Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,6,Mod(1,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(162.629193290\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 6) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 66.0000 | 1.18064 | 0.590322 | − | 0.807168i | \(-0.299001\pi\) | ||||
0.590322 | + | 0.807168i | \(0.299001\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | −176.000 | −1.35759 | −0.678793 | − | 0.734329i | \(-0.737497\pi\) | ||||
−0.678793 | + | 0.734329i | \(0.737497\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −264.000 | −0.834841 | ||||||||
\(11\) | 60.0000 | 0.149510 | 0.0747549 | − | 0.997202i | \(-0.476183\pi\) | ||||
0.0747549 | + | 0.997202i | \(0.476183\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 704.000 | 0.959959 | ||||||||
\(15\) | −594.000 | −0.681645 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −414.000 | −0.347439 | −0.173719 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173719 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −956.000 | −0.607539 | −0.303769 | − | 0.952746i | \(-0.598245\pi\) | ||||
−0.303769 | + | 0.952746i | \(0.598245\pi\) | |||||||
\(20\) | 1056.00 | 0.590322 | ||||||||
\(21\) | 1584.00 | 0.783803 | ||||||||
\(22\) | −240.000 | −0.105719 | ||||||||
\(23\) | 600.000 | 0.236500 | 0.118250 | − | 0.992984i | \(-0.462272\pi\) | ||||
0.118250 | + | 0.992984i | \(0.462272\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 1231.00 | 0.393920 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −2816.00 | −0.678793 | ||||||||
\(29\) | 5574.00 | 1.23076 | 0.615378 | − | 0.788232i | \(-0.289003\pi\) | ||||
0.615378 | + | 0.788232i | \(0.289003\pi\) | |||||||
\(30\) | 2376.00 | 0.481996 | ||||||||
\(31\) | 3592.00 | 0.671324 | 0.335662 | − | 0.941983i | \(-0.391040\pi\) | ||||
0.335662 | + | 0.941983i | \(0.391040\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −540.000 | −0.0863195 | ||||||||
\(34\) | 1656.00 | 0.245676 | ||||||||
\(35\) | −11616.0 | −1.60283 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 8458.00 | 1.01570 | 0.507848 | − | 0.861447i | \(-0.330441\pi\) | ||||
0.507848 | + | 0.861447i | \(0.330441\pi\) | |||||||
\(38\) | 3824.00 | 0.429595 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4224.00 | −0.417421 | ||||||||
\(41\) | −19194.0 | −1.78322 | −0.891612 | − | 0.452800i | \(-0.850425\pi\) | ||||
−0.891612 | + | 0.452800i | \(0.850425\pi\) | |||||||
\(42\) | −6336.00 | −0.554232 | ||||||||
\(43\) | 13316.0 | 1.09825 | 0.549127 | − | 0.835739i | \(-0.314960\pi\) | ||||
0.549127 | + | 0.835739i | \(0.314960\pi\) | |||||||
\(44\) | 960.000 | 0.0747549 | ||||||||
\(45\) | 5346.00 | 0.393548 | ||||||||
\(46\) | −2400.00 | −0.167231 | ||||||||
\(47\) | 19680.0 | 1.29951 | 0.649756 | − | 0.760143i | \(-0.274871\pi\) | ||||
0.649756 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 14169.0 | 0.843042 | ||||||||
\(50\) | −4924.00 | −0.278544 | ||||||||
\(51\) | 3726.00 | 0.200594 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31266.0 | −1.52891 | −0.764456 | − | 0.644676i | \(-0.776992\pi\) | ||||
−0.764456 | + | 0.644676i | \(0.776992\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 3960.00 | 0.176518 | ||||||||
\(56\) | 11264.0 | 0.479979 | ||||||||
\(57\) | 8604.00 | 0.350763 | ||||||||
\(58\) | −22296.0 | −0.870276 | ||||||||
\(59\) | −26340.0 | −0.985112 | −0.492556 | − | 0.870281i | \(-0.663937\pi\) | ||||
−0.492556 | + | 0.870281i | \(0.663937\pi\) | |||||||
\(60\) | −9504.00 | −0.340823 | ||||||||
\(61\) | −31090.0 | −1.06978 | −0.534892 | − | 0.844920i | \(-0.679648\pi\) | ||||
−0.534892 | + | 0.844920i | \(0.679648\pi\) | |||||||
\(62\) | −14368.0 | −0.474698 | ||||||||
\(63\) | −14256.0 | −0.452529 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2160.00 | 0.0610371 | ||||||||
\(67\) | 16804.0 | 0.457326 | 0.228663 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228663 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(68\) | −6624.00 | −0.173719 | ||||||||
\(69\) | −5400.00 | −0.136544 | ||||||||
\(70\) | 46464.0 | 1.13337 | ||||||||
\(71\) | −6120.00 | −0.144081 | −0.0720403 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720403 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 25558.0 | 0.561332 | 0.280666 | − | 0.959806i | \(-0.409445\pi\) | ||||
0.280666 | + | 0.959806i | \(0.409445\pi\) | |||||||
\(74\) | −33832.0 | −0.718205 | ||||||||
\(75\) | −11079.0 | −0.227430 | ||||||||
\(76\) | −15296.0 | −0.303769 | ||||||||
\(77\) | −10560.0 | −0.202972 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74408.0 | 1.34138 | 0.670690 | − | 0.741738i | \(-0.265998\pi\) | ||||
0.670690 | + | 0.741738i | \(0.265998\pi\) | |||||||
\(80\) | 16896.0 | 0.295161 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 76776.0 | 1.26093 | ||||||||
\(83\) | 6468.00 | 0.103056 | 0.0515282 | − | 0.998672i | \(-0.483591\pi\) | ||||
0.0515282 | + | 0.998672i | \(0.483591\pi\) | |||||||
\(84\) | 25344.0 | 0.391902 | ||||||||
\(85\) | −27324.0 | −0.410201 | ||||||||
\(86\) | −53264.0 | −0.776583 | ||||||||
\(87\) | −50166.0 | −0.710577 | ||||||||
\(88\) | −3840.00 | −0.0528597 | ||||||||
\(89\) | 32742.0 | 0.438157 | 0.219079 | − | 0.975707i | \(-0.429695\pi\) | ||||
0.219079 | + | 0.975707i | \(0.429695\pi\) | |||||||
\(90\) | −21384.0 | −0.278280 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9600.00 | 0.118250 | ||||||||
\(93\) | −32328.0 | −0.387589 | ||||||||
\(94\) | −78720.0 | −0.918894 | ||||||||
\(95\) | −63096.0 | −0.717287 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −166082. | −1.79223 | −0.896114 | − | 0.443824i | \(-0.853622\pi\) | ||||
−0.896114 | + | 0.443824i | \(0.853622\pi\) | |||||||
\(98\) | −56676.0 | −0.596120 | ||||||||
\(99\) | 4860.00 | 0.0498366 | ||||||||
\(100\) | 19696.0 | 0.196960 | ||||||||
\(101\) | −22002.0 | −0.214614 | −0.107307 | − | 0.994226i | \(-0.534223\pi\) | ||||
−0.107307 | + | 0.994226i | \(0.534223\pi\) | |||||||
\(102\) | −14904.0 | −0.141841 | ||||||||
\(103\) | −79264.0 | −0.736178 | −0.368089 | − | 0.929791i | \(-0.619988\pi\) | ||||
−0.368089 | + | 0.929791i | \(0.619988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 104544. | 0.925392 | ||||||||
\(106\) | 125064. | 1.08110 | ||||||||
\(107\) | 227988. | 1.92510 | 0.962548 | − | 0.271110i | \(-0.0873908\pi\) | ||||
0.962548 | + | 0.271110i | \(0.0873908\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 8530.00 | 0.0687674 | 0.0343837 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343837 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(110\) | −15840.0 | −0.124817 | ||||||||
\(111\) | −76122.0 | −0.586412 | ||||||||
\(112\) | −45056.0 | −0.339397 | ||||||||
\(113\) | −195438. | −1.43984 | −0.719918 | − | 0.694059i | \(-0.755821\pi\) | ||||
−0.719918 | + | 0.694059i | \(0.755821\pi\) | |||||||
\(114\) | −34416.0 | −0.248027 | ||||||||
\(115\) | 39600.0 | 0.279223 | ||||||||
\(116\) | 89184.0 | 0.615378 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 105360. | 0.696580 | ||||||||
\(119\) | 72864.0 | 0.471678 | ||||||||
\(120\) | 38016.0 | 0.240998 | ||||||||
\(121\) | −157451. | −0.977647 | ||||||||
\(122\) | 124360. | 0.756452 | ||||||||
\(123\) | 172746. | 1.02954 | ||||||||
\(124\) | 57472.0 | 0.335662 | ||||||||
\(125\) | −125004. | −0.715565 | ||||||||
\(126\) | 57024.0 | 0.319986 | ||||||||
