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: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68929 | −0.597254 | −0.298627 | − | 0.954370i | \(-0.596529\pi\) | ||||
−0.298627 | + | 0.954370i | \(0.596529\pi\) | |||||||
\(3\) | 2.43988 | 0.469554 | 0.234777 | − | 0.972049i | \(-0.424564\pi\) | ||||
0.234777 | + | 0.972049i | \(0.424564\pi\) | |||||||
\(4\) | −5.14630 | −0.643288 | ||||||||
\(5\) | −3.14907 | −0.281662 | −0.140831 | − | 0.990034i | \(-0.544977\pi\) | ||||
−0.140831 | + | 0.990034i | \(0.544977\pi\) | |||||||
\(6\) | −4.12166 | −0.280443 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.2079 | 0.981460 | ||||||||
\(9\) | −21.0470 | −0.779519 | ||||||||
\(10\) | 5.31970 | 0.168224 | ||||||||
\(11\) | 30.9193 | 0.847501 | 0.423750 | − | 0.905779i | \(-0.360713\pi\) | ||||
0.423750 | + | 0.905779i | \(0.360713\pi\) | |||||||
\(12\) | −12.5563 | −0.302059 | ||||||||
\(13\) | −31.4823 | −0.671662 | −0.335831 | − | 0.941922i | \(-0.609017\pi\) | ||||
−0.335831 | + | 0.941922i | \(0.609017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.68335 | −0.132256 | ||||||||
\(16\) | 3.65483 | 0.0571068 | ||||||||
\(17\) | 88.8707 | 1.26790 | 0.633950 | − | 0.773374i | \(-0.281432\pi\) | ||||
0.633950 | + | 0.773374i | \(0.281432\pi\) | |||||||
\(18\) | 35.5545 | 0.465571 | ||||||||
\(19\) | −44.4699 | −0.536953 | −0.268476 | − | 0.963286i | \(-0.586520\pi\) | ||||
−0.268476 | + | 0.963286i | \(0.586520\pi\) | |||||||
\(20\) | 16.2061 | 0.181190 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −52.2316 | −0.506173 | ||||||||
\(23\) | 92.8471 | 0.841737 | 0.420869 | − | 0.907122i | \(-0.361725\pi\) | ||||
0.420869 | + | 0.907122i | \(0.361725\pi\) | |||||||
\(24\) | 54.1845 | 0.460849 | ||||||||
\(25\) | −115.083 | −0.920667 | ||||||||
\(26\) | 53.1826 | 0.401153 | ||||||||
\(27\) | −117.229 | −0.835581 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −267.929 | −1.71563 | −0.857814 | − | 0.513960i | \(-0.828178\pi\) | ||||
−0.857814 | + | 0.513960i | \(0.828178\pi\) | |||||||
\(30\) | 12.9794 | 0.0789901 | ||||||||
\(31\) | 95.7085 | 0.554508 | 0.277254 | − | 0.960797i | \(-0.410576\pi\) | ||||
0.277254 | + | 0.960797i | \(0.410576\pi\) | |||||||
\(32\) | −183.837 | −1.01557 | ||||||||
\(33\) | 75.4392 | 0.397948 | ||||||||
\(34\) | −150.128 | −0.757258 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 108.314 | 0.501455 | ||||||||
\(37\) | 148.796 | 0.661134 | 0.330567 | − | 0.943782i | \(-0.392760\pi\) | ||||
0.330567 | + | 0.943782i | \(0.392760\pi\) | |||||||
\(38\) | 75.1226 | 0.320697 | ||||||||
\(39\) | −76.8128 | −0.315382 | ||||||||
\(40\) | −69.9344 | −0.276440 | ||||||||
\(41\) | −41.0000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 168.504 | 0.597596 | 0.298798 | − | 0.954316i | \(-0.403414\pi\) | ||||
0.298798 | + | 0.954316i | \(0.403414\pi\) | |||||||
\(44\) | −159.120 | −0.545187 | ||||||||
\(45\) | 66.2786 | 0.219561 | ||||||||
\(46\) | −156.846 | −0.502731 | ||||||||
\(47\) | 246.163 | 0.763969 | 0.381985 | − | 0.924169i | \(-0.375241\pi\) | ||||
0.381985 | + | 0.924169i | \(0.375241\pi\) | |||||||
\(48\) | 8.91734 | 0.0268147 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 194.409 | 0.549872 | ||||||||
\(51\) | 216.833 | 0.595348 | ||||||||
\(52\) | 162.017 | 0.432072 | ||||||||
\(53\) | 454.822 | 1.17877 | 0.589383 | − | 0.807853i | \(-0.299371\pi\) | ||||
0.589383 | + | 0.807853i | \(0.299371\pi\) | |||||||
\(54\) | 198.033 | 0.499054 | ||||||||
\(55\) | −97.3671 | −0.238709 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −108.501 | −0.252129 | ||||||||
\(58\) | 452.610 | 1.02467 | ||||||||
\(59\) | −682.541 | −1.50609 | −0.753044 | − | 0.657970i | \(-0.771415\pi\) | ||||
−0.753044 | + | 0.657970i | \(0.771415\pi\) | |||||||
\(60\) | 39.5408 | 0.0850783 | ||||||||
\(61\) | 371.262 | 0.779266 | 0.389633 | − | 0.920970i | \(-0.372602\pi\) | ||||
0.389633 | + | 0.920970i | \(0.372602\pi\) | |||||||
\(62\) | −161.679 | −0.331182 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 281.316 | 0.549445 | ||||||||
\(65\) | 99.1400 | 0.189182 | ||||||||
\(66\) | −127.439 | −0.237676 | ||||||||
\(67\) | −431.247 | −0.786346 | −0.393173 | − | 0.919465i | \(-0.628623\pi\) | ||||
−0.393173 | + | 0.919465i | \(0.628623\pi\) | |||||||
\(68\) | −457.355 | −0.815625 | ||||||||
\(69\) | 226.535 | 0.395241 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 988.008 | 1.65148 | 0.825739 | − | 0.564053i | \(-0.190758\pi\) | ||||
0.825739 | + | 0.564053i | \(0.190758\pi\) | |||||||
\(72\) | −467.410 | −0.765067 | ||||||||
\(73\) | 621.701 | 0.996776 | 0.498388 | − | 0.866954i | \(-0.333926\pi\) | ||||
0.498388 | + | 0.866954i | \(0.333926\pi\) | |||||||
\(74\) | −251.360 | −0.394865 | ||||||||
\(75\) | −280.789 | −0.432303 | ||||||||
\(76\) | 228.856 | 0.345415 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 129.759 | 0.188363 | ||||||||
\(79\) | −1.99994 | −0.00284824 | −0.00142412 | − | 0.999999i | \(-0.500453\pi\) | ||||
−0.00142412 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(80\) | −11.5093 | −0.0160848 | ||||||||
\(81\) | 282.246 | 0.387168 | ||||||||
\(82\) | 69.2609 | 0.0932754 | ||||||||
\(83\) | −565.566 | −0.747938 | −0.373969 | − | 0.927441i | \(-0.622003\pi\) | ||||
−0.373969 | + | 0.927441i | \(0.622003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −279.860 | −0.357119 | ||||||||
\(86\) | −284.652 | −0.356917 | ||||||||
\(87\) | −653.714 | −0.805581 | ||||||||
\(88\) | 686.652 | 0.831788 | ||||||||
\(89\) | 839.802 | 1.00021 | 0.500106 | − | 0.865964i | \(-0.333295\pi\) | ||||
0.500106 | + | 0.865964i | \(0.333295\pi\) | |||||||
\(90\) | −111.964 | −0.131133 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −477.819 | −0.541479 | ||||||||
\(93\) | 233.517 | 0.260372 | ||||||||
\(94\) | −415.840 | −0.456284 | ||||||||
\(95\) | 140.039 | 0.151239 | ||||||||
\(96\) | −448.540 | −0.476864 | ||||||||
\(97\) | −880.803 | −0.921979 | −0.460989 | − | 0.887406i | \(-0.652505\pi\) | ||||
−0.460989 | + | 0.887406i | \(0.652505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −650.758 | −0.660643 | ||||||||
\(100\) | 592.254 | 0.592254 | ||||||||
\(101\) | −1178.89 | −1.16143 | −0.580715 | − | 0.814107i | \(-0.697227\pi\) | ||||
−0.580715 | + | 0.814107i | \(0.697227\pi\) | |||||||
\(102\) | −366.294 | −0.355574 | ||||||||
\(103\) | 598.786 | 0.572817 | 0.286408 | − | 0.958108i | \(-0.407539\pi\) | ||||
0.286408 | + | 0.958108i | \(0.407539\pi\) | |||||||
\(104\) | −699.155 | −0.659209 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −768.326 | −0.704023 | ||||||||
\(107\) | −114.469 | −0.103421 | −0.0517107 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517107 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(108\) | 603.294 | 0.537519 | ||||||||
\(109\) | 879.117 | 0.772515 | 0.386257 | − | 0.922391i | \(-0.373768\pi\) | ||||
0.386257 | + | 0.922391i | \(0.373768\pi\) | |||||||
\(110\) | 164.481 | 0.142570 | ||||||||
