Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, 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("147.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(8.67328077084\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | −18.0000 | −1.60997 | −0.804984 | − | 0.593296i | \(-0.797826\pi\) | ||||
−0.804984 | + | 0.593296i | \(0.797826\pi\) | |||||||
\(6\) | −12.0000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −72.0000 | −2.27684 | ||||||||
\(11\) | −50.0000 | −1.37051 | −0.685253 | − | 0.728305i | \(-0.740308\pi\) | ||||
−0.685253 | + | 0.728305i | \(0.740308\pi\) | |||||||
\(12\) | −24.0000 | −0.577350 | ||||||||
\(13\) | 36.0000 | 0.768046 | 0.384023 | − | 0.923323i | \(-0.374538\pi\) | ||||
0.384023 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000 | 0.929516 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | −126.000 | −1.79762 | −0.898808 | − | 0.438342i | \(-0.855566\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 36.0000 | 0.471405 | ||||||||
\(19\) | 72.0000 | 0.869365 | 0.434682 | − | 0.900584i | \(-0.356861\pi\) | ||||
0.434682 | + | 0.900584i | \(0.356861\pi\) | |||||||
\(20\) | −144.000 | −1.60997 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −200.000 | −1.93819 | ||||||||
\(23\) | 14.0000 | 0.126922 | 0.0634609 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634609 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | 144.000 | 1.08618 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.000 | 1.01172 | 0.505860 | − | 0.862616i | \(-0.331175\pi\) | ||||
0.505860 | + | 0.862616i | \(0.331175\pi\) | |||||||
\(30\) | 216.000 | 1.31453 | ||||||||
\(31\) | 36.0000 | 0.208574 | 0.104287 | − | 0.994547i | \(-0.466744\pi\) | ||||
0.104287 | + | 0.994547i | \(0.466744\pi\) | |||||||
\(32\) | −256.000 | −1.41421 | ||||||||
\(33\) | 150.000 | 0.791262 | ||||||||
\(34\) | −504.000 | −2.54221 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 72.0000 | 0.333333 | ||||||||
\(37\) | −162.000 | −0.719801 | −0.359900 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359900 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(38\) | 288.000 | 1.22947 | ||||||||
\(39\) | −108.000 | −0.443432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 270.000 | 1.02846 | 0.514231 | − | 0.857652i | \(-0.328078\pi\) | ||||
0.514231 | + | 0.857652i | \(0.328078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −324.000 | −1.14906 | −0.574529 | − | 0.818484i | \(-0.694815\pi\) | ||||
−0.574529 | + | 0.818484i | \(0.694815\pi\) | |||||||
\(44\) | −400.000 | −1.37051 | ||||||||
\(45\) | −162.000 | −0.536656 | ||||||||
\(46\) | 56.0000 | 0.179495 | ||||||||
\(47\) | 72.0000 | 0.223453 | 0.111726 | − | 0.993739i | \(-0.464362\pi\) | ||||
0.111726 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(48\) | 192.000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 796.000 | 2.25143 | ||||||||
\(51\) | 378.000 | 1.03785 | ||||||||
\(52\) | 288.000 | 0.768046 | ||||||||
\(53\) | −22.0000 | −0.0570176 | −0.0285088 | − | 0.999594i | \(-0.509076\pi\) | ||||
−0.0285088 | + | 0.999594i | \(0.509076\pi\) | |||||||
\(54\) | −108.000 | −0.272166 | ||||||||
\(55\) | 900.000 | 2.20647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −216.000 | −0.501928 | ||||||||
\(58\) | 632.000 | 1.43079 | ||||||||
\(59\) | −468.000 | −1.03268 | −0.516342 | − | 0.856382i | \(-0.672707\pi\) | ||||
−0.516342 | + | 0.856382i | \(0.672707\pi\) | |||||||
\(60\) | 432.000 | 0.929516 | ||||||||
\(61\) | −792.000 | −1.66238 | −0.831190 | − | 0.555988i | \(-0.812340\pi\) | ||||
−0.831190 | + | 0.555988i | \(0.812340\pi\) | |||||||
\(62\) | 144.000 | 0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −648.000 | −1.23653 | ||||||||
\(66\) | 600.000 | 1.11901 | ||||||||
\(67\) | 232.000 | 0.423034 | 0.211517 | − | 0.977374i | \(-0.432160\pi\) | ||||
0.211517 | + | 0.977374i | \(0.432160\pi\) | |||||||
\(68\) | −1008.00 | −1.79762 | ||||||||
\(69\) | −42.0000 | −0.0732783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −734.000 | −1.22690 | −0.613449 | − | 0.789734i | \(-0.710218\pi\) | ||||
−0.613449 | + | 0.789734i | \(0.710218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −180.000 | −0.288595 | −0.144297 | − | 0.989534i | \(-0.546092\pi\) | ||||
−0.144297 | + | 0.989534i | \(0.546092\pi\) | |||||||
\(74\) | −648.000 | −1.01795 | ||||||||
\(75\) | −597.000 | −0.919142 | ||||||||
\(76\) | 576.000 | 0.869365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −432.000 | −0.627107 | ||||||||
\(79\) | 236.000 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(80\) | 1152.00 | 1.60997 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1080.00 | 1.45446 | ||||||||
\(83\) | −36.0000 | −0.0476086 | −0.0238043 | − | 0.999717i | \(-0.507578\pi\) | ||||
−0.0238043 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2268.00 | 2.89411 | ||||||||
\(86\) | −1296.00 | −1.62501 | ||||||||
\(87\) | −474.000 | −0.584116 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −234.000 | −0.278696 | −0.139348 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139348 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(90\) | −648.000 | −0.758947 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 112.000 | 0.126922 | ||||||||
\(93\) | −108.000 | −0.120420 | ||||||||
\(94\) | 288.000 | 0.316010 | ||||||||
\(95\) | −1296.00 | −1.39965 | ||||||||
\(96\) | 768.000 | 0.816497 | ||||||||
\(97\) | −468.000 | −0.489878 | −0.244939 | − | 0.969538i | \(-0.578768\pi\) | ||||
−0.244939 | + | 0.969538i | \(0.578768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −450.000 | −0.456835 | ||||||||
\(100\) | 1592.00 | 1.59200 | ||||||||
\(101\) | 666.000 | 0.656133 | 0.328067 | − | 0.944655i | \(-0.393603\pi\) | ||||
0.328067 | + | 0.944655i | \(0.393603\pi\) | |||||||
\(102\) | 1512.00 | 1.46775 | ||||||||
\(103\) | 252.000 | 0.241071 | 0.120535 | − | 0.992709i | \(-0.461539\pi\) | ||||
0.120535 | + | 0.992709i | \(0.461539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −88.0000 | −0.0806351 | ||||||||
\(107\) | 670.000 | 0.605340 | 0.302670 | − | 0.953095i | \(-0.402122\pi\) | ||||
0.302670 | + | 0.953095i | \(0.402122\pi\) | |||||||
\(108\) | −216.000 | −0.192450 | ||||||||
\(109\) | 162.000 | 0.142356 | 0.0711779 | − | 0.997464i | \(-0.477324\pi\) | ||||
0.0711779 | + | 0.997464i | \(0.477324\pi\) | |||||||
\(110\) | 3600.00 | 3.12042 | ||||||||
\(111\) | 486.000 | 0.415577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1390.00 | −1.15717 | −0.578585 | − | 0.815622i | \(-0.696395\pi\) | ||||
−0.578585 | + | 0.815622i | \(0.696395\pi\) | |||||||
\(114\) | −864.000 | −0.709833 | ||||||||
\(115\) | −252.000 | −0.204340 | ||||||||
\(116\) | 1264.00 | 1.01172 | ||||||||
\(117\) | 324.000 | 0.256015 | ||||||||
\(118\) | −1872.00 | −1.46044 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | −3168.00 | −2.35096 | ||||||||
