Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,4,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(118.534837202\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.34 | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.18565 | 1.12630 | 0.563150 | − | 0.826355i | \(-0.309589\pi\) | ||||
0.563150 | + | 0.826355i | \(0.309589\pi\) | |||||||
\(3\) | 5.56348 | 1.07069 | 0.535346 | − | 0.844633i | \(-0.320181\pi\) | ||||
0.535346 | + | 0.844633i | \(0.320181\pi\) | |||||||
\(4\) | 2.14840 | 0.268550 | ||||||||
\(5\) | 0.334741 | 0.0299402 | 0.0149701 | − | 0.999888i | \(-0.495235\pi\) | ||||
0.0149701 | + | 0.999888i | \(0.495235\pi\) | |||||||
\(6\) | 17.7233 | 1.20592 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −18.6412 | −0.823832 | ||||||||
\(9\) | 3.95229 | 0.146381 | ||||||||
\(10\) | 1.06637 | 0.0337216 | ||||||||
\(11\) | −38.4554 | −1.05407 | −0.527034 | − | 0.849844i | \(-0.676696\pi\) | ||||
−0.527034 | + | 0.849844i | \(0.676696\pi\) | |||||||
\(12\) | 11.9526 | 0.287534 | ||||||||
\(13\) | 84.0040 | 1.79219 | 0.896097 | − | 0.443858i | \(-0.146391\pi\) | ||||
0.896097 | + | 0.443858i | \(0.146391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.86233 | 0.0320567 | ||||||||
\(16\) | −76.5716 | −1.19643 | ||||||||
\(17\) | 95.0435 | 1.35597 | 0.677983 | − | 0.735077i | \(-0.262854\pi\) | ||||
0.677983 | + | 0.735077i | \(0.262854\pi\) | |||||||
\(18\) | 12.5906 | 0.164869 | ||||||||
\(19\) | 31.7289 | 0.383111 | 0.191555 | − | 0.981482i | \(-0.438647\pi\) | ||||
0.191555 | + | 0.981482i | \(0.438647\pi\) | |||||||
\(20\) | 0.719157 | 0.00804042 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −122.506 | −1.18720 | ||||||||
\(23\) | 119.788 | 1.08598 | 0.542989 | − | 0.839740i | \(-0.317293\pi\) | ||||
0.542989 | + | 0.839740i | \(0.317293\pi\) | |||||||
\(24\) | −103.710 | −0.882070 | ||||||||
\(25\) | −124.888 | −0.999104 | ||||||||
\(26\) | 267.608 | 2.01855 | ||||||||
\(27\) | −128.225 | −0.913963 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −134.970 | −0.864252 | −0.432126 | − | 0.901813i | \(-0.642237\pi\) | ||||
−0.432126 | + | 0.901813i | \(0.642237\pi\) | |||||||
\(30\) | 5.93273 | 0.0361054 | ||||||||
\(31\) | 320.716 | 1.85814 | 0.929070 | − | 0.369905i | \(-0.120610\pi\) | ||||
0.929070 | + | 0.369905i | \(0.120610\pi\) | |||||||
\(32\) | −94.8011 | −0.523707 | ||||||||
\(33\) | −213.946 | −1.12858 | ||||||||
\(34\) | 302.776 | 1.52722 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.49108 | 0.0393106 | ||||||||
\(37\) | 347.490 | 1.54397 | 0.771987 | − | 0.635639i | \(-0.219263\pi\) | ||||
0.771987 | + | 0.635639i | \(0.219263\pi\) | |||||||
\(38\) | 101.077 | 0.431497 | ||||||||
\(39\) | 467.355 | 1.91889 | ||||||||
\(40\) | −6.23998 | −0.0246657 | ||||||||
\(41\) | −41.0000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −253.641 | −0.899531 | −0.449765 | − | 0.893147i | \(-0.648492\pi\) | ||||
−0.449765 | + | 0.893147i | \(0.648492\pi\) | |||||||
\(44\) | −82.6175 | −0.283070 | ||||||||
\(45\) | 1.32299 | 0.00438268 | ||||||||
\(46\) | 381.603 | 1.22314 | ||||||||
\(47\) | −30.5280 | −0.0947441 | −0.0473720 | − | 0.998877i | \(-0.515085\pi\) | ||||
−0.0473720 | + | 0.998877i | \(0.515085\pi\) | |||||||
\(48\) | −426.004 | −1.28101 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −397.850 | −1.12529 | ||||||||
\(51\) | 528.772 | 1.45182 | ||||||||
\(52\) | 180.474 | 0.481293 | ||||||||
\(53\) | 156.112 | 0.404596 | 0.202298 | − | 0.979324i | \(-0.435159\pi\) | ||||
0.202298 | + | 0.979324i | \(0.435159\pi\) | |||||||
\(54\) | −408.482 | −1.02940 | ||||||||
\(55\) | −12.8726 | −0.0315590 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 176.523 | 0.410193 | ||||||||
\(58\) | −429.968 | −0.973407 | ||||||||
\(59\) | 710.575 | 1.56795 | 0.783974 | − | 0.620793i | \(-0.213189\pi\) | ||||
0.783974 | + | 0.620793i | \(0.213189\pi\) | |||||||
\(60\) | 4.00102 | 0.00860882 | ||||||||
\(61\) | 414.183 | 0.869356 | 0.434678 | − | 0.900586i | \(-0.356862\pi\) | ||||
0.434678 | + | 0.900586i | \(0.356862\pi\) | |||||||
\(62\) | 1021.69 | 2.09282 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 310.569 | 0.606580 | ||||||||
\(65\) | 28.1196 | 0.0536586 | ||||||||
\(66\) | −681.558 | −1.27112 | ||||||||
\(67\) | 79.2811 | 0.144563 | 0.0722816 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722816 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(68\) | 204.191 | 0.364144 | ||||||||
\(69\) | 666.437 | 1.16275 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −227.985 | −0.381083 | −0.190541 | − | 0.981679i | \(-0.561024\pi\) | ||||
−0.190541 | + | 0.981679i | \(0.561024\pi\) | |||||||
\(72\) | −73.6754 | −0.120593 | ||||||||
\(73\) | −17.1435 | −0.0274862 | −0.0137431 | − | 0.999906i | \(-0.504375\pi\) | ||||
−0.0137431 | + | 0.999906i | \(0.504375\pi\) | |||||||
\(74\) | 1106.98 | 1.73898 | ||||||||
\(75\) | −694.811 | −1.06973 | ||||||||
\(76\) | 68.1662 | 0.102884 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1488.83 | 2.16124 | ||||||||
\(79\) | −450.298 | −0.641297 | −0.320649 | − | 0.947198i | \(-0.603901\pi\) | ||||
−0.320649 | + | 0.947198i | \(0.603901\pi\) | |||||||
\(80\) | −25.6317 | −0.0358214 | ||||||||
\(81\) | −820.091 | −1.12495 | ||||||||
\(82\) | −130.612 | −0.175898 | ||||||||
\(83\) | −350.037 | −0.462910 | −0.231455 | − | 0.972846i | \(-0.574349\pi\) | ||||
−0.231455 | + | 0.972846i | \(0.574349\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.8150 | 0.0405979 | ||||||||
\(86\) | −808.011 | −1.01314 | ||||||||
\(87\) | −750.903 | −0.925348 | ||||||||
\(88\) | 716.855 | 0.868375 | ||||||||
\(89\) | 201.814 | 0.240362 | 0.120181 | − | 0.992752i | \(-0.461652\pi\) | ||||
0.120181 | + | 0.992752i | \(0.461652\pi\) | |||||||
\(90\) | 4.21460 | 0.00493620 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 257.352 | 0.291639 | ||||||||
\(93\) | 1784.30 | 1.98949 | ||||||||
\(94\) | −97.2518 | −0.106710 | ||||||||
\(95\) | 10.6210 | 0.0114704 | ||||||||
\(96\) | −527.424 | −0.560729 | ||||||||
\(97\) | 366.814 | 0.383962 | 0.191981 | − | 0.981399i | \(-0.438509\pi\) | ||||
0.191981 | + | 0.981399i | \(0.438509\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −151.987 | −0.154296 | ||||||||
\(100\) | −268.309 | −0.268309 | ||||||||
\(101\) | 617.231 | 0.608087 | 0.304043 | − | 0.952658i | \(-0.401663\pi\) | ||||
0.304043 | + | 0.952658i | \(0.401663\pi\) | |||||||
\(102\) | 1684.49 | 1.63519 | ||||||||
\(103\) | 1763.38 | 1.68690 | 0.843452 | − | 0.537205i | \(-0.180520\pi\) | ||||
0.843452 | + | 0.537205i | \(0.180520\pi\) | |||||||
\(104\) | −1565.93 | −1.47647 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 497.318 | 0.455696 | ||||||||
\(107\) | 1205.89 | 1.08951 | 0.544756 | − | 0.838595i | \(-0.316622\pi\) | ||||
0.544756 | + | 0.838595i | \(0.316622\pi\) | |||||||
\(108\) | −275.479 | −0.245444 | ||||||||
\(109\) | 1367.96 | 1.20208 | 0.601042 | − | 0.799217i | \(-0.294752\pi\) | ||||
0.601042 | + | 0.799217i | \(0.294752\pi\) | |||||||