\(111\) | 363.045 | 0.310438 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −846.595 | −0.704787 | −0.352394 | − | 0.935852i | \(-0.614632\pi\) | ||||
−0.352394 | + | 0.935852i | \(0.614632\pi\) | |||||||
\(114\) | 183.290 | 0.150585 | ||||||||
\(115\) | −292.382 | −0.237085 | ||||||||
\(116\) | 1378.85 | 1.10364 | ||||||||
\(117\) | 662.607 | 0.523573 | ||||||||
\(118\) | 1153.01 | 0.899517 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −170.631 | −0.129804 | ||||||||
\(121\) | −374.999 | −0.281742 | ||||||||
\(122\) | −627.169 | −0.465420 | ||||||||
\(123\) | −100.035 | −0.0733321 | ||||||||
\(124\) | −492.545 | −0.356708 | ||||||||
\(125\) | 756.040 | 0.540978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 418.541 | 0.292437 | 0.146219 | − | 0.989252i | \(-0.453290\pi\) | ||||
0.146219 | + | 0.989252i | \(0.453290\pi\) | |||||||
\(128\) | 995.475 | 0.687409 | ||||||||
\(129\) | 411.129 | 0.280604 | ||||||||
\(130\) | −167.476 | −0.112989 | ||||||||
\(131\) | −1143.15 | −0.762425 | −0.381213 | − | 0.924487i | \(-0.624493\pi\) | ||||
−0.381213 | + | 0.924487i | \(0.624493\pi\) | |||||||
\(132\) | −388.233 | −0.255995 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 728.501 | 0.469648 | ||||||||
\(135\) | 369.162 | 0.235351 | ||||||||
\(136\) | 1973.63 | 1.24439 | ||||||||
\(137\) | −1367.40 | −0.852734 | −0.426367 | − | 0.904550i | \(-0.640207\pi\) | ||||
−0.426367 | + | 0.904550i | \(0.640207\pi\) | |||||||
\(138\) | −382.684 | −0.236059 | ||||||||
\(139\) | 922.992 | 0.563217 | 0.281608 | − | 0.959529i | \(-0.409132\pi\) | ||||
0.281608 | + | 0.959529i | \(0.409132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 600.607 | 0.358725 | ||||||||
\(142\) | −1669.03 | −0.986352 | ||||||||
\(143\) | −973.408 | −0.569234 | ||||||||
\(144\) | −76.9233 | −0.0445158 | ||||||||
\(145\) | 843.730 | 0.483227 | ||||||||
\(146\) | −1050.23 | −0.595328 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −765.751 | −0.425300 | ||||||||
\(149\) | −2513.00 | −1.38170 | −0.690850 | − | 0.722998i | \(-0.742763\pi\) | ||||
−0.690850 | + | 0.722998i | \(0.742763\pi\) | |||||||
\(150\) | 474.334 | 0.258195 | ||||||||
\(151\) | 3372.62 | 1.81761 | 0.908807 | − | 0.417217i | \(-0.136994\pi\) | ||||
0.908807 | + | 0.417217i | \(0.136994\pi\) | |||||||
\(152\) | −987.584 | −0.526998 | ||||||||
\(153\) | −1870.46 | −0.988352 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −301.393 | −0.156184 | ||||||||
\(156\) | 395.302 | 0.202881 | ||||||||
\(157\) | −2162.49 | −1.09927 | −0.549635 | − | 0.835405i | \(-0.685233\pi\) | ||||
−0.549635 | + | 0.835405i | \(0.685233\pi\) | |||||||
\(158\) | 3.37848 | 0.00170112 | ||||||||
\(159\) | 1109.71 | 0.553495 | ||||||||
\(160\) | 578.918 | 0.286047 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −476.795 | −0.231238 | ||||||||
\(163\) | 3439.36 | 1.65271 | 0.826353 | − | 0.563152i | \(-0.190412\pi\) | ||||
0.826353 | + | 0.563152i | \(0.190412\pi\) | |||||||
\(164\) | 210.998 | 0.100465 | ||||||||
\(165\) | −237.564 | −0.112087 | ||||||||
\(166\) | 955.404 | 0.446709 | ||||||||
\(167\) | −3151.34 | −1.46023 | −0.730113 | − | 0.683327i | \(-0.760533\pi\) | ||||
−0.730113 | + | 0.683327i | \(0.760533\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1205.87 | −0.548870 | ||||||||
\(170\) | 472.765 | 0.213291 | ||||||||
\(171\) | 935.959 | 0.418565 | ||||||||
\(172\) | −867.173 | −0.384426 | ||||||||
\(173\) | 2765.67 | 1.21544 | 0.607718 | − | 0.794153i | \(-0.292085\pi\) | ||||
0.607718 | + | 0.794153i | \(0.292085\pi\) | |||||||
\(174\) | 1104.31 | 0.481136 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 113.005 | 0.0483980 | ||||||||
\(177\) | −1665.31 | −0.707190 | ||||||||
\(178\) | −1418.67 | −0.597380 | ||||||||
\(179\) | −1738.20 | −0.725807 | −0.362903 | − | 0.931827i | \(-0.618214\pi\) | ||||
−0.362903 | + | 0.931827i | \(0.618214\pi\) | |||||||
\(180\) | −341.090 | −0.141241 | ||||||||
\(181\) | −1847.83 | −0.758829 | −0.379414 | − | 0.925227i | \(-0.623875\pi\) | ||||
−0.379414 | + | 0.925227i | \(0.623875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 905.833 | 0.365908 | ||||||||
\(184\) | 2061.94 | 0.826132 | ||||||||
\(185\) | −468.571 | −0.186216 | ||||||||
\(186\) | −394.478 | −0.155508 | ||||||||
\(187\) | 2747.82 | 1.07455 | ||||||||
\(188\) | −1266.83 | −0.491452 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −236.567 | −0.0903282 | ||||||||
\(191\) | −1177.08 | −0.445920 | −0.222960 | − | 0.974828i | \(-0.571572\pi\) | ||||
−0.222960 | + | 0.974828i | \(0.571572\pi\) | |||||||
\(192\) | 686.376 | 0.257994 | ||||||||
\(193\) | −3950.31 | −1.47331 | −0.736657 | − | 0.676267i | \(-0.763597\pi\) | ||||
−0.736657 | + | 0.676267i | \(0.763597\pi\) | |||||||
\(194\) | 1487.93 | 0.550656 | ||||||||
\(195\) | 241.889 | 0.0888310 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3984.90 | −1.44118 | −0.720590 | − | 0.693362i | \(-0.756129\pi\) | ||||
−0.720590 | + | 0.693362i | \(0.756129\pi\) | |||||||
\(198\) | 1099.32 | 0.394572 | ||||||||
\(199\) | 800.612 | 0.285195 | 0.142598 | − | 0.989781i | \(-0.454455\pi\) | ||||
0.142598 | + | 0.989781i | \(0.454455\pi\) | |||||||
\(200\) | −2555.76 | −0.903598 | ||||||||
\(201\) | −1052.19 | −0.369232 | ||||||||
\(202\) | 1991.49 | 0.693668 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1115.89 | −0.382980 | ||||||||
\(205\) | 129.112 | 0.0439882 | ||||||||
\(206\) | −1011.52 | −0.342117 | ||||||||
\(207\) | −1954.15 | −0.656150 | ||||||||
\(208\) | −115.062 | −0.0383564 | ||||||||
\(209\) | −1374.98 | −0.455068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −320.362 | −0.104524 | −0.0522621 | − | 0.998633i | \(-0.516643\pi\) | ||||
−0.0522621 | + | 0.998633i | \(0.516643\pi\) | |||||||
\(212\) | −2340.65 | −0.758286 | ||||||||
\(213\) | 2410.62 | 0.775458 | ||||||||
\(214\) | 193.371 | 0.0617689 | ||||||||
\(215\) | −530.632 | −0.168320 | ||||||||
\(216\) | −2603.40 | −0.820089 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1485.08 | −0.461387 | ||||||||
\(219\) | 1516.87 | 0.468040 | ||||||||
\(220\) | 501.080 | 0.153558 | ||||||||
\(221\) | −2797.85 | −0.851600 | ||||||||
\(222\) | −613.287 | −0.185411 | ||||||||
\(223\) | −6154.08 | −1.84802 | −0.924008 | − | 0.382373i | \(-0.875107\pi\) | ||||
−0.924008 | + | 0.382373i | \(0.875107\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2422.16 | 0.717677 | ||||||||
\(226\) | 1430.14 | 0.420937 | ||||||||
\(227\) | 1151.15 | 0.336582 | 0.168291 | − | 0.985737i | \(-0.446175\pi\) | ||||
0.168291 | + | 0.985737i | \(0.446175\pi\) | |||||||
\(228\) | 558.380 | 0.162191 | ||||||||
\(229\) | 1025.45 | 0.295910 | 0.147955 | − | 0.988994i | \(-0.452731\pi\) | ||||
0.147955 | + | 0.988994i | \(0.452731\pi\) | |||||||
\(230\) | 493.919 | 0.141600 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5950.15 | −1.68382 | ||||||||
\(233\) | −4846.25 | −1.36261 | −0.681306 | − | 0.731999i | \(-0.738588\pi\) | ||||
−0.681306 | + | 0.731999i | \(0.738588\pi\) | |||||||
\(234\) | −1119.34 | −0.312706 | ||||||||
\(235\) | −775.185 | −0.215181 | ||||||||