\(123\) | −810.000 | −0.593782 | ||||||||
\(124\) | 288.000 | 0.208574 | ||||||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 916.000 | 0.640015 | 0.320007 | − | 0.947415i | \(-0.396315\pi\) | ||||
0.320007 | + | 0.947415i | \(0.396315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 972.000 | 0.663410 | ||||||||
\(130\) | −2592.00 | −1.74872 | ||||||||
\(131\) | −2268.00 | −1.51264 | −0.756321 | − | 0.654201i | \(-0.773005\pi\) | ||||
−0.756321 | + | 0.654201i | \(0.773005\pi\) | |||||||
\(132\) | 1200.00 | 0.791262 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 928.000 | 0.598261 | ||||||||
\(135\) | 486.000 | 0.309839 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 806.000 | 0.502637 | 0.251318 | − | 0.967904i | \(-0.419136\pi\) | ||||
0.251318 | + | 0.967904i | \(0.419136\pi\) | |||||||
\(138\) | −168.000 | −0.103631 | ||||||||
\(139\) | −2628.00 | −1.60363 | −0.801813 | − | 0.597575i | \(-0.796131\pi\) | ||||
−0.801813 | + | 0.597575i | \(0.796131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −216.000 | −0.129011 | ||||||||
\(142\) | −2936.00 | −1.73510 | ||||||||
\(143\) | −1800.00 | −1.05261 | ||||||||
\(144\) | −576.000 | −0.333333 | ||||||||
\(145\) | −2844.00 | −1.62884 | ||||||||
\(146\) | −720.000 | −0.408134 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1296.00 | −0.719801 | ||||||||
\(149\) | −2390.00 | −1.31407 | −0.657035 | − | 0.753860i | \(-0.728190\pi\) | ||||
−0.657035 | + | 0.753860i | \(0.728190\pi\) | |||||||
\(150\) | −2388.00 | −1.29986 | ||||||||
\(151\) | 3240.00 | 1.74614 | 0.873071 | − | 0.487593i | \(-0.162125\pi\) | ||||
0.873071 | + | 0.487593i | \(0.162125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1134.00 | −0.599206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −648.000 | −0.335798 | ||||||||
\(156\) | −864.000 | −0.443432 | ||||||||
\(157\) | −3024.00 | −1.53721 | −0.768603 | − | 0.639726i | \(-0.779048\pi\) | ||||
−0.768603 | + | 0.639726i | \(0.779048\pi\) | |||||||
\(158\) | 944.000 | 0.475320 | ||||||||
\(159\) | 66.0000 | 0.0329191 | ||||||||
\(160\) | 4608.00 | 2.27684 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 324.000 | 0.157135 | ||||||||
\(163\) | −1784.00 | −0.857262 | −0.428631 | − | 0.903480i | \(-0.641004\pi\) | ||||
−0.428631 | + | 0.903480i | \(0.641004\pi\) | |||||||
\(164\) | 2160.00 | 1.02846 | ||||||||
\(165\) | −2700.00 | −1.27391 | ||||||||
\(166\) | −144.000 | −0.0673287 | ||||||||
\(167\) | 3024.00 | 1.40122 | 0.700611 | − | 0.713543i | \(-0.252911\pi\) | ||||
0.700611 | + | 0.713543i | \(0.252911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −901.000 | −0.410105 | ||||||||
\(170\) | 9072.00 | 4.09289 | ||||||||
\(171\) | 648.000 | 0.289788 | ||||||||
\(172\) | −2592.00 | −1.14906 | ||||||||
\(173\) | −1566.00 | −0.688213 | −0.344106 | − | 0.938931i | \(-0.611818\pi\) | ||||
−0.344106 | + | 0.938931i | \(0.611818\pi\) | |||||||
\(174\) | −1896.00 | −0.826065 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3200.00 | 1.37051 | ||||||||
\(177\) | 1404.00 | 0.596221 | ||||||||
\(178\) | −936.000 | −0.394136 | ||||||||
\(179\) | 3802.00 | 1.58757 | 0.793784 | − | 0.608199i | \(-0.208108\pi\) | ||||
0.793784 | + | 0.608199i | \(0.208108\pi\) | |||||||
\(180\) | −1296.00 | −0.536656 | ||||||||
\(181\) | 468.000 | 0.192189 | 0.0960944 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960944 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2376.00 | 0.959776 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2916.00 | 1.15886 | ||||||||
\(186\) | −432.000 | −0.170300 | ||||||||
\(187\) | 6300.00 | 2.46365 | ||||||||
\(188\) | 576.000 | 0.223453 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5184.00 | −1.97940 | ||||||||
\(191\) | 482.000 | 0.182598 | 0.0912992 | − | 0.995824i | \(-0.470898\pi\) | ||||
0.0912992 | + | 0.995824i | \(0.470898\pi\) | |||||||
\(192\) | 1536.00 | 0.577350 | ||||||||
\(193\) | −810.000 | −0.302099 | −0.151049 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151049 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(194\) | −1872.00 | −0.692793 | ||||||||
\(195\) | 1944.00 | 0.713911 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2462.00 | −0.890407 | −0.445204 | − | 0.895429i | \(-0.646869\pi\) | ||||
−0.445204 | + | 0.895429i | \(0.646869\pi\) | |||||||
\(198\) | −1800.00 | −0.646063 | ||||||||
\(199\) | 4536.00 | 1.61582 | 0.807911 | − | 0.589305i | \(-0.200598\pi\) | ||||
0.807911 | + | 0.589305i | \(0.200598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −696.000 | −0.244239 | ||||||||
\(202\) | 2664.00 | 0.927913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3024.00 | 1.03785 | ||||||||
\(205\) | −4860.00 | −1.65579 | ||||||||
\(206\) | 1008.00 | 0.340926 | ||||||||
\(207\) | 126.000 | 0.0423073 | ||||||||
\(208\) | −2304.00 | −0.768046 | ||||||||
\(209\) | −3600.00 | −1.19147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2916.00 | 0.951402 | 0.475701 | − | 0.879607i | \(-0.342195\pi\) | ||||
0.475701 | + | 0.879607i | \(0.342195\pi\) | |||||||
\(212\) | −176.000 | −0.0570176 | ||||||||
\(213\) | 2202.00 | 0.708350 | ||||||||
\(214\) | 2680.00 | 0.856080 | ||||||||
\(215\) | 5832.00 | 1.84995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 648.000 | 0.201322 | ||||||||
\(219\) | 540.000 | 0.166620 | ||||||||
\(220\) | 7200.00 | 2.20647 | ||||||||
\(221\) | −4536.00 | −1.38065 | ||||||||
\(222\) | 1944.00 | 0.587715 | ||||||||
\(223\) | 1080.00 | 0.324315 | 0.162157 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162157 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1791.00 | 0.530667 | ||||||||
\(226\) | −5560.00 | −1.63649 | ||||||||
\(227\) | 1332.00 | 0.389462 | 0.194731 | − | 0.980857i | \(-0.437617\pi\) | ||||
0.194731 | + | 0.980857i | \(0.437617\pi\) | |||||||
\(228\) | −1728.00 | −0.501928 | ||||||||
\(229\) | −1620.00 | −0.467479 | −0.233739 | − | 0.972299i | \(-0.575096\pi\) | ||||
−0.233739 | + | 0.972299i | \(0.575096\pi\) | |||||||
\(230\) | −1008.00 | −0.288981 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6718.00 | 1.88889 | 0.944444 | − | 0.328673i | \(-0.106601\pi\) | ||||
0.944444 | + | 0.328673i | \(0.106601\pi\) | |||||||
\(234\) | 1296.00 | 0.362061 | ||||||||
\(235\) | −1296.00 | −0.359752 | ||||||||
\(236\) | −3744.00 | −1.03268 | ||||||||
\(237\) | −708.000 | −0.194049 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3578.00 | −0.968375 | −0.484187 | − | 0.874964i | \(-0.660885\pi\) | ||||
−0.484187 | + | 0.874964i | \(0.660885\pi\) | |||||||
\(240\) | −3456.00 | −0.929516 | ||||||||
\(241\) | 756.000 | 0.202067 | 0.101034 | − | 0.994883i | \(-0.467785\pi\) | ||||
0.101034 | + | 0.994883i | \(0.467785\pi\) | |||||||
\(242\) | 4676.00 | 1.24209 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −6336.00 | −1.66238 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3240.00 | −0.839735 | ||||||||