\(110\) | −41.0078 | −0.0355449 | ||||||||
\(111\) | 1933.25 | 1.65312 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1254.42 | 1.04430 | 0.522149 | − | 0.852855i | \(-0.325131\pi\) | ||||
0.522149 | + | 0.852855i | \(0.325131\pi\) | |||||||
\(114\) | 562.341 | 0.462000 | ||||||||
\(115\) | 40.0980 | 0.0325144 | ||||||||
\(116\) | −289.969 | −0.232095 | ||||||||
\(117\) | 332.008 | 0.262343 | ||||||||
\(118\) | 2263.65 | 1.76598 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −34.7160 | −0.0264093 | ||||||||
\(121\) | 147.821 | 0.111060 | ||||||||
\(122\) | 1319.44 | 0.979155 | ||||||||
\(123\) | −228.103 | −0.167214 | ||||||||
\(124\) | 689.025 | 0.499002 | ||||||||
\(125\) | −83.6479 | −0.0598535 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1594.98 | −1.11443 | −0.557213 | − | 0.830370i | \(-0.688129\pi\) | ||||
−0.557213 | + | 0.830370i | \(0.688129\pi\) | |||||||
\(128\) | 1747.77 | 1.20690 | ||||||||
\(129\) | −1411.12 | −0.963120 | ||||||||
\(130\) | 89.5794 | 0.0604357 | ||||||||
\(131\) | 2879.80 | 1.92068 | 0.960340 | − | 0.278831i | \(-0.0899470\pi\) | ||||
0.960340 | + | 0.278831i | \(0.0899470\pi\) | |||||||
\(132\) | −459.641 | −0.303080 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 252.562 | 0.162821 | ||||||||
\(135\) | −42.9224 | −0.0273642 | ||||||||
\(136\) | −1771.72 | −1.11709 | ||||||||
\(137\) | 1995.31 | 1.24431 | 0.622155 | − | 0.782894i | \(-0.286257\pi\) | ||||
0.622155 | + | 0.782894i | \(0.286257\pi\) | |||||||
\(138\) | 2123.04 | 1.30960 | ||||||||
\(139\) | 2973.25 | 1.81430 | 0.907149 | − | 0.420809i | \(-0.138254\pi\) | ||||
0.907149 | + | 0.420809i | \(0.138254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −169.842 | −0.101442 | ||||||||
\(142\) | −726.282 | −0.429213 | ||||||||
\(143\) | −3230.41 | −1.88910 | ||||||||
\(144\) | −302.633 | −0.175135 | ||||||||
\(145\) | −45.1801 | −0.0258759 | ||||||||
\(146\) | −54.6132 | −0.0309577 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 746.546 | 0.414633 | ||||||||
\(149\) | −964.246 | −0.530162 | −0.265081 | − | 0.964226i | \(-0.585399\pi\) | ||||
−0.265081 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(150\) | −2213.43 | −1.20484 | ||||||||
\(151\) | 830.906 | 0.447802 | 0.223901 | − | 0.974612i | \(-0.428121\pi\) | ||||
0.223901 | + | 0.974612i | \(0.428121\pi\) | |||||||
\(152\) | −591.464 | −0.315619 | ||||||||
\(153\) | 375.639 | 0.198488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 107.357 | 0.0556330 | ||||||||
\(156\) | 1004.06 | 0.515317 | ||||||||
\(157\) | −1780.72 | −0.905203 | −0.452602 | − | 0.891713i | \(-0.649504\pi\) | ||||
−0.452602 | + | 0.891713i | \(0.649504\pi\) | |||||||
\(158\) | −1434.49 | −0.722293 | ||||||||
\(159\) | 868.524 | 0.433198 | ||||||||
\(160\) | −31.7338 | −0.0156799 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2612.53 | −1.26703 | ||||||||
\(163\) | −619.337 | −0.297609 | −0.148804 | − | 0.988867i | \(-0.547542\pi\) | ||||
−0.148804 | + | 0.988867i | \(0.547542\pi\) | |||||||
\(164\) | −88.0843 | −0.0419404 | ||||||||
\(165\) | −71.6166 | −0.0337900 | ||||||||
\(166\) | −1115.10 | −0.521375 | ||||||||
\(167\) | −3246.91 | −1.50451 | −0.752256 | − | 0.658870i | \(-0.771035\pi\) | ||||
−0.752256 | + | 0.658870i | \(0.771035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4859.68 | 2.21196 | ||||||||
\(170\) | 101.352 | 0.0457254 | ||||||||
\(171\) | 125.402 | 0.0560801 | ||||||||
\(172\) | −544.920 | −0.241569 | ||||||||
\(173\) | −1580.78 | −0.694707 | −0.347354 | − | 0.937734i | \(-0.612920\pi\) | ||||
−0.347354 | + | 0.937734i | \(0.612920\pi\) | |||||||
\(174\) | −2392.12 | −1.04222 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2944.59 | 1.26112 | ||||||||
\(177\) | 3953.27 | 1.67879 | ||||||||
\(178\) | 642.910 | 0.270720 | ||||||||
\(179\) | 1744.65 | 0.728500 | 0.364250 | − | 0.931301i | \(-0.381325\pi\) | ||||
0.364250 | + | 0.931301i | \(0.381325\pi\) | |||||||
\(180\) | 2.84232 | 0.00117697 | ||||||||
\(181\) | 3300.30 | 1.35530 | 0.677650 | − | 0.735385i | \(-0.262999\pi\) | ||||
0.677650 | + | 0.735385i | \(0.262999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2304.30 | 0.930812 | ||||||||
\(184\) | −2232.99 | −0.894663 | ||||||||
\(185\) | 116.319 | 0.0462268 | ||||||||
\(186\) | 5684.15 | 2.24077 | ||||||||
\(187\) | −3654.94 | −1.42928 | ||||||||
\(188\) | −65.5863 | −0.0254435 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 33.8347 | 0.0129191 | ||||||||
\(191\) | −344.459 | −0.130493 | −0.0652466 | − | 0.997869i | \(-0.520783\pi\) | ||||
−0.0652466 | + | 0.997869i | \(0.520783\pi\) | |||||||
\(192\) | 1727.84 | 0.649460 | ||||||||
\(193\) | −4943.31 | −1.84366 | −0.921832 | − | 0.387589i | \(-0.873308\pi\) | ||||
−0.921832 | + | 0.387589i | \(0.873308\pi\) | |||||||
\(194\) | 1168.54 | 0.432456 | ||||||||
\(195\) | 156.443 | 0.0574519 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4236.61 | −1.53221 | −0.766106 | − | 0.642714i | \(-0.777808\pi\) | ||||
−0.766106 | + | 0.642714i | \(0.777808\pi\) | |||||||
\(198\) | −484.178 | −0.173783 | ||||||||
\(199\) | −5314.50 | −1.89314 | −0.946570 | − | 0.322499i | \(-0.895477\pi\) | ||||
−0.946570 | + | 0.322499i | \(0.895477\pi\) | |||||||
\(200\) | 2328.06 | 0.823093 | ||||||||
\(201\) | 441.079 | 0.154783 | ||||||||
\(202\) | 1966.28 | 0.684887 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1136.01 | 0.389886 | ||||||||
\(205\) | −13.7244 | −0.00467587 | ||||||||
\(206\) | 5617.52 | 1.89996 | ||||||||
\(207\) | 473.436 | 0.158967 | ||||||||
\(208\) | −6432.32 | −2.14424 | ||||||||
\(209\) | −1220.15 | −0.403825 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2434.28 | −0.794232 | −0.397116 | − | 0.917768i | \(-0.629989\pi\) | ||||
−0.397116 | + | 0.917768i | \(0.629989\pi\) | |||||||
\(212\) | 335.390 | 0.108654 | ||||||||
\(213\) | −1268.39 | −0.408022 | ||||||||
\(214\) | 3841.55 | 1.22712 | ||||||||
\(215\) | −84.9040 | −0.0269321 | ||||||||
\(216\) | 2390.27 | 0.752952 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4357.86 | 1.35391 | ||||||||
\(219\) | −95.3774 | −0.0294293 | ||||||||
\(220\) | −27.6555 | −0.00847516 | ||||||||
\(221\) | 7984.04 | 2.43016 | ||||||||
\(222\) | 6158.68 | 1.86191 | ||||||||
\(223\) | −3471.06 | −1.04233 | −0.521164 | − | 0.853457i | \(-0.674502\pi\) | ||||
−0.521164 | + | 0.853457i | \(0.674502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −493.593 | −0.146250 | ||||||||
\(226\) | 3996.14 | 1.17619 | ||||||||
\(227\) | −3789.52 | −1.10802 | −0.554008 | − | 0.832511i | \(-0.686902\pi\) | ||||
−0.554008 | + | 0.832511i | \(0.686902\pi\) | |||||||
\(228\) | 379.241 | 0.110157 | ||||||||
\(229\) | −2395.61 | −0.691295 | −0.345647 | − | 0.938364i | \(-0.612341\pi\) | ||||
−0.345647 | + | 0.938364i | \(0.612341\pi\) | |||||||
\(230\) | 127.738 | 0.0366209 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2516.00 | 0.711999 | ||||||||
\(233\) | −1024.74 | −0.288124 | −0.144062 | − | 0.989569i | \(-0.546016\pi\) | ||||
