Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.11196169353.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 87x^{4} + 179x^{3} + 2574x^{2} - 2664x - 25992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.57904\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −11.4115 | −1.02068 | −0.510338 | − | 0.859974i | \(-0.670480\pi\) | ||||
−0.510338 | + | 0.859974i | \(0.670480\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −8.90590 | −0.480873 | −0.240437 | − | 0.970665i | \(-0.577291\pi\) | ||||
−0.240437 | + | 0.970665i | \(0.577291\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −22.8230 | −0.721727 | ||||||||
\(11\) | 22.5981 | 0.619416 | 0.309708 | − | 0.950832i | \(-0.399769\pi\) | ||||
0.309708 | + | 0.950832i | \(0.399769\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −11.4947 | −0.245236 | −0.122618 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122618 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(14\) | −17.8118 | −0.340029 | ||||||||
\(15\) | 34.2345 | 0.589287 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 31.6273 | 0.451221 | 0.225610 | − | 0.974218i | \(-0.427562\pi\) | ||||
0.225610 | + | 0.974218i | \(0.427562\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −45.6460 | −0.510338 | ||||||||
\(21\) | 26.7177 | 0.277632 | ||||||||
\(22\) | 45.1962 | 0.437993 | ||||||||
\(23\) | −49.6096 | −0.449753 | −0.224877 | − | 0.974387i | \(-0.572198\pi\) | ||||
−0.224877 | + | 0.974387i | \(0.572198\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 5.22231 | 0.0417784 | ||||||||
\(26\) | −22.9895 | −0.173408 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −35.6236 | −0.240437 | ||||||||
\(29\) | −23.8498 | −0.152717 | −0.0763586 | − | 0.997080i | \(-0.524329\pi\) | ||||
−0.0763586 | + | 0.997080i | \(0.524329\pi\) | |||||||
\(30\) | 68.4690 | 0.416689 | ||||||||
\(31\) | 155.008 | 0.898073 | 0.449037 | − | 0.893513i | \(-0.351767\pi\) | ||||
0.449037 | + | 0.893513i | \(0.351767\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −67.7942 | −0.357620 | ||||||||
\(34\) | 63.2547 | 0.319061 | ||||||||
\(35\) | 101.630 | 0.490816 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −88.9835 | −0.395373 | −0.197686 | − | 0.980265i | \(-0.563343\pi\) | ||||
−0.197686 | + | 0.980265i | \(0.563343\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 34.4842 | 0.141587 | ||||||||
\(40\) | −91.2920 | −0.360863 | ||||||||
\(41\) | −1.75763 | −0.00669500 | −0.00334750 | − | 0.999994i | \(-0.501066\pi\) | ||||
−0.00334750 | + | 0.999994i | \(0.501066\pi\) | |||||||
\(42\) | 53.4354 | 0.196316 | ||||||||
\(43\) | 502.441 | 1.78190 | 0.890949 | − | 0.454104i | \(-0.150040\pi\) | ||||
0.890949 | + | 0.454104i | \(0.150040\pi\) | |||||||
\(44\) | 90.3923 | 0.309708 | ||||||||
\(45\) | −102.703 | −0.340225 | ||||||||
\(46\) | −99.2193 | −0.318024 | ||||||||
\(47\) | 178.728 | 0.554683 | 0.277341 | − | 0.960771i | \(-0.410547\pi\) | ||||
0.277341 | + | 0.960771i | \(0.410547\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | −263.685 | −0.768761 | ||||||||
\(50\) | 10.4446 | 0.0295418 | ||||||||
\(51\) | −94.8820 | −0.260512 | ||||||||
\(52\) | −45.9790 | −0.122618 | ||||||||
\(53\) | −22.4292 | −0.0581299 | −0.0290650 | − | 0.999578i | \(-0.509253\pi\) | ||||
−0.0290650 | + | 0.999578i | \(0.509253\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −257.878 | −0.632223 | ||||||||
\(56\) | −71.2472 | −0.170014 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47.6997 | −0.107987 | ||||||||
\(59\) | 604.207 | 1.33324 | 0.666619 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666619 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(60\) | 136.938 | 0.294644 | ||||||||
\(61\) | −688.976 | −1.44614 | −0.723069 | − | 0.690776i | \(-0.757269\pi\) | ||||
−0.723069 | + | 0.690776i | \(0.757269\pi\) | |||||||
\(62\) | 310.016 | 0.635034 | ||||||||
\(63\) | −80.1531 | −0.160291 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 131.172 | 0.250306 | ||||||||
\(66\) | −135.588 | −0.252876 | ||||||||
\(67\) | 370.614 | 0.675786 | 0.337893 | − | 0.941184i | \(-0.390286\pi\) | ||||
0.337893 | + | 0.941184i | \(0.390286\pi\) | |||||||
\(68\) | 126.509 | 0.225610 | ||||||||
\(69\) | 148.829 | 0.259665 | ||||||||
\(70\) | 203.259 | 0.347059 | ||||||||
\(71\) | −569.852 | −0.952522 | −0.476261 | − | 0.879304i | \(-0.658008\pi\) | ||||
−0.476261 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 686.896 | 1.10130 | 0.550652 | − | 0.834735i | \(-0.314379\pi\) | ||||
0.550652 | + | 0.834735i | \(0.314379\pi\) | |||||||
\(74\) | −177.967 | −0.279571 | ||||||||
\(75\) | −15.6669 | −0.0241208 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −201.256 | −0.297861 | ||||||||
\(78\) | 68.9684 | 0.100117 | ||||||||
\(79\) | 610.842 | 0.869937 | 0.434969 | − | 0.900446i | \(-0.356759\pi\) | ||||
0.434969 | + | 0.900446i | \(0.356759\pi\) | |||||||
\(80\) | −182.584 | −0.255169 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −3.51525 | −0.00473408 | ||||||||
\(83\) | −625.214 | −0.826821 | −0.413410 | − | 0.910545i | \(-0.635663\pi\) | ||||
−0.413410 | + | 0.910545i | \(0.635663\pi\) | |||||||
\(84\) | 106.871 | 0.138816 | ||||||||
\(85\) | −360.915 | −0.460550 | ||||||||
\(86\) | 1004.88 | 1.25999 | ||||||||
\(87\) | 71.5495 | 0.0881714 | ||||||||
\(88\) | 180.785 | 0.218997 | ||||||||
\(89\) | −2.01030 | −0.00239428 | −0.00119714 | − | 0.999999i | \(-0.500381\pi\) | ||||
−0.00119714 | + | 0.999999i | \(0.500381\pi\) | |||||||
\(90\) | −205.407 | −0.240576 | ||||||||
\(91\) | 102.371 | 0.117927 | ||||||||
\(92\) | −198.439 | −0.224877 | ||||||||
\(93\) | −465.024 | −0.518503 | ||||||||
\(94\) | 357.455 | 0.392220 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 178.624 | 0.186974 | 0.0934870 | − | 0.995621i | \(-0.470199\pi\) | ||||
0.0934870 | + | 0.995621i | \(0.470199\pi\) | |||||||
\(98\) | −527.370 | −0.543596 | ||||||||
\(99\) | 203.383 | 0.206472 | ||||||||
\(100\) | 20.8892 | 0.0208892 | ||||||||
\(101\) | 209.428 | 0.206325 | 0.103163 | − | 0.994665i | \(-0.467104\pi\) | ||||
0.103163 | + | 0.994665i | \(0.467104\pi\) | |||||||
\(102\) | −189.764 | −0.184210 | ||||||||
\(103\) | 335.696 | 0.321137 | 0.160569 | − | 0.987025i | \(-0.448667\pi\) | ||||
0.160569 | + | 0.987025i | \(0.448667\pi\) | |||||||
\(104\) | −91.9579 | −0.0867040 | ||||||||
\(105\) | −304.889 | −0.283373 | ||||||||
\(106\) | −44.8584 | −0.0411041 | ||||||||
\(107\) | −1600.65 | −1.44617 | −0.723086 | − | 0.690758i | \(-0.757277\pi\) | ||||
−0.723086 | + | 0.690758i | \(0.757277\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −796.409 | −0.699836 | −0.349918 | − | 0.936780i | \(-0.613791\pi\) | ||||
−0.349918 | + | 0.936780i | \(0.613791\pi\) | |||||||
\(110\) | −515.756 | −0.447049 | ||||||||
\(111\) | 266.950 | 0.228269 | ||||||||
\(112\) | −142.494 | −0.120218 | ||||||||
\(113\) | −1222.16 | −1.01744 | −0.508722 | − | 0.860931i | \(-0.669882\pi\) | ||||
−0.508722 | + | 0.860931i | \(0.669882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 566.120 | 0.459052 | ||||||||
