Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1694,4,Mod(1,1694)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1694, 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("1694.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1694 = 2 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1694.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: | \(99.9492355497\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1694.1 |
$q$-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 | ||||||||
\(3\) | −2.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 18.0000 | 1.60997 | 0.804984 | − | 0.593296i | \(-0.202174\pi\) | ||||
0.804984 | + | 0.593296i | \(0.202174\pi\) | |||||||
\(6\) | 4.00000 | 0.272166 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | −36.0000 | −1.13842 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −8.00000 | −0.192450 | ||||||||
\(13\) | −56.0000 | −1.19474 | −0.597369 | − | 0.801966i | \(-0.703787\pi\) | ||||
−0.597369 | + | 0.801966i | \(0.703787\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | −36.0000 | −0.619677 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −36.0000 | −0.513605 | −0.256802 | − | 0.966464i | \(-0.582669\pi\) | ||||
−0.256802 | + | 0.966464i | \(0.582669\pi\) | |||||||
\(18\) | 46.0000 | 0.602350 | ||||||||
\(19\) | 28.0000 | 0.338086 | 0.169043 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169043 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(20\) | 72.0000 | 0.804984 | ||||||||
\(21\) | 14.0000 | 0.145479 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 180.000 | 1.63185 | 0.815926 | − | 0.578156i | \(-0.196228\pi\) | ||||
0.815926 | + | 0.578156i | \(0.196228\pi\) | |||||||
\(24\) | 16.0000 | 0.136083 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | 112.000 | 0.844808 | ||||||||
\(27\) | 100.000 | 0.712778 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 72.0000 | 0.438178 | ||||||||
\(31\) | −334.000 | −1.93510 | −0.967551 | − | 0.252675i | \(-0.918690\pi\) | ||||
−0.967551 | + | 0.252675i | \(0.918690\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 72.0000 | 0.363173 | ||||||||
\(35\) | −126.000 | −0.608511 | ||||||||
\(36\) | −92.0000 | −0.425926 | ||||||||
\(37\) | 386.000 | 1.71508 | 0.857541 | − | 0.514416i | \(-0.171991\pi\) | ||||
0.857541 | + | 0.514416i | \(0.171991\pi\) | |||||||
\(38\) | −56.0000 | −0.239063 | ||||||||
\(39\) | 112.000 | 0.459855 | ||||||||
\(40\) | −144.000 | −0.569210 | ||||||||
\(41\) | 444.000 | 1.69125 | 0.845624 | − | 0.533779i | \(-0.179229\pi\) | ||||
0.845624 | + | 0.533779i | \(0.179229\pi\) | |||||||
\(42\) | −28.0000 | −0.102869 | ||||||||
\(43\) | 316.000 | 1.12069 | 0.560344 | − | 0.828260i | \(-0.310669\pi\) | ||||
0.560344 | + | 0.828260i | \(0.310669\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −414.000 | −1.37146 | ||||||||
\(46\) | −360.000 | −1.15389 | ||||||||
\(47\) | −402.000 | −1.24761 | −0.623806 | − | 0.781580i | \(-0.714414\pi\) | ||||
−0.623806 | + | 0.781580i | \(0.714414\pi\) | |||||||
\(48\) | −32.0000 | −0.0962250 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −398.000 | −1.12571 | ||||||||
\(51\) | 72.0000 | 0.197687 | ||||||||
\(52\) | −224.000 | −0.597369 | ||||||||
\(53\) | −486.000 | −1.25957 | −0.629785 | − | 0.776769i | \(-0.716857\pi\) | ||||
−0.629785 | + | 0.776769i | \(0.716857\pi\) | |||||||
\(54\) | −200.000 | −0.504010 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | −56.0000 | −0.130129 | ||||||||
\(58\) | −108.000 | −0.244502 | ||||||||
\(59\) | −282.000 | −0.622259 | −0.311129 | − | 0.950368i | \(-0.600707\pi\) | ||||
−0.311129 | + | 0.950368i | \(0.600707\pi\) | |||||||
\(60\) | −144.000 | −0.309839 | ||||||||
\(61\) | −380.000 | −0.797607 | −0.398803 | − | 0.917036i | \(-0.630574\pi\) | ||||
−0.398803 | + | 0.917036i | \(0.630574\pi\) | |||||||
\(62\) | 668.000 | 1.36832 | ||||||||
\(63\) | 161.000 | 0.321970 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1008.00 | −1.92349 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 176.000 | 0.320923 | 0.160461 | − | 0.987042i | \(-0.448702\pi\) | ||||
0.160461 | + | 0.987042i | \(0.448702\pi\) | |||||||
\(68\) | −144.000 | −0.256802 | ||||||||
\(69\) | −360.000 | −0.628100 | ||||||||
\(70\) | 252.000 | 0.430282 | ||||||||
\(71\) | −324.000 | −0.541574 | −0.270787 | − | 0.962639i | \(-0.587284\pi\) | ||||
−0.270787 | + | 0.962639i | \(0.587284\pi\) | |||||||
\(72\) | 184.000 | 0.301175 | ||||||||
\(73\) | −800.000 | −1.28264 | −0.641321 | − | 0.767272i | \(-0.721613\pi\) | ||||
−0.641321 | + | 0.767272i | \(0.721613\pi\) | |||||||
\(74\) | −772.000 | −1.21275 | ||||||||
\(75\) | −398.000 | −0.612761 | ||||||||
\(76\) | 112.000 | 0.169043 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −224.000 | −0.325167 | ||||||||
\(79\) | 1144.00 | 1.62924 | 0.814621 | − | 0.579994i | \(-0.196945\pi\) | ||||
0.814621 | + | 0.579994i | \(0.196945\pi\) | |||||||
\(80\) | 288.000 | 0.402492 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | −888.000 | −1.19589 | ||||||||
\(83\) | −468.000 | −0.618912 | −0.309456 | − | 0.950914i | \(-0.600147\pi\) | ||||
−0.309456 | + | 0.950914i | \(0.600147\pi\) | |||||||
\(84\) | 56.0000 | 0.0727393 | ||||||||
\(85\) | −648.000 | −0.826888 | ||||||||
\(86\) | −632.000 | −0.792445 | ||||||||
\(87\) | −108.000 | −0.133090 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −870.000 | −1.03618 | −0.518089 | − | 0.855327i | \(-0.673356\pi\) | ||||
−0.518089 | + | 0.855327i | \(0.673356\pi\) | |||||||
\(90\) | 828.000 | 0.969765 | ||||||||
\(91\) | 392.000 | 0.451569 | ||||||||
\(92\) | 720.000 | 0.815926 | ||||||||
\(93\) | 668.000 | 0.744821 | ||||||||
\(94\) | 804.000 | 0.882194 | ||||||||
\(95\) | 504.000 | 0.544309 | ||||||||
\(96\) | 64.0000 | 0.0680414 | ||||||||
\(97\) | −1330.00 | −1.39218 | −0.696088 | − | 0.717957i | \(-0.745078\pi\) | ||||
−0.696088 | + | 0.717957i | \(0.745078\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 796.000 | 0.796000 | ||||||||
\(101\) | 120.000 | 0.118222 | 0.0591111 | − | 0.998251i | \(-0.481173\pi\) | ||||
0.0591111 | + | 0.998251i | \(0.481173\pi\) | |||||||
\(102\) | −144.000 | −0.139786 | ||||||||
\(103\) | −1210.00 | −1.15752 | −0.578761 | − | 0.815497i | \(-0.696464\pi\) | ||||
−0.578761 | + | 0.815497i | \(0.696464\pi\) | |||||||
\(104\) | 448.000 | 0.422404 | ||||||||
\(105\) | 252.000 | 0.234216 | ||||||||
\(106\) | 972.000 | 0.890651 | ||||||||
\(107\) | −1236.00 | −1.11672 | −0.558358 | − | 0.829600i | \(-0.688568\pi\) | ||||
−0.558358 | + | 0.829600i | \(0.688568\pi\) | |||||||
\(108\) | 400.000 | 0.356389 | ||||||||
\(109\) | 694.000 | 0.609845 | 0.304923 | − | 0.952377i | \(-0.401369\pi\) | ||||
0.304923 | + | 0.952377i | \(0.401369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −772.000 | −0.660135 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | 978.000 | 0.814181 | 0.407091 | − | 0.913388i | \(-0.366543\pi\) | ||||
0.407091 | + | 0.913388i | \(0.366543\pi\) | |||||||
\(114\) | 112.000 | 0.0920154 | ||||||||
