Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1728.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 54) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1728.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.0000 | 1.64461 | 0.822304 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822304 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 79.0000 | 1.68544 | 0.842718 | − | 0.538356i | \(-0.180954\pi\) | ||||
0.842718 | + | 0.538356i | \(0.180954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −108.000 | −1.54081 | −0.770407 | − | 0.637552i | \(-0.779947\pi\) | ||||
−0.770407 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.0000 | 0.132820 | 0.0664098 | − | 0.997792i | \(-0.478846\pi\) | ||||
0.0664098 | + | 0.997792i | \(0.478846\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 132.000 | 1.19669 | 0.598346 | − | 0.801238i | \(-0.295825\pi\) | ||||
0.598346 | + | 0.801238i | \(0.295825\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −96.0000 | −0.614716 | −0.307358 | − | 0.951594i | \(-0.599445\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | −0.115874 | −0.0579372 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579372 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −84.0000 | −0.405674 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 169.000 | 0.750903 | 0.375452 | − | 0.926842i | \(-0.377488\pi\) | ||||
0.375452 | + | 0.926842i | \(0.377488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 192.000 | 0.731350 | 0.365675 | − | 0.930743i | \(-0.380838\pi\) | ||||
0.365675 | + | 0.930743i | \(0.380838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 488.000 | 1.73068 | 0.865341 | − | 0.501184i | \(-0.167102\pi\) | ||||
0.865341 | + | 0.501184i | \(0.167102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −204.000 | −0.633116 | −0.316558 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316558 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −294.000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −360.000 | −0.933015 | −0.466508 | − | 0.884517i | \(-0.654488\pi\) | ||||
−0.466508 | + | 0.884517i | \(0.654488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −720.000 | −1.76518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 156.000 | 0.344228 | 0.172114 | − | 0.985077i | \(-0.444940\pi\) | ||||
0.172114 | + | 0.985077i | \(0.444940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −83.0000 | −0.174214 | −0.0871071 | − | 0.996199i | \(-0.527762\pi\) | ||||
−0.0871071 | + | 0.996199i | \(0.527762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −948.000 | −1.80900 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.0000 | 0.0857010 | 0.0428505 | − | 0.999081i | \(-0.486356\pi\) | ||||
0.0428505 | + | 0.999081i | \(0.486356\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −216.000 | −0.361049 | −0.180525 | − | 0.983570i | \(-0.557780\pi\) | ||||
−0.180525 | + | 0.983570i | \(0.557780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −511.000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 420.000 | 0.621603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 529.000 | 0.753382 | 0.376691 | − | 0.926339i | \(-0.377062\pi\) | ||||
0.376691 | + | 0.926339i | \(0.377062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1128.00 | −1.49174 | −0.745868 | − | 0.666094i | \(-0.767965\pi\) | ||||
−0.745868 | + | 0.666094i | \(0.767965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1296.00 | 1.65378 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36.0000 | 0.0428763 | 0.0214382 | − | 0.999770i | \(-0.493175\pi\) | ||||
0.0214382 | + | 0.999770i | \(0.493175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 553.000 | 0.637035 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −132.000 | −0.142557 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 605.000 | 0.633283 | 0.316641 | − | 0.948545i | \(-0.397445\pi\) | ||||
0.316641 | + | 0.948545i | \(0.397445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1248.00 | −1.22951 | −0.614756 | − | 0.788718i | \(-0.710745\pi\) | ||||
−0.614756 | + | 0.788718i | \(0.710745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −965.000 | −0.923148 | −0.461574 | − | 0.887102i | \(-0.652715\pi\) | ||||
−0.461574 | + | 0.887102i | \(0.652715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1332.00 | 1.20345 | 0.601726 | − | 0.798703i | \(-0.294480\pi\) | ||||
0.601726 | + | 0.798703i | \(0.294480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1942.00 | 1.70651 | 0.853256 | − | 0.521492i | \(-0.174624\pi\) | ||||
0.853256 | + | 0.521492i | \(0.174624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 516.000 | 0.429568 | 0.214784 | − | 0.976662i | \(-0.431095\pi\) | ||||
0.214784 | + | 0.976662i | \(0.431095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1584.00 | −1.28442 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −756.000 | −0.582373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 52.0000 | 0.0363327 | 0.0181664 | − | 0.999835i | \(-0.494217\pi\) | ||||