\(116\) | −95.3993 | −0.0763586 | ||||||||
\(117\) | −103.453 | −0.0817453 | ||||||||
\(118\) | 1208.41 | 0.942741 | ||||||||
\(119\) | −281.670 | −0.216980 | ||||||||
\(120\) | 273.876 | 0.208345 | ||||||||
\(121\) | −820.327 | −0.616324 | ||||||||
\(122\) | −1377.95 | −1.02257 | ||||||||
\(123\) | 5.27288 | 0.00386536 | ||||||||
\(124\) | 620.032 | 0.449037 | ||||||||
\(125\) | 1366.84 | 0.978033 | ||||||||
\(126\) | −160.306 | −0.113343 | ||||||||
\(127\) | −1460.41 | −1.02040 | −0.510199 | − | 0.860056i | \(-0.670428\pi\) | ||||
−0.510199 | + | 0.860056i | \(0.670428\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1507.32 | −1.02878 | ||||||||
\(130\) | 262.344 | 0.176993 | ||||||||
\(131\) | −1838.66 | −1.22629 | −0.613146 | − | 0.789970i | \(-0.710096\pi\) | ||||
−0.613146 | + | 0.789970i | \(0.710096\pi\) | |||||||
\(132\) | −271.177 | −0.178810 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 741.228 | 0.477853 | ||||||||
\(135\) | 308.110 | 0.196429 | ||||||||
\(136\) | 253.019 | 0.159531 | ||||||||
\(137\) | −2147.39 | −1.33915 | −0.669576 | − | 0.742743i | \(-0.733524\pi\) | ||||
−0.669576 | + | 0.742743i | \(0.733524\pi\) | |||||||
\(138\) | 297.658 | 0.183611 | ||||||||
\(139\) | −2942.22 | −1.79537 | −0.897684 | − | 0.440640i | \(-0.854752\pi\) | ||||
−0.897684 | + | 0.440640i | \(0.854752\pi\) | |||||||
\(140\) | 406.519 | 0.245408 | ||||||||
\(141\) | −536.183 | −0.320246 | ||||||||
\(142\) | −1139.70 | −0.673534 | ||||||||
\(143\) | −259.759 | −0.151903 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 272.162 | 0.155875 | ||||||||
\(146\) | 1373.79 | 0.778739 | ||||||||
\(147\) | 791.055 | 0.443844 | ||||||||
\(148\) | −355.934 | −0.197686 | ||||||||
\(149\) | 2973.88 | 1.63510 | 0.817550 | − | 0.575857i | \(-0.195332\pi\) | ||||
0.817550 | + | 0.575857i | \(0.195332\pi\) | |||||||
\(150\) | −31.3338 | −0.0170560 | ||||||||
\(151\) | −718.878 | −0.387427 | −0.193713 | − | 0.981058i | \(-0.562053\pi\) | ||||
−0.193713 | + | 0.981058i | \(0.562053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 284.646 | 0.150407 | ||||||||
\(154\) | −402.512 | −0.210619 | ||||||||
\(155\) | −1768.87 | −0.916641 | ||||||||
\(156\) | 137.937 | 0.0707935 | ||||||||
\(157\) | 1658.74 | 0.843199 | 0.421599 | − | 0.906782i | \(-0.361469\pi\) | ||||
0.421599 | + | 0.906782i | \(0.361469\pi\) | |||||||
\(158\) | 1221.68 | 0.615139 | ||||||||
\(159\) | 67.2875 | 0.0335613 | ||||||||
\(160\) | −365.168 | −0.180432 | ||||||||
\(161\) | 441.818 | 0.216274 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −942.731 | −0.453008 | −0.226504 | − | 0.974010i | \(-0.572730\pi\) | ||||
−0.226504 | + | 0.974010i | \(0.572730\pi\) | |||||||
\(164\) | −7.03050 | −0.00334750 | ||||||||
\(165\) | 773.634 | 0.365014 | ||||||||
\(166\) | −1250.43 | −0.584651 | ||||||||
\(167\) | −1960.33 | −0.908353 | −0.454176 | − | 0.890912i | \(-0.650066\pi\) | ||||
−0.454176 | + | 0.890912i | \(0.650066\pi\) | |||||||
\(168\) | 213.742 | 0.0981579 | ||||||||
\(169\) | −2064.87 | −0.939859 | ||||||||
\(170\) | −721.830 | −0.325658 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2009.77 | 0.890949 | ||||||||
\(173\) | −3342.82 | −1.46907 | −0.734537 | − | 0.678568i | \(-0.762601\pi\) | ||||
−0.734537 | + | 0.678568i | \(0.762601\pi\) | |||||||
\(174\) | 143.099 | 0.0623466 | ||||||||
\(175\) | −46.5093 | −0.0200901 | ||||||||
\(176\) | 361.569 | 0.154854 | ||||||||
\(177\) | −1812.62 | −0.769745 | ||||||||
\(178\) | −4.02060 | −0.00169302 | ||||||||
\(179\) | −2848.38 | −1.18937 | −0.594686 | − | 0.803958i | \(-0.702724\pi\) | ||||
−0.594686 | + | 0.803958i | \(0.702724\pi\) | |||||||
\(180\) | −410.814 | −0.170113 | ||||||||
\(181\) | −2373.50 | −0.974699 | −0.487350 | − | 0.873207i | \(-0.662036\pi\) | ||||
−0.487350 | + | 0.873207i | \(0.662036\pi\) | |||||||
\(182\) | 204.742 | 0.0833873 | ||||||||
\(183\) | 2066.93 | 0.834928 | ||||||||
\(184\) | −396.877 | −0.159012 | ||||||||
\(185\) | 1015.43 | 0.403547 | ||||||||
\(186\) | −930.048 | −0.366637 | ||||||||
\(187\) | 714.717 | 0.279493 | ||||||||
\(188\) | 714.910 | 0.277341 | ||||||||
\(189\) | 240.459 | 0.0925441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4815.13 | 1.82414 | 0.912070 | − | 0.410034i | \(-0.134483\pi\) | ||||
0.912070 | + | 0.410034i | \(0.134483\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −1984.38 | −0.740097 | −0.370049 | − | 0.929012i | \(-0.620659\pi\) | ||||
−0.370049 | + | 0.929012i | \(0.620659\pi\) | |||||||
\(194\) | 357.247 | 0.132211 | ||||||||
\(195\) | −393.517 | −0.144514 | ||||||||
\(196\) | −1054.74 | −0.384380 | ||||||||
\(197\) | 421.647 | 0.152493 | 0.0762464 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762464 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(198\) | 406.765 | 0.145998 | ||||||||
\(199\) | −1722.81 | −0.613703 | −0.306852 | − | 0.951757i | \(-0.599276\pi\) | ||||
−0.306852 | + | 0.951757i | \(0.599276\pi\) | |||||||
\(200\) | 41.7784 | 0.0147709 | ||||||||
\(201\) | −1111.84 | −0.390165 | ||||||||
\(202\) | 418.856 | 0.145894 | ||||||||
\(203\) | 212.404 | 0.0734377 | ||||||||
\(204\) | −379.528 | −0.130256 | ||||||||
\(205\) | 20.0571 | 0.00683342 | ||||||||
\(206\) | 671.393 | 0.227078 | ||||||||
\(207\) | −446.487 | −0.149918 | ||||||||
\(208\) | −183.916 | −0.0613090 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −609.778 | −0.200375 | ||||||||
\(211\) | −906.017 | −0.295606 | −0.147803 | − | 0.989017i | \(-0.547220\pi\) | ||||
−0.147803 | + | 0.989017i | \(0.547220\pi\) | |||||||
\(212\) | −89.7167 | −0.0290650 | ||||||||
\(213\) | 1709.56 | 0.549939 | ||||||||
\(214\) | −3201.30 | −1.02260 | ||||||||
\(215\) | −5733.61 | −1.81874 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −1380.49 | −0.431859 | ||||||||
\(218\) | −1592.82 | −0.494859 | ||||||||
\(219\) | −2060.69 | −0.635838 | ||||||||
\(220\) | −1031.51 | −0.316111 | ||||||||
\(221\) | −363.548 | −0.110656 | ||||||||
\(222\) | 533.901 | 0.161410 | ||||||||
\(223\) | −5229.06 | −1.57024 | −0.785120 | − | 0.619344i | \(-0.787399\pi\) | ||||
−0.785120 | + | 0.619344i | \(0.787399\pi\) | |||||||
\(224\) | −284.989 | −0.0850072 | ||||||||
\(225\) | 47.0007 | 0.0139261 | ||||||||
\(226\) | −2444.32 | −0.719442 | ||||||||
\(227\) | −44.6697 | −0.0130609 | −0.00653047 | − | 0.999979i | \(-0.502079\pi\) | ||||
−0.00653047 | + | 0.999979i | \(0.502079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3847.75 | 1.11033 | 0.555167 | − | 0.831739i | \(-0.312654\pi\) | ||||
0.555167 | + | 0.831739i | \(0.312654\pi\) | |||||||
\(230\) | 1132.24 | 0.324599 | ||||||||
\(231\) | 603.769 | 0.171970 | ||||||||
\(232\) | −190.799 | −0.0539937 | ||||||||
\(233\) | −1134.64 | −0.319024 | −0.159512 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159512 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(234\) | −206.905 | −0.0578027 | ||||||||
\(235\) | −2039.55 | −0.566151 | ||||||||
\(236\) | 2416.83 | 0.666619 | ||||||||
\(237\) | −1832.53 | −0.502259 | ||||||||
\(238\) | −563.340 | −0.153428 | ||||||||
\(239\) | 4302.04 | 1.16433 | 0.582167 | − | 0.813070i | \(-0.302205\pi\) | ||||
0.582167 | + | 0.813070i | \(0.302205\pi\) | |||||||
\(240\) | 547.752 | 0.147322 | ||||||||
\(241\) | 3633.24 | 0.971110 | 0.485555 | − | 0.874206i | \(-0.338618\pi\) | ||||
0.485555 | + | 0.874206i | \(0.338618\pi\) | |||||||
\(242\) | −1640.65 | −0.435807 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2755.91 | −0.723069 | ||||||||
\(245\) | 3009.04 | 0.784655 | ||||||||
\(246\) | 10.5458 | 0.00273322 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1240.06 | 0.317517 | ||||||||
\(249\) | 1875.64 | 0.477365 | ||||||||
\(250\) | 2733.69 | 0.691574 | ||||||||
\(251\) | −2787.48 | −0.700973 | −0.350487 | − | 0.936568i | \(-0.613984\pi\) | ||||
−0.350487 | + | 0.936568i | \(0.613984\pi\) | |||||||
\(252\) | −320.612 | −0.0801456 | ||||||||
\(253\) | −1121.08 | −0.278584 | ||||||||
\(254\) | −2920.82 | −0.721531 | ||||||||
\(255\) | 1082.75 | 0.265899 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3709.83 | −0.900440 | −0.450220 | − | 0.892918i | \(-0.648654\pi\) | ||||
−0.450220 | + | 0.892918i | \(0.648654\pi\) | |||||||
\(258\) | −3014.65 | −0.727457 | ||||||||
\(259\) | 792.478 | 0.190124 | ||||||||
\(260\) | 524.689 | 0.125153 | ||||||||
\(261\) | −214.648 | −0.0509058 | ||||||||
\(262\) | −3677.31 | −0.867119 | ||||||||
\(263\) | 1472.97 | 0.345350 | 0.172675 | − | 0.984979i | \(-0.444759\pi\) | ||||
0.172675 | + | 0.984979i | \(0.444759\pi\) | |||||||
\(264\) | −542.354 | −0.126438 | ||||||||
\(265\) | 255.951 | 0.0593318 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.03090 | 0.00138234 | ||||||||
\(268\) | 1482.46 | 0.337893 | ||||||||
\(269\) | −2136.66 | −0.484292 | −0.242146 | − | 0.970240i | \(-0.577851\pi\) | ||||
−0.242146 | + | 0.970240i | \(0.577851\pi\) | |||||||
\(270\) | 616.221 | 0.138896 | ||||||||
\(271\) | 4135.19 | 0.926919 | 0.463460 | − | 0.886118i | \(-0.346608\pi\) | ||||
0.463460 | + | 0.886118i | \(0.346608\pi\) | |||||||
\(272\) | 506.037 | 0.112805 | ||||||||
\(273\) | −307.113 | −0.0680854 | ||||||||
\(274\) | −4294.78 | −0.946924 | ||||||||
\(275\) | 118.014 | 0.0258782 | ||||||||
\(276\) | 595.316 | 0.129833 | ||||||||
\(277\) | −3980.29 | −0.863366 | −0.431683 | − | 0.902025i | \(-0.642080\pi\) | ||||
−0.431683 | + | 0.902025i | \(0.642080\pi\) | |||||||
\(278\) | −5884.45 | −1.26952 | ||||||||
\(279\) | 1395.07 | 0.299358 | ||||||||
\(280\) | 813.037 | 0.173530 | ||||||||
\(281\) | −5639.72 | −1.19729 | −0.598643 | − | 0.801016i | \(-0.704293\pi\) | ||||
−0.598643 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(282\) | −1072.37 | −0.226448 | ||||||||
\(283\) | −6784.86 | −1.42515 | −0.712576 | − | 0.701594i | \(-0.752472\pi\) | ||||
−0.712576 | + | 0.701594i | \(0.752472\pi\) | |||||||
\(284\) | −2279.41 | −0.476261 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −519.518 | −0.107412 | ||||||||
\(287\) | 15.6532 | 0.00321945 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −3912.71 | −0.796400 | ||||||||
\(290\) | 544.325 | 0.110220 | ||||||||
\(291\) | −535.871 | −0.107949 | ||||||||
\(292\) | 2747.59 | 0.550652 | ||||||||
\(293\) | 2129.26 | 0.424549 | 0.212275 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212275 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(294\) | 1582.11 | 0.313845 | ||||||||
\(295\) | −6894.90 | −1.36080 | ||||||||
\(296\) | −711.868 | −0.139785 | ||||||||
\(297\) | −610.148 | −0.119207 | ||||||||
\(298\) | 5947.77 | 1.15619 | ||||||||
\(299\) | 570.250 | 0.110296 | ||||||||
\(300\) | −62.6677 | −0.0120604 | ||||||||
\(301\) | −4474.69 | −0.856867 | ||||||||
\(302\) | −1437.76 | −0.273952 | ||||||||
\(303\) | −628.283 | −0.119122 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7862.25 | 1.47604 | ||||||||
\(306\) | 569.292 | 0.106354 | ||||||||
\(307\) | 5402.40 | 1.00434 | 0.502168 | − | 0.864770i | \(-0.332536\pi\) | ||||
0.502168 | + | 0.864770i | \(0.332536\pi\) | |||||||
\(308\) | −805.025 | −0.148930 | ||||||||
\(309\) | −1007.09 | −0.185409 | ||||||||
\(310\) | −3537.75 | −0.648163 | ||||||||
\(311\) | 5553.87 | 1.01264 | 0.506320 | − | 0.862346i | \(-0.331006\pi\) | ||||
0.506320 | + | 0.862346i | \(0.331006\pi\) | |||||||
\(312\) | 275.874 | 0.0500586 | ||||||||
\(313\) | −7915.75 | −1.42947 | −0.714735 | − | 0.699395i | \(-0.753453\pi\) | ||||
−0.714735 | + | 0.699395i | \(0.753453\pi\) | |||||||
\(314\) | 3317.49 | 0.596232 | ||||||||
\(315\) | 914.667 | 0.163605 | ||||||||
\(316\) | 2443.37 | 0.434969 | ||||||||
\(317\) | 9137.51 | 1.61897 | 0.809486 | − | 0.587140i | \(-0.199746\pi\) | ||||
0.809486 | + | 0.587140i | \(0.199746\pi\) | |||||||
\(318\) | 134.575 | 0.0237314 | ||||||||
\(319\) | −538.960 | −0.0945956 | ||||||||
\(320\) | −730.336 | −0.127584 | ||||||||
\(321\) | 4801.94 | 0.834948 | ||||||||
\(322\) | 883.637 | 0.152929 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −60.0290 | −0.0102456 | ||||||||
\(326\) | −1885.46 | −0.320325 | ||||||||
\(327\) | 2389.23 | 0.404050 | ||||||||
\(328\) | −14.0610 | −0.00236704 | ||||||||
\(329\) | −1591.73 | −0.266732 | ||||||||
\(330\) | 1547.27 | 0.258104 | ||||||||
\(331\) | −6052.53 | −1.00507 | −0.502534 | − | 0.864558i | \(-0.667599\pi\) | ||||
−0.502534 | + | 0.864558i | \(0.667599\pi\) | |||||||
\(332\) | −2500.86 | −0.413410 | ||||||||
\(333\) | −800.851 | −0.131791 | ||||||||
\(334\) | −3920.66 | −0.642302 | ||||||||
\(335\) | −4229.26 | −0.689759 | ||||||||
\(336\) | 427.483 | 0.0694081 | ||||||||
\(337\) | −4682.35 | −0.756866 | −0.378433 | − | 0.925629i | \(-0.623537\pi\) | ||||
−0.378433 | + | 0.925629i | \(0.623537\pi\) | |||||||
\(338\) | −4129.74 | −0.664581 | ||||||||
\(339\) | 3666.48 | 0.587422 | ||||||||
\(340\) | −1443.66 | −0.230275 | ||||||||
\(341\) | 3502.88 | 0.556281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5403.08 | 0.850550 | ||||||||
\(344\) | 4019.53 | 0.629996 | ||||||||
\(345\) | −1698.36 | −0.265034 | ||||||||
\(346\) | −6685.64 | −1.03879 | ||||||||
\(347\) | 10835.8 | 1.67635 | 0.838177 | − | 0.545398i | \(-0.183621\pi\) | ||||
0.838177 | + | 0.545398i | \(0.183621\pi\) | |||||||
\(348\) | 286.198 | 0.0440857 | ||||||||
\(349\) | −2515.07 | −0.385755 | −0.192878 | − | 0.981223i | \(-0.561782\pi\) | ||||
−0.192878 | + | 0.981223i | \(0.561782\pi\) | |||||||
\(350\) | −93.0186 | −0.0142059 | ||||||||
\(351\) | 310.358 | 0.0471957 | ||||||||
\(352\) | 723.139 | 0.109498 | ||||||||
\(353\) | 6382.88 | 0.962398 | 0.481199 | − | 0.876611i | \(-0.340201\pi\) | ||||
0.481199 | + | 0.876611i | \(0.340201\pi\) | |||||||
\(354\) | −3625.24 | −0.544292 | ||||||||
\(355\) | 6502.87 | 0.972215 | ||||||||
\(356\) | −8.04120 | −0.00119714 | ||||||||
\(357\) | 845.009 | 0.125273 | ||||||||
\(358\) | −5696.76 | −0.841014 | ||||||||
\(359\) | 9122.32 | 1.34111 | 0.670554 | − | 0.741861i | \(-0.266056\pi\) | ||||
0.670554 | + | 0.741861i | \(0.266056\pi\) | |||||||
\(360\) | −821.628 | −0.120288 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −4746.99 | −0.689216 | ||||||||
\(363\) | 2460.98 | 0.355835 | ||||||||
\(364\) | 409.484 | 0.0589637 | ||||||||
\(365\) | −7838.52 | −1.12407 | ||||||||
\(366\) | 4133.86 | 0.590383 | ||||||||
\(367\) | 5891.16 | 0.837918 | 0.418959 | − | 0.908005i | \(-0.362395\pi\) | ||||
0.418959 | + | 0.908005i | \(0.362395\pi\) | |||||||
\(368\) | −793.754 | −0.112438 | ||||||||
\(369\) | −15.8186 | −0.00223167 | ||||||||
\(370\) | 2030.87 | 0.285351 | ||||||||
\(371\) | 199.752 | 0.0279531 | ||||||||
\(372\) | −1860.10 | −0.259251 | ||||||||
\(373\) | −8439.77 | −1.17157 | −0.585784 | − | 0.810468i | \(-0.699213\pi\) | ||||
−0.585784 | + | 0.810468i | \(0.699213\pi\) | |||||||
\(374\) | 1429.43 | 0.197632 | ||||||||
\(375\) | −4100.53 | −0.564668 | ||||||||
\(376\) | 1429.82 | 0.196110 | ||||||||
\(377\) | 274.147 | 0.0374518 | ||||||||
\(378\) | 480.919 | 0.0654386 | ||||||||
\(379\) | −3600.45 | −0.487976 | −0.243988 | − | 0.969778i | \(-0.578456\pi\) | ||||
−0.243988 | + | 0.969778i | \(0.578456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4381.24 | 0.589127 | ||||||||
\(382\) | 9630.27 | 1.28986 | ||||||||
\(383\) | 12097.7 | 1.61400 | 0.807001 | − | 0.590550i | \(-0.201089\pi\) | ||||
0.807001 | + | 0.590550i | \(0.201089\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 2296.64 | 0.304019 | ||||||||
\(386\) | −3968.76 | −0.523328 | ||||||||
\(387\) | 4521.97 | 0.593966 | ||||||||
\(388\) | 714.494 | 0.0934870 | ||||||||
\(389\) | −8898.22 | −1.15979 | −0.579894 | − | 0.814692i | \(-0.696906\pi\) | ||||
−0.579894 | + | 0.814692i | \(0.696906\pi\) | |||||||
\(390\) | −787.033 | −0.102187 | ||||||||
\(391\) | −1569.02 | −0.202938 | ||||||||
\(392\) | −2109.48 | −0.271798 | ||||||||
\(393\) | 5515.97 | 0.707999 | ||||||||
\(394\) | 843.293 | 0.107829 | ||||||||
\(395\) | −6970.62 | −0.887924 | ||||||||
\(396\) | 813.531 | 0.103236 | ||||||||
\(397\) | 6367.09 | 0.804924 | 0.402462 | − | 0.915437i | \(-0.368155\pi\) | ||||
0.402462 | + | 0.915437i | \(0.368155\pi\) | |||||||
\(398\) | −3445.63 | −0.433954 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 83.5569 | 0.0104446 | ||||||||
\(401\) | −9439.78 | −1.17556 | −0.587781 | − | 0.809020i | \(-0.699998\pi\) | ||||
−0.587781 | + | 0.809020i | \(0.699998\pi\) | |||||||
\(402\) | −2223.68 | −0.275889 | ||||||||
\(403\) | −1781.78 | −0.220240 | ||||||||
\(404\) | 837.711 | 0.103163 | ||||||||
\(405\) | −924.331 | −0.113408 | ||||||||
\(406\) | 424.808 | 0.0519283 | ||||||||
\(407\) | −2010.86 | −0.244900 | ||||||||
\(408\) | −759.056 | −0.0921051 | ||||||||
\(409\) | −6532.56 | −0.789766 | −0.394883 | − | 0.918731i | \(-0.629215\pi\) | ||||
−0.394883 | + | 0.918731i | \(0.629215\pi\) | |||||||
\(410\) | 40.1143 | 0.00483196 | ||||||||
\(411\) | 6442.17 | 0.773160 | ||||||||
\(412\) | 1342.79 | 0.160569 | ||||||||
\(413\) | −5381.00 | −0.641118 | ||||||||
\(414\) | −892.973 | −0.106008 | ||||||||
\(415\) | 7134.63 | 0.843916 | ||||||||
\(416\) | −367.832 | −0.0433520 | ||||||||
\(417\) | 8826.67 | 1.03656 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1449.51 | 0.169005 | 0.0845026 | − | 0.996423i | \(-0.473070\pi\) | ||||
0.0845026 | + | 0.996423i | \(0.473070\pi\) | |||||||
\(420\) | −1219.56 | −0.141686 | ||||||||
\(421\) | −3286.42 | −0.380452 | −0.190226 | − | 0.981740i | \(-0.560922\pi\) | ||||
−0.190226 | + | 0.981740i | \(0.560922\pi\) | |||||||
\(422\) | −1812.03 | −0.209025 | ||||||||
\(423\) | 1608.55 | 0.184894 | ||||||||
\(424\) | −179.433 | −0.0205520 | ||||||||
\(425\) | 165.168 | 0.0188513 | ||||||||
\(426\) | 3419.11 | 0.388865 | ||||||||
\(427\) | 6135.95 | 0.695409 | ||||||||
\(428\) | −6402.59 | −0.723086 | ||||||||
\(429\) | 779.277 | 0.0877013 | ||||||||
\(430\) | −11467.2 | −1.28604 | ||||||||
\(431\) | −12362.6 | −1.38164 | −0.690820 | − | 0.723027i | \(-0.742750\pi\) | ||||
−0.690820 | + | 0.723027i | \(0.742750\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 15249.7 | 1.69250 | 0.846252 | − | 0.532784i | \(-0.178854\pi\) | ||||
0.846252 | + | 0.532784i | \(0.178854\pi\) | |||||||
\(434\) | −2760.97 | −0.305371 | ||||||||
\(435\) | −816.487 | −0.0899944 | ||||||||
\(436\) | −3185.63 | −0.349918 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −4121.38 | −0.449605 | ||||||||
\(439\) | −10069.7 | −1.09476 | −0.547381 | − | 0.836883i | \(-0.684375\pi\) | ||||
−0.547381 | + | 0.836883i | \(0.684375\pi\) | |||||||
\(440\) | −2063.02 | −0.223525 | ||||||||
\(441\) | −2373.16 | −0.256254 | ||||||||
\(442\) | −727.096 | −0.0782453 | ||||||||
\(443\) | −3914.56 | −0.419834 | −0.209917 | − | 0.977719i | \(-0.567319\pi\) | ||||
−0.209917 | + | 0.977719i | \(0.567319\pi\) | |||||||
\(444\) | 1067.80 | 0.114134 | ||||||||
\(445\) | 22.9405 | 0.00244379 | ||||||||
\(446\) | −10458.1 | −1.11033 | ||||||||
\(447\) | −8921.65 | −0.944026 | ||||||||
\(448\) | −569.978 | −0.0601092 | ||||||||
\(449\) | −7976.98 | −0.838434 | −0.419217 | − | 0.907886i | \(-0.637695\pi\) | ||||
−0.419217 | + | 0.907886i | \(0.637695\pi\) | |||||||
\(450\) | 94.0015 | 0.00984727 | ||||||||
\(451\) | −39.7190 | −0.00414699 | ||||||||
\(452\) | −4888.64 | −0.508722 | ||||||||
\(453\) | 2156.63 | 0.223681 | ||||||||
\(454\) | −89.3394 | −0.00923548 | ||||||||
\(455\) | −1168.21 | −0.120366 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14557.8 | 1.49012 | 0.745061 | − | 0.666996i | \(-0.232420\pi\) | ||||
0.745061 | + | 0.666996i | \(0.232420\pi\) | |||||||
\(458\) | 7695.50 | 0.785125 | ||||||||
\(459\) | −853.938 | −0.0868375 | ||||||||
\(460\) | 2264.48 | 0.229526 | ||||||||
\(461\) | 14712.2 | 1.48637 | 0.743185 | − | 0.669086i | \(-0.233314\pi\) | ||||
0.743185 | + | 0.669086i | \(0.233314\pi\) | |||||||
\(462\) | 1207.54 | 0.121601 | ||||||||
\(463\) | −18580.1 | −1.86499 | −0.932494 | − | 0.361186i | \(-0.882372\pi\) | ||||
−0.932494 | + | 0.361186i | \(0.882372\pi\) | |||||||
\(464\) | −381.597 | −0.0381793 | ||||||||
\(465\) | 5306.62 | 0.529223 | ||||||||
\(466\) | −2269.28 | −0.225584 | ||||||||
\(467\) | 2580.33 | 0.255681 | 0.127841 | − | 0.991795i | \(-0.459195\pi\) | ||||
0.127841 | + | 0.991795i | \(0.459195\pi\) | |||||||
\(468\) | −413.811 | −0.0408727 | ||||||||
\(469\) | −3300.65 | −0.324968 | ||||||||
\(470\) | −4079.10 | −0.400329 | ||||||||
\(471\) | −4976.23 | −0.486821 | ||||||||
\(472\) | 4833.65 | 0.471371 | ||||||||
\(473\) | 11354.2 | 1.10374 | ||||||||
\(474\) | −3665.05 | −0.355150 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1126.68 | −0.108490 | ||||||||
\(477\) | −201.863 | −0.0193766 | ||||||||
\(478\) | 8604.07 | 0.823308 | ||||||||
\(479\) | 6293.95 | 0.600371 | 0.300186 | − | 0.953881i | \(-0.402951\pi\) | ||||
0.300186 | + | 0.953881i | \(0.402951\pi\) | |||||||
\(480\) | 1095.50 | 0.104172 | ||||||||
\(481\) | 1022.84 | 0.0969596 | ||||||||
\(482\) | 7266.48 | 0.686678 | ||||||||
\(483\) | −1325.46 | −0.124866 | ||||||||
\(484\) | −3281.31 | −0.308162 | ||||||||
\(485\) | −2038.36 | −0.190840 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −13084.2 | −1.21746 | −0.608730 | − | 0.793378i | \(-0.708321\pi\) | ||||
−0.608730 | + | 0.793378i | \(0.708321\pi\) | |||||||
\(488\) | −5511.81 | −0.511287 | ||||||||
\(489\) | 2828.19 | 0.261544 | ||||||||
\(490\) | 6018.08 | 0.554835 | ||||||||