\(115\) | 3240.00 | 2.62723 | ||||||||
\(116\) | 216.000 | 0.172889 | ||||||||
\(117\) | 1288.00 | 1.01774 | ||||||||
\(118\) | 564.000 | 0.440003 | ||||||||
\(119\) | 252.000 | 0.194124 | ||||||||
\(120\) | 288.000 | 0.219089 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 760.000 | 0.563993 | ||||||||
\(123\) | −888.000 | −0.650961 | ||||||||
\(124\) | −1336.00 | −0.967551 | ||||||||
\(125\) | 1332.00 | 0.953102 | ||||||||
\(126\) | −322.000 | −0.227667 | ||||||||
\(127\) | 1216.00 | 0.849626 | 0.424813 | − | 0.905281i | \(-0.360340\pi\) | ||||
0.424813 | + | 0.905281i | \(0.360340\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −632.000 | −0.431353 | ||||||||
\(130\) | 2016.00 | 1.36011 | ||||||||
\(131\) | −1680.00 | −1.12048 | −0.560238 | − | 0.828332i | \(-0.689290\pi\) | ||||
−0.560238 | + | 0.828332i | \(0.689290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −196.000 | −0.127785 | ||||||||
\(134\) | −352.000 | −0.226927 | ||||||||
\(135\) | 1800.00 | 1.14755 | ||||||||
\(136\) | 288.000 | 0.181587 | ||||||||
\(137\) | 1062.00 | 0.662283 | 0.331142 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331142 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(138\) | 720.000 | 0.444134 | ||||||||
\(139\) | 508.000 | 0.309986 | 0.154993 | − | 0.987916i | \(-0.450465\pi\) | ||||
0.154993 | + | 0.987916i | \(0.450465\pi\) | |||||||
\(140\) | −504.000 | −0.304256 | ||||||||
\(141\) | 804.000 | 0.480206 | ||||||||
\(142\) | 648.000 | 0.382950 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −368.000 | −0.212963 | ||||||||
\(145\) | 972.000 | 0.556691 | ||||||||
\(146\) | 1600.00 | 0.906965 | ||||||||
\(147\) | −98.0000 | −0.0549857 | ||||||||
\(148\) | 1544.00 | 0.857541 | ||||||||
\(149\) | −2598.00 | −1.42843 | −0.714216 | − | 0.699925i | \(-0.753217\pi\) | ||||
−0.714216 | + | 0.699925i | \(0.753217\pi\) | |||||||
\(150\) | 796.000 | 0.433288 | ||||||||
\(151\) | −2648.00 | −1.42709 | −0.713547 | − | 0.700607i | \(-0.752912\pi\) | ||||
−0.713547 | + | 0.700607i | \(0.752912\pi\) | |||||||
\(152\) | −224.000 | −0.119532 | ||||||||
\(153\) | 828.000 | 0.437515 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6012.00 | −3.11545 | ||||||||
\(156\) | 448.000 | 0.229928 | ||||||||
\(157\) | −790.000 | −0.401585 | −0.200793 | − | 0.979634i | \(-0.564352\pi\) | ||||
−0.200793 | + | 0.979634i | \(0.564352\pi\) | |||||||
\(158\) | −2288.00 | −1.15205 | ||||||||
\(159\) | 972.000 | 0.484809 | ||||||||
\(160\) | −576.000 | −0.284605 | ||||||||
\(161\) | −1260.00 | −0.616782 | ||||||||
\(162\) | −842.000 | −0.408357 | ||||||||
\(163\) | −160.000 | −0.0768845 | −0.0384422 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384422 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(164\) | 1776.00 | 0.845624 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 936.000 | 0.437637 | ||||||||
\(167\) | −264.000 | −0.122329 | −0.0611645 | − | 0.998128i | \(-0.519481\pi\) | ||||
−0.0611645 | + | 0.998128i | \(0.519481\pi\) | |||||||
\(168\) | −112.000 | −0.0514344 | ||||||||
\(169\) | 939.000 | 0.427401 | ||||||||
\(170\) | 1296.00 | 0.584698 | ||||||||
\(171\) | −644.000 | −0.287999 | ||||||||
\(172\) | 1264.00 | 0.560344 | ||||||||
\(173\) | −1632.00 | −0.717218 | −0.358609 | − | 0.933488i | \(-0.616749\pi\) | ||||
−0.358609 | + | 0.933488i | \(0.616749\pi\) | |||||||
\(174\) | 216.000 | 0.0941087 | ||||||||
\(175\) | −1393.00 | −0.601719 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 564.000 | 0.239508 | ||||||||
\(178\) | 1740.00 | 0.732688 | ||||||||
\(179\) | −708.000 | −0.295634 | −0.147817 | − | 0.989015i | \(-0.547225\pi\) | ||||
−0.147817 | + | 0.989015i | \(0.547225\pi\) | |||||||
\(180\) | −1656.00 | −0.685728 | ||||||||
\(181\) | 902.000 | 0.370415 | 0.185208 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185208 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(182\) | −784.000 | −0.319307 | ||||||||
\(183\) | 760.000 | 0.306999 | ||||||||
\(184\) | −1440.00 | −0.576947 | ||||||||
\(185\) | 6948.00 | 2.76123 | ||||||||
\(186\) | −1336.00 | −0.526668 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1608.00 | −0.623806 | ||||||||
\(189\) | −700.000 | −0.269405 | ||||||||
\(190\) | −1008.00 | −0.384884 | ||||||||
\(191\) | 1824.00 | 0.690995 | 0.345497 | − | 0.938420i | \(-0.387710\pi\) | ||||
0.345497 | + | 0.938420i | \(0.387710\pi\) | |||||||
\(192\) | −128.000 | −0.0481125 | ||||||||
\(193\) | −2090.00 | −0.779490 | −0.389745 | − | 0.920923i | \(-0.627437\pi\) | ||||
−0.389745 | + | 0.920923i | \(0.627437\pi\) | |||||||
\(194\) | 2660.00 | 0.984417 | ||||||||
\(195\) | 2016.00 | 0.740353 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 1602.00 | 0.579380 | 0.289690 | − | 0.957121i | \(-0.406448\pi\) | ||||
0.289690 | + | 0.957121i | \(0.406448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3274.00 | −1.16627 | −0.583135 | − | 0.812375i | \(-0.698174\pi\) | ||||
−0.583135 | + | 0.812375i | \(0.698174\pi\) | |||||||
\(200\) | −1592.00 | −0.562857 | ||||||||
\(201\) | −352.000 | −0.123523 | ||||||||
\(202\) | −240.000 | −0.0835957 | ||||||||
\(203\) | −378.000 | −0.130692 | ||||||||
\(204\) | 288.000 | 0.0988433 | ||||||||
\(205\) | 7992.00 | 2.72286 | ||||||||
\(206\) | 2420.00 | 0.818492 | ||||||||
\(207\) | −4140.00 | −1.39010 | ||||||||
\(208\) | −896.000 | −0.298685 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −504.000 | −0.165616 | ||||||||
\(211\) | 4948.00 | 1.61438 | 0.807190 | − | 0.590291i | \(-0.200987\pi\) | ||||
0.807190 | + | 0.590291i | \(0.200987\pi\) | |||||||
\(212\) | −1944.00 | −0.629785 | ||||||||
\(213\) | 648.000 | 0.208452 | ||||||||
\(214\) | 2472.00 | 0.789638 | ||||||||
\(215\) | 5688.00 | 1.80427 | ||||||||
\(216\) | −800.000 | −0.252005 | ||||||||
\(217\) | 2338.00 | 0.731400 | ||||||||
\(218\) | −1388.00 | −0.431226 | ||||||||
\(219\) | 1600.00 | 0.493689 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2016.00 | 0.613624 | ||||||||
\(222\) | 1544.00 | 0.466786 | ||||||||
\(223\) | 2342.00 | 0.703282 | 0.351641 | − | 0.936135i | \(-0.385624\pi\) | ||||
0.351641 | + | 0.936135i | \(0.385624\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −4577.00 | −1.35615 | ||||||||
\(226\) | −1956.00 | −0.575713 | ||||||||
\(227\) | −2064.00 | −0.603491 | −0.301746 | − | 0.953388i | \(-0.597569\pi\) | ||||
−0.301746 | + | 0.953388i | \(0.597569\pi\) | |||||||
\(228\) | −224.000 | −0.0650647 | ||||||||
\(229\) | −1666.00 | −0.480753 | −0.240376 | − | 0.970680i | \(-0.577271\pi\) | ||||
−0.240376 | + | 0.970680i | \(0.577271\pi\) | |||||||
\(230\) | −6480.00 | −1.85773 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −432.000 | −0.122251 | ||||||||
\(233\) | −4158.00 | −1.16910 | −0.584549 | − | 0.811359i | \(-0.698728\pi\) | ||||
−0.584549 | + | 0.811359i | \(0.698728\pi\) | |||||||
\(234\) | −2576.00 | −0.719651 | ||||||||
\(235\) | −7236.00 | −2.00862 | ||||||||
\(236\) | −1128.00 | −0.311129 | ||||||||
\(237\) | −2288.00 | −0.627095 | ||||||||
\(238\) | −504.000 | −0.137267 | ||||||||