\(127\) | 173000. | 0.951780 | 0.475890 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475890 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −119844. | −0.634077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 151260. | 0.770098 | 0.385049 | − | 0.922896i | \(-0.374185\pi\) | ||||
0.385049 | + | 0.922896i | \(0.374185\pi\) | |||||||
\(132\) | −8640.00 | −0.0431597 | ||||||||
\(133\) | 168256. | 0.824786 | ||||||||
\(134\) | −67216.0 | −0.323378 | ||||||||
\(135\) | −48114.0 | −0.227215 | ||||||||
\(136\) | 26496.0 | 0.122838 | ||||||||
\(137\) | 128454. | 0.584718 | 0.292359 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292359 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(138\) | 21600.0 | 0.0965508 | ||||||||
\(139\) | 154196. | 0.676918 | 0.338459 | − | 0.940981i | \(-0.390094\pi\) | ||||
0.338459 | + | 0.940981i | \(0.390094\pi\) | |||||||
\(140\) | −185856. | −0.801413 | ||||||||
\(141\) | −177120. | −0.750274 | ||||||||
\(142\) | 24480.0 | 0.101880 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 367884. | 1.45308 | ||||||||
\(146\) | −102232. | −0.396922 | ||||||||
\(147\) | −127521. | −0.486730 | ||||||||
\(148\) | 135328. | 0.507848 | ||||||||
\(149\) | −29454.0 | −0.108687 | −0.0543436 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543436 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(150\) | 44316.0 | 0.160817 | ||||||||
\(151\) | 203872. | 0.727638 | 0.363819 | − | 0.931470i | \(-0.381473\pi\) | ||||
0.363819 | + | 0.931470i | \(0.381473\pi\) | |||||||
\(152\) | 61184.0 | 0.214797 | ||||||||
\(153\) | −33534.0 | −0.115813 | ||||||||
\(154\) | 42240.0 | 0.143523 | ||||||||
\(155\) | 237072. | 0.792594 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 136142. | 0.440801 | 0.220401 | − | 0.975409i | \(-0.429263\pi\) | ||||
0.220401 | + | 0.975409i | \(0.429263\pi\) | |||||||
\(158\) | −297632. | −0.948499 | ||||||||
\(159\) | 281394. | 0.882718 | ||||||||
\(160\) | −67584.0 | −0.208710 | ||||||||
\(161\) | −105600. | −0.321070 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 171124. | 0.504478 | 0.252239 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252239 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(164\) | −307104. | −0.891612 | ||||||||
\(165\) | −35640.0 | −0.101913 | ||||||||
\(166\) | −25872.0 | −0.0728718 | ||||||||
\(167\) | 676200. | 1.87622 | 0.938110 | − | 0.346336i | \(-0.112574\pi\) | ||||
0.938110 | + | 0.346336i | \(0.112574\pi\) | |||||||
\(168\) | −101376. | −0.277116 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 109296. | 0.290056 | ||||||||
\(171\) | −77436.0 | −0.202513 | ||||||||
\(172\) | 213056. | 0.549127 | ||||||||
\(173\) | 133158. | 0.338261 | 0.169131 | − | 0.985594i | \(-0.445904\pi\) | ||||
0.169131 | + | 0.985594i | \(0.445904\pi\) | |||||||
\(174\) | 200664. | 0.502454 | ||||||||
\(175\) | −216656. | −0.534781 | ||||||||
\(176\) | 15360.0 | 0.0373774 | ||||||||
\(177\) | 237060. | 0.568755 | ||||||||
\(178\) | −130968. | −0.309824 | ||||||||
\(179\) | −693396. | −1.61752 | −0.808758 | − | 0.588141i | \(-0.799860\pi\) | ||||
−0.808758 | + | 0.588141i | \(0.799860\pi\) | |||||||
\(180\) | 85536.0 | 0.196774 | ||||||||
\(181\) | 377174. | 0.855747 | 0.427873 | − | 0.903839i | \(-0.359263\pi\) | ||||
0.427873 | + | 0.903839i | \(0.359263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 279810. | 0.617640 | ||||||||
\(184\) | −38400.0 | −0.0836155 | ||||||||
\(185\) | 558228. | 1.19917 | ||||||||
\(186\) | 129312. | 0.274067 | ||||||||
\(187\) | −24840.0 | −0.0519455 | ||||||||
\(188\) | 314880. | 0.649756 | ||||||||
\(189\) | 128304. | 0.261268 | ||||||||
\(190\) | 252384. | 0.507198 | ||||||||
\(191\) | −265344. | −0.526291 | −0.263145 | − | 0.964756i | \(-0.584760\pi\) | ||||
−0.263145 | + | 0.964756i | \(0.584760\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −295298. | −0.570647 | −0.285323 | − | 0.958431i | \(-0.592101\pi\) | ||||
−0.285323 | + | 0.958431i | \(0.592101\pi\) | |||||||
\(194\) | 664328. | 1.26730 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 226704. | 0.421521 | ||||||||
\(197\) | −201294. | −0.369543 | −0.184772 | − | 0.982781i | \(-0.559155\pi\) | ||||
−0.184772 | + | 0.982781i | \(0.559155\pi\) | |||||||
\(198\) | −19440.0 | −0.0352398 | ||||||||
\(199\) | 652448. | 1.16792 | 0.583960 | − | 0.811782i | \(-0.301502\pi\) | ||||
0.583960 | + | 0.811782i | \(0.301502\pi\) | |||||||
\(200\) | −78784.0 | −0.139272 | ||||||||
\(201\) | −151236. | −0.264037 | ||||||||
\(202\) | 88008.0 | 0.151755 | ||||||||
\(203\) | −981024. | −1.67086 | ||||||||
\(204\) | 59616.0 | 0.100297 | ||||||||
\(205\) | −1.26680e6 | −2.10535 | ||||||||
\(206\) | 317056. | 0.520557 | ||||||||
\(207\) | 48600.0 | 0.0788334 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −57360.0 | −0.0908330 | ||||||||
\(210\) | −418176. | −0.654351 | ||||||||
\(211\) | −1.14706e6 | −1.77370 | −0.886850 | − | 0.462058i | \(-0.847111\pi\) | ||||
−0.886850 | + | 0.462058i | \(0.847111\pi\) | |||||||
\(212\) | −500256. | −0.764456 | ||||||||
\(213\) | 55080.0 | 0.0831850 | ||||||||
\(214\) | −911952. | −1.36125 | ||||||||
\(215\) | 878856. | 1.29665 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −632192. | −0.911380 | ||||||||
\(218\) | −34120.0 | −0.0486259 | ||||||||
\(219\) | −230022. | −0.324085 | ||||||||
\(220\) | 63360.0 | 0.0882589 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 304488. | 0.414656 | ||||||||
\(223\) | −701960. | −0.945258 | −0.472629 | − | 0.881262i | \(-0.656695\pi\) | ||||
−0.472629 | + | 0.881262i | \(0.656695\pi\) | |||||||
\(224\) | 180224. | 0.239990 | ||||||||
\(225\) | 99711.0 | 0.131307 | ||||||||
\(226\) | 781752. | 1.01812 | ||||||||
\(227\) | −1.23611e6 | −1.59218 | −0.796089 | − | 0.605179i | \(-0.793101\pi\) | ||||
−0.796089 | + | 0.605179i | \(0.793101\pi\) | |||||||
\(228\) | 137664. | 0.175381 | ||||||||
\(229\) | −105830. | −0.133358 | −0.0666792 | − | 0.997774i | \(-0.521240\pi\) | ||||
−0.0666792 | + | 0.997774i | \(0.521240\pi\) | |||||||
\(230\) | −158400. | −0.197440 | ||||||||
\(231\) | 95040.0 | 0.117186 | ||||||||
\(232\) | −356736. | −0.435138 | ||||||||
\(233\) | −438678. | −0.529366 | −0.264683 | − | 0.964335i | \(-0.585267\pi\) | ||||
−0.264683 | + | 0.964335i | \(0.585267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.29888e6 | 1.53426 | ||||||||
\(236\) | −421440. | −0.492556 | ||||||||
\(237\) | −669672. | −0.774446 | ||||||||
\(238\) | −291456. | −0.333527 | ||||||||
\(239\) | −28464.0 | −0.0322330 | −0.0161165 | − | 0.999870i | \(-0.505130\pi\) | ||||
−0.0161165 | + | 0.999870i | \(0.505130\pi\) | |||||||
\(240\) | −152064. | −0.170411 | ||||||||
\(241\) | −892562. | −0.989910 | −0.494955 | − | 0.868919i | \(-0.664815\pi\) | ||||
−0.494955 | + | 0.868919i | \(0.664815\pi\) | |||||||
\(242\) | 629804. | 0.691301 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −497440. | −0.534892 | ||||||||
\(245\) | 935154. | 0.995332 | ||||||||
\(246\) | −690984. | −0.727998 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −229888. | −0.237349 | ||||||||
\(249\) | −58212.0 | −0.0594996 | ||||||||
\(250\) | 500016. | 0.505981 | ||||||||
\(251\) | −110124. | −0.110331 | −0.0551655 | − | 0.998477i | \(-0.517569\pi\) | ||||
−0.0551655 | + | 0.998477i | \(0.517569\pi\) | |||||||
\(252\) | −228096. | −0.226264 | ||||||||
\(253\) | 36000.0 | 0.0353591 | ||||||||
\(254\) | −692000. | −0.673010 | ||||||||