\(491\) | −9209.00 | −0.846429 | −0.423214 | − | 0.906030i | \(-0.639098\pi\) | ||||
−0.423214 | + | 0.906030i | \(0.639098\pi\) | |||||||
\(492\) | 21.0915 | 0.00193268 | ||||||||
\(493\) | −754.306 | −0.0689092 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2320.90 | −0.210741 | ||||||||
\(496\) | 2480.13 | 0.224518 | ||||||||
\(497\) | 5075.05 | 0.458042 | ||||||||
\(498\) | 3751.28 | 0.337548 | ||||||||
\(499\) | 16314.8 | 1.46363 | 0.731814 | − | 0.681504i | \(-0.238674\pi\) | ||||
0.731814 | + | 0.681504i | \(0.238674\pi\) | |||||||
\(500\) | 5467.37 | 0.489017 | ||||||||
\(501\) | 5880.99 | 0.524438 | ||||||||
\(502\) | −5574.96 | −0.495663 | ||||||||
\(503\) | 1752.64 | 0.155361 | 0.0776804 | − | 0.996978i | \(-0.475249\pi\) | ||||
0.0776804 | + | 0.996978i | \(0.475249\pi\) | |||||||
\(504\) | −641.225 | −0.0566715 | ||||||||
\(505\) | −2389.88 | −0.210591 | ||||||||
\(506\) | −2242.17 | −0.196989 | ||||||||
\(507\) | 6194.61 | 0.542628 | ||||||||
\(508\) | −5841.65 | −0.510199 | ||||||||
\(509\) | −13310.5 | −1.15909 | −0.579546 | − | 0.814939i | \(-0.696770\pi\) | ||||
−0.579546 | + | 0.814939i | \(0.696770\pi\) | |||||||
\(510\) | 2165.49 | 0.188019 | ||||||||
\(511\) | −6117.43 | −0.529587 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7419.67 | −0.636707 | ||||||||
\(515\) | −3830.80 | −0.327777 | ||||||||
\(516\) | −6029.30 | −0.514390 | ||||||||
\(517\) | 4038.90 | 0.343579 | ||||||||
\(518\) | 1584.96 | 0.134438 | ||||||||
\(519\) | 10028.5 | 0.848171 | ||||||||
\(520\) | 1049.38 | 0.0884966 | ||||||||
\(521\) | −8874.93 | −0.746291 | −0.373146 | − | 0.927773i | \(-0.621721\pi\) | ||||
−0.373146 | + | 0.927773i | \(0.621721\pi\) | |||||||
\(522\) | −429.297 | −0.0359958 | ||||||||
\(523\) | −11948.7 | −0.999009 | −0.499504 | − | 0.866311i | \(-0.666485\pi\) | ||||
−0.499504 | + | 0.866311i | \(0.666485\pi\) | |||||||
\(524\) | −7354.62 | −0.613146 | ||||||||
\(525\) | 139.528 | 0.0115990 | ||||||||
\(526\) | 2945.93 | 0.244199 | ||||||||
\(527\) | 4902.49 | 0.405229 | ||||||||
\(528\) | −1084.71 | −0.0894050 | ||||||||
\(529\) | −9705.88 | −0.797722 | ||||||||
\(530\) | 511.901 | 0.0419539 | ||||||||
\(531\) | 5437.86 | 0.444412 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.2034 | 0.00164185 | ||||||||
\(534\) | 12.0618 | 0.000977463 0 | ||||||||
\(535\) | 18265.8 | 1.47607 | ||||||||
\(536\) | 2964.91 | 0.238927 | ||||||||
\(537\) | 8545.13 | 0.686685 | ||||||||
\(538\) | −4273.32 | −0.342446 | ||||||||
\(539\) | −5958.77 | −0.476183 | ||||||||
\(540\) | 1232.44 | 0.0982145 | ||||||||
\(541\) | 13510.3 | 1.07367 | 0.536834 | − | 0.843688i | \(-0.319620\pi\) | ||||
0.536834 | + | 0.843688i | \(0.319620\pi\) | |||||||
\(542\) | 8270.39 | 0.655431 | ||||||||
\(543\) | 7120.49 | 0.562743 | ||||||||
\(544\) | 1012.07 | 0.0797653 | ||||||||
\(545\) | 9088.22 | 0.714305 | ||||||||
\(546\) | −614.226 | −0.0481437 | ||||||||
\(547\) | −4364.02 | −0.341119 | −0.170559 | − | 0.985347i | \(-0.554557\pi\) | ||||
−0.170559 | + | 0.985347i | \(0.554557\pi\) | |||||||
\(548\) | −8589.56 | −0.669576 | ||||||||
\(549\) | −6200.79 | −0.482046 | ||||||||
\(550\) | 236.028 | 0.0182987 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1190.63 | 0.0918055 | ||||||||
\(553\) | −5440.09 | −0.418330 | ||||||||
\(554\) | −7960.58 | −0.610492 | ||||||||
\(555\) | −3046.30 | −0.232988 | ||||||||
\(556\) | −11768.9 | −0.897684 | ||||||||
\(557\) | −7108.39 | −0.540740 | −0.270370 | − | 0.962756i | \(-0.587146\pi\) | ||||
−0.270370 | + | 0.962756i | \(0.587146\pi\) | |||||||
\(558\) | 2790.14 | 0.211678 | ||||||||
\(559\) | −5775.43 | −0.436985 | ||||||||
\(560\) | 1626.07 | 0.122704 | ||||||||
\(561\) | −2144.15 | −0.161366 | ||||||||
\(562\) | −11279.4 | −0.846609 | ||||||||
\(563\) | 16491.3 | 1.23450 | 0.617250 | − | 0.786767i | \(-0.288247\pi\) | ||||
0.617250 | + | 0.786767i | \(0.288247\pi\) | |||||||
\(564\) | −2144.73 | −0.160123 | ||||||||
\(565\) | 13946.7 | 1.03848 | ||||||||
\(566\) | −13569.7 | −1.00774 | ||||||||
\(567\) | −721.378 | −0.0534304 | ||||||||
\(568\) | −4558.82 | −0.336767 | ||||||||
\(569\) | −9189.59 | −0.677061 | −0.338531 | − | 0.940955i | \(-0.609930\pi\) | ||||
−0.338531 | + | 0.940955i | \(0.609930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13551.8 | 0.993213 | 0.496606 | − | 0.867976i | \(-0.334579\pi\) | ||||
0.496606 | + | 0.867976i | \(0.334579\pi\) | |||||||
\(572\) | −1039.04 | −0.0759515 | ||||||||
\(573\) | −14445.4 | −1.05317 | ||||||||
\(574\) | 31.3065 | 0.00227649 | ||||||||
\(575\) | −259.077 | −0.0187900 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −15075.1 | −1.08767 | −0.543836 | − | 0.839192i | \(-0.683029\pi\) | ||||
−0.543836 | + | 0.839192i | \(0.683029\pi\) | |||||||
\(578\) | −7825.42 | −0.563140 | ||||||||
\(579\) | 5953.14 | 0.427295 | ||||||||
\(580\) | 1088.65 | 0.0779374 | ||||||||
\(581\) | 5568.09 | 0.397596 | ||||||||
\(582\) | −1071.74 | −0.0763318 | ||||||||
\(583\) | −506.856 | −0.0360066 | ||||||||
\(584\) | 5495.17 | 0.389369 | ||||||||
\(585\) | 1180.55 | 0.0834354 | ||||||||
\(586\) | 4258.53 | 0.300202 | ||||||||
\(587\) | −830.183 | −0.0583736 | −0.0291868 | − | 0.999574i | \(-0.509292\pi\) | ||||
−0.0291868 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(588\) | 3164.22 | 0.221922 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −13789.8 | −0.962233 | ||||||||
\(591\) | −1264.94 | −0.0880418 | ||||||||
\(592\) | −1423.74 | −0.0988432 | ||||||||
\(593\) | 27716.6 | 1.91936 | 0.959682 | − | 0.281087i | \(-0.0906951\pi\) | ||||
0.959682 | + | 0.281087i | \(0.0906951\pi\) | |||||||
\(594\) | −1220.30 | −0.0842919 | ||||||||
\(595\) | 3214.27 | 0.221466 | ||||||||
\(596\) | 11895.5 | 0.817550 | ||||||||
\(597\) | 5168.44 | 0.354322 | ||||||||
\(598\) | 1140.50 | 0.0779908 | ||||||||
\(599\) | −8672.10 | −0.591540 | −0.295770 | − | 0.955259i | \(-0.595576\pi\) | ||||
−0.295770 | + | 0.955259i | \(0.595576\pi\) | |||||||
\(600\) | −125.335 | −0.00852799 | ||||||||
\(601\) | 6303.27 | 0.427813 | 0.213907 | − | 0.976854i | \(-0.431381\pi\) | ||||
0.213907 | + | 0.976854i | \(0.431381\pi\) | |||||||
\(602\) | −8949.39 | −0.605897 | ||||||||
\(603\) | 3335.52 | 0.225262 | ||||||||
\(604\) | −2875.51 | −0.193713 | ||||||||
\(605\) | 9361.16 | 0.629066 | ||||||||
\(606\) | −1256.57 | −0.0842319 | ||||||||
\(607\) | −12646.6 | −0.845650 | −0.422825 | − | 0.906211i | \(-0.638962\pi\) | ||||
−0.422825 | + | 0.906211i | \(0.638962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −637.212 | −0.0423993 | ||||||||
\(610\) | 15724.5 | 1.04372 | ||||||||
\(611\) | −2054.43 | −0.136028 | ||||||||
\(612\) | 1138.58 | 0.0752035 | ||||||||
\(613\) | −10791.9 | −0.711062 | −0.355531 | − | 0.934665i | \(-0.615700\pi\) | ||||
−0.355531 | + | 0.934665i | \(0.615700\pi\) | |||||||
\(614\) | 10804.8 | 0.710173 | ||||||||
\(615\) | −60.1714 | −0.00394528 | ||||||||
\(616\) | −1610.05 | −0.105310 | ||||||||
\(617\) | −21538.9 | −1.40539 | −0.702694 | − | 0.711492i | \(-0.748020\pi\) | ||||
−0.702694 | + | 0.711492i | \(0.748020\pi\) | |||||||
\(618\) | −2014.18 | −0.131104 | ||||||||
\(619\) | −21147.7 | −1.37318 | −0.686588 | − | 0.727046i | \(-0.740893\pi\) | ||||
−0.686588 | + | 0.727046i | \(0.740893\pi\) | |||||||
\(620\) | −7075.50 | −0.458321 | ||||||||
\(621\) | 1339.46 | 0.0865550 | ||||||||
\(622\) | 11107.7 | 0.716044 | ||||||||
\(623\) | 17.9035 | 0.00115135 | ||||||||
\(624\) | 551.747 | 0.0353968 | ||||||||
\(625\) | −16250.5 | −1.04003 | ||||||||
\(626\) | −15831.5 | −1.01079 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6634.98 | 0.421599 | ||||||||
\(629\) | −2814.31 | −0.178400 | ||||||||
\(630\) | 1829.33 | 0.115686 | ||||||||
\(631\) | 8694.83 | 0.548551 | 0.274276 | − | 0.961651i | \(-0.411562\pi\) | ||||
0.274276 | + | 0.961651i | \(0.411562\pi\) | |||||||
\(632\) | 4886.73 | 0.307569 | ||||||||
\(633\) | 2718.05 | 0.170668 | ||||||||
\(634\) | 18275.0 | 1.14479 | ||||||||
\(635\) | 16665.5 | 1.04150 | ||||||||
\(636\) | 269.150 | 0.0167807 | ||||||||
\(637\) | 3030.99 | 0.188528 | ||||||||
\(638\) | −1077.92 | −0.0668892 | ||||||||
\(639\) | −5128.67 | −0.317507 | ||||||||
\(640\) | −1460.67 | −0.0902158 | ||||||||
\(641\) | 7230.41 | 0.445529 | 0.222764 | − | 0.974872i | \(-0.428492\pi\) | ||||
0.222764 | + | 0.974872i | \(0.428492\pi\) | |||||||
\(642\) | 9603.89 | 0.590397 | ||||||||
\(643\) | 3209.68 | 0.196854 | 0.0984271 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984271 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(644\) | 1767.27 | 0.108137 | ||||||||
\(645\) | 17200.8 | 1.05005 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17589.5 | −1.06880 | −0.534401 | − | 0.845231i | \(-0.679463\pi\) | ||||
−0.534401 | + | 0.845231i | \(0.679463\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 13653.9 | 0.825829 | ||||||||
\(650\) | −120.058 | −0.00724471 | ||||||||
\(651\) | 4141.46 | 0.249334 | ||||||||
\(652\) | −3770.92 | −0.226504 | ||||||||
\(653\) | −4309.56 | −0.258264 | −0.129132 | − | 0.991627i | \(-0.541219\pi\) | ||||
−0.129132 | + | 0.991627i | \(0.541219\pi\) | |||||||
\(654\) | 4778.45 | 0.285707 | ||||||||
\(655\) | 20981.8 | 1.25165 | ||||||||
\(656\) | −28.1220 | −0.00167375 | ||||||||
\(657\) | 6182.07 | 0.367101 | ||||||||
\(658\) | −3183.46 | −0.188608 | ||||||||
\(659\) | −32200.1 | −1.90339 | −0.951697 | − | 0.307039i | \(-0.900662\pi\) | ||||
−0.951697 | + | 0.307039i | \(0.900662\pi\) | |||||||
\(660\) | 3094.54 | 0.182507 | ||||||||
\(661\) | 23276.6 | 1.36967 | 0.684836 | − | 0.728697i | \(-0.259874\pi\) | ||||
0.684836 | + | 0.728697i | \(0.259874\pi\) | |||||||
\(662\) | −12105.1 | −0.710690 | ||||||||
\(663\) | 1090.64 | 0.0638870 | ||||||||
\(664\) | −5001.71 | −0.292325 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1601.70 | −0.0931903 | ||||||||
\(667\) | 1183.18 | 0.0686851 | ||||||||
\(668\) | −7841.32 | −0.454176 | ||||||||
\(669\) | 15687.2 | 0.906578 | ||||||||
\(670\) | −8458.52 | −0.487733 | ||||||||
\(671\) | −15569.5 | −0.895761 | ||||||||
\(672\) | 854.966 | 0.0490789 | ||||||||
\(673\) | 9207.85 | 0.527394 | 0.263697 | − | 0.964605i | \(-0.415058\pi\) | ||||
0.263697 | + | 0.964605i | \(0.415058\pi\) | |||||||
\(674\) | −9364.70 | −0.535185 | ||||||||
\(675\) | −141.002 | −0.00804026 | ||||||||
\(676\) | −8259.48 | −0.469930 | ||||||||
\(677\) | 17786.3 | 1.00972 | 0.504862 | − | 0.863200i | \(-0.331543\pi\) | ||||
0.504862 | + | 0.863200i | \(0.331543\pi\) | |||||||
\(678\) | 7332.96 | 0.415370 | ||||||||
\(679\) | −1590.80 | −0.0899108 | ||||||||
\(680\) | −2887.32 | −0.162829 | ||||||||
\(681\) | 134.009 | 0.00754074 | ||||||||
\(682\) | 7005.77 | 0.393350 | ||||||||
\(683\) | 27734.5 | 1.55378 | 0.776888 | − | 0.629638i | \(-0.216797\pi\) | ||||
0.776888 | + | 0.629638i | \(0.216797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24504.9 | 1.36684 | ||||||||
\(686\) | 10806.2 | 0.601430 | ||||||||
\(687\) | −11543.3 | −0.641052 | ||||||||
\(688\) | 8039.06 | 0.445474 | ||||||||
\(689\) | 257.818 | 0.0142555 | ||||||||
\(690\) | −3396.72 | −0.187407 | ||||||||
\(691\) | −4636.28 | −0.255242 | −0.127621 | − | 0.991823i | \(-0.540734\pi\) | ||||
−0.127621 | + | 0.991823i | \(0.540734\pi\) | |||||||
\(692\) | −13371.3 | −0.734537 | ||||||||
\(693\) | −1811.31 | −0.0992869 | ||||||||
\(694\) | 21671.6 | 1.18536 | ||||||||
\(695\) | 33575.2 | 1.83249 | ||||||||
\(696\) | 572.396 | 0.0311733 | ||||||||
\(697\) | −55.5890 | −0.00302092 | ||||||||
\(698\) | −5030.14 | −0.272770 | ||||||||
\(699\) | 3403.92 | 0.184189 | ||||||||
\(700\) | −186.037 | −0.0100451 | ||||||||
\(701\) | 19023.6 | 1.02498 | 0.512490 | − | 0.858693i | \(-0.328723\pi\) | ||||
0.512490 | + | 0.858693i | \(0.328723\pi\) | |||||||
\(702\) | 620.716 | 0.0333724 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1446.28 | 0.0774270 | ||||||||
\(705\) | 6118.65 | 0.326867 | ||||||||
\(706\) | 12765.8 | 0.680518 | ||||||||
\(707\) | −1865.14 | −0.0992163 | ||||||||
\(708\) | −7250.48 | −0.384872 | ||||||||
\(709\) | 29121.4 | 1.54256 | 0.771281 | − | 0.636495i | \(-0.219616\pi\) | ||||
0.771281 | + | 0.636495i | \(0.219616\pi\) | |||||||
\(710\) | 13005.7 | 0.687460 | ||||||||
\(711\) | 5497.58 | 0.289979 | ||||||||
\(712\) | −16.0824 | −0.000846508 0 | ||||||||
\(713\) | −7689.89 | −0.403911 | ||||||||
\(714\) | 1690.02 | 0.0885817 | ||||||||
\(715\) | 2964.24 | 0.155044 | ||||||||
\(716\) | −11393.5 | −0.594686 | ||||||||
\(717\) | −12906.1 | −0.672228 | ||||||||
\(718\) | 18244.6 | 0.948307 | ||||||||
\(719\) | 10801.5 | 0.560259 | 0.280130 | − | 0.959962i | \(-0.409623\pi\) | ||||
0.280130 | + | 0.959962i | \(0.409623\pi\) | |||||||
\(720\) | −1643.26 | −0.0850563 | ||||||||
\(721\) | −2989.68 | −0.154426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10899.7 | −0.560670 | ||||||||
\(724\) | −9493.98 | −0.487350 | ||||||||
\(725\) | −124.551 | −0.00638029 | ||||||||
\(726\) | 4921.96 | 0.251613 | ||||||||
\(727\) | −18235.3 | −0.930276 | −0.465138 | − | 0.885238i | \(-0.653995\pi\) | ||||
−0.465138 | + | 0.885238i | \(0.653995\pi\) | |||||||
\(728\) | 818.968 | 0.0416936 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −15677.0 | −0.794840 | ||||||||
\(731\) | 15890.9 | 0.804029 | ||||||||
\(732\) | 8267.72 | 0.417464 | ||||||||
\(733\) | 5867.74 | 0.295675 | 0.147838 | − | 0.989012i | \(-0.452769\pi\) | ||||
0.147838 | + | 0.989012i | \(0.452769\pi\) | |||||||
\(734\) | 11782.3 | 0.592498 | ||||||||
\(735\) | −9027.12 | −0.453021 | ||||||||
\(736\) | −1587.51 | −0.0795059 | ||||||||
\(737\) | 8375.16 | 0.418593 | ||||||||
\(738\) | −31.6373 | −0.00157803 | ||||||||
\(739\) | −28368.8 | −1.41213 | −0.706065 | − | 0.708147i | \(-0.749531\pi\) | ||||
−0.706065 | + | 0.708147i | \(0.749531\pi\) | |||||||
\(740\) | 4061.74 | 0.201774 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 399.504 | 0.0197658 | ||||||||
\(743\) | −2691.78 | −0.132909 | −0.0664547 | − | 0.997789i | \(-0.521169\pi\) | ||||
−0.0664547 | + | 0.997789i | \(0.521169\pi\) | |||||||
\(744\) | −3720.19 | −0.183318 | ||||||||
\(745\) | −33936.5 | −1.66891 | ||||||||
\(746\) | −16879.5 | −0.828423 | ||||||||
\(747\) | −5626.92 | −0.275607 | ||||||||
\(748\) | 2858.87 | 0.139747 | ||||||||
\(749\) | 14255.2 | 0.695426 | ||||||||
\(750\) | −8201.06 | −0.399280 | ||||||||
\(751\) | −2589.67 | −0.125830 | −0.0629151 | − | 0.998019i | \(-0.520040\pi\) | ||||
−0.0629151 | + | 0.998019i | \(0.520040\pi\) | |||||||
\(752\) | 2859.64 | 0.138671 | ||||||||
\(753\) | 8362.44 | 0.404707 | ||||||||
\(754\) | 548.295 | 0.0264824 | ||||||||
\(755\) | 8203.47 | 0.395437 | ||||||||
\(756\) | 961.837 | 0.0462721 | ||||||||
\(757\) | 12079.4 | 0.579965 | 0.289983 | − | 0.957032i | \(-0.406350\pi\) | ||||
0.289983 | + | 0.957032i | \(0.406350\pi\) | |||||||
\(758\) | −7200.90 | −0.345051 | ||||||||
\(759\) | 3363.25 | 0.160841 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15595.8 | −0.742900 | −0.371450 | − | 0.928453i | \(-0.621139\pi\) | ||||
−0.371450 | + | 0.928453i | \(0.621139\pi\) | |||||||
\(762\) | 8762.47 | 0.416576 | ||||||||
\(763\) | 7092.73 | 0.336532 | ||||||||
\(764\) | 19260.5 | 0.912070 | ||||||||
\(765\) | −3248.24 | −0.153517 | ||||||||
\(766\) | 24195.4 | 1.14127 | ||||||||
\(767\) | −6945.20 | −0.326958 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 16923.3 | 0.793587 | 0.396794 | − | 0.917908i | \(-0.370123\pi\) | ||||
0.396794 | + | 0.917908i | \(0.370123\pi\) | |||||||
\(770\) | 4593.27 | 0.214974 | ||||||||
\(771\) | 11129.5 | 0.519869 | ||||||||
\(772\) | −7937.52 | −0.370049 | ||||||||
\(773\) | 9481.75 | 0.441184 | 0.220592 | − | 0.975366i | \(-0.429201\pi\) | ||||
0.220592 | + | 0.975366i | \(0.429201\pi\) | |||||||
\(774\) | 9043.95 | 0.419997 | ||||||||
\(775\) | 809.499 | 0.0375201 | ||||||||
\(776\) | 1428.99 | 0.0661053 | ||||||||
\(777\) | −2377.43 | −0.109768 | ||||||||
\(778\) | −17796.4 | −0.820094 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1574.07 | −0.0722572 | ||||||||
\(781\) | −12877.6 | −0.590007 | ||||||||
\(782\) | −3138.04 | −0.143499 | ||||||||
\(783\) | 643.945 | 0.0293905 | ||||||||
\(784\) | −4218.96 | −0.192190 | ||||||||
\(785\) | −18928.8 | −0.860632 | ||||||||
\(786\) | 11031.9 | 0.500631 | ||||||||
\(787\) | −1689.69 | −0.0765323 | −0.0382662 | − | 0.999268i | \(-0.512183\pi\) | ||||
−0.0382662 | + | 0.999268i | \(0.512183\pi\) | |||||||
\(788\) | 1686.59 | 0.0762464 | ||||||||
\(789\) | −4418.90 | −0.199388 | ||||||||
\(790\) | −13941.2 | −0.627857 | ||||||||
\(791\) | 10884.4 | 0.489262 | ||||||||
\(792\) | 1627.06 | 0.0729989 | ||||||||
\(793\) | 7919.60 | 0.354645 | ||||||||
\(794\) | 12734.2 | 0.569167 | ||||||||
\(795\) | −767.852 | −0.0342552 | ||||||||
\(796\) | −6891.25 | −0.306852 | ||||||||
\(797\) | 4265.09 | 0.189557 | 0.0947787 | − | 0.995498i | \(-0.469786\pi\) | ||||
0.0947787 | + | 0.995498i | \(0.469786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5652.67 | 0.250284 | ||||||||
\(800\) | 167.114 | 0.00738545 | ||||||||
\(801\) | −18.0927 | −0.000798095 0 | ||||||||
\(802\) | −18879.6 | −0.831247 | ||||||||
\(803\) | 15522.5 | 0.682165 | ||||||||
\(804\) | −4447.37 | −0.195083 | ||||||||
\(805\) | −5041.81 | −0.220746 | ||||||||
\(806\) | −3563.55 | −0.155733 | ||||||||
\(807\) | 6409.99 | 0.279606 | ||||||||
\(808\) | 1675.42 | 0.0729470 | ||||||||
\(809\) | 1622.16 | 0.0704969 | 0.0352484 | − | 0.999379i | \(-0.488778\pi\) | ||||
0.0352484 | + | 0.999379i | \(0.488778\pi\) | |||||||
\(810\) | −1848.66 | −0.0801918 | ||||||||
\(811\) | −39797.7 | −1.72316 | −0.861582 | − | 0.507619i | \(-0.830526\pi\) | ||||
−0.861582 | + | 0.507619i | \(0.830526\pi\) | |||||||
\(812\) | 849.617 | 0.0367188 | ||||||||
\(813\) | −12405.6 | −0.535157 | ||||||||
\(814\) | −4021.71 | −0.173171 | ||||||||
\(815\) | 10758.0 | 0.462375 | ||||||||
\(816\) | −1518.11 | −0.0651281 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13065.1 | −0.558449 | ||||||||
\(819\) | 921.339 | 0.0393091 | ||||||||
\(820\) | 80.2286 | 0.00341671 | ||||||||
\(821\) | −29942.3 | −1.27283 | −0.636414 | − | 0.771347i | \(-0.719583\pi\) | ||||
−0.636414 | + | 0.771347i | \(0.719583\pi\) | |||||||
\(822\) | 12884.3 | 0.546707 | ||||||||
\(823\) | 661.147 | 0.0280026 | 0.0140013 | − | 0.999902i | \(-0.495543\pi\) | ||||
0.0140013 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(824\) | 2685.57 | 0.113539 | ||||||||
\(825\) | −354.042 | −0.0149408 | ||||||||
\(826\) | −10762.0 | −0.453339 | ||||||||
\(827\) | 22338.6 | 0.939287 | 0.469643 | − | 0.882856i | \(-0.344382\pi\) | ||||
0.469643 | + | 0.882856i | \(0.344382\pi\) | |||||||
\(828\) | −1785.95 | −0.0749589 | ||||||||
\(829\) | 40601.8 | 1.70104 | 0.850519 | − | 0.525945i | \(-0.176288\pi\) | ||||
0.850519 | + | 0.525945i | \(0.176288\pi\) | |||||||
\(830\) | 14269.3 | 0.596739 | ||||||||
\(831\) | 11940.9 | 0.498465 | ||||||||
\(832\) | −735.663 | −0.0306545 | ||||||||
\(833\) | −8339.65 | −0.346881 | ||||||||
\(834\) | 17653.3 | 0.732956 | ||||||||
\(835\) | 22370.3 | 0.927133 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4185.22 | −0.172834 | ||||||||
\(838\) | 2899.02 | 0.119505 | ||||||||
\(839\) | −16173.5 | −0.665519 | −0.332760 | − | 0.943012i | \(-0.607980\pi\) | ||||
−0.332760 | + | 0.943012i | \(0.607980\pi\) | |||||||
\(840\) | −2439.11 | −0.100187 | ||||||||
\(841\) | −23820.2 | −0.976677 | ||||||||
\(842\) | −6572.84 | −0.269020 | ||||||||
\(843\) | 16919.2 | 0.691254 | ||||||||
\(844\) | −3624.07 | −0.147803 | ||||||||
\(845\) | 23563.3 | 0.959291 | ||||||||
\(846\) | 3217.10 | 0.130740 | ||||||||
\(847\) | 7305.75 | 0.296374 | ||||||||
\(848\) | −358.867 | −0.0145325 | ||||||||
\(849\) | 20354.6 | 0.822812 | ||||||||
\(850\) | 330.335 | 0.0133299 | ||||||||
\(851\) | 4414.44 | 0.177820 | ||||||||
\(852\) | 6838.23 | 0.274969 | ||||||||
\(853\) | 10860.7 | 0.435947 | 0.217973 | − | 0.975955i | \(-0.430055\pi\) | ||||
0.217973 | + | 0.975955i | \(0.430055\pi\) | |||||||
\(854\) | 12271.9 | 0.491728 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12805.2 | −0.511299 | ||||||||
\(857\) | −33673.4 | −1.34220 | −0.671098 | − | 0.741369i | \(-0.734177\pi\) | ||||
−0.671098 | + | 0.741369i | \(0.734177\pi\) | |||||||
\(858\) | 1558.55 | 0.0620142 | ||||||||
\(859\) | −25309.8 | −1.00531 | −0.502654 | − | 0.864488i | \(-0.667643\pi\) | ||||
−0.502654 | + | 0.864488i | \(0.667643\pi\) | |||||||
\(860\) | −22934.4 | −0.909370 | ||||||||
\(861\) | −46.9597 | −0.00185875 | ||||||||
\(862\) | −24725.2 | −0.976967 | ||||||||
\(863\) | 26842.5 | 1.05878 | 0.529392 | − | 0.848378i | \(-0.322420\pi\) | ||||
0.529392 | + | 0.848378i | \(0.322420\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 38146.6 | 1.49945 | ||||||||
\(866\) | 30499.4 | 1.19678 | ||||||||
\(867\) | 11738.1 | 0.459802 | ||||||||
\(868\) | −5521.94 | −0.215930 | ||||||||
\(869\) | 13803.9 | 0.538853 | ||||||||
\(870\) | −1632.97 | −0.0636356 | ||||||||
\(871\) | −4260.11 | −0.165727 | ||||||||
\(872\) | −6371.27 | −0.247429 | ||||||||
\(873\) | 1607.61 | 0.0623247 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12173.0 | −0.470310 | ||||||||
\(876\) | −8242.76 | −0.317919 | ||||||||
\(877\) | 27145.7 | 1.04521 | 0.522603 | − | 0.852576i | \(-0.324961\pi\) | ||||
0.522603 | + | 0.852576i | \(0.324961\pi\) | |||||||
\(878\) | −20139.4 | −0.774114 | ||||||||
\(879\) | −6387.79 | −0.245114 | ||||||||
\(880\) | −4126.05 | −0.158056 | ||||||||
\(881\) | −11515.1 | −0.440356 | −0.220178 | − | 0.975460i | \(-0.570664\pi\) | ||||
−0.220178 | + | 0.975460i | \(0.570664\pi\) | |||||||
\(882\) | −4746.33 | −0.181199 | ||||||||
\(883\) | 28678.2 | 1.09298 | 0.546488 | − | 0.837467i | \(-0.315964\pi\) | ||||
0.546488 | + | 0.837467i | \(0.315964\pi\) | |||||||
\(884\) | −1454.19 | −0.0553278 | ||||||||
\(885\) | 20684.7 | 0.785660 | ||||||||
\(886\) | −7829.13 | −0.296868 | ||||||||
\(887\) | −966.906 | −0.0366015 | −0.0183008 | − | 0.999833i | \(-0.505826\pi\) | ||||
−0.0183008 | + | 0.999833i | \(0.505826\pi\) | |||||||
\(888\) | 2135.60 | 0.0807051 | ||||||||
\(889\) | 13006.3 | 0.490683 | ||||||||
\(890\) | 45.8811 | 0.00172802 | ||||||||
\(891\) | 1830.44 | 0.0688240 | ||||||||
\(892\) | −20916.2 | −0.785120 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −17843.3 | −0.667527 | ||||||||
\(895\) | 32504.3 | 1.21396 | ||||||||
\(896\) | −1139.96 | −0.0425036 | ||||||||
\(897\) | −1710.75 | −0.0636792 | ||||||||
\(898\) | −15954.0 | −0.592863 | ||||||||
\(899\) | −3696.91 | −0.137151 | ||||||||
\(900\) | 188.003 | 0.00696307 | ||||||||
\(901\) | −709.375 | −0.0262294 | ||||||||
\(902\) | −79.4379 | −0.00293237 | ||||||||
\(903\) | 13424.1 | 0.494712 | ||||||||
\(904\) | −9777.28 | −0.359721 | ||||||||
\(905\) | 27085.1 | 0.994852 | ||||||||
\(906\) | 4313.27 | 0.158166 | ||||||||
\(907\) | −38400.2 | −1.40580 | −0.702899 | − | 0.711290i | \(-0.748111\pi\) | ||||
−0.702899 | + | 0.711290i | \(0.748111\pi\) | |||||||
\(908\) | −178.679 | −0.00653047 | ||||||||
\(909\) | 1884.85 | 0.0687751 | ||||||||
\(910\) | −2336.41 | −0.0851113 | ||||||||
\(911\) | 16835.2 | 0.612265 | 0.306133 | − | 0.951989i | \(-0.400965\pi\) | ||||
0.306133 | + | 0.951989i | \(0.400965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14128.6 | −0.512146 | ||||||||
\(914\) | 29115.6 | 1.05368 | ||||||||
\(915\) | −23586.8 | −0.852190 | ||||||||
\(916\) | 15391.0 | 0.555167 | ||||||||
\(917\) | 16374.9 | 0.589691 | ||||||||
\(918\) | −1707.88 | −0.0614034 | ||||||||
\(919\) | −37958.3 | −1.36249 | −0.681246 | − | 0.732055i | \(-0.738561\pi\) | ||||
−0.681246 | + | 0.732055i | \(0.738561\pi\) | |||||||
\(920\) | 4528.96 | 0.162299 | ||||||||
\(921\) | −16207.2 | −0.579854 | ||||||||
\(922\) | 29424.5 | 1.05102 | ||||||||
\(923\) | 6550.30 | 0.233592 | ||||||||
\(924\) | 2415.07 | 0.0859850 | ||||||||
\(925\) | −464.699 | −0.0165181 | ||||||||
\(926\) | −37160.1 | −1.31875 | ||||||||
\(927\) | 3021.27 | 0.107046 | ||||||||
\(928\) | −763.194 | −0.0269969 | ||||||||
\(929\) | 29436.6 | 1.03959 | 0.519797 | − | 0.854290i | \(-0.326007\pi\) | ||||
0.519797 | + | 0.854290i | \(0.326007\pi\) | |||||||
\(930\) | 10613.2 | 0.374217 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4538.56 | −0.159512 | ||||||||
\(933\) | −16661.6 | −0.584648 | ||||||||
\(934\) | 5160.65 | 0.180794 | ||||||||
\(935\) | −8155.99 | −0.285272 | ||||||||
\(936\) | −827.621 | −0.0289013 | ||||||||
\(937\) | 9758.20 | 0.340220 | 0.170110 | − | 0.985425i | \(-0.445588\pi\) | ||||
0.170110 | + | 0.985425i | \(0.445588\pi\) | |||||||
\(938\) | −6601.30 | −0.229787 | ||||||||
\(939\) | 23747.2 | 0.825305 | ||||||||
\(940\) | −8158.19 | −0.283076 | ||||||||
\(941\) | 47858.3 | 1.65795 | 0.828977 | − | 0.559282i | \(-0.188923\pi\) | ||||
0.828977 | + | 0.559282i | \(0.188923\pi\) | |||||||
\(942\) | −9952.47 | −0.344235 | ||||||||
\(943\) | 87.1952 | 0.00301110 | ||||||||
\(944\) | 9667.30 | 0.333309 | ||||||||
\(945\) | −2744.00 | −0.0944575 | ||||||||
\(946\) | 22708.4 | 0.780459 | ||||||||
\(947\) | 31063.9 | 1.06593 | 0.532967 | − | 0.846136i | \(-0.321077\pi\) | ||||
0.532967 | + | 0.846136i | \(0.321077\pi\) | |||||||
\(948\) | −7330.10 | −0.251129 | ||||||||
\(949\) | −7895.69 | −0.270079 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27412.5 | −0.934714 | ||||||||
\(952\) | −2253.36 | −0.0767140 | ||||||||
\(953\) | −32651.6 | −1.10985 | −0.554927 | − | 0.831899i | \(-0.687254\pi\) | ||||
−0.554927 | + | 0.831899i | \(0.687254\pi\) | |||||||
\(954\) | −403.725 | −0.0137014 | ||||||||
\(955\) | −54947.9 | −1.86186 | ||||||||
\(956\) | 17208.1 | 0.582167 | ||||||||
\(957\) | 1616.88 | 0.0546148 | ||||||||
\(958\) | 12587.9 | 0.424527 | ||||||||
\(959\) | 19124.4 | 0.643963 | ||||||||
\(960\) | 2191.01 | 0.0736609 | ||||||||
\(961\) | −5763.51 | −0.193465 | ||||||||
\(962\) | 2045.68 | 0.0685608 | ||||||||
\(963\) | −14405.8 | −0.482058 | ||||||||
\(964\) | 14533.0 | 0.485555 | ||||||||
\(965\) | 22644.7 | 0.755399 | ||||||||
\(966\) | −2650.91 | −0.0882936 | ||||||||
\(967\) | 20568.7 | 0.684016 | 0.342008 | − | 0.939697i | \(-0.388893\pi\) | ||||
0.342008 | + | 0.939697i | \(0.388893\pi\) | |||||||
\(968\) | −6562.61 | −0.217903 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4076.73 | −0.134944 | ||||||||
\(971\) | −42239.2 | −1.39601 | −0.698003 | − | 0.716095i | \(-0.745928\pi\) | ||||
−0.698003 | + | 0.716095i | \(0.745928\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 26203.1 | 0.863345 | ||||||||
\(974\) | −26168.5 | −0.860874 | ||||||||
\(975\) | 180.087 | 0.00591528 | ||||||||
\(976\) | −11023.6 | −0.361534 | ||||||||
\(977\) | 16357.1 | 0.535630 | 0.267815 | − | 0.963470i | \(-0.413698\pi\) | ||||
0.267815 | + | 0.963470i | \(0.413698\pi\) | |||||||
\(978\) | 5656.38 | 0.184940 | ||||||||
\(979\) | −45.4289 | −0.00148306 | ||||||||
\(980\) | 12036.2 | 0.392328 | ||||||||
\(981\) | −7167.68 | −0.233279 | ||||||||
\(982\) | −18418.0 | −0.598515 | ||||||||
\(983\) | 34375.0 | 1.11535 | 0.557676 | − | 0.830059i | \(-0.311693\pi\) | ||||
0.557676 | + | 0.830059i | \(0.311693\pi\) | |||||||
\(984\) | 42.1830 | 0.00136661 | ||||||||
\(985\) | −4811.62 | −0.155646 | ||||||||
\(986\) | −1508.61 | −0.0487262 | ||||||||
\(987\) | 4775.19 | 0.153998 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24925.9 | −0.801414 | ||||||||
\(990\) | −4641.80 | −0.149016 | ||||||||
\(991\) | 16405.4 | 0.525867 | 0.262934 | − | 0.964814i | \(-0.415310\pi\) | ||||
0.262934 | + | 0.964814i | \(0.415310\pi\) | |||||||
\(992\) | 4960.26 | 0.158758 | ||||||||
\(993\) | 18157.6 | 0.580276 | ||||||||
\(994\) | 10150.1 | 0.323885 | ||||||||
\(995\) | 19659.9 | 0.626392 | ||||||||
\(996\) | 7502.57 | 0.238683 | ||||||||
\(997\) | −37217.7 | −1.18224 | −0.591121 | − | 0.806583i | \(-0.701314\pi\) | ||||
−0.591121 | + | 0.806583i | \(0.701314\pi\) | |||||||
\(998\) | 32629.6 | 1.03494 | ||||||||
\(999\) | 2402.55 | 0.0760895 |
(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 | 2166.4.a.bf.1.1 | 6 | ||
19.4 | even | 9 | 114.4.i.a.73.1 | yes | 12 | ||
19.5 | even | 9 | 114.4.i.a.25.1 | ✓ | 12 | ||
19.18 | odd | 2 | 2166.4.a.bd.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.i.a.25.1 | ✓ | 12 | 19.5 | even | 9 | ||
114.4.i.a.73.1 | yes | 12 | 19.4 | even | 9 | ||
2166.4.a.bd.1.1 | 6 | 19.18 | odd | 2 | |||
2166.4.a.bf.1.1 | 6 | 1.1 | even | 1 | trivial |