\(247\) | 2592.00 | 0.667713 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 108.000 | 0.0274868 | ||||||||
\(250\) | −5328.00 | −1.34789 | ||||||||
\(251\) | 6516.00 | 1.63859 | 0.819295 | − | 0.573372i | \(-0.194365\pi\) | ||||
0.819295 | + | 0.573372i | \(0.194365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −700.000 | −0.173947 | ||||||||
\(254\) | 3664.00 | 0.905117 | ||||||||
\(255\) | −6804.00 | −1.67091 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 6030.00 | 1.46358 | 0.731792 | − | 0.681528i | \(-0.238684\pi\) | ||||
0.731792 | + | 0.681528i | \(0.238684\pi\) | |||||||
\(258\) | 3888.00 | 0.938203 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5184.00 | −1.23653 | ||||||||
\(261\) | 1422.00 | 0.337240 | ||||||||
\(262\) | −9072.00 | −2.13920 | ||||||||
\(263\) | 590.000 | 0.138331 | 0.0691653 | − | 0.997605i | \(-0.477966\pi\) | ||||
0.0691653 | + | 0.997605i | \(0.477966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 396.000 | 0.0917966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 702.000 | 0.160905 | ||||||||
\(268\) | 1856.00 | 0.423034 | ||||||||
\(269\) | 990.000 | 0.224392 | 0.112196 | − | 0.993686i | \(-0.464212\pi\) | ||||
0.112196 | + | 0.993686i | \(0.464212\pi\) | |||||||
\(270\) | 1944.00 | 0.438178 | ||||||||
\(271\) | 3420.00 | 0.766606 | 0.383303 | − | 0.923623i | \(-0.374787\pi\) | ||||
0.383303 | + | 0.923623i | \(0.374787\pi\) | |||||||
\(272\) | 8064.00 | 1.79762 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3224.00 | 0.710836 | ||||||||
\(275\) | −9950.00 | −2.18185 | ||||||||
\(276\) | −336.000 | −0.0732783 | ||||||||
\(277\) | −2734.00 | −0.593033 | −0.296516 | − | 0.955028i | \(-0.595825\pi\) | ||||
−0.296516 | + | 0.955028i | \(0.595825\pi\) | |||||||
\(278\) | −10512.0 | −2.26787 | ||||||||
\(279\) | 324.000 | 0.0695246 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 598.000 | 0.126953 | 0.0634763 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634763 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(282\) | −864.000 | −0.182448 | ||||||||
\(283\) | −3600.00 | −0.756176 | −0.378088 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378088 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(284\) | −5872.00 | −1.22690 | ||||||||
\(285\) | 3888.00 | 0.808089 | ||||||||
\(286\) | −7200.00 | −1.48862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2304.00 | −0.471405 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | −11376.0 | −2.30352 | ||||||||
\(291\) | 1404.00 | 0.282831 | ||||||||
\(292\) | −1440.00 | −0.288595 | ||||||||
\(293\) | −7902.00 | −1.57556 | −0.787781 | − | 0.615955i | \(-0.788770\pi\) | ||||
−0.787781 | + | 0.615955i | \(0.788770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8424.00 | 1.66259 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1350.00 | 0.263754 | ||||||||
\(298\) | −9560.00 | −1.85838 | ||||||||
\(299\) | 504.000 | 0.0974818 | ||||||||
\(300\) | −4776.00 | −0.919142 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12960.0 | 2.46942 | ||||||||
\(303\) | −1998.00 | −0.378819 | ||||||||
\(304\) | −4608.00 | −0.869365 | ||||||||
\(305\) | 14256.0 | 2.67638 | ||||||||
\(306\) | −4536.00 | −0.847405 | ||||||||
\(307\) | 10224.0 | 1.90070 | 0.950349 | − | 0.311185i | \(-0.100726\pi\) | ||||
0.950349 | + | 0.311185i | \(0.100726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −756.000 | −0.139182 | ||||||||
\(310\) | −2592.00 | −0.474889 | ||||||||
\(311\) | −3888.00 | −0.708901 | −0.354451 | − | 0.935075i | \(-0.615332\pi\) | ||||
−0.354451 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5112.00 | −0.923154 | −0.461577 | − | 0.887100i | \(-0.652716\pi\) | ||||
−0.461577 | + | 0.887100i | \(0.652716\pi\) | |||||||
\(314\) | −12096.0 | −2.17394 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | −10102.0 | −1.78986 | −0.894929 | − | 0.446209i | \(-0.852774\pi\) | ||||
−0.894929 | + | 0.446209i | \(0.852774\pi\) | |||||||
\(318\) | 264.000 | 0.0465547 | ||||||||
\(319\) | −7900.00 | −1.38657 | ||||||||
\(320\) | 9216.00 | 1.60997 | ||||||||
\(321\) | −2010.00 | −0.349493 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9072.00 | −1.56279 | ||||||||
\(324\) | 648.000 | 0.111111 | ||||||||
\(325\) | 7164.00 | 1.22273 | ||||||||
\(326\) | −7136.00 | −1.21235 | ||||||||
\(327\) | −486.000 | −0.0821892 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10800.0 | −1.80158 | ||||||||
\(331\) | 5508.00 | 0.914644 | 0.457322 | − | 0.889301i | \(-0.348809\pi\) | ||||
0.457322 | + | 0.889301i | \(0.348809\pi\) | |||||||
\(332\) | −288.000 | −0.0476086 | ||||||||
\(333\) | −1458.00 | −0.239934 | ||||||||
\(334\) | 12096.0 | 1.98163 | ||||||||
\(335\) | −4176.00 | −0.681072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9234.00 | −1.49261 | −0.746303 | − | 0.665607i | \(-0.768173\pi\) | ||||
−0.746303 | + | 0.665607i | \(0.768173\pi\) | |||||||
\(338\) | −3604.00 | −0.579976 | ||||||||
\(339\) | 4170.00 | 0.668092 | ||||||||
\(340\) | 18144.0 | 2.89411 | ||||||||
\(341\) | −1800.00 | −0.285852 | ||||||||
\(342\) | 2592.00 | 0.409823 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 756.000 | 0.117976 | ||||||||
\(346\) | −6264.00 | −0.973280 | ||||||||
\(347\) | −6494.00 | −1.00466 | −0.502329 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502329 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(348\) | −3792.00 | −0.584116 | ||||||||
\(349\) | −10080.0 | −1.54605 | −0.773023 | − | 0.634378i | \(-0.781256\pi\) | ||||
−0.773023 | + | 0.634378i | \(0.781256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −972.000 | −0.147811 | ||||||||
\(352\) | 12800.0 | 1.93819 | ||||||||
\(353\) | 738.000 | 0.111274 | 0.0556371 | − | 0.998451i | \(-0.482281\pi\) | ||||
0.0556371 | + | 0.998451i | \(0.482281\pi\) | |||||||
\(354\) | 5616.00 | 0.843184 | ||||||||
\(355\) | 13212.0 | 1.97527 | ||||||||
\(356\) | −1872.00 | −0.278696 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15208.0 | 2.24516 | ||||||||
\(359\) | 194.000 | 0.0285207 | 0.0142603 | − | 0.999898i | \(-0.495461\pi\) | ||||
0.0142603 | + | 0.999898i | \(0.495461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1675.00 | −0.244205 | ||||||||
\(362\) | 1872.00 | 0.271796 | ||||||||
\(363\) | −3507.00 | −0.507079 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3240.00 | 0.464628 | ||||||||
\(366\) | 9504.00 | 1.35733 | ||||||||
\(367\) | 4752.00 | 0.675892 | 0.337946 | − | 0.941165i | \(-0.390268\pi\) | ||||
0.337946 | + | 0.941165i | \(0.390268\pi\) | |||||||
\(368\) | −896.000 | −0.126922 | ||||||||
\(369\) | 2430.00 | 0.342820 | ||||||||
\(370\) | 11664.0 | 1.63887 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −864.000 | −0.120420 | ||||||||
\(373\) | −2306.00 | −0.320108 | −0.160054 | − | 0.987108i | \(-0.551167\pi\) | ||||
−0.160054 | + | 0.987108i | \(0.551167\pi\) | |||||||