\(236\) | 3512.56 | 0.968848 | ||||||||
\(237\) | −4.87960 | −0.00133740 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −56.3860 | −0.0152607 | −0.00763035 | − | 0.999971i | \(-0.502429\pi\) | ||||
−0.00763035 | + | 0.999971i | \(0.502429\pi\) | |||||||
\(240\) | −28.0814 | −0.00755268 | ||||||||
\(241\) | −5160.49 | −1.37932 | −0.689661 | − | 0.724132i | \(-0.742240\pi\) | ||||
−0.689661 | + | 0.724132i | \(0.742240\pi\) | |||||||
\(242\) | 633.482 | 0.168272 | ||||||||
\(243\) | 3853.82 | 1.01738 | ||||||||
\(244\) | −1910.63 | −0.501292 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 168.988 | 0.0437979 | ||||||||
\(247\) | 1400.01 | 0.360651 | ||||||||
\(248\) | 2125.49 | 0.544228 | ||||||||
\(249\) | −1379.91 | −0.351198 | ||||||||
\(250\) | −1277.17 | −0.323102 | ||||||||
\(251\) | −2112.47 | −0.531228 | −0.265614 | − | 0.964079i | \(-0.585575\pi\) | ||||
−0.265614 | + | 0.964079i | \(0.585575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2870.76 | 0.713373 | ||||||||
\(254\) | −707.037 | −0.174659 | ||||||||
\(255\) | −682.825 | −0.167687 | ||||||||
\(256\) | −3932.17 | −0.960003 | ||||||||
\(257\) | −2960.23 | −0.718499 | −0.359250 | − | 0.933241i | \(-0.616967\pi\) | ||||
−0.359250 | + | 0.933241i | \(0.616967\pi\) | |||||||
\(258\) | −694.516 | −0.167592 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −510.204 | −0.121698 | ||||||||
\(261\) | 5639.11 | 1.33736 | ||||||||
\(262\) | 1931.12 | 0.455362 | ||||||||
\(263\) | −375.879 | −0.0881281 | −0.0440641 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440641 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(264\) | 1675.35 | 0.390570 | ||||||||
\(265\) | −1432.27 | −0.332014 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2049.01 | 0.469653 | ||||||||
\(268\) | 2219.33 | 0.505847 | ||||||||
\(269\) | 6616.45 | 1.49967 | 0.749837 | − | 0.661623i | \(-0.230132\pi\) | ||||
0.749837 | + | 0.661623i | \(0.230132\pi\) | |||||||
\(270\) | −623.621 | −0.140564 | ||||||||
\(271\) | 2417.18 | 0.541820 | 0.270910 | − | 0.962605i | \(-0.412675\pi\) | ||||
0.270910 | + | 0.962605i | \(0.412675\pi\) | |||||||
\(272\) | 324.807 | 0.0724057 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2309.93 | 0.509299 | ||||||||
\(275\) | −3558.29 | −0.780266 | ||||||||
\(276\) | −1165.82 | −0.254254 | ||||||||
\(277\) | −2344.24 | −0.508489 | −0.254245 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254245 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(278\) | −1559.20 | −0.336384 | ||||||||
\(279\) | −2014.38 | −0.432250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4543.98 | −0.964666 | −0.482333 | − | 0.875988i | \(-0.660210\pi\) | ||||
−0.482333 | + | 0.875988i | \(0.660210\pi\) | |||||||
\(282\) | −1014.60 | −0.214250 | ||||||||
\(283\) | 1962.32 | 0.412184 | 0.206092 | − | 0.978533i | \(-0.433925\pi\) | ||||
0.206092 | + | 0.978533i | \(0.433925\pi\) | |||||||
\(284\) | −5084.58 | −1.06238 | ||||||||
\(285\) | 341.678 | 0.0710150 | ||||||||
\(286\) | 1644.37 | 0.339977 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3869.23 | 0.791654 | ||||||||
\(289\) | 2985.00 | 0.607571 | ||||||||
\(290\) | −1425.30 | −0.288609 | ||||||||
\(291\) | −2149.05 | −0.432919 | ||||||||
\(292\) | −3199.46 | −0.641214 | ||||||||
\(293\) | 9747.58 | 1.94355 | 0.971775 | − | 0.235911i | \(-0.0758074\pi\) | ||||
0.971775 | + | 0.235911i | \(0.0758074\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2149.37 | 0.424208 | ||||||||
\(296\) | 3304.46 | 0.648877 | ||||||||
\(297\) | −3624.63 | −0.708155 | ||||||||
\(298\) | 4245.19 | 0.825225 | ||||||||
\(299\) | −2923.04 | −0.565363 | ||||||||
\(300\) | 1445.02 | 0.278095 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5697.33 | −1.08558 | ||||||||
\(303\) | −2876.36 | −0.545354 | ||||||||
\(304\) | −162.530 | −0.0306636 | ||||||||
\(305\) | −1169.13 | −0.219489 | ||||||||
\(306\) | 3159.75 | 0.590297 | ||||||||
\(307\) | 6227.92 | 1.15781 | 0.578903 | − | 0.815397i | \(-0.303481\pi\) | ||||
0.578903 | + | 0.815397i | \(0.303481\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1460.96 | 0.268969 | ||||||||
\(310\) | 509.140 | 0.0932814 | ||||||||
\(311\) | 3386.20 | 0.617408 | 0.308704 | − | 0.951158i | \(-0.400105\pi\) | ||||
0.308704 | + | 0.951158i | \(0.400105\pi\) | |||||||
\(312\) | −1705.85 | −0.309535 | ||||||||
\(313\) | 2416.88 | 0.436453 | 0.218227 | − | 0.975898i | \(-0.429973\pi\) | ||||
0.218227 | + | 0.975898i | \(0.429973\pi\) | |||||||
\(314\) | 3653.07 | 0.656544 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2923 | 0.00183224 | ||||||||
\(317\) | −9609.55 | −1.70261 | −0.851303 | − | 0.524675i | \(-0.824187\pi\) | ||||
−0.851303 | + | 0.524675i | \(0.824187\pi\) | |||||||
\(318\) | −1874.62 | −0.330577 | ||||||||
\(319\) | −8284.18 | −1.45400 | ||||||||
\(320\) | −885.884 | −0.154758 | ||||||||
\(321\) | −279.289 | −0.0485620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3952.07 | −0.680803 | ||||||||
\(324\) | −1452.52 | −0.249061 | ||||||||
\(325\) | 3623.08 | 0.618377 | ||||||||
\(326\) | −5810.07 | −0.987085 | ||||||||
\(327\) | 2144.94 | 0.362738 | ||||||||
\(328\) | −910.524 | −0.153278 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 401.314 | 0.0669442 | ||||||||
\(331\) | 1737.05 | 0.288450 | 0.144225 | − | 0.989545i | \(-0.453931\pi\) | ||||
0.144225 | + | 0.989545i | \(0.453931\pi\) | |||||||
\(332\) | 2910.57 | 0.481140 | ||||||||
\(333\) | −3131.72 | −0.515367 | ||||||||
\(334\) | 5323.52 | 0.872126 | ||||||||
\(335\) | 1358.03 | 0.221484 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11068.8 | −1.78918 | −0.894591 | − | 0.446887i | \(-0.852533\pi\) | ||||
−0.894591 | + | 0.446887i | \(0.852533\pi\) | |||||||
\(338\) | 2037.06 | 0.327815 | ||||||||
\(339\) | −2065.59 | −0.330936 | ||||||||
\(340\) | 1440.25 | 0.229730 | ||||||||
\(341\) | 2959.24 | 0.469946 | ||||||||
\(342\) | −1581.11 | −0.249990 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3742.12 | 0.586517 | ||||||||
\(345\) | −713.377 | −0.111324 | ||||||||
\(346\) | −4672.03 | −0.725924 | ||||||||
\(347\) | 3247.91 | 0.502469 | 0.251235 | − | 0.967926i | \(-0.419163\pi\) | ||||
0.251235 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(348\) | 3364.21 | 0.518220 | ||||||||
\(349\) | 412.528 | 0.0632726 | 0.0316363 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316363 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3690.62 | 0.561228 | ||||||||
\(352\) | −5684.11 | −0.860694 | ||||||||
\(353\) | −6264.56 | −0.944558 | −0.472279 | − | 0.881449i | \(-0.656569\pi\) | ||||
−0.472279 | + | 0.881449i | \(0.656569\pi\) | |||||||
\(354\) | 2813.20 | 0.422372 | ||||||||
\(355\) | −3111.31 | −0.465158 | ||||||||
\(356\) | −4321.87 | −0.643424 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2936.33 | 0.433491 | ||||||||
\(359\) | −1539.53 | −0.226333 | −0.113166 | − | 0.993576i | \(-0.536099\pi\) | ||||
−0.113166 | + | 0.993576i | \(0.536099\pi\) | |||||||
\(360\) | 1471.91 | 0.215490 | ||||||||
