | 1.08212 | 0.541061 | − | 0.840984i | \(-0.318023\pi\) | ||||
0.541061 | + | 0.840984i | \(0.318023\pi\) | |||||||
\(368\) | −46.4354 | −0.00657776 | ||||||||
\(369\) | −275.406 | −0.0388538 | ||||||||
\(370\) | 4788.18 | 0.672772 | ||||||||
\(371\) | 6647.31 | 0.930219 | ||||||||
\(372\) | −21277.5 | −2.96555 | ||||||||
\(373\) | −7669.36 | −1.06462 | −0.532312 | − | 0.846548i | \(-0.678677\pi\) | ||||
−0.532312 | + | 0.846548i | \(0.678677\pi\) | |||||||
\(374\) | −31058.8 | −4.29415 | ||||||||
\(375\) | −4291.62 | −0.590983 | ||||||||
\(376\) | 2913.80 | 0.399649 | ||||||||
\(377\) | 1827.75 | 0.249692 | ||||||||
\(378\) | −17662.8 | −2.40338 | ||||||||
\(379\) | 8689.95 | 1.17776 | 0.588882 | − | 0.808219i | \(-0.299568\pi\) | ||||
0.588882 | + | 0.808219i | \(0.299568\pi\) | |||||||
\(380\) | −945.177 | −0.127596 | ||||||||
\(381\) | −9172.53 | −1.23339 | ||||||||
\(382\) | 17167.5 | 2.29939 | ||||||||
\(383\) | −5710.24 | −0.761827 | −0.380913 | − | 0.924611i | \(-0.624390\pi\) | ||||
−0.380913 | + | 0.924611i | \(0.624390\pi\) | |||||||
\(384\) | 8754.19 | 1.16337 | ||||||||
\(385\) | −6001.30 | −0.794427 | ||||||||
\(386\) | 1006.96 | 0.132780 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3380.86 | 0.442363 | ||||||||
\(389\) | 13486.0 | 1.75775 | 0.878877 | − | 0.477049i | \(-0.158293\pi\) | ||||
0.878877 | + | 0.477049i | \(0.158293\pi\) | |||||||
\(390\) | −2419.63 | −0.314161 | ||||||||
\(391\) | −37.8431 | −0.00489464 | ||||||||
\(392\) | −14323.2 | −1.84549 | ||||||||
\(393\) | −3119.36 | −0.400384 | ||||||||
\(394\) | 4057.23 | 0.518782 | ||||||||
\(395\) | −531.674 | −0.0677251 | ||||||||
\(396\) | 894.345 | 0.113491 | ||||||||
\(397\) | 10965.7 | 1.38628 | 0.693139 | − | 0.720804i | \(-0.256227\pi\) | ||||
0.693139 | + | 0.720804i | \(0.256227\pi\) | |||||||
\(398\) | 15325.8 | 1.93019 | ||||||||
\(399\) | 2069.25 | 0.259629 | ||||||||
\(400\) | −12221.8 | −1.52773 | ||||||||
\(401\) | −11989.3 | −1.49307 | −0.746533 | − | 0.665349i | \(-0.768283\pi\) | ||||
−0.746533 | + | 0.665349i | \(0.768283\pi\) | |||||||
\(402\) | −14586.7 | −1.80974 | ||||||||
\(403\) | −6047.60 | −0.747525 | ||||||||
\(404\) | −343.319 | −0.0422790 | ||||||||
\(405\) | −2558.51 | −0.313910 | ||||||||
\(406\) | 8805.74 | 1.07641 | ||||||||
\(407\) | −19240.4 | −2.34328 | ||||||||
\(408\) | −22780.2 | −2.76419 | ||||||||
\(409\) | 1648.50 | 0.199298 | 0.0996491 | − | 0.995023i | \(-0.468228\pi\) | ||||
0.0996491 | + | 0.995023i | \(0.468228\pi\) | |||||||
\(410\) | 6588.87 | 0.793661 | ||||||||
\(411\) | −7990.75 | −0.959014 | ||||||||
\(412\) | 10888.1 | 1.30199 | ||||||||
\(413\) | −17559.4 | −2.09211 | ||||||||
\(414\) | 1.58204 | 0.000187809 0 | ||||||||
\(415\) | 315.601 | 0.0373307 | ||||||||
\(416\) | −4059.85 | −0.478487 | ||||||||
\(417\) | −6113.61 | −0.717949 | ||||||||
\(418\) | 5514.01 | 0.645213 | ||||||||
\(419\) | −12568.0 | −1.46536 | −0.732680 | − | 0.680573i | \(-0.761731\pi\) | ||||
−0.732680 | + | 0.680573i | \(0.761731\pi\) | |||||||
\(420\) | −8029.48 | −0.932853 | ||||||||
\(421\) | −1815.80 | −0.210205 | −0.105103 | − | 0.994461i | \(-0.533517\pi\) | ||||
−0.105103 | + | 0.994461i | \(0.533517\pi\) | |||||||
\(422\) | 2949.49 | 0.340234 | ||||||||
\(423\) | −42.9158 | −0.00493295 | ||||||||
\(424\) | 12992.0 | 1.48808 | ||||||||
\(425\) | −9960.32 | −1.13682 | ||||||||
\(426\) | −10685.7 | −1.21531 | ||||||||
\(427\) | 19710.6 | 2.23388 | ||||||||
\(428\) | 20245.4 | 2.28645 | ||||||||
\(429\) | 9722.85 | 1.09423 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6971.17 | 0.779093 | 0.389547 | − | 0.921007i | \(-0.372632\pi\) | ||||
0.389547 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(432\) | −14923.8 | −1.66209 | ||||||||
\(433\) | −10300.9 | −1.14326 | −0.571629 | − | 0.820512i | \(-0.693688\pi\) | ||||
−0.571629 | + | 0.820512i | \(0.693688\pi\) | |||||||
\(434\) | −29136.1 | −3.22253 | ||||||||
\(435\) | 1242.17 | 0.136913 | ||||||||
\(436\) | 7072.49 | 0.776860 | ||||||||
\(437\) | 6.71844 | 0.000735439 0 | ||||||||
\(438\) | −2134.27 | −0.232830 | ||||||||
\(439\) | −9438.10 | −1.02610 | −0.513048 | − | 0.858360i | \(-0.671484\pi\) | ||||
−0.513048 | + | 0.858360i | \(0.671484\pi\) | |||||||
\(440\) | −11729.3 | −1.27085 | ||||||||
\(441\) | 210.959 | 0.0227793 | ||||||||
\(442\) | −11811.1 | −1.27103 | ||||||||
\(443\) | 14850.9 | 1.59275 | 0.796374 | − | 0.604805i | \(-0.206749\pi\) | ||||