0.0181664 | + | 0.999835i | \(0.494217\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 48.0000 | 0.0320136 | 0.0160068 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160068 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 77.0000 | 0.0502011 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2364.00 | 1.47423 | 0.737117 | − | 0.675765i | \(-0.236186\pi\) | ||||
0.737117 | + | 0.675765i | \(0.236186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 173.000 | 0.105566 | 0.0527830 | − | 0.998606i | \(-0.483191\pi\) | ||||
0.0527830 | + | 0.998606i | \(0.483191\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4740.00 | 2.77188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1152.00 | 0.659782 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1608.00 | 0.884111 | 0.442055 | − | 0.896988i | \(-0.354249\pi\) | ||||
0.442055 | + | 0.896988i | \(0.354249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 997.000 | 0.537316 | 0.268658 | − | 0.963236i | \(-0.413420\pi\) | ||||
0.268658 | + | 0.963236i | \(0.413420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 240.000 | 0.124369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −614.000 | −0.312118 | −0.156059 | − | 0.987748i | \(-0.549879\pi\) | ||||
−0.156059 | + | 0.987748i | \(0.549879\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 924.000 | 0.452307 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2693.00 | 1.29406 | 0.647031 | − | 0.762464i | \(-0.276011\pi\) | ||||
0.647031 | + | 0.762464i | \(0.276011\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1164.00 | −0.539359 | −0.269680 | − | 0.962950i | \(-0.586918\pi\) | ||||
−0.269680 | + | 0.962950i | \(0.586918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4044.00 | 1.84069 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3648.00 | 1.60319 | 0.801596 | − | 0.597866i | \(-0.203984\pi\) | ||||
0.801596 | + | 0.597866i | \(0.203984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 133.000 | 0.0574506 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1800.00 | 0.751611 | 0.375805 | − | 0.926699i | \(-0.377366\pi\) | ||||
0.375805 | + | 0.926699i | \(0.377366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 547.000 | 0.224631 | 0.112315 | − | 0.993673i | \(-0.464173\pi\) | ||||
0.112315 | + | 0.993673i | \(0.464173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2028.00 | −0.805954 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6480.00 | −2.53403 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3156.00 | −1.19560 | −0.597801 | − | 0.801644i | \(-0.703959\pi\) | ||||
−0.597801 | + | 0.801644i | \(0.703959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1127.00 | 0.420328 | 0.210164 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210164 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1116.00 | −0.403613 | −0.201806 | − | 0.979425i | \(-0.564681\pi\) | ||||
−0.201806 | + | 0.979425i | \(0.564681\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3283.00 | 1.16948 | 0.584738 | − | 0.811222i | \(-0.301197\pi\) | ||||
0.584738 | + | 0.811222i | \(0.301197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −672.000 | −0.232341 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2304.00 | −0.784968 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 660.000 | 0.218436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −295.000 | −0.0962495 | −0.0481247 | − | 0.998841i | \(-0.515324\pi\) | ||||
−0.0481247 | + | 0.998841i | \(0.515324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5856.00 | −1.85756 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −140.000 | −0.0437964 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8532.00 | −2.59694 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2644.00 | 0.793970 | 0.396985 | − | 0.917825i | \(-0.370056\pi\) | ||||
0.396985 | + | 0.917825i | \(0.370056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6024.00 | −1.76135 | −0.880676 | − | 0.473719i | \(-0.842911\pi\) | ||||
−0.880676 | + | 0.473719i | \(0.842911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4462.00 | 1.28759 | 0.643793 | − | 0.765200i | \(-0.277360\pi\) | ||||
0.643793 | + | 0.765200i | \(0.277360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1008.00 | −0.283417 | −0.141709 | − | 0.989908i | \(-0.545260\pi\) | ||||
−0.141709 | + | 0.989908i | \(0.545260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2448.00 | 0.679532 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5064.00 | 1.37056 | 0.685278 | − | 0.728281i | \(-0.259681\pi\) | ||||
0.685278 | + | 0.728281i | \(0.259681\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6257.00 | 1.67240 | 0.836201 | − | 0.548423i | \(-0.184772\pi\) | ||||
0.836201 | + | 0.548423i | \(0.184772\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3528.00 | 0.919982 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 869.000 | 0.223859 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2160.00 | −0.543179 | −0.271590 | − | 0.962413i | \(-0.587549\pi\) | ||||