\(361\) | −4881.42 | −0.711682 | ||||||||
\(362\) | 3121.52 | 0.453213 | ||||||||
\(363\) | −914.951 | −0.132293 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1957.78 | −0.280754 | ||||||||
\(366\) | −1530.21 | −0.218540 | ||||||||
\(367\) | −7303.35 | −1.03878 | −0.519389 | − | 0.854538i | \(-0.673841\pi\) | ||||
−0.519389 | + | 0.854538i | \(0.673841\pi\) | |||||||
\(368\) | 339.341 | 0.0480689 | ||||||||
\(369\) | 862.927 | 0.121740 | ||||||||
\(370\) | 791.552 | 0.111218 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1201.75 | −0.167494 | ||||||||
\(373\) | −5959.70 | −0.827296 | −0.413648 | − | 0.910437i | \(-0.635746\pi\) | ||||
−0.413648 | + | 0.910437i | \(0.635746\pi\) | |||||||
\(374\) | −4641.86 | −0.641777 | ||||||||
\(375\) | 1844.64 | 0.254019 | ||||||||
\(376\) | 5466.76 | 0.749805 | ||||||||
\(377\) | 8435.02 | 1.15232 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9369.35 | −1.26984 | −0.634922 | − | 0.772576i | \(-0.718968\pi\) | ||||
−0.634922 | + | 0.772576i | \(0.718968\pi\) | |||||||
\(380\) | −720.684 | −0.0972903 | ||||||||
\(381\) | 1021.19 | 0.137315 | ||||||||
\(382\) | 1988.43 | 0.266327 | ||||||||
\(383\) | −820.810 | −0.109508 | −0.0547538 | − | 0.998500i | \(-0.517437\pi\) | ||||
−0.0547538 | + | 0.998500i | \(0.517437\pi\) | |||||||
\(384\) | 2428.83 | 0.322776 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6673.22 | 0.879943 | ||||||||
\(387\) | −3546.51 | −0.465837 | ||||||||
\(388\) | 4532.88 | 0.593098 | ||||||||
\(389\) | 2529.60 | 0.329707 | 0.164853 | − | 0.986318i | \(-0.447285\pi\) | ||||
0.164853 | + | 0.986318i | \(0.447285\pi\) | |||||||
\(390\) | −408.621 | −0.0530547 | ||||||||
\(391\) | 8251.38 | 1.06724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2789.15 | −0.358000 | ||||||||
\(394\) | 6731.65 | 0.860750 | ||||||||
\(395\) | 6.29796 | 0.000802240 0 | ||||||||
\(396\) | 3349.00 | 0.424983 | ||||||||
\(397\) | 4374.51 | 0.553024 | 0.276512 | − | 0.961011i | \(-0.410822\pi\) | ||||
0.276512 | + | 0.961011i | \(0.410822\pi\) | |||||||
\(398\) | −1352.46 | −0.170334 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −420.610 | −0.0525763 | ||||||||
\(401\) | 3055.07 | 0.380456 | 0.190228 | − | 0.981740i | \(-0.439077\pi\) | ||||
0.190228 | + | 0.981740i | \(0.439077\pi\) | |||||||
\(402\) | 1777.45 | 0.220525 | ||||||||
\(403\) | −3013.12 | −0.372442 | ||||||||
\(404\) | 6066.95 | 0.747133 | ||||||||
\(405\) | −888.813 | −0.109051 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4600.67 | 0.560312 | ||||||||
\(408\) | 4815.42 | 0.584310 | ||||||||
\(409\) | −7461.57 | −0.902080 | −0.451040 | − | 0.892504i | \(-0.648947\pi\) | ||||
−0.451040 | + | 0.892504i | \(0.648947\pi\) | |||||||
\(410\) | −218.108 | −0.0262721 | ||||||||
\(411\) | −3336.28 | −0.400405 | ||||||||
\(412\) | −3081.53 | −0.368486 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3301.13 | 0.391888 | ||||||||
\(415\) | 1781.01 | 0.210666 | ||||||||
\(416\) | 5787.61 | 0.682118 | ||||||||
\(417\) | 2251.99 | 0.264461 | ||||||||
\(418\) | 2322.74 | 0.271791 | ||||||||
\(419\) | −10294.7 | −1.20030 | −0.600152 | − | 0.799886i | \(-0.704893\pi\) | ||||
−0.600152 | + | 0.799886i | \(0.704893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15953.1 | −1.84681 | −0.923404 | − | 0.383830i | \(-0.874605\pi\) | ||||
−0.923404 | + | 0.383830i | \(0.874605\pi\) | |||||||
\(422\) | 541.183 | 0.0624275 | ||||||||
\(423\) | −5180.99 | −0.595528 | ||||||||
\(424\) | 10100.7 | 1.15691 | ||||||||
\(425\) | −10227.5 | −1.16731 | ||||||||
\(426\) | −4072.23 | −0.463146 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 589.090 | 0.0665298 | ||||||||
\(429\) | −2374.99 | −0.267286 | ||||||||
\(430\) | 896.391 | 0.100530 | ||||||||
\(431\) | −3756.52 | −0.419826 | −0.209913 | − | 0.977720i | \(-0.567318\pi\) | ||||
−0.209913 | + | 0.977720i | \(0.567318\pi\) | |||||||
\(432\) | −428.451 | −0.0477173 | ||||||||
\(433\) | 4310.02 | 0.478352 | 0.239176 | − | 0.970976i | \(-0.423123\pi\) | ||||
0.239176 | + | 0.970976i | \(0.423123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2058.60 | 0.226901 | ||||||||
\(436\) | −4524.20 | −0.496949 | ||||||||
\(437\) | −4128.91 | −0.451973 | ||||||||
\(438\) | −2562.44 | −0.279539 | ||||||||
\(439\) | −3261.02 | −0.354533 | −0.177266 | − | 0.984163i | \(-0.556725\pi\) | ||||
−0.177266 | + | 0.984163i | \(0.556725\pi\) | |||||||
\(440\) | −2162.32 | −0.234283 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4726.38 | 0.508622 | ||||||||
\(443\) | −3661.52 | −0.392696 | −0.196348 | − | 0.980534i | \(-0.562908\pi\) | ||||
−0.196348 | + | 0.980534i | \(0.562908\pi\) | |||||||
\(444\) | −1868.34 | −0.199701 | ||||||||
\(445\) | −2644.60 | −0.281721 | ||||||||
\(446\) | 10396.0 | 1.10373 | ||||||||
\(447\) | −6131.41 | −0.648783 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7347.50 | −0.772272 | −0.386136 | − | 0.922442i | \(-0.626190\pi\) | ||||
−0.386136 | + | 0.922442i | \(0.626190\pi\) | |||||||
\(450\) | −4091.73 | −0.428635 | ||||||||
\(451\) | −1267.69 | −0.132357 | ||||||||
\(452\) | 4356.83 | 0.453381 | ||||||||
\(453\) | 8228.77 | 0.853468 | ||||||||
\(454\) | −1944.62 | −0.201025 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2409.58 | −0.247454 | ||||||||
\(457\) | 467.894 | 0.0478932 | 0.0239466 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239466 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(458\) | −1732.28 | −0.176733 | ||||||||
\(459\) | −10418.2 | −1.05943 | ||||||||
\(460\) | 1504.69 | 0.152514 | ||||||||
\(461\) | −10249.8 | −1.03554 | −0.517769 | − | 0.855521i | \(-0.673237\pi\) | ||||
−0.517769 | + | 0.855521i | \(0.673237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10382.5 | −1.04215 | −0.521077 | − | 0.853510i | \(-0.674469\pi\) | ||||
−0.521077 | + | 0.853510i | \(0.674469\pi\) | |||||||
\(464\) | −979.237 | −0.0979740 | ||||||||
\(465\) | −735.362 | −0.0733368 | ||||||||
\(466\) | 8186.72 | 0.813825 | ||||||||
\(467\) | −7058.57 | −0.699425 | −0.349713 | − | 0.936857i | \(-0.613721\pi\) | ||||
−0.349713 | + | 0.936857i | \(0.613721\pi\) | |||||||
\(468\) | −3409.98 | −0.336808 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1309.51 | 0.128518 | ||||||||
\(471\) | −5276.21 | −0.516167 | ||||||||
\(472\) | −15157.8 | −1.47817 | ||||||||
\(473\) | 5210.02 | 0.506463 | ||||||||
\(474\) | 8.24306 | 0.000798769 0 | ||||||||
\(475\) | 5117.75 | 0.494355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9572.65 | −0.918871 | ||||||||
\(478\) | 95.2523 | 0.00911451 | ||||||||
\(479\) | 12450.9 | 1.18768 | 0.593838 | − | 0.804584i | \(-0.297612\pi\) | ||||
0.593838 | + | 0.804584i | \(0.297612\pi\) | |||||||
\(480\) | 1412.49 | 0.134314 | ||||||||
\(481\) | −4684.44 | −0.444059 | ||||||||
\(482\) | 8717.57 | 0.823806 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1929.86 | 0.181241 | ||||||||
\(485\) | 2773.71 | 0.259686 | ||||||||
\(486\) | −6510.22 | −0.607633 | ||||||||
\(487\) | −6239.35 | −0.580558 | −0.290279 | − | 0.956942i | \(-0.593748\pi\) | ||||