−0.144062 | + | 0.989569i | \(0.546016\pi\) | |||||||
\(234\) | 1057.66 | 0.295477 | ||||||||
\(235\) | −10.2190 | −0.00283665 | ||||||||
\(236\) | 1526.60 | 0.421072 | ||||||||
\(237\) | −2505.22 | −0.686632 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3485.78 | −0.943417 | −0.471709 | − | 0.881755i | \(-0.656363\pi\) | ||||
−0.471709 | + | 0.881755i | \(0.656363\pi\) | |||||||
\(240\) | −142.601 | −0.0383536 | ||||||||
\(241\) | 1096.77 | 0.293149 | 0.146574 | − | 0.989200i | \(-0.453175\pi\) | ||||
0.146574 | + | 0.989200i | \(0.453175\pi\) | |||||||
\(242\) | 470.907 | 0.125087 | ||||||||
\(243\) | −1100.47 | −0.290516 | ||||||||
\(244\) | 889.830 | 0.233465 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −726.656 | −0.188333 | ||||||||
\(247\) | 2665.35 | 0.686608 | ||||||||
\(248\) | −5978.53 | −1.53079 | ||||||||
\(249\) | −1947.42 | −0.495634 | ||||||||
\(250\) | −266.473 | −0.0674130 | ||||||||
\(251\) | 2249.47 | 0.565679 | 0.282839 | − | 0.959167i | \(-0.408724\pi\) | ||||
0.282839 | + | 0.959167i | \(0.408724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4606.50 | −1.14470 | ||||||||
\(254\) | −5081.07 | −1.25518 | ||||||||
\(255\) | 177.002 | 0.0434678 | ||||||||
\(256\) | 3083.25 | 0.752747 | ||||||||
\(257\) | −3910.19 | −0.949071 | −0.474535 | − | 0.880236i | \(-0.657384\pi\) | ||||
−0.474535 | + | 0.880236i | \(0.657384\pi\) | |||||||
\(258\) | −4495.35 | −1.08476 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 60.4121 | 0.0144100 | ||||||||
\(261\) | −533.441 | −0.126510 | ||||||||
\(262\) | 9174.04 | 2.16326 | ||||||||
\(263\) | −2775.19 | −0.650668 | −0.325334 | − | 0.945599i | \(-0.605477\pi\) | ||||
−0.325334 | + | 0.945599i | \(0.605477\pi\) | |||||||
\(264\) | 3988.21 | 0.929762 | ||||||||
\(265\) | 52.2571 | 0.0121137 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1122.79 | 0.257354 | ||||||||
\(268\) | 170.327 | 0.0388224 | ||||||||
\(269\) | 4768.24 | 1.08076 | 0.540381 | − | 0.841420i | \(-0.318280\pi\) | ||||
0.540381 | + | 0.841420i | \(0.318280\pi\) | |||||||
\(270\) | −136.736 | −0.0308203 | ||||||||
\(271\) | 3104.12 | 0.695800 | 0.347900 | − | 0.937532i | \(-0.386895\pi\) | ||||
0.347900 | + | 0.937532i | \(0.386895\pi\) | |||||||
\(272\) | −7277.63 | −1.62232 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6356.36 | 1.40147 | ||||||||
\(275\) | 4802.62 | 1.05312 | ||||||||
\(276\) | 1431.77 | 0.312255 | ||||||||
\(277\) | 519.963 | 0.112785 | 0.0563927 | − | 0.998409i | \(-0.482040\pi\) | ||||
0.0563927 | + | 0.998409i | \(0.482040\pi\) | |||||||
\(278\) | 9471.74 | 2.04344 | ||||||||
\(279\) | 1267.56 | 0.271996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5250.42 | −1.11464 | −0.557320 | − | 0.830298i | \(-0.688170\pi\) | ||||
−0.557320 | + | 0.830298i | \(0.688170\pi\) | |||||||
\(282\) | −541.058 | −0.114254 | ||||||||
\(283\) | 1231.10 | 0.258591 | 0.129295 | − | 0.991606i | \(-0.458728\pi\) | ||||
0.129295 | + | 0.991606i | \(0.458728\pi\) | |||||||
\(284\) | −489.803 | −0.102340 | ||||||||
\(285\) | 59.0895 | 0.0122813 | ||||||||
\(286\) | −10291.0 | −2.12769 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −374.681 | −0.0766608 | ||||||||
\(289\) | 4120.26 | 0.838645 | ||||||||
\(290\) | −143.928 | −0.0291440 | ||||||||
\(291\) | 2040.76 | 0.411105 | ||||||||
\(292\) | −36.8310 | −0.00738141 | ||||||||
\(293\) | −8826.81 | −1.75996 | −0.879979 | − | 0.475012i | \(-0.842444\pi\) | ||||
−0.879979 | + | 0.475012i | \(0.842444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 237.859 | 0.0469447 | ||||||||
\(296\) | −6477.63 | −1.27197 | ||||||||
\(297\) | 4930.97 | 0.963379 | ||||||||
\(298\) | −3071.75 | −0.597121 | ||||||||
\(299\) | 10062.7 | 1.94628 | ||||||||
\(300\) | −1492.73 | −0.287276 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2646.98 | 0.504359 | ||||||||
\(303\) | 3433.95 | 0.651073 | ||||||||
\(304\) | −2429.53 | −0.458365 | ||||||||
\(305\) | 138.644 | 0.0260287 | ||||||||
\(306\) | 1196.66 | 0.223557 | ||||||||
\(307\) | 7650.76 | 1.42232 | 0.711160 | − | 0.703031i | \(-0.248170\pi\) | ||||
0.711160 | + | 0.703031i | \(0.248170\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9810.53 | 1.80615 | ||||||||
\(310\) | 342.002 | 0.0626594 | ||||||||
\(311\) | −3281.49 | −0.598316 | −0.299158 | − | 0.954204i | \(-0.596706\pi\) | ||||
−0.299158 | + | 0.954204i | \(0.596706\pi\) | |||||||
\(312\) | −8712.04 | −1.58084 | ||||||||
\(313\) | −1642.86 | −0.296677 | −0.148338 | − | 0.988937i | \(-0.547392\pi\) | ||||
−0.148338 | + | 0.988937i | \(0.547392\pi\) | |||||||
\(314\) | −5672.76 | −1.01953 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −967.419 | −0.172220 | ||||||||
\(317\) | 6739.27 | 1.19405 | 0.597027 | − | 0.802221i | \(-0.296349\pi\) | ||||
0.597027 | + | 0.802221i | \(0.296349\pi\) | |||||||
\(318\) | 2766.82 | 0.487910 | ||||||||
\(319\) | 5190.34 | 0.910981 | ||||||||
\(320\) | 103.960 | 0.0181611 | ||||||||
\(321\) | 6708.94 | 1.16653 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3015.62 | 0.519485 | ||||||||
\(324\) | −1761.88 | −0.302106 | ||||||||
\(325\) | −10491.1 | −1.79059 | ||||||||
\(326\) | −1973.00 | −0.335197 | ||||||||
\(327\) | 7610.64 | 1.28706 | ||||||||
\(328\) | 764.289 | 0.128661 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −228.146 | −0.0380576 | ||||||||
\(331\) | 10497.7 | 1.74322 | 0.871612 | − | 0.490197i | \(-0.163075\pi\) | ||||
0.871612 | + | 0.490197i | \(0.163075\pi\) | |||||||
\(332\) | −752.018 | −0.124314 | ||||||||
\(333\) | 1373.38 | 0.226008 | ||||||||
\(334\) | −10343.5 | −1.69453 | ||||||||
\(335\) | 26.5387 | 0.00432825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2807.64 | −0.453834 | −0.226917 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226917 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(338\) | 15481.2 | 2.49133 | ||||||||
\(339\) | 6978.92 | 1.11812 | ||||||||
\(340\) | 68.3512 | 0.0109025 | ||||||||
\(341\) | −12333.3 | −1.95861 | ||||||||
\(342\) | 399.486 | 0.0631630 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4728.16 | 0.741062 | ||||||||
\(345\) | 223.084 | 0.0348129 | ||||||||
\(346\) | −5035.81 | −0.782448 | ||||||||
\(347\) | −5630.87 | −0.871126 | −0.435563 | − | 0.900158i | \(-0.643451\pi\) | ||||
−0.435563 | + | 0.900158i | \(0.643451\pi\) | |||||||
\(348\) | −1613.24 | −0.248502 | ||||||||
\(349\) | −325.221 | −0.0498817 | −0.0249408 | − | 0.999689i | \(-0.507940\pi\) | ||||
−0.0249408 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10771.5 | −1.63800 | ||||||||
\(352\) | 3645.62 | 0.552023 | ||||||||
\(353\) | 480.480 | 0.0724458 | 0.0362229 | − | 0.999344i | \(-0.488467\pi\) | ||||
0.0362229 | + | 0.999344i | \(0.488467\pi\) | |||||||
\(354\) | 12593.7 | 1.89082 | ||||||||
\(355\) | −76.3161 | −0.0114097 | ||||||||
\(356\) | 433.577 | 0.0645492 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5557.86 | 0.820509 | ||||||||
\(359\) | −11037.5 | −1.62266 | −0.811332 | − | 0.584585i | \(-0.801257\pi\) | ||||
−0.811332 | + | 0.584585i | \(0.801257\pi\) | |||||||
\(360\) | −24.6622 | −0.00361059 | ||||||||
\(361\) | −5852.28 | −0.853226 | ||||||||
\(362\) | 10513.6 | 1.52647 | ||||||||
\(363\) | 822.399 | 0.118911 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.73864 | −0.000822942 0 | ||||||||
\(366\) | 7340.70 | 1.04837 | ||||||||
\(367\) | 7472.00 | 1.06277 | 0.531383 | − | 0.847132i | \(-0.321673\pi\) | ||||
0.531383 | + | 0.847132i | \(0.321673\pi\) | |||||||
\(368\) | −9172.34 | −1.29930 | ||||||||
\(369\) | −162.044 | −0.0228609 | ||||||||
\(370\) | 370.553 | 0.0520653 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3833.38 | 0.534278 | ||||||||
\(373\) | −6358.92 | −0.882715 | −0.441357 | − | 0.897331i | \(-0.645503\pi\) | ||||
−0.441357 | + | 0.897331i | \(0.645503\pi\) | |||||||
\(374\) | −11643.4 | −1.60980 | ||||||||
\(375\) | −465.373 | −0.0640847 | ||||||||
\(376\) | 569.079 | 0.0780532 | ||||||||
\(377\) | −11338.0 | −1.54891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8642.35 | 1.17131 | 0.585656 | − | 0.810559i | \(-0.300837\pi\) | ||||
0.585656 | + | 0.810559i | \(0.300837\pi\) | |||||||
\(380\) | 22.8180 | 0.00308037 | ||||||||
\(381\) | −8873.66 | −1.19321 | ||||||||
\(382\) | −1097.33 | −0.146974 | ||||||||
\(383\) | 1494.74 | 0.199419 | 0.0997095 | − | 0.995017i | \(-0.468209\pi\) | ||||
0.0997095 | + | 0.995017i | \(0.468209\pi\) | |||||||
\(384\) | 9723.70 | 1.29222 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15747.7 | −2.07652 | ||||||||
\(387\) | −1002.46 | −0.131674 | ||||||||
\(388\) | 788.062 | 0.103113 | ||||||||
\(389\) | −12987.4 | −1.69277 | −0.846383 | − | 0.532574i | \(-0.821225\pi\) | ||||
−0.846383 | + | 0.532574i | \(0.821225\pi\) | |||||||
\(390\) | 498.373 | 0.0647080 | ||||||||
\(391\) | 11385.1 | 1.47255 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16021.7 | 2.05646 | ||||||||
\(394\) | −13496.4 | −1.72573 | ||||||||
\(395\) | −150.733 | −0.0192006 | ||||||||
\(396\) | −326.528 | −0.0414360 | ||||||||
\(397\) | 5665.16 | 0.716187 | 0.358093 | − | 0.933686i | \(-0.383427\pi\) | ||||
0.358093 | + | 0.933686i | \(0.383427\pi\) | |||||||
\(398\) | −16930.2 | −2.13224 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9562.87 | 1.19536 | ||||||||
\(401\) | −14464.0 | −1.80124 | −0.900619 | − | 0.434609i | \(-0.856887\pi\) | ||||
−0.900619 | + | 0.434609i | \(0.856887\pi\) | |||||||
\(402\) | 1405.12 | 0.174331 | ||||||||
\(403\) | 26941.4 | 3.33015 | ||||||||
\(404\) | 1326.06 | 0.163301 | ||||||||
\(405\) | −274.519 | −0.0336813 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13362.9 | −1.62745 | ||||||||
\(408\) | −9856.95 | −1.19606 | ||||||||
\(409\) | 9111.03 | 1.10149 | 0.550747 | − | 0.834672i | \(-0.314343\pi\) | ||||
0.550747 | + | 0.834672i | \(0.314343\pi\) | |||||||
\(410\) | −43.7212 | −0.00526643 | ||||||||
\(411\) | 11100.8 | 1.33227 | ||||||||
\(412\) | 3788.44 | 0.453017 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1508.20 | 0.179044 | ||||||||
\(415\) | −117.172 | −0.0138596 | ||||||||
\(416\) | −7963.67 | −0.938584 | ||||||||
\(417\) | 16541.6 | 1.94255 | ||||||||
\(418\) | −3886.97 | −0.454827 | ||||||||
\(419\) | −1605.47 | −0.187189 | −0.0935945 | − | 0.995610i | \(-0.529836\pi\) | ||||
−0.0935945 | + | 0.995610i | \(0.529836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6930.23 | −0.802277 | −0.401138 | − | 0.916017i | \(-0.631385\pi\) | ||||
−0.401138 | + | 0.916017i | \(0.631385\pi\) | |||||||
\(422\) | −7754.79 | −0.894543 | ||||||||
\(423\) | −120.656 | −0.0138687 | ||||||||
\(424\) | −2910.11 | −0.333319 | ||||||||
\(425\) | −11869.8 | −1.35475 | ||||||||
\(426\) | −4040.66 | −0.459555 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2590.73 | 0.292588 | ||||||||
\(429\) | −17972.3 | −2.02264 | ||||||||
\(430\) | −270.475 | −0.0303336 | ||||||||
\(431\) | −374.715 | −0.0418780 | −0.0209390 | − | 0.999781i | \(-0.506666\pi\) | ||||
−0.0209390 | + | 0.999781i | \(0.506666\pi\) | |||||||
\(432\) | 9818.42 | 1.09349 | ||||||||
\(433\) | −8798.22 | −0.976479 | −0.488240 | − | 0.872710i | \(-0.662361\pi\) | ||||
−0.488240 | + | 0.872710i | \(0.662361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −251.358 | −0.0277051 | ||||||||
\(436\) | 2938.93 | 0.322819 | ||||||||
\(437\) | 3800.73 | 0.416050 | ||||||||
\(438\) | −303.840 | −0.0331462 | ||||||||
\(439\) | 6402.67 | 0.696088 | 0.348044 | − | 0.937478i | \(-0.386846\pi\) | ||||
0.348044 | + | 0.937478i | \(0.386846\pi\) | |||||||
\(440\) | 239.961 | 0.0259993 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25434.4 | 2.73708 | ||||||||
\(443\) | −432.334 | −0.0463675 | −0.0231838 | − | 0.999731i | \(-0.507380\pi\) | ||||
−0.0231838 | + | 0.999731i | \(0.507380\pi\) | |||||||
\(444\) | 4153.39 | 0.443945 | ||||||||
\(445\) | 67.5555 | 0.00719649 | ||||||||
\(446\) | −11057.6 | −1.17397 | ||||||||
\(447\) | −5364.56 | −0.567640 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2840.47 | 0.298553 | 0.149276 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149276 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(450\) | −1572.42 | −0.164721 | ||||||||
\(451\) | 1576.67 | 0.164618 | ||||||||
\(452\) | 2694.98 | 0.280446 | ||||||||
\(453\) | 4622.73 | 0.479458 | ||||||||
\(454\) | −12072.1 | −1.24796 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3290.60 | −0.337930 | ||||||||
\(457\) | 1239.04 | 0.126827 | 0.0634133 | − | 0.997987i | \(-0.479801\pi\) | ||||
0.0634133 | + | 0.997987i | \(0.479801\pi\) | |||||||
\(458\) | −7631.60 | −0.778605 | ||||||||
\(459\) | −12187.0 | −1.23930 | ||||||||
\(460\) | 86.1463 | 0.00873173 | ||||||||
\(461\) | 2295.98 | 0.231962 | 0.115981 | − | 0.993251i | \(-0.462999\pi\) | ||||
0.115981 | + | 0.993251i | \(0.462999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12105.9 | 1.21513 | 0.607567 | − | 0.794268i | \(-0.292146\pi\) | ||||
0.607567 | + | 0.794268i | \(0.292146\pi\) | |||||||
\(464\) | 10334.9 | 1.03402 | ||||||||
\(465\) | 597.278 | 0.0595658 | ||||||||
\(466\) | −3264.46 | −0.324514 | ||||||||
\(467\) | 1050.00 | 0.104043 | 0.0520215 | − | 0.998646i | \(-0.483434\pi\) | ||||
0.0520215 | + | 0.998646i | \(0.483434\pi\) | |||||||
\(468\) | 713.285 | 0.0704522 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −32.5542 | −0.00319492 | ||||||||
\(471\) | −9906.99 | −0.969194 | ||||||||
\(472\) | −13246.0 | −1.29173 | ||||||||
\(473\) | 9753.86 | 0.948167 | ||||||||
\(474\) | −7980.78 | −0.773353 | ||||||||
\(475\) | −3962.55 | −0.382767 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 616.999 | 0.0592252 | ||||||||
\(478\) | −11104.5 | −1.06257 | ||||||||
\(479\) | −8044.42 | −0.767347 | −0.383673 | − | 0.923469i | \(-0.625341\pi\) | ||||
−0.383673 | + | 0.923469i | \(0.625341\pi\) | |||||||
\(480\) | −176.551 | −0.0167883 | ||||||||
\(481\) | 29190.6 | 2.76710 | ||||||||
\(482\) | 3493.92 | 0.330173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 317.578 | 0.0298252 | ||||||||
\(485\) | 122.788 | 0.0114959 | ||||||||
\(486\) | −3505.73 | −0.327208 | ||||||||
\(487\) | −5873.37 | −0.546505 | −0.273252 | − | 0.961942i | \(-0.588099\pi\) | ||||
−0.273252 | + | 0.961942i | \(0.588099\pi\) | |||||||
\(488\) | −7720.86 | −0.716203 | ||||||||
\(489\) | −3445.67 | −0.318647 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2136.28 | 0.196352 | 0.0981762 | − | 0.995169i | \(-0.468699\pi\) | ||||
0.0981762 | + | 0.995169i | \(0.468699\pi\) | |||||||
\(492\) | −490.055 | −0.0449052 | ||||||||
\(493\) | −12828.0 | −1.17190 | ||||||||
\(494\) | 8490.89 | 0.773326 | ||||||||
\(495\) | −50.8764 | −0.00461964 | ||||||||
\(496\) | −24557.7 | −2.22313 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6203.81 | −0.558232 | ||||||||
\(499\) | 11060.7 | 0.992274 | 0.496137 | − | 0.868244i | \(-0.334751\pi\) | ||||
0.496137 | + | 0.868244i | \(0.334751\pi\) | |||||||
\(500\) | −179.709 | −0.0160736 | ||||||||
\(501\) | −18064.1 | −1.61087 | ||||||||
\(502\) | 7166.04 | 0.637123 | ||||||||
\(503\) | 14041.1 | 1.24465 | 0.622326 | − | 0.782758i | \(-0.286188\pi\) | ||||
0.622326 | + | 0.782758i | \(0.286188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 206.613 | 0.0182062 | ||||||||
\(506\) | −14674.7 | −1.28927 | ||||||||
\(507\) | 27036.7 | 2.36833 | ||||||||
\(508\) | −3426.66 | −0.299278 | ||||||||
\(509\) | 13576.2 | 1.18223 | 0.591115 | − | 0.806587i | \(-0.298688\pi\) | ||||
0.591115 | + | 0.806587i | \(0.298688\pi\) | |||||||
\(510\) | 563.867 | 0.0489578 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4160.01 | −0.359079 | ||||||||
\(513\) | −4068.45 | −0.350149 | ||||||||
\(514\) | −12456.5 | −1.06894 | ||||||||
\(515\) | 590.277 | 0.0505062 | ||||||||
\(516\) | −3031.65 | −0.258646 | ||||||||
\(517\) | 1173.97 | 0.0998667 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8794.62 | −0.743817 | ||||||||
\(520\) | −524.183 | −0.0442057 | ||||||||
\(521\) | −3978.01 | −0.334510 | −0.167255 | − | 0.985914i | \(-0.553490\pi\) | ||||
−0.167255 | + | 0.985914i | \(0.553490\pi\) | |||||||
\(522\) | −1699.36 | −0.142488 | ||||||||
\(523\) | −16138.4 | −1.34930 | −0.674650 | − | 0.738138i | \(-0.735705\pi\) | ||||
−0.674650 | + | 0.738138i | \(0.735705\pi\) | |||||||
\(524\) | 6186.95 | 0.515798 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8840.81 | −0.732847 | ||||||||
\(527\) | 30482.0 | 2.51957 | ||||||||
\(528\) | 16382.2 | 1.35027 | ||||||||
\(529\) | 2182.13 | 0.179348 | ||||||||
\(530\) | 166.473 | 0.0136436 | ||||||||
\(531\) | 2808.40 | 0.229518 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3444.16 | −0.279894 | ||||||||
\(534\) | 3576.82 | 0.289858 | ||||||||
\(535\) | 403.661 | 0.0326202 | ||||||||
\(536\) | −1477.89 | −0.119096 | ||||||||
\(537\) | 9706.34 | 0.779999 | ||||||||
\(538\) | 15190.0 | 1.21726 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −92.2143 | −0.00734865 | ||||||||
\(541\) | −7125.75 | −0.566284 | −0.283142 | − | 0.959078i | \(-0.591377\pi\) | ||||
−0.283142 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(542\) | 9888.65 | 0.783679 | ||||||||
\(543\) | 18361.1 | 1.45111 | ||||||||
\(544\) | −9010.22 | −0.710129 | ||||||||
\(545\) | 457.914 | 0.0359906 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13164.9 | −1.02905 | −0.514524 | − | 0.857476i | \(-0.672031\pi\) | ||||
−0.514524 | + | 0.857476i | \(0.672031\pi\) | |||||||
\(548\) | 4286.71 | 0.334159 | ||||||||
\(549\) | 1636.97 | 0.127257 | ||||||||
\(550\) | 15299.5 | 1.18613 | ||||||||
\(551\) | −4282.45 | −0.331104 | ||||||||
\(552\) | −12423.2 | −0.957909 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1656.42 | 0.127030 | ||||||||
\(555\) | 647.140 | 0.0494947 | ||||||||
\(556\) | 6387.71 | 0.487229 | ||||||||
\(557\) | −19798.1 | −1.50606 | −0.753028 | − | 0.657989i | \(-0.771407\pi\) | ||||
−0.753028 | + | 0.657989i | \(0.771407\pi\) | |||||||
\(558\) | 4038.02 | 0.306349 | ||||||||
\(559\) | −21306.8 | −1.61213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20334.2 | −1.53032 | ||||||||
\(562\) | −16726.0 | −1.25542 | ||||||||
\(563\) | 6539.11 | 0.489504 | 0.244752 | − | 0.969586i | \(-0.421293\pi\) | ||||
0.244752 | + | 0.969586i | \(0.421293\pi\) | |||||||
\(564\) | −364.888 | −0.0272421 | ||||||||
\(565\) | 419.905 | 0.0312665 | ||||||||
\(566\) | 3921.85 | 0.291250 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4249.92 | 0.313948 | ||||||||
\(569\) | 4152.49 | 0.305943 | 0.152971 | − | 0.988231i | \(-0.451116\pi\) | ||||
0.152971 | + | 0.988231i | \(0.451116\pi\) | |||||||
\(570\) | 188.239 | 0.0138324 | ||||||||
\(571\) | −16030.8 | −1.17490 | −0.587451 | − | 0.809260i | \(-0.699868\pi\) | ||||
−0.587451 | + | 0.809260i | \(0.699868\pi\) | |||||||
\(572\) | −6940.21 | −0.507316 | ||||||||
\(573\) | −1916.39 | −0.139718 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14960.1 | −1.08500 | ||||||||
\(576\) | 1227.46 | 0.0887918 | ||||||||
\(577\) | 16743.8 | 1.20807 | 0.604033 | − | 0.796960i | \(-0.293560\pi\) | ||||
0.604033 | + | 0.796960i | \(0.293560\pi\) | |||||||
\(578\) | 13125.7 | 0.944565 | ||||||||
\(579\) | −27502.0 | −1.97400 | ||||||||
\(580\) | −97.0648 | −0.00694896 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 6501.16 | 0.463027 | ||||||||
\(583\) | −6003.34 | −0.426472 | ||||||||
\(584\) | 319.575 | 0.0226440 | ||||||||
\(585\) | 111.137 | 0.00785461 | ||||||||
\(586\) | −28119.2 | −1.98224 | ||||||||
\(587\) | 20200.5 | 1.42038 | 0.710190 | − | 0.704010i | \(-0.248609\pi\) | ||||
0.710190 | + | 0.704010i | \(0.248609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10176.0 | 0.711873 | ||||||||
\(590\) | 757.736 | 0.0528737 | ||||||||
\(591\) | −23570.3 | −1.64053 | ||||||||
\(592\) | −26607.9 | −1.84726 | ||||||||
\(593\) | 15556.5 | 1.07728 | 0.538642 | − | 0.842535i | \(-0.318938\pi\) | ||||
0.538642 | + | 0.842535i | \(0.318938\pi\) | |||||||
\(594\) | 15708.4 | 1.08505 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2071.58 | −0.142375 | ||||||||
\(597\) | −29567.1 | −2.02697 | ||||||||
\(598\) | 32056.2 | 2.19210 | ||||||||
\(599\) | 25922.9 | 1.76825 | 0.884125 | − | 0.467250i | \(-0.154755\pi\) | ||||
0.884125 | + | 0.467250i | \(0.154755\pi\) | |||||||
\(600\) | 12952.1 | 0.881279 | ||||||||
\(601\) | 16623.4 | 1.12826 | 0.564128 | − | 0.825687i | \(-0.309212\pi\) | ||||
0.564128 | + | 0.825687i | \(0.309212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 313.342 | 0.0211613 | ||||||||
\(604\) | 1785.12 | 0.120257 | ||||||||
\(605\) | 49.4818 | 0.00332516 | ||||||||
\(606\) | 10939.4 | 0.733303 | ||||||||
\(607\) | 8474.16 | 0.566649 | 0.283324 | − | 0.959024i | \(-0.408563\pi\) | ||||
0.283324 | + | 0.959024i | \(0.408563\pi\) | |||||||
\(608\) | −3007.93 | −0.200638 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 441.673 | 0.0293161 | ||||||||
\(611\) | −2564.48 | −0.169800 | ||||||||
\(612\) | 807.022 | 0.0533038 | ||||||||
\(613\) | −29418.5 | −1.93834 | −0.969169 | − | 0.246395i | \(-0.920754\pi\) | ||||
−0.969169 | + | 0.246395i | \(0.920754\pi\) | |||||||
\(614\) | 24372.7 | 1.60196 | ||||||||
\(615\) | −76.3554 | −0.00500642 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 722.623 | 0.0471503 | 0.0235751 | − | 0.999722i | \(-0.492495\pi\) | ||||
0.0235751 | + | 0.999722i | \(0.492495\pi\) | |||||||
\(618\) | 31253.0 | 2.03427 | ||||||||
\(619\) | 12086.3 | 0.784799 | 0.392399 | − | 0.919795i | \(-0.371645\pi\) | ||||
0.392399 | + | 0.919795i | \(0.371645\pi\) | |||||||
\(620\) | 230.645 | 0.0149402 | ||||||||
\(621\) | −15359.9 | −0.992544 | ||||||||
\(622\) | −10453.7 | −0.673883 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −35786.1 | −2.29582 | ||||||||
\(625\) | 15583.0 | 0.997312 | ||||||||
\(626\) | −5233.58 | −0.334147 | ||||||||
\(627\) | −6788.26 | −0.432372 | ||||||||
\(628\) | −3825.69 | −0.243092 | ||||||||
\(629\) | 33026.7 | 2.09358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15819.6 | 0.998047 | 0.499023 | − | 0.866588i | \(-0.333692\pi\) | ||||
0.499023 | + | 0.866588i | \(0.333692\pi\) | |||||||
\(632\) | 8394.09 | 0.528321 | ||||||||
\(633\) | −13543.1 | −0.850378 | ||||||||
\(634\) | 21469.0 | 1.34486 | ||||||||
\(635\) | −533.908 | −0.0333661 | ||||||||
\(636\) | 1865.93 | 0.116335 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16534.6 | 1.02604 | ||||||||
\(639\) | −901.064 | −0.0557833 | ||||||||
\(640\) | 585.052 | 0.0361347 | ||||||||
\(641\) | 15252.1 | 0.939812 | 0.469906 | − | 0.882716i | \(-0.344288\pi\) | ||||
0.469906 | + | 0.882716i | \(0.344288\pi\) | |||||||
\(642\) | 21372.4 | 1.31386 | ||||||||
\(643\) | 8815.11 | 0.540644 | 0.270322 | − | 0.962770i | \(-0.412870\pi\) | ||||
0.270322 | + | 0.962770i | \(0.412870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −472.361 | −0.0288360 | ||||||||
\(646\) | 9606.73 | 0.585096 | ||||||||
\(647\) | −598.573 | −0.0363714 | −0.0181857 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181857 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(648\) | 15287.5 | 0.926773 | ||||||||
\(649\) | −27325.5 | −1.65273 | ||||||||
\(650\) | −33421.0 | −2.01674 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1330.58 | −0.0799227 | ||||||||
\(653\) | −2615.66 | −0.156751 | −0.0783757 | − | 0.996924i | \(-0.524973\pi\) | ||||
−0.0783757 | + | 0.996924i | \(0.524973\pi\) | |||||||
\(654\) | 24244.9 | 1.44962 | ||||||||
\(655\) | 963.988 | 0.0575055 | ||||||||
\(656\) | 3139.43 | 0.186851 | ||||||||
\(657\) | −67.7560 | −0.00402346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11736.3 | 0.693748 | 0.346874 | − | 0.937912i | \(-0.387243\pi\) | ||||
0.346874 | + | 0.937912i | \(0.387243\pi\) | |||||||
\(660\) | −153.861 | −0.00907428 | ||||||||
\(661\) | 23690.7 | 1.39404 | 0.697020 | − | 0.717051i | \(-0.254509\pi\) | ||||
0.697020 | + | 0.717051i | \(0.254509\pi\) | |||||||
\(662\) | 33442.1 | 1.96339 | ||||||||
\(663\) | 44419.0 | 2.60195 | ||||||||
\(664\) | 6525.10 | 0.381360 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4375.12 | 0.254553 | ||||||||
\(667\) | −16167.8 | −0.938559 | ||||||||
\(668\) | −6975.66 | −0.404036 | ||||||||
\(669\) | −19311.1 | −1.11601 | ||||||||
\(670\) | 84.5431 | 0.00487490 | ||||||||
\(671\) | −15927.6 | −0.916361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15904.6 | −0.910961 | −0.455481 | − | 0.890246i | \(-0.650533\pi\) | ||||
−0.455481 | + | 0.890246i | \(0.650533\pi\) | |||||||
\(674\) | −8944.18 | −0.511153 | ||||||||
\(675\) | 16013.8 | 0.913144 | ||||||||
\(676\) | 10440.5 | 0.594021 | ||||||||
\(677\) | 11161.5 | 0.633638 | 0.316819 | − | 0.948486i | \(-0.397385\pi\) | ||||
0.316819 | + | 0.948486i | \(0.397385\pi\) | |||||||
\(678\) | 22232.4 | 1.25934 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −593.069 | −0.0334458 | ||||||||
\(681\) | −21082.9 | −1.18634 | ||||||||
\(682\) | −39289.6 | −2.20598 | ||||||||
\(683\) | −25946.3 | −1.45360 | −0.726800 | − | 0.686849i | \(-0.758993\pi\) | ||||
−0.726800 | + | 0.686849i | \(0.758993\pi\) | |||||||
\(684\) | 269.412 | 0.0150603 | ||||||||
\(685\) | 667.912 | 0.0372549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13327.9 | −0.740164 | ||||||||
\(688\) | 19421.7 | 1.07623 | ||||||||
\(689\) | 13114.0 | 0.725115 | ||||||||
\(690\) | 710.669 | 0.0392097 | ||||||||
\(691\) | −7479.42 | −0.411766 | −0.205883 | − | 0.978577i | \(-0.566007\pi\) | ||||
−0.205883 | + | 0.978577i | \(0.566007\pi\) | |||||||
\(692\) | −3396.14 | −0.186563 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17938.0 | −0.981149 | ||||||||
\(695\) | 995.269 | 0.0543204 | ||||||||
\(696\) | 13997.7 | 0.762331 | ||||||||
\(697\) | −3896.78 | −0.211766 | ||||||||
\(698\) | −1036.04 | −0.0561817 | ||||||||
\(699\) | −5701.11 | −0.308492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6592.06 | 0.355176 | 0.177588 | − | 0.984105i | \(-0.443170\pi\) | ||||
0.177588 | + | 0.984105i | \(0.443170\pi\) | |||||||
\(702\) | −34314.1 | −1.84488 | ||||||||
\(703\) | 11025.5 | 0.591512 | ||||||||
\(704\) | −11943.1 | −0.639377 | ||||||||
\(705\) | −56.8532 | −0.00303718 | ||||||||
\(706\) | 1530.64 | 0.0815956 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8493.19 | 0.450838 | ||||||||
\(709\) | −5097.27 | −0.270003 | −0.135001 | − | 0.990845i | \(-0.543104\pi\) | ||||
−0.135001 | + | 0.990845i | \(0.543104\pi\) | |||||||
\(710\) | −243.117 | −0.0128507 | ||||||||
\(711\) | −1779.71 | −0.0938738 | ||||||||
\(712\) | −3762.05 | −0.198018 | ||||||||
\(713\) | 38417.9 | 2.01790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1081.35 | −0.0565599 | ||||||||
\(716\) | 3748.21 | 0.195638 | ||||||||
\(717\) | −19393.1 | −1.01011 | ||||||||
\(718\) | −35161.6 | −1.82761 | ||||||||
\(719\) | 9877.35 | 0.512327 | 0.256163 | − | 0.966633i | \(-0.417541\pi\) | ||||
0.256163 | + | 0.966633i | \(0.417541\pi\) | |||||||
\(720\) | −101.304 | −0.00524357 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18643.3 | −0.960988 | ||||||||
\(723\) | 6101.83 | 0.313872 | ||||||||
\(724\) | 7090.35 | 0.363965 | ||||||||
\(725\) | 16856.1 | 0.863478 | ||||||||
\(726\) | 2619.88 | 0.133930 | ||||||||
\(727\) | −19002.3 | −0.969405 | −0.484703 | − | 0.874679i | \(-0.661072\pi\) | ||||
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16020.0 | 0.813901 | ||||||||
\(730\) | −18.2813 | −0.000926879 0 | ||||||||
\(731\) | −24106.9 | −1.21973 | ||||||||
\(732\) | 4950.55 | 0.249969 | ||||||||
\(733\) | 4605.75 | 0.232083 | 0.116042 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116042 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(734\) | 23803.2 | 1.19699 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11356.0 | −0.568734 | ||||||||
\(737\) | −3048.79 | −0.152379 | ||||||||
\(738\) | −516.216 | −0.0257482 | ||||||||
\(739\) | 15279.3 | 0.760566 | 0.380283 | − | 0.924870i | \(-0.375827\pi\) | ||||
0.380283 | + | 0.924870i | \(0.375827\pi\) | |||||||
\(740\) | 249.900 | 0.0124142 | ||||||||
\(741\) | 14828.6 | 0.735146 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36053.8 | −1.78020 | −0.890098 | − | 0.455769i | \(-0.849364\pi\) | ||||
−0.890098 | + | 0.455769i | \(0.849364\pi\) | |||||||
\(744\) | −33261.4 | −1.63901 | ||||||||
\(745\) | −322.773 | −0.0158731 | ||||||||
\(746\) | −20257.3 | −0.994201 | ||||||||
\(747\) | −1383.45 | −0.0677612 | ||||||||
\(748\) | −7852.26 | −0.383833 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1482.52 | −0.0721785 | ||||||||
\(751\) | 6492.85 | 0.315482 | 0.157741 | − | 0.987480i | \(-0.449579\pi\) | ||||
0.157741 | + | 0.987480i | \(0.449579\pi\) | |||||||
\(752\) | 2337.58 | 0.113355 | ||||||||
\(753\) | 12514.9 | 0.605668 | ||||||||
\(754\) | −36119.1 | −1.74453 | ||||||||
\(755\) | 278.139 | 0.0134073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10407.2 | −0.499680 | −0.249840 | − | 0.968287i | \(-0.580378\pi\) | ||||
−0.249840 | + | 0.968287i | \(0.580378\pi\) | |||||||
\(758\) | 27531.5 | 1.31925 | ||||||||
\(759\) | −25628.1 | −1.22562 | ||||||||
\(760\) | −197.987 | −0.00944968 | ||||||||
\(761\) | −36057.9 | −1.71761 | −0.858803 | − | 0.512306i | \(-0.828791\pi\) | ||||
−0.858803 | + | 0.512306i | \(0.828791\pi\) | |||||||
\(762\) | −28268.4 | −1.34391 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −740.035 | −0.0350439 | ||||||||
\(765\) | 125.742 | 0.00594276 | ||||||||
\(766\) | 4761.72 | 0.224606 | ||||||||
\(767\) | 59691.2 | 2.81007 | ||||||||
\(768\) | 17153.6 | 0.805961 | ||||||||
\(769\) | 11977.1 | 0.561645 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21754.3 | −1.01616 | ||||||||
\(772\) | −10620.2 | −0.495115 | ||||||||
\(773\) | −14624.3 | −0.680465 | −0.340232 | − | 0.940341i | \(-0.610506\pi\) | ||||
−0.340232 | + | 0.940341i | \(0.610506\pi\) | |||||||
\(774\) | −3193.49 | −0.148305 | ||||||||
\(775\) | −40053.6 | −1.85647 | ||||||||
\(776\) | −6837.85 | −0.316320 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41373.3 | −1.90656 | ||||||||
\(779\) | −1300.88 | −0.0598318 | ||||||||
\(780\) | 336.101 | 0.0154287 | ||||||||
\(781\) | 8767.28 | 0.401687 | ||||||||
\(782\) | 36268.9 | 1.65853 | ||||||||
\(783\) | 17306.6 | 0.789895 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −596.081 | −0.0271020 | ||||||||
\(786\) | 51039.6 | 2.31619 | ||||||||
\(787\) | −16830.0 | −0.762292 | −0.381146 | − | 0.924515i | \(-0.624471\pi\) | ||||
−0.381146 | + | 0.924515i | \(0.624471\pi\) | |||||||
\(788\) | −9101.91 | −0.411475 | ||||||||
\(789\) | −15439.7 | −0.696665 | ||||||||
\(790\) | −480.185 | −0.0216256 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2833.22 | 0.127114 | ||||||||
\(793\) | 34793.0 | 1.55805 | ||||||||
\(794\) | 18047.2 | 0.806641 | ||||||||
\(795\) | 290.731 | 0.0129700 | ||||||||
\(796\) | −11417.7 | −0.508402 | ||||||||
\(797\) | 20542.8 | 0.913004 | 0.456502 | − | 0.889722i | \(-0.349102\pi\) | ||||
0.456502 | + | 0.889722i | \(0.349102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2901.49 | −0.128470 | ||||||||
\(800\) | 11839.5 | 0.523237 | ||||||||
\(801\) | 797.628 | 0.0351845 | ||||||||
\(802\) | −46077.2 | −2.02873 | ||||||||
\(803\) | 659.260 | 0.0289723 | ||||||||
\(804\) | 947.612 | 0.0415668 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 85826.1 | 3.75074 | ||||||||
\(807\) | 26528.0 | 1.15716 | ||||||||
\(808\) | −11505.9 | −0.500961 | ||||||||
\(809\) | −35693.0 | −1.55117 | −0.775587 | − | 0.631240i | \(-0.782546\pi\) | ||||
−0.775587 | + | 0.631240i | \(0.782546\pi\) | |||||||
\(810\) | −874.521 | −0.0379352 | ||||||||
\(811\) | −5527.05 | −0.239311 | −0.119655 | − | 0.992815i | \(-0.538179\pi\) | ||||
−0.119655 | + | 0.992815i | \(0.538179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17269.7 | 0.744988 | ||||||||
\(814\) | −42569.5 | −1.83300 | ||||||||
\(815\) | −207.318 | −0.00891047 | ||||||||
\(816\) | −40488.9 | −1.73700 | ||||||||
\(817\) | −8047.72 | −0.344620 | ||||||||
\(818\) | 29024.6 | 1.24061 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.4855 | −0.00125570 | ||||||||
\(821\) | 6140.52 | 0.261030 | 0.130515 | − | 0.991446i | \(-0.458337\pi\) | ||||
0.130515 | + | 0.991446i | \(0.458337\pi\) | |||||||
\(822\) | 35363.5 | 1.50054 | ||||||||
\(823\) | 36144.8 | 1.53090 | 0.765450 | − | 0.643496i | \(-0.222517\pi\) | ||||
0.765450 | + | 0.643496i | \(0.222517\pi\) | |||||||
\(824\) | −32871.5 | −1.38973 | ||||||||
\(825\) | 26719.3 | 1.12757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12049.0 | 0.506633 | 0.253316 | − | 0.967383i | \(-0.418479\pi\) | ||||
0.253316 | + | 0.967383i | \(0.418479\pi\) | |||||||
\(828\) | 1017.13 | 0.0426904 | ||||||||
\(829\) | −9448.89 | −0.395867 | −0.197933 | − | 0.980215i | \(-0.563423\pi\) | ||||
−0.197933 | + | 0.980215i | \(0.563423\pi\) | |||||||
\(830\) | −373.269 | −0.0156101 | ||||||||
\(831\) | 2892.80 | 0.120758 | ||||||||
\(832\) | 26089.0 | 1.08711 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 52695.8 | 2.18790 | ||||||||
\(835\) | −1086.88 | −0.0450454 | ||||||||
\(836\) | −2621.36 | −0.108447 | ||||||||
\(837\) | −41124.0 | −1.69827 | ||||||||
\(838\) | −5114.46 | −0.210831 | ||||||||
\(839\) | −26070.9 | −1.07279 | −0.536393 | − | 0.843968i | \(-0.680214\pi\) | ||||
−0.536393 | + | 0.843968i | \(0.680214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6172.07 | −0.253068 | ||||||||
\(842\) | −22077.3 | −0.903604 | ||||||||
\(843\) | −29210.6 | −1.19344 | ||||||||
\(844\) | −5229.81 | −0.213291 | ||||||||
\(845\) | 1626.73 | 0.0662265 | ||||||||
\(846\) | −384.367 | −0.0156203 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11953.7 | −0.484071 | ||||||||
\(849\) | 6849.18 | 0.276871 | ||||||||
\(850\) | −37813.0 | −1.52585 | ||||||||
\(851\) | 41625.1 | 1.67672 | ||||||||
\(852\) | −2725.01 | −0.109574 | ||||||||
\(853\) | −258.991 | −0.0103959 | −0.00519794 | − | 0.999986i | \(-0.501655\pi\) | ||||
−0.00519794 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41.9771 | 0.00167905 | ||||||||
\(856\) | −22479.2 | −0.897575 | ||||||||
\(857\) | −37899.8 | −1.51066 | −0.755329 | − | 0.655346i | \(-0.772523\pi\) | ||||
−0.755329 | + | 0.655346i | \(0.772523\pi\) | |||||||
\(858\) | −57253.6 | −2.27810 | ||||||||
\(859\) | −30576.7 | −1.21451 | −0.607254 | − | 0.794508i | \(-0.707729\pi\) | ||||
−0.607254 | + | 0.794508i | \(0.707729\pi\) | |||||||
\(860\) | −182.407 | −0.00723261 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1193.71 | −0.0471671 | ||||||||
\(863\) | 19691.6 | 0.776721 | 0.388360 | − | 0.921508i | \(-0.373042\pi\) | ||||
0.388360 | + | 0.921508i | \(0.373042\pi\) | |||||||
\(864\) | 12155.9 | 0.478649 | ||||||||
\(865\) | −529.152 | −0.0207997 | ||||||||
\(866\) | −28028.1 | −1.09981 | ||||||||
\(867\) | 22923.0 | 0.897931 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17316.4 | 0.675971 | ||||||||
\(870\) | −800.741 | −0.0312042 | ||||||||
\(871\) | 6659.93 | 0.259085 | ||||||||
\(872\) | −25500.5 | −0.990315 | ||||||||
\(873\) | 1449.76 | 0.0562048 | ||||||||
\(874\) | 12107.8 | 0.468596 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −204.909 | −0.00790322 | ||||||||
\(877\) | 26049.7 | 1.00301 | 0.501503 | − | 0.865156i | \(-0.332780\pi\) | ||||