\(239\) | −72.0000 | −0.0194866 | −0.00974329 | − | 0.999953i | \(-0.503101\pi\) | ||||
−0.00974329 | + | 0.999953i | \(0.503101\pi\) | |||||||
\(240\) | −576.000 | −0.154919 | ||||||||
\(241\) | −6860.00 | −1.83357 | −0.916787 | − | 0.399376i | \(-0.869227\pi\) | ||||
−0.916787 | + | 0.399376i | \(0.869227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3542.00 | −0.935059 | ||||||||
\(244\) | −1520.00 | −0.398803 | ||||||||
\(245\) | 882.000 | 0.229996 | ||||||||
\(246\) | 1776.00 | 0.460299 | ||||||||
\(247\) | −1568.00 | −0.403925 | ||||||||
\(248\) | 2672.00 | 0.684162 | ||||||||
\(249\) | 936.000 | 0.238219 | ||||||||
\(250\) | −2664.00 | −0.673945 | ||||||||
\(251\) | −150.000 | −0.0377208 | −0.0188604 | − | 0.999822i | \(-0.506004\pi\) | ||||
−0.0188604 | + | 0.999822i | \(0.506004\pi\) | |||||||
\(252\) | 644.000 | 0.160985 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2432.00 | −0.600777 | ||||||||
\(255\) | 1296.00 | 0.318269 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2430.00 | −0.589802 | −0.294901 | − | 0.955528i | \(-0.595287\pi\) | ||||
−0.294901 | + | 0.955528i | \(0.595287\pi\) | |||||||
\(258\) | 1264.00 | 0.305012 | ||||||||
\(259\) | −2702.00 | −0.648240 | ||||||||
\(260\) | −4032.00 | −0.961746 | ||||||||
\(261\) | −1242.00 | −0.294551 | ||||||||
\(262\) | 3360.00 | 0.792296 | ||||||||
\(263\) | −3048.00 | −0.714630 | −0.357315 | − | 0.933984i | \(-0.616308\pi\) | ||||
−0.357315 | + | 0.933984i | \(0.616308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8748.00 | −2.02787 | ||||||||
\(266\) | 392.000 | 0.0903574 | ||||||||
\(267\) | 1740.00 | 0.398825 | ||||||||
\(268\) | 704.000 | 0.160461 | ||||||||
\(269\) | −3834.00 | −0.869008 | −0.434504 | − | 0.900670i | \(-0.643076\pi\) | ||||
−0.434504 | + | 0.900670i | \(0.643076\pi\) | |||||||
\(270\) | −3600.00 | −0.811441 | ||||||||
\(271\) | 3508.00 | 0.786331 | 0.393166 | − | 0.919468i | \(-0.371380\pi\) | ||||
0.393166 | + | 0.919468i | \(0.371380\pi\) | |||||||
\(272\) | −576.000 | −0.128401 | ||||||||
\(273\) | −784.000 | −0.173809 | ||||||||
\(274\) | −2124.00 | −0.468305 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1440.00 | −0.314050 | ||||||||
\(277\) | −8294.00 | −1.79905 | −0.899527 | − | 0.436864i | \(-0.856089\pi\) | ||||
−0.899527 | + | 0.436864i | \(0.856089\pi\) | |||||||
\(278\) | −1016.00 | −0.219193 | ||||||||
\(279\) | 7682.00 | 1.64842 | ||||||||
\(280\) | 1008.00 | 0.215141 | ||||||||
\(281\) | −8022.00 | −1.70303 | −0.851517 | − | 0.524327i | \(-0.824317\pi\) | ||||
−0.851517 | + | 0.524327i | \(0.824317\pi\) | |||||||
\(282\) | −1608.00 | −0.339557 | ||||||||
\(283\) | −392.000 | −0.0823392 | −0.0411696 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411696 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(284\) | −1296.00 | −0.270787 | ||||||||
\(285\) | −1008.00 | −0.209504 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3108.00 | −0.639231 | ||||||||
\(288\) | 736.000 | 0.150588 | ||||||||
\(289\) | −3617.00 | −0.736210 | ||||||||
\(290\) | −1944.00 | −0.393640 | ||||||||
\(291\) | 2660.00 | 0.535849 | ||||||||
\(292\) | −3200.00 | −0.641321 | ||||||||
\(293\) | 2748.00 | 0.547918 | 0.273959 | − | 0.961741i | \(-0.411667\pi\) | ||||
0.273959 | + | 0.961741i | \(0.411667\pi\) | |||||||
\(294\) | 196.000 | 0.0388808 | ||||||||
\(295\) | −5076.00 | −1.00182 | ||||||||
\(296\) | −3088.00 | −0.606373 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5196.00 | 1.01005 | ||||||||
\(299\) | −10080.0 | −1.94964 | ||||||||
\(300\) | −1592.00 | −0.306381 | ||||||||
\(301\) | −2212.00 | −0.423580 | ||||||||
\(302\) | 5296.00 | 1.00911 | ||||||||
\(303\) | −240.000 | −0.0455038 | ||||||||
\(304\) | 448.000 | 0.0845216 | ||||||||
\(305\) | −6840.00 | −1.28412 | ||||||||
\(306\) | −1656.00 | −0.309370 | ||||||||
\(307\) | 3064.00 | 0.569615 | 0.284807 | − | 0.958585i | \(-0.408070\pi\) | ||||
0.284807 | + | 0.958585i | \(0.408070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2420.00 | 0.445531 | ||||||||
\(310\) | 12024.0 | 2.20296 | ||||||||
\(311\) | 4062.00 | 0.740627 | 0.370313 | − | 0.928907i | \(-0.379250\pi\) | ||||
0.370313 | + | 0.928907i | \(0.379250\pi\) | |||||||
\(312\) | −896.000 | −0.162583 | ||||||||
\(313\) | −4870.00 | −0.879453 | −0.439726 | − | 0.898132i | \(-0.644925\pi\) | ||||
−0.439726 | + | 0.898132i | \(0.644925\pi\) | |||||||
\(314\) | 1580.00 | 0.283964 | ||||||||
\(315\) | 2898.00 | 0.518361 | ||||||||
\(316\) | 4576.00 | 0.814621 | ||||||||
\(317\) | 4806.00 | 0.851520 | 0.425760 | − | 0.904836i | \(-0.360007\pi\) | ||||
0.425760 | + | 0.904836i | \(0.360007\pi\) | |||||||
\(318\) | −1944.00 | −0.342812 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1152.00 | 0.201246 | ||||||||
\(321\) | 2472.00 | 0.429824 | ||||||||
\(322\) | 2520.00 | 0.436131 | ||||||||
\(323\) | −1008.00 | −0.173643 | ||||||||
\(324\) | 1684.00 | 0.288752 | ||||||||
\(325\) | −11144.0 | −1.90202 | ||||||||
\(326\) | 320.000 | 0.0543655 | ||||||||
\(327\) | −1388.00 | −0.234730 | ||||||||
\(328\) | −3552.00 | −0.597946 | ||||||||
\(329\) | 2814.00 | 0.471553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6620.00 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | −1872.00 | −0.309456 | ||||||||
\(333\) | −8878.00 | −1.46100 | ||||||||
\(334\) | 528.000 | 0.0864996 | ||||||||
\(335\) | 3168.00 | 0.516676 | ||||||||
\(336\) | 224.000 | 0.0363696 | ||||||||
\(337\) | −1094.00 | −0.176837 | −0.0884184 | − | 0.996083i | \(-0.528181\pi\) | ||||
−0.0884184 | + | 0.996083i | \(0.528181\pi\) | |||||||
\(338\) | −1878.00 | −0.302218 | ||||||||
\(339\) | −1956.00 | −0.313379 | ||||||||
\(340\) | −2592.00 | −0.413444 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1288.00 | 0.203646 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −2528.00 | −0.396223 | ||||||||
\(345\) | −6480.00 | −1.01122 | ||||||||
\(346\) | 3264.00 | 0.507150 | ||||||||
\(347\) | −3468.00 | −0.536519 | −0.268259 | − | 0.963347i | \(-0.586448\pi\) | ||||
−0.268259 | + | 0.963347i | \(0.586448\pi\) | |||||||
\(348\) | −432.000 | −0.0665449 | ||||||||
\(349\) | 8188.00 | 1.25586 | 0.627928 | − | 0.778272i | \(-0.283903\pi\) | ||||
0.627928 | + | 0.778272i | \(0.283903\pi\) | |||||||
\(350\) | 2786.00 | 0.425480 | ||||||||
\(351\) | −5600.00 | −0.851584 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5070.00 | −0.764444 | −0.382222 | − | 0.924070i | \(-0.624841\pi\) | ||||
−0.382222 | + | 0.924070i | \(0.624841\pi\) | |||||||
\(354\) | −1128.00 | −0.169357 | ||||||||
\(355\) | −5832.00 | −0.871917 | ||||||||
\(356\) | −3480.00 | −0.518089 | ||||||||
\(357\) | −504.000 | −0.0747185 | ||||||||
\(358\) | 1416.00 | 0.209044 | ||||||||
\(359\) | −1656.00 | −0.243455 | −0.121727 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121727 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(360\) | 3312.00 | 0.484883 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | −1804.00 | −0.261923 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1568.00 | 0.225784 | ||||||||
\(365\) | −14400.0 | −2.06501 | ||||||||