−0.271590 | + | 0.962413i | \(0.587549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7920.00 | 1.96809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −168.000 | −0.0407765 | −0.0203882 | − | 0.999792i | \(-0.506490\pi\) | ||||
−0.0203882 | + | 0.999792i | \(0.506490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1183.00 | 0.283815 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2424.00 | 0.568328 | 0.284164 | − | 0.958776i | \(-0.408284\pi\) | ||||
0.284164 | + | 0.958776i | \(0.408284\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4320.00 | 1.00142 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 396.000 | 0.0897567 | 0.0448783 | − | 0.998992i | \(-0.485710\pi\) | ||||
0.0448783 | + | 0.998992i | \(0.485710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1811.00 | −0.405942 | −0.202971 | − | 0.979185i | \(-0.565060\pi\) | ||||
−0.202971 | + | 0.979185i | \(0.565060\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1140.00 | 0.249980 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3022.00 | 0.655503 | 0.327752 | − | 0.944764i | \(-0.393709\pi\) | ||||
0.327752 | + | 0.944764i | \(0.393709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3072.00 | −0.652171 | −0.326086 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326086 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8080.00 | −1.69719 | −0.848597 | − | 0.529039i | \(-0.822552\pi\) | ||||
−0.848597 | + | 0.529039i | \(0.822552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1344.00 | 0.276424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6751.00 | 1.37411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4668.00 | 0.930742 | 0.465371 | − | 0.885116i | \(-0.345921\pi\) | ||||
0.465371 | + | 0.885116i | \(0.345921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1872.00 | −0.369465 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10428.0 | 2.01695 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3416.00 | 0.654136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 996.000 | 0.186986 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6752.00 | 1.25523 | 0.627617 | − | 0.778522i | \(-0.284030\pi\) | ||||
0.627617 | + | 0.778522i | \(0.284030\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1812.00 | −0.330383 | −0.165191 | − | 0.986262i | \(-0.552824\pi\) | ||||
−0.165191 | + | 0.986262i | \(0.552824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6203.00 | 1.12017 | 0.560087 | − | 0.828434i | \(-0.310768\pi\) | ||||
0.560087 | + | 0.828434i | \(0.310768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10968.0 | −1.94329 | −0.971647 | − | 0.236436i | \(-0.924021\pi\) | ||||
−0.971647 | + | 0.236436i | \(0.924021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5760.00 | −1.01097 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1188.00 | −0.204650 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1501.00 | 0.256186 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1428.00 | −0.239295 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8165.00 | 1.35586 | 0.677929 | − | 0.735127i | \(-0.262878\pi\) | ||||
0.677929 | + | 0.735127i | \(0.262878\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −564.000 | −0.0919839 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6523.00 | −1.05439 | −0.527197 | − | 0.849743i | \(-0.676757\pi\) | ||||
−0.527197 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1200.00 | −0.190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4459.00 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6168.00 | 0.954224 | 0.477112 | − | 0.878843i | \(-0.341684\pi\) | ||||
0.477112 | + | 0.878843i | \(0.341684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6001.00 | 0.920419 | 0.460209 | − | 0.887810i | \(-0.347774\pi\) | ||||
0.460209 | + | 0.887810i | \(0.347774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −552.000 | −0.0832294 | −0.0416147 | − | 0.999134i | \(-0.513250\pi\) | ||||
−0.0416147 | + | 0.999134i | \(0.513250\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2592.00 | 0.387519 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5004.00 | 0.735657 | 0.367829 | − | 0.929894i | \(-0.380101\pi\) | ||||
0.367829 | + | 0.929894i | \(0.380101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6738.00 | −0.982359 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6132.00 | 0.879352 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4291.00 | 0.610323 | 0.305161 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305161 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2520.00 | −0.352647 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2833.00 | 0.393263 | 0.196632 | − | 0.980477i | \(-0.437000\pi\) | ||||
0.196632 | + | 0.980477i | \(0.437000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7584.00 | −1.03606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5137.00 | −0.696227 | −0.348113 | − | 0.937452i | \(-0.613178\pi\) | ||||
−0.348113 | + | 0.937452i | \(0.613178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5088.00 | −0.678811 | −0.339406 | − | 0.940640i | \(-0.610226\pi\) | ||||
−0.339406 | + | 0.940640i | \(0.610226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5040.00 | −0.667175 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7980.00 | −1.04011 | −0.520054 | − | 0.854133i | \(-0.674088\pi\) | ||||
−0.520054 | + | 0.854133i | \(0.674088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14256.0 | −1.84388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6348.00 | −0.808614 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1834.00 | 0.231853 | 0.115927 | − | 0.993258i | \(-0.463016\pi\) | ||||
0.115927 | + | 0.993258i | \(0.463016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1464.00 | −0.182316 | −0.0911579 | − | 0.995836i | \(-0.529057\pi\) | ||||
−0.0911579 | + | 0.995836i | \(0.529057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1580.00 | −0.195299 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10140.0 | 1.23494 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −151.000 | −0.0182554 | −0.00912771 | − | 0.999958i | \(-0.502905\pi\) | ||||
−0.00912771 | + | 0.999958i | \(0.502905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1092.00 | 0.130106 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13536.0 | 1.60110 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11508.0 | −1.34177 | −0.670886 | − | 0.741560i | \(-0.734086\pi\) | ||||
−0.670886 | + | 0.741560i | \(0.734086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6271.00 | 0.725962 | 0.362981 | − | 0.931797i | \(-0.381759\pi\) | ||||
0.362981 | + | 0.931797i | \(0.381759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2052.00 | −0.234204 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −581.000 | −0.0658467 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9468.00 | −1.05814 | −0.529069 | − | 0.848579i | \(-0.677459\pi\) | ||||
−0.529069 | + | 0.848579i | \(0.677459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3026.00 | 0.335844 | 0.167922 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167922 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1452.00 | 0.158944 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11180.0 | −1.21547 | −0.607736 | − | 0.794139i | \(-0.707922\pi\) | ||||
−0.607736 | + | 0.794139i | \(0.707922\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −840.000 | −0.0900894 | −0.0450447 | − | 0.998985i | \(-0.514343\pi\) | ||||
−0.0450447 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −432.000 | −0.0460197 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12780.0 | 1.34326 | 0.671632 | − | 0.740885i | \(-0.265594\pi\) | ||||
0.671632 | + | 0.740885i | \(0.265594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11520.0 | 1.20278 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6636.00 | −0.683737 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15658.0 | −1.60274 | −0.801368 | − | 0.598172i | \(-0.795894\pi\) | ||||
−0.801368 | + | 0.598172i | \(0.795894\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15564.0 | 1.57242 | 0.786212 | − | 0.617956i | \(-0.212039\pi\) | ||||
0.786212 | + | 0.617956i | \(0.212039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4183.00 | 0.419871 | 0.209936 | − | 0.977715i | \(-0.432675\pi\) | ||||
0.209936 | + | 0.977715i | \(0.432675\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13932.0 | 1.38051 | 0.690253 | − | 0.723568i | \(-0.257499\pi\) | ||||
0.690253 | + | 0.723568i | \(0.257499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 329.000 | 0.0323919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29280.0 | 2.84629 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 209.000 | 0.0201886 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2712.00 | 0.258694 | 0.129347 | − | 0.991599i | \(-0.458712\pi\) | ||||
0.129347 | + | 0.991599i | \(0.458712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13351.0 | 1.26560 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7260.00 | −0.679711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9439.00 | 0.878279 | 0.439140 | − | 0.898419i | \(-0.355283\pi\) | ||||
0.439140 | + | 0.898419i | \(0.355283\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11724.0 | −1.07759 | −0.538795 | − | 0.842437i | \(-0.681120\pi\) | ||||
−0.538795 | + | 0.842437i | \(0.681120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10368.0 | 0.947163 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1512.00 | −0.136464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11968.0 | −1.07367 | −0.536835 | − | 0.843687i | \(-0.680380\pi\) | ||||
−0.536835 | + | 0.843687i | \(0.680380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8892.00 | −0.788220 | −0.394110 | − | 0.919063i | \(-0.628947\pi\) | ||||