\(374\) | 25200.0 | 3.48412 | ||||||||
\(375\) | 3996.00 | 0.550273 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5688.00 | 0.777047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7452.00 | −1.00998 | −0.504991 | − | 0.863124i | \(-0.668504\pi\) | ||||
−0.504991 | + | 0.863124i | \(0.668504\pi\) | |||||||
\(380\) | −10368.0 | −1.39965 | ||||||||
\(381\) | −2748.00 | −0.369513 | ||||||||
\(382\) | 1928.00 | 0.258233 | ||||||||
\(383\) | 1152.00 | 0.153693 | 0.0768465 | − | 0.997043i | \(-0.475515\pi\) | ||||
0.0768465 | + | 0.997043i | \(0.475515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3240.00 | −0.427232 | ||||||||
\(387\) | −2916.00 | −0.383020 | ||||||||
\(388\) | −3744.00 | −0.489878 | ||||||||
\(389\) | 1894.00 | 0.246863 | 0.123431 | − | 0.992353i | \(-0.460610\pi\) | ||||
0.123431 | + | 0.992353i | \(0.460610\pi\) | |||||||
\(390\) | 7776.00 | 1.00962 | ||||||||
\(391\) | −1764.00 | −0.228157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6804.00 | 0.873324 | ||||||||
\(394\) | −9848.00 | −1.25923 | ||||||||
\(395\) | −4248.00 | −0.541114 | ||||||||
\(396\) | −3600.00 | −0.456835 | ||||||||
\(397\) | −9216.00 | −1.16508 | −0.582541 | − | 0.812801i | \(-0.697942\pi\) | ||||
−0.582541 | + | 0.812801i | \(0.697942\pi\) | |||||||
\(398\) | 18144.0 | 2.28512 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12736.0 | −1.59200 | ||||||||
\(401\) | −11650.0 | −1.45081 | −0.725403 | − | 0.688324i | \(-0.758347\pi\) | ||||
−0.725403 | + | 0.688324i | \(0.758347\pi\) | |||||||
\(402\) | −2784.00 | −0.345406 | ||||||||
\(403\) | 1296.00 | 0.160194 | ||||||||
\(404\) | 5328.00 | 0.656133 | ||||||||
\(405\) | −1458.00 | −0.178885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8100.00 | 0.986492 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7524.00 | 0.909628 | 0.454814 | − | 0.890586i | \(-0.349706\pi\) | ||||
0.454814 | + | 0.890586i | \(0.349706\pi\) | |||||||
\(410\) | −19440.0 | −2.34164 | ||||||||
\(411\) | −2418.00 | −0.290197 | ||||||||
\(412\) | 2016.00 | 0.241071 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 504.000 | 0.0598315 | ||||||||
\(415\) | 648.000 | 0.0766484 | ||||||||
\(416\) | −9216.00 | −1.08618 | ||||||||
\(417\) | 7884.00 | 0.925854 | ||||||||
\(418\) | −14400.0 | −1.68499 | ||||||||
\(419\) | 3852.00 | 0.449123 | 0.224561 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224561 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10402.0 | 1.20419 | 0.602093 | − | 0.798426i | \(-0.294334\pi\) | ||||
0.602093 | + | 0.798426i | \(0.294334\pi\) | |||||||
\(422\) | 11664.0 | 1.34548 | ||||||||
\(423\) | 648.000 | 0.0744843 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25074.0 | −2.86181 | ||||||||
\(426\) | 8808.00 | 1.00176 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5360.00 | 0.605340 | ||||||||
\(429\) | 5400.00 | 0.607726 | ||||||||
\(430\) | 23328.0 | 2.61622 | ||||||||
\(431\) | −10390.0 | −1.16118 | −0.580590 | − | 0.814196i | \(-0.697178\pi\) | ||||
−0.580590 | + | 0.814196i | \(0.697178\pi\) | |||||||
\(432\) | 1728.00 | 0.192450 | ||||||||
\(433\) | −11232.0 | −1.24659 | −0.623297 | − | 0.781985i | \(-0.714207\pi\) | ||||
−0.623297 | + | 0.781985i | \(0.714207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8532.00 | 0.940409 | ||||||||
\(436\) | 1296.00 | 0.142356 | ||||||||
\(437\) | 1008.00 | 0.110341 | ||||||||
\(438\) | 2160.00 | 0.235637 | ||||||||
\(439\) | −14616.0 | −1.58903 | −0.794514 | − | 0.607245i | \(-0.792275\pi\) | ||||
−0.794514 | + | 0.607245i | \(0.792275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18144.0 | −1.95254 | ||||||||
\(443\) | 11938.0 | 1.28034 | 0.640171 | − | 0.768232i | \(-0.278863\pi\) | ||||
0.640171 | + | 0.768232i | \(0.278863\pi\) | |||||||
\(444\) | 3888.00 | 0.415577 | ||||||||
\(445\) | 4212.00 | 0.448692 | ||||||||
\(446\) | 4320.00 | 0.458650 | ||||||||
\(447\) | 7170.00 | 0.758679 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8186.00 | 0.860404 | 0.430202 | − | 0.902733i | \(-0.358442\pi\) | ||||
0.430202 | + | 0.902733i | \(0.358442\pi\) | |||||||
\(450\) | 7164.00 | 0.750476 | ||||||||
\(451\) | −13500.0 | −1.40951 | ||||||||
\(452\) | −11120.0 | −1.15717 | ||||||||
\(453\) | −9720.00 | −1.00814 | ||||||||
\(454\) | 5328.00 | 0.550783 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2106.00 | 0.215568 | 0.107784 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107784 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(458\) | −6480.00 | −0.661115 | ||||||||
\(459\) | 3402.00 | 0.345952 | ||||||||
\(460\) | −2016.00 | −0.204340 | ||||||||
\(461\) | −9486.00 | −0.958367 | −0.479183 | − | 0.877715i | \(-0.659067\pi\) | ||||
−0.479183 | + | 0.877715i | \(0.659067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12652.0 | −1.26995 | −0.634977 | − | 0.772531i | \(-0.718990\pi\) | ||||
−0.634977 | + | 0.772531i | \(0.718990\pi\) | |||||||
\(464\) | −10112.0 | −1.01172 | ||||||||
\(465\) | 1944.00 | 0.193873 | ||||||||
\(466\) | 26872.0 | 2.67129 | ||||||||
\(467\) | 3708.00 | 0.367421 | 0.183711 | − | 0.982980i | \(-0.441189\pi\) | ||||
0.183711 | + | 0.982980i | \(0.441189\pi\) | |||||||
\(468\) | 2592.00 | 0.256015 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5184.00 | −0.508766 | ||||||||
\(471\) | 9072.00 | 0.887507 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16200.0 | 1.57479 | ||||||||
\(474\) | −2832.00 | −0.274426 | ||||||||
\(475\) | 14328.0 | 1.38403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −198.000 | −0.0190059 | ||||||||
\(478\) | −14312.0 | −1.36949 | ||||||||
\(479\) | 8064.00 | 0.769214 | 0.384607 | − | 0.923080i | \(-0.374337\pi\) | ||||
0.384607 | + | 0.923080i | \(0.374337\pi\) | |||||||
\(480\) | −13824.0 | −1.31453 | ||||||||
\(481\) | −5832.00 | −0.552841 | ||||||||
\(482\) | 3024.00 | 0.285766 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9352.00 | 0.878287 | ||||||||
\(485\) | 8424.00 | 0.788689 | ||||||||
\(486\) | −972.000 | −0.0907218 | ||||||||
\(487\) | −11664.0 | −1.08531 | −0.542655 | − | 0.839955i | \(-0.682581\pi\) | ||||
−0.542655 | + | 0.839955i | \(0.682581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5352.00 | 0.494940 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9814.00 | −0.902036 | −0.451018 | − | 0.892515i | \(-0.648939\pi\) | ||||
−0.451018 | + | 0.892515i | \(0.648939\pi\) | |||||||
\(492\) | −6480.00 | −0.593782 | ||||||||
\(493\) | −19908.0 | −1.81868 | ||||||||
\(494\) | 10368.0 | 0.944288 | ||||||||
\(495\) | 8100.00 | 0.735491 | ||||||||
\(496\) | −2304.00 | −0.208574 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 432.000 | 0.0388723 | ||||||||
\(499\) | −15228.0 | −1.36613 | −0.683065 | − | 0.730358i | \(-0.739353\pi\) | ||||
−0.683065 | + | 0.730358i | \(0.739353\pi\) | |||||||
\(500\) | −10656.0 | −0.953102 | ||||||||
\(501\) | −9072.00 | −0.808996 | ||||||||