\(366\) | −1520.00 | −0.217081 | ||||||||
\(367\) | 10166.0 | 1.44594 | 0.722971 | − | 0.690878i | \(-0.242776\pi\) | ||||
0.722971 | + | 0.690878i | \(0.242776\pi\) | |||||||
\(368\) | 2880.00 | 0.407963 | ||||||||
\(369\) | −10212.0 | −1.44069 | ||||||||
\(370\) | −13896.0 | −1.95248 | ||||||||
\(371\) | 3402.00 | 0.476073 | ||||||||
\(372\) | 2672.00 | 0.372411 | ||||||||
\(373\) | 2722.00 | 0.377855 | 0.188927 | − | 0.981991i | \(-0.439499\pi\) | ||||
0.188927 | + | 0.981991i | \(0.439499\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2664.00 | −0.366849 | ||||||||
\(376\) | 3216.00 | 0.441097 | ||||||||
\(377\) | −3024.00 | −0.413114 | ||||||||
\(378\) | 1400.00 | 0.190498 | ||||||||
\(379\) | −5872.00 | −0.795843 | −0.397921 | − | 0.917420i | \(-0.630268\pi\) | ||||
−0.397921 | + | 0.917420i | \(0.630268\pi\) | |||||||
\(380\) | 2016.00 | 0.272154 | ||||||||
\(381\) | −2432.00 | −0.327021 | ||||||||
\(382\) | −3648.00 | −0.488607 | ||||||||
\(383\) | 12330.0 | 1.64500 | 0.822498 | − | 0.568768i | \(-0.192580\pi\) | ||||
0.822498 | + | 0.568768i | \(0.192580\pi\) | |||||||
\(384\) | 256.000 | 0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4180.00 | 0.551182 | ||||||||
\(387\) | −7268.00 | −0.954659 | ||||||||
\(388\) | −5320.00 | −0.696088 | ||||||||
\(389\) | −14586.0 | −1.90113 | −0.950565 | − | 0.310526i | \(-0.899495\pi\) | ||||
−0.950565 | + | 0.310526i | \(0.899495\pi\) | |||||||
\(390\) | −4032.00 | −0.523508 | ||||||||
\(391\) | −6480.00 | −0.838127 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 3360.00 | 0.431271 | ||||||||
\(394\) | −3204.00 | −0.409683 | ||||||||
\(395\) | 20592.0 | 2.62303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1874.00 | 0.236910 | 0.118455 | − | 0.992959i | \(-0.462206\pi\) | ||||
0.118455 | + | 0.992959i | \(0.462206\pi\) | |||||||
\(398\) | 6548.00 | 0.824677 | ||||||||
\(399\) | 392.000 | 0.0491843 | ||||||||
\(400\) | 3184.00 | 0.398000 | ||||||||
\(401\) | 13338.0 | 1.66102 | 0.830509 | − | 0.557006i | \(-0.188050\pi\) | ||||
0.830509 | + | 0.557006i | \(0.188050\pi\) | |||||||
\(402\) | 704.000 | 0.0873441 | ||||||||
\(403\) | 18704.0 | 2.31194 | ||||||||
\(404\) | 480.000 | 0.0591111 | ||||||||
\(405\) | 7578.00 | 0.929763 | ||||||||
\(406\) | 756.000 | 0.0924129 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −576.000 | −0.0698928 | ||||||||
\(409\) | 8200.00 | 0.991354 | 0.495677 | − | 0.868507i | \(-0.334920\pi\) | ||||
0.495677 | + | 0.868507i | \(0.334920\pi\) | |||||||
\(410\) | −15984.0 | −1.92535 | ||||||||
\(411\) | −2124.00 | −0.254913 | ||||||||
\(412\) | −4840.00 | −0.578761 | ||||||||
\(413\) | 1974.00 | 0.235192 | ||||||||
\(414\) | 8280.00 | 0.982946 | ||||||||
\(415\) | −8424.00 | −0.996429 | ||||||||
\(416\) | 1792.00 | 0.211202 | ||||||||
\(417\) | −1016.00 | −0.119314 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7362.00 | −0.858370 | −0.429185 | − | 0.903216i | \(-0.641199\pi\) | ||||
−0.429185 | + | 0.903216i | \(0.641199\pi\) | |||||||
\(420\) | 1008.00 | 0.117108 | ||||||||
\(421\) | −11710.0 | −1.35561 | −0.677803 | − | 0.735243i | \(-0.737068\pi\) | ||||
−0.677803 | + | 0.735243i | \(0.737068\pi\) | |||||||
\(422\) | −9896.00 | −1.14154 | ||||||||
\(423\) | 9246.00 | 1.06278 | ||||||||
\(424\) | 3888.00 | 0.445325 | ||||||||
\(425\) | −7164.00 | −0.817659 | ||||||||
\(426\) | −1296.00 | −0.147398 | ||||||||
\(427\) | 2660.00 | 0.301467 | ||||||||
\(428\) | −4944.00 | −0.558358 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11376.0 | −1.27581 | ||||||||
\(431\) | 936.000 | 0.104607 | 0.0523034 | − | 0.998631i | \(-0.483344\pi\) | ||||
0.0523034 | + | 0.998631i | \(0.483344\pi\) | |||||||
\(432\) | 1600.00 | 0.178195 | ||||||||
\(433\) | 9038.00 | 1.00309 | 0.501546 | − | 0.865131i | \(-0.332765\pi\) | ||||
0.501546 | + | 0.865131i | \(0.332765\pi\) | |||||||
\(434\) | −4676.00 | −0.517178 | ||||||||
\(435\) | −1944.00 | −0.214270 | ||||||||
\(436\) | 2776.00 | 0.304923 | ||||||||
\(437\) | 5040.00 | 0.551707 | ||||||||
\(438\) | −3200.00 | −0.349091 | ||||||||
\(439\) | −1964.00 | −0.213523 | −0.106762 | − | 0.994285i | \(-0.534048\pi\) | ||||
−0.106762 | + | 0.994285i | \(0.534048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1127.00 | −0.121693 | ||||||||
\(442\) | −4032.00 | −0.433897 | ||||||||
\(443\) | 10068.0 | 1.07979 | 0.539893 | − | 0.841734i | \(-0.318465\pi\) | ||||
0.539893 | + | 0.841734i | \(0.318465\pi\) | |||||||
\(444\) | −3088.00 | −0.330068 | ||||||||
\(445\) | −15660.0 | −1.66821 | ||||||||
\(446\) | −4684.00 | −0.497296 | ||||||||
\(447\) | 5196.00 | 0.549804 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 3270.00 | 0.343699 | 0.171849 | − | 0.985123i | \(-0.445026\pi\) | ||||
0.171849 | + | 0.985123i | \(0.445026\pi\) | |||||||
\(450\) | 9154.00 | 0.958942 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3912.00 | 0.407091 | ||||||||
\(453\) | 5296.00 | 0.549289 | ||||||||
\(454\) | 4128.00 | 0.426733 | ||||||||
\(455\) | 7056.00 | 0.727012 | ||||||||
\(456\) | 448.000 | 0.0460077 | ||||||||
\(457\) | 15526.0 | 1.58922 | 0.794612 | − | 0.607117i | \(-0.207674\pi\) | ||||
0.794612 | + | 0.607117i | \(0.207674\pi\) | |||||||
\(458\) | 3332.00 | 0.339944 | ||||||||
\(459\) | −3600.00 | −0.366086 | ||||||||
\(460\) | 12960.0 | 1.31362 | ||||||||
\(461\) | −10548.0 | −1.06566 | −0.532830 | − | 0.846222i | \(-0.678872\pi\) | ||||
−0.532830 | + | 0.846222i | \(0.678872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3796.00 | −0.381026 | −0.190513 | − | 0.981685i | \(-0.561015\pi\) | ||||
−0.190513 | + | 0.981685i | \(0.561015\pi\) | |||||||
\(464\) | 864.000 | 0.0864444 | ||||||||
\(465\) | 12024.0 | 1.19914 | ||||||||
\(466\) | 8316.00 | 0.826677 | ||||||||
\(467\) | 7122.00 | 0.705711 | 0.352855 | − | 0.935678i | \(-0.385211\pi\) | ||||
0.352855 | + | 0.935678i | \(0.385211\pi\) | |||||||
\(468\) | 5152.00 | 0.508870 | ||||||||
\(469\) | −1232.00 | −0.121297 | ||||||||
\(470\) | 14472.0 | 1.42031 | ||||||||
\(471\) | 1580.00 | 0.154570 | ||||||||
\(472\) | 2256.00 | 0.220002 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4576.00 | 0.443423 | ||||||||
\(475\) | 5572.00 | 0.538233 | ||||||||
\(476\) | 1008.00 | 0.0970622 | ||||||||
\(477\) | 11178.0 | 1.07297 | ||||||||
\(478\) | 144.000 | 0.0137791 | ||||||||
\(479\) | −2292.00 | −0.218631 | −0.109315 | − | 0.994007i | \(-0.534866\pi\) | ||||
−0.109315 | + | 0.994007i | \(0.534866\pi\) | |||||||
\(480\) | 1152.00 | 0.109545 | ||||||||
\(481\) | −21616.0 | −2.04907 | ||||||||
\(482\) | 13720.0 | 1.29653 | ||||||||
\(483\) | 2520.00 | 0.237400 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23940.0 | −2.24136 | ||||||||
\(486\) | 7084.00 | 0.661187 | ||||||||
\(487\) | 5132.00 | 0.477522 | 0.238761 | − | 0.971078i | \(-0.423259\pi\) | ||||
0.238761 | + | 0.971078i | \(0.423259\pi\) | |||||||
\(488\) | 3040.00 | 0.281997 | ||||||||
\(489\) | 320.000 | 0.0295928 | ||||||||
\(490\) | −1764.00 | −0.162631 | ||||||||
\(491\) | −4188.00 | −0.384932 | −0.192466 | − | 0.981304i | \(-0.561649\pi\) | ||||