−0.290279 | + | 0.956942i | \(0.593748\pi\) | |||||||
\(488\) | 8244.95 | 0.764818 | ||||||||
\(489\) | 8391.60 | 0.776035 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19789.8 | 1.81894 | 0.909471 | − | 0.415766i | \(-0.136487\pi\) | ||||
0.909471 | + | 0.415766i | \(0.136487\pi\) | |||||||
\(492\) | 514.810 | 0.0471736 | ||||||||
\(493\) | −23811.1 | −2.17525 | ||||||||
\(494\) | −2365.03 | −0.215400 | ||||||||
\(495\) | 2049.29 | 0.186078 | ||||||||
\(496\) | 349.799 | 0.0316662 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2331.07 | 0.209754 | ||||||||
\(499\) | −6244.64 | −0.560218 | −0.280109 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280109 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(500\) | −3890.81 | −0.348005 | ||||||||
\(501\) | −7688.87 | −0.685655 | ||||||||
\(502\) | 3568.58 | 0.317278 | ||||||||
\(503\) | −17641.9 | −1.56384 | −0.781921 | − | 0.623378i | \(-0.785760\pi\) | ||||
−0.781921 | + | 0.623378i | \(0.785760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3712.43 | 0.327130 | ||||||||
\(506\) | −4849.55 | −0.426065 | ||||||||
\(507\) | −2942.17 | −0.257724 | ||||||||
\(508\) | −2153.94 | −0.188121 | ||||||||
\(509\) | 8303.68 | 0.723093 | 0.361546 | − | 0.932354i | \(-0.382249\pi\) | ||||
0.361546 | + | 0.932354i | \(0.382249\pi\) | |||||||
\(510\) | 1153.49 | 0.100152 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1321.22 | −0.114044 | ||||||||
\(513\) | 5213.15 | 0.448667 | ||||||||
\(514\) | 5000.69 | 0.429127 | ||||||||
\(515\) | −1885.62 | −0.161341 | ||||||||
\(516\) | −2115.79 | −0.180509 | ||||||||
\(517\) | 7611.17 | 0.647464 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6747.90 | 0.570713 | ||||||||
\(520\) | 2201.69 | 0.185674 | ||||||||
\(521\) | −3965.57 | −0.333464 | −0.166732 | − | 0.986002i | \(-0.553321\pi\) | ||||
−0.166732 | + | 0.986002i | \(0.553321\pi\) | |||||||
\(522\) | −9526.09 | −0.798746 | ||||||||
\(523\) | −21295.8 | −1.78050 | −0.890249 | − | 0.455474i | \(-0.849470\pi\) | ||||
−0.890249 | + | 0.455474i | \(0.849470\pi\) | |||||||
\(524\) | 5883.01 | 0.490459 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 634.968 | 0.0526349 | ||||||||
\(527\) | 8505.68 | 0.703061 | ||||||||
\(528\) | 275.717 | 0.0227255 | ||||||||
\(529\) | −3546.42 | −0.291478 | ||||||||
\(530\) | 2419.52 | 0.198296 | ||||||||
\(531\) | 14365.4 | 1.17402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1290.77 | 0.104896 | ||||||||
\(534\) | −3461.37 | −0.280502 | ||||||||
\(535\) | 360.470 | 0.0291299 | ||||||||
\(536\) | −9577.09 | −0.771767 | ||||||||
\(537\) | −4241.00 | −0.340806 | ||||||||
\(538\) | −11177.1 | −0.895686 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1899.82 | −0.151399 | ||||||||
\(541\) | 7730.61 | 0.614353 | 0.307177 | − | 0.951653i | \(-0.400616\pi\) | ||||
0.307177 | + | 0.951653i | \(0.400616\pi\) | |||||||
\(542\) | −4083.32 | −0.323604 | ||||||||
\(543\) | −4508.47 | −0.356311 | ||||||||
\(544\) | −16337.7 | −1.28764 | ||||||||
\(545\) | −2768.40 | −0.217588 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17761.6 | −1.38835 | −0.694177 | − | 0.719804i | \(-0.744232\pi\) | ||||
−0.694177 | + | 0.719804i | \(0.744232\pi\) | |||||||
\(548\) | 7037.04 | 0.548553 | ||||||||
\(549\) | −7813.95 | −0.607452 | ||||||||
\(550\) | 6010.98 | 0.466017 | ||||||||
\(551\) | 11914.8 | 0.921212 | ||||||||
\(552\) | 5030.88 | 0.387914 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3960.10 | 0.303697 | ||||||||
\(555\) | −1143.25 | −0.0874387 | ||||||||
\(556\) | −4749.99 | −0.362310 | ||||||||
\(557\) | 5504.34 | 0.418719 | 0.209359 | − | 0.977839i | \(-0.432862\pi\) | ||||
0.209359 | + | 0.977839i | \(0.432862\pi\) | |||||||
\(558\) | 3402.87 | 0.258163 | ||||||||
\(559\) | −5304.89 | −0.401383 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6704.33 | 0.504558 | ||||||||
\(562\) | 7676.09 | 0.576150 | ||||||||
\(563\) | 25944.4 | 1.94215 | 0.971073 | − | 0.238784i | \(-0.0767487\pi\) | ||||
0.971073 | + | 0.238784i | \(0.0767487\pi\) | |||||||
\(564\) | −3090.90 | −0.230763 | ||||||||
\(565\) | 2665.99 | 0.198512 | ||||||||
\(566\) | −3314.93 | −0.246178 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21941.6 | 1.62086 | ||||||||
\(569\) | 600.070 | 0.0442113 | 0.0221057 | − | 0.999756i | \(-0.492963\pi\) | ||||
0.0221057 | + | 0.999756i | \(0.492963\pi\) | |||||||
\(570\) | −577.193 | −0.0424140 | ||||||||
\(571\) | 898.195 | 0.0658289 | 0.0329144 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329144 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(572\) | 5009.45 | 0.366181 | ||||||||
\(573\) | −2871.93 | −0.209384 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10685.2 | −0.774959 | ||||||||
\(576\) | −5920.85 | −0.428303 | ||||||||
\(577\) | 18984.3 | 1.36972 | 0.684859 | − | 0.728675i | \(-0.259864\pi\) | ||||
0.684859 | + | 0.728675i | \(0.259864\pi\) | |||||||
\(578\) | −5042.52 | −0.362874 | ||||||||
\(579\) | −9638.27 | −0.691801 | ||||||||
\(580\) | −4342.09 | −0.310854 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3630.37 | 0.258563 | ||||||||
\(583\) | 14062.8 | 0.999006 | ||||||||
\(584\) | 13806.7 | 0.978296 | ||||||||
\(585\) | −2086.60 | −0.147471 | ||||||||
\(586\) | −16466.5 | −1.16079 | ||||||||
\(587\) | 13253.8 | 0.931930 | 0.465965 | − | 0.884803i | \(-0.345707\pi\) | ||||
0.465965 | + | 0.884803i | \(0.345707\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4256.15 | −0.297745 | ||||||||
\(590\) | −3630.91 | −0.253360 | ||||||||
\(591\) | −9722.66 | −0.676712 | ||||||||
\(592\) | 543.826 | 0.0377552 | ||||||||
\(593\) | −4020.79 | −0.278439 | −0.139219 | − | 0.990262i | \(-0.544459\pi\) | ||||
−0.139219 | + | 0.990262i | \(0.544459\pi\) | |||||||
\(594\) | 6123.04 | 0.422949 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12932.7 | 0.888830 | ||||||||
\(597\) | 1953.39 | 0.133915 | ||||||||
\(598\) | 4937.85 | 0.337665 | ||||||||
\(599\) | −16551.6 | −1.12901 | −0.564507 | − | 0.825428i | \(-0.690934\pi\) | ||||
−0.564507 | + | 0.825428i | \(0.690934\pi\) | |||||||
\(600\) | −6235.74 | −0.424288 | ||||||||
\(601\) | −20266.4 | −1.37551 | −0.687757 | − | 0.725941i | \(-0.741404\pi\) | ||||
−0.687757 | + | 0.725941i | \(0.741404\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9076.45 | 0.612971 | ||||||||
\(604\) | −17356.5 | −1.16925 | ||||||||
\(605\) | 1180.90 | 0.0793561 | ||||||||
\(606\) | 4859.00 | 0.325715 | ||||||||
\(607\) | 26773.8 | 1.79031 | 0.895153 | − | 0.445760i | \(-0.147066\pi\) | ||||
0.895153 | + | 0.445760i | \(0.147066\pi\) | |||||||
\(608\) | 8175.24 | 0.545312 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1975.00 | 0.131091 | ||||||||
\(611\) | −7749.76 | −0.513129 | ||||||||
\(612\) | 9625.96 | 0.635795 | ||||||||
\(613\) | −4354.71 | −0.286925 | −0.143462 | − | 0.989656i | \(-0.545824\pi\) | ||||
−0.143462 | + | 0.989656i | \(0.545824\pi\) | |||||||
\(614\) | −10520.8 | −0.691504 | ||||||||