\(502\) | 26064.0 | 2.31732 | ||||||||
\(503\) | 11088.0 | 0.982882 | 0.491441 | − | 0.870911i | \(-0.336470\pi\) | ||||
0.491441 | + | 0.870911i | \(0.336470\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11988.0 | −1.05635 | ||||||||
\(506\) | −2800.00 | −0.245998 | ||||||||
\(507\) | 2703.00 | 0.236774 | ||||||||
\(508\) | 7328.00 | 0.640015 | ||||||||
\(509\) | 5814.00 | 0.506289 | 0.253144 | − | 0.967429i | \(-0.418535\pi\) | ||||
0.253144 | + | 0.967429i | \(0.418535\pi\) | |||||||
\(510\) | −27216.0 | −2.36303 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16384.0 | 1.41421 | ||||||||
\(513\) | −1944.00 | −0.167309 | ||||||||
\(514\) | 24120.0 | 2.06982 | ||||||||
\(515\) | −4536.00 | −0.388117 | ||||||||
\(516\) | 7776.00 | 0.663410 | ||||||||
\(517\) | −3600.00 | −0.306243 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4698.00 | 0.397340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11682.0 | 0.982337 | 0.491169 | − | 0.871065i | \(-0.336570\pi\) | ||||
0.491169 | + | 0.871065i | \(0.336570\pi\) | |||||||
\(522\) | 5688.00 | 0.476929 | ||||||||
\(523\) | 2988.00 | 0.249820 | 0.124910 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124910 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(524\) | −18144.0 | −1.51264 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2360.00 | 0.195629 | ||||||||
\(527\) | −4536.00 | −0.374936 | ||||||||
\(528\) | −9600.00 | −0.791262 | ||||||||
\(529\) | −11971.0 | −0.983891 | ||||||||
\(530\) | 1584.00 | 0.129820 | ||||||||
\(531\) | −4212.00 | −0.344228 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9720.00 | 0.789906 | ||||||||
\(534\) | 2808.00 | 0.227554 | ||||||||
\(535\) | −12060.0 | −0.974578 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11406.0 | −0.916583 | ||||||||
\(538\) | 3960.00 | 0.317338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3888.00 | 0.309839 | ||||||||
\(541\) | 7130.00 | 0.566622 | 0.283311 | − | 0.959028i | \(-0.408567\pi\) | ||||
0.283311 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(542\) | 13680.0 | 1.08414 | ||||||||
\(543\) | −1404.00 | −0.110960 | ||||||||
\(544\) | 32256.0 | 2.54221 | ||||||||
\(545\) | −2916.00 | −0.229188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5488.00 | −0.428976 | −0.214488 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214488 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(548\) | 6448.00 | 0.502637 | ||||||||
\(549\) | −7128.00 | −0.554127 | ||||||||
\(550\) | −39800.0 | −3.08560 | ||||||||
\(551\) | 11376.0 | 0.879553 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10936.0 | −0.838675 | ||||||||
\(555\) | −8748.00 | −0.669067 | ||||||||
\(556\) | −21024.0 | −1.60363 | ||||||||
\(557\) | 5746.00 | 0.437102 | 0.218551 | − | 0.975826i | \(-0.429867\pi\) | ||||
0.218551 | + | 0.975826i | \(0.429867\pi\) | |||||||
\(558\) | 1296.00 | 0.0983227 | ||||||||
\(559\) | −11664.0 | −0.882531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18900.0 | −1.42239 | ||||||||
\(562\) | 2392.00 | 0.179538 | ||||||||
\(563\) | −13068.0 | −0.978243 | −0.489121 | − | 0.872216i | \(-0.662682\pi\) | ||||
−0.489121 | + | 0.872216i | \(0.662682\pi\) | |||||||
\(564\) | −1728.00 | −0.129011 | ||||||||
\(565\) | 25020.0 | 1.86301 | ||||||||
\(566\) | −14400.0 | −1.06939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1130.00 | −0.0832549 | −0.0416275 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416275 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(570\) | 15552.0 | 1.14281 | ||||||||
\(571\) | 16864.0 | 1.23597 | 0.617983 | − | 0.786192i | \(-0.287950\pi\) | ||||
0.617983 | + | 0.786192i | \(0.287950\pi\) | |||||||
\(572\) | −14400.0 | −1.05261 | ||||||||
\(573\) | −1446.00 | −0.105423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2786.00 | 0.202060 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | 2088.00 | 0.150649 | 0.0753246 | − | 0.997159i | \(-0.476001\pi\) | ||||
0.0753246 | + | 0.997159i | \(0.476001\pi\) | |||||||
\(578\) | 43852.0 | 3.15571 | ||||||||
\(579\) | 2430.00 | 0.174417 | ||||||||
\(580\) | −22752.0 | −1.62884 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5616.00 | 0.399984 | ||||||||
\(583\) | 1100.00 | 0.0781430 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5832.00 | −0.412177 | ||||||||
\(586\) | −31608.0 | −2.22818 | ||||||||
\(587\) | −10260.0 | −0.721423 | −0.360712 | − | 0.932677i | \(-0.617466\pi\) | ||||
−0.360712 | + | 0.932677i | \(0.617466\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2592.00 | 0.181327 | ||||||||
\(590\) | 33696.0 | 2.35126 | ||||||||
\(591\) | 7386.00 | 0.514077 | ||||||||
\(592\) | 10368.0 | 0.719801 | ||||||||
\(593\) | −3582.00 | −0.248052 | −0.124026 | − | 0.992279i | \(-0.539581\pi\) | ||||
−0.124026 | + | 0.992279i | \(0.539581\pi\) | |||||||
\(594\) | 5400.00 | 0.373005 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19120.0 | −1.31407 | ||||||||
\(597\) | −13608.0 | −0.932895 | ||||||||
\(598\) | 2016.00 | 0.137860 | ||||||||
\(599\) | 7034.00 | 0.479802 | 0.239901 | − | 0.970797i | \(-0.422885\pi\) | ||||
0.239901 | + | 0.970797i | \(0.422885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18072.0 | 1.22658 | 0.613288 | − | 0.789859i | \(-0.289846\pi\) | ||||
0.613288 | + | 0.789859i | \(0.289846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2088.00 | 0.141011 | ||||||||
\(604\) | 25920.0 | 1.74614 | ||||||||
\(605\) | −21042.0 | −1.41401 | ||||||||
\(606\) | −7992.00 | −0.535731 | ||||||||
\(607\) | −28584.0 | −1.91135 | −0.955674 | − | 0.294425i | \(-0.904872\pi\) | ||||
−0.955674 | + | 0.294425i | \(0.904872\pi\) | |||||||
\(608\) | −18432.0 | −1.22947 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 57024.0 | 3.78497 | ||||||||
\(611\) | 2592.00 | 0.171622 | ||||||||
\(612\) | −9072.00 | −0.599206 | ||||||||
\(613\) | −10910.0 | −0.718843 | −0.359421 | − | 0.933175i | \(-0.617026\pi\) | ||||
−0.359421 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(614\) | 40896.0 | 2.68799 | ||||||||
\(615\) | 14580.0 | 0.955971 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5522.00 | −0.360304 | −0.180152 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180152 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(618\) | −3024.00 | −0.196834 | ||||||||
\(619\) | −2412.00 | −0.156618 | −0.0783089 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783089 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(620\) | −5184.00 | −0.335798 | ||||||||
\(621\) | −378.000 | −0.0244261 | ||||||||
\(622\) | −15552.0 | −1.00254 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6912.00 | 0.443432 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | −20448.0 | −1.30554 | ||||||||
\(627\) | 10800.0 | 0.687895 | ||||||||
\(628\) | −24192.0 | −1.53721 | ||||||||
\(629\) | 20412.0 | 1.29393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24676.0 | 1.55679 | 0.778396 | − | 0.627773i | \(-0.216034\pi\) | ||||
0.778396 | + | 0.627773i | \(0.216034\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8748.00 | −0.549292 | ||||||||
\(634\) | −40408.0 | −2.53124 | ||||||||
\(635\) | −16488.0 | −1.03040 | ||||||||
\(636\) | 528.000 | 0.0329191 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −31600.0 | −1.96090 | ||||||||
\(639\) | −6606.00 | −0.408966 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27482.0 | −1.69341 | −0.846703 | − | 0.532065i | \(-0.821416\pi\) | ||||
−0.846703 | + | 0.532065i | \(0.821416\pi\) | |||||||
\(642\) | −8040.00 | −0.494258 | ||||||||
\(643\) | 22752.0 | 1.39541 | 0.697707 | − | 0.716383i | \(-0.254204\pi\) | ||||
0.697707 | + | 0.716383i | \(0.254204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17496.0 | −1.06807 | ||||||||
\(646\) | −36288.0 | −2.21011 | ||||||||
\(647\) | −14832.0 | −0.901246 | −0.450623 | − | 0.892714i | \(-0.648798\pi\) | ||||
−0.450623 | + | 0.892714i | \(0.648798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23400.0 | 1.41530 | ||||||||
\(650\) | 28656.0 | 1.72920 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14272.0 | −0.857262 | ||||||||
\(653\) | 2822.00 | 0.169117 | 0.0845585 | − | 0.996419i | \(-0.473052\pi\) | ||||
0.0845585 | + | 0.996419i | \(0.473052\pi\) | |||||||
\(654\) | −1944.00 | −0.116233 | ||||||||
\(655\) | 40824.0 | 2.43531 | ||||||||
\(656\) | −17280.0 | −1.02846 | ||||||||
\(657\) | −1620.00 | −0.0961982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15826.0 | −0.935498 | −0.467749 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(660\) | −21600.0 | −1.27391 | ||||||||
\(661\) | 23832.0 | 1.40236 | 0.701178 | − | 0.712986i | \(-0.252658\pi\) | ||||
0.701178 | + | 0.712986i | \(0.252658\pi\) | |||||||
\(662\) | 22032.0 | 1.29350 | ||||||||
\(663\) | 13608.0 | 0.797121 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5832.00 | −0.339317 | ||||||||
\(667\) | 2212.00 | 0.128409 | ||||||||
\(668\) | 24192.0 | 1.40122 | ||||||||
\(669\) | −3240.00 | −0.187243 | ||||||||
\(670\) | −16704.0 | −0.963182 | ||||||||
\(671\) | 39600.0 | 2.27830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13770.0 | 0.788699 | 0.394350 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394350 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(674\) | −36936.0 | −2.11086 | ||||||||
\(675\) | −5373.00 | −0.306381 | ||||||||
\(676\) | −7208.00 | −0.410105 | ||||||||
\(677\) | −8334.00 | −0.473119 | −0.236560 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236560 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(678\) | 16680.0 | 0.944825 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3996.00 | −0.224856 | ||||||||
\(682\) | −7200.00 | −0.404255 | ||||||||
\(683\) | −18598.0 | −1.04192 | −0.520961 | − | 0.853580i | \(-0.674426\pi\) | ||||
−0.520961 | + | 0.853580i | \(0.674426\pi\) | |||||||
\(684\) | 5184.00 | 0.289788 | ||||||||
\(685\) | −14508.0 | −0.809229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4860.00 | 0.269899 | ||||||||
\(688\) | 20736.0 | 1.14906 | ||||||||
\(689\) | −792.000 | −0.0437922 | ||||||||
\(690\) | 3024.00 | 0.166843 | ||||||||
\(691\) | −8964.00 | −0.493497 | −0.246749 | − | 0.969080i | \(-0.579362\pi\) | ||||
−0.246749 | + | 0.969080i | \(0.579362\pi\) | |||||||
\(692\) | −12528.0 | −0.688213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25976.0 | −1.42080 | ||||||||
\(695\) | 47304.0 | 2.58179 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34020.0 | −1.84878 | ||||||||
\(698\) | −40320.0 | −2.18644 | ||||||||
\(699\) | −20154.0 | −1.09055 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3542.00 | 0.190841 | 0.0954205 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954205 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(702\) | −3888.00 | −0.209036 | ||||||||
\(703\) | −11664.0 | −0.625770 | ||||||||
\(704\) | 25600.0 | 1.37051 | ||||||||
\(705\) | 3888.00 | 0.207703 | ||||||||
\(706\) | 2952.00 | 0.157365 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11232.0 | 0.596221 | ||||||||
\(709\) | −486.000 | −0.0257435 | −0.0128717 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128717 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(710\) | 52848.0 | 2.79345 | ||||||||
\(711\) | 2124.00 | 0.112034 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 504.000 | 0.0264726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32400.0 | 1.69467 | ||||||||
\(716\) | 30416.0 | 1.58757 | ||||||||
\(717\) | 10734.0 | 0.559091 | ||||||||
\(718\) | 776.000 | 0.0403343 | ||||||||
\(719\) | 26928.0 | 1.39672 | 0.698362 | − | 0.715744i | \(-0.253912\pi\) | ||||
0.698362 | + | 0.715744i | \(0.253912\pi\) | |||||||
\(720\) | 10368.0 | 0.536656 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6700.00 | −0.345358 | ||||||||
\(723\) | −2268.00 | −0.116664 | ||||||||
\(724\) | 3744.00 | 0.192189 | ||||||||
\(725\) | 31442.0 | 1.61066 | ||||||||
\(726\) | −14028.0 | −0.717118 | ||||||||
\(727\) | −20628.0 | −1.05234 | −0.526169 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526169 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 12960.0 | 0.657084 | ||||||||
\(731\) | 40824.0 | 2.06557 | ||||||||
\(732\) | 19008.0 | 0.959776 | ||||||||
\(733\) | 9756.00 | 0.491604 | 0.245802 | − | 0.969320i | \(-0.420949\pi\) | ||||
0.245802 | + | 0.969320i | \(0.420949\pi\) | |||||||
\(734\) | 19008.0 | 0.955856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3584.00 | −0.179495 | ||||||||
\(737\) | −11600.0 | −0.579771 | ||||||||
\(738\) | 9720.00 | 0.484821 | ||||||||
\(739\) | 19064.0 | 0.948959 | 0.474479 | − | 0.880267i | \(-0.342636\pi\) | ||||
0.474479 | + | 0.880267i | \(0.342636\pi\) | |||||||
\(740\) | 23328.0 | 1.15886 | ||||||||
\(741\) | −7776.00 | −0.385504 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3766.00 | −0.185950 | −0.0929752 | − | 0.995668i | \(-0.529638\pi\) | ||||
−0.0929752 | + | 0.995668i | \(0.529638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43020.0 | 2.11561 | ||||||||
\(746\) | −9224.00 | −0.452701 | ||||||||
\(747\) | −324.000 | −0.0158695 | ||||||||
\(748\) | 50400.0 | 2.46365 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15984.0 | 0.778204 | ||||||||
\(751\) | −11664.0 | −0.566745 | −0.283372 | − | 0.959010i | \(-0.591453\pi\) | ||||
−0.283372 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(752\) | −4608.00 | −0.223453 | ||||||||
\(753\) | −19548.0 | −0.946041 | ||||||||
\(754\) | 22752.0 | 1.09891 | ||||||||
\(755\) | −58320.0 | −2.81123 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34182.0 | −1.64117 | −0.820585 | − | 0.571524i | \(-0.806352\pi\) | ||||
−0.820585 | + | 0.571524i | \(0.806352\pi\) | |||||||
\(758\) | −29808.0 | −1.42833 | ||||||||