\(255\) | 245916. | 0.236830 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 140802. | 0.132977 | 0.0664884 | − | 0.997787i | \(-0.478820\pi\) | ||||
0.0664884 | + | 0.997787i | \(0.478820\pi\) | |||||||
\(258\) | 479376. | 0.448360 | ||||||||
\(259\) | −1.48861e6 | −1.37889 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 451494. | 0.410252 | ||||||||
\(262\) | −605040. | −0.544541 | ||||||||
\(263\) | −938760. | −0.836884 | −0.418442 | − | 0.908244i | \(-0.637424\pi\) | ||||
−0.418442 | + | 0.908244i | \(0.637424\pi\) | |||||||
\(264\) | 34560.0 | 0.0305186 | ||||||||
\(265\) | −2.06356e6 | −1.80510 | ||||||||
\(266\) | −673024. | −0.583212 | ||||||||
\(267\) | −294678. | −0.252970 | ||||||||
\(268\) | 268864. | 0.228663 | ||||||||
\(269\) | −1.11451e6 | −0.939078 | −0.469539 | − | 0.882912i | \(-0.655580\pi\) | ||||
−0.469539 | + | 0.882912i | \(0.655580\pi\) | |||||||
\(270\) | 192456. | 0.160665 | ||||||||
\(271\) | −567704. | −0.469568 | −0.234784 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234784 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(272\) | −105984. | −0.0868596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −513816. | −0.413458 | ||||||||
\(275\) | 73860.0 | 0.0588949 | ||||||||
\(276\) | −86400.0 | −0.0682718 | ||||||||
\(277\) | −1.21326e6 | −0.950066 | −0.475033 | − | 0.879968i | \(-0.657564\pi\) | ||||
−0.475033 | + | 0.879968i | \(0.657564\pi\) | |||||||
\(278\) | −616784. | −0.478653 | ||||||||
\(279\) | 290952. | 0.223775 | ||||||||
\(280\) | 743424. | 0.566685 | ||||||||
\(281\) | −687738. | −0.519586 | −0.259793 | − | 0.965664i | \(-0.583654\pi\) | ||||
−0.259793 | + | 0.965664i | \(0.583654\pi\) | |||||||
\(282\) | 708480. | 0.530524 | ||||||||
\(283\) | −830908. | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(284\) | −97920.0 | −0.0720403 | ||||||||
\(285\) | 567864. | 0.414126 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37814e6 | 2.42088 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.24846e6 | −0.879286 | ||||||||
\(290\) | −1.47154e6 | −1.02749 | ||||||||
\(291\) | 1.49474e6 | 1.03474 | ||||||||
\(292\) | 408928. | 0.280666 | ||||||||
\(293\) | 1.31263e6 | 0.893248 | 0.446624 | − | 0.894722i | \(-0.352626\pi\) | ||||
0.446624 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(294\) | 510084. | 0.344170 | ||||||||
\(295\) | −1.73844e6 | −1.16307 | ||||||||
\(296\) | −541312. | −0.359102 | ||||||||
\(297\) | −43740.0 | −0.0287732 | ||||||||
\(298\) | 117816. | 0.0768535 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −177264. | −0.113715 | ||||||||
\(301\) | −2.34362e6 | −1.49097 | ||||||||
\(302\) | −815488. | −0.514518 | ||||||||
\(303\) | 198018. | 0.123908 | ||||||||
\(304\) | −244736. | −0.151885 | ||||||||
\(305\) | −2.05194e6 | −1.26303 | ||||||||
\(306\) | 134136. | 0.0818921 | ||||||||
\(307\) | −1.69022e6 | −1.02352 | −0.511761 | − | 0.859128i | \(-0.671007\pi\) | ||||
−0.511761 | + | 0.859128i | \(0.671007\pi\) | |||||||
\(308\) | −168960. | −0.101486 | ||||||||
\(309\) | 713376. | 0.425033 | ||||||||
\(310\) | −948288. | −0.560449 | ||||||||
\(311\) | −1.50204e6 | −0.880604 | −0.440302 | − | 0.897850i | \(-0.645129\pi\) | ||||
−0.440302 | + | 0.897850i | \(0.645129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 810842. | 0.467816 | 0.233908 | − | 0.972259i | \(-0.424848\pi\) | ||||
0.233908 | + | 0.972259i | \(0.424848\pi\) | |||||||
\(314\) | −544568. | −0.311694 | ||||||||
\(315\) | −940896. | −0.534275 | ||||||||
\(316\) | 1.19053e6 | 0.670690 | ||||||||
\(317\) | −903558. | −0.505019 | −0.252510 | − | 0.967594i | \(-0.581256\pi\) | ||||
−0.252510 | + | 0.967594i | \(0.581256\pi\) | |||||||
\(318\) | −1.12558e6 | −0.624176 | ||||||||
\(319\) | 334440. | 0.184010 | ||||||||
\(320\) | 270336. | 0.147580 | ||||||||
\(321\) | −2.05189e6 | −1.11146 | ||||||||
\(322\) | 422400. | 0.227031 | ||||||||
\(323\) | 395784. | 0.211082 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −684496. | −0.356720 | ||||||||
\(327\) | −76770.0 | −0.0397029 | ||||||||
\(328\) | 1.22842e6 | 0.630465 | ||||||||
\(329\) | −3.46368e6 | −1.76420 | ||||||||
\(330\) | 142560. | 0.0720631 | ||||||||
\(331\) | −1.12197e6 | −0.562875 | −0.281438 | − | 0.959580i | \(-0.590811\pi\) | ||||
−0.281438 | + | 0.959580i | \(0.590811\pi\) | |||||||
\(332\) | 103488. | 0.0515282 | ||||||||
\(333\) | 685098. | 0.338565 | ||||||||
\(334\) | −2.70480e6 | −1.32669 | ||||||||
\(335\) | 1.10906e6 | 0.539939 | ||||||||
\(336\) | 405504. | 0.195951 | ||||||||
\(337\) | −2.75217e6 | −1.32008 | −0.660041 | − | 0.751229i | \(-0.729461\pi\) | ||||
−0.660041 | + | 0.751229i | \(0.729461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.75894e6 | 0.831289 | ||||||||
\(340\) | −437184. | −0.205101 | ||||||||
\(341\) | 215520. | 0.100369 | ||||||||
\(342\) | 309744. | 0.143198 | ||||||||
\(343\) | 464288. | 0.213085 | ||||||||
\(344\) | −852224. | −0.388291 | ||||||||
\(345\) | −356400. | −0.161209 | ||||||||
\(346\) | −532632. | −0.239187 | ||||||||
\(347\) | 1.91749e6 | 0.854889 | 0.427445 | − | 0.904042i | \(-0.359414\pi\) | ||||
0.427445 | + | 0.904042i | \(0.359414\pi\) | |||||||
\(348\) | −802656. | −0.355289 | ||||||||
\(349\) | −1.83659e6 | −0.807140 | −0.403570 | − | 0.914949i | \(-0.632231\pi\) | ||||
−0.403570 | + | 0.914949i | \(0.632231\pi\) | |||||||
\(350\) | 866624. | 0.378147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −61440.0 | −0.0264298 | ||||||||
\(353\) | 622014. | 0.265683 | 0.132841 | − | 0.991137i | \(-0.457590\pi\) | ||||
0.132841 | + | 0.991137i | \(0.457590\pi\) | |||||||
\(354\) | −948240. | −0.402170 | ||||||||
\(355\) | −403920. | −0.170108 | ||||||||
\(356\) | 523872. | 0.219079 | ||||||||
\(357\) | −655776. | −0.272323 | ||||||||
\(358\) | 2.77358e6 | 1.14376 | ||||||||
\(359\) | −3.74062e6 | −1.53182 | −0.765909 | − | 0.642949i | \(-0.777711\pi\) | ||||
−0.765909 | + | 0.642949i | \(0.777711\pi\) | |||||||
\(360\) | −342144. | −0.139140 | ||||||||
\(361\) | −1.56216e6 | −0.630897 | ||||||||
\(362\) | −1.50870e6 | −0.605104 | ||||||||
\(363\) | 1.41706e6 | 0.564445 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.68683e6 | 0.662733 | ||||||||
\(366\) | −1.11924e6 | −0.436738 | ||||||||
\(367\) | 16232.0 | 0.00629081 | 0.00314541 | − | 0.999995i | \(-0.498999\pi\) | ||||
0.00314541 | + | 0.999995i | \(0.498999\pi\) | |||||||
\(368\) | 153600. | 0.0591251 | ||||||||
\(369\) | −1.55471e6 | −0.594408 | ||||||||
\(370\) | −2.23291e6 | −0.847944 | ||||||||
\(371\) | 5.50282e6 | 2.07563 | ||||||||
\(372\) | −517248. | −0.193795 | ||||||||
\(373\) | 293606. | 0.109268 | 0.0546340 | − | 0.998506i | \(-0.482601\pi\) | ||||
0.0546340 | + | 0.998506i | \(0.482601\pi\) | |||||||
\(374\) | 99360.0 | 0.0367310 | ||||||||
\(375\) | 1.12504e6 | 0.413131 | ||||||||
\(376\) | −1.25952e6 | −0.459447 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −513216. | −0.184744 | ||||||||
\(379\) | −3.18012e6 | −1.13722 | −0.568611 | − | 0.822607i | \(-0.692519\pi\) | ||||
−0.568611 | + | 0.822607i | \(0.692519\pi\) | |||||||
\(380\) | −1.00954e6 | −0.358643 | ||||||||
\(381\) | −1.55700e6 | −0.549511 | ||||||||
\(382\) | 1.06138e6 | 0.372144 | ||||||||
\(383\) | 2.97984e6 | 1.03800 | 0.518998 | − | 0.854775i | \(-0.326305\pi\) | ||||
0.518998 | + | 0.854775i | \(0.326305\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −696960. | −0.239638 | ||||||||
\(386\) | 1.18119e6 | 0.403508 | ||||||||