\(615\) | 315.017 | 0.0206548 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23574.0 | −1.53817 | −0.769087 | − | 0.639144i | \(-0.779289\pi\) | ||||
−0.769087 | + | 0.639144i | \(0.779289\pi\) | |||||||
\(618\) | −2467.99 | −0.160643 | ||||||||
\(619\) | 25975.9 | 1.68669 | 0.843343 | − | 0.537376i | \(-0.180585\pi\) | ||||
0.843343 | + | 0.537376i | \(0.180585\pi\) | |||||||
\(620\) | 1551.06 | 0.100471 | ||||||||
\(621\) | −10884.3 | −0.703339 | ||||||||
\(622\) | −5720.27 | −0.368749 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −280.738 | −0.0180104 | ||||||||
\(625\) | 12004.6 | 0.768294 | ||||||||
\(626\) | −4082.80 | −0.260673 | ||||||||
\(627\) | −3354.78 | −0.213679 | ||||||||
\(628\) | 11128.8 | 0.707147 | ||||||||
\(629\) | 13223.6 | 0.838252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13625.7 | −0.859635 | −0.429817 | − | 0.902916i | \(-0.641422\pi\) | ||||
−0.429817 | + | 0.902916i | \(0.641422\pi\) | |||||||
\(632\) | −44.4145 | −0.00279543 | ||||||||
\(633\) | −781.643 | −0.0490798 | ||||||||
\(634\) | 16233.3 | 1.01689 | ||||||||
\(635\) | −1318.02 | −0.0823684 | ||||||||
\(636\) | −5710.90 | −0.356057 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13994.4 | 0.868405 | ||||||||
\(639\) | −20794.6 | −1.28736 | ||||||||
\(640\) | −3134.82 | −0.193617 | ||||||||
\(641\) | 14845.7 | 0.914772 | 0.457386 | − | 0.889268i | \(-0.348786\pi\) | ||||
0.457386 | + | 0.889268i | \(0.348786\pi\) | |||||||
\(642\) | 471.800 | 0.0290039 | ||||||||
\(643\) | 14609.6 | 0.896030 | 0.448015 | − | 0.894026i | \(-0.352131\pi\) | ||||
0.448015 | + | 0.894026i | \(0.352131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1294.68 | −0.0790354 | ||||||||
\(646\) | 6676.20 | 0.406612 | ||||||||
\(647\) | 3694.79 | 0.224509 | 0.112254 | − | 0.993679i | \(-0.464193\pi\) | ||||
0.112254 | + | 0.993679i | \(0.464193\pi\) | |||||||
\(648\) | 6268.09 | 0.379990 | ||||||||
\(649\) | −21103.7 | −1.27641 | ||||||||
\(650\) | −6120.43 | −0.369328 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17700.0 | −1.06317 | ||||||||
\(653\) | −16775.5 | −1.00532 | −0.502662 | − | 0.864483i | \(-0.667646\pi\) | ||||
−0.502662 | + | 0.864483i | \(0.667646\pi\) | |||||||
\(654\) | −3623.42 | −0.216646 | ||||||||
\(655\) | 3599.87 | 0.214746 | ||||||||
\(656\) | −149.848 | −0.00891858 | ||||||||
\(657\) | −13084.9 | −0.777005 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2029.04 | 0.119939 | 0.0599697 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599697 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(660\) | 1222.57 | 0.0721040 | ||||||||
\(661\) | 6719.58 | 0.395403 | 0.197701 | − | 0.980262i | \(-0.436652\pi\) | ||||
0.197701 | + | 0.980262i | \(0.436652\pi\) | |||||||
\(662\) | −2934.38 | −0.172278 | ||||||||
\(663\) | −6826.40 | −0.399873 | ||||||||
\(664\) | −12560.0 | −0.734072 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5290.38 | 0.307805 | ||||||||
\(667\) | −24876.5 | −1.44411 | ||||||||
\(668\) | 16217.7 | 0.939345 | ||||||||
\(669\) | −15015.2 | −0.867744 | ||||||||
\(670\) | −2294.10 | −0.132282 | ||||||||
\(671\) | 11479.1 | 0.660428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24199.9 | 1.38609 | 0.693045 | − | 0.720894i | \(-0.256269\pi\) | ||||
0.693045 | + | 0.720894i | \(0.256269\pi\) | |||||||
\(674\) | 18698.3 | 1.06860 | ||||||||
\(675\) | 13491.1 | 0.769291 | ||||||||
\(676\) | 6205.76 | 0.353081 | ||||||||
\(677\) | −17159.3 | −0.974128 | −0.487064 | − | 0.873366i | \(-0.661932\pi\) | ||||
−0.487064 | + | 0.873366i | \(0.661932\pi\) | |||||||
\(678\) | 3489.37 | 0.197653 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6215.11 | −0.350498 | ||||||||
\(681\) | 2808.65 | 0.158044 | ||||||||
\(682\) | −4999.01 | −0.280677 | ||||||||
\(683\) | 2440.06 | 0.136700 | 0.0683501 | − | 0.997661i | \(-0.478226\pi\) | ||||
0.0683501 | + | 0.997661i | \(0.478226\pi\) | |||||||
\(684\) | −4816.73 | −0.269258 | ||||||||
\(685\) | 4306.03 | 0.240183 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2501.96 | 0.138946 | ||||||||
\(688\) | 615.854 | 0.0341268 | ||||||||
\(689\) | −14318.8 | −0.791733 | ||||||||
\(690\) | 1205.10 | 0.0664889 | ||||||||
\(691\) | 20546.8 | 1.13117 | 0.565583 | − | 0.824691i | \(-0.308651\pi\) | ||||
0.565583 | + | 0.824691i | \(0.308651\pi\) | |||||||
\(692\) | −14233.0 | −0.781875 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5486.66 | −0.300102 | ||||||||
\(695\) | −2906.57 | −0.158637 | ||||||||
\(696\) | −14517.6 | −0.790645 | ||||||||
\(697\) | −3643.70 | −0.198013 | ||||||||
\(698\) | −696.879 | −0.0377898 | ||||||||
\(699\) | −11824.3 | −0.639820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7033.05 | −0.378937 | −0.189468 | − | 0.981887i | \(-0.560676\pi\) | ||||
−0.189468 | + | 0.981887i | \(0.560676\pi\) | |||||||
\(702\) | −6234.53 | −0.335196 | ||||||||
\(703\) | −6616.97 | −0.354998 | ||||||||
\(704\) | 8698.08 | 0.465655 | ||||||||
\(705\) | −1891.36 | −0.101039 | ||||||||
\(706\) | 10582.7 | 0.564141 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8570.21 | 0.454927 | ||||||||
\(709\) | 4233.67 | 0.224258 | 0.112129 | − | 0.993694i | \(-0.464233\pi\) | ||||
0.112129 | + | 0.993694i | \(0.464233\pi\) | |||||||
\(710\) | 5255.90 | 0.277818 | ||||||||
\(711\) | 42.0927 | 0.00222025 | ||||||||
\(712\) | 18650.2 | 0.981667 | ||||||||
\(713\) | 8886.26 | 0.466750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3065.33 | 0.160332 | ||||||||
\(716\) | 8945.32 | 0.466902 | ||||||||
\(717\) | −137.575 | −0.00716573 | ||||||||
\(718\) | 2600.72 | 0.135178 | ||||||||
\(719\) | −6827.15 | −0.354117 | −0.177058 | − | 0.984200i | \(-0.556658\pi\) | ||||
−0.177058 | + | 0.984200i | \(0.556658\pi\) | |||||||
\(720\) | 242.237 | 0.0125384 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8246.14 | 0.425055 | ||||||||
\(723\) | −12591.0 | −0.647667 | ||||||||
\(724\) | 9509.48 | 0.488145 | ||||||||
\(725\) | 30834.2 | 1.57952 | ||||||||
\(726\) | 1545.62 | 0.0790127 | ||||||||
\(727\) | −24222.3 | −1.23570 | −0.617851 | − | 0.786295i | \(-0.711997\pi\) | ||||
−0.617851 | + | 0.786295i | \(0.711997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1782.21 | 0.0905456 | ||||||||
\(730\) | 3307.26 | 0.167681 | ||||||||
\(731\) | 14975.1 | 0.757692 | ||||||||
\(732\) | −4661.69 | −0.235384 | ||||||||
\(733\) | −33556.0 | −1.69088 | −0.845442 | − | 0.534067i | \(-0.820663\pi\) | ||||
−0.845442 | + | 0.534067i | \(0.820663\pi\) | |||||||
\(734\) | 12337.5 | 0.620415 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17068.8 | −0.854841 | ||||||||
\(737\) | −13333.8 | −0.666429 | ||||||||
\(738\) | −1457.73 | −0.0727099 | ||||||||
\(739\) | 27588.9 | 1.37331 | 0.686653 | − | 0.726985i | \(-0.259079\pi\) | ||||
0.686653 | + | 0.726985i | \(0.259079\pi\) | |||||||
\(740\) | 2411.41 | 0.119791 | ||||||||
\(741\) | 3415.86 | 0.169345 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7503.10 | −0.370474 | −0.185237 | − | 0.982694i | \(-0.559305\pi\) | ||||
−0.185237 | + | 0.982694i | \(0.559305\pi\) | |||||||
\(744\) | 5185.92 | 0.255544 | ||||||||
\(745\) | 7913.63 | 0.389172 | ||||||||
\(746\) | 10067.7 | 0.494106 | ||||||||
\(747\) | 11903.5 | 0.583032 | ||||||||
\(748\) | −14141.1 | −0.691242 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3116.14 | −0.151714 | ||||||||
\(751\) | −14203.4 | −0.690132 | −0.345066 | − | 0.938578i | \(-0.612143\pi\) | ||||
−0.345066 | + | 0.938578i | \(0.612143\pi\) | |||||||
\(752\) | 899.684 | 0.0436278 | ||||||||
\(753\) | −5154.17 | −0.249440 | ||||||||
\(754\) | −14249.2 | −0.688229 | ||||||||
\(755\) | −10620.6 | −0.511952 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15469.6 | −0.742739 | −0.371370 | − | 0.928485i | \(-0.621112\pi\) | ||||
−0.371370 | + | 0.928485i | \(0.621112\pi\) | |||||||
\(758\) | 15827.5 | 0.758420 | ||||||||
\(759\) | 7004.31 | 0.334967 | ||||||||
\(760\) | 3109.98 | 0.148435 | ||||||||
\(761\) | −25298.7 | −1.20509 | −0.602547 | − | 0.798083i | \(-0.705847\pi\) | ||||
−0.602547 | + | 0.798083i | \(0.705847\pi\) | |||||||
\(762\) | −1725.08 | −0.0820120 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6057.62 | 0.286855 | ||||||||
\(765\) | 5890.22 | 0.278381 | ||||||||
\(766\) | 1386.59 | 0.0654039 | ||||||||
\(767\) | 21487.9 | 1.01158 | ||||||||
\(768\) | −9594.01 | −0.450773 | ||||||||
\(769\) | 37278.1 | 1.74809 | 0.874046 | − | 0.485843i | \(-0.161487\pi\) | ||||
0.874046 | + | 0.485843i | \(0.161487\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7222.60 | −0.337374 | ||||||||
\(772\) | 20329.5 | 0.947765 | ||||||||
\(773\) | −37946.9 | −1.76566 | −0.882830 | − | 0.469692i | \(-0.844365\pi\) | ||||
−0.882830 | + | 0.469692i | \(0.844365\pi\) | |||||||
\(774\) | 5991.08 | 0.278223 | ||||||||
\(775\) | −11014.5 | −0.510517 | ||||||||
\(776\) | −19560.8 | −0.904886 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4273.23 | −0.196919 | ||||||||
\(779\) | 1823.27 | 0.0838580 | ||||||||
\(780\) | −1244.83 | −0.0571439 | ||||||||
\(781\) | 30548.5 | 1.39963 | ||||||||
\(782\) | −13939.0 | −0.637413 | ||||||||
\(783\) | 31409.0 | 1.43355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6809.84 | 0.309623 | ||||||||
\(786\) | 4711.68 | 0.213817 | ||||||||
\(787\) | 29896.1 | 1.35410 | 0.677052 | − | 0.735935i | \(-0.263257\pi\) | ||||
0.677052 | + | 0.735935i | \(0.263257\pi\) | |||||||
\(788\) | 20507.5 | 0.927093 | ||||||||
\(789\) | −917.098 | −0.0413809 | ||||||||
\(790\) | −10.6391 | −0.000479141 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14452.0 | −0.648394 | ||||||||
\(793\) | −11688.2 | −0.523403 | ||||||||
\(794\) | −7389.81 | −0.330296 | ||||||||
\(795\) | −3494.56 | −0.155898 | ||||||||
\(796\) | −4120.19 | −0.183463 | ||||||||
\(797\) | 2482.95 | 0.110352 | 0.0551760 | − | 0.998477i | \(-0.482428\pi\) | ||||
0.0551760 | + | 0.998477i | \(0.482428\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21876.7 | 0.968637 | ||||||||
\(800\) | 21156.6 | 0.934999 | ||||||||
\(801\) | −17675.3 | −0.779683 | ||||||||
\(802\) | −5160.89 | −0.227229 | ||||||||
\(803\) | 19222.5 | 0.844768 | ||||||||
\(804\) | 5414.88 | 0.237522 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5090.03 | 0.222443 | ||||||||
\(807\) | 16143.3 | 0.704178 | ||||||||
\(808\) | −26180.8 | −1.13990 | ||||||||
\(809\) | −13931.9 | −0.605464 | −0.302732 | − | 0.953076i | \(-0.597899\pi\) | ||||
−0.302732 | + | 0.953076i | \(0.597899\pi\) | |||||||
\(810\) | 1501.46 | 0.0651309 | ||||||||
\(811\) | −23457.0 | −1.01564 | −0.507822 | − | 0.861462i | \(-0.669549\pi\) | ||||
−0.507822 | + | 0.861462i | \(0.669549\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5897.62 | 0.254414 | ||||||||
\(814\) | −7771.87 | −0.334648 | ||||||||
\(815\) | −10830.8 | −0.465504 | ||||||||
\(816\) | 792.490 | 0.0339984 | ||||||||
\(817\) | −7493.37 | −0.320881 | ||||||||
\(818\) | 12604.7 | 0.538771 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −664.450 | −0.0282971 | ||||||||
\(821\) | −29634.9 | −1.25976 | −0.629881 | − | 0.776691i | \(-0.716896\pi\) | ||||
−0.629881 | + | 0.776691i | \(0.716896\pi\) | |||||||
\(822\) | 5635.94 | 0.239143 | ||||||||
\(823\) | 42873.9 | 1.81591 | 0.907953 | − | 0.419073i | \(-0.137645\pi\) | ||||
0.907953 | + | 0.419073i | \(0.137645\pi\) | |||||||
\(824\) | 13297.8 | 0.562197 | ||||||||
\(825\) | −8681.79 | −0.366377 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32579.8 | 1.36990 | 0.684952 | − | 0.728589i | \(-0.259823\pi\) | ||||
0.684952 | + | 0.728589i | \(0.259823\pi\) | |||||||
\(828\) | 10056.7 | 0.422093 | ||||||||
\(829\) | 36526.5 | 1.53030 | 0.765150 | − | 0.643852i | \(-0.222665\pi\) | ||||
0.765150 | + | 0.643852i | \(0.222665\pi\) | |||||||
\(830\) | −3008.64 | −0.125821 | ||||||||
\(831\) | −5719.65 | −0.238763 | ||||||||
\(832\) | −8856.45 | −0.369041 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3804.25 | −0.157950 | ||||||||
\(835\) | 9923.79 | 0.411290 | ||||||||
\(836\) | 7076.05 | 0.292740 | ||||||||
\(837\) | −11219.8 | −0.463336 | ||||||||
\(838\) | 17390.7 | 0.716886 | ||||||||
\(839\) | 15136.4 | 0.622845 | 0.311423 | − | 0.950272i | \(-0.399195\pi\) | ||||
0.311423 | + | 0.950272i | \(0.399195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47397.1 | 1.94338 | ||||||||
\(842\) | 26949.4 | 1.10301 | ||||||||
\(843\) | −11086.7 | −0.452963 | ||||||||
\(844\) | 1648.68 | 0.0672391 | ||||||||
\(845\) | 3797.37 | 0.154596 | ||||||||
\(846\) | 8752.19 | 0.355682 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1662.30 | 0.0673156 | ||||||||
\(849\) | 4787.83 | 0.193543 | ||||||||
\(850\) | 17277.3 | 0.697183 | ||||||||
\(851\) | 13815.3 | 0.556501 | ||||||||
\(852\) | −12405.8 | −0.498843 | ||||||||
\(853\) | −2912.85 | −0.116922 | −0.0584608 | − | 0.998290i | \(-0.518619\pi\) | ||||
−0.0584608 | + | 0.998290i | \(0.518619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2947.41 | −0.117894 | ||||||||
\(856\) | −2542.11 | −0.101504 | ||||||||
\(857\) | −7934.06 | −0.316245 | −0.158123 | − | 0.987419i | \(-0.550544\pi\) | ||||
−0.158123 | + | 0.987419i | \(0.550544\pi\) | |||||||
\(858\) | 4012.05 | 0.159638 | ||||||||
\(859\) | 17792.9 | 0.706734 | 0.353367 | − | 0.935485i | \(-0.385037\pi\) | ||||
0.353367 | + | 0.935485i | \(0.385037\pi\) | |||||||
\(860\) | 2730.79 | 0.108278 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6345.85 | 0.250743 | ||||||||
\(863\) | −26295.2 | −1.03719 | −0.518597 | − | 0.855019i | \(-0.673545\pi\) | ||||
−0.518597 | + | 0.855019i | \(0.673545\pi\) | |||||||
\(864\) | 21551.0 | 0.848588 | ||||||||
\(865\) | −8709.32 | −0.342342 | ||||||||
\(866\) | −7280.87 | −0.285698 | ||||||||
\(867\) | 7283.02 | 0.285287 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.8366 | −0.00241388 | ||||||||
\(870\) | −3477.56 | −0.135518 | ||||||||
\(871\) | 13576.6 | 0.528159 | ||||||||
\(872\) | 19523.3 | 0.758192 | ||||||||
\(873\) | 18538.3 | 0.718700 | ||||||||
\(874\) | 6974.92 | 0.269943 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7806.29 | −0.301085 | ||||||||