0.796374 | + | 0.604805i | \(0.206749\pi\) | |||||||
\(444\) | −25742.9 | −2.75158 | ||||||||
\(445\) | −3161.83 | −0.336821 | ||||||||
\(446\) | 11494.8 | 1.22039 | ||||||||
\(447\) | −2558.03 | −0.270673 | ||||||||
\(448\) | 2169.91 | 0.228836 | ||||||||
\(449\) | 18024.3 | 1.89448 | 0.947240 | − | 0.320526i | \(-0.103860\pi\) | ||||
0.947240 | + | 0.320526i | \(0.103860\pi\) | |||||||
\(450\) | 416.393 | 0.0436199 | ||||||||
\(451\) | −26476.2 | −2.76434 | ||||||||
\(452\) | 14808.9 | 1.54104 | ||||||||
\(453\) | 11668.9 | 1.21027 | ||||||||
\(454\) | 15345.6 | 1.58635 | ||||||||
\(455\) | −2282.18 | −0.235144 | ||||||||
\(456\) | 4044.28 | 0.415330 | ||||||||
\(457\) | 1076.30 | 0.110169 | 0.0550847 | − | 0.998482i | \(-0.482457\pi\) | ||||
0.0550847 | + | 0.998482i | \(0.482457\pi\) | |||||||
\(458\) | 7650.98 | 0.780582 | ||||||||
\(459\) | −12162.3 | −1.23679 | ||||||||
\(460\) | −26.0702 | −0.00264245 | ||||||||
\(461\) | −13661.5 | −1.38021 | −0.690107 | − | 0.723708i | \(-0.742436\pi\) | ||||
−0.690107 | + | 0.723708i | \(0.742436\pi\) | |||||||
\(462\) | 46842.7 | 4.71714 | ||||||||
\(463\) | 18341.2 | 1.84101 | 0.920504 | − | 0.390734i | \(-0.127779\pi\) | ||||
0.920504 | + | 0.390734i | \(0.127779\pi\) | |||||||
\(464\) | 7440.20 | 0.744403 | ||||||||
\(465\) | −4110.03 | −0.409889 | ||||||||
\(466\) | 14841.7 | 1.47538 | ||||||||
\(467\) | −2240.22 | −0.221980 | −0.110990 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110990 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(468\) | 340.103 | 0.0335925 | ||||||||
\(469\) | −13758.1 | −1.35456 | ||||||||
\(470\) | 1026.73 | 0.100765 | ||||||||
\(471\) | −2279.28 | −0.222980 | ||||||||
\(472\) | −34319.3 | −3.34676 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4149.94 | 0.402137 | ||||||||
\(475\) | 1768.30 | 0.170811 | ||||||||
\(476\) | −39194.9 | −3.77415 | ||||||||
\(477\) | −191.352 | −0.0183677 | ||||||||
\(478\) | 18697.7 | 1.78915 | ||||||||
\(479\) | −17597.1 | −1.67857 | −0.839284 | − | 0.543694i | \(-0.817025\pi\) | ||||
−0.839284 | + | 0.543694i | \(0.817025\pi\) | |||||||
\(480\) | −2759.13 | −0.262368 | ||||||||
\(481\) | −7316.79 | −0.693591 | ||||||||
\(482\) | 11252.8 | 1.06338 | ||||||||
\(483\) | 57.0746 | 0.00537678 | ||||||||
\(484\) | 62410.6 | 5.86125 | ||||||||
\(485\) | 653.059 | 0.0611420 | ||||||||
\(486\) | 1030.92 | 0.0962213 | ||||||||
\(487\) | 9889.77 | 0.920222 | 0.460111 | − | 0.887861i | \(-0.347810\pi\) | ||||
0.460111 | + | 0.887861i | \(0.347810\pi\) | |||||||
\(488\) | 38523.8 | 3.57355 | ||||||||
\(489\) | 7590.64 | 0.701964 | ||||||||
\(490\) | −5047.03 | −0.465309 | ||||||||
\(491\) | −3422.49 | −0.314572 | −0.157286 | − | 0.987553i | \(-0.550274\pi\) | ||||
−0.157286 | + | 0.987553i | \(0.550274\pi\) | |||||||
\(492\) | −35424.0 | −3.24601 | ||||||||
\(493\) | 6063.47 | 0.553925 | ||||||||
\(494\) | 2096.88 | 0.190978 | ||||||||
\(495\) | 172.755 | 0.0156864 | ||||||||
\(496\) | −24617.9 | −2.22858 | ||||||||
\(497\) | −10078.7 | −0.909638 | ||||||||
\(498\) | −2463.40 | −0.221662 | ||||||||
\(499\) | −15634.3 | −1.40258 | −0.701291 | − | 0.712875i | \(-0.747393\pi\) | ||||
−0.701291 | + | 0.712875i | \(0.747393\pi\) | |||||||
\(500\) | −14431.8 | −1.29082 | ||||||||
\(501\) | −9558.93 | −0.852418 | ||||||||
\(502\) | 19009.9 | 1.69014 | ||||||||
\(503\) | 101.907 | 0.00903342 | 0.00451671 | − | 0.999990i | \(-0.498562\pi\) | ||||
0.00451671 | + | 0.999990i | \(0.498562\pi\) | |||||||
\(504\) | 898.236 | 0.0793861 | ||||||||
\(505\) | −66.3167 | −0.00584367 | ||||||||
\(506\) | 152.089 | 0.0133620 | ||||||||
\(507\) | −7870.75 | −0.689452 | ||||||||
\(508\) | −30845.3 | −2.69397 | ||||||||
\(509\) | 4998.09 | 0.435239 | 0.217619 | − | 0.976034i | \(-0.430171\pi\) | ||||
0.217619 | + | 0.976034i | \(0.430171\pi\) | |||||||
\(510\) | −8026.99 | −0.696944 | ||||||||
\(511\) | −2013.04 | −0.174269 | ||||||||
\(512\) | 25943.1 | 2.23933 | ||||||||
\(513\) | 2159.23 | 0.185833 | ||||||||
\(514\) | −15869.5 | −1.36182 | ||||||||
\(515\) | 2103.19 | 0.179956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4125.71 | −0.350965 | ||||||||
\(518\) | −35250.8 | −2.99002 | ||||||||
\(519\) | 7686.41 | 0.650089 | ||||||||
\(520\) | −4460.46 | −0.376162 | ||||||||
\(521\) | 1425.38 | 0.119860 | 0.0599298 | − | 0.998203i | \(-0.480912\pi\) | ||||
0.0599298 | + | 0.998203i | \(0.480912\pi\) | |||||||
\(522\) | −253.485 | −0.0212543 | ||||||||