−0.394110 | + | 0.919063i | \(0.628947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14976.0 | 1.31965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6756.00 | 0.588319 | 0.294160 | − | 0.955756i | \(-0.404960\pi\) | ||||
0.294160 | + | 0.955756i | \(0.404960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3577.00 | −0.309662 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11580.0 | 0.990827 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12240.0 | −1.04123 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6228.00 | −0.523711 | −0.261856 | − | 0.965107i | \(-0.584334\pi\) | ||||
−0.261856 | + | 0.965107i | \(0.584334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11639.0 | 0.973113 | 0.486556 | − | 0.873649i | \(-0.338253\pi\) | ||||
0.486556 | + | 0.873649i | \(0.338253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2160.00 | 0.178541 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5257.00 | 0.432070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15168.0 | 1.23264 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15984.0 | −1.29168 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17640.0 | −1.40966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17705.0 | −1.40702 | −0.703510 | − | 0.710686i | \(-0.748385\pi\) | ||||
−0.703510 | + | 0.710686i | \(0.748385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23304.0 | −1.83162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3485.00 | 0.272409 | 0.136205 | − | 0.990681i | \(-0.456510\pi\) | ||||
0.136205 | + | 0.990681i | \(0.456510\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1056.00 | −0.0816463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3703.00 | 0.284751 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19116.0 | 1.45417 | 0.727083 | − | 0.686549i | \(-0.240875\pi\) | ||||
0.727083 | + | 0.686549i | \(0.240875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38552.0 | 2.91695 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22368.0 | 1.67442 | 0.837210 | − | 0.546881i | \(-0.184185\pi\) | ||||
0.837210 | + | 0.546881i | \(0.184185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6192.00 | −0.461061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8340.00 | 0.614466 | 0.307233 | − | 0.951634i | \(-0.400597\pi\) | ||||
0.307233 | + | 0.951634i | \(0.400597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14677.0 | −1.07568 | −0.537840 | − | 0.843047i | \(-0.680760\pi\) | ||||
−0.537840 | + | 0.843047i | \(0.680760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2508.00 | 0.181897 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10069.0 | −0.726478 | −0.363239 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363239 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7896.00 | −0.563823 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21600.0 | −1.53444 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1572.00 | 0.110534 | 0.0552669 | − | 0.998472i | \(-0.482399\pi\) | ||||
0.0552669 | + | 0.998472i | \(0.482399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −220.000 | −0.0153904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1368.00 | 0.0947336 | 0.0473668 | − | 0.998878i | \(-0.484917\pi\) | ||||
0.0473668 | + | 0.998878i | \(0.484917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9072.00 | 0.625068 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23712.0 | 1.61744 | 0.808720 | − | 0.588194i | \(-0.200161\pi\) | ||||
0.808720 | + | 0.588194i | \(0.200161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11014.0 | −0.747538 | −0.373769 | − | 0.927522i | \(-0.621935\pi\) | ||||
−0.373769 | + | 0.927522i | \(0.621935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27228.0 | −1.82971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6415.00 | 0.428957 | 0.214478 | − | 0.976729i | \(-0.431195\pi\) | ||||
0.214478 | + | 0.976729i | \(0.431195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16116.0 | −1.06708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15851.0 | −1.04440 | −0.522199 | − | 0.852824i | \(-0.674888\pi\) | ||||
−0.522199 | + | 0.852824i | \(0.674888\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5772.00 | 0.376616 | 0.188308 | − | 0.982110i | \(-0.439700\pi\) | ||||
0.188308 | + | 0.982110i | \(0.439700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27781.0 | −1.80390 | −0.901949 | − | 0.431843i | \(-0.857863\pi\) | ||||
−0.901949 | + | 0.431843i | \(0.857863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 252.000 | 0.0162057 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18252.0 | −1.15700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29869.0 | 1.88442 | 0.942208 | − | 0.335029i | \(-0.108746\pi\) | ||||
0.942208 | + | 0.335029i | \(0.108746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −624.000 | −0.0389964 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23226.0 | −1.44466 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3480.00 | 0.214433 | 0.107217 | − | 0.994236i | \(-0.465806\pi\) | ||||
0.107217 | + | 0.994236i | \(0.465806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7432.00 | −0.455816 | −0.227908 | − | 0.973683i | \(-0.573188\pi\) | ||||
−0.227908 | + | 0.973683i | \(0.573188\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12960.0 | 0.787496 | 0.393748 | − | 0.919218i | \(-0.371178\pi\) | ||||
0.393748 | + | 0.919218i | \(0.371178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9360.00 | 0.566120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23592.0 | −1.41382 | −0.706911 | − | 0.707302i | \(-0.749912\pi\) | ||||
−0.706911 | + | 0.707302i | \(0.749912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −576.000 | −0.0343606 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32280.0 | 1.90812 | 0.954059 | − | 0.299618i | \(-0.0968591\pi\) | ||||
0.954059 | + | 0.299618i | \(0.0968591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22619.0 | −1.33098 | −0.665490 | − | 0.746407i | \(-0.731777\pi\) | ||||
−0.665490 | + | 0.746407i | \(0.731777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −924.000 | −0.0538815 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12672.0 | −0.735625 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4980.00 | −0.286514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19861.0 | −1.13757 | −0.568786 | − | 0.822486i | \(-0.692587\pi\) | ||||
−0.568786 | + | 0.822486i | \(0.692587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8292.00 | 0.470735 | 0.235367 | − | 0.971906i | \(-0.424371\pi\) | ||||
0.235367 | + | 0.971906i | \(0.424371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4235.00 | 0.239358 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19728.0 | 1.10523 | 0.552614 | − | 0.833437i | \(-0.313630\pi\) | ||||
0.552614 | + | 0.833437i | \(0.313630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28368.0 | −1.58231 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28440.0 | −1.57254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27272.0 | 1.50141 | 0.750706 | − | 0.660636i | \(-0.229713\pi\) | ||||
0.750706 | + | 0.660636i | \(0.229713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2076.00 | −0.113305 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20736.0 | −1.12688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21996.0 | 1.18513 | 0.592566 | − | 0.805522i | \(-0.298115\pi\) | ||||
0.592566 | + | 0.805522i | \(0.298115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1859.00 | 0.0997347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8736.00 | −0.464712 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2009.00 | −0.106417 | −0.0532084 | − | 0.998583i | \(-0.516945\pi\) | ||||
−0.0532084 | + | 0.998583i | \(0.516945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2640.00 | −0.138666 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −56880.0 | −2.97509 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26280.0 | −1.36311 | −0.681557 | − | 0.731765i | \(-0.738697\pi\) | ||||
−0.681557 | + | 0.731765i | \(0.738697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6755.00 | −0.348917 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1824.00 | −0.0934368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20900.0 | −1.06621 | −0.533107 | − | 0.846048i | \(-0.678976\pi\) | ||||
−0.533107 | + | 0.846048i | \(0.678976\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −52704.0 | −2.66666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17638.0 | 0.888778 | 0.444389 | − | 0.895834i | \(-0.353421\pi\) | ||||
0.444389 | + | 0.895834i | \(0.353421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2820.00 | 0.140944 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30080.0 | 1.49731 | 0.748654 | − | 0.662961i | \(-0.230700\pi\) | ||||
0.748654 | + | 0.662961i | \(0.230700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15708.0 | −0.775600 | −0.387800 | − | 0.921744i | \(-0.626765\pi\) | ||||
−0.387800 | + | 0.921744i | \(0.626765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19296.0 | −0.948927 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9324.00 | 0.454862 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20423.0 | −0.992338 | −0.496169 | − | 0.868226i | \(-0.665260\pi\) | ||||
−0.496169 | + | 0.868226i | \(0.665260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11964.0 | −0.576708 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4399.00 | 0.211208 | 0.105604 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105604 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20652.0 | −0.983751 | −0.491875 | − | 0.870666i | \(-0.663688\pi\) | ||||
−0.491875 | + | 0.870666i | \(0.663688\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13594.0 | 0.645001 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12324.0 | 0.580175 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27407.0 | 1.28520 | 0.642602 | − | 0.766200i | \(-0.277855\pi\) | ||||
0.642602 | + | 0.766200i | \(0.277855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5976.00 | −0.278062 | −0.139031 | − | 0.990288i | \(-0.544399\pi\) | ||||
−0.139031 | + | 0.990288i | \(0.544399\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −380.000 | −0.0176129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2112.00 | 0.0971377 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12960.0 | −0.593784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7368.00 | 0.335000 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24131.0 | 1.09298 | 0.546491 | − | 0.837465i | \(-0.315963\pi\) | ||||
0.546491 | + | 0.837465i | \(0.315963\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3612.00 | 0.162361 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6557.00 | −0.293627 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −912.000 | −0.0405329 | −0.0202664 | − | 0.999795i | \(-0.506451\pi\) | ||||
−0.0202664 | + | 0.999795i | \(0.506451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22032.0 | 0.975515 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30660.0 | −1.34741 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11088.0 | −0.485467 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12888.0 | −0.560096 | −0.280048 | − | 0.959986i | \(-0.590350\pi\) | ||||
−0.280048 | + | 0.959986i | \(0.590350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6856.00 | −0.296852 | −0.148426 | − | 0.988924i | \(-0.547421\pi\) | ||||
−0.148426 | + | 0.988924i | \(0.547421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32316.0 | −1.38893 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5368.00 | 0.229868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −636.000 | −0.0270360 | −0.0135180 | − | 0.999909i | \(-0.504303\pi\) | ||||
−0.0135180 | + | 0.999909i | \(0.504303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39827.0 | −1.68686 | −0.843428 | − | 0.537243i | \(-0.819466\pi\) | ||||
−0.843428 | + | 0.537243i | \(0.819466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38124.0 | 1.60302 | 0.801512 | − | 0.597978i | \(-0.204029\pi\) | ||||
0.801512 | + | 0.597978i | \(0.204029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18965.0 | −0.794550 | −0.397275 | − | 0.917700i | \(-0.630044\pi\) | ||||
−0.397275 | + | 0.917700i | \(0.630044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31752.0 | 1.32070 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13968.0 | 0.578901 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27816.0 | −1.14459 | −0.572297 | − | 0.820046i | \(-0.693948\pi\) | ||||
−0.572297 | + | 0.820046i | \(0.693948\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15173.0 | −0.622125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −48528.0 | −1.97564 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15883.0 | 0.644329 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22308.0 | 0.898600 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12337.0 | 0.495206 | 0.247603 | − | 0.968862i | \(-0.420357\pi\) | ||||
0.247603 | + | 0.968862i | \(0.420357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11352.0 | −0.452482 | −0.226241 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226241 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2527.00 | −0.100373 | −0.0501863 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501863 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26388.0 | 1.04086 | 0.520428 | − | 0.853906i | \(-0.325773\pi\) | ||||
0.520428 | + | 0.853906i | \(0.325773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43776.0 | −1.72073 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31740.0 | 1.23902 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3713.00 | 0.144443 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8904.00 | 0.344012 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6383.00 | −0.245768 | −0.122884 | − | 0.992421i | \(-0.539214\pi\) | ||||
−0.122884 | + | 0.992421i | \(0.539214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28908.0 | 1.10549 | 0.552744 | − | 0.833351i | \(-0.313581\pi\) | ||||
0.552744 | + | 0.833351i | \(0.313581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36893.0 | 1.40606 | 0.703028 | − | 0.711162i | \(-0.251831\pi\) | ||||
0.703028 | + | 0.711162i | \(0.251831\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45528.0 | 1.72343 | 0.861714 | − | 0.507394i | \(-0.169391\pi\) | ||||
0.861714 | + | 0.507394i | \(0.169391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 364.000 | 0.0137325 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2244.00 | −0.0840903 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21600.0 | −0.806713 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1920.00 | 0.0712298 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38880.0 | 1.43760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6564.00 | −0.241099 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31201.0 | −1.14224 | −0.571120 | − | 0.820866i | \(-0.693491\pi\) | ||||
−0.571120 | + | 0.820866i | \(0.693491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23856.0 | −0.867601 | −0.433801 | − | 0.901009i | \(-0.642828\pi\) | ||||
−0.433801 | + | 0.901009i | \(0.642828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67680.0 | −2.45332 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 336.000 | 0.0121000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23492.0 | −0.843231 | −0.421616 | − | 0.906775i | \(-0.638537\pi\) | ||||
−0.421616 | + | 0.906775i | \(0.638537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17064.0 | −0.608525 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3211.00 | 0.114137 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15096.0 | −0.533136 | −0.266568 | − | 0.963816i | \(-0.585890\pi\) | ||||
−0.266568 | + | 0.963816i | \(0.585890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3234.00 | −0.113845 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 77760.0 | 2.71981 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14965.0 | −0.521756 | −0.260878 | − | 0.965372i | \(-0.584012\pi\) | ||||
−0.260878 | + | 0.965372i | \(0.584012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19524.0 | −0.676370 | −0.338185 | − | 0.941080i | \(-0.609813\pi\) | ||||
−0.338185 | + | 0.941080i | \(0.609813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25344.0 | 0.875201 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11076.0 | 0.380065 | 0.190033 | − | 0.981778i | \(-0.439141\pi\) | ||||
0.190033 | + | 0.981778i | \(0.439141\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40369.0 | −1.38086 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44748.0 | −1.52102 | −0.760509 | − | 0.649328i | \(-0.775050\pi\) | ||||
−0.760509 | + | 0.649328i | \(0.775050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37872.0 | 1.28326 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16548.0 | 0.557208 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29391.0 | −0.986573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13524.0 | −0.451143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41519.0 | −1.38072 | −0.690362 | − | 0.723464i | \(-0.742549\pi\) | ||||
−0.690362 | + | 0.723464i | \(0.742549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28404.0 | 0.938752 | 0.469376 | − | 0.882999i | \(-0.344479\pi\) | ||||
0.469376 | + | 0.882999i | \(0.344479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1211.00 | 0.0399002 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43032.0 | 1.40913 | 0.704563 | − | 0.709642i | \(-0.251143\pi\) | ||||
0.704563 | + | 0.709642i | \(0.251143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2160.00 | 0.0705147 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18132.0 | −0.588322 | −0.294161 | − | 0.955756i | \(-0.595040\pi\) | ||||
−0.294161 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13392.0 | 0.433203 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64416.0 | 2.07109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44467.0 | 1.42537 | 0.712685 | − | 0.701485i | \(-0.247479\pi\) | ||||
0.712685 | + | 0.701485i | \(0.247479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39396.0 | −1.25521 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19550.0 | −0.621018 | −0.310509 | − | 0.950570i | \(-0.600499\pi\) | ||||
−0.310509 | + | 0.950570i | \(0.600499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1728.4.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 1728.4.a.bb.1.1 | 1 | |||
4.3 | odd | 2 | 1728.4.a.e.1.1 | 1 | |||
8.3 | odd | 2 | 54.4.a.d.1.1 | yes | 1 | ||
8.5 | even | 2 | 432.4.a.m.1.1 | 1 | |||
12.11 | even | 2 | 1728.4.a.ba.1.1 | 1 | |||
24.5 | odd | 2 | 432.4.a.b.1.1 | 1 | |||
24.11 | even | 2 | 54.4.a.a.1.1 | ✓ | 1 | ||
40.3 | even | 4 | 1350.4.c.t.649.1 | 2 | |||
40.19 | odd | 2 | 1350.4.a.h.1.1 | 1 | |||
40.27 | even | 4 | 1350.4.c.t.649.2 | 2 | |||
72.11 | even | 6 | 162.4.c.h.109.1 | 2 | |||
72.43 | odd | 6 | 162.4.c.a.109.1 | 2 | |||
72.59 | even | 6 | 162.4.c.h.55.1 | 2 | |||
72.67 | odd | 6 | 162.4.c.a.55.1 | 2 | |||
120.59 | even | 2 | 1350.4.a.v.1.1 | 1 | |||
120.83 | odd | 4 | 1350.4.c.a.649.2 | 2 | |||
120.107 | odd | 4 | 1350.4.c.a.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.4.a.a.1.1 | ✓ | 1 | 24.11 | even | 2 | ||
54.4.a.d.1.1 | yes | 1 | 8.3 | odd | 2 | ||
162.4.c.a.55.1 | 2 | 72.67 | odd | 6 | |||
162.4.c.a.109.1 | 2 | 72.43 | odd | 6 | |||
162.4.c.h.55.1 | 2 | 72.59 | even | 6 | |||
162.4.c.h.109.1 | 2 | 72.11 | even | 6 | |||
432.4.a.b.1.1 | 1 | 24.5 | odd | 2 | |||
432.4.a.m.1.1 | 1 | 8.5 | even | 2 | |||
1350.4.a.h.1.1 | 1 | 40.19 | odd | 2 | |||
1350.4.a.v.1.1 | 1 | 120.59 | even | 2 | |||
1350.4.c.a.649.1 | 2 | 120.107 | odd | 4 | |||
1350.4.c.a.649.2 | 2 | 120.83 | odd | 4 | |||
1350.4.c.t.649.1 | 2 | 40.3 | even | 4 | |||
1350.4.c.t.649.2 | 2 | 40.27 | even | 4 | |||
1728.4.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
1728.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1728.4.a.ba.1.1 | 1 | 12.11 | even | 2 | |||
1728.4.a.bb.1.1 | 1 | 3.2 | odd | 2 |