\(759\) | 2100.00 | 0.100428 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4734.00 | 0.225502 | 0.112751 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112751 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(762\) | −10992.0 | −0.522570 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3856.00 | 0.182598 | ||||||||
\(765\) | 20412.0 | 0.964703 | ||||||||
\(766\) | 4608.00 | 0.217355 | ||||||||
\(767\) | −16848.0 | −0.793150 | ||||||||
\(768\) | −12288.0 | −0.577350 | ||||||||
\(769\) | 30240.0 | 1.41805 | 0.709026 | − | 0.705182i | \(-0.249135\pi\) | ||||
0.709026 | + | 0.705182i | \(0.249135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18090.0 | −0.845001 | ||||||||
\(772\) | −6480.00 | −0.302099 | ||||||||
\(773\) | −27702.0 | −1.28897 | −0.644484 | − | 0.764618i | \(-0.722928\pi\) | ||||
−0.644484 | + | 0.764618i | \(0.722928\pi\) | |||||||
\(774\) | −11664.0 | −0.541672 | ||||||||
\(775\) | 7164.00 | 0.332050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7576.00 | 0.349117 | ||||||||
\(779\) | 19440.0 | 0.894108 | ||||||||
\(780\) | 15552.0 | 0.713911 | ||||||||
\(781\) | 36700.0 | 1.68147 | ||||||||
\(782\) | −7056.00 | −0.322662 | ||||||||
\(783\) | −4266.00 | −0.194705 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54432.0 | 2.47486 | ||||||||
\(786\) | 27216.0 | 1.23507 | ||||||||
\(787\) | 22644.0 | 1.02563 | 0.512815 | − | 0.858499i | \(-0.328603\pi\) | ||||
0.512815 | + | 0.858499i | \(0.328603\pi\) | |||||||
\(788\) | −19696.0 | −0.890407 | ||||||||
\(789\) | −1770.00 | −0.0798652 | ||||||||
\(790\) | −16992.0 | −0.765251 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28512.0 | −1.27679 | ||||||||
\(794\) | −36864.0 | −1.64768 | ||||||||
\(795\) | −1188.00 | −0.0529988 | ||||||||
\(796\) | 36288.0 | 1.61582 | ||||||||
\(797\) | −30150.0 | −1.33998 | −0.669992 | − | 0.742368i | \(-0.733703\pi\) | ||||
−0.669992 | + | 0.742368i | \(0.733703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9072.00 | −0.401682 | ||||||||
\(800\) | −50944.0 | −2.25143 | ||||||||
\(801\) | −2106.00 | −0.0928987 | ||||||||
\(802\) | −46600.0 | −2.05175 | ||||||||
\(803\) | 9000.00 | 0.395521 | ||||||||
\(804\) | −5568.00 | −0.244239 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5184.00 | 0.226549 | ||||||||
\(807\) | −2970.00 | −0.129553 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11318.0 | −0.491866 | −0.245933 | − | 0.969287i | \(-0.579094\pi\) | ||||
−0.245933 | + | 0.969287i | \(0.579094\pi\) | |||||||
\(810\) | −5832.00 | −0.252982 | ||||||||
\(811\) | 29628.0 | 1.28284 | 0.641418 | − | 0.767192i | \(-0.278347\pi\) | ||||
0.641418 | + | 0.767192i | \(0.278347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10260.0 | −0.442600 | ||||||||
\(814\) | 32400.0 | 1.39511 | ||||||||
\(815\) | 32112.0 | 1.38016 | ||||||||
\(816\) | −24192.0 | −1.03785 | ||||||||
\(817\) | −23328.0 | −0.998952 | ||||||||
\(818\) | 30096.0 | 1.28641 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38880.0 | −1.65579 | ||||||||
\(821\) | 17770.0 | 0.755393 | 0.377696 | − | 0.925930i | \(-0.376716\pi\) | ||||
0.377696 | + | 0.925930i | \(0.376716\pi\) | |||||||
\(822\) | −9672.00 | −0.410401 | ||||||||
\(823\) | 7868.00 | 0.333246 | 0.166623 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166623 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29850.0 | 1.25969 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35726.0 | 1.50219 | 0.751097 | − | 0.660192i | \(-0.229525\pi\) | ||||
0.751097 | + | 0.660192i | \(0.229525\pi\) | |||||||
\(828\) | 1008.00 | 0.0423073 | ||||||||
\(829\) | −27108.0 | −1.13571 | −0.567853 | − | 0.823130i | \(-0.692226\pi\) | ||||
−0.567853 | + | 0.823130i | \(0.692226\pi\) | |||||||
\(830\) | 2592.00 | 0.108397 | ||||||||
\(831\) | 8202.00 | 0.342388 | ||||||||
\(832\) | −18432.0 | −0.768046 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31536.0 | 1.30936 | ||||||||
\(835\) | −54432.0 | −2.25592 | ||||||||
\(836\) | −28800.0 | −1.19147 | ||||||||
\(837\) | −972.000 | −0.0401401 | ||||||||
\(838\) | 15408.0 | 0.635156 | ||||||||
\(839\) | −23256.0 | −0.956956 | −0.478478 | − | 0.878099i | \(-0.658811\pi\) | ||||
−0.478478 | + | 0.878099i | \(0.658811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 575.000 | 0.0235762 | ||||||||
\(842\) | 41608.0 | 1.70298 | ||||||||
\(843\) | −1794.00 | −0.0732961 | ||||||||
\(844\) | 23328.0 | 0.951402 | ||||||||
\(845\) | 16218.0 | 0.660256 | ||||||||
\(846\) | 2592.00 | 0.105337 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1408.00 | 0.0570176 | ||||||||
\(849\) | 10800.0 | 0.436578 | ||||||||
\(850\) | −100296. | −4.04721 | ||||||||
\(851\) | −2268.00 | −0.0913584 | ||||||||
\(852\) | 17616.0 | 0.708350 | ||||||||
\(853\) | −35280.0 | −1.41614 | −0.708068 | − | 0.706144i | \(-0.750433\pi\) | ||||
−0.708068 | + | 0.706144i | \(0.750433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11664.0 | −0.466550 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19710.0 | 0.785625 | 0.392813 | − | 0.919619i | \(-0.371502\pi\) | ||||
0.392813 | + | 0.919619i | \(0.371502\pi\) | |||||||
\(858\) | 21600.0 | 0.859454 | ||||||||
\(859\) | −3888.00 | −0.154432 | −0.0772159 | − | 0.997014i | \(-0.524603\pi\) | ||||
−0.0772159 | + | 0.997014i | \(0.524603\pi\) | |||||||
\(860\) | 46656.0 | 1.84995 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41560.0 | −1.64216 | ||||||||
\(863\) | −36634.0 | −1.44500 | −0.722500 | − | 0.691370i | \(-0.757007\pi\) | ||||
−0.722500 | + | 0.691370i | \(0.757007\pi\) | |||||||
\(864\) | 6912.00 | 0.272166 | ||||||||
\(865\) | 28188.0 | 1.10800 | ||||||||
\(866\) | −44928.0 | −1.76295 | ||||||||
\(867\) | −32889.0 | −1.28831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11800.0 | −0.460630 | ||||||||
\(870\) | 34128.0 | 1.32994 | ||||||||
\(871\) | 8352.00 | 0.324910 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4212.00 | −0.163293 | ||||||||
\(874\) | 4032.00 | 0.156046 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4320.00 | 0.166620 | ||||||||
\(877\) | 1226.00 | 0.0472053 | 0.0236027 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236027 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(878\) | −58464.0 | −2.24723 | ||||||||
\(879\) | 23706.0 | 0.909651 | ||||||||
\(880\) | −57600.0 | −2.20647 | ||||||||
\(881\) | 38538.0 | 1.47376 | 0.736878 | − | 0.676026i | \(-0.236299\pi\) | ||||
0.736878 | + | 0.676026i | \(0.236299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37260.0 | −1.42004 | −0.710022 | − | 0.704180i | \(-0.751315\pi\) | ||||
−0.710022 | + | 0.704180i | \(0.751315\pi\) | |||||||
\(884\) | −36288.0 | −1.38065 | ||||||||
\(885\) | −25272.0 | −0.959897 | ||||||||
\(886\) | 47752.0 | 1.81068 | ||||||||
\(887\) | −26640.0 | −1.00844 | −0.504219 | − | 0.863576i | \(-0.668219\pi\) | ||||
−0.504219 | + | 0.863576i | \(0.668219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16848.0 | 0.634546 | ||||||||
