Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | 18.0000 | 1.60997 | 0.804984 | − | 0.593296i | \(-0.202174\pi\) | ||||
0.804984 | + | 0.593296i | \(0.202174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −72.0000 | −2.27684 | ||||||||
\(11\) | 50.0000 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.0000 | 0.768046 | 0.384023 | − | 0.923323i | \(-0.374538\pi\) | ||||
0.384023 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 126.000 | 1.79762 | 0.898808 | − | 0.438342i | \(-0.144434\pi\) | ||||
0.898808 | + | 0.438342i | \(0.144434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 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 | \(-0.520214\pi\) | ||||
−0.0634609 | + | 0.997984i | \(0.520214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 199.000 | 1.59200 | ||||||||
\(26\) | −144.000 | −1.08618 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −158.000 | −1.01172 | −0.505860 | − | 0.862616i | \(-0.668825\pi\) | ||||
−0.505860 | + | 0.862616i | \(0.668825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.0000 | 0.208574 | 0.104287 | − | 0.994547i | \(-0.466744\pi\) | ||||
0.104287 | + | 0.994547i | \(0.466744\pi\) | |||||||
\(32\) | 256.000 | 1.41421 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −504.000 | −2.54221 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −162.000 | −0.719801 | −0.359900 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359900 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(38\) | −288.000 | −1.22947 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −270.000 | −1.02846 | −0.514231 | − | 0.857652i | \(-0.671922\pi\) | ||||
−0.514231 | + | 0.857652i | \(0.671922\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 56.0000 | 0.179495 | ||||||||
\(47\) | −72.0000 | −0.223453 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −796.000 | −2.25143 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 288.000 | 0.768046 | ||||||||
\(53\) | 22.0000 | 0.0570176 | 0.0285088 | − | 0.999594i | \(-0.490924\pi\) | ||||
0.0285088 | + | 0.999594i | \(0.490924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 900.000 | 2.20647 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 632.000 | 1.43079 | ||||||||
\(59\) | 468.000 | 1.03268 | 0.516342 | − | 0.856382i | \(-0.327293\pi\) | ||||
0.516342 | + | 0.856382i | \(0.327293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 232.000 | 0.423034 | 0.211517 | − | 0.977374i | \(-0.432160\pi\) | ||||
0.211517 | + | 0.977374i | \(0.432160\pi\) | |||||||
\(68\) | 1008.00 | 1.79762 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 734.000 | 1.22690 | 0.613449 | − | 0.789734i | \(-0.289782\pi\) | ||||
0.613449 | + | 0.789734i | \(0.289782\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 576.000 | 0.869365 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 236.000 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(80\) | −1152.00 | −1.60997 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1080.00 | 1.45446 | ||||||||
\(83\) | 36.0000 | 0.0476086 | 0.0238043 | − | 0.999717i | \(-0.492422\pi\) | ||||
0.0238043 | + | 0.999717i | \(0.492422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2268.00 | 2.89411 | ||||||||
\(86\) | 1296.00 | 1.62501 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 234.000 | 0.278696 | 0.139348 | − | 0.990243i | \(-0.455499\pi\) | ||||
0.139348 | + | 0.990243i | \(0.455499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −112.000 | −0.126922 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 288.000 | 0.316010 | ||||||||
\(95\) | 1296.00 | 1.39965 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −468.000 | −0.489878 | −0.244939 | − | 0.969538i | \(-0.578768\pi\) | ||||
−0.244939 | + | 0.969538i | \(0.578768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1592.00 | 1.59200 | ||||||||
\(101\) | −666.000 | −0.656133 | −0.328067 | − | 0.944655i | \(-0.606397\pi\) | ||||
−0.328067 | + | 0.944655i | \(0.606397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | \(-0.597878\pi\) | ||||
−0.302670 | + | 0.953095i | \(0.597878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 162.000 | 0.142356 | 0.0711779 | − | 0.997464i | \(-0.477324\pi\) | ||||
0.0711779 | + | 0.997464i | \(0.477324\pi\) | |||||||
\(110\) | −3600.00 | −3.12042 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1390.00 | 1.15717 | 0.578585 | − | 0.815622i | \(-0.303605\pi\) | ||||
0.578585 | + | 0.815622i | \(0.303605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −252.000 | −0.204340 | ||||||||
\(116\) | −1264.00 | −1.01172 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1872.00 | −1.46044 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1169.00 | 0.878287 | ||||||||
\(122\) | 3168.00 | 2.35096 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2592.00 | −1.74872 | ||||||||
\(131\) | 2268.00 | 1.51264 | 0.756321 | − | 0.654201i | \(-0.226995\pi\) | ||||
0.756321 | + | 0.654201i | \(0.226995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −928.000 | −0.598261 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −806.000 | −0.502637 | −0.251318 | − | 0.967904i | \(-0.580864\pi\) | ||||
−0.251318 | + | 0.967904i | \(0.580864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2628.00 | −1.60363 | −0.801813 | − | 0.597575i | \(-0.796131\pi\) | ||||
−0.801813 | + | 0.597575i | \(0.796131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2936.00 | −1.73510 | ||||||||
\(143\) | 1800.00 | 1.05261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −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 | \(-0.271810\pi\) | ||||
0.657035 | + | 0.753860i | \(0.271810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3240.00 | 1.74614 | 0.873071 | − | 0.487593i | \(-0.162125\pi\) | ||||
0.873071 | + | 0.487593i | \(0.162125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 648.000 | 0.335798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3024.00 | −1.53721 | −0.768603 | − | 0.639726i | \(-0.779048\pi\) | ||||
−0.768603 | + | 0.639726i | \(0.779048\pi\) | |||||||
\(158\) | −944.000 | −0.475320 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4608.00 | 2.27684 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1784.00 | −0.857262 | −0.428631 | − | 0.903480i | \(-0.641004\pi\) | ||||
−0.428631 | + | 0.903480i | \(0.641004\pi\) | |||||||
\(164\) | −2160.00 | −1.02846 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −144.000 | −0.0673287 | ||||||||
\(167\) | −3024.00 | −1.40122 | −0.700611 | − | 0.713543i | \(-0.747089\pi\) | ||||
−0.700611 | + | 0.713543i | \(0.747089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −901.000 | −0.410105 | ||||||||
\(170\) | −9072.00 | −4.09289 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2592.00 | −1.14906 | ||||||||
\(173\) | 1566.00 | 0.688213 | 0.344106 | − | 0.938931i | \(-0.388182\pi\) | ||||
0.344106 | + | 0.938931i | \(0.388182\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3200.00 | −1.37051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −936.000 | −0.394136 | ||||||||
\(179\) | −3802.00 | −1.58757 | −0.793784 | − | 0.608199i | \(-0.791892\pi\) | ||||
−0.793784 | + | 0.608199i | \(0.791892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 468.000 | 0.192189 | 0.0960944 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960944 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2916.00 | −1.15886 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 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 | \(-0.529102\pi\) | ||||
−0.0912992 | + | 0.995824i | \(0.529102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −810.000 | −0.302099 | −0.151049 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151049 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(194\) | 1872.00 | 0.692793 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2462.00 | 0.890407 | 0.445204 | − | 0.895429i | \(-0.353131\pi\) | ||||
0.445204 | + | 0.895429i | \(0.353131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4536.00 | 1.61582 | 0.807911 | − | 0.589305i | \(-0.200598\pi\) | ||||
0.807911 | + | 0.589305i | \(0.200598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2664.00 | 0.927913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4860.00 | −1.65579 | ||||||||
\(206\) | −1008.00 | −0.340926 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2680.00 | 0.856080 | ||||||||
\(215\) | −5832.00 | −1.84995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −648.000 | −0.201322 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7200.00 | 2.20647 | ||||||||
\(221\) | 4536.00 | 1.38065 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1080.00 | 0.324315 | 0.162157 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162157 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5560.00 | −1.63649 | ||||||||
\(227\) | −1332.00 | −0.389462 | −0.194731 | − | 0.980857i | \(-0.562383\pi\) | ||||
−0.194731 | + | 0.980857i | \(0.562383\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −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 | \(-0.893399\pi\) | ||||
−0.944444 | + | 0.328673i | \(0.893399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1296.00 | −0.359752 | ||||||||
\(236\) | 3744.00 | 1.03268 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3578.00 | 0.968375 | 0.484187 | − | 0.874964i | \(-0.339115\pi\) | ||||
0.484187 | + | 0.874964i | \(0.339115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 756.000 | 0.202067 | 0.101034 | − | 0.994883i | \(-0.467785\pi\) | ||||
0.101034 | + | 0.994883i | \(0.467785\pi\) | |||||||
\(242\) | −4676.00 | −1.24209 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6336.00 | −1.66238 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2592.00 | 0.667713 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5328.00 | −1.34789 | ||||||||
\(251\) | −6516.00 | −1.63859 | −0.819295 | − | 0.573372i | \(-0.805635\pi\) | ||||
−0.819295 | + | 0.573372i | \(0.805635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −700.000 | −0.173947 | ||||||||
\(254\) | −3664.00 | −0.905117 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | −6030.00 | −1.46358 | −0.731792 | − | 0.681528i | \(-0.761316\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5184.00 | 1.23653 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9072.00 | −2.13920 | ||||||||
\(263\) | −590.000 | −0.138331 | −0.0691653 | − | 0.997605i | \(-0.522034\pi\) | ||||
−0.0691653 | + | 0.997605i | \(0.522034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 396.000 | 0.0917966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1856.00 | 0.423034 | ||||||||
\(269\) | −990.000 | −0.224392 | −0.112196 | − | 0.993686i | \(-0.535788\pi\) | ||||
−0.112196 | + | 0.993686i | \(0.535788\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2734.00 | −0.593033 | −0.296516 | − | 0.955028i | \(-0.595825\pi\) | ||||
−0.296516 | + | 0.955028i | \(0.595825\pi\) | |||||||
\(278\) | 10512.0 | 2.26787 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −598.000 | −0.126953 | −0.0634763 | − | 0.997983i | \(-0.520219\pi\) | ||||
−0.0634763 | + | 0.997983i | \(0.520219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3600.00 | −0.756176 | −0.378088 | − | 0.925770i | \(-0.623418\pi\) | ||||
−0.378088 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(284\) | 5872.00 | 1.22690 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7200.00 | −1.48862 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | 11376.0 | 2.30352 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1440.00 | −0.288595 | ||||||||
\(293\) | 7902.00 | 1.57556 | 0.787781 | − | 0.615955i | \(-0.211230\pi\) | ||||
0.787781 | + | 0.615955i | \(0.211230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8424.00 | 1.66259 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9560.00 | −1.85838 | ||||||||
\(299\) | −504.000 | −0.0974818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12960.0 | −2.46942 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4608.00 | −0.869365 | ||||||||
\(305\) | −14256.0 | −2.67638 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10224.0 | 1.90070 | 0.950349 | − | 0.311185i | \(-0.100726\pi\) | ||||
0.950349 | + | 0.311185i | \(0.100726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2592.00 | −0.474889 | ||||||||
\(311\) | 3888.00 | 0.708901 | 0.354451 | − | 0.935075i | \(-0.384668\pi\) | ||||
0.354451 | + | 0.935075i | \(0.384668\pi\) | |||||||
\(312\) | 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 | \(-0.147226\pi\) | ||||
0.894929 | + | 0.446209i | \(0.147226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7900.00 | −1.38657 | ||||||||
\(320\) | −9216.00 | −1.60997 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9072.00 | 1.56279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7164.00 | 1.22273 | ||||||||
\(326\) | 7136.00 | 1.21235 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5508.00 | 0.914644 | 0.457322 | − | 0.889301i | \(-0.348809\pi\) | ||||
0.457322 | + | 0.889301i | \(0.348809\pi\) | |||||||
\(332\) | 288.000 | 0.0476086 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18144.0 | 2.89411 | ||||||||
\(341\) | 1800.00 | 0.285852 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6264.00 | −0.973280 | ||||||||
\(347\) | 6494.00 | 1.00466 | 0.502329 | − | 0.864677i | \(-0.332477\pi\) | ||||
0.502329 | + | 0.864677i | \(0.332477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10080.0 | −1.54605 | −0.773023 | − | 0.634378i | \(-0.781256\pi\) | ||||
−0.773023 | + | 0.634378i | \(0.781256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12800.0 | 1.93819 | ||||||||
\(353\) | −738.000 | −0.111274 | −0.0556371 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556371 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 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 | \(-0.504539\pi\) | ||||
−0.0142603 | + | 0.999898i | \(0.504539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1675.00 | −0.244205 | ||||||||
\(362\) | −1872.00 | −0.271796 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3240.00 | −0.464628 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4752.00 | 0.675892 | 0.337946 | − | 0.941165i | \(-0.390268\pi\) | ||||
0.337946 | + | 0.941165i | \(0.390268\pi\) | |||||||
\(368\) | 896.000 | 0.126922 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11664.0 | 1.63887 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2306.00 | −0.320108 | −0.160054 | − | 0.987108i | \(-0.551167\pi\) | ||||
−0.160054 | + | 0.987108i | \(0.551167\pi\) | |||||||
\(374\) | −25200.0 | −3.48412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1928.00 | 0.258233 | ||||||||
\(383\) | −1152.00 | −0.153693 | −0.0768465 | − | 0.997043i | \(-0.524485\pi\) | ||||
−0.0768465 | + | 0.997043i | \(0.524485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3240.00 | 0.427232 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3744.00 | −0.489878 | ||||||||
\(389\) | −1894.00 | −0.246863 | −0.123431 | − | 0.992353i | \(-0.539390\pi\) | ||||
−0.123431 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1764.00 | −0.228157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9848.00 | −1.25923 | ||||||||
\(395\) | 4248.00 | 0.541114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −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 | \(-0.241653\pi\) | ||||
0.725403 | + | 0.688324i | \(0.241653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1296.00 | 0.160194 | ||||||||
\(404\) | −5328.00 | −0.656133 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2016.00 | 0.241071 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 648.000 | 0.0766484 | ||||||||
\(416\) | 9216.00 | 1.08618 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14400.0 | −1.68499 | ||||||||
\(419\) | −3852.00 | −0.449123 | −0.224561 | − | 0.974460i | \(-0.572095\pi\) | ||||
−0.224561 | + | 0.974460i | \(0.572095\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25074.0 | 2.86181 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5360.00 | −0.605340 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23328.0 | 2.61622 | ||||||||
\(431\) | 10390.0 | 1.16118 | 0.580590 | − | 0.814196i | \(-0.302822\pi\) | ||||
0.580590 | + | 0.814196i | \(0.302822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11232.0 | −1.24659 | −0.623297 | − | 0.781985i | \(-0.714207\pi\) | ||||
−0.623297 | + | 0.781985i | \(0.714207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1296.00 | 0.142356 | ||||||||
\(437\) | −1008.00 | −0.110341 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −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 | \(-0.721137\pi\) | ||||
−0.640171 | + | 0.768232i | \(0.721137\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4212.00 | 0.448692 | ||||||||
\(446\) | −4320.00 | −0.458650 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8186.00 | −0.860404 | −0.430202 | − | 0.902733i | \(-0.641558\pi\) | ||||
−0.430202 | + | 0.902733i | \(0.641558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13500.0 | −1.40951 | ||||||||
\(452\) | 11120.0 | 1.15717 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2016.00 | −0.204340 | ||||||||
\(461\) | 9486.00 | 0.958367 | 0.479183 | − | 0.877715i | \(-0.340933\pi\) | ||||
0.479183 | + | 0.877715i | \(0.340933\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26872.0 | 2.67129 | ||||||||
\(467\) | −3708.00 | −0.367421 | −0.183711 | − | 0.982980i | \(-0.558811\pi\) | ||||
−0.183711 | + | 0.982980i | \(0.558811\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5184.00 | 0.508766 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16200.0 | −1.57479 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14328.0 | 1.38403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14312.0 | −1.36949 | ||||||||
\(479\) | −8064.00 | −0.769214 | −0.384607 | − | 0.923080i | \(-0.625663\pi\) | ||||
−0.384607 | + | 0.923080i | \(0.625663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5832.00 | −0.552841 | ||||||||
\(482\) | −3024.00 | −0.285766 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9352.00 | 0.878287 | ||||||||
\(485\) | −8424.00 | −0.788689 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11664.0 | −1.08531 | −0.542655 | − | 0.839955i | \(-0.682581\pi\) | ||||
−0.542655 | + | 0.839955i | \(0.682581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9814.00 | 0.902036 | 0.451018 | − | 0.892515i | \(-0.351061\pi\) | ||||
0.451018 | + | 0.892515i | \(0.351061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19908.0 | −1.81868 | ||||||||
\(494\) | −10368.0 | −0.944288 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2304.00 | −0.208574 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15228.0 | −1.36613 | −0.683065 | − | 0.730358i | \(-0.739353\pi\) | ||||
−0.683065 | + | 0.730358i | \(0.739353\pi\) | |||||||
\(500\) | 10656.0 | 0.953102 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26064.0 | 2.31732 | ||||||||
\(503\) | −11088.0 | −0.982882 | −0.491441 | − | 0.870911i | \(-0.663530\pi\) | ||||
−0.491441 | + | 0.870911i | \(0.663530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11988.0 | −1.05635 | ||||||||
\(506\) | 2800.00 | 0.245998 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7328.00 | 0.640015 | ||||||||
\(509\) | −5814.00 | −0.506289 | −0.253144 | − | 0.967429i | \(-0.581465\pi\) | ||||
−0.253144 | + | 0.967429i | \(0.581465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16384.0 | −1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24120.0 | 2.06982 | ||||||||
\(515\) | 4536.00 | 0.388117 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3600.00 | −0.306243 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11682.0 | −0.982337 | −0.491169 | − | 0.871065i | \(-0.663430\pi\) | ||||
−0.491169 | + | 0.871065i | \(0.663430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11971.0 | −0.983891 | ||||||||
\(530\) | −1584.00 | −0.129820 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9720.00 | −0.789906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12060.0 | −0.974578 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3960.00 | 0.317338 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7130.00 | 0.566622 | 0.283311 | − | 0.959028i | \(-0.408567\pi\) | ||||
0.283311 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(542\) | −13680.0 | −1.08414 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −39800.0 | −3.08560 | ||||||||
\(551\) | −11376.0 | −0.879553 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10936.0 | 0.838675 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21024.0 | −1.60363 | ||||||||
\(557\) | −5746.00 | −0.437102 | −0.218551 | − | 0.975826i | \(-0.570133\pi\) | ||||
−0.218551 | + | 0.975826i | \(0.570133\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11664.0 | −0.882531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2392.00 | 0.179538 | ||||||||
\(563\) | 13068.0 | 0.978243 | 0.489121 | − | 0.872216i | \(-0.337318\pi\) | ||||
0.489121 | + | 0.872216i | \(0.337318\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25020.0 | 1.86301 | ||||||||
\(566\) | 14400.0 | 1.06939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1130.00 | 0.0832549 | 0.0416275 | − | 0.999133i | \(-0.486746\pi\) | ||||
0.0416275 | + | 0.999133i | \(0.486746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16864.0 | 1.23597 | 0.617983 | − | 0.786192i | \(-0.287950\pi\) | ||||
0.617983 | + | 0.786192i | \(0.287950\pi\) | |||||||
\(572\) | 14400.0 | 1.05261 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2786.00 | −0.202060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2088.00 | 0.150649 | 0.0753246 | − | 0.997159i | \(-0.476001\pi\) | ||||
0.0753246 | + | 0.997159i | \(0.476001\pi\) | |||||||
\(578\) | −43852.0 | −3.15571 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −22752.0 | −1.62884 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1100.00 | 0.0781430 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31608.0 | −2.22818 | ||||||||
\(587\) | 10260.0 | 0.721423 | 0.360712 | − | 0.932677i | \(-0.382534\pi\) | ||||
0.360712 | + | 0.932677i | \(0.382534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2592.00 | 0.181327 | ||||||||
\(590\) | −33696.0 | −2.35126 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10368.0 | 0.719801 | ||||||||
\(593\) | 3582.00 | 0.248052 | 0.124026 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124026 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19120.0 | 1.31407 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2016.00 | 0.137860 | ||||||||
\(599\) | −7034.00 | −0.479802 | −0.239901 | − | 0.970797i | \(-0.577115\pi\) | ||||
−0.239901 | + | 0.970797i | \(0.577115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18072.0 | 1.22658 | 0.613288 | − | 0.789859i | \(-0.289846\pi\) | ||||
0.613288 | + | 0.789859i | \(0.289846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25920.0 | 1.74614 | ||||||||
\(605\) | 21042.0 | 1.41401 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −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 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10910.0 | −0.718843 | −0.359421 | − | 0.933175i | \(-0.617026\pi\) | ||||
−0.359421 | + | 0.933175i | \(0.617026\pi\) | |||||||
\(614\) | −40896.0 | −2.68799 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5522.00 | 0.360304 | 0.180152 | − | 0.983639i | \(-0.442341\pi\) | ||||
0.180152 | + | 0.983639i | \(0.442341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2412.00 | −0.156618 | −0.0783089 | − | 0.996929i | \(-0.524952\pi\) | ||||
−0.0783089 | + | 0.996929i | \(0.524952\pi\) | |||||||
\(620\) | 5184.00 | 0.335798 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15552.0 | −1.00254 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −899.000 | −0.0575360 | ||||||||
\(626\) | 20448.0 | 1.30554 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −40408.0 | −2.53124 | ||||||||
\(635\) | 16488.0 | 1.03040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31600.0 | 1.96090 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27482.0 | 1.69341 | 0.846703 | − | 0.532065i | \(-0.178584\pi\) | ||||
0.846703 | + | 0.532065i | \(0.178584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22752.0 | 1.39541 | 0.697707 | − | 0.716383i | \(-0.254204\pi\) | ||||
0.697707 | + | 0.716383i | \(0.254204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36288.0 | −2.21011 | ||||||||
\(647\) | 14832.0 | 0.901246 | 0.450623 | − | 0.892714i | \(-0.351202\pi\) | ||||
0.450623 | + | 0.892714i | \(0.351202\pi\) | |||||||
\(648\) | 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 | \(-0.526948\pi\) | ||||
−0.0845585 | + | 0.996419i | \(0.526948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40824.0 | 2.43531 | ||||||||
\(656\) | 17280.0 | 1.02846 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15826.0 | 0.935498 | 0.467749 | − | 0.883861i | \(-0.345065\pi\) | ||||
0.467749 | + | 0.883861i | \(0.345065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23832.0 | 1.40236 | 0.701178 | − | 0.712986i | \(-0.252658\pi\) | ||||
0.701178 | + | 0.712986i | \(0.252658\pi\) | |||||||
\(662\) | −22032.0 | −1.29350 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2212.00 | 0.128409 | ||||||||
\(668\) | −24192.0 | −1.40122 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7208.00 | −0.410105 | ||||||||
\(677\) | 8334.00 | 0.473119 | 0.236560 | − | 0.971617i | \(-0.423980\pi\) | ||||
0.236560 | + | 0.971617i | \(0.423980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7200.00 | −0.404255 | ||||||||
\(683\) | 18598.0 | 1.04192 | 0.520961 | − | 0.853580i | \(-0.325574\pi\) | ||||
0.520961 | + | 0.853580i | \(0.325574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14508.0 | −0.809229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20736.0 | 1.14906 | ||||||||
\(689\) | 792.000 | 0.0437922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3542.00 | −0.190841 | −0.0954205 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954205 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11664.0 | −0.625770 | ||||||||
\(704\) | −25600.0 | −1.37051 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2952.00 | 0.157365 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −486.000 | −0.0257435 | −0.0128717 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128717 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(710\) | −52848.0 | −2.79345 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −504.000 | −0.0264726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32400.0 | 1.69467 | ||||||||
\(716\) | −30416.0 | −1.58757 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 776.000 | 0.0403343 | ||||||||
\(719\) | −26928.0 | −1.39672 | −0.698362 | − | 0.715744i | \(-0.746088\pi\) | ||||
−0.698362 | + | 0.715744i | \(0.746088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6700.00 | 0.345358 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3744.00 | 0.192189 | ||||||||
\(725\) | −31442.0 | −1.61066 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20628.0 | −1.05234 | −0.526169 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526169 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12960.0 | 0.657084 | ||||||||
\(731\) | −40824.0 | −2.06557 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19064.0 | 0.948959 | 0.474479 | − | 0.880267i | \(-0.342636\pi\) | ||||
0.474479 | + | 0.880267i | \(0.342636\pi\) | |||||||
\(740\) | −23328.0 | −1.15886 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3766.00 | 0.185950 | 0.0929752 | − | 0.995668i | \(-0.470362\pi\) | ||||
0.0929752 | + | 0.995668i | \(0.470362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43020.0 | 2.11561 | ||||||||
\(746\) | 9224.00 | 0.452701 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 50400.0 | 2.46365 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11664.0 | −0.566745 | −0.283372 | − | 0.959010i | \(-0.591453\pi\) | ||||
−0.283372 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(752\) | 4608.00 | 0.223453 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4734.00 | −0.225502 | −0.112751 | − | 0.993623i | \(-0.535966\pi\) | ||||
−0.112751 | + | 0.993623i | \(0.535966\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3856.00 | −0.182598 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4608.00 | 0.217355 | ||||||||
\(767\) | 16848.0 | 0.793150 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30240.0 | 1.41805 | 0.709026 | − | 0.705182i | \(-0.249135\pi\) | ||||
0.709026 | + | 0.705182i | \(0.249135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6480.00 | −0.302099 | ||||||||
\(773\) | 27702.0 | 1.28897 | 0.644484 | − | 0.764618i | \(-0.277072\pi\) | ||||
0.644484 | + | 0.764618i | \(0.277072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7164.00 | 0.332050 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7576.00 | 0.349117 | ||||||||
\(779\) | −19440.0 | −0.894108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36700.0 | 1.68147 | ||||||||
\(782\) | 7056.00 | 0.322662 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −54432.0 | −2.47486 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22644.0 | 1.02563 | 0.512815 | − | 0.858499i | \(-0.328603\pi\) | ||||
0.512815 | + | 0.858499i | \(0.328603\pi\) | |||||||
\(788\) | 19696.0 | 0.890407 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16992.0 | −0.765251 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28512.0 | −1.27679 | ||||||||
\(794\) | 36864.0 | 1.64768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36288.0 | 1.61582 | ||||||||
\(797\) | 30150.0 | 1.33998 | 0.669992 | − | 0.742368i | \(-0.266297\pi\) | ||||
0.669992 | + | 0.742368i | \(0.266297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9072.00 | −0.401682 | ||||||||
\(800\) | 50944.0 | 2.25143 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −46600.0 | −2.05175 | ||||||||
\(803\) | −9000.00 | −0.395521 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5184.00 | −0.226549 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11318.0 | 0.491866 | 0.245933 | − | 0.969287i | \(-0.420906\pi\) | ||||
0.245933 | + | 0.969287i | \(0.420906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29628.0 | 1.28284 | 0.641418 | − | 0.767192i | \(-0.278347\pi\) | ||||
0.641418 | + | 0.767192i | \(0.278347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32400.0 | 1.39511 | ||||||||
\(815\) | −32112.0 | −1.38016 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −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 | \(-0.623284\pi\) | ||||
−0.377696 | + | 0.925930i | \(0.623284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7868.00 | 0.333246 | 0.166623 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166623 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35726.0 | −1.50219 | −0.751097 | − | 0.660192i | \(-0.770475\pi\) | ||||
−0.751097 | + | 0.660192i | \(0.770475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27108.0 | −1.13571 | −0.567853 | − | 0.823130i | \(-0.692226\pi\) | ||||
−0.567853 | + | 0.823130i | \(0.692226\pi\) | |||||||
\(830\) | −2592.00 | −0.108397 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18432.0 | −0.768046 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54432.0 | −2.25592 | ||||||||
\(836\) | 28800.0 | 1.19147 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15408.0 | 0.635156 | ||||||||
\(839\) | 23256.0 | 0.956956 | 0.478478 | − | 0.878099i | \(-0.341189\pi\) | ||||
0.478478 | + | 0.878099i | \(0.341189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 575.000 | 0.0235762 | ||||||||
\(842\) | −41608.0 | −1.70298 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23328.0 | 0.951402 | ||||||||
\(845\) | −16218.0 | −0.660256 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1408.00 | −0.0570176 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −100296. | −4.04721 | ||||||||
\(851\) | 2268.00 | 0.0913584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35280.0 | −1.41614 | −0.708068 | − | 0.706144i | \(-0.750433\pi\) | ||||
−0.708068 | + | 0.706144i | \(0.750433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19710.0 | −0.785625 | −0.392813 | − | 0.919619i | \(-0.628498\pi\) | ||||
−0.392813 | + | 0.919619i | \(0.628498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −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 | \(-0.242993\pi\) | ||||
0.722500 | + | 0.691370i | \(0.242993\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28188.0 | 1.10800 | ||||||||
\(866\) | 44928.0 | 1.76295 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11800.0 | 0.460630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8352.00 | 0.324910 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4032.00 | 0.156046 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1226.00 | 0.0472053 | 0.0236027 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236027 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(878\) | 58464.0 | 2.24723 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −57600.0 | −2.20647 | ||||||||
\(881\) | −38538.0 | −1.47376 | −0.736878 | − | 0.676026i | \(-0.763701\pi\) | ||||
−0.736878 | + | 0.676026i | \(0.763701\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47752.0 | 1.81068 | ||||||||
\(887\) | 26640.0 | 1.00844 | 0.504219 | − | 0.863576i | \(-0.331781\pi\) | ||||
0.504219 | + | 0.863576i | \(0.331781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16848.0 | −0.634546 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8640.00 | 0.324315 | ||||||||
\(893\) | −5184.00 | −0.194262 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −68436.0 | −2.55594 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32744.0 | 1.21679 | ||||||||
\(899\) | −5688.00 | −0.211018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2772.00 | 0.102496 | ||||||||
\(902\) | 54000.0 | 1.99335 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8424.00 | 0.309418 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12636.0 | −0.462593 | −0.231296 | − | 0.972883i | \(-0.574297\pi\) | ||||
−0.231296 | + | 0.972883i | \(0.574297\pi\) | |||||||
\(908\) | −10656.0 | −0.389462 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33638.0 | 1.22336 | 0.611678 | − | 0.791107i | \(-0.290495\pi\) | ||||
0.611678 | + | 0.791107i | \(0.290495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1800.00 | 0.0652479 | ||||||||
\(914\) | −8424.00 | −0.304859 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12960.0 | −0.467479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36936.0 | 1.32580 | 0.662898 | − | 0.748710i | \(-0.269326\pi\) | ||||
0.662898 | + | 0.748710i | \(0.269326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37944.0 | −1.35534 | ||||||||
\(923\) | 26424.0 | 0.942315 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32238.0 | −1.14592 | ||||||||
\(926\) | 50608.0 | 1.79598 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40448.0 | −1.43079 | ||||||||
\(929\) | −22302.0 | −0.787626 | −0.393813 | − | 0.919191i | \(-0.628844\pi\) | ||||
−0.393813 | + | 0.919191i | \(0.628844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −53744.0 | −1.88889 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10368.0 | −0.359752 | ||||||||
\(941\) | 13554.0 | 0.469551 | 0.234776 | − | 0.972050i | \(-0.424564\pi\) | ||||
0.234776 | + | 0.972050i | \(0.424564\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.779733\pi\) | ||||
−0.769978 | + | 0.638070i | \(0.779733\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6480.00 | −0.221654 | ||||||||
\(950\) | −57312.0 | −1.95731 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38362.0 | −1.30395 | −0.651976 | − | 0.758239i | \(-0.726060\pi\) | ||||
−0.651976 | + | 0.758239i | \(0.726060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8676.00 | −0.293978 | ||||||||
\(956\) | 28624.0 | 0.968375 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32256.0 | 1.08783 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28495.0 | −0.956497 | ||||||||
\(962\) | 23328.0 | 0.781835 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33696.0 | 1.11537 | ||||||||
\(971\) | 17820.0 | 0.588951 | 0.294475 | − | 0.955659i | \(-0.404855\pi\) | ||||
0.294475 | + | 0.955659i | \(0.404855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 46656.0 | 1.53486 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50688.0 | 1.66238 | ||||||||
\(977\) | −34438.0 | −1.12771 | −0.563853 | − | 0.825875i | \(-0.690682\pi\) | ||||
−0.563853 | + | 0.825875i | \(0.690682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11700.0 | 0.381955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −39256.0 | −1.27567 | ||||||||
\(983\) | 26064.0 | 0.845689 | 0.422845 | − | 0.906202i | \(-0.361032\pi\) | ||||
0.422845 | + | 0.906202i | \(0.361032\pi\) | |||||||
\(984\) | 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 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33696.0 | 1.08011 | 0.540055 | − | 0.841630i | \(-0.318403\pi\) | ||||
0.540055 | + | 0.841630i | \(0.318403\pi\) | |||||||
\(992\) | 9216.00 | 0.294968 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 81648.0 | 2.60142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36072.0 | −1.14585 | −0.572925 | − | 0.819608i | \(-0.694191\pi\) | ||||
−0.572925 | + | 0.819608i | \(0.694191\pi\) | |||||||
\(998\) | 60912.0 | 1.93200 | ||||||||
\(999\) | 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 | 441.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 147.4.a.f.1.1 | ✓ | 1 | ||
7.2 | even | 3 | 441.4.e.l.361.1 | 2 | |||
7.3 | odd | 6 | 441.4.e.o.226.1 | 2 | |||
7.4 | even | 3 | 441.4.e.l.226.1 | 2 | |||
7.5 | odd | 6 | 441.4.e.o.361.1 | 2 | |||
7.6 | odd | 2 | 441.4.a.a.1.1 | 1 | |||
12.11 | even | 2 | 2352.4.a.t.1.1 | 1 | |||
21.2 | odd | 6 | 147.4.e.d.67.1 | 2 | |||
21.5 | even | 6 | 147.4.e.a.67.1 | 2 | |||
21.11 | odd | 6 | 147.4.e.d.79.1 | 2 | |||
21.17 | even | 6 | 147.4.e.a.79.1 | 2 | |||
21.20 | even | 2 | 147.4.a.h.1.1 | yes | 1 | ||
84.83 | odd | 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 | 3.2 | odd | 2 | ||
147.4.a.h.1.1 | yes | 1 | 21.20 | even | 2 | ||
147.4.e.a.67.1 | 2 | 21.5 | even | 6 | |||
147.4.e.a.79.1 | 2 | 21.17 | even | 6 | |||
147.4.e.d.67.1 | 2 | 21.2 | odd | 6 | |||
147.4.e.d.79.1 | 2 | 21.11 | odd | 6 | |||
441.4.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
441.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
441.4.e.l.226.1 | 2 | 7.4 | even | 3 | |||
441.4.e.l.361.1 | 2 | 7.2 | even | 3 | |||
441.4.e.o.226.1 | 2 | 7.3 | odd | 6 | |||
441.4.e.o.361.1 | 2 | 7.5 | odd | 6 | |||
2352.4.a.s.1.1 | 1 | 84.83 | odd | 2 | |||
2352.4.a.t.1.1 | 1 | 12.11 | even | 2 |