0.501503 | + | 0.865156i | \(0.332780\pi\) | |||||||
\(878\) | 20396.7 | 0.784004 | ||||||||
\(879\) | −49107.8 | −1.88437 | ||||||||
\(880\) | 985.677 | 0.0377582 | ||||||||
\(881\) | 3519.60 | 0.134595 | 0.0672976 | − | 0.997733i | \(-0.478562\pi\) | ||||
0.0672976 | + | 0.997733i | \(0.478562\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6444.89 | 0.245626 | 0.122813 | − | 0.992430i | \(-0.460808\pi\) | ||||
0.122813 | + | 0.992430i | \(0.460808\pi\) | |||||||
\(884\) | 17152.9 | 0.652617 | ||||||||
\(885\) | 1323.32 | 0.0502633 | ||||||||
\(886\) | −1377.27 | −0.0522237 | ||||||||
\(887\) | −5990.84 | −0.226779 | −0.113389 | − | 0.993551i | \(-0.536171\pi\) | ||||
−0.113389 | + | 0.993551i | \(0.536171\pi\) | |||||||
\(888\) | −36038.1 | −1.36189 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 215.209 | 0.00810540 | ||||||||
\(891\) | 31537.0 | 1.18578 | ||||||||
\(892\) | −7457.21 | −0.279917 | ||||||||
\(893\) | −968.620 | −0.0362974 | ||||||||
\(894\) | −17089.6 | −0.639332 | ||||||||
\(895\) | 584.008 | 0.0218114 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 55983.4 | 2.08387 | ||||||||
\(898\) | 9048.76 | 0.336260 | ||||||||
\(899\) | −43287.1 | −1.60590 | ||||||||
\(900\) | −1060.43 | −0.0392753 | ||||||||
\(901\) | 14837.4 | 0.548619 | ||||||||
\(902\) | 5022.74 | 0.185409 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23383.8 | −0.860325 | ||||||||
\(905\) | 1104.75 | 0.0405779 | ||||||||
\(906\) | 14726.4 | 0.540013 | ||||||||
\(907\) | −32147.6 | −1.17690 | −0.588448 | − | 0.808535i | \(-0.700261\pi\) | ||||
−0.588448 | + | 0.808535i | \(0.700261\pi\) | |||||||
\(908\) | −8141.40 | −0.297557 | ||||||||
\(909\) | 2439.47 | 0.0890124 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21326.8 | 0.775620 | 0.387810 | − | 0.921739i | \(-0.373232\pi\) | ||||
0.387810 | + | 0.921739i | \(0.373232\pi\) | |||||||
\(912\) | −13516.6 | −0.490768 | ||||||||
\(913\) | 13460.8 | 0.487939 | ||||||||
\(914\) | 3947.15 | 0.142845 | ||||||||
\(915\) | 771.344 | 0.0278687 | ||||||||
\(916\) | −5146.73 | −0.185647 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −38823.6 | −1.39583 | ||||||||
\(919\) | 41696.0 | 1.49665 | 0.748326 | − | 0.663331i | \(-0.230858\pi\) | ||||
0.748326 | + | 0.663331i | \(0.230858\pi\) | |||||||
\(920\) | −747.474 | −0.0267864 | ||||||||
\(921\) | 42564.8 | 1.52287 | ||||||||
\(922\) | 7314.19 | 0.261258 | ||||||||
\(923\) | −19151.7 | −0.682974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −43397.3 | −1.54259 | ||||||||
\(926\) | 38565.1 | 1.36860 | ||||||||
\(927\) | 6969.39 | 0.246931 | ||||||||
\(928\) | 12795.3 | 0.452615 | ||||||||
\(929\) | −5066.09 | −0.178916 | −0.0894581 | − | 0.995991i | \(-0.528514\pi\) | ||||
−0.0894581 | + | 0.995991i | \(0.528514\pi\) | |||||||
\(930\) | 1902.72 | 0.0670889 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2201.54 | −0.0773755 | ||||||||
\(933\) | −18256.5 | −0.640612 | ||||||||
\(934\) | 3344.93 | 0.117183 | ||||||||
\(935\) | −1223.46 | −0.0427930 | ||||||||
\(936\) | −6189.03 | −0.216127 | ||||||||
\(937\) | 17184.7 | 0.599147 | 0.299573 | − | 0.954073i | \(-0.403156\pi\) | ||||
0.299573 | + | 0.954073i | \(0.403156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9140.01 | −0.317649 | ||||||||
\(940\) | −21.9545 | −0.000761782 0 | ||||||||
\(941\) | 5988.82 | 0.207471 | 0.103735 | − | 0.994605i | \(-0.466921\pi\) | ||||
0.103735 | + | 0.994605i | \(0.466921\pi\) | |||||||
\(942\) | −31560.3 | −1.09160 | ||||||||
\(943\) | −4911.30 | −0.169601 | ||||||||
\(944\) | −54409.8 | −1.87594 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31072.4 | 1.06792 | ||||||||
\(947\) | −15936.9 | −0.546863 | −0.273432 | − | 0.961891i | \(-0.588159\pi\) | ||||
−0.273432 | + | 0.961891i | \(0.588159\pi\) | |||||||
\(948\) | −5382.21 | −0.184395 | ||||||||
\(949\) | −1440.12 | −0.0492606 | ||||||||
\(950\) | −12623.3 | −0.431110 | ||||||||
\(951\) | 37493.8 | 1.27846 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11105.9 | 0.377499 | 0.188750 | − | 0.982025i | \(-0.439557\pi\) | ||||
0.188750 | + | 0.982025i | \(0.439557\pi\) | |||||||
\(954\) | 1965.54 | 0.0667053 | ||||||||
\(955\) | −115.305 | −0.00390699 | ||||||||
\(956\) | −7488.85 | −0.253354 | ||||||||
\(957\) | 28876.3 | 0.975380 | ||||||||
\(958\) | −25626.8 | −0.864262 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 578.381 | 0.0194450 | ||||||||
\(961\) | 73067.8 | 2.45268 | ||||||||
\(962\) | 92991.1 | 3.11658 | ||||||||
\(963\) | 4766.02 | 0.159484 | ||||||||
\(964\) | 2356.29 | 0.0787250 | ||||||||
\(965\) | −1654.73 | −0.0551997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24762.2 | −0.823473 | −0.411736 | − | 0.911303i | \(-0.635078\pi\) | ||||
−0.411736 | + | 0.911303i | \(0.635078\pi\) | |||||||
\(968\) | −2755.56 | −0.0914949 | ||||||||
\(969\) | 16777.3 | 0.556208 | ||||||||
\(970\) | 391.160 | 0.0129478 | ||||||||
\(971\) | −17148.7 | −0.566763 | −0.283382 | − | 0.959007i | \(-0.591456\pi\) | ||||
−0.283382 | + | 0.959007i | \(0.591456\pi\) | |||||||
\(972\) | −2364.25 | −0.0780179 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18710.5 | −0.615528 | ||||||||
\(975\) | −58366.9 | −1.91717 | ||||||||
\(976\) | −31714.6 | −1.04012 | ||||||||
\(977\) | 11486.5 | 0.376138 | 0.188069 | − | 0.982156i | \(-0.439777\pi\) | ||||
0.188069 | + | 0.982156i | \(0.439777\pi\) | |||||||
\(978\) | −10976.7 | −0.358892 | ||||||||
\(979\) | −7760.85 | −0.253358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5406.59 | 0.175962 | ||||||||
\(982\) | 6805.45 | 0.221151 | ||||||||
\(983\) | −27252.6 | −0.884255 | −0.442128 | − | 0.896952i | \(-0.645776\pi\) | ||||
−0.442128 | + | 0.896952i | \(0.645776\pi\) | |||||||
\(984\) | 4252.10 | 0.137756 | ||||||||
\(985\) | −1418.17 | −0.0458747 | ||||||||
\(986\) | −40865.7 | −1.31991 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5726.23 | 0.184388 | ||||||||
\(989\) | −30383.1 | −0.976870 | ||||||||
\(990\) | −162.074 | −0.00520310 | ||||||||
\(991\) | −58095.0 | −1.86221 | −0.931104 | − | 0.364754i | \(-0.881153\pi\) | ||||
−0.931104 | + | 0.364754i | \(0.881153\pi\) | |||||||
\(992\) | −30404.2 | −0.973120 | ||||||||
\(993\) | 58403.9 | 1.86646 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1778.98 | −0.0566810 | ||||||||
\(996\) | −4183.83 | −0.133102 | ||||||||
\(997\) | 16161.0 | 0.513363 | 0.256681 | − | 0.966496i | \(-0.417371\pi\) | ||||
0.256681 | + | 0.966496i | \(0.417371\pi\) | |||||||
\(998\) | 35235.6 | 1.11760 | ||||||||
\(999\) | −44557.1 | −1.41113 |
(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 | 2009.4.a.l.1.34 | 44 | ||
7.2 | even | 3 | 287.4.e.b.165.11 | ✓ | 88 | ||
7.4 | even | 3 | 287.4.e.b.247.11 | yes | 88 | ||
7.6 | odd | 2 | 2009.4.a.m.1.34 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.4.e.b.165.11 | ✓ | 88 | 7.2 | even | 3 | ||
287.4.e.b.247.11 | yes | 88 | 7.4 | even | 3 | ||
2009.4.a.l.1.34 | 44 | 1.1 | even | 1 | trivial | ||
2009.4.a.m.1.34 | 44 | 7.6 | odd | 2 |