\(877\) | 31547.9 | 1.21471 | 0.607353 | − | 0.794432i | \(-0.292231\pi\) | ||||
0.607353 | + | 0.794432i | \(0.292231\pi\) | |||||||
\(878\) | 5508.81 | 0.211746 | ||||||||
\(879\) | 23782.9 | 0.912602 | ||||||||
\(880\) | −355.860 | −0.0136319 | ||||||||
\(881\) | 19775.2 | 0.756234 | 0.378117 | − | 0.925758i | \(-0.376572\pi\) | ||||
0.378117 | + | 0.925758i | \(0.376572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7278.33 | 0.277390 | 0.138695 | − | 0.990335i | \(-0.455709\pi\) | ||||
0.138695 | + | 0.990335i | \(0.455709\pi\) | |||||||
\(884\) | 14398.6 | 0.547824 | ||||||||
\(885\) | 5244.20 | 0.199188 | ||||||||
\(886\) | 6185.37 | 0.234539 | ||||||||
\(887\) | 2685.15 | 0.101644 | 0.0508221 | − | 0.998708i | \(-0.483816\pi\) | ||||
0.0508221 | + | 0.998708i | \(0.483816\pi\) | |||||||
\(888\) | 8062.46 | 0.304683 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4467.49 | 0.168259 | ||||||||
\(891\) | 8726.83 | 0.328125 | ||||||||
\(892\) | 31670.7 | 1.18881 | ||||||||
\(893\) | −10946.8 | −0.410215 | ||||||||
\(894\) | 10357.7 | 0.387488 | ||||||||
\(895\) | 5473.73 | 0.204432 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7131.84 | −0.265469 | ||||||||
\(898\) | 12412.1 | 0.461243 | ||||||||
\(899\) | −25643.1 | −0.951330 | ||||||||
\(900\) | −12465.2 | −0.461673 | ||||||||
\(901\) | 40420.4 | 1.49456 | ||||||||
\(902\) | 2141.49 | 0.0790510 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18801.1 | −0.691721 | ||||||||
\(905\) | 5818.95 | 0.213733 | ||||||||
\(906\) | −13900.8 | −0.509737 | ||||||||
\(907\) | −35185.6 | −1.28811 | −0.644057 | − | 0.764977i | \(-0.722750\pi\) | ||||
−0.644057 | + | 0.764977i | \(0.722750\pi\) | |||||||
\(908\) | −5924.14 | −0.216519 | ||||||||
\(909\) | 24812.2 | 0.905356 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10496.0 | 0.381720 | 0.190860 | − | 0.981617i | \(-0.438872\pi\) | ||||
0.190860 | + | 0.981617i | \(0.438872\pi\) | |||||||
\(912\) | −396.553 | −0.0143982 | ||||||||
\(913\) | −17486.9 | −0.633878 | ||||||||
\(914\) | −790.409 | −0.0286044 | ||||||||
\(915\) | −2852.54 | −0.103062 | ||||||||
\(916\) | −5277.26 | −0.190355 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 17599.3 | 0.632750 | ||||||||
\(919\) | 23701.1 | 0.850738 | 0.425369 | − | 0.905020i | \(-0.360144\pi\) | ||||
0.425369 | + | 0.905020i | \(0.360144\pi\) | |||||||
\(920\) | −6493.20 | −0.232690 | ||||||||
\(921\) | 15195.3 | 0.543652 | ||||||||
\(922\) | 17314.9 | 0.618479 | ||||||||
\(923\) | −31104.7 | −1.10923 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17124.0 | −0.608684 | ||||||||
\(926\) | 17539.1 | 0.622430 | ||||||||
\(927\) | −12602.7 | −0.446522 | ||||||||
\(928\) | 49255.4 | 1.74234 | ||||||||
\(929\) | −56090.7 | −1.98092 | −0.990460 | − | 0.137800i | \(-0.955997\pi\) | ||||
−0.990460 | + | 0.137800i | \(0.955997\pi\) | |||||||
\(930\) | 1242.24 | 0.0438007 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24940.3 | 0.876551 | ||||||||
\(933\) | 8261.91 | 0.289907 | ||||||||
\(934\) | 11924.0 | 0.417735 | ||||||||
\(935\) | −8653.08 | −0.302659 | ||||||||
\(936\) | 14715.1 | 0.513866 | ||||||||
\(937\) | 16422.6 | 0.572577 | 0.286288 | − | 0.958143i | \(-0.407578\pi\) | ||||
0.286288 | + | 0.958143i | \(0.407578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5896.88 | 0.204939 | ||||||||
\(940\) | 3989.34 | 0.138423 | ||||||||
\(941\) | 47774.6 | 1.65506 | 0.827528 | − | 0.561424i | \(-0.189746\pi\) | ||||
0.827528 | + | 0.561424i | \(0.189746\pi\) | |||||||
\(942\) | 8913.04 | 0.308283 | ||||||||
\(943\) | −3806.73 | −0.131457 | ||||||||
\(944\) | −2494.57 | −0.0860078 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8801.24 | −0.302487 | ||||||||
\(947\) | 13672.4 | 0.469160 | 0.234580 | − | 0.972097i | \(-0.424628\pi\) | ||||
0.234580 | + | 0.972097i | \(0.424628\pi\) | |||||||
\(948\) | 25.1119 | 0.000860334 0 | ||||||||
\(949\) | −19572.6 | −0.669496 | ||||||||
\(950\) | −8645.36 | −0.295255 | ||||||||
\(951\) | −23446.1 | −0.799466 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2821.39 | 0.0959012 | 0.0479506 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479506 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(954\) | 16171.0 | 0.548799 | ||||||||
\(955\) | 3706.72 | 0.125599 | ||||||||
\(956\) | 290.179 | 0.00981702 | ||||||||
\(957\) | −20212.4 | −0.682730 | ||||||||
\(958\) | −21033.2 | −0.709345 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2161.45 | −0.0726671 | ||||||||
\(961\) | −20630.9 | −0.692521 | ||||||||
\(962\) | 7913.38 | 0.265216 | ||||||||
\(963\) | 2409.22 | 0.0806190 | ||||||||
\(964\) | 26557.5 | 0.887301 | ||||||||
\(965\) | 12439.8 | 0.414976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19660.0 | −0.653798 | −0.326899 | − | 0.945059i | \(-0.606004\pi\) | ||||
−0.326899 | + | 0.945059i | \(0.606004\pi\) | |||||||
\(968\) | −8327.95 | −0.276519 | ||||||||
\(969\) | −9642.57 | −0.319674 | ||||||||
\(970\) | −4685.60 | −0.155099 | ||||||||
\(971\) | 52982.9 | 1.75108 | 0.875541 | − | 0.483143i | \(-0.160505\pi\) | ||||
0.875541 | + | 0.483143i | \(0.160505\pi\) | |||||||
\(972\) | −19832.9 | −0.654466 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10540.1 | 0.346741 | ||||||||
\(975\) | 8839.87 | 0.290361 | ||||||||
\(976\) | 1356.90 | 0.0445013 | ||||||||
\(977\) | −5245.98 | −0.171785 | −0.0858925 | − | 0.996304i | \(-0.527374\pi\) | ||||
−0.0858925 | + | 0.996304i | \(0.527374\pi\) | |||||||
\(978\) | −14175.8 | −0.463490 | ||||||||
\(979\) | 25966.0 | 0.847680 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18502.8 | −0.602190 | ||||||||
\(982\) | −33430.7 | −1.08637 | ||||||||
\(983\) | −39339.2 | −1.27643 | −0.638213 | − | 0.769860i | \(-0.720326\pi\) | ||||
−0.638213 | + | 0.769860i | \(0.720326\pi\) | |||||||
\(984\) | −2221.57 | −0.0719725 | ||||||||
\(985\) | 12548.7 | 0.405925 | ||||||||
\(986\) | 40223.8 | 1.29917 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7204.89 | −0.232002 | ||||||||
\(989\) | 15645.1 | 0.503019 | ||||||||
\(990\) | −3461.84 | −0.111136 | ||||||||
\(991\) | 2368.20 | 0.0759115 | 0.0379557 | − | 0.999279i | \(-0.487915\pi\) | ||||
0.0379557 | + | 0.999279i | \(0.487915\pi\) | |||||||
\(992\) | −17594.8 | −0.563141 | ||||||||
\(993\) | 4238.19 | 0.135443 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2521.19 | −0.0803286 | ||||||||
\(996\) | 7101.43 | 0.225921 | ||||||||
\(997\) | −14564.0 | −0.462634 | −0.231317 | − | 0.972878i | \(-0.574303\pi\) | ||||
−0.231317 | + | 0.972878i | \(0.574303\pi\) | |||||||
\(998\) | 10549.0 | 0.334592 | ||||||||
\(999\) | −17443.2 | −0.552431 |
(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.k.1.14 | 36 | ||
7.3 | odd | 6 | 287.4.e.a.247.23 | yes | 72 | ||
7.5 | odd | 6 | 287.4.e.a.165.23 | ✓ | 72 | ||
7.6 | odd | 2 | 2009.4.a.j.1.14 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.4.e.a.165.23 | ✓ | 72 | 7.5 | odd | 6 | ||
287.4.e.a.247.23 | yes | 72 | 7.3 | odd | 6 | ||
2009.4.a.j.1.14 | 36 | 7.6 | odd | 2 | |||
2009.4.a.k.1.14 | 36 | 1.1 | even | 1 | trivial |