\(891\) | −4050.00 | −0.152278 | ||||||||
\(892\) | 8640.00 | 0.324315 | ||||||||
\(893\) | 5184.00 | 0.194262 | ||||||||
\(894\) | 28680.0 | 1.07293 | ||||||||
\(895\) | −68436.0 | −2.55594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1512.00 | −0.0562812 | ||||||||
\(898\) | 32744.0 | 1.21679 | ||||||||
\(899\) | 5688.00 | 0.211018 | ||||||||
\(900\) | 14328.0 | 0.530667 | ||||||||
\(901\) | 2772.00 | 0.102496 | ||||||||
\(902\) | −54000.0 | −1.99335 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8424.00 | −0.309418 | ||||||||
\(906\) | −38880.0 | −1.42572 | ||||||||
\(907\) | −12636.0 | −0.462593 | −0.231296 | − | 0.972883i | \(-0.574297\pi\) | ||||
−0.231296 | + | 0.972883i | \(0.574297\pi\) | |||||||
\(908\) | 10656.0 | 0.389462 | ||||||||
\(909\) | 5994.00 | 0.218711 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33638.0 | −1.22336 | −0.611678 | − | 0.791107i | \(-0.709505\pi\) | ||||
−0.611678 | + | 0.791107i | \(0.709505\pi\) | |||||||
\(912\) | 13824.0 | 0.501928 | ||||||||
\(913\) | 1800.00 | 0.0652479 | ||||||||
\(914\) | 8424.00 | 0.304859 | ||||||||
\(915\) | −42768.0 | −1.54521 | ||||||||
\(916\) | −12960.0 | −0.467479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13608.0 | 0.489249 | ||||||||
\(919\) | 36936.0 | 1.32580 | 0.662898 | − | 0.748710i | \(-0.269326\pi\) | ||||
0.662898 | + | 0.748710i | \(0.269326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30672.0 | −1.09737 | ||||||||
\(922\) | −37944.0 | −1.35534 | ||||||||
\(923\) | −26424.0 | −0.942315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32238.0 | −1.14592 | ||||||||
\(926\) | −50608.0 | −1.79598 | ||||||||
\(927\) | 2268.00 | 0.0803570 | ||||||||
\(928\) | −40448.0 | −1.43079 | ||||||||
\(929\) | 22302.0 | 0.787626 | 0.393813 | − | 0.919191i | \(-0.371156\pi\) | ||||
0.393813 | + | 0.919191i | \(0.371156\pi\) | |||||||
\(930\) | 7776.00 | 0.274178 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 53744.0 | 1.88889 | ||||||||
\(933\) | 11664.0 | 0.409284 | ||||||||
\(934\) | 14832.0 | 0.519612 | ||||||||
\(935\) | −113400. | −3.96639 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13824.0 | −0.481975 | −0.240987 | − | 0.970528i | \(-0.577471\pi\) | ||||
−0.240987 | + | 0.970528i | \(0.577471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15336.0 | 0.532983 | ||||||||
\(940\) | −10368.0 | −0.359752 | ||||||||
\(941\) | −13554.0 | −0.469551 | −0.234776 | − | 0.972050i | \(-0.575436\pi\) | ||||
−0.234776 | + | 0.972050i | \(0.575436\pi\) | |||||||
\(942\) | 36288.0 | 1.25512 | ||||||||
\(943\) | 3780.00 | 0.130534 | ||||||||
\(944\) | 29952.0 | 1.03268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64800.0 | 2.22709 | ||||||||
\(947\) | 44878.0 | 1.53996 | 0.769978 | − | 0.638070i | \(-0.220267\pi\) | ||||
0.769978 | + | 0.638070i | \(0.220267\pi\) | |||||||
\(948\) | −5664.00 | −0.194049 | ||||||||
\(949\) | −6480.00 | −0.221654 | ||||||||
\(950\) | 57312.0 | 1.95731 | ||||||||
\(951\) | 30306.0 | 1.03337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38362.0 | 1.30395 | 0.651976 | − | 0.758239i | \(-0.273940\pi\) | ||||
0.651976 | + | 0.758239i | \(0.273940\pi\) | |||||||
\(954\) | −792.000 | −0.0268784 | ||||||||
\(955\) | −8676.00 | −0.293978 | ||||||||
\(956\) | −28624.0 | −0.968375 | ||||||||
\(957\) | 23700.0 | 0.800535 | ||||||||
\(958\) | 32256.0 | 1.08783 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27648.0 | −0.929516 | ||||||||
\(961\) | −28495.0 | −0.956497 | ||||||||
\(962\) | −23328.0 | −0.781835 | ||||||||
\(963\) | 6030.00 | 0.201780 | ||||||||
\(964\) | 6048.00 | 0.202067 | ||||||||
\(965\) | 14580.0 | 0.486370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26444.0 | 0.879402 | 0.439701 | − | 0.898144i | \(-0.355084\pi\) | ||||
0.439701 | + | 0.898144i | \(0.355084\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27216.0 | 0.902274 | ||||||||
\(970\) | 33696.0 | 1.11537 | ||||||||
\(971\) | −17820.0 | −0.588951 | −0.294475 | − | 0.955659i | \(-0.595145\pi\) | ||||
−0.294475 | + | 0.955659i | \(0.595145\pi\) | |||||||
\(972\) | −1944.00 | −0.0641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −46656.0 | −1.53486 | ||||||||
\(975\) | −21492.0 | −0.705943 | ||||||||
\(976\) | 50688.0 | 1.66238 | ||||||||
\(977\) | 34438.0 | 1.12771 | 0.563853 | − | 0.825875i | \(-0.309318\pi\) | ||||
0.563853 | + | 0.825875i | \(0.309318\pi\) | |||||||
\(978\) | 21408.0 | 0.699951 | ||||||||
\(979\) | 11700.0 | 0.381955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1458.00 | 0.0474519 | ||||||||
\(982\) | −39256.0 | −1.27567 | ||||||||
\(983\) | −26064.0 | −0.845689 | −0.422845 | − | 0.906202i | \(-0.638968\pi\) | ||||
−0.422845 | + | 0.906202i | \(0.638968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44316.0 | 1.43353 | ||||||||
\(986\) | −79632.0 | −2.57201 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20736.0 | 0.667713 | ||||||||
\(989\) | −4536.00 | −0.145841 | ||||||||
\(990\) | 32400.0 | 1.04014 | ||||||||
\(991\) | 33696.0 | 1.08011 | 0.540055 | − | 0.841630i | \(-0.318403\pi\) | ||||
0.540055 | + | 0.841630i | \(0.318403\pi\) | |||||||
\(992\) | −9216.00 | −0.294968 | ||||||||
\(993\) | −16524.0 | −0.528070 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −81648.0 | −2.60142 | ||||||||
\(996\) | 864.000 | 0.0274868 | ||||||||
\(997\) | −36072.0 | −1.14585 | −0.572925 | − | 0.819608i | \(-0.694191\pi\) | ||||
−0.572925 | + | 0.819608i | \(0.694191\pi\) | |||||||
\(998\) | −60912.0 | −1.93200 | ||||||||
\(999\) | 4374.00 | 0.138526 |
(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 | 147.4.a.f.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 441.4.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 2352.4.a.t.1.1 | 1 | |||
7.2 | even | 3 | 147.4.e.d.67.1 | 2 | |||
7.3 | odd | 6 | 147.4.e.a.79.1 | 2 | |||
7.4 | even | 3 | 147.4.e.d.79.1 | 2 | |||
7.5 | odd | 6 | 147.4.e.a.67.1 | 2 | |||
7.6 | odd | 2 | 147.4.a.h.1.1 | yes | 1 | ||
21.2 | odd | 6 | 441.4.e.l.361.1 | 2 | |||
21.5 | even | 6 | 441.4.e.o.361.1 | 2 | |||
21.11 | odd | 6 | 441.4.e.l.226.1 | 2 | |||
21.17 | even | 6 | 441.4.e.o.226.1 | 2 | |||
21.20 | even | 2 | 441.4.a.a.1.1 | 1 | |||
28.27 | even | 2 | 2352.4.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.f.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
147.4.a.h.1.1 | yes | 1 | 7.6 | odd | 2 | ||
147.4.e.a.67.1 | 2 | 7.5 | odd | 6 | |||
147.4.e.a.79.1 | 2 | 7.3 | odd | 6 | |||
147.4.e.d.67.1 | 2 | 7.2 | even | 3 | |||
147.4.e.d.79.1 | 2 | 7.4 | even | 3 | |||
441.4.a.a.1.1 | 1 | 21.20 | even | 2 | |||
441.4.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
441.4.e.l.226.1 | 2 | 21.11 | odd | 6 | |||
441.4.e.l.361.1 | 2 | 21.2 | odd | 6 | |||
441.4.e.o.226.1 | 2 | 21.17 | even | 6 | |||
441.4.e.o.361.1 | 2 | 21.5 | even | 6 | |||
2352.4.a.s.1.1 | 1 | 28.27 | even | 2 | |||
2352.4.a.t.1.1 | 1 | 4.3 | odd | 2 |