\(387\) | 1.07860e6 | 0.366085 | ||||||||
\(388\) | −2.65731e6 | −0.896114 | ||||||||
\(389\) | 3.45977e6 | 1.15924 | 0.579620 | − | 0.814887i | \(-0.303201\pi\) | ||||
0.579620 | + | 0.814887i | \(0.303201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −248400. | −0.0821693 | ||||||||
\(392\) | −906816. | −0.298060 | ||||||||
\(393\) | −1.36134e6 | −0.444616 | ||||||||
\(394\) | 805176. | 0.261307 | ||||||||
\(395\) | 4.91093e6 | 1.58369 | ||||||||
\(396\) | 77760.0 | 0.0249183 | ||||||||
\(397\) | 3.90416e6 | 1.24323 | 0.621615 | − | 0.783323i | \(-0.286477\pi\) | ||||
0.621615 | + | 0.783323i | \(0.286477\pi\) | |||||||
\(398\) | −2.60979e6 | −0.825844 | ||||||||
\(399\) | −1.51430e6 | −0.476191 | ||||||||
\(400\) | 315136. | 0.0984800 | ||||||||
\(401\) | −5.44115e6 | −1.68978 | −0.844890 | − | 0.534940i | \(-0.820334\pi\) | ||||
−0.844890 | + | 0.534940i | \(0.820334\pi\) | |||||||
\(402\) | 604944. | 0.186702 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −352032. | −0.107307 | ||||||||
\(405\) | 433026. | 0.131183 | ||||||||
\(406\) | 3.92410e6 | 1.18148 | ||||||||
\(407\) | 507480. | 0.151856 | ||||||||
\(408\) | −238464. | −0.0709206 | ||||||||
\(409\) | −1.96995e6 | −0.582299 | −0.291150 | − | 0.956678i | \(-0.594038\pi\) | ||||
−0.291150 | + | 0.956678i | \(0.594038\pi\) | |||||||
\(410\) | 5.06722e6 | 1.48871 | ||||||||
\(411\) | −1.15609e6 | −0.337587 | ||||||||
\(412\) | −1.26822e6 | −0.368089 | ||||||||
\(413\) | 4.63584e6 | 1.33738 | ||||||||
\(414\) | −194400. | −0.0557437 | ||||||||
\(415\) | 426888. | 0.121673 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.38776e6 | −0.390819 | ||||||||
\(418\) | 229440. | 0.0642286 | ||||||||
\(419\) | 139020. | 0.0386850 | 0.0193425 | − | 0.999813i | \(-0.493843\pi\) | ||||
0.0193425 | + | 0.999813i | \(0.493843\pi\) | |||||||
\(420\) | 1.67270e6 | 0.462696 | ||||||||
\(421\) | −4.32743e6 | −1.18994 | −0.594970 | − | 0.803748i | \(-0.702836\pi\) | ||||
−0.594970 | + | 0.803748i | \(0.702836\pi\) | |||||||
\(422\) | 4.58824e6 | 1.25419 | ||||||||
\(423\) | 1.59408e6 | 0.433171 | ||||||||
\(424\) | 2.00102e6 | 0.540552 | ||||||||
\(425\) | −509634. | −0.136863 | ||||||||
\(426\) | −220320. | −0.0588207 | ||||||||
\(427\) | 5.47184e6 | 1.45232 | ||||||||
\(428\) | 3.64781e6 | 0.962548 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.51542e6 | −0.916867 | ||||||||
\(431\) | 2.79936e6 | 0.725881 | 0.362941 | − | 0.931812i | \(-0.381773\pi\) | ||||
0.362941 | + | 0.931812i | \(0.381773\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −5.90241e6 | −1.51290 | −0.756449 | − | 0.654052i | \(-0.773068\pi\) | ||||
−0.756449 | + | 0.654052i | \(0.773068\pi\) | |||||||
\(434\) | 2.52877e6 | 0.644443 | ||||||||
\(435\) | −3.31096e6 | −0.838939 | ||||||||
\(436\) | 136480. | 0.0343837 | ||||||||
\(437\) | −573600. | −0.143683 | ||||||||
\(438\) | 920088. | 0.229163 | ||||||||
\(439\) | −446512. | −0.110579 | −0.0552894 | − | 0.998470i | \(-0.517608\pi\) | ||||
−0.0552894 | + | 0.998470i | \(0.517608\pi\) | |||||||
\(440\) | −253440. | −0.0624085 | ||||||||
\(441\) | 1.14769e6 | 0.281014 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.49525e6 | 0.846193 | 0.423096 | − | 0.906085i | \(-0.360943\pi\) | ||||
0.423096 | + | 0.906085i | \(0.360943\pi\) | |||||||
\(444\) | −1.21795e6 | −0.293206 | ||||||||
\(445\) | 2.16097e6 | 0.517308 | ||||||||
\(446\) | 2.80784e6 | 0.668398 | ||||||||
\(447\) | 265086. | 0.0627506 | ||||||||
\(448\) | −720896. | −0.169698 | ||||||||
\(449\) | 1.20613e6 | 0.282343 | 0.141171 | − | 0.989985i | \(-0.454913\pi\) | ||||
0.141171 | + | 0.989985i | \(0.454913\pi\) | |||||||
\(450\) | −398844. | −0.0928478 | ||||||||
\(451\) | −1.15164e6 | −0.266609 | ||||||||
\(452\) | −3.12701e6 | −0.719918 | ||||||||
\(453\) | −1.83485e6 | −0.420102 | ||||||||
\(454\) | 4.94443e6 | 1.12584 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −550656. | −0.124013 | ||||||||
\(457\) | −233546. | −0.0523097 | −0.0261548 | − | 0.999658i | \(-0.508326\pi\) | ||||
−0.0261548 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(458\) | 423320. | 0.0942986 | ||||||||
\(459\) | 301806. | 0.0668646 | ||||||||
\(460\) | 633600. | 0.139611 | ||||||||
\(461\) | 1.74489e6 | 0.382398 | 0.191199 | − | 0.981551i | \(-0.438762\pi\) | ||||
0.191199 | + | 0.981551i | \(0.438762\pi\) | |||||||
\(462\) | −380160. | −0.0828632 | ||||||||
\(463\) | 2.91786e6 | 0.632576 | 0.316288 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316288 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(464\) | 1.42694e6 | 0.307689 | ||||||||
\(465\) | −2.13365e6 | −0.457605 | ||||||||
\(466\) | 1.75471e6 | 0.374318 | ||||||||
\(467\) | −5.31076e6 | −1.12684 | −0.563422 | − | 0.826169i | \(-0.690516\pi\) | ||||
−0.563422 | + | 0.826169i | \(0.690516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.95750e6 | −0.620859 | ||||||||
\(470\) | −5.19552e6 | −1.08489 | ||||||||
\(471\) | −1.22528e6 | −0.254497 | ||||||||
\(472\) | 1.68576e6 | 0.348290 | ||||||||
\(473\) | 798960. | 0.164200 | ||||||||
\(474\) | 2.67869e6 | 0.547616 | ||||||||
\(475\) | −1.17684e6 | −0.239322 | ||||||||
\(476\) | 1.16582e6 | 0.235839 | ||||||||
\(477\) | −2.53255e6 | −0.509638 | ||||||||
\(478\) | 113856. | 0.0227922 | ||||||||
\(479\) | −2.34466e6 | −0.466918 | −0.233459 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233459 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(480\) | 608256. | 0.120499 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.57025e6 | 0.699972 | ||||||||
\(483\) | 950400. | 0.185370 | ||||||||
\(484\) | −2.51922e6 | −0.488823 | ||||||||
\(485\) | −1.09614e7 | −2.11598 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −9.81531e6 | −1.87535 | −0.937674 | − | 0.347517i | \(-0.887025\pi\) | ||||
−0.937674 | + | 0.347517i | \(0.887025\pi\) | |||||||
\(488\) | 1.98976e6 | 0.378226 | ||||||||
\(489\) | −1.54012e6 | −0.291260 | ||||||||
\(490\) | −3.74062e6 | −0.703806 | ||||||||
\(491\) | −5.94520e6 | −1.11292 | −0.556458 | − | 0.830876i | \(-0.687840\pi\) | ||||
−0.556458 | + | 0.830876i | \(0.687840\pi\) | |||||||
\(492\) | 2.76394e6 | 0.514772 | ||||||||
\(493\) | −2.30764e6 | −0.427612 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 320760. | 0.0588393 | ||||||||
\(496\) | 919552. | 0.167831 | ||||||||
\(497\) | 1.07712e6 | 0.195602 | ||||||||
\(498\) | 232848. | 0.0420726 | ||||||||
\(499\) | −6.47832e6 | −1.16469 | −0.582346 | − | 0.812941i | \(-0.697865\pi\) | ||||
−0.582346 | + | 0.812941i | \(0.697865\pi\) | |||||||
\(500\) | −2.00006e6 | −0.357782 | ||||||||
\(501\) | −6.08580e6 | −1.08324 | ||||||||
\(502\) | 440496. | 0.0780158 | ||||||||
\(503\) | 4.71794e6 | 0.831444 | 0.415722 | − | 0.909492i | \(-0.363529\pi\) | ||||
0.415722 | + | 0.909492i | \(0.363529\pi\) | |||||||
\(504\) | 912384. | 0.159993 | ||||||||
\(505\) | −1.45213e6 | −0.253383 | ||||||||
\(506\) | −144000. | −0.0250027 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.76800e6 | 0.475890 | ||||||||
\(509\) | 1.90771e6 | 0.326375 | 0.163188 | − | 0.986595i | \(-0.447822\pi\) | ||||
0.163188 | + | 0.986595i | \(0.447822\pi\) | |||||||
\(510\) | −983664. | −0.167464 | ||||||||
\(511\) | −4.49821e6 | −0.762057 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 696924. | 0.116921 | ||||||||
\(514\) | −563208. | −0.0940288 | ||||||||
\(515\) | −5.23142e6 | −0.869164 | ||||||||
\(516\) | −1.91750e6 | −0.317039 | ||||||||