\(523\) | 4492.23 | 0.375586 | 0.187793 | − | 0.982209i | \(-0.439867\pi\) | ||||
0.187793 | + | 0.982209i | \(0.439867\pi\) | |||||||
\(524\) | −10489.8 | −0.874518 | ||||||||
\(525\) | 15022.1 | 1.24879 | ||||||||
\(526\) | 10271.2 | 0.851420 | ||||||||
\(527\) | −20062.6 | −1.65833 | ||||||||
\(528\) | 39578.6 | 3.26220 | ||||||||
\(529\) | −12166.8 | −0.999985 | ||||||||
\(530\) | 4577.93 | 0.375194 | ||||||||
\(531\) | 505.470 | 0.0413098 | ||||||||
\(532\) | 6958.44 | 0.567080 | ||||||||
\(533\) | −10068.4 | −0.818221 | ||||||||
\(534\) | 24679.5 | 1.99997 | ||||||||
\(535\) | 3910.68 | 0.316025 | ||||||||
\(536\) | −26889.8 | −2.16691 | ||||||||
\(537\) | 21917.3 | 1.76127 | ||||||||
\(538\) | −23367.4 | −1.87257 | ||||||||
\(539\) | 20280.6 | 1.62068 | ||||||||
\(540\) | −8378.65 | −0.667703 | ||||||||
\(541\) | −14116.5 | −1.12184 | −0.560922 | − | 0.827869i | \(-0.689553\pi\) | ||||
−0.560922 | + | 0.827869i | \(0.689553\pi\) | |||||||
\(542\) | 30273.6 | 2.39920 | ||||||||
\(543\) | 2152.75 | 0.170135 | ||||||||
\(544\) | −13468.3 | −1.06149 | ||||||||
\(545\) | 1366.15 | 0.107375 | ||||||||
\(546\) | 17813.4 | 1.39623 | ||||||||
\(547\) | −5870.12 | −0.458845 | −0.229423 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229423 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(548\) | −26871.2 | −2.09467 | ||||||||
\(549\) | −567.396 | −0.0441091 | ||||||||
\(550\) | 40030.0 | 3.10342 | ||||||||
\(551\) | −1076.48 | −0.0832294 | ||||||||
\(552\) | 111.551 | 0.00860128 | ||||||||
\(553\) | 3914.21 | 0.300993 | ||||||||
\(554\) | 13022.0 | 0.998650 | ||||||||
\(555\) | −4972.59 | −0.380315 | ||||||||
\(556\) | −20558.8 | −1.56814 | ||||||||
\(557\) | 19618.5 | 1.49239 | 0.746196 | − | 0.665726i | \(-0.231878\pi\) | ||||
0.746196 | + | 0.665726i | \(0.231878\pi\) | |||||||
\(558\) | 838.721 | 0.0636306 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −9290.06 | −0.701029 | ||||||||
\(561\) | 32255.0 | 2.42747 | ||||||||
\(562\) | 21904.5 | 1.64410 | ||||||||
\(563\) | −16594.0 | −1.24219 | −0.621094 | − | 0.783736i | \(-0.713312\pi\) | ||||
−0.621094 | + | 0.783736i | \(0.713312\pi\) | |||||||
\(564\) | −5520.03 | −0.412119 | ||||||||
\(565\) | 2860.53 | 0.212997 | ||||||||
\(566\) | 38878.6 | 2.88726 | ||||||||
\(567\) | 18835.9 | 1.39512 | ||||||||
\(568\) | −19698.4 | −1.45516 | ||||||||
\(569\) | −3166.05 | −0.233265 | −0.116633 | − | 0.993175i | \(-0.537210\pi\) | ||||
−0.116633 | + | 0.993175i | \(0.537210\pi\) | |||||||
\(570\) | 1425.07 | 0.104718 | ||||||||
\(571\) | 9197.67 | 0.674099 | 0.337049 | − | 0.941487i | \(-0.390571\pi\) | ||||
0.337049 | + | 0.941487i | \(0.390571\pi\) | |||||||
\(572\) | 32695.9 | 2.39001 | ||||||||
\(573\) | −17828.7 | −1.29984 | ||||||||
\(574\) | −48507.6 | −3.52730 | ||||||||
\(575\) | 48.7738 | 0.00353740 | ||||||||
\(576\) | −62.4636 | −0.00451849 | ||||||||
\(577\) | 2852.95 | 0.205840 | 0.102920 | − | 0.994690i | \(-0.467181\pi\) | ||||
0.102920 | + | 0.994690i | \(0.467181\pi\) | |||||||
\(578\) | −14273.0 | −1.02713 | ||||||||
\(579\) | −1045.74 | −0.0750599 | ||||||||
\(580\) | 4177.14 | 0.299045 | ||||||||
\(581\) | −2323.47 | −0.165910 | ||||||||
\(582\) | −5097.40 | −0.363048 | ||||||||
\(583\) | −18395.6 | −1.30681 | ||||||||
\(584\) | −3934.42 | −0.278780 | ||||||||
\(585\) | 65.6957 | 0.00464304 | ||||||||
\(586\) | 15872.0 | 1.11888 | ||||||||
\(587\) | −1209.16 | −0.0850208 | −0.0425104 | − | 0.999096i | \(-0.513536\pi\) | ||||
−0.0425104 | + | 0.999096i | \(0.513536\pi\) | |||||||
\(588\) | 27134.6 | 1.90308 | ||||||||
\(589\) | 3561.80 | 0.249171 | ||||||||
\(590\) | −12093.0 | −0.843829 | ||||||||
\(591\) | −4213.49 | −0.293265 | ||||||||
\(592\) | −29784.4 | −2.06779 | ||||||||
\(593\) | 3344.49 | 0.231605 | 0.115803 | − | 0.993272i | \(-0.463056\pi\) | ||||
0.115803 | + | 0.993272i | \(0.463056\pi\) | |||||||
\(594\) | 48879.7 | 3.37636 | ||||||||
\(595\) | −7571.03 | −0.521650 | ||||||||
\(596\) | −8602.12 | −0.591203 | ||||||||
\(597\) | −15916.1 | −1.09113 | ||||||||
\(598\) | 57.8368 | 0.00395505 | ||||||||
\(599\) | −19435.1 | −1.32570 | −0.662851 | − | 0.748752i | \(-0.730654\pi\) | ||||
−0.662851 | + | 0.748752i | \(0.730654\pi\) | |||||||
\(600\) | 29360.2 | 1.99771 | ||||||||
\(601\) | 3263.80 | 0.221519 | 0.110760 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110760 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 396.045 | 0.0267466 | ||||||||
\(604\) | 39240.0 | 2.64346 | ||||||||
\(605\) | 12055.5 | 0.810123 | ||||||||
\(606\) | 517.630 | 0.0346985 | ||||||||
\(607\) | −13079.9 | −0.874622 | −0.437311 | − | 0.899310i | \(-0.644069\pi\) | ||||
−0.437311 | + | 0.899310i | \(0.644069\pi\) | |||||||
\(608\) | 2391.09 | 0.159493 | ||||||||
\(609\) | −9144.88 | −0.608488 | ||||||||
\(610\) | 13574.5 | 0.901009 | ||||||||
\(611\) | −1568.94 | −0.103883 | ||||||||
\(612\) | 1128.28 | 0.0745226 | ||||||||
\(613\) | −24182.4 | −1.59334 | −0.796671 | − | 0.604413i | \(-0.793408\pi\) | ||||
−0.796671 | + | 0.604413i | \(0.793408\pi\) | |||||||
\(614\) | −24987.4 | −1.64236 | ||||||||
\(615\) | −6842.64 | −0.448653 | ||||||||
\(616\) | 86352.0 | 5.64809 | ||||||||
\(617\) | −4358.65 | −0.284396 | −0.142198 | − | 0.989838i | \(-0.545417\pi\) | ||||
−0.142198 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(618\) | −16416.3 | −1.06854 | ||||||||
\(619\) | −2248.54 | −0.146004 | −0.0730019 | − | 0.997332i | \(-0.523258\pi\) | ||||
−0.0730019 | + | 0.997332i | \(0.523258\pi\) | |||||||
\(620\) | −13821.2 | −0.895277 | ||||||||
\(621\) | 59.5566 | 0.00384851 | ||||||||
\(622\) | 40355.6 | 2.60147 | ||||||||
\(623\) | 23277.6 | 1.49694 | ||||||||
\(624\) | 15051.0 | 0.965583 | ||||||||
\(625\) | 11375.0 | 0.728001 | ||||||||
\(626\) | 19709.7 | 1.25840 | ||||||||
\(627\) | −5726.38 | −0.364736 | ||||||||
\(628\) | −7664.74 | −0.487032 | ||||||||
\(629\) | −24273.1 | −1.53868 | ||||||||
\(630\) | 316.508 | 0.0200159 | ||||||||
\(631\) | 19871.2 | 1.25366 | 0.626829 | − | 0.779157i | \(-0.284352\pi\) | ||||
0.626829 | + | 0.779157i | \(0.284352\pi\) | |||||||
\(632\) | 7650.20 | 0.481501 | ||||||||
\(633\) | −3063.09 | −0.192333 | ||||||||
\(634\) | −14893.7 | −0.932973 | ||||||||
\(635\) | −5958.19 | −0.372352 | ||||||||
\(636\) | −24612.5 | −1.53451 | ||||||||
\(637\) | 7712.34 | 0.479708 | ||||||||
\(638\) | −24368.8 | −1.51218 | ||||||||
\(639\) | 290.128 | 0.0179613 | ||||||||
\(640\) | 5686.45 | 0.351214 | ||||||||
\(641\) | −2163.67 | −0.133323 | −0.0666613 | − | 0.997776i | \(-0.521235\pi\) | ||||
−0.0666613 | + | 0.997776i | \(0.521235\pi\) | |||||||
\(642\) | −30524.6 | −1.87649 | ||||||||
\(643\) | −19895.6 | −1.22023 | −0.610115 | − | 0.792313i | \(-0.708877\pi\) | ||||
−0.610115 | + | 0.792313i | \(0.708877\pi\) | |||||||
\(644\) | 191.930 | 0.0117439 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6956.29 | 0.423671 | ||||||||
\(647\) | −3789.98 | −0.230293 | −0.115146 | − | 0.993349i | \(-0.536734\pi\) | ||||
−0.115146 | + | 0.993349i | \(0.536734\pi\) | |||||||
\(648\) | 36814.2 | 2.23179 | ||||||||
\(649\) | 48593.4 | 2.93907 | ||||||||
\(650\) | 15222.7 | 0.918588 | ||||||||
\(651\) | 30258.3 | 1.82168 | ||||||||
\(652\) | 25525.7 | 1.53323 | ||||||||
\(653\) | 16510.4 | 0.989436 | 0.494718 | − | 0.869054i | \(-0.335271\pi\) | ||||
0.494718 | + | 0.869054i | \(0.335271\pi\) | |||||||
\(654\) | −10663.4 | −0.637570 | ||||||||
\(655\) | −2026.24 | −0.120873 | ||||||||
\(656\) | −40985.4 | −2.43934 | ||||||||
\(657\) | 57.9479 | 0.00344104 | ||||||||
\(658\) | −7558.81 | −0.447831 | ||||||||
\(659\) | −14640.9 | −0.865448 | −0.432724 | − | 0.901526i | \(-0.642448\pi\) | ||||
−0.432724 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(660\) | 22220.6 | 1.31051 | ||||||||
\(661\) | −30193.4 | −1.77668 | −0.888341 | − | 0.459184i | \(-0.848142\pi\) | ||||
−0.888341 | + | 0.459184i | \(0.848142\pi\) | |||||||
\(662\) | −30706.1 | −1.80276 | ||||||||
\(663\) | 12266.0 | 0.718510 | ||||||||
\(664\) | −4541.15 | −0.265408 | ||||||||
\(665\) | 1344.12 | 0.0783799 | ||||||||
\(666\) | 1014.74 | 0.0590396 | ||||||||
\(667\) | −29.6917 | −0.00172364 | ||||||||
\(668\) | −32144.7 | −1.86185 | ||||||||
\(669\) | −11937.5 | −0.689883 | ||||||||
\(670\) | −9475.05 | −0.546348 | ||||||||
\(671\) | −54546.7 | −3.13823 | ||||||||
\(672\) | 20312.9 | 1.16605 | ||||||||
\(673\) | −9061.92 | −0.519036 | −0.259518 | − | 0.965738i | \(-0.583564\pi\) | ||||
−0.259518 | + | 0.965738i | \(0.583564\pi\) | |||||||
\(674\) | −3582.63 | −0.204744 | ||||||||
\(675\) | 15675.3 | 0.893842 | ||||||||
\(676\) | −26467.7 | −1.50590 | ||||||||
\(677\) | 4678.54 | 0.265599 | 0.132800 | − | 0.991143i | \(-0.457603\pi\) | ||||
0.132800 | + | 0.991143i | \(0.457603\pi\) | |||||||
\(678\) | −22327.7 | −1.26473 | ||||||||
\(679\) | −4807.85 | −0.271736 | ||||||||
\(680\) | −14797.3 | −0.834489 | ||||||||
\(681\) | −15936.6 | −0.896758 | ||||||||
\(682\) | 80630.5 | 4.52713 | ||||||||
\(683\) | 28517.5 | 1.59764 | 0.798822 | − | 0.601568i | \(-0.205457\pi\) | ||||
0.798822 | + | 0.601568i | \(0.205457\pi\) | |||||||
\(684\) | −200.308 | −0.0111973 | ||||||||
\(685\) | −5190.54 | −0.289519 | ||||||||
\(686\) | −6633.49 | −0.369195 | ||||||||
\(687\) | −7945.65 | −0.441260 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6995.52 | −0.386804 | ||||||||
\(690\) | 39.3067 | 0.00216866 | ||||||||
\(691\) | 18910.7 | 1.04109 | 0.520547 | − | 0.853833i | \(-0.325728\pi\) | ||||
0.520547 | + | 0.853833i | \(0.325728\pi\) | |||||||
\(692\) | 25847.8 | 1.41992 | ||||||||
\(693\) | −1271.83 | −0.0697156 | ||||||||
\(694\) | −1742.81 | −0.0953261 | ||||||||
\(695\) | −3971.21 | −0.216743 | ||||||||
\(696\) | −17873.4 | −0.973404 | ||||||||
\(697\) | −33401.5 | −1.81517 | ||||||||
\(698\) | 36598.8 | 1.98465 | ||||||||
\(699\) | −15413.3 | −0.834026 | ||||||||
\(700\) | 50516.1 | 2.72761 | ||||||||
\(701\) | 11193.1 | 0.603080 | 0.301540 | − | 0.953454i | \(-0.402499\pi\) | ||||
0.301540 | + | 0.953454i | \(0.402499\pi\) | |||||||
\(702\) | 18588.1 | 0.999375 | ||||||||
\(703\) | 4309.31 | 0.231193 | ||||||||
\(704\) | −6004.95 | −0.321477 | ||||||||
\(705\) | −1066.27 | −0.0569618 | ||||||||
\(706\) | −19436.1 | −1.03610 | ||||||||
\(707\) | 488.227 | 0.0259712 | ||||||||
\(708\) | 65015.9 | 3.45120 | ||||||||
\(709\) | 12502.4 | 0.662251 | 0.331125 | − | 0.943587i | \(-0.392572\pi\) | ||||
0.331125 | + | 0.943587i | \(0.392572\pi\) | |||||||
\(710\) | −6941.07 | −0.366893 | ||||||||
\(711\) | −112.676 | −0.00594327 | ||||||||
\(712\) | 45495.3 | 2.39467 | ||||||||
\(713\) | 98.2428 | 0.00516020 | ||||||||
\(714\) | 59095.1 | 3.09745 | ||||||||
\(715\) | 6315.66 | 0.330339 | ||||||||
\(716\) | 73703.4 | 3.84696 | ||||||||
\(717\) | −19417.8 | −1.01140 | ||||||||
\(718\) | 30853.8 | 1.60370 | ||||||||
\(719\) | 24760.3 | 1.28429 | 0.642143 | − | 0.766585i | \(-0.278045\pi\) | ||||
0.642143 | + | 0.766585i | \(0.278045\pi\) | |||||||
\(720\) | 267.426 | 0.0138422 | ||||||||
\(721\) | −15483.8 | −0.799786 | ||||||||
\(722\) | 33541.3 | 1.72892 | ||||||||
\(723\) | −11686.2 | −0.601126 | ||||||||
\(724\) | 7239.24 | 0.371608 | ||||||||
\(725\) | −7814.87 | −0.400327 | ||||||||
\(726\) | −94098.0 | −4.81034 | ||||||||
\(727\) | 11567.8 | 0.590131 | 0.295066 | − | 0.955477i | \(-0.404658\pi\) | ||||
0.295066 | + | 0.955477i | \(0.404658\pi\) | |||||||
\(728\) | 32838.1 | 1.67179 | ||||||||
\(729\) | 19126.6 | 0.971732 | ||||||||
\(730\) | −1386.36 | −0.0702895 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −72981.2 | −3.68506 | ||||||||
\(733\) | −4270.99 | −0.215215 | −0.107607 | − | 0.994193i | \(-0.534319\pi\) | ||||
−0.107607 | + | 0.994193i | \(0.534319\pi\) | |||||||
\(734\) | −38574.2 | −1.93978 | ||||||||
\(735\) | 5241.41 | 0.263037 | ||||||||
\(736\) | 65.9519 | 0.00330302 | ||||||||
\(737\) | 38073.8 | 1.90294 | ||||||||
\(738\) | 1396.35 | 0.0696484 | ||||||||
\(739\) | 21299.1 | 1.06022 | 0.530109 | − | 0.847929i | \(-0.322151\pi\) | ||||
0.530109 | + | 0.847929i | \(0.322151\pi\) | |||||||
\(740\) | −16721.8 | −0.830683 | ||||||||
\(741\) | −2177.64 | −0.107959 | ||||||||
\(742\) | −33703.0 | −1.66749 | ||||||||
\(743\) | −11126.4 | −0.549378 | −0.274689 | − | 0.961533i | \(-0.588575\pi\) | ||||
−0.274689 | + | 0.961533i | \(0.588575\pi\) | |||||||
\(744\) | 59138.8 | 2.91416 | ||||||||
\(745\) | −1661.62 | −0.0817141 | ||||||||
\(746\) | 38884.9 | 1.90842 | ||||||||
\(747\) | 66.8841 | 0.00327598 | ||||||||
\(748\) | 108467. | 5.30206 | ||||||||
\(749\) | −28790.7 | −1.40452 | ||||||||
\(750\) | 21759.2 | 1.05938 | ||||||||
\(751\) | −29708.9 | −1.44354 | −0.721768 | − | 0.692136i | \(-0.756670\pi\) | ||||
−0.721768 | + | 0.692136i | \(0.756670\pi\) | |||||||
\(752\) | −6386.64 | −0.309703 | ||||||||
\(753\) | −19742.0 | −0.955431 | ||||||||
\(754\) | −9267.00 | −0.447592 | ||||||||
\(755\) | 7579.74 | 0.365371 | ||||||||
\(756\) | 61684.0 | 2.96749 | ||||||||
\(757\) | 32375.3 | 1.55443 | 0.777213 | − | 0.629237i | \(-0.216633\pi\) | ||||
0.777213 | + | 0.629237i | \(0.216633\pi\) | |||||||
\(758\) | −44059.5 | −2.11123 | ||||||||
\(759\) | −157.947 | −0.00755350 | ||||||||
\(760\) | 2627.04 | 0.125385 | ||||||||
\(761\) | 29515.1 | 1.40594 | 0.702972 | − | 0.711218i | \(-0.251856\pi\) | ||||
0.702972 | + | 0.711218i | \(0.251856\pi\) | |||||||
\(762\) | 46506.2 | 2.21095 | ||||||||
\(763\) | −10057.7 | −0.477210 | ||||||||
\(764\) | −59954.3 | −2.83910 | ||||||||
\(765\) | 217.942 | 0.0103003 | ||||||||
\(766\) | 28951.8 | 1.36563 | ||||||||
\(767\) | 18479.2 | 0.869941 | ||||||||
\(768\) | −40755.2 | −1.91488 | ||||||||
\(769\) | 948.011 | 0.0444553 | 0.0222277 | − | 0.999753i | \(-0.492924\pi\) | ||||
0.0222277 | + | 0.999753i | \(0.492924\pi\) | |||||||
\(770\) | 30427.6 | 1.42407 | ||||||||
\(771\) | 16480.7 | 0.769828 | ||||||||
\(772\) | −3516.62 | −0.163945 | ||||||||
\(773\) | 12922.3 | 0.601270 | 0.300635 | − | 0.953739i | \(-0.402801\pi\) | ||||
0.300635 | + | 0.953739i | \(0.402801\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25857.6 | 1.19849 | ||||||||
\(776\) | −9396.80 | −0.434698 | ||||||||
\(777\) | 36608.5 | 1.69025 | ||||||||
\(778\) | −68376.1 | −3.15090 | ||||||||
\(779\) | 5929.91 | 0.272736 | ||||||||
\(780\) | 8450.08 | 0.387899 | ||||||||
\(781\) | 27891.5 | 1.27789 | ||||||||
\(782\) | 191.870 | 0.00877401 | ||||||||
\(783\) | −9542.56 | −0.435534 | ||||||||
\(784\) | 31394.5 | 1.43014 | ||||||||
\(785\) | −1480.55 | −0.0673160 | ||||||||
\(786\) | 15815.7 | 0.717719 | ||||||||
\(787\) | −24604.3 | −1.11442 | −0.557211 | − | 0.830371i | \(-0.688128\pi\) | ||||
−0.557211 | + | 0.830371i | \(0.688128\pi\) | |||||||
\(788\) | −14169.1 | −0.640549 | ||||||||
\(789\) | −10666.8 | −0.481304 | ||||||||
\(790\) | 2695.67 | 0.121402 | ||||||||
\(791\) | −21059.4 | −0.946632 | ||||||||
\(792\) | −2485.76 | −0.111525 | ||||||||
\(793\) | −20743.1 | −0.928891 | ||||||||
\(794\) | −55597.9 | −2.48501 | ||||||||
\(795\) | −4754.25 | −0.212095 | ||||||||
\(796\) | −53522.5 | −2.38323 | ||||||||
\(797\) | 18527.4 | 0.823432 | 0.411716 | − | 0.911312i | \(-0.364930\pi\) | ||||
0.411716 | + | 0.911312i | \(0.364930\pi\) | |||||||
\(798\) | −10491.4 | −0.465404 | ||||||||
\(799\) | −5204.86 | −0.230457 | ||||||||
\(800\) | 17358.6 | 0.767149 | ||||||||
\(801\) | −670.075 | −0.0295580 | ||||||||
\(802\) | 60787.9 | 2.67643 | ||||||||
\(803\) | 5570.83 | 0.244820 | ||||||||
\(804\) | 50941.1 | 2.23452 | ||||||||
\(805\) | 37.0739 | 0.00162321 | ||||||||
\(806\) | 30662.3 | 1.33999 | ||||||||
\(807\) | 24267.4 | 1.05855 | ||||||||
\(808\) | 954.224 | 0.0415464 | ||||||||
\(809\) | −12328.4 | −0.535778 | −0.267889 | − | 0.963450i | \(-0.586326\pi\) | ||||
−0.267889 | + | 0.963450i | \(0.586326\pi\) | |||||||
\(810\) | 12972.1 | 0.562707 | ||||||||
\(811\) | −14172.8 | −0.613655 | −0.306828 | − | 0.951765i | \(-0.599268\pi\) | ||||
−0.306828 | + | 0.951765i | \(0.599268\pi\) | |||||||
\(812\) | −30752.3 | −1.32906 | ||||||||
\(813\) | −31439.6 | −1.35625 | ||||||||
\(814\) | 97552.2 | 4.20050 | ||||||||
\(815\) | 4930.64 | 0.211918 | ||||||||
\(816\) | 49931.1 | 2.14208 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −8358.15 | −0.357257 | ||||||||
\(819\) | −483.655 | −0.0206352 | ||||||||
\(820\) | −23010.3 | −0.979947 | ||||||||
\(821\) | 3310.52 | 0.140728 | 0.0703642 | − | 0.997521i | \(-0.477584\pi\) | ||||
0.0703642 | + | 0.997521i | \(0.477584\pi\) | |||||||
\(822\) | 40514.4 | 1.71910 | ||||||||
\(823\) | −25536.1 | −1.08157 | −0.540785 | − | 0.841161i | \(-0.681873\pi\) | ||||
−0.540785 | + | 0.841161i | \(0.681873\pi\) | |||||||
\(824\) | −30262.5 | −1.27942 | ||||||||
\(825\) | −41571.7 | −1.75435 | ||||||||
\(826\) | 89029.0 | 3.75026 | ||||||||
\(827\) | −32268.2 | −1.35680 | −0.678401 | − | 0.734692i | \(-0.737327\pi\) | ||||
−0.678401 | + | 0.734692i | \(0.737327\pi\) | |||||||
\(828\) | −5.52495 | −0.000231890 0 | ||||||||
\(829\) | −27155.4 | −1.13769 | −0.568846 | − | 0.822444i | \(-0.692610\pi\) | ||||
−0.568846 | + | 0.822444i | \(0.692610\pi\) | |||||||
\(830\) | −1600.15 | −0.0669180 | ||||||||
\(831\) | −13523.6 | −0.564533 | ||||||||
\(832\) | −2283.57 | −0.0951546 | ||||||||
\(833\) | 25585.3 | 1.06420 | ||||||||
\(834\) | 30997.0 | 1.28698 | ||||||||
\(835\) | −6209.18 | −0.257338 | ||||||||
\(836\) | −19256.6 | −0.796655 | ||||||||
\(837\) | 31574.1 | 1.30390 | ||||||||
\(838\) | 63721.7 | 2.62677 | ||||||||
\(839\) | −30776.5 | −1.26642 | −0.633208 | − | 0.773982i | \(-0.718262\pi\) | ||||
−0.633208 | + | 0.773982i | \(0.718262\pi\) | |||||||
\(840\) | 22317.2 | 0.916688 | ||||||||
\(841\) | −19631.6 | −0.804936 | ||||||||
\(842\) | 9206.38 | 0.376809 | ||||||||
\(843\) | −22748.1 | −0.929404 | ||||||||
\(844\) | −10300.5 | −0.420093 | ||||||||
\(845\) | −5112.59 | −0.208140 | ||||||||
\(846\) | 217.590 | 0.00884267 | ||||||||
\(847\) | −88752.9 | −3.60046 | ||||||||
\(848\) | −28476.5 | −1.15317 | ||||||||
\(849\) | −40376.0 | −1.63216 | ||||||||
\(850\) | 50500.5 | 2.03782 | ||||||||
\(851\) | 118.861 | 0.00478789 | ||||||||
\(852\) | 37317.6 | 1.50056 | ||||||||
\(853\) | 35765.6 | 1.43563 | 0.717813 | − | 0.696236i | \(-0.245143\pi\) | ||||
0.717813 | + | 0.696236i | \(0.245143\pi\) | |||||||
\(854\) | −99936.2 | −4.00439 | ||||||||
\(855\) | −38.6922 | −0.00154765 | ||||||||
\(856\) | −56270.4 | −2.24683 | ||||||||
\(857\) | −9888.39 | −0.394143 | −0.197072 | − | 0.980389i | \(-0.563143\pi\) | ||||
−0.197072 | + | 0.980389i | \(0.563143\pi\) | |||||||
\(858\) | −49296.4 | −1.96148 | ||||||||
\(859\) | 33387.3 | 1.32615 | 0.663073 | − | 0.748554i | \(-0.269252\pi\) | ||||
0.663073 | + | 0.748554i | \(0.269252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50375.8 | 1.99397 | ||||||||
\(862\) | −35344.9 | −1.39658 | ||||||||
\(863\) | 12883.2 | 0.508167 | 0.254084 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254084 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(864\) | 21196.2 | 0.834617 | ||||||||
\(865\) | 4992.86 | 0.196257 | ||||||||
\(866\) | 52227.3 | 2.04937 | ||||||||
\(867\) | 14822.8 | 0.580632 | ||||||||
\(868\) | 101752. | 3.97891 | ||||||||
\(869\) | −10832.1 | −0.422846 | ||||||||
\(870\) | −6297.98 | −0.245427 | ||||||||
\(871\) | 14478.8 | 0.563255 | ||||||||
\(872\) | −19657.4 | −0.763397 | ||||||||
\(873\) | 138.400 | 0.00536557 | ||||||||
\(874\) | −34.0636 | −0.00131833 | ||||||||
\(875\) | 20523.2 | 0.792928 | ||||||||
\(876\) | 7453.53 | 0.287479 | ||||||||
\(877\) | 43358.1 | 1.66944 | 0.834719 | − | 0.550676i | \(-0.185630\pi\) | ||||
0.834719 | + | 0.550676i | \(0.185630\pi\) | |||||||
\(878\) | 47852.7 | 1.83935 | ||||||||
\(879\) | −16483.3 | −0.632499 | ||||||||
\(880\) | 25709.1 | 0.984832 | ||||||||
\(881\) | −50023.1 | −1.91296 | −0.956482 | − | 0.291790i | \(-0.905749\pi\) | ||||
−0.956482 | + | 0.291790i | \(0.905749\pi\) | |||||||
\(882\) | −1069.60 | −0.0408336 | ||||||||
\(883\) | 12280.1 | 0.468017 | 0.234008 | − | 0.972235i | \(-0.424816\pi\) | ||||
0.234008 | + | 0.972235i | \(0.424816\pi\) | |||||||
\(884\) | 41248.0 | 1.56937 | ||||||||
\(885\) | 12558.7 | 0.477013 | ||||||||
\(886\) | −75296.4 | −2.85512 | ||||||||
\(887\) | 13525.7 | 0.512004 | 0.256002 | − | 0.966676i | \(-0.417595\pi\) | ||||
0.256002 | + | 0.966676i | \(0.417595\pi\) | |||||||
\(888\) | 71550.1 | 2.70390 | ||||||||
\(889\) | 43864.5 | 1.65486 | ||||||||
\(890\) | 16031.0 | 0.603776 | ||||||||
\(891\) | −52126.0 | −1.95992 | ||||||||
\(892\) | −40143.4 | −1.50684 | ||||||||
\(893\) | 924.042 | 0.0346270 | ||||||||
\(894\) | 12969.6 | 0.485201 | ||||||||
\(895\) | 14236.8 | 0.531715 | ||||||||
\(896\) | −41863.9 | −1.56091 | ||||||||
\(897\) | −60.0643 | −0.00223577 | ||||||||
\(898\) | −91386.4 | −3.39599 | ||||||||
\(899\) | −15741.1 | −0.583978 | ||||||||
\(900\) | −1454.17 | −0.0538582 | ||||||||
\(901\) | −23207.3 | −0.858098 | ||||||||
\(902\) | 134239. | 4.95528 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41159.9 | −1.51433 | ||||||||
\(905\) | 1398.36 | 0.0513624 | ||||||||
\(906\) | −59163.1 | −2.16950 | ||||||||
\(907\) | −24879.6 | −0.910818 | −0.455409 | − | 0.890282i | \(-0.650507\pi\) | ||||
−0.455409 | + | 0.890282i | \(0.650507\pi\) | |||||||
\(908\) | −53591.5 | −1.95870 | ||||||||
\(909\) | −14.0542 | −0.000512816 0 | ||||||||
\(910\) | 11571.0 | 0.421513 | ||||||||
\(911\) | −19747.9 | −0.718198 | −0.359099 | − | 0.933299i | \(-0.616916\pi\) | ||||
−0.359099 | + | 0.933299i | \(0.616916\pi\) | |||||||
\(912\) | −8864.48 | −0.321856 | ||||||||
\(913\) | 6429.91 | 0.233077 | ||||||||
\(914\) | −5457.04 | −0.197487 | ||||||||
\(915\) | −14097.3 | −0.509337 | ||||||||
\(916\) | −26719.6 | −0.963798 | ||||||||
\(917\) | 14917.3 | 0.537200 | ||||||||
\(918\) | 61664.9 | 2.21704 | ||||||||
\(919\) | 9581.27 | 0.343914 | 0.171957 | − | 0.985104i | \(-0.444991\pi\) | ||||
0.171957 | + | 0.985104i | \(0.444991\pi\) | |||||||
\(920\) | 72.4598 | 0.00259666 | ||||||||
\(921\) | 25949.8 | 0.928419 | ||||||||
\(922\) | 69265.9 | 2.47413 | ||||||||
\(923\) | 10606.6 | 0.378246 | ||||||||
\(924\) | −163589. | −5.82433 | ||||||||
\(925\) | 31284.2 | 1.11202 | ||||||||
\(926\) | −92992.7 | −3.30014 | ||||||||
\(927\) | 445.720 | 0.0157922 | ||||||||
\(928\) | −10567.3 | −0.373801 | ||||||||
\(929\) | 35400.6 | 1.25022 | 0.625111 | − | 0.780536i | \(-0.285054\pi\) | ||||
0.625111 | + | 0.780536i | \(0.285054\pi\) | |||||||
\(930\) | 20838.5 | 0.734756 | ||||||||
\(931\) | −4542.27 | −0.159900 | ||||||||
\(932\) | −51831.6 | −1.82168 | ||||||||
\(933\) | −41909.9 | −1.47060 | ||||||||
\(934\) | 11358.3 | 0.397916 | ||||||||
\(935\) | 20951.9 | 0.732834 | ||||||||
\(936\) | −945.288 | −0.0330104 | ||||||||
\(937\) | −24831.3 | −0.865745 | −0.432872 | − | 0.901455i | \(-0.642500\pi\) | ||||
−0.432872 | + | 0.901455i | \(0.642500\pi\) | |||||||
\(938\) | 69755.8 | 2.42815 | ||||||||
\(939\) | −20468.8 | −0.711368 | ||||||||
\(940\) | −3585.64 | −0.124416 | ||||||||
\(941\) | 18196.9 | 0.630394 | 0.315197 | − | 0.949026i | \(-0.397929\pi\) | ||||
0.315197 | + | 0.949026i | \(0.397929\pi\) | |||||||
\(942\) | 11556.3 | 0.399708 | ||||||||
\(943\) | 163.561 | 0.00564822 | ||||||||
\(944\) | 75223.0 | 2.59354 | ||||||||
\(945\) | 11915.1 | 0.410157 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38685.4 | −1.32746 | −0.663732 | − | 0.747971i | \(-0.731028\pi\) | ||||
−0.663732 | + | 0.747971i | \(0.731028\pi\) | |||||||
\(948\) | −14492.9 | −0.496526 | ||||||||
\(949\) | 2118.48 | 0.0724646 | ||||||||
\(950\) | −8965.56 | −0.306191 | ||||||||
\(951\) | 15467.3 | 0.527406 | ||||||||
\(952\) | 108939. | 3.70875 | ||||||||
\(953\) | −41792.1 | −1.42054 | −0.710272 | − | 0.703927i | \(-0.751428\pi\) | ||||
−0.710272 | + | 0.703927i | \(0.751428\pi\) | |||||||
\(954\) | 970.184 | 0.0329254 | ||||||||
\(955\) | −11581.0 | −0.392411 | ||||||||
\(956\) | −65298.1 | −2.20909 | ||||||||
\(957\) | 25307.3 | 0.854827 | ||||||||
\(958\) | 89220.4 | 3.00896 | ||||||||
\(959\) | 38213.0 | 1.28672 | ||||||||
\(960\) | −1551.95 | −0.0521759 | ||||||||
\(961\) | 22292.7 | 0.748304 | ||||||||
\(962\) | 37097.3 | 1.24331 | ||||||||
\(963\) | 828.776 | 0.0277331 | ||||||||
\(964\) | −39298.2 | −1.31298 | ||||||||
\(965\) | −679.283 | −0.0226600 | ||||||||
\(966\) | −289.378 | −0.00963827 | ||||||||
\(967\) | 7635.19 | 0.253910 | 0.126955 | − | 0.991908i | \(-0.459480\pi\) | ||||
0.126955 | + | 0.991908i | \(0.459480\pi\) | |||||||
\(968\) | −173465. | −5.75968 | ||||||||
\(969\) | −7224.20 | −0.239499 | ||||||||
\(970\) | −3311.12 | −0.109602 | ||||||||
\(971\) | 14594.5 | 0.482349 | 0.241175 | − | 0.970482i | \(-0.422467\pi\) | ||||
0.241175 | + | 0.970482i | \(0.422467\pi\) | |||||||
\(972\) | −3600.29 | −0.118806 | ||||||||
\(973\) | 29236.3 | 0.963280 | ||||||||
\(974\) | −50142.7 | −1.64957 | ||||||||
\(975\) | −15809.0 | −0.519274 | ||||||||
\(976\) | −84438.8 | −2.76928 | ||||||||
\(977\) | 21327.7 | 0.698398 | 0.349199 | − | 0.937049i | \(-0.386454\pi\) | ||||
0.349199 | + | 0.937049i | \(0.386454\pi\) | |||||||
\(978\) | −38485.8 | −1.25832 | ||||||||
\(979\) | −64417.8 | −2.10296 | ||||||||
\(980\) | 17625.8 | 0.574525 | ||||||||
\(981\) | 289.523 | 0.00942278 | ||||||||
\(982\) | 17352.6 | 0.563893 | ||||||||
\(983\) | −14871.0 | −0.482515 | −0.241258 | − | 0.970461i | \(-0.577560\pi\) | ||||
−0.241258 | + | 0.970461i | \(0.577560\pi\) | |||||||
\(984\) | 98458.0 | 3.18976 | ||||||||
\(985\) | −2736.95 | −0.0885346 | ||||||||
\(986\) | −30742.8 | −0.992952 | ||||||||
\(987\) | 7849.93 | 0.253157 | ||||||||
\(988\) | −7322.94 | −0.235803 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −875.897 | −0.0281190 | ||||||||
\(991\) | 21864.6 | 0.700860 | 0.350430 | − | 0.936589i | \(-0.386036\pi\) | ||||
0.350430 | + | 0.936589i | \(0.386036\pi\) | |||||||
\(992\) | 34964.6 | 1.11908 | ||||||||
\(993\) | 31888.7 | 1.01909 | ||||||||
\(994\) | 51100.5 | 1.63059 | ||||||||
\(995\) | −10338.6 | −0.329403 | ||||||||
\(996\) | 8602.94 | 0.273689 | ||||||||
\(997\) | 2007.96 | 0.0637840 | 0.0318920 | − | 0.999491i | \(-0.489847\pi\) | ||||
0.0318920 | + | 0.999491i | \(0.489847\pi\) | |||||||
\(998\) | 79268.6 | 2.51423 | ||||||||
\(999\) | 38200.4 | 1.20982 |
(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.g.1.2 | 30 | ||
43.32 | odd | 14 | 43.4.e.a.35.1 | yes | 60 | ||
43.39 | odd | 14 | 43.4.e.a.16.1 | ✓ | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.29 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.16.1 | ✓ | 60 | 43.39 | odd | 14 | ||
43.4.e.a.35.1 | yes | 60 | 43.32 | odd | 14 | ||
1849.4.a.g.1.2 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.29 | 30 | 43.42 | odd | 2 |