Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,4,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(85.0217523183\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.59373 | −1.62413 | −0.812065 | − | 0.583567i | \(-0.801657\pi\) | ||||
−0.812065 | + | 0.583567i | \(0.801657\pi\) | |||||||
\(3\) | 3.62650 | 0.697921 | 0.348960 | − | 0.937137i | \(-0.386535\pi\) | ||||
0.348960 | + | 0.937137i | \(0.386535\pi\) | |||||||
\(4\) | 13.1024 | 1.63780 | ||||||||
\(5\) | −18.1051 | −1.61937 | −0.809685 | − | 0.586865i | \(-0.800362\pi\) | ||||
−0.809685 | + | 0.586865i | \(0.800362\pi\) | |||||||
\(6\) | −16.6592 | −1.13351 | ||||||||
\(7\) | 32.3039 | 1.74425 | 0.872124 | − | 0.489284i | \(-0.162742\pi\) | ||||
0.872124 | + | 0.489284i | \(0.162742\pi\) | |||||||
\(8\) | −23.4390 | −1.03587 | ||||||||
\(9\) | −13.8485 | −0.512906 | ||||||||
\(10\) | 83.1700 | 2.63007 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 47.5158 | 1.14305 | ||||||||
\(13\) | −58.9805 | −1.25833 | −0.629163 | − | 0.777273i | \(-0.716602\pi\) | ||||
−0.629163 | + | 0.777273i | \(0.716602\pi\) | |||||||
\(14\) | −148.396 | −2.83289 | ||||||||
\(15\) | −65.6582 | −1.13019 | ||||||||
\(16\) | 2.85335 | 0.0445836 | ||||||||
\(17\) | 39.7546 | 0.567171 | 0.283585 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283585 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(18\) | 63.6162 | 0.833027 | ||||||||
\(19\) | 69.6703 | 0.841235 | 0.420617 | − | 0.907238i | \(-0.361813\pi\) | ||||
0.420617 | + | 0.907238i | \(0.361813\pi\) | |||||||
\(20\) | −237.220 | −2.65220 | ||||||||
\(21\) | 117.150 | 1.21735 | ||||||||
\(22\) | 50.5311 | 0.489694 | ||||||||
\(23\) | 96.1871 | 0.872017 | 0.436009 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436009 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(24\) | −85.0015 | −0.722953 | ||||||||
\(25\) | 202.795 | 1.62236 | ||||||||
\(26\) | 270.941 | 2.04369 | ||||||||
\(27\) | −148.137 | −1.05589 | ||||||||
\(28\) | 423.259 | 2.85673 | ||||||||
\(29\) | −195.274 | −1.25040 | −0.625199 | − | 0.780466i | \(-0.714982\pi\) | ||||
−0.625199 | + | 0.780466i | \(0.714982\pi\) | |||||||
\(30\) | 301.616 | 1.83558 | ||||||||
\(31\) | 138.590 | 0.802954 | 0.401477 | − | 0.915869i | \(-0.368497\pi\) | ||||
0.401477 | + | 0.915869i | \(0.368497\pi\) | |||||||
\(32\) | 174.404 | 0.963457 | ||||||||
\(33\) | −39.8915 | −0.210431 | ||||||||
\(34\) | −182.622 | −0.921159 | ||||||||
\(35\) | −584.866 | −2.82458 | ||||||||
\(36\) | −181.448 | −0.840037 | ||||||||
\(37\) | 274.090 | 1.21784 | 0.608921 | − | 0.793231i | \(-0.291603\pi\) | ||||
0.608921 | + | 0.793231i | \(0.291603\pi\) | |||||||
\(38\) | −320.047 | −1.36627 | ||||||||
\(39\) | −213.893 | −0.878212 | ||||||||
\(40\) | 424.365 | 1.67745 | ||||||||
\(41\) | −188.058 | −0.716337 | −0.358168 | − | 0.933657i | \(-0.616599\pi\) | ||||
−0.358168 | + | 0.933657i | \(0.616599\pi\) | |||||||
\(42\) | −538.157 | −1.97713 | ||||||||
\(43\) | −102.168 | −0.362335 | −0.181167 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181167 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(44\) | −144.126 | −0.493815 | ||||||||
\(45\) | 250.728 | 0.830585 | ||||||||
\(46\) | −441.858 | −1.41627 | ||||||||
\(47\) | −483.643 | −1.50099 | −0.750495 | − | 0.660876i | \(-0.770185\pi\) | ||||
−0.750495 | + | 0.660876i | \(0.770185\pi\) | |||||||
\(48\) | 10.3477 | 0.0311158 | ||||||||
\(49\) | 700.545 | 2.04240 | ||||||||
\(50\) | −931.584 | −2.63492 | ||||||||
\(51\) | 144.170 | 0.395840 | ||||||||
\(52\) | −772.785 | −2.06088 | ||||||||
\(53\) | 97.5033 | 0.252700 | 0.126350 | − | 0.991986i | \(-0.459674\pi\) | ||||
0.126350 | + | 0.991986i | \(0.459674\pi\) | |||||||
\(54\) | 680.502 | 1.71490 | ||||||||
\(55\) | 199.156 | 0.488258 | ||||||||
\(56\) | −757.171 | −1.80681 | ||||||||
\(57\) | 252.660 | 0.587115 | ||||||||
\(58\) | 897.038 | 2.03081 | ||||||||
\(59\) | 224.646 | 0.495702 | 0.247851 | − | 0.968798i | \(-0.420276\pi\) | ||||
0.247851 | + | 0.968798i | \(0.420276\pi\) | |||||||
\(60\) | −860.279 | −1.85102 | ||||||||
\(61\) | 365.823 | 0.767850 | 0.383925 | − | 0.923364i | \(-0.374572\pi\) | ||||
0.383925 | + | 0.923364i | \(0.374572\pi\) | |||||||
\(62\) | −636.647 | −1.30410 | ||||||||
\(63\) | −447.360 | −0.894637 | ||||||||
\(64\) | −823.994 | −1.60936 | ||||||||
\(65\) | 1067.85 | 2.03770 | ||||||||
\(66\) | 183.251 | 0.341767 | ||||||||
\(67\) | 984.876 | 1.79585 | 0.897923 | − | 0.440152i | \(-0.145075\pi\) | ||||
0.897923 | + | 0.440152i | \(0.145075\pi\) | |||||||
\(68\) | 520.880 | 0.928911 | ||||||||
\(69\) | 348.823 | 0.608599 | ||||||||
\(70\) | 2686.72 | 4.58749 | ||||||||
\(71\) | −679.941 | −1.13654 | −0.568269 | − | 0.822843i | \(-0.692387\pi\) | ||||
−0.568269 | + | 0.822843i | \(0.692387\pi\) | |||||||
\(72\) | 324.594 | 0.531303 | ||||||||
\(73\) | −1090.10 | −1.74775 | −0.873877 | − | 0.486147i | \(-0.838402\pi\) | ||||
−0.873877 | + | 0.486147i | \(0.838402\pi\) | |||||||
\(74\) | −1259.10 | −1.97793 | ||||||||
\(75\) | 735.435 | 1.13228 | ||||||||
\(76\) | 912.847 | 1.37777 | ||||||||
\(77\) | −355.343 | −0.525911 | ||||||||
\(78\) | 982.567 | 1.42633 | ||||||||
\(79\) | −581.652 | −0.828366 | −0.414183 | − | 0.910194i | \(-0.635933\pi\) | ||||
−0.414183 | + | 0.910194i | \(0.635933\pi\) | |||||||
\(80\) | −51.6601 | −0.0721972 | ||||||||
\(81\) | −163.311 | −0.224020 | ||||||||
\(82\) | 863.890 | 1.16342 | ||||||||
\(83\) | 671.747 | 0.888359 | 0.444180 | − | 0.895938i | \(-0.353495\pi\) | ||||
0.444180 | + | 0.895938i | \(0.353495\pi\) | |||||||
\(84\) | 1534.95 | 1.99377 | ||||||||
\(85\) | −719.760 | −0.918458 | ||||||||
\(86\) | 469.330 | 0.588479 | ||||||||
\(87\) | −708.163 | −0.872679 | ||||||||
\(88\) | 257.829 | 0.312325 | ||||||||
\(89\) | 554.120 | 0.659962 | 0.329981 | − | 0.943988i | \(-0.392958\pi\) | ||||
0.329981 | + | 0.943988i | \(0.392958\pi\) | |||||||
\(90\) | −1151.78 | −1.34898 | ||||||||
\(91\) | −1905.30 | −2.19483 | ||||||||
\(92\) | 1260.28 | 1.42819 | ||||||||
\(93\) | 502.598 | 0.560398 | ||||||||
\(94\) | 2221.72 | 2.43780 | ||||||||
\(95\) | −1261.39 | −1.36227 | ||||||||
\(96\) | 632.478 | 0.672417 | ||||||||
\(97\) | −374.347 | −0.391847 | −0.195924 | − | 0.980619i | \(-0.562771\pi\) | ||||
−0.195924 | + | 0.980619i | \(0.562771\pi\) | |||||||
\(98\) | −3218.11 | −3.31713 | ||||||||
\(99\) | 152.333 | 0.154647 | ||||||||
\(100\) | 2657.09 | 2.65709 | ||||||||
\(101\) | 434.204 | 0.427771 | 0.213886 | − | 0.976859i | \(-0.431388\pi\) | ||||
0.213886 | + | 0.976859i | \(0.431388\pi\) | |||||||
\(102\) | −662.279 | −0.642896 | ||||||||
\(103\) | −964.644 | −0.922808 | −0.461404 | − | 0.887190i | \(-0.652654\pi\) | ||||
−0.461404 | + | 0.887190i | \(0.652654\pi\) | |||||||
\(104\) | 1382.44 | 1.30346 | ||||||||
\(105\) | −2121.02 | −1.97134 | ||||||||
\(106\) | −447.904 | −0.410418 | ||||||||
\(107\) | 498.850 | 0.450707 | 0.225354 | − | 0.974277i | \(-0.427646\pi\) | ||||
0.225354 | + | 0.974277i | \(0.427646\pi\) | |||||||
\(108\) | −1940.95 | −1.72933 | ||||||||
\(109\) | 1748.15 | 1.53617 | 0.768086 | − | 0.640347i | \(-0.221209\pi\) | ||||
0.768086 | + | 0.640347i | \(0.221209\pi\) | |||||||
\(110\) | −914.870 | −0.792995 | ||||||||
\(111\) | 993.988 | 0.849957 | ||||||||
\(112\) | 92.1744 | 0.0777648 | ||||||||
\(113\) | −1952.14 | −1.62515 | −0.812573 | − | 0.582859i | \(-0.801934\pi\) | ||||
−0.812573 | + | 0.582859i | \(0.801934\pi\) | |||||||
\(114\) | −1160.65 | −0.953552 | ||||||||
\(115\) | −1741.48 | −1.41212 | ||||||||
\(116\) | −2558.56 | −2.04790 | ||||||||
\(117\) | 816.790 | 0.645404 | ||||||||
\(118\) | −1031.96 | −0.805084 | ||||||||
\(119\) | 1284.23 | 0.989287 | ||||||||
\(120\) | 1538.96 | 1.17073 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1680.49 | −1.24709 | ||||||||
\(123\) | −681.995 | −0.499946 | ||||||||
\(124\) | 1815.86 | 1.31508 | ||||||||
\(125\) | −1408.48 | −1.00782 | ||||||||
\(126\) | 2055.05 | 1.45301 | ||||||||
\(127\) | −395.076 | −0.276042 | −0.138021 | − | 0.990429i | \(-0.544074\pi\) | ||||
−0.138021 | + | 0.990429i | \(0.544074\pi\) | |||||||
\(128\) | 2389.97 | 1.65036 | ||||||||
\(129\) | −370.511 | −0.252881 | ||||||||
\(130\) | −4905.41 | −3.30948 | ||||||||
\(131\) | 131.000 | 0.0873704 | ||||||||
\(132\) | −522.674 | −0.344643 | ||||||||
\(133\) | 2250.63 | 1.46732 | ||||||||
\(134\) | −4524.26 | −2.91669 | ||||||||
\(135\) | 2682.04 | 1.70987 | ||||||||
\(136\) | −931.806 | −0.587513 | ||||||||
\(137\) | 2423.84 | 1.51155 | 0.755775 | − | 0.654832i | \(-0.227260\pi\) | ||||
0.755775 | + | 0.654832i | \(0.227260\pi\) | |||||||
\(138\) | −1602.40 | −0.988444 | ||||||||
\(139\) | −1904.44 | −1.16211 | −0.581053 | − | 0.813866i | \(-0.697359\pi\) | ||||
−0.581053 | + | 0.813866i | \(0.697359\pi\) | |||||||
\(140\) | −7663.14 | −4.62610 | ||||||||
\(141\) | −1753.93 | −1.04757 | ||||||||
\(142\) | 3123.47 | 1.84588 | ||||||||
\(143\) | 648.785 | 0.379400 | ||||||||
\(144\) | −39.5145 | −0.0228672 | ||||||||
\(145\) | 3535.46 | 2.02486 | ||||||||
\(146\) | 5007.61 | 2.83858 | ||||||||
\(147\) | 2540.53 | 1.42544 | ||||||||
\(148\) | 3591.23 | 1.99458 | ||||||||
\(149\) | −1.40500 | −0.000772496 0 | −0.000386248 | − | 1.00000i | \(-0.500123\pi\) | ||||
−0.000386248 | 1.00000i | \(0.500123\pi\) | ||||||||
\(150\) | −3378.39 | −1.83896 | ||||||||
\(151\) | 1440.02 | 0.776075 | 0.388038 | − | 0.921644i | \(-0.373153\pi\) | ||||
0.388038 | + | 0.921644i | \(0.373153\pi\) | |||||||
\(152\) | −1633.00 | −0.871407 | ||||||||
\(153\) | −550.540 | −0.290905 | ||||||||
\(154\) | 1632.35 | 0.854147 | ||||||||
\(155\) | −2509.19 | −1.30028 | ||||||||
\(156\) | −2802.51 | −1.43833 | ||||||||
\(157\) | 1358.03 | 0.690334 | 0.345167 | − | 0.938541i | \(-0.387822\pi\) | ||||
0.345167 | + | 0.938541i | \(0.387822\pi\) | |||||||
\(158\) | 2671.95 | 1.34537 | ||||||||
\(159\) | 353.596 | 0.176365 | ||||||||
\(160\) | −3157.61 | −1.56019 | ||||||||
\(161\) | 3107.22 | 1.52101 | ||||||||
\(162\) | 750.207 | 0.363838 | ||||||||
\(163\) | −386.881 | −0.185907 | −0.0929536 | − | 0.995670i | \(-0.529631\pi\) | ||||
−0.0929536 | + | 0.995670i | \(0.529631\pi\) | |||||||
\(164\) | −2464.01 | −1.17321 | ||||||||
\(165\) | 722.240 | 0.340766 | ||||||||
\(166\) | −3085.83 | −1.44281 | ||||||||
\(167\) | 416.683 | 0.193077 | 0.0965385 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965385 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(168\) | −2745.88 | −1.26101 | ||||||||
\(169\) | 1281.70 | 0.583386 | ||||||||
\(170\) | 3306.39 | 1.49170 | ||||||||
\(171\) | −964.828 | −0.431475 | ||||||||
\(172\) | −1338.64 | −0.593431 | ||||||||
\(173\) | 217.165 | 0.0954376 | 0.0477188 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477188 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(174\) | 3253.11 | 1.41734 | ||||||||
\(175\) | 6551.06 | 2.82979 | ||||||||
\(176\) | −31.3868 | −0.0134424 | ||||||||
\(177\) | 814.679 | 0.345961 | ||||||||
\(178\) | −2545.48 | −1.07186 | ||||||||
\(179\) | −1678.93 | −0.701058 | −0.350529 | − | 0.936552i | \(-0.613998\pi\) | ||||
−0.350529 | + | 0.936552i | \(0.613998\pi\) | |||||||
\(180\) | 3285.13 | 1.36033 | ||||||||
\(181\) | −2528.26 | −1.03825 | −0.519127 | − | 0.854697i | \(-0.673743\pi\) | ||||
−0.519127 | + | 0.854697i | \(0.673743\pi\) | |||||||
\(182\) | 8752.45 | 3.56470 | ||||||||
\(183\) | 1326.66 | 0.535898 | ||||||||
\(184\) | −2254.53 | −0.903293 | ||||||||
\(185\) | −4962.43 | −1.97213 | ||||||||
\(186\) | −2308.80 | −0.910159 | ||||||||
\(187\) | −437.300 | −0.171008 | ||||||||
\(188\) | −6336.87 | −2.45832 | ||||||||
\(189\) | −4785.41 | −1.84173 | ||||||||
\(190\) | 5794.48 | 2.21250 | ||||||||
\(191\) | −810.342 | −0.306986 | −0.153493 | − | 0.988150i | \(-0.549052\pi\) | ||||
−0.153493 | + | 0.988150i | \(0.549052\pi\) | |||||||
\(192\) | −2988.22 | −1.12321 | ||||||||
\(193\) | −2801.65 | −1.04491 | −0.522454 | − | 0.852667i | \(-0.674984\pi\) | ||||
−0.522454 | + | 0.852667i | \(0.674984\pi\) | |||||||
\(194\) | 1719.65 | 0.636411 | ||||||||
\(195\) | 3872.55 | 1.42215 | ||||||||
\(196\) | 9178.80 | 3.34504 | ||||||||
\(197\) | −4516.03 | −1.63327 | −0.816634 | − | 0.577156i | \(-0.804163\pi\) | ||||
−0.816634 | + | 0.577156i | \(0.804163\pi\) | |||||||
\(198\) | −699.778 | −0.251167 | ||||||||
\(199\) | 5388.06 | 1.91934 | 0.959672 | − | 0.281120i | \(-0.0907060\pi\) | ||||
0.959672 | + | 0.281120i | \(0.0907060\pi\) | |||||||
\(200\) | −4753.30 | −1.68054 | ||||||||
\(201\) | 3571.66 | 1.25336 | ||||||||
\(202\) | −1994.62 | −0.694756 | ||||||||
\(203\) | −6308.13 | −2.18100 | ||||||||
\(204\) | 1888.97 | 0.648306 | ||||||||
\(205\) | 3404.82 | 1.16001 | ||||||||
\(206\) | 4431.32 | 1.49876 | ||||||||
\(207\) | −1332.04 | −0.447263 | ||||||||
\(208\) | −168.292 | −0.0561007 | ||||||||
\(209\) | −766.373 | −0.253642 | ||||||||
\(210\) | 9743.39 | 3.20170 | ||||||||
\(211\) | 3916.21 | 1.27774 | 0.638870 | − | 0.769314i | \(-0.279402\pi\) | ||||
0.638870 | + | 0.769314i | \(0.279402\pi\) | |||||||
\(212\) | 1277.53 | 0.413872 | ||||||||
\(213\) | −2465.81 | −0.793213 | ||||||||
\(214\) | −2291.58 | −0.732007 | ||||||||
\(215\) | 1849.75 | 0.586754 | ||||||||
\(216\) | 3472.18 | 1.09376 | ||||||||
\(217\) | 4477.01 | 1.40055 | ||||||||
\(218\) | −8030.55 | −2.49494 | ||||||||
\(219\) | −3953.24 | −1.21979 | ||||||||
\(220\) | 2609.42 | 0.799668 | ||||||||
\(221\) | −2344.74 | −0.713686 | ||||||||
\(222\) | −4566.12 | −1.38044 | ||||||||
\(223\) | −5735.99 | −1.72247 | −0.861233 | − | 0.508210i | \(-0.830307\pi\) | ||||
−0.861233 | + | 0.508210i | \(0.830307\pi\) | |||||||
\(224\) | 5633.95 | 1.68051 | ||||||||
\(225\) | −2808.40 | −0.832117 | ||||||||
\(226\) | 8967.60 | 2.63945 | ||||||||
\(227\) | 368.988 | 0.107888 | 0.0539441 | − | 0.998544i | \(-0.482821\pi\) | ||||
0.0539441 | + | 0.998544i | \(0.482821\pi\) | |||||||
\(228\) | 3310.44 | 0.961576 | ||||||||
\(229\) | 529.455 | 0.152783 | 0.0763916 | − | 0.997078i | \(-0.475660\pi\) | ||||
0.0763916 | + | 0.997078i | \(0.475660\pi\) | |||||||
\(230\) | 7999.88 | 2.29346 | ||||||||
\(231\) | −1288.65 | −0.367044 | ||||||||
\(232\) | 4577.03 | 1.29524 | ||||||||
\(233\) | −4632.58 | −1.30254 | −0.651268 | − | 0.758848i | \(-0.725762\pi\) | ||||
−0.651268 | + | 0.758848i | \(0.725762\pi\) | |||||||
\(234\) | −3752.11 | −1.04822 | ||||||||
\(235\) | 8756.40 | 2.43066 | ||||||||
\(236\) | 2943.40 | 0.811859 | ||||||||
\(237\) | −2109.36 | −0.578134 | ||||||||
\(238\) | −5899.41 | −1.60673 | ||||||||
\(239\) | −536.451 | −0.145189 | −0.0725944 | − | 0.997362i | \(-0.523128\pi\) | ||||
−0.0725944 | + | 0.997362i | \(0.523128\pi\) | |||||||
\(240\) | −187.346 | −0.0503880 | ||||||||
\(241\) | −5934.44 | −1.58619 | −0.793093 | − | 0.609100i | \(-0.791531\pi\) | ||||
−0.793093 | + | 0.609100i | \(0.791531\pi\) | |||||||
\(242\) | −555.842 | −0.147648 | ||||||||
\(243\) | 3407.45 | 0.899540 | ||||||||
\(244\) | 4793.15 | 1.25758 | ||||||||
\(245\) | −12683.4 | −3.30741 | ||||||||
\(246\) | 3132.90 | 0.811978 | ||||||||
\(247\) | −4109.19 | −1.05855 | ||||||||
\(248\) | −3248.42 | −0.831753 | ||||||||
\(249\) | 2436.09 | 0.620005 | ||||||||
\(250\) | 6470.17 | 1.63684 | ||||||||
\(251\) | −1674.40 | −0.421064 | −0.210532 | − | 0.977587i | \(-0.567520\pi\) | ||||
−0.210532 | + | 0.977587i | \(0.567520\pi\) | |||||||
\(252\) | −5861.49 | −1.46523 | ||||||||
\(253\) | −1058.06 | −0.262923 | ||||||||
\(254\) | 1814.87 | 0.448328 | ||||||||
\(255\) | −2610.21 | −0.641011 | ||||||||
\(256\) | −4386.94 | −1.07103 | ||||||||
\(257\) | 674.774 | 0.163779 | 0.0818896 | − | 0.996641i | \(-0.473905\pi\) | ||||
0.0818896 | + | 0.996641i | \(0.473905\pi\) | |||||||
\(258\) | 1702.03 | 0.410712 | ||||||||
\(259\) | 8854.19 | 2.12422 | ||||||||
\(260\) | 13991.3 | 3.33733 | ||||||||
\(261\) | 2704.25 | 0.641337 | ||||||||
\(262\) | −601.779 | −0.141901 | ||||||||
\(263\) | −6969.05 | −1.63395 | −0.816977 | − | 0.576670i | \(-0.804352\pi\) | ||||
−0.816977 | + | 0.576670i | \(0.804352\pi\) | |||||||
\(264\) | 935.017 | 0.217978 | ||||||||
\(265\) | −1765.31 | −0.409215 | ||||||||
\(266\) | −10338.8 | −2.38312 | ||||||||
\(267\) | 2009.52 | 0.460601 | ||||||||
\(268\) | 12904.2 | 2.94123 | ||||||||
\(269\) | −4193.78 | −0.950554 | −0.475277 | − | 0.879836i | \(-0.657652\pi\) | ||||
−0.475277 | + | 0.879836i | \(0.657652\pi\) | |||||||
\(270\) | −12320.6 | −2.77706 | ||||||||
\(271\) | 1107.09 | 0.248158 | 0.124079 | − | 0.992272i | \(-0.460402\pi\) | ||||
0.124079 | + | 0.992272i | \(0.460402\pi\) | |||||||
\(272\) | 113.434 | 0.0252865 | ||||||||
\(273\) | −6909.58 | −1.53182 | ||||||||
\(274\) | −11134.5 | −2.45495 | ||||||||
\(275\) | −2230.74 | −0.489159 | ||||||||
\(276\) | 4570.41 | 0.996762 | ||||||||
\(277\) | −5691.73 | −1.23460 | −0.617298 | − | 0.786729i | \(-0.711773\pi\) | ||||
−0.617298 | + | 0.786729i | \(0.711773\pi\) | |||||||
\(278\) | 8748.50 | 1.88741 | ||||||||
\(279\) | −1919.27 | −0.411840 | ||||||||
\(280\) | 13708.7 | 2.92589 | ||||||||
\(281\) | 8965.19 | 1.90327 | 0.951634 | − | 0.307234i | \(-0.0994034\pi\) | ||||
0.951634 | + | 0.307234i | \(0.0994034\pi\) | |||||||
\(282\) | 8057.09 | 1.70139 | ||||||||
\(283\) | −2207.05 | −0.463588 | −0.231794 | − | 0.972765i | \(-0.574460\pi\) | ||||
−0.231794 | + | 0.972765i | \(0.574460\pi\) | |||||||
\(284\) | −8908.84 | −1.86142 | ||||||||
\(285\) | −4574.43 | −0.950757 | ||||||||
\(286\) | −2980.35 | −0.616194 | ||||||||
\(287\) | −6075.03 | −1.24947 | ||||||||
\(288\) | −2415.23 | −0.494163 | ||||||||
\(289\) | −3332.57 | −0.678318 | ||||||||
\(290\) | −16241.0 | −3.28863 | ||||||||
\(291\) | −1357.57 | −0.273479 | ||||||||
\(292\) | −14282.9 | −2.86247 | ||||||||
\(293\) | −4345.90 | −0.866519 | −0.433260 | − | 0.901269i | \(-0.642637\pi\) | ||||
−0.433260 | + | 0.901269i | \(0.642637\pi\) | |||||||
\(294\) | −11670.5 | −2.31509 | ||||||||
\(295\) | −4067.24 | −0.802724 | ||||||||
\(296\) | −6424.39 | −1.26152 | ||||||||
\(297\) | 1629.51 | 0.318363 | ||||||||
\(298\) | 6.45418 | 0.00125463 | ||||||||
\(299\) | −5673.16 | −1.09728 | ||||||||
\(300\) | 9635.95 | 1.85444 | ||||||||
\(301\) | −3300.41 | −0.632002 | ||||||||
\(302\) | −6615.08 | −1.26045 | ||||||||
\(303\) | 1574.64 | 0.298550 | ||||||||
\(304\) | 198.794 | 0.0375052 | ||||||||
\(305\) | −6623.26 | −1.24343 | ||||||||
\(306\) | 2529.03 | 0.472468 | ||||||||
\(307\) | 2845.14 | 0.528927 | 0.264464 | − | 0.964396i | \(-0.414805\pi\) | ||||
0.264464 | + | 0.964396i | \(0.414805\pi\) | |||||||
\(308\) | −4655.84 | −0.861336 | ||||||||
\(309\) | −3498.29 | −0.644047 | ||||||||
\(310\) | 11526.6 | 2.11182 | ||||||||
\(311\) | 902.017 | 0.164465 | 0.0822327 | − | 0.996613i | \(-0.473795\pi\) | ||||
0.0822327 | + | 0.996613i | \(0.473795\pi\) | |||||||
\(312\) | 5013.43 | 0.909710 | ||||||||
\(313\) | −7517.88 | −1.35762 | −0.678811 | − | 0.734313i | \(-0.737505\pi\) | ||||
−0.678811 | + | 0.734313i | \(0.737505\pi\) | |||||||
\(314\) | −6238.42 | −1.12119 | ||||||||
\(315\) | 8099.50 | 1.44875 | ||||||||
\(316\) | −7621.02 | −1.35670 | ||||||||
\(317\) | −9025.87 | −1.59919 | −0.799595 | − | 0.600540i | \(-0.794952\pi\) | ||||
−0.799595 | + | 0.600540i | \(0.794952\pi\) | |||||||
\(318\) | −1624.33 | −0.286439 | ||||||||
\(319\) | 2148.02 | 0.377009 | ||||||||
\(320\) | 14918.5 | 2.60615 | ||||||||
\(321\) | 1809.08 | 0.314558 | ||||||||
\(322\) | −14273.7 | −2.47033 | ||||||||
\(323\) | 2769.71 | 0.477124 | ||||||||
\(324\) | −2139.76 | −0.366900 | ||||||||
\(325\) | −11960.9 | −2.04145 | ||||||||
\(326\) | 1777.23 | 0.301937 | ||||||||
\(327\) | 6339.68 | 1.07213 | ||||||||
\(328\) | 4407.90 | 0.742029 | ||||||||
\(329\) | −15623.6 | −2.61810 | ||||||||
\(330\) | −3317.78 | −0.553447 | ||||||||
\(331\) | −9045.70 | −1.50210 | −0.751052 | − | 0.660243i | \(-0.770453\pi\) | ||||
−0.751052 | + | 0.660243i | \(0.770453\pi\) | |||||||
\(332\) | 8801.49 | 1.45495 | ||||||||
\(333\) | −3795.73 | −0.624639 | ||||||||
\(334\) | −1914.13 | −0.313582 | ||||||||
\(335\) | −17831.3 | −2.90814 | ||||||||
\(336\) | 334.271 | 0.0542737 | ||||||||
\(337\) | 6694.79 | 1.08216 | 0.541081 | − | 0.840971i | \(-0.318015\pi\) | ||||
0.541081 | + | 0.840971i | \(0.318015\pi\) | |||||||
\(338\) | −5887.78 | −0.947494 | ||||||||
\(339\) | −7079.43 | −1.13422 | ||||||||
\(340\) | −9430.57 | −1.50425 | ||||||||
\(341\) | −1524.49 | −0.242100 | ||||||||
\(342\) | 4432.16 | 0.700771 | ||||||||
\(343\) | 11550.1 | 1.81821 | ||||||||
\(344\) | 2394.70 | 0.375331 | ||||||||
\(345\) | −6315.47 | −0.985546 | ||||||||
\(346\) | −997.596 | −0.155003 | ||||||||
\(347\) | −9541.54 | −1.47613 | −0.738065 | − | 0.674730i | \(-0.764260\pi\) | ||||
−0.738065 | + | 0.674730i | \(0.764260\pi\) | |||||||
\(348\) | −9278.62 | −1.42927 | ||||||||
\(349\) | 1839.41 | 0.282125 | 0.141062 | − | 0.990001i | \(-0.454948\pi\) | ||||
0.141062 | + | 0.990001i | \(0.454948\pi\) | |||||||
\(350\) | −30093.8 | −4.59595 | ||||||||
\(351\) | 8737.20 | 1.32865 | ||||||||
\(352\) | −1918.45 | −0.290493 | ||||||||
\(353\) | 7673.58 | 1.15701 | 0.578503 | − | 0.815680i | \(-0.303637\pi\) | ||||
0.578503 | + | 0.815680i | \(0.303637\pi\) | |||||||
\(354\) | −3742.42 | −0.561885 | ||||||||
\(355\) | 12310.4 | 1.84047 | ||||||||
\(356\) | 7260.30 | 1.08088 | ||||||||
\(357\) | 4657.26 | 0.690444 | ||||||||
\(358\) | 7712.58 | 1.13861 | ||||||||
\(359\) | −7420.53 | −1.09092 | −0.545461 | − | 0.838136i | \(-0.683645\pi\) | ||||
−0.545461 | + | 0.838136i | \(0.683645\pi\) | |||||||
\(360\) | −5876.81 | −0.860375 | ||||||||
\(361\) | −2005.05 | −0.292324 | ||||||||
\(362\) | 11614.2 | 1.68626 | ||||||||
\(363\) | 438.807 | 0.0634473 | ||||||||
\(364\) | −24964.0 | −3.59470 | ||||||||
\(365\) | 19736.3 | 2.83026 | ||||||||
\(366\) | −6094.31 | −0.870368 | ||||||||
\(367\) | 7846.49 | 1.11603 | 0.558016 | − | 0.829830i | \(-0.311563\pi\) | ||||
0.558016 | + | 0.829830i | \(0.311563\pi\) | |||||||
\(368\) | 274.455 | 0.0388776 | ||||||||
\(369\) | 2604.32 | 0.367414 | ||||||||
\(370\) | 22796.1 | 3.20300 | ||||||||
\(371\) | 3149.74 | 0.440772 | ||||||||
\(372\) | 6585.24 | 0.917819 | ||||||||
\(373\) | 10319.3 | 1.43248 | 0.716238 | − | 0.697856i | \(-0.245863\pi\) | ||||
0.716238 | + | 0.697856i | \(0.245863\pi\) | |||||||
\(374\) | 2008.84 | 0.277740 | ||||||||
\(375\) | −5107.85 | −0.703382 | ||||||||
\(376\) | 11336.1 | 1.55482 | ||||||||
\(377\) | 11517.4 | 1.57341 | ||||||||
\(378\) | 21982.9 | 2.99121 | ||||||||
\(379\) | −811.104 | −0.109930 | −0.0549652 | − | 0.998488i | \(-0.517505\pi\) | ||||
−0.0549652 | + | 0.998488i | \(0.517505\pi\) | |||||||
\(380\) | −16527.2 | −2.23112 | ||||||||
\(381\) | −1432.74 | −0.192655 | ||||||||
\(382\) | 3722.49 | 0.498585 | ||||||||
\(383\) | −6367.04 | −0.849453 | −0.424726 | − | 0.905322i | \(-0.639630\pi\) | ||||
−0.424726 | + | 0.905322i | \(0.639630\pi\) | |||||||
\(384\) | 8667.24 | 1.15182 | ||||||||
\(385\) | 6433.53 | 0.851644 | ||||||||
\(386\) | 12870.0 | 1.69707 | ||||||||
\(387\) | 1414.86 | 0.185844 | ||||||||
\(388\) | −4904.84 | −0.641767 | ||||||||
\(389\) | −9823.30 | −1.28036 | −0.640182 | − | 0.768224i | \(-0.721141\pi\) | ||||
−0.640182 | + | 0.768224i | \(0.721141\pi\) | |||||||
\(390\) | −17789.5 | −2.30976 | ||||||||
\(391\) | 3823.88 | 0.494582 | ||||||||
\(392\) | −16420.0 | −2.11566 | ||||||||
\(393\) | 475.072 | 0.0609776 | ||||||||
\(394\) | 20745.4 | 2.65264 | ||||||||
\(395\) | 10530.9 | 1.34143 | ||||||||
\(396\) | 1995.93 | 0.253281 | ||||||||
\(397\) | −11297.4 | −1.42821 | −0.714105 | − | 0.700039i | \(-0.753166\pi\) | ||||
−0.714105 | + | 0.700039i | \(0.753166\pi\) | |||||||
\(398\) | −24751.3 | −3.11727 | ||||||||
\(399\) | 8161.90 | 1.02408 | ||||||||
\(400\) | 578.643 | 0.0723304 | ||||||||
\(401\) | −11002.2 | −1.37013 | −0.685065 | − | 0.728482i | \(-0.740226\pi\) | ||||
−0.685065 | + | 0.728482i | \(0.740226\pi\) | |||||||
\(402\) | −16407.2 | −2.03562 | ||||||||
\(403\) | −8174.13 | −1.01038 | ||||||||
\(404\) | 5689.10 | 0.700603 | ||||||||
\(405\) | 2956.76 | 0.362772 | ||||||||
\(406\) | 28977.9 | 3.54223 | ||||||||
\(407\) | −3014.99 | −0.367193 | ||||||||
\(408\) | −3379.20 | −0.410037 | ||||||||
\(409\) | −3883.19 | −0.469466 | −0.234733 | − | 0.972060i | \(-0.575422\pi\) | ||||
−0.234733 | + | 0.972060i | \(0.575422\pi\) | |||||||
\(410\) | −15640.8 | −1.88401 | ||||||||
\(411\) | 8790.05 | 1.05494 | ||||||||
\(412\) | −12639.1 | −1.51137 | ||||||||
\(413\) | 7256.95 | 0.864627 | ||||||||
\(414\) | 6119.06 | 0.726413 | ||||||||
\(415\) | −12162.0 | −1.43858 | ||||||||
\(416\) | −10286.5 | −1.21234 | ||||||||
\(417\) | −6906.47 | −0.811058 | ||||||||
\(418\) | 3520.51 | 0.411947 | ||||||||
\(419\) | 4884.16 | 0.569467 | 0.284734 | − | 0.958607i | \(-0.408095\pi\) | ||||
0.284734 | + | 0.958607i | \(0.408095\pi\) | |||||||
\(420\) | −27790.4 | −3.22865 | ||||||||
\(421\) | −3879.96 | −0.449163 | −0.224581 | − | 0.974455i | \(-0.572101\pi\) | ||||
−0.224581 | + | 0.974455i | \(0.572101\pi\) | |||||||
\(422\) | −17990.0 | −2.07522 | ||||||||
\(423\) | 6697.71 | 0.769867 | ||||||||
\(424\) | −2285.38 | −0.261764 | ||||||||
\(425\) | 8062.01 | 0.920153 | ||||||||
\(426\) | 11327.3 | 1.28828 | ||||||||
\(427\) | 11817.5 | 1.33932 | ||||||||
\(428\) | 6536.12 | 0.738167 | ||||||||
\(429\) | 2352.82 | 0.264791 | ||||||||
\(430\) | −8497.27 | −0.952965 | ||||||||
\(431\) | 8673.91 | 0.969391 | 0.484695 | − | 0.874683i | \(-0.338930\pi\) | ||||
0.484695 | + | 0.874683i | \(0.338930\pi\) | |||||||
\(432\) | −422.687 | −0.0470753 | ||||||||
\(433\) | −12252.4 | −1.35985 | −0.679924 | − | 0.733283i | \(-0.737987\pi\) | ||||
−0.679924 | + | 0.733283i | \(0.737987\pi\) | |||||||
\(434\) | −20566.2 | −2.27468 | ||||||||
\(435\) | 12821.4 | 1.41319 | ||||||||
\(436\) | 22905.0 | 2.51594 | ||||||||
\(437\) | 6701.38 | 0.733571 | ||||||||
\(438\) | 18160.1 | 1.98110 | ||||||||
\(439\) | −14320.4 | −1.55690 | −0.778448 | − | 0.627709i | \(-0.783993\pi\) | ||||
−0.778448 | + | 0.627709i | \(0.783993\pi\) | |||||||
\(440\) | −4668.01 | −0.505770 | ||||||||
\(441\) | −9701.47 | −1.04756 | ||||||||
\(442\) | 10771.1 | 1.15912 | ||||||||
\(443\) | −2874.85 | −0.308325 | −0.154163 | − | 0.988045i | \(-0.549268\pi\) | ||||
−0.154163 | + | 0.988045i | \(0.549268\pi\) | |||||||
\(444\) | 13023.6 | 1.39206 | ||||||||
\(445\) | −10032.4 | −1.06872 | ||||||||
\(446\) | 26349.6 | 2.79751 | ||||||||
\(447\) | −5.09523 | −0.000539141 0 | ||||||||
\(448\) | −26618.2 | −2.80713 | ||||||||
\(449\) | −726.986 | −0.0764112 | −0.0382056 | − | 0.999270i | \(-0.512164\pi\) | ||||
−0.0382056 | + | 0.999270i | \(0.512164\pi\) | |||||||
\(450\) | 12901.0 | 1.35147 | ||||||||
\(451\) | 2068.64 | 0.215984 | ||||||||
\(452\) | −25577.6 | −2.66166 | ||||||||
\(453\) | 5222.25 | 0.541639 | ||||||||
\(454\) | −1695.03 | −0.175224 | ||||||||
\(455\) | 34495.7 | 3.55425 | ||||||||
\(456\) | −5922.08 | −0.608173 | ||||||||
\(457\) | −473.509 | −0.0484678 | −0.0242339 | − | 0.999706i | \(-0.507715\pi\) | ||||
−0.0242339 | + | 0.999706i | \(0.507715\pi\) | |||||||
\(458\) | −2432.17 | −0.248140 | ||||||||
\(459\) | −5889.13 | −0.598869 | ||||||||
\(460\) | −22817.5 | −2.31276 | ||||||||
\(461\) | −11551.7 | −1.16706 | −0.583531 | − | 0.812091i | \(-0.698329\pi\) | ||||
−0.583531 | + | 0.812091i | \(0.698329\pi\) | |||||||
\(462\) | 5919.73 | 0.596127 | ||||||||
\(463\) | −15168.1 | −1.52251 | −0.761255 | − | 0.648453i | \(-0.775416\pi\) | ||||
−0.761255 | + | 0.648453i | \(0.775416\pi\) | |||||||
\(464\) | −557.186 | −0.0557472 | ||||||||
\(465\) | −9099.59 | −0.907491 | ||||||||
\(466\) | 21280.9 | 2.11549 | ||||||||
\(467\) | 144.213 | 0.0142899 | 0.00714493 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714493 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(468\) | 10701.9 | 1.05704 | ||||||||
\(469\) | 31815.4 | 3.13240 | ||||||||
\(470\) | −40224.5 | −3.94770 | ||||||||
\(471\) | 4924.90 | 0.481799 | ||||||||
\(472\) | −5265.47 | −0.513481 | ||||||||
\(473\) | 1123.84 | 0.109248 | ||||||||
\(474\) | 9689.84 | 0.938965 | ||||||||
\(475\) | 14128.8 | 1.36478 | ||||||||
\(476\) | 16826.5 | 1.62025 | ||||||||
\(477\) | −1350.27 | −0.129612 | ||||||||
\(478\) | 2464.31 | 0.235806 | ||||||||
\(479\) | 10302.9 | 0.982778 | 0.491389 | − | 0.870940i | \(-0.336489\pi\) | ||||
0.491389 | + | 0.870940i | \(0.336489\pi\) | |||||||
\(480\) | −11451.1 | −1.08889 | ||||||||
\(481\) | −16166.0 | −1.53244 | ||||||||
\(482\) | 27261.2 | 2.57617 | ||||||||
\(483\) | 11268.3 | 1.06155 | ||||||||
\(484\) | 1585.39 | 0.148891 | ||||||||
\(485\) | 6777.59 | 0.634546 | ||||||||
\(486\) | −15652.9 | −1.46097 | ||||||||
\(487\) | −20568.3 | −1.91383 | −0.956917 | − | 0.290361i | \(-0.906225\pi\) | ||||
−0.956917 | + | 0.290361i | \(0.906225\pi\) | |||||||
\(488\) | −8574.51 | −0.795389 | ||||||||
\(489\) | −1403.03 | −0.129748 | ||||||||
\(490\) | 58264.3 | 5.37166 | ||||||||
\(491\) | −9273.92 | −0.852395 | −0.426198 | − | 0.904630i | \(-0.640147\pi\) | ||||
−0.426198 | + | 0.904630i | \(0.640147\pi\) | |||||||
\(492\) | −8935.75 | −0.818811 | ||||||||
\(493\) | −7763.05 | −0.709189 | ||||||||
\(494\) | 18876.5 | 1.71922 | ||||||||
\(495\) | −2758.01 | −0.250431 | ||||||||
\(496\) | 395.446 | 0.0357985 | ||||||||
\(497\) | −21964.8 | −1.98240 | ||||||||
\(498\) | −11190.8 | −1.00697 | ||||||||
\(499\) | −12293.6 | −1.10288 | −0.551438 | − | 0.834216i | \(-0.685921\pi\) | ||||
−0.551438 | + | 0.834216i | \(0.685921\pi\) | |||||||
\(500\) | −18454.4 | −1.65061 | ||||||||
\(501\) | 1511.10 | 0.134752 | ||||||||
\(502\) | 7691.73 | 0.683862 | ||||||||
\(503\) | −7386.50 | −0.654767 | −0.327383 | − | 0.944892i | \(-0.606167\pi\) | ||||
−0.327383 | + | 0.944892i | \(0.606167\pi\) | |||||||
\(504\) | 10485.7 | 0.926724 | ||||||||
\(505\) | −7861.30 | −0.692719 | ||||||||
\(506\) | 4860.43 | 0.427021 | ||||||||
\(507\) | 4648.08 | 0.407157 | ||||||||
\(508\) | −5176.44 | −0.452101 | ||||||||
\(509\) | 16470.8 | 1.43430 | 0.717148 | − | 0.696920i | \(-0.245447\pi\) | ||||
0.717148 | + | 0.696920i | \(0.245447\pi\) | |||||||
\(510\) | 11990.6 | 1.04109 | ||||||||
\(511\) | −35214.4 | −3.04852 | ||||||||
\(512\) | 1032.67 | 0.0891369 | ||||||||
\(513\) | −10320.8 | −0.888251 | ||||||||
\(514\) | −3099.73 | −0.265999 | ||||||||
\(515\) | 17465.0 | 1.49437 | ||||||||
\(516\) | −4854.57 | −0.414168 | ||||||||
\(517\) | 5320.07 | 0.452565 | ||||||||
\(518\) | −40673.8 | −3.45001 | ||||||||
\(519\) | 787.548 | 0.0666079 | ||||||||
\(520\) | −25029.3 | −2.11078 | ||||||||
\(521\) | −11500.3 | −0.967057 | −0.483529 | − | 0.875329i | \(-0.660645\pi\) | ||||
−0.483529 | + | 0.875329i | \(0.660645\pi\) | |||||||
\(522\) | −12422.6 | −1.04161 | ||||||||
\(523\) | 13606.4 | 1.13761 | 0.568803 | − | 0.822474i | \(-0.307407\pi\) | ||||
0.568803 | + | 0.822474i | \(0.307407\pi\) | |||||||
\(524\) | 1716.41 | 0.143095 | ||||||||
\(525\) | 23757.5 | 1.97497 | ||||||||
\(526\) | 32014.0 | 2.65376 | ||||||||
\(527\) | 5509.60 | 0.455412 | ||||||||
\(528\) | −113.824 | −0.00938177 | ||||||||
\(529\) | −2915.05 | −0.239586 | ||||||||
\(530\) | 8109.35 | 0.664618 | ||||||||
\(531\) | −3111.00 | −0.254249 | ||||||||
\(532\) | 29488.6 | 2.40318 | ||||||||
\(533\) | 11091.8 | 0.901385 | ||||||||
\(534\) | −9231.19 | −0.748076 | ||||||||
\(535\) | −9031.73 | −0.729861 | ||||||||
\(536\) | −23084.5 | −1.86026 | ||||||||
\(537\) | −6088.66 | −0.489283 | ||||||||
\(538\) | 19265.1 | 1.54382 | ||||||||
\(539\) | −7705.99 | −0.615808 | ||||||||
\(540\) | 35141.1 | 2.80043 | ||||||||
\(541\) | 5423.43 | 0.431001 | 0.215501 | − | 0.976504i | \(-0.430862\pi\) | ||||
0.215501 | + | 0.976504i | \(0.430862\pi\) | |||||||
\(542\) | −5085.68 | −0.403042 | ||||||||
\(543\) | −9168.74 | −0.724620 | ||||||||
\(544\) | 6933.37 | 0.546444 | ||||||||
\(545\) | −31650.5 | −2.48763 | ||||||||
\(546\) | 31740.8 | 2.48788 | ||||||||
\(547\) | 9026.78 | 0.705589 | 0.352795 | − | 0.935701i | \(-0.385231\pi\) | ||||
0.352795 | + | 0.935701i | \(0.385231\pi\) | |||||||
\(548\) | 31758.0 | 2.47561 | ||||||||
\(549\) | −5066.09 | −0.393835 | ||||||||
\(550\) | 10247.4 | 0.794457 | ||||||||
\(551\) | −13604.8 | −1.05188 | ||||||||
\(552\) | −8176.05 | −0.630427 | ||||||||
\(553\) | −18789.6 | −1.44488 | ||||||||
\(554\) | 26146.3 | 2.00514 | ||||||||
\(555\) | −17996.3 | −1.37639 | ||||||||
\(556\) | −24952.7 | −1.90329 | ||||||||
\(557\) | −15918.6 | −1.21094 | −0.605468 | − | 0.795869i | \(-0.707014\pi\) | ||||
−0.605468 | + | 0.795869i | \(0.707014\pi\) | |||||||
\(558\) | 8816.59 | 0.668882 | ||||||||
\(559\) | 6025.89 | 0.455936 | ||||||||
\(560\) | −1668.83 | −0.125930 | ||||||||
\(561\) | −1585.87 | −0.119350 | ||||||||
\(562\) | −41183.7 | −3.09115 | ||||||||
\(563\) | 19016.9 | 1.42356 | 0.711782 | − | 0.702401i | \(-0.247889\pi\) | ||||
0.711782 | + | 0.702401i | \(0.247889\pi\) | |||||||
\(564\) | −22980.7 | −1.71571 | ||||||||
\(565\) | 35343.6 | 2.63171 | ||||||||
\(566\) | 10138.6 | 0.752928 | ||||||||
\(567\) | −5275.59 | −0.390747 | ||||||||
\(568\) | 15937.1 | 1.17730 | ||||||||
\(569\) | −10773.7 | −0.793776 | −0.396888 | − | 0.917867i | \(-0.629910\pi\) | ||||
−0.396888 | + | 0.917867i | \(0.629910\pi\) | |||||||
\(570\) | 21013.7 | 1.54415 | ||||||||
\(571\) | 19005.4 | 1.39291 | 0.696453 | − | 0.717602i | \(-0.254761\pi\) | ||||
0.696453 | + | 0.717602i | \(0.254761\pi\) | |||||||
\(572\) | 8500.63 | 0.621380 | ||||||||
\(573\) | −2938.71 | −0.214252 | ||||||||
\(574\) | 27907.1 | 2.02930 | ||||||||
\(575\) | 19506.2 | 1.41472 | ||||||||
\(576\) | 11411.1 | 0.825452 | ||||||||
\(577\) | 12089.2 | 0.872235 | 0.436117 | − | 0.899890i | \(-0.356353\pi\) | ||||
0.436117 | + | 0.899890i | \(0.356353\pi\) | |||||||
\(578\) | 15309.0 | 1.10168 | ||||||||
\(579\) | −10160.2 | −0.729264 | ||||||||
\(580\) | 46323.0 | 3.31630 | ||||||||
\(581\) | 21700.1 | 1.54952 | ||||||||
\(582\) | 6236.32 | 0.444165 | ||||||||
\(583\) | −1072.54 | −0.0761920 | ||||||||
\(584\) | 25550.7 | 1.81044 | ||||||||
\(585\) | −14788.1 | −1.04515 | ||||||||
\(586\) | 19963.9 | 1.40734 | ||||||||
\(587\) | 5657.90 | 0.397830 | 0.198915 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198915 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(588\) | 33287.0 | 2.33458 | ||||||||
\(589\) | 9655.63 | 0.675473 | ||||||||
\(590\) | 18683.8 | 1.30373 | ||||||||
\(591\) | −16377.4 | −1.13989 | ||||||||
\(592\) | 782.074 | 0.0542957 | ||||||||
\(593\) | 1814.29 | 0.125639 | 0.0628195 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628195 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(594\) | −7485.53 | −0.517062 | ||||||||
\(595\) | −23251.1 | −1.60202 | ||||||||
\(596\) | −18.4088 | −0.00126519 | ||||||||
\(597\) | 19539.8 | 1.33955 | ||||||||
\(598\) | 26061.0 | 1.78213 | ||||||||
\(599\) | 10468.4 | 0.714070 | 0.357035 | − | 0.934091i | \(-0.383788\pi\) | ||||
0.357035 | + | 0.934091i | \(0.383788\pi\) | |||||||
\(600\) | −17237.8 | −1.17289 | ||||||||
\(601\) | −3466.70 | −0.235291 | −0.117645 | − | 0.993056i | \(-0.537535\pi\) | ||||
−0.117645 | + | 0.993056i | \(0.537535\pi\) | |||||||
\(602\) | 15161.2 | 1.02645 | ||||||||
\(603\) | −13639.0 | −0.921102 | ||||||||
\(604\) | 18867.7 | 1.27105 | ||||||||
\(605\) | −2190.72 | −0.147215 | ||||||||
\(606\) | −7233.48 | −0.484885 | ||||||||
\(607\) | 24467.1 | 1.63606 | 0.818032 | − | 0.575173i | \(-0.195065\pi\) | ||||
0.818032 | + | 0.575173i | \(0.195065\pi\) | |||||||
\(608\) | 12150.8 | 0.810494 | ||||||||
\(609\) | −22876.5 | −1.52217 | ||||||||
\(610\) | 30425.5 | 2.01949 | ||||||||
\(611\) | 28525.5 | 1.88874 | ||||||||
\(612\) | −7213.39 | −0.476444 | ||||||||
\(613\) | 4635.69 | 0.305439 | 0.152719 | − | 0.988270i | \(-0.451197\pi\) | ||||
0.152719 | + | 0.988270i | \(0.451197\pi\) | |||||||
\(614\) | −13069.8 | −0.859047 | ||||||||
\(615\) | 12347.6 | 0.809597 | ||||||||
\(616\) | 8328.88 | 0.544773 | ||||||||
\(617\) | −21768.8 | −1.42039 | −0.710194 | − | 0.704006i | \(-0.751393\pi\) | ||||
−0.710194 | + | 0.704006i | \(0.751393\pi\) | |||||||
\(618\) | 16070.2 | 1.04602 | ||||||||
\(619\) | −10131.7 | −0.657882 | −0.328941 | − | 0.944350i | \(-0.606692\pi\) | ||||
−0.328941 | + | 0.944350i | \(0.606692\pi\) | |||||||
\(620\) | −32876.4 | −2.12959 | ||||||||
\(621\) | −14248.9 | −0.920753 | ||||||||
\(622\) | −4143.63 | −0.267113 | ||||||||
\(623\) | 17900.3 | 1.15114 | ||||||||
\(624\) | −610.311 | −0.0391538 | ||||||||
\(625\) | 151.310 | 0.00968386 | ||||||||
\(626\) | 34535.2 | 2.20496 | ||||||||
\(627\) | −2779.26 | −0.177022 | ||||||||
\(628\) | 17793.4 | 1.13063 | ||||||||
\(629\) | 10896.3 | 0.690724 | ||||||||
\(630\) | −37206.9 | −2.35295 | ||||||||
\(631\) | 588.064 | 0.0371006 | 0.0185503 | − | 0.999828i | \(-0.494095\pi\) | ||||
0.0185503 | + | 0.999828i | \(0.494095\pi\) | |||||||
\(632\) | 13633.3 | 0.858076 | ||||||||
\(633\) | 14202.2 | 0.891762 | ||||||||
\(634\) | 41462.4 | 2.59729 | ||||||||
\(635\) | 7152.89 | 0.447014 | ||||||||
\(636\) | 4632.95 | 0.288850 | ||||||||
\(637\) | −41318.5 | −2.57001 | ||||||||
\(638\) | −9867.42 | −0.612312 | ||||||||
\(639\) | 9416.14 | 0.582937 | ||||||||
\(640\) | −43270.7 | −2.67254 | ||||||||
\(641\) | 5438.26 | 0.335099 | 0.167549 | − | 0.985864i | \(-0.446415\pi\) | ||||
0.167549 | + | 0.985864i | \(0.446415\pi\) | |||||||
\(642\) | −8310.44 | −0.510883 | ||||||||
\(643\) | 24143.0 | 1.48073 | 0.740364 | − | 0.672207i | \(-0.234653\pi\) | ||||
0.740364 | + | 0.672207i | \(0.234653\pi\) | |||||||
\(644\) | 40712.0 | 2.49111 | ||||||||
\(645\) | 6708.13 | 0.409508 | ||||||||
\(646\) | −12723.3 | −0.774911 | ||||||||
\(647\) | 22789.0 | 1.38474 | 0.692370 | − | 0.721543i | \(-0.256567\pi\) | ||||
0.692370 | + | 0.721543i | \(0.256567\pi\) | |||||||
\(648\) | 3827.84 | 0.232055 | ||||||||
\(649\) | −2471.10 | −0.149460 | ||||||||
\(650\) | 54945.3 | 3.31559 | ||||||||
\(651\) | 16235.9 | 0.977474 | ||||||||
\(652\) | −5069.06 | −0.304478 | ||||||||
\(653\) | 7687.12 | 0.460674 | 0.230337 | − | 0.973111i | \(-0.426017\pi\) | ||||
0.230337 | + | 0.973111i | \(0.426017\pi\) | |||||||
\(654\) | −29122.8 | −1.74127 | ||||||||
\(655\) | −2371.77 | −0.141485 | ||||||||
\(656\) | −536.596 | −0.0319368 | ||||||||
\(657\) | 15096.2 | 0.896435 | ||||||||
\(658\) | 71770.5 | 4.25213 | ||||||||
\(659\) | 1478.67 | 0.0874062 | 0.0437031 | − | 0.999045i | \(-0.486084\pi\) | ||||
0.0437031 | + | 0.999045i | \(0.486084\pi\) | |||||||
\(660\) | 9463.07 | 0.558105 | ||||||||
\(661\) | 253.566 | 0.0149207 | 0.00746035 | − | 0.999972i | \(-0.497625\pi\) | ||||
0.00746035 | + | 0.999972i | \(0.497625\pi\) | |||||||
\(662\) | 41553.5 | 2.43961 | ||||||||
\(663\) | −8503.22 | −0.498096 | ||||||||
\(664\) | −15745.1 | −0.920221 | ||||||||
\(665\) | −40747.8 | −2.37614 | ||||||||
\(666\) | 17436.6 | 1.01449 | ||||||||
\(667\) | −18782.9 | −1.09037 | ||||||||
\(668\) | 5459.53 | 0.316221 | ||||||||
\(669\) | −20801.6 | −1.20215 | ||||||||
\(670\) | 81912.1 | 4.72320 | ||||||||
\(671\) | −4024.05 | −0.231515 | ||||||||
\(672\) | 20431.5 | 1.17286 | ||||||||
\(673\) | 11530.3 | 0.660417 | 0.330209 | − | 0.943908i | \(-0.392881\pi\) | ||||
0.330209 | + | 0.943908i | \(0.392881\pi\) | |||||||
\(674\) | −30754.1 | −1.75757 | ||||||||
\(675\) | −30041.4 | −1.71303 | ||||||||
\(676\) | 16793.3 | 0.955468 | ||||||||
\(677\) | −1862.76 | −0.105748 | −0.0528741 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528741 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(678\) | 32521.0 | 1.84213 | ||||||||
\(679\) | −12092.9 | −0.683480 | ||||||||
\(680\) | 16870.4 | 0.951400 | ||||||||
\(681\) | 1338.14 | 0.0752974 | ||||||||
\(682\) | 7003.12 | 0.393201 | ||||||||
\(683\) | 18395.7 | 1.03059 | 0.515294 | − | 0.857013i | \(-0.327683\pi\) | ||||
0.515294 | + | 0.857013i | \(0.327683\pi\) | |||||||
\(684\) | −12641.5 | −0.706669 | ||||||||
\(685\) | −43883.8 | −2.44776 | ||||||||
\(686\) | −53058.1 | −2.95301 | ||||||||
\(687\) | 1920.07 | 0.106631 | ||||||||
\(688\) | −291.519 | −0.0161542 | ||||||||
\(689\) | −5750.79 | −0.317979 | ||||||||
\(690\) | 29011.6 | 1.60065 | ||||||||
\(691\) | 21621.6 | 1.19034 | 0.595170 | − | 0.803600i | \(-0.297085\pi\) | ||||
0.595170 | + | 0.803600i | \(0.297085\pi\) | |||||||
\(692\) | 2845.37 | 0.156308 | ||||||||
\(693\) | 4920.96 | 0.269743 | ||||||||
\(694\) | 43831.3 | 2.39743 | ||||||||
\(695\) | 34480.1 | 1.88188 | ||||||||
\(696\) | 16598.6 | 0.903978 | ||||||||
\(697\) | −7476.18 | −0.406285 | ||||||||
\(698\) | −8449.77 | −0.458207 | ||||||||
\(699\) | −16800.1 | −0.909067 | ||||||||
\(700\) | 85834.5 | 4.63463 | ||||||||
\(701\) | 1405.85 | 0.0757464 | 0.0378732 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378732 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(702\) | −40136.4 | −2.15791 | ||||||||
\(703\) | 19095.9 | 1.02449 | ||||||||
\(704\) | 9063.93 | 0.485241 | ||||||||
\(705\) | 31755.1 | 1.69641 | ||||||||
\(706\) | −35250.4 | −1.87913 | ||||||||
\(707\) | 14026.5 | 0.746139 | ||||||||
\(708\) | 10674.2 | 0.566613 | ||||||||
\(709\) | −28703.0 | −1.52040 | −0.760201 | − | 0.649688i | \(-0.774900\pi\) | ||||
−0.760201 | + | 0.649688i | \(0.774900\pi\) | |||||||
\(710\) | −56550.7 | −2.98917 | ||||||||
\(711\) | 8054.99 | 0.424874 | ||||||||
\(712\) | −12988.0 | −0.683633 | ||||||||
\(713\) | 13330.6 | 0.700189 | ||||||||
\(714\) | −21394.2 | −1.12137 | ||||||||
\(715\) | −11746.3 | −0.614388 | ||||||||
\(716\) | −21998.0 | −1.14819 | ||||||||
\(717\) | −1945.44 | −0.101330 | ||||||||
\(718\) | 34087.9 | 1.77180 | ||||||||
\(719\) | 35372.0 | 1.83471 | 0.917353 | − | 0.398075i | \(-0.130322\pi\) | ||||
0.917353 | + | 0.398075i | \(0.130322\pi\) | |||||||
\(720\) | 715.414 | 0.0370304 | ||||||||
\(721\) | −31161.8 | −1.60961 | ||||||||
\(722\) | 9210.66 | 0.474772 | ||||||||
\(723\) | −21521.3 | −1.10703 | ||||||||
\(724\) | −33126.2 | −1.70045 | ||||||||
\(725\) | −39600.6 | −2.02859 | ||||||||
\(726\) | −2015.76 | −0.103047 | ||||||||
\(727\) | −38127.7 | −1.94509 | −0.972543 | − | 0.232724i | \(-0.925236\pi\) | ||||
−0.972543 | + | 0.232724i | \(0.925236\pi\) | |||||||
\(728\) | 44658.3 | 2.27356 | ||||||||
\(729\) | 16766.5 | 0.851828 | ||||||||
\(730\) | −90663.3 | −4.59671 | ||||||||
\(731\) | −4061.63 | −0.205506 | ||||||||
\(732\) | 17382.4 | 0.877693 | ||||||||
\(733\) | −9573.10 | −0.482388 | −0.241194 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241194 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(734\) | −36044.7 | −1.81258 | ||||||||
\(735\) | −45996.5 | −2.30831 | ||||||||
\(736\) | 16775.4 | 0.840151 | ||||||||
\(737\) | −10833.6 | −0.541468 | ||||||||
\(738\) | −11963.6 | −0.596727 | ||||||||
\(739\) | −8470.31 | −0.421631 | −0.210816 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210816 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(740\) | −65019.6 | −3.22996 | ||||||||
\(741\) | −14902.0 | −0.738783 | ||||||||
\(742\) | −14469.1 | −0.715871 | ||||||||
\(743\) | 2325.07 | 0.114803 | 0.0574013 | − | 0.998351i | \(-0.481719\pi\) | ||||
0.0574013 | + | 0.998351i | \(0.481719\pi\) | |||||||
\(744\) | −11780.4 | −0.580497 | ||||||||
\(745\) | 25.4376 | 0.00125096 | ||||||||
\(746\) | −47404.1 | −2.32653 | ||||||||
\(747\) | −9302.67 | −0.455645 | ||||||||
\(748\) | −5729.67 | −0.280077 | ||||||||
\(749\) | 16114.8 | 0.786145 | ||||||||
\(750\) | 23464.1 | 1.14238 | ||||||||
\(751\) | 24549.9 | 1.19286 | 0.596431 | − | 0.802664i | \(-0.296585\pi\) | ||||
0.596431 | + | 0.802664i | \(0.296585\pi\) | |||||||
\(752\) | −1380.00 | −0.0669195 | ||||||||
\(753\) | −6072.20 | −0.293869 | ||||||||
\(754\) | −52907.7 | −2.55542 | ||||||||
\(755\) | −26071.7 | −1.25675 | ||||||||
\(756\) | −62700.3 | −3.01639 | ||||||||
\(757\) | 9628.86 | 0.462308 | 0.231154 | − | 0.972917i | \(-0.425750\pi\) | ||||
0.231154 | + | 0.972917i | \(0.425750\pi\) | |||||||
\(758\) | 3725.99 | 0.178541 | ||||||||
\(759\) | −3837.05 | −0.183499 | ||||||||
\(760\) | 29565.6 | 1.41113 | ||||||||
\(761\) | −34572.3 | −1.64684 | −0.823420 | − | 0.567433i | \(-0.807937\pi\) | ||||
−0.823420 | + | 0.567433i | \(0.807937\pi\) | |||||||
\(762\) | 6581.64 | 0.312897 | ||||||||
\(763\) | 56472.2 | 2.67947 | ||||||||
\(764\) | −10617.4 | −0.502780 | ||||||||
\(765\) | 9967.58 | 0.471083 | ||||||||
\(766\) | 29248.5 | 1.37962 | ||||||||
\(767\) | −13249.7 | −0.623755 | ||||||||
\(768\) | −15909.3 | −0.747495 | ||||||||
\(769\) | −7895.86 | −0.370263 | −0.185131 | − | 0.982714i | \(-0.559271\pi\) | ||||
−0.185131 | + | 0.982714i | \(0.559271\pi\) | |||||||
\(770\) | −29553.9 | −1.38318 | ||||||||
\(771\) | 2447.07 | 0.114305 | ||||||||
\(772\) | −36708.3 | −1.71135 | ||||||||
\(773\) | 2264.52 | 0.105368 | 0.0526838 | − | 0.998611i | \(-0.483222\pi\) | ||||
0.0526838 | + | 0.998611i | \(0.483222\pi\) | |||||||
\(774\) | −6499.51 | −0.301835 | ||||||||
\(775\) | 28105.4 | 1.30268 | ||||||||
\(776\) | 8774.32 | 0.405902 | ||||||||
\(777\) | 32109.7 | 1.48254 | ||||||||
\(778\) | 45125.6 | 2.07948 | ||||||||
\(779\) | −13102.1 | −0.602607 | ||||||||
\(780\) | 50739.7 | 2.32919 | ||||||||
\(781\) | 7479.35 | 0.342679 | ||||||||
\(782\) | −17565.9 | −0.803266 | ||||||||
\(783\) | 28927.4 | 1.32028 | ||||||||
\(784\) | 1998.90 | 0.0910576 | ||||||||
\(785\) | −24587.2 | −1.11791 | ||||||||
\(786\) | −2182.35 | −0.0990356 | ||||||||
\(787\) | −12234.3 | −0.554135 | −0.277068 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277068 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(788\) | −59170.8 | −2.67496 | ||||||||
\(789\) | −25273.3 | −1.14037 | ||||||||
\(790\) | −48376.0 | −2.17866 | ||||||||
\(791\) | −63061.7 | −2.83466 | ||||||||
\(792\) | −3570.54 | −0.160194 | ||||||||
\(793\) | −21576.4 | −0.966205 | ||||||||
\(794\) | 51897.1 | 2.31960 | ||||||||
\(795\) | −6401.89 | −0.285600 | ||||||||
\(796\) | 70596.5 | 3.14350 | ||||||||
\(797\) | −34297.0 | −1.52429 | −0.762147 | − | 0.647404i | \(-0.775855\pi\) | ||||
−0.762147 | + | 0.647404i | \(0.775855\pi\) | |||||||
\(798\) | −37493.6 | −1.66323 | ||||||||
\(799\) | −19227.0 | −0.851317 | ||||||||
\(800\) | 35368.2 | 1.56307 | ||||||||
\(801\) | −7673.72 | −0.338499 | ||||||||
\(802\) | 50541.1 | 2.22527 | ||||||||
\(803\) | 11991.1 | 0.526968 | ||||||||
\(804\) | 46797.2 | 2.05275 | ||||||||
\(805\) | −56256.5 | −2.46308 | ||||||||
\(806\) | 37549.8 | 1.64098 | ||||||||
\(807\) | −15208.7 | −0.663412 | ||||||||
\(808\) | −10177.3 | −0.443114 | ||||||||
\(809\) | −13392.4 | −0.582016 | −0.291008 | − | 0.956721i | \(-0.593991\pi\) | ||||
−0.291008 | + | 0.956721i | \(0.593991\pi\) | |||||||
\(810\) | −13582.6 | −0.589188 | ||||||||
\(811\) | −17875.0 | −0.773953 | −0.386976 | − | 0.922090i | \(-0.626481\pi\) | ||||
−0.386976 | + | 0.922090i | \(0.626481\pi\) | |||||||
\(812\) | −82651.5 | −3.57204 | ||||||||
\(813\) | 4014.87 | 0.173195 | ||||||||
\(814\) | 13850.1 | 0.596369 | ||||||||
\(815\) | 7004.52 | 0.301052 | ||||||||
\(816\) | 411.367 | 0.0176480 | ||||||||
\(817\) | −7118.04 | −0.304809 | ||||||||
\(818\) | 17838.4 | 0.762474 | ||||||||
\(819\) | 26385.5 | 1.12574 | ||||||||
\(820\) | 44611.2 | 1.89987 | ||||||||
\(821\) | 27091.3 | 1.15163 | 0.575817 | − | 0.817579i | \(-0.304684\pi\) | ||||
0.575817 | + | 0.817579i | \(0.304684\pi\) | |||||||
\(822\) | −40379.1 | −1.71336 | ||||||||
\(823\) | 9454.93 | 0.400459 | 0.200230 | − | 0.979749i | \(-0.435831\pi\) | ||||
0.200230 | + | 0.979749i | \(0.435831\pi\) | |||||||
\(824\) | 22610.3 | 0.955906 | ||||||||
\(825\) | −8089.79 | −0.341394 | ||||||||
\(826\) | −33336.5 | −1.40427 | ||||||||
\(827\) | 5966.77 | 0.250888 | 0.125444 | − | 0.992101i | \(-0.459964\pi\) | ||||
0.125444 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(828\) | −17453.0 | −0.732527 | ||||||||
\(829\) | 30513.2 | 1.27837 | 0.639183 | − | 0.769054i | \(-0.279272\pi\) | ||||
0.639183 | + | 0.769054i | \(0.279272\pi\) | |||||||
\(830\) | 55869.2 | 2.33644 | ||||||||
\(831\) | −20641.1 | −0.861650 | ||||||||
\(832\) | 48599.5 | 2.02510 | ||||||||
\(833\) | 27849.8 | 1.15839 | ||||||||
\(834\) | 31726.5 | 1.31726 | ||||||||
\(835\) | −7544.08 | −0.312663 | ||||||||
\(836\) | −10041.3 | −0.415414 | ||||||||
\(837\) | −20530.4 | −0.847830 | ||||||||
\(838\) | −22436.5 | −0.924889 | ||||||||
\(839\) | 36892.3 | 1.51807 | 0.759037 | − | 0.651048i | \(-0.225670\pi\) | ||||
0.759037 | + | 0.651048i | \(0.225670\pi\) | |||||||
\(840\) | 49714.5 | 2.04204 | ||||||||
\(841\) | 13743.1 | 0.563494 | ||||||||
\(842\) | 17823.5 | 0.729498 | ||||||||
\(843\) | 32512.3 | 1.32833 | ||||||||
\(844\) | 51311.7 | 2.09268 | ||||||||
\(845\) | −23205.3 | −0.944717 | ||||||||
\(846\) | −30767.5 | −1.25036 | ||||||||
\(847\) | 3908.78 | 0.158568 | ||||||||
\(848\) | 278.211 | 0.0112663 | ||||||||
\(849\) | −8003.88 | −0.323548 | ||||||||
\(850\) | −37034.7 | −1.49445 | ||||||||
\(851\) | 26363.9 | 1.06198 | ||||||||
\(852\) | −32308.0 | −1.29912 | ||||||||
\(853\) | −1880.79 | −0.0754948 | −0.0377474 | − | 0.999287i | \(-0.512018\pi\) | ||||
−0.0377474 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(854\) | −54286.5 | −2.17523 | ||||||||
\(855\) | 17468.3 | 0.698717 | ||||||||
\(856\) | −11692.5 | −0.466872 | ||||||||
\(857\) | −29396.5 | −1.17172 | −0.585861 | − | 0.810412i | \(-0.699243\pi\) | ||||
−0.585861 | + | 0.810412i | \(0.699243\pi\) | |||||||
\(858\) | −10808.2 | −0.430055 | ||||||||
\(859\) | 25201.3 | 1.00100 | 0.500499 | − | 0.865737i | \(-0.333150\pi\) | ||||
0.500499 | + | 0.865737i | \(0.333150\pi\) | |||||||
\(860\) | 24236.2 | 0.960984 | ||||||||
\(861\) | −22031.1 | −0.872031 | ||||||||
\(862\) | −39845.6 | −1.57442 | ||||||||
\(863\) | 4903.67 | 0.193422 | 0.0967108 | − | 0.995313i | \(-0.469168\pi\) | ||||
0.0967108 | + | 0.995313i | \(0.469168\pi\) | |||||||
\(864\) | −25835.8 | −1.01730 | ||||||||
\(865\) | −3931.78 | −0.154549 | ||||||||
\(866\) | 56284.4 | 2.20857 | ||||||||
\(867\) | −12085.6 | −0.473412 | ||||||||
\(868\) | 58659.6 | 2.29382 | ||||||||
\(869\) | 6398.17 | 0.249762 | ||||||||
\(870\) | −58897.9 | −2.29520 | ||||||||
\(871\) | −58088.5 | −2.25976 | ||||||||
\(872\) | −40974.9 | −1.59127 | ||||||||
\(873\) | 5184.14 | 0.200981 | ||||||||
\(874\) | −30784.4 | −1.19141 | ||||||||
\(875\) | −45499.4 | −1.75790 | ||||||||
\(876\) | −51796.8 | −1.99778 | ||||||||
\(877\) | −18951.8 | −0.729710 | −0.364855 | − | 0.931064i | \(-0.618881\pi\) | ||||
−0.364855 | + | 0.931064i | \(0.618881\pi\) | |||||||
\(878\) | 65784.3 | 2.52860 | ||||||||
\(879\) | −15760.4 | −0.604762 | ||||||||
\(880\) | 568.262 | 0.0217683 | ||||||||
\(881\) | 41138.9 | 1.57322 | 0.786609 | − | 0.617452i | \(-0.211835\pi\) | ||||
0.786609 | + | 0.617452i | \(0.211835\pi\) | |||||||
\(882\) | 44566.0 | 1.70138 | ||||||||
\(883\) | −21304.9 | −0.811967 | −0.405984 | − | 0.913880i | \(-0.633071\pi\) | ||||
−0.405984 | + | 0.913880i | \(0.633071\pi\) | |||||||
\(884\) | −30721.7 | −1.16887 | ||||||||
\(885\) | −14749.8 | −0.560238 | ||||||||
\(886\) | 13206.3 | 0.500760 | ||||||||
\(887\) | −8578.08 | −0.324717 | −0.162358 | − | 0.986732i | \(-0.551910\pi\) | ||||
−0.162358 | + | 0.986732i | \(0.551910\pi\) | |||||||
\(888\) | −23298.1 | −0.880442 | ||||||||
\(889\) | −12762.5 | −0.481486 | ||||||||
\(890\) | 46086.2 | 1.73574 | ||||||||
\(891\) | 1796.42 | 0.0675447 | ||||||||
\(892\) | −75155.1 | −2.82105 | ||||||||
\(893\) | −33695.5 | −1.26268 | ||||||||
\(894\) | 23.4061 | 0.000875635 0 | ||||||||
\(895\) | 30397.3 | 1.13527 | ||||||||
\(896\) | 77205.5 | 2.87863 | ||||||||
\(897\) | −20573.7 | −0.765816 | ||||||||
\(898\) | 3339.58 | 0.124102 | ||||||||
\(899\) | −27063.1 | −1.00401 | ||||||||
\(900\) | −36796.7 | −1.36284 | ||||||||
\(901\) | 3876.20 | 0.143324 | ||||||||
\(902\) | −9502.79 | −0.350785 | ||||||||
\(903\) | −11969.0 | −0.441088 | ||||||||
\(904\) | 45756.1 | 1.68343 | ||||||||
\(905\) | 45774.4 | 1.68132 | ||||||||
\(906\) | −23989.6 | −0.879692 | ||||||||
\(907\) | −4897.99 | −0.179311 | −0.0896556 | − | 0.995973i | \(-0.528577\pi\) | ||||
−0.0896556 | + | 0.995973i | \(0.528577\pi\) | |||||||
\(908\) | 4834.62 | 0.176699 | ||||||||
\(909\) | −6013.06 | −0.219407 | ||||||||
\(910\) | −158464. | −5.77256 | ||||||||
\(911\) | −5563.86 | −0.202348 | −0.101174 | − | 0.994869i | \(-0.532260\pi\) | ||||
−0.101174 | + | 0.994869i | \(0.532260\pi\) | |||||||
\(912\) | 720.926 | 0.0261757 | ||||||||
\(913\) | −7389.22 | −0.267850 | ||||||||
\(914\) | 2175.17 | 0.0787181 | ||||||||
\(915\) | −24019.3 | −0.867817 | ||||||||
\(916\) | 6937.12 | 0.250228 | ||||||||
\(917\) | 4231.82 | 0.152396 | ||||||||
\(918\) | 27053.1 | 0.972641 | ||||||||
\(919\) | −49598.3 | −1.78030 | −0.890150 | − | 0.455667i | \(-0.849401\pi\) | ||||
−0.890150 | + | 0.455667i | \(0.849401\pi\) | |||||||
\(920\) | 40818.4 | 1.46276 | ||||||||
\(921\) | 10317.9 | 0.369149 | ||||||||
\(922\) | 53065.4 | 1.89546 | ||||||||
\(923\) | 40103.2 | 1.43013 | ||||||||
\(924\) | −16884.4 | −0.601144 | ||||||||
\(925\) | 55584.0 | 1.97577 | ||||||||
\(926\) | 69678.3 | 2.47275 | ||||||||
\(927\) | 13358.9 | 0.473314 | ||||||||
\(928\) | −34056.7 | −1.20470 | ||||||||
\(929\) | −905.345 | −0.0319735 | −0.0159868 | − | 0.999872i | \(-0.505089\pi\) | ||||
−0.0159868 | + | 0.999872i | \(0.505089\pi\) | |||||||
\(930\) | 41801.1 | 1.47388 | ||||||||
\(931\) | 48807.2 | 1.71814 | ||||||||
\(932\) | −60697.9 | −2.13329 | ||||||||
\(933\) | 3271.17 | 0.114784 | ||||||||
\(934\) | −662.475 | −0.0232086 | ||||||||
\(935\) | 7917.36 | 0.276926 | ||||||||
\(936\) | −19144.7 | −0.668552 | ||||||||
\(937\) | 22056.5 | 0.769002 | 0.384501 | − | 0.923125i | \(-0.374374\pi\) | ||||
0.384501 | + | 0.923125i | \(0.374374\pi\) | |||||||
\(938\) | −146151. | −5.08743 | ||||||||
\(939\) | −27263.6 | −0.947513 | ||||||||
\(940\) | 114730. | 3.98092 | ||||||||
\(941\) | 18429.7 | 0.638460 | 0.319230 | − | 0.947677i | \(-0.396576\pi\) | ||||
0.319230 | + | 0.947677i | \(0.396576\pi\) | |||||||
\(942\) | −22623.7 | −0.782504 | ||||||||
\(943\) | −18088.8 | −0.624658 | ||||||||
\(944\) | 640.993 | 0.0221001 | ||||||||
\(945\) | 86640.4 | 2.98245 | ||||||||
\(946\) | −5162.63 | −0.177433 | ||||||||
\(947\) | 23340.5 | 0.800912 | 0.400456 | − | 0.916316i | \(-0.368852\pi\) | ||||
0.400456 | + | 0.916316i | \(0.368852\pi\) | |||||||
\(948\) | −27637.7 | −0.946866 | ||||||||
\(949\) | 64294.4 | 2.19925 | ||||||||
\(950\) | −64903.7 | −2.21658 | ||||||||
\(951\) | −32732.3 | −1.11611 | ||||||||
\(952\) | −30101.0 | −1.02477 | ||||||||
\(953\) | 34053.3 | 1.15750 | 0.578748 | − | 0.815506i | \(-0.303541\pi\) | ||||
0.578748 | + | 0.815506i | \(0.303541\pi\) | |||||||
\(954\) | 6202.79 | 0.210506 | ||||||||
\(955\) | 14671.3 | 0.497123 | ||||||||
\(956\) | −7028.79 | −0.237790 | ||||||||
\(957\) | 7789.79 | 0.263122 | ||||||||
\(958\) | −47328.7 | −1.59616 | ||||||||
\(959\) | 78299.5 | 2.63652 | ||||||||
\(960\) | 54101.9 | 1.81889 | ||||||||
\(961\) | −10583.7 | −0.355265 | ||||||||
\(962\) | 74262.1 | 2.48888 | ||||||||
\(963\) | −6908.31 | −0.231171 | ||||||||
\(964\) | −77755.3 | −2.59785 | ||||||||
\(965\) | 50724.2 | 1.69209 | ||||||||
\(966\) | −51763.8 | −1.72409 | ||||||||
\(967\) | −3932.44 | −0.130774 | −0.0653871 | − | 0.997860i | \(-0.520828\pi\) | ||||
−0.0653871 | + | 0.997860i | \(0.520828\pi\) | |||||||
\(968\) | −2836.12 | −0.0941697 | ||||||||
\(969\) | 10044.4 | 0.332995 | ||||||||
\(970\) | −31134.5 | −1.03058 | ||||||||
\(971\) | −7261.24 | −0.239984 | −0.119992 | − | 0.992775i | \(-0.538287\pi\) | ||||
−0.119992 | + | 0.992775i | \(0.538287\pi\) | |||||||
\(972\) | 44645.8 | 1.47327 | ||||||||
\(973\) | −61521.0 | −2.02700 | ||||||||
\(974\) | 94485.1 | 3.10832 | ||||||||
\(975\) | −43376.3 | −1.42477 | ||||||||
\(976\) | 1043.82 | 0.0342335 | ||||||||
\(977\) | −32946.0 | −1.07885 | −0.539424 | − | 0.842034i | \(-0.681358\pi\) | ||||
−0.539424 | + | 0.842034i | \(0.681358\pi\) | |||||||
\(978\) | 6445.12 | 0.210728 | ||||||||
\(979\) | −6095.32 | −0.198986 | ||||||||
\(980\) | −166183. | −5.41686 | ||||||||
\(981\) | −24209.3 | −0.787912 | ||||||||
\(982\) | 42601.9 | 1.38440 | ||||||||
\(983\) | −14071.9 | −0.456585 | −0.228293 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228293 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(984\) | 15985.3 | 0.517877 | ||||||||
\(985\) | 81763.2 | 2.64486 | ||||||||
\(986\) | 35661.4 | 1.15181 | ||||||||
\(987\) | −56658.9 | −1.82723 | ||||||||
\(988\) | −53840.2 | −1.73369 | ||||||||
\(989\) | −9827.20 | −0.315962 | ||||||||
\(990\) | 12669.6 | 0.406732 | ||||||||
\(991\) | −22138.1 | −0.709625 | −0.354813 | − | 0.934937i | \(-0.615455\pi\) | ||||
−0.354813 | + | 0.934937i | \(0.615455\pi\) | |||||||
\(992\) | 24170.8 | 0.773611 | ||||||||
\(993\) | −32804.3 | −1.04835 | ||||||||
\(994\) | 100900. | 3.21968 | ||||||||
\(995\) | −97551.4 | −3.10813 | ||||||||
\(996\) | 31918.6 | 1.01544 | ||||||||
\(997\) | 27681.9 | 0.879333 | 0.439667 | − | 0.898161i | \(-0.355097\pi\) | ||||
0.439667 | + | 0.898161i | \(0.355097\pi\) | |||||||
\(998\) | 56473.3 | 1.79121 | ||||||||
\(999\) | −40602.9 | −1.28591 |
(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 | 1441.4.a.a.1.10 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.4.a.a.1.10 | ✓ | 77 | 1.1 | even | 1 | trivial |