\(517\) | 1.18080e6 | 0.194290 | ||||||||
\(518\) | 5.95443e6 | 0.975025 | ||||||||
\(519\) | −1.19842e6 | −0.195295 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.01974e6 | 1.29439 | 0.647196 | − | 0.762324i | \(-0.275941\pi\) | ||||
0.647196 | + | 0.762324i | \(0.275941\pi\) | |||||||
\(522\) | −1.80598e6 | −0.290092 | ||||||||
\(523\) | 1.91162e6 | 0.305596 | 0.152798 | − | 0.988257i | \(-0.451172\pi\) | ||||
0.152798 | + | 0.988257i | \(0.451172\pi\) | |||||||
\(524\) | 2.42016e6 | 0.385049 | ||||||||
\(525\) | 1.94990e6 | 0.308756 | ||||||||
\(526\) | 3.75504e6 | 0.591766 | ||||||||
\(527\) | −1.48709e6 | −0.233244 | ||||||||
\(528\) | −138240. | −0.0215799 | ||||||||
\(529\) | −6.07634e6 | −0.944068 | ||||||||
\(530\) | 8.25422e6 | 1.27640 | ||||||||
\(531\) | −2.13354e6 | −0.328371 | ||||||||
\(532\) | 2.69210e6 | 0.412393 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.17871e6 | 0.178877 | ||||||||
\(535\) | 1.50472e7 | 2.27285 | ||||||||
\(536\) | −1.07546e6 | −0.161689 | ||||||||
\(537\) | 6.24056e6 | 0.933874 | ||||||||
\(538\) | 4.45802e6 | 0.664028 | ||||||||
\(539\) | 850140. | 0.126043 | ||||||||
\(540\) | −769824. | −0.113608 | ||||||||
\(541\) | 1.19900e7 | 1.76128 | 0.880639 | − | 0.473788i | \(-0.157114\pi\) | ||||
0.880639 | + | 0.473788i | \(0.157114\pi\) | |||||||
\(542\) | 2.27082e6 | 0.332035 | ||||||||
\(543\) | −3.39457e6 | −0.494066 | ||||||||
\(544\) | 423936. | 0.0614190 | ||||||||
\(545\) | 562980. | 0.0811898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.45809e6 | 0.637061 | 0.318530 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318530 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(548\) | 2.05526e6 | 0.292359 | ||||||||
\(549\) | −2.51829e6 | −0.356595 | ||||||||
\(550\) | −295440. | −0.0416450 | ||||||||
\(551\) | −5.32874e6 | −0.747732 | ||||||||
\(552\) | 345600. | 0.0482754 | ||||||||
\(553\) | −1.30958e7 | −1.82104 | ||||||||
\(554\) | 4.85303e6 | 0.671798 | ||||||||
\(555\) | −5.02405e6 | −0.692344 | ||||||||
\(556\) | 2.46714e6 | 0.338459 | ||||||||
\(557\) | −9.02612e6 | −1.23272 | −0.616358 | − | 0.787466i | \(-0.711393\pi\) | ||||
−0.616358 | + | 0.787466i | \(0.711393\pi\) | |||||||
\(558\) | −1.16381e6 | −0.158233 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.97370e6 | −0.400707 | ||||||||
\(561\) | 223560. | 0.0299907 | ||||||||
\(562\) | 2.75095e6 | 0.367403 | ||||||||
\(563\) | 6.84899e6 | 0.910658 | 0.455329 | − | 0.890323i | \(-0.349522\pi\) | ||||
0.455329 | + | 0.890323i | \(0.349522\pi\) | |||||||
\(564\) | −2.83392e6 | −0.375137 | ||||||||
\(565\) | −1.28989e7 | −1.69993 | ||||||||
\(566\) | 3.32363e6 | 0.436086 | ||||||||
\(567\) | −1.15474e6 | −0.150843 | ||||||||
\(568\) | 391680. | 0.0509402 | ||||||||
\(569\) | −5.46322e6 | −0.707405 | −0.353703 | − | 0.935358i | \(-0.615077\pi\) | ||||
−0.353703 | + | 0.935358i | \(0.615077\pi\) | |||||||
\(570\) | −2.27146e6 | −0.292831 | ||||||||
\(571\) | −1.02324e7 | −1.31337 | −0.656684 | − | 0.754166i | \(-0.728041\pi\) | ||||
−0.656684 | + | 0.754166i | \(0.728041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.38810e6 | 0.303854 | ||||||||
\(574\) | −1.35126e7 | −1.71182 | ||||||||
\(575\) | 738600. | 0.0931622 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.59437e7 | −1.99365 | −0.996825 | − | 0.0796186i | \(-0.974630\pi\) | ||||
−0.996825 | + | 0.0796186i | \(0.974630\pi\) | |||||||
\(578\) | 4.99384e6 | 0.621749 | ||||||||
\(579\) | 2.65768e6 | 0.329463 | ||||||||
\(580\) | 5.88614e6 | 0.726542 | ||||||||
\(581\) | −1.13837e6 | −0.139908 | ||||||||
\(582\) | −5.97895e6 | −0.731674 | ||||||||
\(583\) | −1.87596e6 | −0.228587 | ||||||||
\(584\) | −1.63571e6 | −0.198461 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.25050e6 | −0.631622 | ||||||||
\(587\) | 9.47713e6 | 1.13522 | 0.567612 | − | 0.823296i | \(-0.307867\pi\) | ||||
0.567612 | + | 0.823296i | \(0.307867\pi\) | |||||||
\(588\) | −2.04034e6 | −0.243365 | ||||||||
\(589\) | −3.43395e6 | −0.407855 | ||||||||
\(590\) | 6.95376e6 | 0.822412 | ||||||||
\(591\) | 1.81165e6 | 0.213356 | ||||||||
\(592\) | 2.16525e6 | 0.253924 | ||||||||
\(593\) | −2.45349e6 | −0.286515 | −0.143258 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143258 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(594\) | 174960. | 0.0203457 | ||||||||
\(595\) | 4.80902e6 | 0.556884 | ||||||||
\(596\) | −471264. | −0.0543436 | ||||||||
\(597\) | −5.87203e6 | −0.674299 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.29978e6 | −1.05902 | −0.529512 | − | 0.848302i | \(-0.677625\pi\) | ||||
−0.529512 | + | 0.848302i | \(0.677625\pi\) | |||||||
\(600\) | 709056. | 0.0804086 | ||||||||
\(601\) | −1.14617e7 | −1.29438 | −0.647192 | − | 0.762327i | \(-0.724057\pi\) | ||||
−0.647192 | + | 0.762327i | \(0.724057\pi\) | |||||||
\(602\) | 9.37446e6 | 1.05428 | ||||||||
\(603\) | 1.36112e6 | 0.152442 | ||||||||
\(604\) | 3.26195e6 | 0.363819 | ||||||||
\(605\) | −1.03918e7 | −1.15425 | ||||||||
\(606\) | −792072. | −0.0876159 | ||||||||
\(607\) | 1.12784e7 | 1.24244 | 0.621219 | − | 0.783637i | \(-0.286638\pi\) | ||||
0.621219 | + | 0.783637i | \(0.286638\pi\) | |||||||
\(608\) | 978944. | 0.107399 | ||||||||
\(609\) | 8.82922e6 | 0.964670 | ||||||||
\(610\) | 8.20776e6 | 0.893100 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −536544. | −0.0579064 | ||||||||
\(613\) | −93782.0 | −0.0100802 | −0.00504009 | − | 0.999987i | \(-0.501604\pi\) | ||||
−0.00504009 | + | 0.999987i | \(0.501604\pi\) | |||||||
\(614\) | 6.76088e6 | 0.723740 | ||||||||
\(615\) | 1.14012e7 | 1.21553 | ||||||||
\(616\) | 675840. | 0.0717616 | ||||||||
\(617\) | 1.49642e7 | 1.58248 | 0.791242 | − | 0.611504i | \(-0.209435\pi\) | ||||
0.791242 | + | 0.611504i | \(0.209435\pi\) | |||||||
\(618\) | −2.85350e6 | −0.300543 | ||||||||
\(619\) | 5.06888e6 | 0.531723 | 0.265861 | − | 0.964011i | \(-0.414344\pi\) | ||||
0.265861 | + | 0.964011i | \(0.414344\pi\) | |||||||
\(620\) | 3.79315e6 | 0.396297 | ||||||||
\(621\) | −437400. | −0.0455145 | ||||||||
\(622\) | 6.00816e6 | 0.622681 | ||||||||
\(623\) | −5.76259e6 | −0.594837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20971e7 | −1.23875 | ||||||||
\(626\) | −3.24337e6 | −0.330796 | ||||||||
\(627\) | 516240. | 0.0524424 | ||||||||
\(628\) | 2.17827e6 | 0.220401 | ||||||||
\(629\) | −3.50161e6 | −0.352892 | ||||||||
\(630\) | 3.76358e6 | 0.377790 | ||||||||
\(631\) | −1.55919e7 | −1.55892 | −0.779462 | − | 0.626450i | \(-0.784507\pi\) | ||||
−0.779462 | + | 0.626450i | \(0.784507\pi\) | |||||||
\(632\) | −4.76211e6 | −0.474250 | ||||||||
\(633\) | 1.03235e7 | 1.02405 | ||||||||
\(634\) | 3.61423e6 | 0.357102 | ||||||||
\(635\) | 1.14180e7 | 1.12371 | ||||||||
\(636\) | 4.50230e6 | 0.441359 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.33776e6 | −0.130115 | ||||||||
\(639\) | −495720. | −0.0480269 | ||||||||
\(640\) | −1.08134e6 | −0.104355 | ||||||||
\(641\) | 1.09701e7 | 1.05455 | 0.527274 | − | 0.849695i | \(-0.323214\pi\) | ||||
0.527274 | + | 0.849695i | \(0.323214\pi\) | |||||||
\(642\) | 8.20757e6 | 0.785917 | ||||||||
\(643\) | 2.83704e6 | 0.270607 | 0.135303 | − | 0.990804i | \(-0.456799\pi\) | ||||
0.135303 | + | 0.990804i | \(0.456799\pi\) | |||||||
\(644\) | −1.68960e6 | −0.160535 | ||||||||
\(645\) | −7.90970e6 | −0.748619 | ||||||||
\(646\) | −1.58314e6 | −0.149258 | ||||||||