−0.192466 | + | 0.981304i | \(0.561649\pi\) | |||||||
\(492\) | −3552.00 | −0.325481 | ||||||||
\(493\) | −1944.00 | −0.177593 | ||||||||
\(494\) | 3136.00 | 0.285618 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5344.00 | −0.483776 | ||||||||
\(497\) | 2268.00 | 0.204696 | ||||||||
\(498\) | −1872.00 | −0.168446 | ||||||||
\(499\) | 3848.00 | 0.345211 | 0.172605 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172605 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(500\) | 5328.00 | 0.476551 | ||||||||
\(501\) | 528.000 | 0.0470844 | ||||||||
\(502\) | 300.000 | 0.0266726 | ||||||||
\(503\) | 1068.00 | 0.0946715 | 0.0473358 | − | 0.998879i | \(-0.484927\pi\) | ||||
0.0473358 | + | 0.998879i | \(0.484927\pi\) | |||||||
\(504\) | −1288.00 | −0.113833 | ||||||||
\(505\) | 2160.00 | 0.190334 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1878.00 | −0.164507 | ||||||||
\(508\) | 4864.00 | 0.424813 | ||||||||
\(509\) | −6162.00 | −0.536593 | −0.268297 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268297 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(510\) | −2592.00 | −0.225050 | ||||||||
\(511\) | 5600.00 | 0.484793 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2800.00 | 0.240981 | ||||||||
\(514\) | 4860.00 | 0.417053 | ||||||||
\(515\) | −21780.0 | −1.86358 | ||||||||
\(516\) | −2528.00 | −0.215676 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5404.00 | 0.458375 | ||||||||
\(519\) | 3264.00 | 0.276057 | ||||||||
\(520\) | 8064.00 | 0.680057 | ||||||||
\(521\) | −20946.0 | −1.76135 | −0.880673 | − | 0.473725i | \(-0.842909\pi\) | ||||
−0.880673 | + | 0.473725i | \(0.842909\pi\) | |||||||
\(522\) | 2484.00 | 0.208279 | ||||||||
\(523\) | 4696.00 | 0.392623 | 0.196311 | − | 0.980542i | \(-0.437104\pi\) | ||||
0.196311 | + | 0.980542i | \(0.437104\pi\) | |||||||
\(524\) | −6720.00 | −0.560238 | ||||||||
\(525\) | 2786.00 | 0.231602 | ||||||||
\(526\) | 6096.00 | 0.505320 | ||||||||
\(527\) | 12024.0 | 0.993878 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20233.0 | 1.66294 | ||||||||
\(530\) | 17496.0 | 1.43392 | ||||||||
\(531\) | 6486.00 | 0.530072 | ||||||||
\(532\) | −784.000 | −0.0638923 | ||||||||
\(533\) | −24864.0 | −2.02060 | ||||||||
\(534\) | −3480.00 | −0.282012 | ||||||||
\(535\) | −22248.0 | −1.79788 | ||||||||
\(536\) | −1408.00 | −0.113463 | ||||||||
\(537\) | 1416.00 | 0.113789 | ||||||||
\(538\) | 7668.00 | 0.614481 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7200.00 | 0.573775 | ||||||||
\(541\) | −19358.0 | −1.53838 | −0.769192 | − | 0.639018i | \(-0.779341\pi\) | ||||
−0.769192 | + | 0.639018i | \(0.779341\pi\) | |||||||
\(542\) | −7016.00 | −0.556020 | ||||||||
\(543\) | −1804.00 | −0.142573 | ||||||||
\(544\) | 1152.00 | 0.0907934 | ||||||||
\(545\) | 12492.0 | 0.981832 | ||||||||
\(546\) | 1568.00 | 0.122901 | ||||||||
\(547\) | −18020.0 | −1.40855 | −0.704277 | − | 0.709925i | \(-0.748729\pi\) | ||||
−0.704277 | + | 0.709925i | \(0.748729\pi\) | |||||||
\(548\) | 4248.00 | 0.331142 | ||||||||
\(549\) | 8740.00 | 0.679443 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1512.00 | 0.116903 | ||||||||
\(552\) | 2880.00 | 0.222067 | ||||||||
\(553\) | −8008.00 | −0.615795 | ||||||||
\(554\) | 16588.0 | 1.27212 | ||||||||
\(555\) | −13896.0 | −1.06280 | ||||||||
\(556\) | 2032.00 | 0.154993 | ||||||||
\(557\) | −14622.0 | −1.11231 | −0.556153 | − | 0.831080i | \(-0.687723\pi\) | ||||
−0.556153 | + | 0.831080i | \(0.687723\pi\) | |||||||
\(558\) | −15364.0 | −1.16561 | ||||||||
\(559\) | −17696.0 | −1.33893 | ||||||||
\(560\) | −2016.00 | −0.152128 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16044.0 | 1.20423 | ||||||||
\(563\) | 2244.00 | 0.167981 | 0.0839905 | − | 0.996467i | \(-0.473233\pi\) | ||||
0.0839905 | + | 0.996467i | \(0.473233\pi\) | |||||||
\(564\) | 3216.00 | 0.240103 | ||||||||
\(565\) | 17604.0 | 1.31081 | ||||||||
\(566\) | 784.000 | 0.0582226 | ||||||||
\(567\) | −2947.00 | −0.218276 | ||||||||
\(568\) | 2592.00 | 0.191475 | ||||||||
\(569\) | 3258.00 | 0.240039 | 0.120020 | − | 0.992772i | \(-0.461704\pi\) | ||||
0.120020 | + | 0.992772i | \(0.461704\pi\) | |||||||
\(570\) | 2016.00 | 0.148142 | ||||||||
\(571\) | 6604.00 | 0.484008 | 0.242004 | − | 0.970275i | \(-0.422195\pi\) | ||||
0.242004 | + | 0.970275i | \(0.422195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3648.00 | −0.265964 | ||||||||
\(574\) | 6216.00 | 0.452005 | ||||||||
\(575\) | 35820.0 | 2.59791 | ||||||||
\(576\) | −1472.00 | −0.106481 | ||||||||
\(577\) | −16594.0 | −1.19726 | −0.598628 | − | 0.801027i | \(-0.704287\pi\) | ||||
−0.598628 | + | 0.801027i | \(0.704287\pi\) | |||||||
\(578\) | 7234.00 | 0.520579 | ||||||||
\(579\) | 4180.00 | 0.300026 | ||||||||
\(580\) | 3888.00 | 0.278346 | ||||||||
\(581\) | 3276.00 | 0.233927 | ||||||||
\(582\) | −5320.00 | −0.378902 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6400.00 | 0.453483 | ||||||||
\(585\) | 23184.0 | 1.63853 | ||||||||
\(586\) | −5496.00 | −0.387436 | ||||||||
\(587\) | −19062.0 | −1.34033 | −0.670164 | − | 0.742213i | \(-0.733776\pi\) | ||||
−0.670164 | + | 0.742213i | \(0.733776\pi\) | |||||||
\(588\) | −392.000 | −0.0274929 | ||||||||
\(589\) | −9352.00 | −0.654232 | ||||||||
\(590\) | 10152.0 | 0.708392 | ||||||||
\(591\) | −3204.00 | −0.223003 | ||||||||
\(592\) | 6176.00 | 0.428770 | ||||||||
\(593\) | 4776.00 | 0.330737 | 0.165368 | − | 0.986232i | \(-0.447119\pi\) | ||||
0.165368 | + | 0.986232i | \(0.447119\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4536.00 | 0.312534 | ||||||||
\(596\) | −10392.0 | −0.714216 | ||||||||
\(597\) | 6548.00 | 0.448897 | ||||||||
\(598\) | 20160.0 | 1.37860 | ||||||||
\(599\) | 7956.00 | 0.542693 | 0.271347 | − | 0.962482i | \(-0.412531\pi\) | ||||
0.271347 | + | 0.962482i | \(0.412531\pi\) | |||||||
\(600\) | 3184.00 | 0.216644 | ||||||||
\(601\) | −14348.0 | −0.973822 | −0.486911 | − | 0.873452i | \(-0.661876\pi\) | ||||
−0.486911 | + | 0.873452i | \(0.661876\pi\) | |||||||
\(602\) | 4424.00 | 0.299516 | ||||||||
\(603\) | −4048.00 | −0.273379 | ||||||||
\(604\) | −10592.0 | −0.713547 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 480.000 | 0.0321760 | ||||||||
\(607\) | −24488.0 | −1.63746 | −0.818729 | − | 0.574180i | \(-0.805321\pi\) | ||||
−0.818729 | + | 0.574180i | \(0.805321\pi\) | |||||||
\(608\) | −896.000 | −0.0597658 | ||||||||
\(609\) | 756.000 | 0.0503032 | ||||||||
\(610\) | 13680.0 | 0.908011 | ||||||||
\(611\) | 22512.0 | 1.49057 | ||||||||
\(612\) | 3312.00 | 0.218758 | ||||||||
\(613\) | 19654.0 | 1.29497 | 0.647486 | − | 0.762078i | \(-0.275821\pi\) | ||||
0.647486 | + | 0.762078i | \(0.275821\pi\) | |||||||
\(614\) | −6128.00 | −0.402778 | ||||||||
\(615\) | −15984.0 | −1.04803 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2694.00 | 0.175780 | 0.0878901 | − | 0.996130i | \(-0.471988\pi\) | ||||
0.0878901 | + | 0.996130i | \(0.471988\pi\) | |||||||
\(618\) | −4840.00 | −0.315038 | ||||||||
\(619\) | 10178.0 | 0.660886 | 0.330443 | − | 0.943826i | \(-0.392802\pi\) | ||||
0.330443 | + | 0.943826i | \(0.392802\pi\) | |||||||
\(620\) | −24048.0 | −1.55773 | ||||||||
\(621\) | 18000.0 | 1.16315 | ||||||||
\(622\) | −8124.00 | −0.523702 | ||||||||
\(623\) | 6090.00 | 0.391638 | ||||||||
\(624\) | 1792.00 | 0.114964 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 9740.00 | 0.621867 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3160.00 | −0.200793 | ||||||||
\(629\) | −13896.0 | −0.880874 | ||||||||
\(630\) | −5796.00 | −0.366537 | ||||||||
\(631\) | −7648.00 | −0.482507 | −0.241254 | − | 0.970462i | \(-0.577559\pi\) | ||||
−0.241254 | + | 0.970462i | \(0.577559\pi\) | |||||||
\(632\) | −9152.00 | −0.576024 | ||||||||
\(633\) | −9896.00 | −0.621375 | ||||||||
\(634\) | −9612.00 | −0.602116 | ||||||||
\(635\) | 21888.0 | 1.36787 | ||||||||
\(636\) | 3888.00 | 0.242404 | ||||||||
\(637\) | −2744.00 | −0.170677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7452.00 | 0.461340 | ||||||||
\(640\) | −2304.00 | −0.142302 | ||||||||
\(641\) | 270.000 | 0.0166371 | 0.00831853 | − | 0.999965i | \(-0.497352\pi\) | ||||
0.00831853 | + | 0.999965i | \(0.497352\pi\) | |||||||
\(642\) | −4944.00 | −0.303932 | ||||||||
\(643\) | 16250.0 | 0.996637 | 0.498318 | − | 0.866994i | \(-0.333951\pi\) | ||||
0.498318 | + | 0.866994i | \(0.333951\pi\) | |||||||
\(644\) | −5040.00 | −0.308391 | ||||||||
\(645\) | −11376.0 | −0.694464 | ||||||||
\(646\) | 2016.00 | 0.122784 | ||||||||
\(647\) | 10242.0 | 0.622341 | 0.311170 | − | 0.950354i | \(-0.399279\pi\) | ||||
0.311170 | + | 0.950354i | \(0.399279\pi\) | |||||||
\(648\) | −3368.00 | −0.204178 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 22288.0 | 1.34493 | ||||||||
\(651\) | −4676.00 | −0.281516 | ||||||||
\(652\) | −640.000 | −0.0384422 | ||||||||
\(653\) | −17322.0 | −1.03807 | −0.519037 | − | 0.854752i | \(-0.673709\pi\) | ||||
−0.519037 | + | 0.854752i | \(0.673709\pi\) | |||||||
\(654\) | 2776.00 | 0.165979 | ||||||||
\(655\) | −30240.0 | −1.80393 | ||||||||
\(656\) | 7104.00 | 0.422812 | ||||||||
\(657\) | 18400.0 | 1.09262 | ||||||||
\(658\) | −5628.00 | −0.333438 | ||||||||
\(659\) | −11676.0 | −0.690186 | −0.345093 | − | 0.938569i | \(-0.612153\pi\) | ||||
−0.345093 | + | 0.938569i | \(0.612153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20710.0 | −1.21865 | −0.609323 | − | 0.792922i | \(-0.708559\pi\) | ||||
−0.609323 | + | 0.792922i | \(0.708559\pi\) | |||||||
\(662\) | −13240.0 | −0.777322 | ||||||||
\(663\) | −4032.00 | −0.236184 | ||||||||
\(664\) | 3744.00 | 0.218818 | ||||||||
\(665\) | −3528.00 | −0.205729 | ||||||||
\(666\) | 17756.0 | 1.03308 | ||||||||
\(667\) | 9720.00 | 0.564258 | ||||||||
\(668\) | −1056.00 | −0.0611645 | ||||||||
\(669\) | −4684.00 | −0.270693 | ||||||||
\(670\) | −6336.00 | −0.365345 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −448.000 | −0.0257172 | ||||||||
\(673\) | 10354.0 | 0.593042 | 0.296521 | − | 0.955026i | \(-0.404173\pi\) | ||||
0.296521 | + | 0.955026i | \(0.404173\pi\) | |||||||
\(674\) | 2188.00 | 0.125042 | ||||||||
\(675\) | 19900.0 | 1.13474 | ||||||||
\(676\) | 3756.00 | 0.213701 | ||||||||
\(677\) | 10920.0 | 0.619926 | 0.309963 | − | 0.950749i | \(-0.399683\pi\) | ||||
0.309963 | + | 0.950749i | \(0.399683\pi\) | |||||||
\(678\) | 3912.00 | 0.221592 | ||||||||
\(679\) | 9310.00 | 0.526193 | ||||||||
\(680\) | 5184.00 | 0.292349 | ||||||||
\(681\) | 4128.00 | 0.232284 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27804.0 | 1.55767 | 0.778836 | − | 0.627227i | \(-0.215810\pi\) | ||||
0.778836 | + | 0.627227i | \(0.215810\pi\) | |||||||
\(684\) | −2576.00 | −0.144000 | ||||||||
\(685\) | 19116.0 | 1.06626 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 3332.00 | 0.185042 | ||||||||
\(688\) | 5056.00 | 0.280172 | ||||||||
\(689\) | 27216.0 | 1.50486 | ||||||||
\(690\) | 12960.0 | 0.715042 | ||||||||
\(691\) | −25834.0 | −1.42225 | −0.711123 | − | 0.703068i | \(-0.751813\pi\) | ||||
−0.711123 | + | 0.703068i | \(0.751813\pi\) | |||||||
\(692\) | −6528.00 | −0.358609 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6936.00 | 0.379376 | ||||||||
\(695\) | 9144.00 | 0.499067 | ||||||||
\(696\) | 864.000 | 0.0470544 | ||||||||
\(697\) | −15984.0 | −0.868633 | ||||||||
\(698\) | −16376.0 | −0.888024 | ||||||||
\(699\) | 8316.00 | 0.449986 | ||||||||
\(700\) | −5572.00 | −0.300860 | ||||||||
\(701\) | 10590.0 | 0.570583 | 0.285292 | − | 0.958441i | \(-0.407910\pi\) | ||||
0.285292 | + | 0.958441i | \(0.407910\pi\) | |||||||
\(702\) | 11200.0 | 0.602161 | ||||||||
\(703\) | 10808.0 | 0.579846 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14472.0 | 0.773116 | ||||||||
\(706\) | 10140.0 | 0.540544 | ||||||||
\(707\) | −840.000 | −0.0446838 | ||||||||
\(708\) | 2256.00 | 0.119754 | ||||||||
\(709\) | −6802.00 | −0.360302 | −0.180151 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180151 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(710\) | 11664.0 | 0.616538 | ||||||||
\(711\) | −26312.0 | −1.38787 | ||||||||
\(712\) | 6960.00 | 0.366344 | ||||||||
\(713\) | −60120.0 | −3.15780 | ||||||||
\(714\) | 1008.00 | 0.0528340 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2832.00 | −0.147817 | ||||||||
\(717\) | 144.000 | 0.00750039 | ||||||||
\(718\) | 3312.00 | 0.172149 | ||||||||
\(719\) | 23010.0 | 1.19350 | 0.596751 | − | 0.802426i | \(-0.296458\pi\) | ||||
0.596751 | + | 0.802426i | \(0.296458\pi\) | |||||||
\(720\) | −6624.00 | −0.342864 | ||||||||
\(721\) | 8470.00 | 0.437502 | ||||||||
\(722\) | 12150.0 | 0.626283 | ||||||||
\(723\) | 13720.0 | 0.705743 | ||||||||
\(724\) | 3608.00 | 0.185208 | ||||||||
\(725\) | 10746.0 | 0.550478 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4682.00 | 0.238853 | 0.119426 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119426 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(728\) | −3136.00 | −0.159654 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 28800.0 | 1.46019 | ||||||||
\(731\) | −11376.0 | −0.575590 | ||||||||
\(732\) | 3040.00 | 0.153499 | ||||||||
\(733\) | 17860.0 | 0.899965 | 0.449982 | − | 0.893037i | \(-0.351430\pi\) | ||||
0.449982 | + | 0.893037i | \(0.351430\pi\) | |||||||
\(734\) | −20332.0 | −1.02244 | ||||||||
\(735\) | −1764.00 | −0.0885253 | ||||||||
\(736\) | −5760.00 | −0.288473 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 20424.0 | 1.01872 | ||||||||
\(739\) | −6860.00 | −0.341474 | −0.170737 | − | 0.985317i | \(-0.554615\pi\) | ||||
−0.170737 | + | 0.985317i | \(0.554615\pi\) | |||||||
\(740\) | 27792.0 | 1.38061 | ||||||||
\(741\) | 3136.00 | 0.155471 | ||||||||
\(742\) | −6804.00 | −0.336634 | ||||||||
\(743\) | 22752.0 | 1.12341 | 0.561703 | − | 0.827339i | \(-0.310147\pi\) | ||||
0.561703 | + | 0.827339i | \(0.310147\pi\) | |||||||
\(744\) | −5344.00 | −0.263334 | ||||||||
\(745\) | −46764.0 | −2.29973 | ||||||||
\(746\) | −5444.00 | −0.267184 | ||||||||
\(747\) | 10764.0 | 0.527221 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8652.00 | 0.422079 | ||||||||
\(750\) | 5328.00 | 0.259401 | ||||||||
\(751\) | 7364.00 | 0.357811 | 0.178906 | − | 0.983866i | \(-0.442744\pi\) | ||||
0.178906 | + | 0.983866i | \(0.442744\pi\) | |||||||
\(752\) | −6432.00 | −0.311903 | ||||||||
\(753\) | 300.000 | 0.0145187 | ||||||||
\(754\) | 6048.00 | 0.292116 | ||||||||
\(755\) | −47664.0 | −2.29758 | ||||||||
\(756\) | −2800.00 | −0.134702 | ||||||||
\(757\) | −34378.0 | −1.65058 | −0.825290 | − | 0.564709i | \(-0.808989\pi\) | ||||
−0.825290 | + | 0.564709i | \(0.808989\pi\) | |||||||
\(758\) | 11744.0 | 0.562746 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4032.00 | −0.192442 | ||||||||
\(761\) | −27456.0 | −1.30786 | −0.653929 | − | 0.756556i | \(-0.726880\pi\) | ||||
−0.653929 | + | 0.756556i | \(0.726880\pi\) | |||||||
\(762\) | 4864.00 | 0.231239 | ||||||||
\(763\) | −4858.00 | −0.230500 | ||||||||
\(764\) | 7296.00 | 0.345497 | ||||||||
\(765\) | 14904.0 | 0.704386 | ||||||||
\(766\) | −24660.0 | −1.16319 | ||||||||
\(767\) | 15792.0 | 0.743437 | ||||||||
\(768\) | −512.000 | −0.0240563 | ||||||||
\(769\) | −7952.00 | −0.372895 | −0.186448 | − | 0.982465i | \(-0.559697\pi\) | ||||
−0.186448 | + | 0.982465i | \(0.559697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4860.00 | 0.227015 | ||||||||
\(772\) | −8360.00 | −0.389745 | ||||||||
\(773\) | −4986.00 | −0.231997 | −0.115999 | − | 0.993249i | \(-0.537007\pi\) | ||||
−0.115999 | + | 0.993249i | \(0.537007\pi\) | |||||||
\(774\) | 14536.0 | 0.675046 | ||||||||
\(775\) | −66466.0 | −3.08068 | ||||||||
\(776\) | 10640.0 | 0.492208 | ||||||||
\(777\) | 5404.00 | 0.249508 | ||||||||
\(778\) | 29172.0 | 1.34430 | ||||||||
\(779\) | 12432.0 | 0.571788 | ||||||||
\(780\) | 8064.00 | 0.370176 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12960.0 | 0.592645 | ||||||||
\(783\) | 5400.00 | 0.246463 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −14220.0 | −0.646540 | ||||||||
\(786\) | −6720.00 | −0.304955 | ||||||||
\(787\) | 42748.0 | 1.93622 | 0.968108 | − | 0.250534i | \(-0.0806062\pi\) | ||||
0.968108 | + | 0.250534i | \(0.0806062\pi\) | |||||||
\(788\) | 6408.00 | 0.289690 | ||||||||
\(789\) | 6096.00 | 0.275061 | ||||||||
\(790\) | −41184.0 | −1.85476 | ||||||||
\(791\) | −6846.00 | −0.307732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21280.0 | 0.952932 | ||||||||
\(794\) | −3748.00 | −0.167521 | ||||||||
\(795\) | 17496.0 | 0.780527 | ||||||||
\(796\) | −13096.0 | −0.583135 | ||||||||
\(797\) | 35610.0 | 1.58265 | 0.791324 | − | 0.611397i | \(-0.209392\pi\) | ||||
0.791324 | + | 0.611397i | \(0.209392\pi\) | |||||||
\(798\) | −784.000 | −0.0347786 | ||||||||
\(799\) | 14472.0 | 0.640779 | ||||||||
\(800\) | −6368.00 | −0.281428 | ||||||||
\(801\) | 20010.0 | 0.882670 | ||||||||
\(802\) | −26676.0 | −1.17452 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1408.00 | −0.0617616 | ||||||||
\(805\) | −22680.0 | −0.993000 | ||||||||
\(806\) | −37408.0 | −1.63479 | ||||||||
\(807\) | 7668.00 | 0.334481 | ||||||||
\(808\) | −960.000 | −0.0417979 | ||||||||
\(809\) | 17046.0 | 0.740798 | 0.370399 | − | 0.928873i | \(-0.379221\pi\) | ||||
0.370399 | + | 0.928873i | \(0.379221\pi\) | |||||||
\(810\) | −15156.0 | −0.657441 | ||||||||
\(811\) | 2176.00 | 0.0942166 | 0.0471083 | − | 0.998890i | \(-0.484999\pi\) | ||||
0.0471083 | + | 0.998890i | \(0.484999\pi\) | |||||||
\(812\) | −1512.00 | −0.0653458 | ||||||||
\(813\) | −7016.00 | −0.302659 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2880.00 | −0.123782 | ||||||||
\(816\) | 1152.00 | 0.0494217 | ||||||||
\(817\) | 8848.00 | 0.378889 | ||||||||
\(818\) | −16400.0 | −0.700993 | ||||||||
\(819\) | −9016.00 | −0.384670 | ||||||||
\(820\) | 31968.0 | 1.36143 | ||||||||
\(821\) | −2094.00 | −0.0890147 | −0.0445074 | − | 0.999009i | \(-0.514172\pi\) | ||||
−0.0445074 | + | 0.999009i | \(0.514172\pi\) | |||||||
\(822\) | 4248.00 | 0.180251 | ||||||||
\(823\) | 7328.00 | 0.310374 | 0.155187 | − | 0.987885i | \(-0.450402\pi\) | ||||
0.155187 | + | 0.987885i | \(0.450402\pi\) | |||||||
\(824\) | 9680.00 | 0.409246 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3948.00 | −0.166306 | ||||||||
\(827\) | 12492.0 | 0.525259 | 0.262630 | − | 0.964897i | \(-0.415410\pi\) | ||||
0.262630 | + | 0.964897i | \(0.415410\pi\) | |||||||
\(828\) | −16560.0 | −0.695048 | ||||||||
\(829\) | −37486.0 | −1.57050 | −0.785249 | − | 0.619180i | \(-0.787465\pi\) | ||||
−0.785249 | + | 0.619180i | \(0.787465\pi\) | |||||||
\(830\) | 16848.0 | 0.704581 | ||||||||
\(831\) | 16588.0 | 0.692456 | ||||||||
\(832\) | −3584.00 | −0.149342 | ||||||||
\(833\) | −1764.00 | −0.0733721 | ||||||||
\(834\) | 2032.00 | 0.0843674 | ||||||||
\(835\) | −4752.00 | −0.196946 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33400.0 | −1.37930 | ||||||||
\(838\) | 14724.0 | 0.606960 | ||||||||
\(839\) | −17574.0 | −0.723149 | −0.361574 | − | 0.932343i | \(-0.617761\pi\) | ||||
−0.361574 | + | 0.932343i | \(0.617761\pi\) | |||||||
\(840\) | −2016.00 | −0.0828079 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 23420.0 | 0.958559 | ||||||||
\(843\) | 16044.0 | 0.655498 | ||||||||
\(844\) | 19792.0 | 0.807190 | ||||||||
\(845\) | 16902.0 | 0.688102 | ||||||||
\(846\) | −18492.0 | −0.751499 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7776.00 | −0.314893 | ||||||||
\(849\) | 784.000 | 0.0316924 | ||||||||
\(850\) | 14328.0 | 0.578172 | ||||||||
\(851\) | 69480.0 | 2.79876 | ||||||||
\(852\) | 2592.00 | 0.104226 | ||||||||
\(853\) | −9440.00 | −0.378921 | −0.189460 | − | 0.981888i | \(-0.560674\pi\) | ||||
−0.189460 | + | 0.981888i | \(0.560674\pi\) | |||||||
\(854\) | −5320.00 | −0.213169 | ||||||||
\(855\) | −11592.0 | −0.463670 | ||||||||
\(856\) | 9888.00 | 0.394819 | ||||||||
\(857\) | 28440.0 | 1.13360 | 0.566798 | − | 0.823857i | \(-0.308182\pi\) | ||||
0.566798 | + | 0.823857i | \(0.308182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24334.0 | −0.966549 | −0.483274 | − | 0.875469i | \(-0.660553\pi\) | ||||
−0.483274 | + | 0.875469i | \(0.660553\pi\) | |||||||
\(860\) | 22752.0 | 0.902136 | ||||||||
\(861\) | 6216.00 | 0.246040 | ||||||||
\(862\) | −1872.00 | −0.0739682 | ||||||||
\(863\) | 39264.0 | 1.54874 | 0.774370 | − | 0.632733i | \(-0.218067\pi\) | ||||
0.774370 | + | 0.632733i | \(0.218067\pi\) | |||||||
\(864\) | −3200.00 | −0.126003 | ||||||||
\(865\) | −29376.0 | −1.15470 | ||||||||
\(866\) | −18076.0 | −0.709293 | ||||||||
\(867\) | 7234.00 | 0.283367 | ||||||||
\(868\) | 9352.00 | 0.365700 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3888.00 | 0.151512 | ||||||||
\(871\) | −9856.00 | −0.383419 | ||||||||
\(872\) | −5552.00 | −0.215613 | ||||||||
\(873\) | 30590.0 | 1.18593 | ||||||||
\(874\) | −10080.0 | −0.390116 | ||||||||
\(875\) | −9324.00 | −0.360239 | ||||||||
\(876\) | 6400.00 | 0.246845 | ||||||||
\(877\) | −32114.0 | −1.23650 | −0.618251 | − | 0.785981i | \(-0.712159\pi\) | ||||
−0.618251 | + | 0.785981i | \(0.712159\pi\) | |||||||
\(878\) | 3928.00 | 0.150984 | ||||||||
\(879\) | −5496.00 | −0.210894 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41454.0 | 1.58527 | 0.792634 | − | 0.609698i | \(-0.208709\pi\) | ||||
0.792634 | + | 0.609698i | \(0.208709\pi\) | |||||||
\(882\) | 2254.00 | 0.0860500 | ||||||||
\(883\) | 2876.00 | 0.109609 | 0.0548047 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548047 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(884\) | 8064.00 | 0.306812 | ||||||||
\(885\) | 10152.0 | 0.385600 | ||||||||
\(886\) | −20136.0 | −0.763524 | ||||||||
\(887\) | −13932.0 | −0.527385 | −0.263693 | − | 0.964607i | \(-0.584940\pi\) | ||||
−0.263693 | + | 0.964607i | \(0.584940\pi\) | |||||||
\(888\) | 6176.00 | 0.233393 | ||||||||
\(889\) | −8512.00 | −0.321129 | ||||||||
\(890\) | 31320.0 | 1.17961 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9368.00 | 0.351641 | ||||||||
\(893\) | −11256.0 | −0.421800 | ||||||||
\(894\) | −10392.0 | −0.388770 | ||||||||
\(895\) | −12744.0 | −0.475961 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 20160.0 | 0.750416 | ||||||||
\(898\) | −6540.00 | −0.243032 | ||||||||
\(899\) | −18036.0 | −0.669115 | ||||||||
\(900\) | −18308.0 | −0.678074 | ||||||||
\(901\) | 17496.0 | 0.646921 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4424.00 | 0.163036 | ||||||||
\(904\) | −7824.00 | −0.287857 | ||||||||
\(905\) | 16236.0 | 0.596357 | ||||||||
\(906\) | −10592.0 | −0.388406 | ||||||||
\(907\) | −19768.0 | −0.723689 | −0.361844 | − | 0.932239i | \(-0.617853\pi\) | ||||
−0.361844 | + | 0.932239i | \(0.617853\pi\) | |||||||
\(908\) | −8256.00 | −0.301746 | ||||||||
\(909\) | −2760.00 | −0.100708 | ||||||||
\(910\) | −14112.0 | −0.514075 | ||||||||
\(911\) | 43836.0 | 1.59424 | 0.797119 | − | 0.603822i | \(-0.206356\pi\) | ||||
0.797119 | + | 0.603822i | \(0.206356\pi\) | |||||||
\(912\) | −896.000 | −0.0325324 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −31052.0 | −1.12375 | ||||||||
\(915\) | 13680.0 | 0.494259 | ||||||||
\(916\) | −6664.00 | −0.240376 | ||||||||
\(917\) | 11760.0 | 0.423500 | ||||||||
\(918\) | 7200.00 | 0.258862 | ||||||||
\(919\) | −31544.0 | −1.13225 | −0.566127 | − | 0.824318i | \(-0.691559\pi\) | ||||
−0.566127 | + | 0.824318i | \(0.691559\pi\) | |||||||
\(920\) | −25920.0 | −0.928866 | ||||||||
\(921\) | −6128.00 | −0.219245 | ||||||||
\(922\) | 21096.0 | 0.753536 | ||||||||
\(923\) | 18144.0 | 0.647039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 76814.0 | 2.73041 | ||||||||
\(926\) | 7592.00 | 0.269426 | ||||||||
\(927\) | 27830.0 | 0.986038 | ||||||||
\(928\) | −1728.00 | −0.0611254 | ||||||||
\(929\) | 11118.0 | 0.392648 | 0.196324 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196324 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(930\) | −24048.0 | −0.847919 | ||||||||
\(931\) | 1372.00 | 0.0482980 | ||||||||
\(932\) | −16632.0 | −0.584549 | ||||||||
\(933\) | −8124.00 | −0.285067 | ||||||||
\(934\) | −14244.0 | −0.499013 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10304.0 | −0.359826 | ||||||||
\(937\) | −10568.0 | −0.368454 | −0.184227 | − | 0.982884i | \(-0.558978\pi\) | ||||
−0.184227 | + | 0.982884i | \(0.558978\pi\) | |||||||
\(938\) | 2464.00 | 0.0857702 | ||||||||
\(939\) | 9740.00 | 0.338501 | ||||||||
\(940\) | −28944.0 | −1.00431 | ||||||||
\(941\) | −14964.0 | −0.518398 | −0.259199 | − | 0.965824i | \(-0.583459\pi\) | ||||
−0.259199 | + | 0.965824i | \(0.583459\pi\) | |||||||
\(942\) | −3160.00 | −0.109298 | ||||||||
\(943\) | 79920.0 | 2.75987 | ||||||||
\(944\) | −4512.00 | −0.155565 | ||||||||
\(945\) | −12600.0 | −0.433733 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3324.00 | 0.114061 | 0.0570304 | − | 0.998372i | \(-0.481837\pi\) | ||||
0.0570304 | + | 0.998372i | \(0.481837\pi\) | |||||||
\(948\) | −9152.00 | −0.313548 | ||||||||
\(949\) | 44800.0 | 1.53242 | ||||||||
\(950\) | −11144.0 | −0.380589 | ||||||||
\(951\) | −9612.00 | −0.327750 | ||||||||
\(952\) | −2016.00 | −0.0686333 | ||||||||
\(953\) | −3906.00 | −0.132768 | −0.0663839 | − | 0.997794i | \(-0.521146\pi\) | ||||
−0.0663839 | + | 0.997794i | \(0.521146\pi\) | |||||||
\(954\) | −22356.0 | −0.758703 | ||||||||
\(955\) | 32832.0 | 1.11248 | ||||||||
\(956\) | −288.000 | −0.00974329 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4584.00 | 0.154595 | ||||||||
\(959\) | −7434.00 | −0.250319 | ||||||||
\(960\) | −2304.00 | −0.0774597 | ||||||||
\(961\) | 81765.0 | 2.74462 | ||||||||
\(962\) | 43232.0 | 1.44891 | ||||||||
\(963\) | 28428.0 | 0.951277 | ||||||||
\(964\) | −27440.0 | −0.916787 | ||||||||
\(965\) | −37620.0 | −1.25495 | ||||||||
\(966\) | −5040.00 | −0.167867 | ||||||||
\(967\) | 36448.0 | 1.21209 | 0.606044 | − | 0.795431i | \(-0.292756\pi\) | ||||
0.606044 | + | 0.795431i | \(0.292756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2016.00 | 0.0668351 | ||||||||
\(970\) | 47880.0 | 1.58488 | ||||||||
\(971\) | −20526.0 | −0.678384 | −0.339192 | − | 0.940717i | \(-0.610154\pi\) | ||||
−0.339192 | + | 0.940717i | \(0.610154\pi\) | |||||||
\(972\) | −14168.0 | −0.467530 | ||||||||
\(973\) | −3556.00 | −0.117164 | ||||||||
\(974\) | −10264.0 | −0.337659 | ||||||||
\(975\) | 22288.0 | 0.732089 | ||||||||
\(976\) | −6080.00 | −0.199402 | ||||||||
\(977\) | 37434.0 | 1.22581 | 0.612907 | − | 0.790155i | \(-0.290000\pi\) | ||||
0.612907 | + | 0.790155i | \(0.290000\pi\) | |||||||
\(978\) | −640.000 | −0.0209253 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3528.00 | 0.114998 | ||||||||
\(981\) | −15962.0 | −0.519498 | ||||||||
\(982\) | 8376.00 | 0.272188 | ||||||||
\(983\) | −52194.0 | −1.69352 | −0.846760 | − | 0.531975i | \(-0.821450\pi\) | ||||
−0.846760 | + | 0.531975i | \(0.821450\pi\) | |||||||
\(984\) | 7104.00 | 0.230150 | ||||||||
\(985\) | 28836.0 | 0.932783 | ||||||||
\(986\) | 3888.00 | 0.125577 | ||||||||
\(987\) | −5628.00 | −0.181501 | ||||||||
\(988\) | −6272.00 | −0.201962 | ||||||||
\(989\) | 56880.0 | 1.82880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15220.0 | −0.487870 | −0.243935 | − | 0.969792i | \(-0.578438\pi\) | ||||
−0.243935 | + | 0.969792i | \(0.578438\pi\) | |||||||
\(992\) | 10688.0 | 0.342081 | ||||||||
\(993\) | −13240.0 | −0.423121 | ||||||||
\(994\) | −4536.00 | −0.144742 | ||||||||
\(995\) | −58932.0 | −1.87766 | ||||||||
\(996\) | 3744.00 | 0.119110 | ||||||||
\(997\) | −37664.0 | −1.19642 | −0.598210 | − | 0.801339i | \(-0.704121\pi\) | ||||
−0.598210 | + | 0.801339i | \(0.704121\pi\) | |||||||
\(998\) | −7696.00 | −0.244101 | ||||||||
\(999\) | 38600.0 | 1.22247 |
(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 | 1694.4.a.c.1.1 | 1 | ||
11.10 | odd | 2 | 154.4.a.d.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 1386.4.a.a.1.1 | 1 | |||
44.43 | even | 2 | 1232.4.a.f.1.1 | 1 | |||
77.76 | even | 2 | 1078.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.4.a.d.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
1078.4.a.g.1.1 | 1 | 77.76 | even | 2 | |||
1232.4.a.f.1.1 | 1 | 44.43 | even | 2 | |||
1386.4.a.a.1.1 | 1 | 33.32 | even | 2 | |||
1694.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial |