Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(1,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, 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("39.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.73549\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.73549 | −1.32069 | −0.660347 | − | 0.750960i | \(-0.729591\pi\) | ||||
−0.660347 | + | 0.750960i | \(0.729591\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 5.95388 | 0.744235 | ||||||||
\(5\) | −3.90776 | −0.349521 | −0.174761 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174761 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(6\) | −11.2065 | −0.762504 | ||||||||
\(7\) | 36.4129 | 1.96611 | 0.983057 | − | 0.183301i | \(-0.0586782\pi\) | ||||
0.983057 | + | 0.183301i | \(0.0586782\pi\) | |||||||
\(8\) | 7.64325 | 0.337787 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 14.5974 | 0.461611 | ||||||||
\(11\) | 19.1943 | 0.526117 | 0.263059 | − | 0.964780i | \(-0.415269\pi\) | ||||
0.263059 | + | 0.964780i | \(0.415269\pi\) | |||||||
\(12\) | 17.8616 | 0.429684 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | −136.020 | −2.59664 | ||||||||
\(15\) | −11.7233 | −0.201796 | ||||||||
\(16\) | −76.1823 | −1.19035 | ||||||||
\(17\) | −83.8839 | −1.19676 | −0.598378 | − | 0.801214i | \(-0.704188\pi\) | ||||
−0.598378 | + | 0.801214i | \(0.704188\pi\) | |||||||
\(18\) | −33.6194 | −0.440232 | ||||||||
\(19\) | 46.8492 | 0.565681 | 0.282840 | − | 0.959167i | \(-0.408723\pi\) | ||||
0.282840 | + | 0.959167i | \(0.408723\pi\) | |||||||
\(20\) | −23.2664 | −0.260126 | ||||||||
\(21\) | 109.239 | 1.13514 | ||||||||
\(22\) | −71.7000 | −0.694840 | ||||||||
\(23\) | 103.905 | 0.941983 | 0.470991 | − | 0.882138i | \(-0.343896\pi\) | ||||
0.470991 | + | 0.882138i | \(0.343896\pi\) | |||||||
\(24\) | 22.9298 | 0.195022 | ||||||||
\(25\) | −109.729 | −0.877835 | ||||||||
\(26\) | −48.5614 | −0.366295 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 216.798 | 1.46325 | ||||||||
\(29\) | 108.341 | 0.693738 | 0.346869 | − | 0.937914i | \(-0.387245\pi\) | ||||
0.346869 | + | 0.937914i | \(0.387245\pi\) | |||||||
\(30\) | 43.7922 | 0.266511 | ||||||||
\(31\) | −147.532 | −0.854759 | −0.427379 | − | 0.904072i | \(-0.640563\pi\) | ||||
−0.427379 | + | 0.904072i | \(0.640563\pi\) | |||||||
\(32\) | 223.432 | 1.23430 | ||||||||
\(33\) | 57.5828 | 0.303754 | ||||||||
\(34\) | 313.347 | 1.58055 | ||||||||
\(35\) | −142.293 | −0.687198 | ||||||||
\(36\) | 53.5849 | 0.248078 | ||||||||
\(37\) | −160.012 | −0.710969 | −0.355484 | − | 0.934682i | \(-0.615684\pi\) | ||||
−0.355484 | + | 0.934682i | \(0.615684\pi\) | |||||||
\(38\) | −175.005 | −0.747092 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | −29.8680 | −0.118064 | ||||||||
\(41\) | 231.490 | 0.881772 | 0.440886 | − | 0.897563i | \(-0.354664\pi\) | ||||
0.440886 | + | 0.897563i | \(0.354664\pi\) | |||||||
\(42\) | −408.060 | −1.49917 | ||||||||
\(43\) | −340.314 | −1.20692 | −0.603458 | − | 0.797395i | \(-0.706211\pi\) | ||||
−0.603458 | + | 0.797395i | \(0.706211\pi\) | |||||||
\(44\) | 114.280 | 0.391555 | ||||||||
\(45\) | −35.1699 | −0.116507 | ||||||||
\(46\) | −388.135 | −1.24407 | ||||||||
\(47\) | 119.653 | 0.371346 | 0.185673 | − | 0.982612i | \(-0.440554\pi\) | ||||
0.185673 | + | 0.982612i | \(0.440554\pi\) | |||||||
\(48\) | −228.547 | −0.687248 | ||||||||
\(49\) | 982.902 | 2.86560 | ||||||||
\(50\) | 409.893 | 1.15935 | ||||||||
\(51\) | −251.652 | −0.690947 | ||||||||
\(52\) | 77.4005 | 0.206414 | ||||||||
\(53\) | −732.879 | −1.89941 | −0.949705 | − | 0.313146i | \(-0.898617\pi\) | ||||
−0.949705 | + | 0.313146i | \(0.898617\pi\) | |||||||
\(54\) | −100.858 | −0.254168 | ||||||||
\(55\) | −75.0067 | −0.183889 | ||||||||
\(56\) | 278.313 | 0.664128 | ||||||||
\(57\) | 140.548 | 0.326596 | ||||||||
\(58\) | −404.706 | −0.916216 | ||||||||
\(59\) | −229.782 | −0.507035 | −0.253518 | − | 0.967331i | \(-0.581588\pi\) | ||||
−0.253518 | + | 0.967331i | \(0.581588\pi\) | |||||||
\(60\) | −69.7991 | −0.150184 | ||||||||
\(61\) | 108.943 | 0.228668 | 0.114334 | − | 0.993442i | \(-0.463527\pi\) | ||||
0.114334 | + | 0.993442i | \(0.463527\pi\) | |||||||
\(62\) | 551.104 | 1.12888 | ||||||||
\(63\) | 327.716 | 0.655371 | ||||||||
\(64\) | −225.170 | −0.439786 | ||||||||
\(65\) | −50.8009 | −0.0969397 | ||||||||
\(66\) | −215.100 | −0.401166 | ||||||||
\(67\) | 10.3955 | 0.0189555 | 0.00947774 | − | 0.999955i | \(-0.496983\pi\) | ||||
0.00947774 | + | 0.999955i | \(0.496983\pi\) | |||||||
\(68\) | −499.435 | −0.890667 | ||||||||
\(69\) | 311.714 | 0.543854 | ||||||||
\(70\) | 531.535 | 0.907579 | ||||||||
\(71\) | −869.201 | −1.45289 | −0.726445 | − | 0.687224i | \(-0.758829\pi\) | ||||
−0.726445 | + | 0.687224i | \(0.758829\pi\) | |||||||
\(72\) | 68.7893 | 0.112596 | ||||||||
\(73\) | −1099.07 | −1.76214 | −0.881072 | − | 0.472982i | \(-0.843178\pi\) | ||||
−0.881072 | + | 0.472982i | \(0.843178\pi\) | |||||||
\(74\) | 597.724 | 0.938973 | ||||||||
\(75\) | −329.188 | −0.506818 | ||||||||
\(76\) | 278.934 | 0.421000 | ||||||||
\(77\) | 698.920 | 1.03441 | ||||||||
\(78\) | −145.684 | −0.211480 | ||||||||
\(79\) | 140.410 | 0.199967 | 0.0999835 | − | 0.994989i | \(-0.468121\pi\) | ||||
0.0999835 | + | 0.994989i | \(0.468121\pi\) | |||||||
\(80\) | 297.703 | 0.416052 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −864.729 | −1.16455 | ||||||||
\(83\) | −159.474 | −0.210898 | −0.105449 | − | 0.994425i | \(-0.533628\pi\) | ||||
−0.105449 | + | 0.994425i | \(0.533628\pi\) | |||||||
\(84\) | 650.395 | 0.844808 | ||||||||
\(85\) | 327.799 | 0.418291 | ||||||||
\(86\) | 1271.24 | 1.59397 | ||||||||
\(87\) | 325.023 | 0.400530 | ||||||||
\(88\) | 146.707 | 0.177716 | ||||||||
\(89\) | 1067.93 | 1.27192 | 0.635959 | − | 0.771723i | \(-0.280605\pi\) | ||||
0.635959 | + | 0.771723i | \(0.280605\pi\) | |||||||
\(90\) | 131.377 | 0.153870 | ||||||||
\(91\) | 473.368 | 0.545302 | ||||||||
\(92\) | 618.636 | 0.701057 | ||||||||
\(93\) | −442.596 | −0.493495 | ||||||||
\(94\) | −446.964 | −0.490434 | ||||||||
\(95\) | −183.075 | −0.197717 | ||||||||
\(96\) | 670.297 | 0.712624 | ||||||||
\(97\) | 858.881 | 0.899032 | 0.449516 | − | 0.893272i | \(-0.351596\pi\) | ||||
0.449516 | + | 0.893272i | \(0.351596\pi\) | |||||||
\(98\) | −3671.62 | −3.78459 | ||||||||
\(99\) | 172.748 | 0.175372 | ||||||||
\(100\) | −653.316 | −0.653316 | ||||||||
\(101\) | −1574.16 | −1.55084 | −0.775421 | − | 0.631444i | \(-0.782462\pi\) | ||||
−0.775421 | + | 0.631444i | \(0.782462\pi\) | |||||||
\(102\) | 940.042 | 0.912530 | ||||||||
\(103\) | −129.724 | −0.124098 | −0.0620489 | − | 0.998073i | \(-0.519763\pi\) | ||||
−0.0620489 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(104\) | 99.3623 | 0.0936853 | ||||||||
\(105\) | −426.879 | −0.396754 | ||||||||
\(106\) | 2737.66 | 2.50854 | ||||||||
\(107\) | −1957.43 | −1.76853 | −0.884263 | − | 0.466990i | \(-0.845339\pi\) | ||||
−0.884263 | + | 0.466990i | \(0.845339\pi\) | |||||||
\(108\) | 160.755 | 0.143228 | ||||||||
\(109\) | 1228.77 | 1.07977 | 0.539886 | − | 0.841738i | \(-0.318467\pi\) | ||||
0.539886 | + | 0.841738i | \(0.318467\pi\) | |||||||
\(110\) | 280.187 | 0.242861 | ||||||||
\(111\) | −480.037 | −0.410478 | ||||||||
\(112\) | −2774.02 | −2.34036 | ||||||||
\(113\) | 1629.50 | 1.35655 | 0.678275 | − | 0.734808i | \(-0.262728\pi\) | ||||
0.678275 | + | 0.734808i | \(0.262728\pi\) | |||||||
\(114\) | −525.014 | −0.431334 | ||||||||
\(115\) | −406.035 | −0.329243 | ||||||||
\(116\) | 645.049 | 0.516304 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 858.349 | 0.669639 | ||||||||
\(119\) | −3054.46 | −2.35296 | ||||||||
\(120\) | −89.6041 | −0.0681641 | ||||||||
\(121\) | −962.580 | −0.723201 | ||||||||
\(122\) | −406.956 | −0.302000 | ||||||||
\(123\) | 694.470 | 0.509092 | ||||||||
\(124\) | −878.388 | −0.636142 | ||||||||
\(125\) | 917.267 | 0.656343 | ||||||||
\(126\) | −1224.18 | −0.865546 | ||||||||
\(127\) | 276.112 | 0.192921 | 0.0964607 | − | 0.995337i | \(-0.469248\pi\) | ||||
0.0964607 | + | 0.995337i | \(0.469248\pi\) | |||||||
\(128\) | −946.337 | −0.653478 | ||||||||
\(129\) | −1020.94 | −0.696813 | ||||||||
\(130\) | 189.766 | 0.128028 | ||||||||
\(131\) | −96.2240 | −0.0641765 | −0.0320883 | − | 0.999485i | \(-0.510216\pi\) | ||||
−0.0320883 | + | 0.999485i | \(0.510216\pi\) | |||||||
\(132\) | 342.841 | 0.226064 | ||||||||
\(133\) | 1705.92 | 1.11219 | ||||||||
\(134\) | −38.8324 | −0.0250344 | ||||||||
\(135\) | −105.510 | −0.0672653 | ||||||||
\(136\) | −641.146 | −0.404249 | ||||||||
\(137\) | 2618.38 | 1.63287 | 0.816435 | − | 0.577438i | \(-0.195947\pi\) | ||||
0.816435 | + | 0.577438i | \(0.195947\pi\) | |||||||
\(138\) | −1164.40 | −0.718265 | ||||||||
\(139\) | 1963.34 | 1.19805 | 0.599023 | − | 0.800732i | \(-0.295556\pi\) | ||||
0.599023 | + | 0.800732i | \(0.295556\pi\) | |||||||
\(140\) | −847.197 | −0.511437 | ||||||||
\(141\) | 358.960 | 0.214396 | ||||||||
\(142\) | 3246.89 | 1.91882 | ||||||||
\(143\) | 249.526 | 0.145919 | ||||||||
\(144\) | −685.641 | −0.396783 | ||||||||
\(145\) | −423.370 | −0.242476 | ||||||||
\(146\) | 4105.57 | 2.32725 | ||||||||
\(147\) | 2948.71 | 1.65446 | ||||||||
\(148\) | −952.694 | −0.529128 | ||||||||
\(149\) | −301.111 | −0.165557 | −0.0827784 | − | 0.996568i | \(-0.526379\pi\) | ||||
−0.0827784 | + | 0.996568i | \(0.526379\pi\) | |||||||
\(150\) | 1229.68 | 0.669352 | ||||||||
\(151\) | 342.973 | 0.184839 | 0.0924197 | − | 0.995720i | \(-0.470540\pi\) | ||||
0.0924197 | + | 0.995720i | \(0.470540\pi\) | |||||||
\(152\) | 358.080 | 0.191080 | ||||||||
\(153\) | −754.955 | −0.398918 | ||||||||
\(154\) | −2610.81 | −1.36614 | ||||||||
\(155\) | 576.520 | 0.298756 | ||||||||
\(156\) | 232.201 | 0.119173 | ||||||||
\(157\) | −1286.97 | −0.654211 | −0.327106 | − | 0.944988i | \(-0.606073\pi\) | ||||
−0.327106 | + | 0.944988i | \(0.606073\pi\) | |||||||
\(158\) | −524.501 | −0.264095 | ||||||||
\(159\) | −2198.64 | −1.09662 | ||||||||
\(160\) | −873.121 | −0.431414 | ||||||||
\(161\) | 3783.47 | 1.85205 | ||||||||
\(162\) | −302.575 | −0.146744 | ||||||||
\(163\) | 532.561 | 0.255910 | 0.127955 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127955 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(164\) | 1378.26 | 0.656246 | ||||||||
\(165\) | −225.020 | −0.106168 | ||||||||
\(166\) | 595.714 | 0.278532 | ||||||||
\(167\) | 41.9542 | 0.0194402 | 0.00972011 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972011 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(168\) | 834.940 | 0.383435 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −1224.49 | −0.552435 | ||||||||
\(171\) | 421.643 | 0.188560 | ||||||||
\(172\) | −2026.19 | −0.898229 | ||||||||
\(173\) | −1066.50 | −0.468694 | −0.234347 | − | 0.972153i | \(-0.575295\pi\) | ||||
−0.234347 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(174\) | −1214.12 | −0.528977 | ||||||||
\(175\) | −3995.57 | −1.72592 | ||||||||
\(176\) | −1462.26 | −0.626263 | ||||||||
\(177\) | −689.346 | −0.292737 | ||||||||
\(178\) | −3989.25 | −1.67982 | ||||||||
\(179\) | 3174.61 | 1.32559 | 0.662797 | − | 0.748799i | \(-0.269369\pi\) | ||||
0.662797 | + | 0.748799i | \(0.269369\pi\) | |||||||
\(180\) | −209.397 | −0.0867086 | ||||||||
\(181\) | −2725.43 | −1.11923 | −0.559613 | − | 0.828754i | \(-0.689050\pi\) | ||||
−0.559613 | + | 0.828754i | \(0.689050\pi\) | |||||||
\(182\) | −1768.26 | −0.720177 | ||||||||
\(183\) | 326.829 | 0.132021 | ||||||||
\(184\) | 794.169 | 0.318190 | ||||||||
\(185\) | 625.290 | 0.248498 | ||||||||
\(186\) | 1653.31 | 0.651757 | ||||||||
\(187\) | −1610.09 | −0.629634 | ||||||||
\(188\) | 712.402 | 0.276368 | ||||||||
\(189\) | 983.149 | 0.378379 | ||||||||
\(190\) | 683.877 | 0.261124 | ||||||||
\(191\) | 784.888 | 0.297343 | 0.148672 | − | 0.988887i | \(-0.452500\pi\) | ||||
0.148672 | + | 0.988887i | \(0.452500\pi\) | |||||||
\(192\) | −675.511 | −0.253910 | ||||||||
\(193\) | −1255.87 | −0.468391 | −0.234195 | − | 0.972190i | \(-0.575246\pi\) | ||||
−0.234195 | + | 0.972190i | \(0.575246\pi\) | |||||||
\(194\) | −3208.34 | −1.18735 | ||||||||
\(195\) | −152.403 | −0.0559682 | ||||||||
\(196\) | 5852.08 | 2.13268 | ||||||||
\(197\) | −2777.35 | −1.00446 | −0.502229 | − | 0.864734i | \(-0.667487\pi\) | ||||
−0.502229 | + | 0.864734i | \(0.667487\pi\) | |||||||
\(198\) | −645.300 | −0.231613 | ||||||||
\(199\) | 1490.43 | 0.530924 | 0.265462 | − | 0.964121i | \(-0.414476\pi\) | ||||
0.265462 | + | 0.964121i | \(0.414476\pi\) | |||||||
\(200\) | −838.689 | −0.296521 | ||||||||
\(201\) | 31.1866 | 0.0109440 | ||||||||
\(202\) | 5880.27 | 2.04819 | ||||||||
\(203\) | 3945.01 | 1.36397 | ||||||||
\(204\) | −1498.30 | −0.514227 | ||||||||
\(205\) | −904.608 | −0.308198 | ||||||||
\(206\) | 484.582 | 0.163895 | ||||||||
\(207\) | 935.141 | 0.313994 | ||||||||
\(208\) | −990.370 | −0.330143 | ||||||||
\(209\) | 899.236 | 0.297614 | ||||||||
\(210\) | 1594.60 | 0.523991 | ||||||||
\(211\) | 2305.63 | 0.752255 | 0.376127 | − | 0.926568i | \(-0.377255\pi\) | ||||
0.376127 | + | 0.926568i | \(0.377255\pi\) | |||||||
\(212\) | −4363.48 | −1.41361 | ||||||||
\(213\) | −2607.60 | −0.838827 | ||||||||
\(214\) | 7311.97 | 2.33568 | ||||||||
\(215\) | 1329.87 | 0.421842 | ||||||||
\(216\) | 206.368 | 0.0650072 | ||||||||
\(217\) | −5372.07 | −1.68055 | ||||||||
\(218\) | −4590.07 | −1.42605 | ||||||||
\(219\) | −3297.21 | −1.01737 | ||||||||
\(220\) | −446.581 | −0.136857 | ||||||||
\(221\) | −1090.49 | −0.331920 | ||||||||
\(222\) | 1793.17 | 0.542116 | ||||||||
\(223\) | 1241.98 | 0.372956 | 0.186478 | − | 0.982459i | \(-0.440293\pi\) | ||||
0.186478 | + | 0.982459i | \(0.440293\pi\) | |||||||
\(224\) | 8135.83 | 2.42678 | ||||||||
\(225\) | −987.564 | −0.292612 | ||||||||
\(226\) | −6086.97 | −1.79159 | ||||||||
\(227\) | −1724.76 | −0.504300 | −0.252150 | − | 0.967688i | \(-0.581138\pi\) | ||||
−0.252150 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(228\) | 836.803 | 0.243064 | ||||||||
\(229\) | −3273.72 | −0.944688 | −0.472344 | − | 0.881414i | \(-0.656592\pi\) | ||||
−0.472344 | + | 0.881414i | \(0.656592\pi\) | |||||||
\(230\) | 1516.74 | 0.434829 | ||||||||
\(231\) | 2096.76 | 0.597215 | ||||||||
\(232\) | 828.076 | 0.234336 | ||||||||
\(233\) | −2129.52 | −0.598752 | −0.299376 | − | 0.954135i | \(-0.596778\pi\) | ||||
−0.299376 | + | 0.954135i | \(0.596778\pi\) | |||||||
\(234\) | −437.052 | −0.122098 | ||||||||
\(235\) | −467.577 | −0.129793 | ||||||||
\(236\) | −1368.10 | −0.377354 | ||||||||
\(237\) | 421.231 | 0.115451 | ||||||||
\(238\) | 11409.9 | 3.10754 | ||||||||
\(239\) | −5082.38 | −1.37553 | −0.687765 | − | 0.725933i | \(-0.741408\pi\) | ||||
−0.687765 | + | 0.725933i | \(0.741408\pi\) | |||||||
\(240\) | 893.108 | 0.240208 | ||||||||
\(241\) | 4765.65 | 1.27379 | 0.636893 | − | 0.770953i | \(-0.280219\pi\) | ||||
0.636893 | + | 0.770953i | \(0.280219\pi\) | |||||||
\(242\) | 3595.71 | 0.955127 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 648.634 | 0.170183 | ||||||||
\(245\) | −3840.95 | −1.00159 | ||||||||
\(246\) | −2594.19 | −0.672355 | ||||||||
\(247\) | 609.039 | 0.156892 | ||||||||
\(248\) | −1127.62 | −0.288727 | ||||||||
\(249\) | −478.422 | −0.121762 | ||||||||
\(250\) | −3426.44 | −0.866829 | ||||||||
\(251\) | −4339.96 | −1.09138 | −0.545689 | − | 0.837988i | \(-0.683732\pi\) | ||||
−0.545689 | + | 0.837988i | \(0.683732\pi\) | |||||||
\(252\) | 1951.18 | 0.487750 | ||||||||
\(253\) | 1994.37 | 0.495594 | ||||||||
\(254\) | −1031.41 | −0.254790 | ||||||||
\(255\) | 983.396 | 0.241500 | ||||||||
\(256\) | 5336.40 | 1.30283 | ||||||||
\(257\) | 4359.49 | 1.05812 | 0.529062 | − | 0.848583i | \(-0.322544\pi\) | ||||
0.529062 | + | 0.848583i | \(0.322544\pi\) | |||||||
\(258\) | 3813.72 | 0.920278 | ||||||||
\(259\) | −5826.51 | −1.39785 | ||||||||
\(260\) | −302.463 | −0.0721459 | ||||||||
\(261\) | 975.068 | 0.231246 | ||||||||
\(262\) | 359.444 | 0.0847576 | ||||||||
\(263\) | 608.077 | 0.142569 | 0.0712844 | − | 0.997456i | \(-0.477290\pi\) | ||||
0.0712844 | + | 0.997456i | \(0.477290\pi\) | |||||||
\(264\) | 440.120 | 0.102604 | ||||||||
\(265\) | 2863.92 | 0.663884 | ||||||||
\(266\) | −6372.43 | −1.46887 | ||||||||
\(267\) | 3203.80 | 0.734342 | ||||||||
\(268\) | 61.8938 | 0.0141073 | ||||||||
\(269\) | 3454.29 | 0.782942 | 0.391471 | − | 0.920190i | \(-0.371966\pi\) | ||||
0.391471 | + | 0.920190i | \(0.371966\pi\) | |||||||
\(270\) | 394.130 | 0.0888370 | ||||||||
\(271\) | 3703.72 | 0.830204 | 0.415102 | − | 0.909775i | \(-0.363746\pi\) | ||||
0.415102 | + | 0.909775i | \(0.363746\pi\) | |||||||
\(272\) | 6390.47 | 1.42456 | ||||||||
\(273\) | 1420.10 | 0.314830 | ||||||||
\(274\) | −9780.92 | −2.15652 | ||||||||
\(275\) | −2106.18 | −0.461844 | ||||||||
\(276\) | 1855.91 | 0.404755 | ||||||||
\(277\) | −3566.89 | −0.773696 | −0.386848 | − | 0.922144i | \(-0.626436\pi\) | ||||
−0.386848 | + | 0.922144i | \(0.626436\pi\) | |||||||
\(278\) | −7334.04 | −1.58225 | ||||||||
\(279\) | −1327.79 | −0.284920 | ||||||||
\(280\) | −1087.58 | −0.232127 | ||||||||
\(281\) | −117.474 | −0.0249392 | −0.0124696 | − | 0.999922i | \(-0.503969\pi\) | ||||
−0.0124696 | + | 0.999922i | \(0.503969\pi\) | |||||||
\(282\) | −1340.89 | −0.283152 | ||||||||
\(283\) | −1737.62 | −0.364984 | −0.182492 | − | 0.983207i | \(-0.558416\pi\) | ||||
−0.182492 | + | 0.983207i | \(0.558416\pi\) | |||||||
\(284\) | −5175.12 | −1.08129 | ||||||||
\(285\) | −549.226 | −0.114152 | ||||||||
\(286\) | −932.100 | −0.192714 | ||||||||
\(287\) | 8429.23 | 1.73366 | ||||||||
\(288\) | 2010.89 | 0.411434 | ||||||||
\(289\) | 2123.51 | 0.432223 | ||||||||
\(290\) | 1581.50 | 0.320237 | ||||||||
\(291\) | 2576.64 | 0.519057 | ||||||||
\(292\) | −6543.74 | −1.31145 | ||||||||
\(293\) | 1904.05 | 0.379643 | 0.189822 | − | 0.981819i | \(-0.439209\pi\) | ||||
0.189822 | + | 0.981819i | \(0.439209\pi\) | |||||||
\(294\) | −11014.9 | −2.18503 | ||||||||
\(295\) | 897.934 | 0.177219 | ||||||||
\(296\) | −1223.01 | −0.240156 | ||||||||
\(297\) | 518.245 | 0.101251 | ||||||||
\(298\) | 1124.80 | 0.218650 | ||||||||
\(299\) | 1350.76 | 0.261259 | ||||||||
\(300\) | −1959.95 | −0.377192 | ||||||||
\(301\) | −12391.8 | −2.37293 | ||||||||
\(302\) | −1281.17 | −0.244117 | ||||||||
\(303\) | −4722.49 | −0.895379 | ||||||||
\(304\) | −3569.08 | −0.673358 | ||||||||
\(305\) | −425.724 | −0.0799242 | ||||||||
\(306\) | 2820.13 | 0.526850 | ||||||||
\(307\) | 2862.39 | 0.532134 | 0.266067 | − | 0.963955i | \(-0.414276\pi\) | ||||
0.266067 | + | 0.963955i | \(0.414276\pi\) | |||||||
\(308\) | 4161.29 | 0.769842 | ||||||||
\(309\) | −389.172 | −0.0716479 | ||||||||
\(310\) | −2153.58 | −0.394566 | ||||||||
\(311\) | 4201.55 | 0.766071 | 0.383036 | − | 0.923734i | \(-0.374879\pi\) | ||||
0.383036 | + | 0.923734i | \(0.374879\pi\) | |||||||
\(312\) | 298.087 | 0.0540892 | ||||||||
\(313\) | 3427.74 | 0.619002 | 0.309501 | − | 0.950899i | \(-0.399838\pi\) | ||||
0.309501 | + | 0.950899i | \(0.399838\pi\) | |||||||
\(314\) | 4807.45 | 0.864014 | ||||||||
\(315\) | −1280.64 | −0.229066 | ||||||||
\(316\) | 835.987 | 0.148823 | ||||||||
\(317\) | 1676.09 | 0.296966 | 0.148483 | − | 0.988915i | \(-0.452561\pi\) | ||||
0.148483 | + | 0.988915i | \(0.452561\pi\) | |||||||
\(318\) | 8212.99 | 1.44831 | ||||||||
\(319\) | 2079.52 | 0.364987 | ||||||||
\(320\) | 879.912 | 0.153714 | ||||||||
\(321\) | −5872.30 | −1.02106 | ||||||||
\(322\) | −14133.1 | −2.44599 | ||||||||
\(323\) | −3929.89 | −0.676982 | ||||||||
\(324\) | 482.264 | 0.0826928 | ||||||||
\(325\) | −1426.48 | −0.243468 | ||||||||
\(326\) | −1989.37 | −0.337979 | ||||||||
\(327\) | 3686.32 | 0.623406 | ||||||||
\(328\) | 1769.34 | 0.297851 | ||||||||
\(329\) | 4356.93 | 0.730108 | ||||||||
\(330\) | 840.560 | 0.140216 | ||||||||
\(331\) | 11156.6 | 1.85264 | 0.926319 | − | 0.376740i | \(-0.122955\pi\) | ||||
0.926319 | + | 0.376740i | \(0.122955\pi\) | |||||||
\(332\) | −949.490 | −0.156958 | ||||||||
\(333\) | −1440.11 | −0.236990 | ||||||||
\(334\) | −156.720 | −0.0256746 | ||||||||
\(335\) | −40.6233 | −0.00662534 | ||||||||
\(336\) | −8322.07 | −1.35121 | ||||||||
\(337\) | 1636.44 | 0.264517 | 0.132259 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132259 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(338\) | −631.298 | −0.101592 | ||||||||
\(339\) | 4888.49 | 0.783205 | ||||||||
\(340\) | 1951.67 | 0.311307 | ||||||||
\(341\) | −2831.77 | −0.449703 | ||||||||
\(342\) | −1575.04 | −0.249031 | ||||||||
\(343\) | 23300.7 | 3.66799 | ||||||||
\(344\) | −2601.10 | −0.407681 | ||||||||
\(345\) | −1218.10 | −0.190088 | ||||||||
\(346\) | 3983.88 | 0.619002 | ||||||||
\(347\) | −2977.87 | −0.460693 | −0.230347 | − | 0.973109i | \(-0.573986\pi\) | ||||
−0.230347 | + | 0.973109i | \(0.573986\pi\) | |||||||
\(348\) | 1935.15 | 0.298088 | ||||||||
\(349\) | 9847.29 | 1.51035 | 0.755177 | − | 0.655521i | \(-0.227551\pi\) | ||||
0.755177 | + | 0.655521i | \(0.227551\pi\) | |||||||
\(350\) | 14925.4 | 2.27942 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 4288.62 | 0.649387 | ||||||||
\(353\) | 4687.34 | 0.706747 | 0.353374 | − | 0.935482i | \(-0.385034\pi\) | ||||
0.353374 | + | 0.935482i | \(0.385034\pi\) | |||||||
\(354\) | 2575.05 | 0.386616 | ||||||||
\(355\) | 3396.63 | 0.507816 | ||||||||
\(356\) | 6358.35 | 0.946606 | ||||||||
\(357\) | −9163.38 | −1.35848 | ||||||||
\(358\) | −11858.7 | −1.75070 | ||||||||
\(359\) | −2069.88 | −0.304301 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(360\) | −268.812 | −0.0393546 | ||||||||
\(361\) | −4664.16 | −0.680005 | ||||||||
\(362\) | 10180.8 | 1.47816 | ||||||||
\(363\) | −2887.74 | −0.417540 | ||||||||
\(364\) | 2818.38 | 0.405833 | ||||||||
\(365\) | 4294.91 | 0.615906 | ||||||||
\(366\) | −1220.87 | −0.174360 | ||||||||
\(367\) | −7299.16 | −1.03818 | −0.519092 | − | 0.854719i | \(-0.673730\pi\) | ||||
−0.519092 | + | 0.854719i | \(0.673730\pi\) | |||||||
\(368\) | −7915.70 | −1.12129 | ||||||||
\(369\) | 2083.41 | 0.293924 | ||||||||
\(370\) | −2335.76 | −0.328191 | ||||||||
\(371\) | −26686.3 | −3.73446 | ||||||||
\(372\) | −2635.16 | −0.367277 | ||||||||
\(373\) | −8964.32 | −1.24438 | −0.622192 | − | 0.782865i | \(-0.713758\pi\) | ||||
−0.622192 | + | 0.782865i | \(0.713758\pi\) | |||||||
\(374\) | 6014.48 | 0.831554 | ||||||||
\(375\) | 2751.80 | 0.378940 | ||||||||
\(376\) | 914.541 | 0.125436 | ||||||||
\(377\) | 1408.43 | 0.192408 | ||||||||
\(378\) | −3672.54 | −0.499723 | ||||||||
\(379\) | −4399.26 | −0.596239 | −0.298120 | − | 0.954529i | \(-0.596359\pi\) | ||||
−0.298120 | + | 0.954529i | \(0.596359\pi\) | |||||||
\(380\) | −1090.01 | −0.147148 | ||||||||
\(381\) | 828.337 | 0.111383 | ||||||||
\(382\) | −2931.94 | −0.392700 | ||||||||
\(383\) | 3529.74 | 0.470917 | 0.235459 | − | 0.971884i | \(-0.424341\pi\) | ||||
0.235459 | + | 0.971884i | \(0.424341\pi\) | |||||||
\(384\) | −2839.01 | −0.377286 | ||||||||
\(385\) | −2731.21 | −0.361547 | ||||||||
\(386\) | 4691.28 | 0.618601 | ||||||||
\(387\) | −3062.82 | −0.402305 | ||||||||
\(388\) | 5113.68 | 0.669092 | ||||||||
\(389\) | −3034.77 | −0.395549 | −0.197775 | − | 0.980248i | \(-0.563371\pi\) | ||||
−0.197775 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(390\) | 569.299 | 0.0739169 | ||||||||
\(391\) | −8715.93 | −1.12732 | ||||||||
\(392\) | 7512.57 | 0.967964 | ||||||||
\(393\) | −288.672 | −0.0370523 | ||||||||
\(394\) | 10374.8 | 1.32658 | ||||||||
\(395\) | −548.690 | −0.0698927 | ||||||||
\(396\) | 1028.52 | 0.130518 | ||||||||
\(397\) | −3997.36 | −0.505344 | −0.252672 | − | 0.967552i | \(-0.581309\pi\) | ||||
−0.252672 | + | 0.967552i | \(0.581309\pi\) | |||||||
\(398\) | −5567.49 | −0.701188 | ||||||||
\(399\) | 5117.75 | 0.642125 | ||||||||
\(400\) | 8359.44 | 1.04493 | ||||||||
\(401\) | −9092.88 | −1.13236 | −0.566181 | − | 0.824281i | \(-0.691580\pi\) | ||||
−0.566181 | + | 0.824281i | \(0.691580\pi\) | |||||||
\(402\) | −116.497 | −0.0144536 | ||||||||
\(403\) | −1917.92 | −0.237067 | ||||||||
\(404\) | −9372.38 | −1.15419 | ||||||||
\(405\) | −316.529 | −0.0388357 | ||||||||
\(406\) | −14736.5 | −1.80138 | ||||||||
\(407\) | −3071.32 | −0.374053 | ||||||||
\(408\) | −1923.44 | −0.233393 | ||||||||
\(409\) | 7143.54 | 0.863631 | 0.431816 | − | 0.901962i | \(-0.357873\pi\) | ||||
0.431816 | + | 0.901962i | \(0.357873\pi\) | |||||||
\(410\) | 3379.15 | 0.407036 | ||||||||
\(411\) | 7855.13 | 0.942738 | ||||||||
\(412\) | −772.361 | −0.0923579 | ||||||||
\(413\) | −8367.04 | −0.996889 | ||||||||
\(414\) | −3493.21 | −0.414691 | ||||||||
\(415\) | 623.187 | 0.0737134 | ||||||||
\(416\) | 2904.62 | 0.342333 | ||||||||
\(417\) | 5890.02 | 0.691692 | ||||||||
\(418\) | −3359.09 | −0.393058 | ||||||||
\(419\) | 8213.84 | 0.957691 | 0.478845 | − | 0.877899i | \(-0.341055\pi\) | ||||
0.478845 | + | 0.877899i | \(0.341055\pi\) | |||||||
\(420\) | −2541.59 | −0.295278 | ||||||||
\(421\) | −7997.40 | −0.925818 | −0.462909 | − | 0.886406i | \(-0.653194\pi\) | ||||
−0.462909 | + | 0.886406i | \(0.653194\pi\) | |||||||
\(422\) | −8612.64 | −0.993499 | ||||||||
\(423\) | 1076.88 | 0.123782 | ||||||||
\(424\) | −5601.58 | −0.641597 | ||||||||
\(425\) | 9204.53 | 1.05055 | ||||||||
\(426\) | 9740.68 | 1.10783 | ||||||||
\(427\) | 3966.94 | 0.449587 | ||||||||
\(428\) | −11654.3 | −1.31620 | ||||||||
\(429\) | 748.577 | 0.0842462 | ||||||||
\(430\) | −4967.70 | −0.557125 | ||||||||
\(431\) | −13694.8 | −1.53053 | −0.765263 | − | 0.643718i | \(-0.777391\pi\) | ||||
−0.765263 | + | 0.643718i | \(0.777391\pi\) | |||||||
\(432\) | −2056.92 | −0.229083 | ||||||||
\(433\) | 6716.57 | 0.745445 | 0.372722 | − | 0.927943i | \(-0.378424\pi\) | ||||
0.372722 | + | 0.927943i | \(0.378424\pi\) | |||||||
\(434\) | 20067.3 | 2.21950 | ||||||||
\(435\) | −1270.11 | −0.139993 | ||||||||
\(436\) | 7315.97 | 0.803604 | ||||||||
\(437\) | 4867.84 | 0.532862 | ||||||||
\(438\) | 12316.7 | 1.34364 | ||||||||
\(439\) | −5933.32 | −0.645061 | −0.322531 | − | 0.946559i | \(-0.604534\pi\) | ||||
−0.322531 | + | 0.946559i | \(0.604534\pi\) | |||||||
\(440\) | −573.295 | −0.0621154 | ||||||||
\(441\) | 8846.12 | 0.955201 | ||||||||
\(442\) | 4073.52 | 0.438365 | ||||||||
\(443\) | −6923.40 | −0.742530 | −0.371265 | − | 0.928527i | \(-0.621076\pi\) | ||||
−0.371265 | + | 0.928527i | \(0.621076\pi\) | |||||||
\(444\) | −2858.08 | −0.305492 | ||||||||
\(445\) | −4173.23 | −0.444562 | ||||||||
\(446\) | −4639.41 | −0.492561 | ||||||||
\(447\) | −903.333 | −0.0955843 | ||||||||
\(448\) | −8199.11 | −0.864669 | ||||||||
\(449\) | 8886.78 | 0.934061 | 0.467030 | − | 0.884241i | \(-0.345324\pi\) | ||||
0.467030 | + | 0.884241i | \(0.345324\pi\) | |||||||
\(450\) | 3689.04 | 0.386451 | ||||||||
\(451\) | 4443.28 | 0.463916 | ||||||||
\(452\) | 9701.84 | 1.00959 | ||||||||
\(453\) | 1028.92 | 0.106717 | ||||||||
\(454\) | 6442.81 | 0.666026 | ||||||||
\(455\) | −1849.81 | −0.190594 | ||||||||
\(456\) | 1074.24 | 0.110320 | ||||||||
\(457\) | 10965.0 | 1.12237 | 0.561184 | − | 0.827691i | \(-0.310346\pi\) | ||||
0.561184 | + | 0.827691i | \(0.310346\pi\) | |||||||
\(458\) | 12228.9 | 1.24764 | ||||||||
\(459\) | −2264.87 | −0.230316 | ||||||||
\(460\) | −2417.48 | −0.245034 | ||||||||
\(461\) | 10069.2 | 1.01729 | 0.508644 | − | 0.860977i | \(-0.330147\pi\) | ||||
0.508644 | + | 0.860977i | \(0.330147\pi\) | |||||||
\(462\) | −7832.42 | −0.788739 | ||||||||
\(463\) | 5599.72 | 0.562076 | 0.281038 | − | 0.959697i | \(-0.409321\pi\) | ||||
0.281038 | + | 0.959697i | \(0.409321\pi\) | |||||||
\(464\) | −8253.66 | −0.825790 | ||||||||
\(465\) | 1729.56 | 0.172487 | ||||||||
\(466\) | 7954.78 | 0.790769 | ||||||||
\(467\) | −13247.8 | −1.31271 | −0.656355 | − | 0.754452i | \(-0.727903\pi\) | ||||
−0.656355 | + | 0.754452i | \(0.727903\pi\) | |||||||
\(468\) | 696.604 | 0.0688046 | ||||||||
\(469\) | 378.532 | 0.0372686 | ||||||||
\(470\) | 1746.63 | 0.171417 | ||||||||
\(471\) | −3860.90 | −0.377709 | ||||||||
\(472\) | −1756.28 | −0.171270 | ||||||||
\(473\) | −6532.08 | −0.634979 | ||||||||
\(474\) | −1573.50 | −0.152476 | ||||||||
\(475\) | −5140.73 | −0.496575 | ||||||||
\(476\) | −18185.9 | −1.75115 | ||||||||
\(477\) | −6595.92 | −0.633137 | ||||||||
\(478\) | 18985.2 | 1.81666 | ||||||||
\(479\) | 16725.4 | 1.59541 | 0.797707 | − | 0.603045i | \(-0.206046\pi\) | ||||
0.797707 | + | 0.603045i | \(0.206046\pi\) | |||||||
\(480\) | −2619.36 | −0.249077 | ||||||||
\(481\) | −2080.16 | −0.197187 | ||||||||
\(482\) | −17802.0 | −1.68228 | ||||||||
\(483\) | 11350.4 | 1.06928 | ||||||||
\(484\) | −5731.09 | −0.538231 | ||||||||
\(485\) | −3356.30 | −0.314231 | ||||||||
\(486\) | −907.724 | −0.0847226 | ||||||||
\(487\) | −5305.86 | −0.493699 | −0.246850 | − | 0.969054i | \(-0.579395\pi\) | ||||
−0.246850 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(488\) | 832.679 | 0.0772410 | ||||||||
\(489\) | 1597.68 | 0.147750 | ||||||||
\(490\) | 14347.8 | 1.32279 | ||||||||
\(491\) | 16200.2 | 1.48901 | 0.744506 | − | 0.667616i | \(-0.232685\pi\) | ||||
0.744506 | + | 0.667616i | \(0.232685\pi\) | |||||||
\(492\) | 4134.79 | 0.378884 | ||||||||
\(493\) | −9088.05 | −0.830234 | ||||||||
\(494\) | −2275.06 | −0.207206 | ||||||||
\(495\) | −675.060 | −0.0612963 | ||||||||
\(496\) | 11239.3 | 1.01746 | ||||||||
\(497\) | −31650.2 | −2.85655 | ||||||||
\(498\) | 1787.14 | 0.160811 | ||||||||
\(499\) | 4392.70 | 0.394076 | 0.197038 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197038 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(500\) | 5461.30 | 0.488473 | ||||||||
\(501\) | 125.863 | 0.0112238 | ||||||||
\(502\) | 16211.9 | 1.44138 | ||||||||
\(503\) | −14955.2 | −1.32568 | −0.662841 | − | 0.748760i | \(-0.730650\pi\) | ||||
−0.662841 | + | 0.748760i | \(0.730650\pi\) | |||||||
\(504\) | 2504.82 | 0.221376 | ||||||||
\(505\) | 6151.46 | 0.542052 | ||||||||
\(506\) | −7449.96 | −0.654528 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 1643.94 | 0.143579 | ||||||||
\(509\) | 13403.4 | 1.16719 | 0.583593 | − | 0.812047i | \(-0.301647\pi\) | ||||
0.583593 | + | 0.812047i | \(0.301647\pi\) | |||||||
\(510\) | −3673.46 | −0.318948 | ||||||||
\(511\) | −40020.4 | −3.46458 | ||||||||
\(512\) | −12363.4 | −1.06716 | ||||||||
\(513\) | 1264.93 | 0.108865 | ||||||||
\(514\) | −16284.8 | −1.39746 | ||||||||
\(515\) | 506.930 | 0.0433748 | ||||||||
\(516\) | −6078.57 | −0.518593 | ||||||||
\(517\) | 2296.66 | 0.195371 | ||||||||
\(518\) | 21764.9 | 1.84613 | ||||||||
\(519\) | −3199.49 | −0.270601 | ||||||||
\(520\) | −388.284 | −0.0327450 | ||||||||
\(521\) | 19643.0 | 1.65178 | 0.825888 | − | 0.563834i | \(-0.190674\pi\) | ||||
0.825888 | + | 0.563834i | \(0.190674\pi\) | |||||||
\(522\) | −3642.35 | −0.305405 | ||||||||
\(523\) | 14657.4 | 1.22548 | 0.612738 | − | 0.790286i | \(-0.290068\pi\) | ||||
0.612738 | + | 0.790286i | \(0.290068\pi\) | |||||||
\(524\) | −572.906 | −0.0477624 | ||||||||
\(525\) | −11986.7 | −0.996462 | ||||||||
\(526\) | −2271.46 | −0.188290 | ||||||||
\(527\) | 12375.6 | 1.02294 | ||||||||
\(528\) | −4386.79 | −0.361573 | ||||||||
\(529\) | −1370.83 | −0.112668 | ||||||||
\(530\) | −10698.1 | −0.876788 | ||||||||
\(531\) | −2068.04 | −0.169012 | ||||||||
\(532\) | 10156.8 | 0.827733 | ||||||||
\(533\) | 3009.37 | 0.244560 | ||||||||
\(534\) | −11967.8 | −0.969842 | ||||||||
\(535\) | 7649.19 | 0.618137 | ||||||||
\(536\) | 79.4558 | 0.00640292 | ||||||||
\(537\) | 9523.82 | 0.765332 | ||||||||
\(538\) | −12903.4 | −1.03403 | ||||||||
\(539\) | 18866.1 | 1.50764 | ||||||||
\(540\) | −628.192 | −0.0500612 | ||||||||
\(541\) | 13921.3 | 1.10633 | 0.553164 | − | 0.833072i | \(-0.313420\pi\) | ||||
0.553164 | + | 0.833072i | \(0.313420\pi\) | |||||||
\(542\) | −13835.2 | −1.09645 | ||||||||
\(543\) | −8176.30 | −0.646185 | ||||||||
\(544\) | −18742.4 | −1.47716 | ||||||||
\(545\) | −4801.75 | −0.377403 | ||||||||
\(546\) | −5304.79 | −0.415795 | ||||||||
\(547\) | −2324.11 | −0.181667 | −0.0908335 | − | 0.995866i | \(-0.528953\pi\) | ||||
−0.0908335 | + | 0.995866i | \(0.528953\pi\) | |||||||
\(548\) | 15589.5 | 1.21524 | ||||||||
\(549\) | 980.488 | 0.0762226 | ||||||||
\(550\) | 7867.60 | 0.609955 | ||||||||
\(551\) | 5075.68 | 0.392434 | ||||||||
\(552\) | 2382.51 | 0.183707 | ||||||||
\(553\) | 5112.75 | 0.393158 | ||||||||
\(554\) | 13324.1 | 1.02182 | ||||||||
\(555\) | 1875.87 | 0.143471 | ||||||||
\(556\) | 11689.5 | 0.891628 | ||||||||
\(557\) | −16962.8 | −1.29037 | −0.645185 | − | 0.764027i | \(-0.723220\pi\) | ||||
−0.645185 | + | 0.764027i | \(0.723220\pi\) | |||||||
\(558\) | 4959.94 | 0.376292 | ||||||||
\(559\) | −4424.08 | −0.334738 | ||||||||
\(560\) | 10840.2 | 0.818006 | ||||||||
\(561\) | −4830.27 | −0.363519 | ||||||||
\(562\) | 438.823 | 0.0329370 | ||||||||
\(563\) | −389.000 | −0.0291197 | −0.0145599 | − | 0.999894i | \(-0.504635\pi\) | ||||
−0.0145599 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(564\) | 2137.21 | 0.159561 | ||||||||
\(565\) | −6367.69 | −0.474143 | ||||||||
\(566\) | 6490.85 | 0.482033 | ||||||||
\(567\) | 2949.45 | 0.218457 | ||||||||
\(568\) | −6643.53 | −0.490768 | ||||||||
\(569\) | 2217.56 | 0.163383 | 0.0816914 | − | 0.996658i | \(-0.473968\pi\) | ||||
0.0816914 | + | 0.996658i | \(0.473968\pi\) | |||||||
\(570\) | 2051.63 | 0.150760 | ||||||||
\(571\) | −17087.3 | −1.25233 | −0.626167 | − | 0.779689i | \(-0.715377\pi\) | ||||
−0.626167 | + | 0.779689i | \(0.715377\pi\) | |||||||
\(572\) | 1485.65 | 0.108598 | ||||||||
\(573\) | 2354.67 | 0.171671 | ||||||||
\(574\) | −31487.3 | −2.28964 | ||||||||
\(575\) | −11401.4 | −0.826906 | ||||||||
\(576\) | −2026.53 | −0.146595 | ||||||||
\(577\) | −3977.26 | −0.286959 | −0.143480 | − | 0.989653i | \(-0.545829\pi\) | ||||
−0.143480 | + | 0.989653i | \(0.545829\pi\) | |||||||
\(578\) | −7932.35 | −0.570835 | ||||||||
\(579\) | −3767.61 | −0.270425 | ||||||||
\(580\) | −2520.70 | −0.180459 | ||||||||
\(581\) | −5806.92 | −0.414650 | ||||||||
\(582\) | −9625.02 | −0.685516 | ||||||||
\(583\) | −14067.1 | −0.999312 | ||||||||
\(584\) | −8400.48 | −0.595230 | ||||||||
\(585\) | −457.208 | −0.0323132 | ||||||||
\(586\) | −7112.54 | −0.501393 | ||||||||
\(587\) | −16880.3 | −1.18693 | −0.593463 | − | 0.804861i | \(-0.702240\pi\) | ||||
−0.593463 | + | 0.804861i | \(0.702240\pi\) | |||||||
\(588\) | 17556.2 | 1.23131 | ||||||||
\(589\) | −6911.75 | −0.483521 | ||||||||
\(590\) | −3354.22 | −0.234053 | ||||||||
\(591\) | −8332.06 | −0.579924 | ||||||||
\(592\) | 12190.1 | 0.846301 | ||||||||
\(593\) | 2423.25 | 0.167810 | 0.0839048 | − | 0.996474i | \(-0.473261\pi\) | ||||
0.0839048 | + | 0.996474i | \(0.473261\pi\) | |||||||
\(594\) | −1935.90 | −0.133722 | ||||||||
\(595\) | 11936.1 | 0.822408 | ||||||||
\(596\) | −1792.78 | −0.123213 | ||||||||
\(597\) | 4471.29 | 0.306529 | ||||||||
\(598\) | −5045.75 | −0.345044 | ||||||||
\(599\) | −3900.55 | −0.266064 | −0.133032 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133032 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(600\) | −2516.07 | −0.171197 | ||||||||
\(601\) | 28653.4 | 1.94476 | 0.972378 | − | 0.233413i | \(-0.0749893\pi\) | ||||
0.972378 | + | 0.233413i | \(0.0749893\pi\) | |||||||
\(602\) | 46289.5 | 3.13392 | ||||||||
\(603\) | 93.5599 | 0.00631850 | ||||||||
\(604\) | 2042.02 | 0.137564 | ||||||||
\(605\) | 3761.54 | 0.252774 | ||||||||
\(606\) | 17640.8 | 1.18252 | ||||||||
\(607\) | 214.736 | 0.0143589 | 0.00717946 | − | 0.999974i | \(-0.497715\pi\) | ||||
0.00717946 | + | 0.999974i | \(0.497715\pi\) | |||||||
\(608\) | 10467.6 | 0.698220 | ||||||||
\(609\) | 11835.0 | 0.787487 | ||||||||
\(610\) | 1590.29 | 0.105555 | ||||||||
\(611\) | 1555.49 | 0.102993 | ||||||||
\(612\) | −4494.91 | −0.296889 | ||||||||
\(613\) | 26438.5 | 1.74199 | 0.870996 | − | 0.491290i | \(-0.163475\pi\) | ||||
0.870996 | + | 0.491290i | \(0.163475\pi\) | |||||||
\(614\) | −10692.4 | −0.702787 | ||||||||
\(615\) | −2713.82 | −0.177938 | ||||||||
\(616\) | 5342.02 | 0.349409 | ||||||||
\(617\) | 6700.96 | 0.437229 | 0.218615 | − | 0.975811i | \(-0.429846\pi\) | ||||
0.218615 | + | 0.975811i | \(0.429846\pi\) | |||||||
\(618\) | 1453.75 | 0.0946250 | ||||||||
\(619\) | −27319.1 | −1.77391 | −0.886953 | − | 0.461860i | \(-0.847182\pi\) | ||||
−0.886953 | + | 0.461860i | \(0.847182\pi\) | |||||||
\(620\) | 3432.53 | 0.222345 | ||||||||
\(621\) | 2805.42 | 0.181285 | ||||||||
\(622\) | −15694.9 | −1.01175 | ||||||||
\(623\) | 38886.6 | 2.50074 | ||||||||
\(624\) | −2971.11 | −0.190608 | ||||||||
\(625\) | 10131.7 | 0.648429 | ||||||||
\(626\) | −12804.3 | −0.817513 | ||||||||
\(627\) | 2697.71 | 0.171828 | ||||||||
\(628\) | −7662.45 | −0.486887 | ||||||||
\(629\) | 13422.4 | 0.850855 | ||||||||
\(630\) | 4783.81 | 0.302526 | ||||||||
\(631\) | −7126.87 | −0.449629 | −0.224815 | − | 0.974402i | \(-0.572178\pi\) | ||||
−0.224815 | + | 0.974402i | \(0.572178\pi\) | |||||||
\(632\) | 1073.19 | 0.0675463 | ||||||||
\(633\) | 6916.88 | 0.434315 | ||||||||
\(634\) | −6261.00 | −0.392202 | ||||||||
\(635\) | −1078.98 | −0.0674301 | ||||||||
\(636\) | −13090.4 | −0.816147 | ||||||||
\(637\) | 12777.7 | 0.794775 | ||||||||
\(638\) | −7768.04 | −0.482037 | ||||||||
\(639\) | −7822.81 | −0.484297 | ||||||||
\(640\) | 3698.06 | 0.228404 | ||||||||
\(641\) | 23615.0 | 1.45513 | 0.727565 | − | 0.686039i | \(-0.240652\pi\) | ||||
0.727565 | + | 0.686039i | \(0.240652\pi\) | |||||||
\(642\) | 21935.9 | 1.34851 | ||||||||
\(643\) | −8144.41 | −0.499509 | −0.249755 | − | 0.968309i | \(-0.580350\pi\) | ||||
−0.249755 | + | 0.968309i | \(0.580350\pi\) | |||||||
\(644\) | 22526.3 | 1.37836 | ||||||||
\(645\) | 3989.60 | 0.243551 | ||||||||
\(646\) | 14680.1 | 0.894086 | ||||||||
\(647\) | 9682.00 | 0.588313 | 0.294157 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294157 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(648\) | 619.103 | 0.0375319 | ||||||||
\(649\) | −4410.50 | −0.266760 | ||||||||
\(650\) | 5328.61 | 0.321546 | ||||||||
\(651\) | −16116.2 | −0.970268 | ||||||||
\(652\) | 3170.80 | 0.190457 | ||||||||
\(653\) | −18193.6 | −1.09030 | −0.545152 | − | 0.838337i | \(-0.683528\pi\) | ||||
−0.545152 | + | 0.838337i | \(0.683528\pi\) | |||||||
\(654\) | −13770.2 | −0.823329 | ||||||||
\(655\) | 376.020 | 0.0224310 | ||||||||
\(656\) | −17635.5 | −1.04962 | ||||||||
\(657\) | −9891.64 | −0.587381 | ||||||||
\(658\) | −16275.3 | −0.964250 | ||||||||
\(659\) | 9300.88 | 0.549789 | 0.274895 | − | 0.961474i | \(-0.411357\pi\) | ||||
0.274895 | + | 0.961474i | \(0.411357\pi\) | |||||||
\(660\) | −1339.74 | −0.0790143 | ||||||||
\(661\) | −5437.29 | −0.319949 | −0.159974 | − | 0.987121i | \(-0.551141\pi\) | ||||
−0.159974 | + | 0.987121i | \(0.551141\pi\) | |||||||
\(662\) | −41675.4 | −2.44677 | ||||||||
\(663\) | −3271.47 | −0.191634 | ||||||||
\(664\) | −1218.90 | −0.0712388 | ||||||||
\(665\) | −6666.32 | −0.388735 | ||||||||
\(666\) | 5379.51 | 0.312991 | ||||||||
\(667\) | 11257.1 | 0.653489 | ||||||||
\(668\) | 249.791 | 0.0144681 | ||||||||
\(669\) | 3725.94 | 0.215326 | ||||||||
\(670\) | 151.748 | 0.00875005 | ||||||||
\(671\) | 2091.08 | 0.120306 | ||||||||
\(672\) | 24407.5 | 1.40110 | ||||||||
\(673\) | −8682.75 | −0.497319 | −0.248659 | − | 0.968591i | \(-0.579990\pi\) | ||||
−0.248659 | + | 0.968591i | \(0.579990\pi\) | |||||||
\(674\) | −6112.89 | −0.349347 | ||||||||
\(675\) | −2962.69 | −0.168939 | ||||||||
\(676\) | 1006.21 | 0.0572489 | ||||||||
\(677\) | 13300.1 | 0.755041 | 0.377521 | − | 0.926001i | \(-0.376777\pi\) | ||||
0.377521 | + | 0.926001i | \(0.376777\pi\) | |||||||
\(678\) | −18260.9 | −1.03437 | ||||||||
\(679\) | 31274.4 | 1.76760 | ||||||||
\(680\) | 2505.45 | 0.141293 | ||||||||
\(681\) | −5174.27 | −0.291158 | ||||||||
\(682\) | 10578.0 | 0.593921 | ||||||||
\(683\) | −504.175 | −0.0282455 | −0.0141228 | − | 0.999900i | \(-0.504496\pi\) | ||||
−0.0141228 | + | 0.999900i | \(0.504496\pi\) | |||||||
\(684\) | 2510.41 | 0.140333 | ||||||||
\(685\) | −10232.0 | −0.570722 | ||||||||
\(686\) | −87039.6 | −4.84429 | ||||||||
\(687\) | −9821.16 | −0.545416 | ||||||||
\(688\) | 25925.9 | 1.43665 | ||||||||
\(689\) | −9527.43 | −0.526802 | ||||||||
\(690\) | 4550.21 | 0.251049 | ||||||||
\(691\) | 13443.8 | 0.740124 | 0.370062 | − | 0.929007i | \(-0.379336\pi\) | ||||
0.370062 | + | 0.929007i | \(0.379336\pi\) | |||||||
\(692\) | −6349.79 | −0.348819 | ||||||||
\(693\) | 6290.28 | 0.344802 | ||||||||
\(694\) | 11123.8 | 0.608435 | ||||||||
\(695\) | −7672.27 | −0.418742 | ||||||||
\(696\) | 2484.23 | 0.135294 | ||||||||
\(697\) | −19418.3 | −1.05527 | ||||||||
\(698\) | −36784.4 | −1.99472 | ||||||||
\(699\) | −6388.55 | −0.345690 | ||||||||
\(700\) | −23789.1 | −1.28449 | ||||||||
\(701\) | 28735.6 | 1.54826 | 0.774128 | − | 0.633030i | \(-0.218189\pi\) | ||||
0.774128 | + | 0.633030i | \(0.218189\pi\) | |||||||
\(702\) | −1311.16 | −0.0704935 | ||||||||
\(703\) | −7496.44 | −0.402181 | ||||||||
\(704\) | −4321.98 | −0.231379 | ||||||||
\(705\) | −1402.73 | −0.0749361 | ||||||||
\(706\) | −17509.5 | −0.933398 | ||||||||
\(707\) | −57319.9 | −3.04913 | ||||||||
\(708\) | −4104.29 | −0.217865 | ||||||||
\(709\) | 17610.2 | 0.932812 | 0.466406 | − | 0.884571i | \(-0.345549\pi\) | ||||
0.466406 | + | 0.884571i | \(0.345549\pi\) | |||||||
\(710\) | −12688.1 | −0.670670 | ||||||||
\(711\) | 1263.69 | 0.0666557 | ||||||||
\(712\) | 8162.48 | 0.429638 | ||||||||
\(713\) | −15329.3 | −0.805168 | ||||||||
\(714\) | 34229.7 | 1.79414 | ||||||||
\(715\) | −975.087 | −0.0510016 | ||||||||
\(716\) | 18901.2 | 0.986553 | ||||||||
\(717\) | −15247.1 | −0.794163 | ||||||||
\(718\) | 7732.02 | 0.401889 | ||||||||
\(719\) | −9226.04 | −0.478544 | −0.239272 | − | 0.970953i | \(-0.576909\pi\) | ||||
−0.239272 | + | 0.970953i | \(0.576909\pi\) | |||||||
\(720\) | 2679.32 | 0.138684 | ||||||||
\(721\) | −4723.63 | −0.243990 | ||||||||
\(722\) | 17422.9 | 0.898079 | ||||||||
\(723\) | 14296.9 | 0.735420 | ||||||||
\(724\) | −16226.9 | −0.832967 | ||||||||
\(725\) | −11888.2 | −0.608987 | ||||||||
\(726\) | 10787.1 | 0.551443 | ||||||||
\(727\) | 33246.0 | 1.69604 | 0.848022 | − | 0.529961i | \(-0.177793\pi\) | ||||
0.848022 | + | 0.529961i | \(0.177793\pi\) | |||||||
\(728\) | 3618.07 | 0.184196 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −16043.6 | −0.813424 | ||||||||
\(731\) | 28546.9 | 1.44438 | ||||||||
\(732\) | 1945.90 | 0.0982549 | ||||||||
\(733\) | −4423.26 | −0.222888 | −0.111444 | − | 0.993771i | \(-0.535548\pi\) | ||||
−0.111444 | + | 0.993771i | \(0.535548\pi\) | |||||||
\(734\) | 27266.0 | 1.37112 | ||||||||
\(735\) | −11522.8 | −0.578267 | ||||||||
\(736\) | 23215.6 | 1.16269 | ||||||||
\(737\) | 199.535 | 0.00997281 | ||||||||
\(738\) | −7782.56 | −0.388184 | ||||||||
\(739\) | −4529.56 | −0.225470 | −0.112735 | − | 0.993625i | \(-0.535961\pi\) | ||||
−0.112735 | + | 0.993625i | \(0.535961\pi\) | |||||||
\(740\) | 3722.90 | 0.184941 | ||||||||
\(741\) | 1827.12 | 0.0905814 | ||||||||
\(742\) | 99686.4 | 4.93208 | ||||||||
\(743\) | 10851.5 | 0.535803 | 0.267901 | − | 0.963446i | \(-0.413670\pi\) | ||||
0.267901 | + | 0.963446i | \(0.413670\pi\) | |||||||
\(744\) | −3382.87 | −0.166696 | ||||||||
\(745\) | 1176.67 | 0.0578656 | ||||||||
\(746\) | 33486.1 | 1.64345 | ||||||||
\(747\) | −1435.27 | −0.0702994 | ||||||||
\(748\) | −9586.29 | −0.468595 | ||||||||
\(749\) | −71275.9 | −3.47712 | ||||||||
\(750\) | −10279.3 | −0.500464 | ||||||||
\(751\) | −33022.6 | −1.60454 | −0.802272 | − | 0.596958i | \(-0.796376\pi\) | ||||
−0.802272 | + | 0.596958i | \(0.796376\pi\) | |||||||
\(752\) | −9115.48 | −0.442031 | ||||||||
\(753\) | −13019.9 | −0.630107 | ||||||||
\(754\) | −5261.18 | −0.254113 | ||||||||
\(755\) | −1340.26 | −0.0646053 | ||||||||
\(756\) | 5853.55 | 0.281603 | ||||||||
\(757\) | −3443.77 | −0.165345 | −0.0826724 | − | 0.996577i | \(-0.526346\pi\) | ||||
−0.0826724 | + | 0.996577i | \(0.526346\pi\) | |||||||
\(758\) | 16433.4 | 0.787450 | ||||||||
\(759\) | 5983.12 | 0.286131 | ||||||||
\(760\) | −1399.29 | −0.0667864 | ||||||||
\(761\) | 19562.6 | 0.931858 | 0.465929 | − | 0.884822i | \(-0.345720\pi\) | ||||
0.465929 | + | 0.884822i | \(0.345720\pi\) | |||||||
\(762\) | −3094.24 | −0.147103 | ||||||||
\(763\) | 44743.2 | 2.12295 | ||||||||
\(764\) | 4673.13 | 0.221293 | ||||||||
\(765\) | 2950.19 | 0.139430 | ||||||||
\(766\) | −13185.3 | −0.621938 | ||||||||
\(767\) | −2987.17 | −0.140626 | ||||||||
\(768\) | 16009.2 | 0.752190 | ||||||||
\(769\) | −17061.1 | −0.800049 | −0.400025 | − | 0.916504i | \(-0.630998\pi\) | ||||
−0.400025 | + | 0.916504i | \(0.630998\pi\) | |||||||
\(770\) | 10202.4 | 0.477493 | ||||||||
\(771\) | 13078.5 | 0.610908 | ||||||||
\(772\) | −7477.29 | −0.348593 | ||||||||
\(773\) | 10798.4 | 0.502448 | 0.251224 | − | 0.967929i | \(-0.419167\pi\) | ||||
0.251224 | + | 0.967929i | \(0.419167\pi\) | |||||||
\(774\) | 11441.1 | 0.531322 | ||||||||
\(775\) | 16188.6 | 0.750337 | ||||||||
\(776\) | 6564.64 | 0.303682 | ||||||||
\(777\) | −17479.5 | −0.807046 | ||||||||
\(778\) | 11336.3 | 0.522400 | ||||||||
\(779\) | 10845.1 | 0.498802 | ||||||||
\(780\) | −907.388 | −0.0416535 | ||||||||
\(781\) | −16683.7 | −0.764391 | ||||||||
\(782\) | 32558.2 | 1.48885 | ||||||||
\(783\) | 2925.20 | 0.133510 | ||||||||
\(784\) | −74879.8 | −3.41107 | ||||||||
\(785\) | 5029.16 | 0.228661 | ||||||||
\(786\) | 1078.33 | 0.0489348 | ||||||||
\(787\) | −35607.0 | −1.61277 | −0.806386 | − | 0.591390i | \(-0.798580\pi\) | ||||
−0.806386 | + | 0.591390i | \(0.798580\pi\) | |||||||
\(788\) | −16536.0 | −0.747553 | ||||||||
\(789\) | 1824.23 | 0.0823122 | ||||||||
\(790\) | 2049.63 | 0.0923069 | ||||||||
\(791\) | 59334.8 | 2.66713 | ||||||||
\(792\) | 1320.36 | 0.0592386 | ||||||||
\(793\) | 1416.26 | 0.0634210 | ||||||||
\(794\) | 14932.1 | 0.667405 | ||||||||
\(795\) | 8591.76 | 0.383293 | ||||||||
\(796\) | 8873.85 | 0.395132 | ||||||||
\(797\) | 22155.3 | 0.984668 | 0.492334 | − | 0.870406i | \(-0.336144\pi\) | ||||
0.492334 | + | 0.870406i | \(0.336144\pi\) | |||||||
\(798\) | −19117.3 | −0.848051 | ||||||||
\(799\) | −10037.0 | −0.444410 | ||||||||
\(800\) | −24517.1 | −1.08351 | ||||||||
\(801\) | 9611.40 | 0.423973 | ||||||||
\(802\) | 33966.4 | 1.49550 | ||||||||
\(803\) | −21095.9 | −0.927094 | ||||||||
\(804\) | 185.681 | 0.00814488 | ||||||||
\(805\) | −14784.9 | −0.647329 | ||||||||
\(806\) | 7164.35 | 0.313094 | ||||||||
\(807\) | 10362.9 | 0.452032 | ||||||||
\(808\) | −12031.7 | −0.523855 | ||||||||
\(809\) | −22524.6 | −0.978889 | −0.489445 | − | 0.872034i | \(-0.662800\pi\) | ||||
−0.489445 | + | 0.872034i | \(0.662800\pi\) | |||||||
\(810\) | 1182.39 | 0.0512901 | ||||||||
\(811\) | 4452.39 | 0.192780 | 0.0963900 | − | 0.995344i | \(-0.469270\pi\) | ||||
0.0963900 | + | 0.995344i | \(0.469270\pi\) | |||||||
\(812\) | 23488.1 | 1.01511 | ||||||||
\(813\) | 11111.2 | 0.479318 | ||||||||
\(814\) | 11472.9 | 0.494010 | ||||||||
\(815\) | −2081.12 | −0.0894460 | ||||||||
\(816\) | 19171.4 | 0.822468 | ||||||||
\(817\) | −15943.4 | −0.682729 | ||||||||
\(818\) | −26684.6 | −1.14059 | ||||||||
\(819\) | 4260.31 | 0.181767 | ||||||||
\(820\) | −5385.93 | −0.229372 | ||||||||
\(821\) | −7097.27 | −0.301701 | −0.150851 | − | 0.988557i | \(-0.548201\pi\) | ||||
−0.150851 | + | 0.988557i | \(0.548201\pi\) | |||||||
\(822\) | −29342.8 | −1.24507 | ||||||||
\(823\) | −12193.8 | −0.516463 | −0.258231 | − | 0.966083i | \(-0.583140\pi\) | ||||
−0.258231 | + | 0.966083i | \(0.583140\pi\) | |||||||
\(824\) | −991.512 | −0.0419187 | ||||||||
\(825\) | −6318.53 | −0.266646 | ||||||||
\(826\) | 31255.0 | 1.31659 | ||||||||
\(827\) | 7427.97 | 0.312329 | 0.156164 | − | 0.987731i | \(-0.450087\pi\) | ||||
0.156164 | + | 0.987731i | \(0.450087\pi\) | |||||||
\(828\) | 5567.72 | 0.233686 | ||||||||
\(829\) | 16966.2 | 0.710810 | 0.355405 | − | 0.934712i | \(-0.384343\pi\) | ||||
0.355405 | + | 0.934712i | \(0.384343\pi\) | |||||||
\(830\) | −2327.91 | −0.0973529 | ||||||||
\(831\) | −10700.7 | −0.446693 | ||||||||
\(832\) | −2927.21 | −0.121975 | ||||||||
\(833\) | −82449.7 | −3.42943 | ||||||||
\(834\) | −22002.1 | −0.913514 | ||||||||
\(835\) | −163.947 | −0.00679477 | ||||||||
\(836\) | 5353.94 | 0.221495 | ||||||||
\(837\) | −3983.36 | −0.164498 | ||||||||
\(838\) | −30682.7 | −1.26482 | ||||||||
\(839\) | 12025.7 | 0.494844 | 0.247422 | − | 0.968908i | \(-0.420417\pi\) | ||||
0.247422 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(840\) | −3262.75 | −0.134018 | ||||||||
\(841\) | −12651.3 | −0.518728 | ||||||||
\(842\) | 29874.2 | 1.22272 | ||||||||
\(843\) | −352.422 | −0.0143986 | ||||||||
\(844\) | 13727.4 | 0.559855 | ||||||||
\(845\) | −660.412 | −0.0268862 | ||||||||
\(846\) | −4022.68 | −0.163478 | ||||||||
\(847\) | −35050.4 | −1.42189 | ||||||||
\(848\) | 55832.5 | 2.26096 | ||||||||
\(849\) | −5212.85 | −0.210724 | ||||||||
\(850\) | −34383.4 | −1.38746 | ||||||||
\(851\) | −16626.0 | −0.669720 | ||||||||
\(852\) | −15525.4 | −0.624284 | ||||||||
\(853\) | −22187.2 | −0.890593 | −0.445297 | − | 0.895383i | \(-0.646902\pi\) | ||||
−0.445297 | + | 0.895383i | \(0.646902\pi\) | |||||||
\(854\) | −14818.5 | −0.593767 | ||||||||
\(855\) | −1647.68 | −0.0659058 | ||||||||
\(856\) | −14961.2 | −0.597385 | ||||||||
\(857\) | 5746.19 | 0.229038 | 0.114519 | − | 0.993421i | \(-0.463467\pi\) | ||||
0.114519 | + | 0.993421i | \(0.463467\pi\) | |||||||
\(858\) | −2796.30 | −0.111264 | ||||||||
\(859\) | 8305.66 | 0.329902 | 0.164951 | − | 0.986302i | \(-0.447253\pi\) | ||||
0.164951 | + | 0.986302i | \(0.447253\pi\) | |||||||
\(860\) | 7917.87 | 0.313950 | ||||||||
\(861\) | 25287.7 | 1.00093 | ||||||||
\(862\) | 51156.9 | 2.02136 | ||||||||
\(863\) | 38086.4 | 1.50229 | 0.751146 | − | 0.660137i | \(-0.229502\pi\) | ||||
0.751146 | + | 0.660137i | \(0.229502\pi\) | |||||||
\(864\) | 6032.67 | 0.237541 | ||||||||
\(865\) | 4167.61 | 0.163819 | ||||||||
\(866\) | −25089.7 | −0.984505 | ||||||||
\(867\) | 6370.53 | 0.249544 | ||||||||
\(868\) | −31984.7 | −1.25073 | ||||||||
\(869\) | 2695.07 | 0.105206 | ||||||||
\(870\) | 4744.49 | 0.184889 | ||||||||
\(871\) | 135.142 | 0.00525731 | ||||||||
\(872\) | 9391.82 | 0.364733 | ||||||||
\(873\) | 7729.93 | 0.299677 | ||||||||
\(874\) | −18183.8 | −0.703748 | ||||||||
\(875\) | 33400.4 | 1.29044 | ||||||||
\(876\) | −19631.2 | −0.757166 | ||||||||
\(877\) | −2098.53 | −0.0808009 | −0.0404005 | − | 0.999184i | \(-0.512863\pi\) | ||||
−0.0404005 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(878\) | 22163.8 | 0.851929 | ||||||||
\(879\) | 5712.14 | 0.219187 | ||||||||
\(880\) | 5714.18 | 0.218892 | ||||||||
\(881\) | 14555.3 | 0.556619 | 0.278309 | − | 0.960491i | \(-0.410226\pi\) | ||||
0.278309 | + | 0.960491i | \(0.410226\pi\) | |||||||
\(882\) | −33044.6 | −1.26153 | ||||||||
\(883\) | 2122.88 | 0.0809066 | 0.0404533 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404533 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(884\) | −6492.65 | −0.247027 | ||||||||
\(885\) | 2693.80 | 0.102318 | ||||||||
\(886\) | 25862.3 | 0.980656 | ||||||||
\(887\) | −12487.3 | −0.472696 | −0.236348 | − | 0.971668i | \(-0.575951\pi\) | ||||
−0.236348 | + | 0.971668i | \(0.575951\pi\) | |||||||
\(888\) | −3669.04 | −0.138654 | ||||||||
\(889\) | 10054.1 | 0.379305 | ||||||||
\(890\) | 15589.1 | 0.587131 | ||||||||
\(891\) | 1554.74 | 0.0584575 | ||||||||
\(892\) | 7394.61 | 0.277567 | ||||||||
\(893\) | 5605.66 | 0.210063 | ||||||||
\(894\) | 3374.39 | 0.126238 | ||||||||
\(895\) | −12405.6 | −0.463323 | ||||||||
\(896\) | −34458.9 | −1.28481 | ||||||||
\(897\) | 4052.28 | 0.150838 | ||||||||
\(898\) | −33196.5 | −1.23361 | ||||||||
\(899\) | −15983.7 | −0.592978 | ||||||||
\(900\) | −5879.84 | −0.217772 | ||||||||
\(901\) | 61476.8 | 2.27313 | ||||||||
\(902\) | −16597.8 | −0.612691 | ||||||||
\(903\) | −37175.5 | −1.37001 | ||||||||
\(904\) | 12454.7 | 0.458226 | ||||||||
\(905\) | 10650.3 | 0.391193 | ||||||||
\(906\) | −3843.52 | −0.140941 | ||||||||
\(907\) | 29679.8 | 1.08655 | 0.543275 | − | 0.839555i | \(-0.317184\pi\) | ||||
0.543275 | + | 0.839555i | \(0.317184\pi\) | |||||||
\(908\) | −10269.0 | −0.375318 | ||||||||
\(909\) | −14167.5 | −0.516948 | ||||||||
\(910\) | 6909.95 | 0.251717 | ||||||||
\(911\) | 24800.0 | 0.901934 | 0.450967 | − | 0.892541i | \(-0.351079\pi\) | ||||
0.450967 | + | 0.892541i | \(0.351079\pi\) | |||||||
\(912\) | −10707.2 | −0.388763 | ||||||||
\(913\) | −3060.99 | −0.110957 | ||||||||
\(914\) | −40959.7 | −1.48230 | ||||||||
\(915\) | −1277.17 | −0.0461442 | ||||||||
\(916\) | −19491.3 | −0.703070 | ||||||||
\(917\) | −3503.80 | −0.126178 | ||||||||
\(918\) | 8460.38 | 0.304177 | ||||||||
\(919\) | −6597.90 | −0.236828 | −0.118414 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118414 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(920\) | −3103.43 | −0.111214 | ||||||||
\(921\) | 8587.17 | 0.307228 | ||||||||
\(922\) | −37613.4 | −1.34353 | ||||||||
\(923\) | −11299.6 | −0.402959 | ||||||||
\(924\) | 12483.9 | 0.444468 | ||||||||
\(925\) | 17558.0 | 0.624113 | ||||||||
\(926\) | −20917.7 | −0.742331 | ||||||||
\(927\) | −1167.51 | −0.0413659 | ||||||||
\(928\) | 24206.8 | 0.856281 | ||||||||
\(929\) | 15056.0 | 0.531724 | 0.265862 | − | 0.964011i | \(-0.414344\pi\) | ||||
0.265862 | + | 0.964011i | \(0.414344\pi\) | |||||||
\(930\) | −6460.75 | −0.227803 | ||||||||
\(931\) | 46048.1 | 1.62102 | ||||||||
\(932\) | −12678.9 | −0.445612 | ||||||||
\(933\) | 12604.7 | 0.442291 | ||||||||
\(934\) | 49487.1 | 1.73369 | ||||||||
\(935\) | 6291.85 | 0.220070 | ||||||||
\(936\) | 894.261 | 0.0312284 | ||||||||
\(937\) | −35777.0 | −1.24737 | −0.623683 | − | 0.781677i | \(-0.714365\pi\) | ||||
−0.623683 | + | 0.781677i | \(0.714365\pi\) | |||||||
\(938\) | −1414.00 | −0.0492205 | ||||||||
\(939\) | 10283.2 | 0.357381 | ||||||||
\(940\) | −2783.90 | −0.0965966 | ||||||||
\(941\) | −22973.6 | −0.795873 | −0.397937 | − | 0.917413i | \(-0.630274\pi\) | ||||
−0.397937 | + | 0.917413i | \(0.630274\pi\) | |||||||
\(942\) | 14422.4 | 0.498838 | ||||||||
\(943\) | 24052.9 | 0.830615 | ||||||||
\(944\) | 17505.3 | 0.603549 | ||||||||
\(945\) | −3841.92 | −0.132251 | ||||||||
\(946\) | 24400.5 | 0.838614 | ||||||||
\(947\) | −51038.3 | −1.75134 | −0.875671 | − | 0.482908i | \(-0.839580\pi\) | ||||
−0.875671 | + | 0.482908i | \(0.839580\pi\) | |||||||
\(948\) | 2507.96 | 0.0859227 | ||||||||
\(949\) | −14287.9 | −0.488731 | ||||||||
\(950\) | 19203.1 | 0.655823 | ||||||||
\(951\) | 5028.26 | 0.171454 | ||||||||
\(952\) | −23346.0 | −0.794799 | ||||||||
\(953\) | −22586.5 | −0.767733 | −0.383866 | − | 0.923389i | \(-0.625408\pi\) | ||||
−0.383866 | + | 0.923389i | \(0.625408\pi\) | |||||||
\(954\) | 24639.0 | 0.836180 | ||||||||
\(955\) | −3067.16 | −0.103928 | ||||||||
\(956\) | −30259.9 | −1.02372 | ||||||||
\(957\) | 6238.57 | 0.210726 | ||||||||
\(958\) | −62477.6 | −2.10706 | ||||||||
\(959\) | 95342.8 | 3.21041 | ||||||||
\(960\) | 2639.74 | 0.0887470 | ||||||||
\(961\) | −8025.32 | −0.269387 | ||||||||
\(962\) | 7770.41 | 0.260424 | ||||||||
\(963\) | −17616.9 | −0.589509 | ||||||||
\(964\) | 28374.1 | 0.947996 | ||||||||
\(965\) | 4907.64 | 0.163712 | ||||||||
\(966\) | −42399.4 | −1.41219 | ||||||||
\(967\) | −36678.7 | −1.21976 | −0.609880 | − | 0.792494i | \(-0.708782\pi\) | ||||
−0.609880 | + | 0.792494i | \(0.708782\pi\) | |||||||
\(968\) | −7357.24 | −0.244288 | ||||||||
\(969\) | −11789.7 | −0.390855 | ||||||||
\(970\) | 12537.4 | 0.415003 | ||||||||
\(971\) | 32635.2 | 1.07859 | 0.539296 | − | 0.842116i | \(-0.318690\pi\) | ||||
0.539296 | + | 0.842116i | \(0.318690\pi\) | |||||||
\(972\) | 1446.79 | 0.0477427 | ||||||||
\(973\) | 71491.0 | 2.35549 | ||||||||
\(974\) | 19820.0 | 0.652026 | ||||||||
\(975\) | −4279.45 | −0.140566 | ||||||||
\(976\) | −8299.54 | −0.272194 | ||||||||
\(977\) | 44432.6 | 1.45499 | 0.727496 | − | 0.686112i | \(-0.240684\pi\) | ||||
0.727496 | + | 0.686112i | \(0.240684\pi\) | |||||||
\(978\) | −5968.12 | −0.195133 | ||||||||
\(979\) | 20498.2 | 0.669178 | ||||||||
\(980\) | −22868.6 | −0.745418 | ||||||||
\(981\) | 11059.0 | 0.359924 | ||||||||
\(982\) | −60515.6 | −1.96653 | ||||||||
\(983\) | 484.485 | 0.0157199 | 0.00785996 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00785996 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(984\) | 5308.01 | 0.171965 | ||||||||
\(985\) | 10853.2 | 0.351079 | ||||||||
\(986\) | 33948.3 | 1.09649 | ||||||||
\(987\) | 13070.8 | 0.421528 | ||||||||
\(988\) | 3626.15 | 0.116764 | ||||||||
\(989\) | −35360.2 | −1.13689 | ||||||||
\(990\) | 2521.68 | 0.0809538 | ||||||||
\(991\) | −48017.1 | −1.53917 | −0.769583 | − | 0.638546i | \(-0.779536\pi\) | ||||
−0.769583 | + | 0.638546i | \(0.779536\pi\) | |||||||
\(992\) | −32963.4 | −1.05503 | ||||||||
\(993\) | 33469.8 | 1.06962 | ||||||||
\(994\) | 118229. | 3.77263 | ||||||||
\(995\) | −5824.25 | −0.185569 | ||||||||
\(996\) | −2848.47 | −0.0906197 | ||||||||
\(997\) | −26561.9 | −0.843755 | −0.421877 | − | 0.906653i | \(-0.638629\pi\) | ||||
−0.421877 | + | 0.906653i | \(0.638629\pi\) | |||||||
\(998\) | −16408.9 | −0.520455 | ||||||||
\(999\) | −4320.33 | −0.136826 |
(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 | 39.4.a.c.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 117.4.a.f.1.3 | 3 | |||
4.3 | odd | 2 | 624.4.a.t.1.2 | 3 | |||
5.4 | even | 2 | 975.4.a.l.1.3 | 3 | |||
7.6 | odd | 2 | 1911.4.a.k.1.1 | 3 | |||
8.3 | odd | 2 | 2496.4.a.bp.1.2 | 3 | |||
8.5 | even | 2 | 2496.4.a.bl.1.2 | 3 | |||
12.11 | even | 2 | 1872.4.a.bk.1.2 | 3 | |||
13.5 | odd | 4 | 507.4.b.g.337.5 | 6 | |||
13.8 | odd | 4 | 507.4.b.g.337.2 | 6 | |||
13.12 | even | 2 | 507.4.a.h.1.3 | 3 | |||
39.38 | odd | 2 | 1521.4.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
117.4.a.f.1.3 | 3 | 3.2 | odd | 2 | |||
507.4.a.h.1.3 | 3 | 13.12 | even | 2 | |||
507.4.b.g.337.2 | 6 | 13.8 | odd | 4 | |||
507.4.b.g.337.5 | 6 | 13.5 | odd | 4 | |||
624.4.a.t.1.2 | 3 | 4.3 | odd | 2 | |||
975.4.a.l.1.3 | 3 | 5.4 | even | 2 | |||
1521.4.a.u.1.1 | 3 | 39.38 | odd | 2 | |||
1872.4.a.bk.1.2 | 3 | 12.11 | even | 2 | |||
1911.4.a.k.1.1 | 3 | 7.6 | odd | 2 | |||
2496.4.a.bl.1.2 | 3 | 8.5 | even | 2 | |||
2496.4.a.bp.1.2 | 3 | 8.3 | odd | 2 |