\(647\) | −6.05686e6 | −0.568835 | −0.284418 | − | 0.958700i | \(-0.591800\pi\) | ||||
−0.284418 | + | 0.958700i | \(0.591800\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −1.58040e6 | −0.147284 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.68973e6 | 0.526186 | ||||||||
\(652\) | 2.73798e6 | 0.252239 | ||||||||
\(653\) | −1.08892e6 | −0.0999341 | −0.0499671 | − | 0.998751i | \(-0.515912\pi\) | ||||
−0.0499671 | + | 0.998751i | \(0.515912\pi\) | |||||||
\(654\) | 307080. | 0.0280742 | ||||||||
\(655\) | 9.98316e6 | 0.909211 | ||||||||
\(656\) | −4.91366e6 | −0.445806 | ||||||||
\(657\) | 2.07020e6 | 0.187111 | ||||||||
\(658\) | 1.38547e7 | 1.24748 | ||||||||
\(659\) | 7.41803e6 | 0.665388 | 0.332694 | − | 0.943035i | \(-0.392042\pi\) | ||||
0.332694 | + | 0.943035i | \(0.392042\pi\) | |||||||
\(660\) | −570240. | −0.0509563 | ||||||||
\(661\) | −767654. | −0.0683379 | −0.0341690 | − | 0.999416i | \(-0.510878\pi\) | ||||
−0.0341690 | + | 0.999416i | \(0.510878\pi\) | |||||||
\(662\) | 4.48789e6 | 0.398013 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −413952. | −0.0364359 | ||||||||
\(665\) | 1.11049e7 | 0.973779 | ||||||||
\(666\) | −2.74039e6 | −0.239402 | ||||||||
\(667\) | 3.34440e6 | 0.291074 | ||||||||
\(668\) | 1.08192e7 | 0.938110 | ||||||||
\(669\) | 6.31764e6 | 0.545745 | ||||||||
\(670\) | −4.43626e6 | −0.381794 | ||||||||
\(671\) | −1.86540e6 | −0.159943 | ||||||||
\(672\) | −1.62202e6 | −0.138558 | ||||||||
\(673\) | 1.42263e6 | 0.121075 | 0.0605373 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605373 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(674\) | 1.10087e7 | 0.933439 | ||||||||
\(675\) | −897399. | −0.0758099 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.16231e6 | −0.516739 | −0.258370 | − | 0.966046i | \(-0.583185\pi\) | ||||
−0.258370 | + | 0.966046i | \(0.583185\pi\) | |||||||
\(678\) | −7.03577e6 | −0.587810 | ||||||||
\(679\) | 2.92304e7 | 2.43310 | ||||||||
\(680\) | 1.74874e6 | 0.145028 | ||||||||
\(681\) | 1.11250e7 | 0.919245 | ||||||||
\(682\) | −862080. | −0.0709719 | ||||||||
\(683\) | −1.50621e7 | −1.23548 | −0.617739 | − | 0.786383i | \(-0.711951\pi\) | ||||
−0.617739 | + | 0.786383i | \(0.711951\pi\) | |||||||
\(684\) | −1.23898e6 | −0.101256 | ||||||||
\(685\) | 8.47796e6 | 0.690343 | ||||||||
\(686\) | −1.85715e6 | −0.150674 | ||||||||
\(687\) | 952470. | 0.0769945 | ||||||||
\(688\) | 3.40890e6 | 0.274563 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.42560e6 | 0.113992 | ||||||||
\(691\) | 5.87636e6 | 0.468180 | 0.234090 | − | 0.972215i | \(-0.424789\pi\) | ||||
0.234090 | + | 0.972215i | \(0.424789\pi\) | |||||||
\(692\) | 2.13053e6 | 0.169131 | ||||||||
\(693\) | −855360. | −0.0676575 | ||||||||
\(694\) | −7.66997e6 | −0.604498 | ||||||||
\(695\) | 1.01769e7 | 0.799199 | ||||||||
\(696\) | 3.21062e6 | 0.251227 | ||||||||
\(697\) | 7.94632e6 | 0.619561 | ||||||||
\(698\) | 7.34636e6 | 0.570734 | ||||||||
\(699\) | 3.94810e6 | 0.305630 | ||||||||
\(700\) | −3.46650e6 | −0.267390 | ||||||||
\(701\) | 3.60077e6 | 0.276758 | 0.138379 | − | 0.990379i | \(-0.455811\pi\) | ||||
0.138379 | + | 0.990379i | \(0.455811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.08585e6 | −0.617074 | ||||||||
\(704\) | 245760. | 0.0186887 | ||||||||
\(705\) | −1.16899e7 | −0.885806 | ||||||||
\(706\) | −2.48806e6 | −0.187866 | ||||||||
\(707\) | 3.87235e6 | 0.291358 | ||||||||
\(708\) | 3.79296e6 | 0.284377 | ||||||||
\(709\) | −9.22516e6 | −0.689221 | −0.344610 | − | 0.938746i | \(-0.611989\pi\) | ||||
−0.344610 | + | 0.938746i | \(0.611989\pi\) | |||||||
\(710\) | 1.61568e6 | 0.120284 | ||||||||
\(711\) | 6.02705e6 | 0.447127 | ||||||||
\(712\) | −2.09549e6 | −0.154912 | ||||||||
\(713\) | 2.15520e6 | 0.158768 | ||||||||
\(714\) | 2.62310e6 | 0.192562 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.10943e7 | −0.808758 | ||||||||
\(717\) | 256176. | 0.0186098 | ||||||||
\(718\) | 1.49625e7 | 1.08316 | ||||||||
\(719\) | −2.63923e7 | −1.90395 | −0.951975 | − | 0.306177i | \(-0.900950\pi\) | ||||
−0.951975 | + | 0.306177i | \(0.900950\pi\) | |||||||
\(720\) | 1.36858e6 | 0.0983870 | ||||||||
\(721\) | 1.39505e7 | 0.999426 | ||||||||
\(722\) | 6.24865e6 | 0.446111 | ||||||||
\(723\) | 8.03306e6 | 0.571525 | ||||||||
\(724\) | 6.03478e6 | 0.427873 | ||||||||
\(725\) | 6.86159e6 | 0.484819 | ||||||||
\(726\) | −5.66824e6 | −0.399123 | ||||||||
\(727\) | −9.79485e6 | −0.687324 | −0.343662 | − | 0.939093i | \(-0.611667\pi\) | ||||
−0.343662 | + | 0.939093i | \(0.611667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −6.74731e6 | −0.468623 | ||||||||
\(731\) | −5.51282e6 | −0.381576 | ||||||||
\(732\) | 4.47696e6 | 0.308820 | ||||||||
\(733\) | −4.07584e6 | −0.280193 | −0.140096 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140096 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(734\) | −64928.0 | −0.00444828 | ||||||||
\(735\) | −8.41639e6 | −0.574655 | ||||||||
\(736\) | −614400. | −0.0418077 | ||||||||
\(737\) | 1.00824e6 | 0.0683747 | ||||||||
\(738\) | 6.21886e6 | 0.420310 | ||||||||
\(739\) | 1.65709e7 | 1.11618 | 0.558089 | − | 0.829781i | \(-0.311535\pi\) | ||||
0.558089 | + | 0.829781i | \(0.311535\pi\) | |||||||
\(740\) | 8.93165e6 | 0.599587 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.20113e7 | −1.46769 | ||||||||
\(743\) | −1.44141e7 | −0.957892 | −0.478946 | − | 0.877844i | \(-0.658981\pi\) | ||||
−0.478946 | + | 0.877844i | \(0.658981\pi\) | |||||||
\(744\) | 2.06899e6 | 0.137033 | ||||||||
\(745\) | −1.94396e6 | −0.128321 | ||||||||
\(746\) | −1.17442e6 | −0.0772641 | ||||||||
\(747\) | 523908. | 0.0343521 | ||||||||
\(748\) | −397440. | −0.0259727 | ||||||||
\(749\) | −4.01259e7 | −2.61349 | ||||||||
\(750\) | −4.50014e6 | −0.292128 | ||||||||
\(751\) | 1.67944e7 | 1.08659 | 0.543295 | − | 0.839542i | \(-0.317177\pi\) | ||||
0.543295 | + | 0.839542i | \(0.317177\pi\) | |||||||
\(752\) | 5.03808e6 | 0.324878 | ||||||||
\(753\) | 991116. | 0.0636997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.34556e7 | 0.859081 | ||||||||
\(756\) | 2.05286e6 | 0.130634 | ||||||||
\(757\) | 1.32943e7 | 0.843188 | 0.421594 | − | 0.906785i | \(-0.361471\pi\) | ||||
0.421594 | + | 0.906785i | \(0.361471\pi\) | |||||||
\(758\) | 1.27205e7 | 0.804137 | ||||||||
\(759\) | −324000. | −0.0204146 | ||||||||
\(760\) | 4.03814e6 | 0.253599 | ||||||||
\(761\) | 2.14786e6 | 0.134445 | 0.0672225 | − | 0.997738i | \(-0.478586\pi\) | ||||
0.0672225 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(762\) | 6.22800e6 | 0.388563 | ||||||||
\(763\) | −1.50128e6 | −0.0933577 | ||||||||
\(764\) | −4.24550e6 | −0.263145 | ||||||||
\(765\) | −2.21324e6 | −0.136734 | ||||||||
\(766\) | −1.19194e7 | −0.733975 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.31059e7 | 0.799193 | 0.399596 | − | 0.916691i | \(-0.369150\pi\) | ||||
0.399596 | + | 0.916691i | \(0.369150\pi\) | |||||||
\(770\) | 2.78784e6 | 0.169450 | ||||||||
\(771\) | −1.26722e6 | −0.0767742 | ||||||||
\(772\) | −4.72477e6 | −0.285323 | ||||||||
\(773\) | 2.37154e7 | 1.42752 | 0.713759 | − | 0.700392i | \(-0.246991\pi\) | ||||
0.713759 | + | 0.700392i | \(0.246991\pi\) | |||||||
\(774\) | −4.31438e6 | −0.258861 | ||||||||
\(775\) | 4.42175e6 | 0.264448 | ||||||||
\(776\) | 1.06292e7 | 0.633648 | ||||||||
\(777\) | 1.33975e7 | 0.796105 | ||||||||
\(778\) | −1.38391e7 | −0.819707 | ||||||||
\(779\) | 1.83495e7 | 1.08338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −367200. | −0.0215415 | ||||||||
\(782\) | 993600. | 0.0581025 | ||||||||
\(783\) | −4.06345e6 | −0.236859 | ||||||||
\(784\) | 3.62726e6 | 0.210760 | ||||||||
\(785\) | 8.98537e6 | 0.520430 | ||||||||
\(786\) | 5.44536e6 | 0.314391 | ||||||||
\(787\) | 8.40048e6 | 0.483468 | 0.241734 | − | 0.970343i | \(-0.422284\pi\) | ||||
0.241734 | + | 0.970343i | \(0.422284\pi\) | |||||||
\(788\) | −3.22070e6 | −0.184772 | ||||||||
\(789\) | 8.44884e6 | 0.483175 | ||||||||
\(790\) | −1.96437e7 | −1.11984 | ||||||||
\(791\) | 3.43971e7 | 1.95470 | ||||||||
\(792\) | −311040. | −0.0176199 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.56166e7 | −0.879097 | ||||||||
\(795\) | 1.85720e7 | 1.04218 | ||||||||
\(796\) | 1.04392e7 | 0.583960 | ||||||||
\(797\) | 5.41023e6 | 0.301696 | 0.150848 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150848 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(798\) | 6.05722e6 | 0.336718 | ||||||||
\(799\) | −8.14752e6 | −0.451501 | ||||||||
\(800\) | −1.26054e6 | −0.0696359 | ||||||||
\(801\) | 2.65210e6 | 0.146052 | ||||||||
\(802\) | 2.17646e7 | 1.19485 | ||||||||
\(803\) | 1.53348e6 | 0.0839246 | ||||||||
\(804\) | −2.41978e6 | −0.132019 | ||||||||
\(805\) | −6.96960e6 | −0.379069 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00306e7 | 0.542177 | ||||||||
\(808\) | 1.40813e6 | 0.0758776 | ||||||||
\(809\) | −2.60777e7 | −1.40087 | −0.700436 | − | 0.713715i | \(-0.747011\pi\) | ||||
−0.700436 | + | 0.713715i | \(0.747011\pi\) | |||||||
\(810\) | −1.73210e6 | −0.0927601 | ||||||||
\(811\) | −1.90021e7 | −1.01449 | −0.507247 | − | 0.861800i | \(-0.669337\pi\) | ||||
−0.507247 | + | 0.861800i | \(0.669337\pi\) | |||||||
\(812\) | −1.56964e7 | −0.835429 | ||||||||
\(813\) | 5.10934e6 | 0.271105 | ||||||||
\(814\) | −2.02992e6 | −0.107379 | ||||||||
\(815\) | 1.12942e7 | 0.595608 | ||||||||
\(816\) | 953856. | 0.0501484 | ||||||||
\(817\) | −1.27301e7 | −0.667231 | ||||||||
\(818\) | 7.87978e6 | 0.411748 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.02689e7 | −1.05268 | ||||||||
\(821\) | 3.10173e7 | 1.60600 | 0.803001 | − | 0.595978i | \(-0.203236\pi\) | ||||
0.803001 | + | 0.595978i | \(0.203236\pi\) | |||||||
\(822\) | 4.62434e6 | 0.238710 | ||||||||
\(823\) | −1.56290e7 | −0.804323 | −0.402162 | − | 0.915569i | \(-0.631741\pi\) | ||||
−0.402162 | + | 0.915569i | \(0.631741\pi\) | |||||||
\(824\) | 5.07290e6 | 0.260278 | ||||||||
\(825\) | −664740. | −0.0340030 | ||||||||
\(826\) | −1.85434e7 | −0.945667 | ||||||||
\(827\) | −1.58421e7 | −0.805467 | −0.402733 | − | 0.915317i | \(-0.631940\pi\) | ||||
−0.402733 | + | 0.915317i | \(0.631940\pi\) | |||||||
\(828\) | 777600. | 0.0394167 | ||||||||
\(829\) | 2.06176e6 | 0.104196 | 0.0520980 | − | 0.998642i | \(-0.483409\pi\) | ||||
0.0520980 | + | 0.998642i | \(0.483409\pi\) | |||||||
\(830\) | −1.70755e6 | −0.0860357 | ||||||||
\(831\) | 1.09193e7 | 0.548521 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.86597e6 | −0.292905 | ||||||||
\(834\) | 5.55106e6 | 0.276351 | ||||||||
\(835\) | 4.46292e7 | 2.21515 | ||||||||
\(836\) | −917760. | −0.0454165 | ||||||||
\(837\) | −2.61857e6 | −0.129196 | ||||||||
\(838\) | −556080. | −0.0273544 | ||||||||
\(839\) | −3.03900e7 | −1.49048 | −0.745240 | − | 0.666796i | \(-0.767665\pi\) | ||||
−0.745240 | + | 0.666796i | \(0.767665\pi\) | |||||||
\(840\) | −6.69082e6 | −0.327176 | ||||||||
\(841\) | 1.05583e7 | 0.514760 | ||||||||
\(842\) | 1.73097e7 | 0.841414 | ||||||||
\(843\) | 6.18964e6 | 0.299983 | ||||||||
\(844\) | −1.83530e7 | −0.886850 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.37632e6 | −0.306298 | ||||||||
\(847\) | 2.77114e7 | 1.32724 | ||||||||
\(848\) | −8.00410e6 | −0.382228 | ||||||||
\(849\) | 7.47817e6 | 0.356062 | ||||||||
\(850\) | 2.03854e6 | 0.0967768 | ||||||||
\(851\) | 5.07480e6 | 0.240212 | ||||||||
\(852\) | 881280. | 0.0415925 | ||||||||
\(853\) | 2.97738e7 | 1.40108 | 0.700538 | − | 0.713615i | \(-0.252944\pi\) | ||||
0.700538 | + | 0.713615i | \(0.252944\pi\) | |||||||
\(854\) | −2.18874e7 | −1.02695 | ||||||||
\(855\) | −5.11078e6 | −0.239096 | ||||||||
\(856\) | −1.45912e7 | −0.680624 | ||||||||
\(857\) | 8.64100e6 | 0.401894 | 0.200947 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200947 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.35663e7 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(860\) | 1.40617e7 | 0.648323 | ||||||||
\(861\) | −3.04033e7 | −1.39770 | ||||||||
\(862\) | −1.11974e7 | −0.513276 | ||||||||
\(863\) | −3.90191e7 | −1.78341 | −0.891703 | − | 0.452621i | \(-0.850489\pi\) | ||||
−0.891703 | + | 0.452621i | \(0.850489\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 8.78843e6 | 0.399366 | ||||||||
\(866\) | 2.36097e7 | 1.06978 | ||||||||
\(867\) | 1.12361e7 | 0.507656 | ||||||||
\(868\) | −1.01151e7 | −0.455690 | ||||||||
\(869\) | 4.46448e6 | 0.200549 | ||||||||
\(870\) | 1.32438e7 | 0.593219 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −545920. | −0.0243130 | ||||||||
\(873\) | −1.34526e7 | −0.597409 | ||||||||
\(874\) | 2.29440e6 | 0.101599 | ||||||||
\(875\) | 2.20007e7 | 0.971441 | ||||||||
\(876\) | −3.68035e6 | −0.162043 | ||||||||
\(877\) | 1.81382e7 | 0.796333 | 0.398166 | − | 0.917313i | \(-0.369647\pi\) | ||||
0.398166 | + | 0.917313i | \(0.369647\pi\) | |||||||
\(878\) | 1.78605e6 | 0.0781910 | ||||||||
\(879\) | −1.18136e7 | −0.515717 | ||||||||
\(880\) | 1.01376e6 | 0.0441294 | ||||||||
\(881\) | 3.05312e7 | 1.32527 | 0.662634 | − | 0.748943i | \(-0.269438\pi\) | ||||
0.662634 | + | 0.748943i | \(0.269438\pi\) | |||||||
\(882\) | −4.59076e6 | −0.198707 | ||||||||
\(883\) | −4.35533e7 | −1.87983 | −0.939916 | − | 0.341405i | \(-0.889097\pi\) | ||||
−0.939916 | + | 0.341405i | \(0.889097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.56460e7 | 0.671497 | ||||||||
\(886\) | −1.39810e7 | −0.598348 | ||||||||
\(887\) | −1.34152e7 | −0.572515 | −0.286257 | − | 0.958153i | \(-0.592411\pi\) | ||||
−0.286257 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(888\) | 4.87181e6 | 0.207328 | ||||||||
\(889\) | −3.04480e7 | −1.29212 | ||||||||
\(890\) | −8.64389e6 | −0.365792 | ||||||||
\(891\) | 393660. | 0.0166122 | ||||||||
\(892\) | −1.12314e7 | −0.472629 | ||||||||
\(893\) | −1.88141e7 | −0.789504 | ||||||||
\(894\) | −1.06034e6 | −0.0443714 | ||||||||
\(895\) | −4.57641e7 | −1.90971 | ||||||||
\(896\) | 2.88358e6 | 0.119995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.82450e6 | −0.199647 | ||||||||
\(899\) | 2.00218e7 | 0.826236 | ||||||||
\(900\) | 1.59538e6 | 0.0656533 | ||||||||
\(901\) | 1.29441e7 | 0.531203 | ||||||||
\(902\) | 4.60656e6 | 0.188521 | ||||||||
\(903\) | 2.10925e7 | 0.860815 | ||||||||
\(904\) | 1.25080e7 | 0.509059 | ||||||||
\(905\) | 2.48935e7 | 1.01033 | ||||||||
\(906\) | 7.33939e6 | 0.297057 | ||||||||
\(907\) | 3.10816e6 | 0.125454 | 0.0627272 | − | 0.998031i | \(-0.480020\pi\) | ||||
0.0627272 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(908\) | −1.97777e7 | −0.796089 | ||||||||
\(909\) | −1.78216e6 | −0.0715381 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.19035e6 | 0.0475203 | 0.0237602 | − | 0.999718i | \(-0.492436\pi\) | ||||
0.0237602 | + | 0.999718i | \(0.492436\pi\) | |||||||
\(912\) | 2.20262e6 | 0.0876906 | ||||||||
\(913\) | 388080. | 0.0154079 | ||||||||
\(914\) | 934184. | 0.0369885 | ||||||||
\(915\) | 1.84675e7 | 0.729213 | ||||||||
\(916\) | −1.69328e6 | −0.0666792 | ||||||||
\(917\) | −2.66218e7 | −1.04547 | ||||||||
\(918\) | −1.20722e6 | −0.0472804 | ||||||||
\(919\) | −4.71996e7 | −1.84353 | −0.921764 | − | 0.387752i | \(-0.873252\pi\) | ||||
−0.921764 | + | 0.387752i | \(0.873252\pi\) | |||||||
\(920\) | −2.53440e6 | −0.0987201 | ||||||||
\(921\) | 1.52120e7 | 0.590931 | ||||||||
\(922\) | −6.97956e6 | −0.270396 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.52064e6 | 0.0585931 | ||||||||
\(925\) | 1.04118e7 | 0.400103 | ||||||||
\(926\) | −1.16715e7 | −0.447299 | ||||||||
\(927\) | −6.42038e6 | −0.245393 | ||||||||
\(928\) | −5.70778e6 | −0.217569 | ||||||||
\(929\) | −1.33595e6 | −0.0507870 | −0.0253935 | − | 0.999678i | \(-0.508084\pi\) | ||||
−0.0253935 | + | 0.999678i | \(0.508084\pi\) | |||||||
\(930\) | 8.53459e6 | 0.323575 | ||||||||
\(931\) | −1.35456e7 | −0.512180 | ||||||||
\(932\) | −7.01885e6 | −0.264683 | ||||||||
\(933\) | 1.35184e7 | 0.508417 | ||||||||
\(934\) | 2.12430e7 | 0.796800 | ||||||||
\(935\) | −1.63944e6 | −0.0613291 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.47238e7 | 0.547861 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(938\) | 1.18300e7 | 0.439014 | ||||||||
\(939\) | −7.29758e6 | −0.270094 | ||||||||
\(940\) | 2.07821e7 | 0.767131 | ||||||||
\(941\) | 2.69196e7 | 0.991049 | 0.495525 | − | 0.868594i | \(-0.334976\pi\) | ||||
0.495525 | + | 0.868594i | \(0.334976\pi\) | |||||||
\(942\) | 4.90111e6 | 0.179956 | ||||||||
\(943\) | −1.15164e7 | −0.421733 | ||||||||
\(944\) | −6.74304e6 | −0.246278 | ||||||||
\(945\) | 8.46806e6 | 0.308464 | ||||||||
\(946\) | −3.19584e6 | −0.116107 | ||||||||
\(947\) | 3.73160e6 | 0.135214 | 0.0676068 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676068 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(948\) | −1.07148e7 | −0.387223 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.70734e6 | 0.169226 | ||||||||
\(951\) | 8.13202e6 | 0.291573 | ||||||||
\(952\) | −4.66330e6 | −0.166763 | ||||||||
\(953\) | 2.18735e7 | 0.780166 | 0.390083 | − | 0.920780i | \(-0.372446\pi\) | ||||
0.390083 | + | 0.920780i | \(0.372446\pi\) | |||||||
\(954\) | 1.01302e7 | 0.360368 | ||||||||
\(955\) | −1.75127e7 | −0.621362 | ||||||||
\(956\) | −455424. | −0.0161165 | ||||||||
\(957\) | −3.00996e6 | −0.106238 | ||||||||
\(958\) | 9.37862e6 | 0.330161 | ||||||||
\(959\) | −2.26079e7 | −0.793805 | ||||||||
\(960\) | −2.43302e6 | −0.0852056 | ||||||||
\(961\) | −1.57267e7 | −0.549324 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.84670e7 | 0.641699 | ||||||||
\(964\) | −1.42810e7 | −0.494955 | ||||||||
\(965\) | −1.94897e7 | −0.673730 | ||||||||
\(966\) | −3.80160e6 | −0.131076 | ||||||||
\(967\) | −1.76025e7 | −0.605352 | −0.302676 | − | 0.953093i | \(-0.597880\pi\) | ||||
−0.302676 | + | 0.953093i | \(0.597880\pi\) | |||||||
\(968\) | 1.00769e7 | 0.345650 | ||||||||
\(969\) | −3.56206e6 | −0.121868 | ||||||||
\(970\) | 4.38456e7 | 1.49623 | ||||||||
\(971\) | 1.67317e7 | 0.569497 | 0.284749 | − | 0.958602i | \(-0.408090\pi\) | ||||
0.284749 | + | 0.958602i | \(0.408090\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −2.71385e7 | −0.918975 | ||||||||
\(974\) | 3.92612e7 | 1.32607 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.95904e6 | −0.267446 | ||||||||
\(977\) | −5.55382e7 | −1.86147 | −0.930733 | − | 0.365699i | \(-0.880830\pi\) | ||||
−0.930733 | + | 0.365699i | \(0.880830\pi\) | |||||||
\(978\) | 6.16046e6 | 0.205952 | ||||||||
\(979\) | 1.96452e6 | 0.0655088 | ||||||||
\(980\) | 1.49625e7 | 0.497666 | ||||||||
\(981\) | 690930. | 0.0229225 | ||||||||
\(982\) | 2.37808e7 | 0.786951 | ||||||||
\(983\) | 3.86784e7 | 1.27669 | 0.638344 | − | 0.769751i | \(-0.279620\pi\) | ||||
0.638344 | + | 0.769751i | \(0.279620\pi\) | |||||||
\(984\) | −1.10557e7 | −0.363999 | ||||||||
\(985\) | −1.32854e7 | −0.436299 | ||||||||
\(986\) | 9.23054e6 | 0.302367 | ||||||||
\(987\) | 3.11731e7 | 1.01856 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.98960e6 | 0.259737 | ||||||||
\(990\) | −1.28304e6 | −0.0416056 | ||||||||
\(991\) | 9.58498e6 | 0.310033 | 0.155016 | − | 0.987912i | \(-0.450457\pi\) | ||||
0.155016 | + | 0.987912i | \(0.450457\pi\) | |||||||
\(992\) | −3.67821e6 | −0.118674 | ||||||||
\(993\) | 1.00977e7 | 0.324976 | ||||||||
\(994\) | −4.30848e6 | −0.138311 | ||||||||
\(995\) | 4.30616e7 | 1.37890 | ||||||||
\(996\) | −931392. | −0.0297498 | ||||||||
\(997\) | −1.03650e7 | −0.330242 | −0.165121 | − | 0.986273i | \(-0.552802\pi\) | ||||
−0.165121 | + | 0.986273i | \(0.552802\pi\) | |||||||
\(998\) | 2.59133e7 | 0.823561 | ||||||||
\(999\) | −6.16588e6 | −0.195471 |
(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 | 1014.6.a.c.1.1 | 1 | ||
13.12 | even | 2 | 6.6.a.a.1.1 | ✓ | 1 | ||
39.38 | odd | 2 | 18.6.a.b.1.1 | 1 | |||
52.51 | odd | 2 | 48.6.a.c.1.1 | 1 | |||
65.12 | odd | 4 | 150.6.c.b.49.2 | 2 | |||
65.38 | odd | 4 | 150.6.c.b.49.1 | 2 | |||
65.64 | even | 2 | 150.6.a.d.1.1 | 1 | |||
91.12 | odd | 6 | 294.6.e.a.67.1 | 2 | |||
91.25 | even | 6 | 294.6.e.g.79.1 | 2 | |||
91.38 | odd | 6 | 294.6.e.a.79.1 | 2 | |||
91.51 | even | 6 | 294.6.e.g.67.1 | 2 | |||
91.90 | odd | 2 | 294.6.a.m.1.1 | 1 | |||
104.51 | odd | 2 | 192.6.a.g.1.1 | 1 | |||
104.77 | even | 2 | 192.6.a.o.1.1 | 1 | |||
117.25 | even | 6 | 162.6.c.e.109.1 | 2 | |||
117.38 | odd | 6 | 162.6.c.h.109.1 | 2 | |||
117.77 | odd | 6 | 162.6.c.h.55.1 | 2 | |||
117.103 | even | 6 | 162.6.c.e.55.1 | 2 | |||
143.142 | odd | 2 | 726.6.a.a.1.1 | 1 | |||
156.155 | even | 2 | 144.6.a.j.1.1 | 1 | |||
195.38 | even | 4 | 450.6.c.j.199.2 | 2 | |||
195.77 | even | 4 | 450.6.c.j.199.1 | 2 | |||
195.194 | odd | 2 | 450.6.a.m.1.1 | 1 | |||
208.51 | odd | 4 | 768.6.d.p.385.2 | 2 | |||
208.77 | even | 4 | 768.6.d.c.385.1 | 2 | |||
208.155 | odd | 4 | 768.6.d.p.385.1 | 2 | |||
208.181 | even | 4 | 768.6.d.c.385.2 | 2 | |||
273.272 | even | 2 | 882.6.a.a.1.1 | 1 | |||
312.77 | odd | 2 | 576.6.a.j.1.1 | 1 | |||
312.155 | even | 2 | 576.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.6.a.a.1.1 | ✓ | 1 | 13.12 | even | 2 | ||
18.6.a.b.1.1 | 1 | 39.38 | odd | 2 | |||
48.6.a.c.1.1 | 1 | 52.51 | odd | 2 | |||
144.6.a.j.1.1 | 1 | 156.155 | even | 2 | |||
150.6.a.d.1.1 | 1 | 65.64 | even | 2 | |||
150.6.c.b.49.1 | 2 | 65.38 | odd | 4 | |||
150.6.c.b.49.2 | 2 | 65.12 | odd | 4 | |||
162.6.c.e.55.1 | 2 | 117.103 | even | 6 | |||
162.6.c.e.109.1 | 2 | 117.25 | even | 6 | |||
162.6.c.h.55.1 | 2 | 117.77 | odd | 6 | |||
162.6.c.h.109.1 | 2 | 117.38 | odd | 6 | |||
192.6.a.g.1.1 | 1 | 104.51 | odd | 2 | |||
192.6.a.o.1.1 | 1 | 104.77 | even | 2 | |||
294.6.a.m.1.1 | 1 | 91.90 | odd | 2 | |||
294.6.e.a.67.1 | 2 | 91.12 | odd | 6 | |||
294.6.e.a.79.1 | 2 | 91.38 | odd | 6 | |||
294.6.e.g.67.1 | 2 | 91.51 | even | 6 | |||
294.6.e.g.79.1 | 2 | 91.25 | even | 6 | |||
450.6.a.m.1.1 | 1 | 195.194 | odd | 2 | |||
450.6.c.j.199.1 | 2 | 195.77 | even | 4 | |||
450.6.c.j.199.2 | 2 | 195.38 | even | 4 | |||
576.6.a.i.1.1 | 1 | 312.155 | even | 2 | |||
576.6.a.j.1.1 | 1 | 312.77 | odd | 2 | |||
726.6.a.a.1.1 | 1 | 143.142 | odd | 2 | |||
768.6.d.c.385.1 | 2 | 208.77 | even | 4 | |||
768.6.d.c.385.2 | 2 | 208.181 | even | 4 | |||
768.6.d.p.385.1 | 2 | 208.155 | odd | 4 | |||
768.6.d.p.385.2 | 2 | 208.51 | odd | 4 | |||
882.6.a.a.1.1 | 1 | 273.272 | even | 2 | |||
1014.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial |