Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 196) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.00000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.0000 | 1.78885 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) | ||||
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44.0000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.0000 | 0.938723 | 0.469362 | − | 0.883006i | \(-0.344484\pi\) | ||||
0.469362 | + | 0.883006i | \(0.344484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −80.0000 | −1.37706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −72.0000 | −1.02721 | −0.513605 | − | 0.858027i | \(-0.671690\pi\) | ||||
−0.513605 | + | 0.858027i | \(0.671690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.000 | 1.20745 | 0.603726 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603726 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 275.000 | 2.20000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 218.000 | 1.39592 | 0.697958 | − | 0.716138i | \(-0.254092\pi\) | ||||
0.697958 | + | 0.716138i | \(0.254092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −280.000 | −1.62224 | −0.811121 | − | 0.584879i | \(-0.801142\pi\) | ||||
−0.811121 | + | 0.584879i | \(0.801142\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 176.000 | 0.928414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.0000 | −0.133296 | −0.0666482 | − | 0.997777i | \(-0.521231\pi\) | ||||
−0.0666482 | + | 0.997777i | \(0.521231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −176.000 | −0.722630 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −120.000 | −0.457094 | −0.228547 | − | 0.973533i | \(-0.573397\pi\) | ||||
−0.228547 | + | 0.973533i | \(0.573397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −220.000 | −0.780225 | −0.390113 | − | 0.920767i | \(-0.627564\pi\) | ||||
−0.390113 | + | 0.920767i | \(0.627564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −220.000 | −0.728793 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 88.0000 | 0.273109 | 0.136554 | − | 0.990633i | \(-0.456397\pi\) | ||||
0.136554 | + | 0.990633i | \(0.456397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 288.000 | 0.790746 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 110.000 | 0.285088 | 0.142544 | − | 0.989788i | \(-0.454472\pi\) | ||||
0.142544 | + | 0.989788i | \(0.454472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −880.000 | −2.15744 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −400.000 | −0.929496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 580.000 | 1.27982 | 0.639912 | − | 0.768449i | \(-0.278971\pi\) | ||||
0.639912 | + | 0.768449i | \(0.278971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −380.000 | −0.797607 | −0.398803 | − | 0.917036i | \(-0.630574\pi\) | ||||
−0.398803 | + | 0.917036i | \(0.630574\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 880.000 | 1.67924 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 980.000 | 1.78696 | 0.893478 | − | 0.449107i | \(-0.148258\pi\) | ||||
0.893478 | + | 0.449107i | \(0.148258\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −480.000 | −0.837467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 112.000 | 0.187211 | 0.0936053 | − | 0.995609i | \(-0.470161\pi\) | ||||
0.0936053 | + | 0.995609i | \(0.470161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 640.000 | 1.02611 | 0.513057 | − | 0.858354i | \(-0.328513\pi\) | ||||
0.513057 | + | 0.858354i | \(0.328513\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1100.00 | −1.69356 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 488.000 | 0.694991 | 0.347496 | − | 0.937682i | \(-0.387032\pi\) | ||||
0.347496 | + | 0.937682i | \(0.387032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 660.000 | 0.872824 | 0.436412 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1440.00 | −1.83753 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −872.000 | −1.07458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −320.000 | −0.381123 | −0.190561 | − | 0.981675i | \(-0.561031\pi\) | ||||
−0.190561 | + | 0.981675i | \(0.561031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1120.00 | 1.24880 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2000.00 | 2.15995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −248.000 | −0.259594 | −0.129797 | − | 0.991541i | \(-0.541433\pi\) | ||||
−0.129797 | + | 0.991541i | \(0.541433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 484.000 | 0.491352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −220.000 | −0.216741 | −0.108370 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108370 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1336.00 | 1.27806 | 0.639029 | − | 0.769183i | \(-0.279336\pi\) | ||||
0.639029 | + | 0.769183i | \(0.279336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −100.000 | −0.0903492 | −0.0451746 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451746 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 682.000 | 0.599300 | 0.299650 | − | 0.954049i | \(-0.403130\pi\) | ||||
0.299650 | + | 0.954049i | \(0.403130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 120.000 | 0.102612 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 370.000 | 0.308024 | 0.154012 | − | 0.988069i | \(-0.450781\pi\) | ||||
0.154012 | + | 0.988069i | \(0.450781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2400.00 | 1.94610 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −484.000 | −0.382443 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 605.000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 480.000 | 0.351871 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3000.00 | 2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 160.000 | 0.111793 | 0.0558965 | − | 0.998437i | \(-0.482198\pi\) | ||||
0.0558965 | + | 0.998437i | \(0.482198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 880.000 | 0.600618 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −300.000 | −0.200085 | −0.100042 | − | 0.994983i | \(-0.531898\pi\) | ||||
−0.100042 | + | 0.994983i | \(0.531898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3040.00 | 1.93809 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1190.00 | 0.742106 | 0.371053 | − | 0.928612i | \(-0.378997\pi\) | ||||
0.371053 | + | 0.928612i | \(0.378997\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2220.00 | 1.35466 | 0.677331 | − | 0.735679i | \(-0.263137\pi\) | ||||
0.677331 | + | 0.735679i | \(0.263137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −352.000 | −0.210239 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1936.00 | −1.13214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4360.00 | 2.49709 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2414.00 | 1.32727 | 0.663633 | − | 0.748058i | \(-0.269014\pi\) | ||||
0.663633 | + | 0.748058i | \(0.269014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2056.00 | −1.10805 | −0.554023 | − | 0.832501i | \(-0.686908\pi\) | ||||
−0.554023 | + | 0.832501i | \(0.686908\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 792.000 | 0.418493 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5600.00 | −2.90195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1060.00 | −0.538836 | −0.269418 | − | 0.963023i | \(-0.586831\pi\) | ||||
−0.269418 | + | 0.963023i | \(0.586831\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −440.000 | −0.219461 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1980.00 | 0.951445 | 0.475723 | − | 0.879595i | \(-0.342187\pi\) | ||||
0.475723 | + | 0.879595i | \(0.342187\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3520.00 | 1.66080 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 488.000 | 0.226123 | 0.113062 | − | 0.993588i | \(-0.463934\pi\) | ||||
0.113062 | + | 0.993588i | \(0.463934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261.000 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1100.00 | −0.491925 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3476.00 | −1.52760 | −0.763802 | − | 0.645451i | \(-0.776669\pi\) | ||||
−0.763802 | + | 0.645451i | \(0.776669\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2320.00 | −0.985208 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 84.0000 | 0.0350752 | 0.0175376 | − | 0.999846i | \(-0.494417\pi\) | ||||
0.0175376 | + | 0.999846i | \(0.494417\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2180.00 | −0.895238 | −0.447619 | − | 0.894224i | \(-0.647728\pi\) | ||||
−0.447619 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1520.00 | 0.613998 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −600.000 | −0.238448 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3168.00 | 1.23886 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −696.000 | −0.263669 | −0.131835 | − | 0.991272i | \(-0.542087\pi\) | ||||
−0.131835 | + | 0.991272i | \(0.542087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2690.00 | 1.00327 | 0.501633 | − | 0.865080i | \(-0.332733\pi\) | ||||
0.501633 | + | 0.865080i | \(0.332733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3520.00 | −1.29268 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5310.00 | 1.92042 | 0.960208 | − | 0.279287i | \(-0.0900980\pi\) | ||||
0.960208 | + | 0.279287i | \(0.0900980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3080.00 | 1.09716 | 0.548581 | − | 0.836097i | \(-0.315168\pi\) | ||||
0.548581 | + | 0.836097i | \(0.315168\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3920.00 | −1.37560 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2400.00 | −0.817674 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1320.00 | −0.443219 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4400.00 | −1.45624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.00130508 | 0.000652539 | − | 1.00000i | \(-0.499792\pi\) | ||||
0.000652539 | 1.00000i | \(0.499792\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −448.000 | −0.144115 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4400.00 | −1.39571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2560.00 | −0.789903 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3168.00 | −0.964266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2416.00 | −0.725504 | −0.362752 | − | 0.931886i | \(-0.618163\pi\) | ||||
−0.362752 | + | 0.931886i | \(0.618163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3025.00 | −0.896296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4972.00 | −1.45376 | −0.726879 | − | 0.686765i | \(-0.759030\pi\) | ||||
−0.726879 | + | 0.686765i | \(0.759030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4460.00 | 1.28701 | 0.643505 | − | 0.765442i | \(-0.277480\pi\) | ||||
0.643505 | + | 0.765442i | \(0.277480\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4550.00 | 1.27932 | 0.639658 | − | 0.768660i | \(-0.279076\pi\) | ||||
0.639658 | + | 0.768660i | \(0.279076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1760.00 | 0.488552 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1952.00 | −0.535004 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2112.00 | 0.571606 | 0.285803 | − | 0.958288i | \(-0.407740\pi\) | ||||
0.285803 | + | 0.958288i | \(0.407740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4840.00 | 1.29366 | 0.646829 | − | 0.762635i | \(-0.276095\pi\) | ||||
0.646829 | + | 0.762635i | \(0.276095\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4400.00 | 1.13346 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2640.00 | −0.671900 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4340.00 | −1.09139 | −0.545694 | − | 0.837985i | \(-0.683734\pi\) | ||||
−0.545694 | + | 0.837985i | \(0.683734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5280.00 | −1.31206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5760.00 | 1.41453 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3520.00 | 0.854364 | 0.427182 | − | 0.904166i | \(-0.359506\pi\) | ||||
0.427182 | + | 0.904166i | \(0.359506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2398.00 | −0.568707 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2560.00 | 0.600214 | 0.300107 | − | 0.953905i | \(-0.402978\pi\) | ||||
0.300107 | + | 0.953905i | \(0.402978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2200.00 | 0.509981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1280.00 | 0.293388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6820.00 | −1.54581 | −0.772905 | − | 0.634522i | \(-0.781197\pi\) | ||||
−0.772905 | + | 0.634522i | \(0.781197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3520.00 | 0.789021 | 0.394511 | − | 0.918891i | \(-0.370914\pi\) | ||||
0.394511 | + | 0.918891i | \(0.370914\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12100.0 | −2.65330 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8690.00 | −1.88495 | −0.942476 | − | 0.334275i | \(-0.891509\pi\) | ||||
−0.942476 | + | 0.334275i | \(0.891509\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3080.00 | 0.660913 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3894.00 | 0.826678 | 0.413339 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413339 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6556.00 | −1.37708 | −0.688540 | − | 0.725198i | \(-0.741748\pi\) | ||||
−0.688540 | + | 0.725198i | \(0.741748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8000.00 | −1.66273 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 271.000 | 0.0551598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 992.000 | 0.199835 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2484.00 | 0.495279 | 0.247640 | − | 0.968852i | \(-0.420345\pi\) | ||||
0.247640 | + | 0.968852i | \(0.420345\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11600.0 | 2.28942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6688.00 | −1.30666 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5280.00 | 1.02124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 880.000 | 0.166847 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7600.00 | −1.42680 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 308.000 | 0.0572589 | 0.0286295 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286295 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5344.00 | −0.983850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1760.00 | 0.320902 | 0.160451 | − | 0.987044i | \(-0.448705\pi\) | ||||
0.160451 | + | 0.987044i | \(0.448705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0000 | −0.00433406 | −0.00216703 | − | 0.999998i | \(-0.500690\pi\) | ||||
−0.00216703 | + | 0.999998i | \(0.500690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4890.00 | −0.866403 | −0.433202 | − | 0.901297i | \(-0.642616\pi\) | ||||
−0.433202 | + | 0.901297i | \(0.642616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9592.00 | −1.68354 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 400.000 | 0.0695509 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7200.00 | −1.24031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12100.0 | 2.06519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2728.00 | −0.461342 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8108.00 | −1.34639 | −0.673196 | − | 0.739464i | \(-0.735079\pi\) | ||||
−0.673196 | + | 0.739464i | \(0.735079\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 330.000 | 0.0543060 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19600.0 | 3.19660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2990.00 | 0.483311 | 0.241655 | − | 0.970362i | \(-0.422310\pi\) | ||||
0.241655 | + | 0.970362i | \(0.422310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1480.00 | −0.237117 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12320.0 | 1.95650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9600.00 | −1.49811 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7860.00 | 1.21599 | 0.607993 | − | 0.793943i | \(-0.291975\pi\) | ||||
0.607993 | + | 0.793943i | \(0.291975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6060.00 | 0.929468 | 0.464734 | − | 0.885450i | \(-0.346150\pi\) | ||||
0.464734 | + | 0.885450i | \(0.346150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6688.00 | 1.01703 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3024.00 | 0.455953 | 0.227976 | − | 0.973667i | \(-0.426789\pi\) | ||||
0.227976 | + | 0.973667i | \(0.426789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2240.00 | 0.334893 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5896.00 | −0.866794 | −0.433397 | − | 0.901203i | \(-0.642685\pi\) | ||||
−0.433397 | + | 0.901203i | \(0.642685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2420.00 | −0.349909 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12800.0 | 1.83557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2192.00 | 0.311775 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1320.00 | 0.186223 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3410.00 | −0.473360 | −0.236680 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236680 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12000.0 | −1.65247 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9592.00 | 1.31038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5916.00 | −0.801806 | −0.400903 | − | 0.916120i | \(-0.631304\pi\) | ||||
−0.400903 | + | 0.916120i | \(0.631304\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −640.000 | −0.0860583 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2040.00 | 0.272165 | 0.136082 | − | 0.990698i | \(-0.456549\pi\) | ||||
0.136082 | + | 0.990698i | \(0.456549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2420.00 | 0.317870 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11778.0 | 1.53514 | 0.767569 | − | 0.640967i | \(-0.221466\pi\) | ||||
0.767569 | + | 0.640967i | \(0.221466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8640.00 | −1.11750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1200.00 | 0.154025 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9760.00 | 1.24324 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4708.00 | −0.595183 | −0.297592 | − | 0.954693i | \(-0.596183\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596183\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5874.00 | −0.731505 | −0.365753 | − | 0.930712i | \(-0.619188\pi\) | ||||
−0.365753 | + | 0.930712i | \(0.619188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12320.0 | −1.52284 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6220.00 | −0.763146 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1320.00 | 0.160762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14040.0 | −1.69739 | −0.848696 | − | 0.528881i | \(-0.822612\pi\) | ||||
−0.848696 | + | 0.528881i | \(0.822612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4760.00 | −0.571274 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13200.0 | 1.56136 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8880.00 | −1.04282 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7940.00 | −0.925762 | −0.462881 | − | 0.886420i | \(-0.653184\pi\) | ||||
−0.462881 | + | 0.886420i | \(0.653184\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5214.00 | 0.603598 | 0.301799 | − | 0.953372i | \(-0.402413\pi\) | ||||
0.301799 | + | 0.953372i | \(0.402413\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −968.000 | −0.111267 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19800.0 | −2.25986 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7744.00 | 0.871524 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10384.0 | −1.16051 | −0.580255 | − | 0.814435i | \(-0.697047\pi\) | ||||
−0.580255 | + | 0.814435i | \(0.697047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6520.00 | −0.723629 | −0.361814 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361814 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17440.0 | −1.92226 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12000.0 | 1.31359 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11520.0 | −1.25244 | −0.626218 | − | 0.779648i | \(-0.715398\pi\) | ||||
−0.626218 | + | 0.779648i | \(0.715398\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13380.0 | −1.43500 | −0.717498 | − | 0.696561i | \(-0.754713\pi\) | ||||
−0.717498 | + | 0.696561i | \(0.754713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6400.00 | −0.681773 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9656.00 | −1.02173 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4098.00 | 0.430727 | 0.215364 | − | 0.976534i | \(-0.430906\pi\) | ||||
0.215364 | + | 0.976534i | \(0.430906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5280.00 | 0.551276 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8224.00 | 0.852974 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16390.0 | −1.67766 | −0.838831 | − | 0.544391i | \(-0.816761\pi\) | ||||
−0.838831 | + | 0.544391i | \(0.816761\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10944.0 | −1.11290 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9540.00 | −0.963822 | −0.481911 | − | 0.876220i | \(-0.660057\pi\) | ||||
−0.481911 | + | 0.876220i | \(0.660057\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8920.00 | 0.895351 | 0.447676 | − | 0.894196i | \(-0.352252\pi\) | ||||
0.447676 | + | 0.894196i | \(0.352252\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22400.0 | 2.23393 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8428.00 | −0.835121 | −0.417560 | − | 0.908649i | \(-0.637115\pi\) | ||||
−0.417560 | + | 0.908649i | \(0.637115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4240.00 | 0.414796 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9680.00 | 0.940987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27500.0 | 2.65639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1210.00 | −0.116147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14520.0 | −1.38504 | −0.692522 | − | 0.721397i | \(-0.743500\pi\) | ||||
−0.692522 | + | 0.721397i | \(0.743500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1320.00 | −0.125129 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4960.00 | −0.464375 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10520.0 | 0.978864 | 0.489432 | − | 0.872042i | \(-0.337204\pi\) | ||||
0.489432 | + | 0.872042i | \(0.337204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7920.00 | −0.732423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5436.00 | 0.499640 | 0.249820 | − | 0.968292i | \(-0.419629\pi\) | ||||
0.249820 | + | 0.968292i | \(0.419629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15696.0 | −1.43390 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9680.00 | 0.878957 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18348.0 | −1.64603 | −0.823015 | − | 0.568019i | \(-0.807710\pi\) | ||||
−0.823015 | + | 0.568019i | \(0.807710\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1952.00 | −0.174070 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20944.0 | −1.85655 | −0.928277 | − | 0.371889i | \(-0.878710\pi\) | ||||
−0.928277 | + | 0.371889i | \(0.878710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4400.00 | −0.387718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1044.00 | 0.0914510 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −260.000 | −0.0226411 | −0.0113205 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113205 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15200.0 | 1.30818 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26720.0 | 2.28626 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3872.00 | −0.329382 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13904.0 | 1.17595 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14600.0 | −1.22771 | −0.613856 | − | 0.789418i | \(-0.710382\pi\) | ||||
−0.613856 | + | 0.789418i | \(0.710382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6820.00 | 0.570206 | 0.285103 | − | 0.958497i | \(-0.407972\pi\) | ||||
0.285103 | + | 0.958497i | \(0.407972\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20160.0 | 1.66638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6380.00 | −0.521409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5280.00 | −0.429085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2000.00 | −0.161622 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −336.000 | −0.0270009 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12166.0 | 0.966834 | 0.483417 | − | 0.875390i | \(-0.339395\pi\) | ||||
0.483417 | + | 0.875390i | \(0.339395\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8720.00 | 0.689155 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13640.0 | 1.07206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22660.0 | −1.77125 | −0.885623 | − | 0.464405i | \(-0.846268\pi\) | ||||
−0.885623 | + | 0.464405i | \(0.846268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4180.00 | 0.324951 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21800.0 | 1.68550 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2400.00 | 0.183557 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8490.00 | −0.645840 | −0.322920 | − | 0.946426i | \(-0.604664\pi\) | ||||
−0.322920 | + | 0.946426i | \(0.604664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9680.00 | −0.732416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12672.0 | −0.953676 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14300.0 | 1.07047 | 0.535234 | − | 0.844704i | \(-0.320224\pi\) | ||||
0.535234 | + | 0.844704i | \(0.320224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7400.00 | 0.551009 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18294.0 | 1.34785 | 0.673923 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673923 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14388.0 | 1.05450 | 0.527250 | − | 0.849710i | \(-0.323223\pi\) | ||||
0.527250 | + | 0.849710i | \(0.323223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2784.00 | 0.202973 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33000.0 | 2.39338 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25232.0 | −1.82049 | −0.910244 | − | 0.414072i | \(-0.864106\pi\) | ||||
−0.910244 | + | 0.414072i | \(0.864106\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10760.0 | −0.772315 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4840.00 | −0.343829 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9680.00 | −0.684135 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16060.0 | 1.12925 | 0.564623 | − | 0.825349i | \(-0.309022\pi\) | ||||
0.564623 | + | 0.825349i | \(0.309022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28000.0 | −1.95878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21240.0 | −1.47834 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23856.0 | 1.65202 | 0.826011 | − | 0.563655i | \(-0.190605\pi\) | ||||
0.826011 | + | 0.563655i | \(0.190605\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12320.0 | −0.844596 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3168.00 | −0.216095 | −0.108048 | − | 0.994146i | \(-0.534460\pi\) | ||||
−0.108048 | + | 0.994146i | \(0.534460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12320.0 | 0.836179 | 0.418089 | − | 0.908406i | \(-0.362700\pi\) | ||||
0.418089 | + | 0.908406i | \(0.362700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10780.0 | −0.728019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12100.0 | 0.813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8928.00 | −0.596996 | −0.298498 | − | 0.954410i | \(-0.596486\pi\) | ||||
−0.298498 | + | 0.954410i | \(0.596486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3872.00 | 0.256374 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4510.00 | −0.297157 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9600.00 | 0.629446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5830.00 | 0.380400 | 0.190200 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190200 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24460.0 | −1.58826 | −0.794128 | − | 0.607751i | \(-0.792072\pi\) | ||||
−0.794128 | + | 0.607751i | \(0.792072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18240.0 | 1.17866 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25625.0 | 1.64000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17600.0 | 1.12101 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2160.00 | 0.136923 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15216.0 | −0.959967 | −0.479984 | − | 0.877277i | \(-0.659357\pi\) | ||||
−0.479984 | + | 0.877277i | \(0.659357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0000 | −0.00100465 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3200.00 | 0.199981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1232.00 | −0.0762710 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12478.0 | 0.768879 | 0.384439 | − | 0.923150i | \(-0.374395\pi\) | ||||
0.384439 | + | 0.923150i | \(0.374395\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15996.0 | 0.981059 | 0.490529 | − | 0.871425i | \(-0.336803\pi\) | ||||
0.490529 | + | 0.871425i | \(0.336803\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17600.0 | 1.07442 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5880.00 | −0.357290 | −0.178645 | − | 0.983914i | \(-0.557171\pi\) | ||||
−0.178645 | + | 0.983914i | \(0.557171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25520.0 | −1.54352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7510.00 | −0.450060 | −0.225030 | − | 0.974352i | \(-0.572248\pi\) | ||||
−0.225030 | + | 0.974352i | \(0.572248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6000.00 | −0.357923 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7040.00 | −0.418047 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16508.0 | 0.975812 | 0.487906 | − | 0.872896i | \(-0.337761\pi\) | ||||
0.487906 | + | 0.872896i | \(0.337761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1220.00 | 0.0717890 | 0.0358945 | − | 0.999356i | \(-0.488572\pi\) | ||||
0.0358945 | + | 0.999356i | \(0.488572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12672.0 | 0.742292 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26160.0 | 1.51862 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9664.00 | 0.558493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16720.0 | 0.961950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13090.0 | −0.749751 | −0.374875 | − | 0.927075i | \(-0.622315\pi\) | ||||
−0.374875 | + | 0.927075i | \(0.622315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 41800.0 | 2.38353 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15108.0 | −0.857677 | −0.428839 | − | 0.903381i | \(-0.641077\pi\) | ||||
−0.428839 | + | 0.903381i | \(0.641077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19888.0 | 1.11910 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1540.00 | −0.0862759 | −0.0431380 | − | 0.999069i | \(-0.513736\pi\) | ||||
−0.0431380 | + | 0.999069i | \(0.513736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23800.0 | 1.32752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17840.0 | −0.990740 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4840.00 | 0.267619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5780.00 | 0.318208 | 0.159104 | − | 0.987262i | \(-0.449140\pi\) | ||||
0.159104 | + | 0.987262i | \(0.449140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44400.0 | 2.42329 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8640.00 | 0.469531 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18200.0 | −0.984817 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10406.0 | −0.560669 | −0.280335 | − | 0.959902i | \(-0.590445\pi\) | ||||
−0.280335 | + | 0.959902i | \(0.590445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3000.00 | −0.160949 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7040.00 | −0.376088 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28642.0 | 1.51717 | 0.758585 | − | 0.651575i | \(-0.225891\pi\) | ||||
0.758585 | + | 0.651575i | \(0.225891\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5368.00 | −0.283144 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33600.0 | −1.76484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38720.0 | −2.02524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8448.00 | −0.440023 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7560.00 | 0.392129 | 0.196064 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196064 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19360.0 | −0.995859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 59950.0 | 3.07102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20360.0 | −1.03867 | −0.519333 | − | 0.854572i | \(-0.673820\pi\) | ||||
−0.519333 | + | 0.854572i | \(0.673820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15840.0 | 0.801455 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23276.0 | −1.17288 | −0.586438 | − | 0.809994i | \(-0.699470\pi\) | ||||
−0.586438 | + | 0.809994i | \(0.699470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43120.0 | −2.15515 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3172.00 | −0.157894 | −0.0789472 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789472 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17600.0 | −0.872540 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6600.00 | 0.325882 | 0.162941 | − | 0.986636i | \(-0.447902\pi\) | ||||
0.162941 | + | 0.986636i | \(0.447902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48280.0 | 2.37429 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7260.00 | −0.355595 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16416.0 | 0.797641 | 0.398820 | − | 0.917029i | \(-0.369420\pi\) | ||||
0.398820 | + | 0.917029i | \(0.369420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17360.0 | 0.840151 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41120.0 | −1.98213 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36850.0 | 1.76927 | 0.884634 | − | 0.466286i | \(-0.154408\pi\) | ||||
0.884634 | + | 0.466286i | \(0.154408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21120.0 | 1.01002 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37400.0 | 1.78154 | 0.890768 | − | 0.454458i | \(-0.150167\pi\) | ||||
0.890768 | + | 0.454458i | \(0.150167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15840.0 | 0.748623 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25520.0 | 1.20140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5720.00 | 0.268229 | 0.134115 | − | 0.990966i | \(-0.457181\pi\) | ||||
0.134115 | + | 0.990966i | \(0.457181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14080.0 | −0.657690 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7356.00 | −0.342273 | −0.171136 | − | 0.985247i | \(-0.554744\pi\) | ||||
−0.171136 | + | 0.985247i | \(0.554744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −77000.0 | −3.56893 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12000.0 | −0.551919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4928.00 | −0.225785 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33136.0 | 1.51237 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21200.0 | −0.963899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38572.0 | −1.74707 | −0.873535 | − | 0.486762i | \(-0.838178\pi\) | ||||
−0.873535 | + | 0.486762i | \(0.838178\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10240.0 | −0.462045 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16720.0 | −0.748732 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8800.00 | −0.392583 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7812.00 | −0.347196 | −0.173598 | − | 0.984817i | \(-0.555539\pi\) | ||||
−0.173598 | + | 0.984817i | \(0.555539\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6336.00 | −0.280540 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3520.00 | 0.155272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28160.0 | −1.23754 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27280.0 | 1.18996 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45018.0 | 1.95643 | 0.978213 | − | 0.207604i | \(-0.0665665\pi\) | ||||
0.978213 | + | 0.207604i | \(0.0665665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2740.00 | 0.118637 | 0.0593184 | − | 0.998239i | \(-0.481107\pi\) | ||||
0.0593184 | + | 0.998239i | \(0.481107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14080.0 | −0.607389 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39600.0 | 1.70200 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22000.0 | −0.942084 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1454.00 | 0.0618087 | 0.0309044 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309044 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37120.0 | −1.57220 | −0.786101 | − | 0.618098i | \(-0.787903\pi\) | ||||
−0.786101 | + | 0.618098i | \(0.787903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48400.0 | 2.04251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7260.00 | 0.305266 | 0.152633 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152633 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11140.0 | 0.466717 | 0.233358 | − | 0.972391i | \(-0.425028\pi\) | ||||
0.233358 | + | 0.972391i | \(0.425028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34760.0 | 1.45104 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9760.00 | 0.404501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42560.0 | −1.75757 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8760.00 | 0.360463 | 0.180232 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180232 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23135.0 | 0.948583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15576.0 | −0.636377 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5220.00 | −0.212513 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26224.0 | 1.06008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3600.00 | −0.145013 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −820.000 | −0.0329147 | −0.0164574 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164574 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22000.0 | −0.879981 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1320.00 | 0.0526142 | 0.0263071 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263071 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42780.0 | 1.69923 | 0.849613 | − | 0.527407i | \(-0.176836\pi\) | ||||
0.849613 | + | 0.527407i | \(0.176836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29880.0 | −1.17859 | −0.589297 | − | 0.807916i | \(-0.700595\pi\) | ||||
−0.589297 | + | 0.807916i | \(0.700595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −69520.0 | −2.73266 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1084.00 | −0.0424620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21472.0 | −0.838191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43120.0 | 1.67746 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2728.00 | 0.105760 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28170.0 | 1.08464 | 0.542322 | − | 0.840171i | \(-0.317545\pi\) | ||||
0.542322 | + | 0.840171i | \(0.317545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9936.00 | −0.381266 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20800.0 | −0.795425 | −0.397713 | − | 0.917510i | \(-0.630196\pi\) | ||||
−0.397713 | + | 0.917510i | \(0.630196\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20900.0 | 0.796536 | 0.398268 | − | 0.917269i | \(-0.369611\pi\) | ||||
0.398268 | + | 0.917269i | \(0.369611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −46400.0 | −1.76239 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11640.0 | 0.440623 | 0.220312 | − | 0.975430i | \(-0.429293\pi\) | ||||
0.220312 | + | 0.975430i | \(0.429293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13684.0 | 0.514513 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8800.00 | 0.329766 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1680.00 | 0.0627444 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21120.0 | −0.786150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61040.0 | −2.26451 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7920.00 | −0.292845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43600.0 | −1.60145 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37580.0 | 1.37577 | 0.687885 | − | 0.725820i | \(-0.258539\pi\) | ||||
0.687885 | + | 0.725820i | \(0.258539\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2420.00 | 0.0883018 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40832.0 | 1.48499 | 0.742494 | − | 0.669852i | \(-0.233643\pi\) | ||||
0.742494 | + | 0.669852i | \(0.233643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29040.0 | −1.05267 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30400.0 | 1.09835 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42768.0 | −1.53513 | −0.767566 | − | 0.640970i | \(-0.778532\pi\) | ||||
−0.767566 | + | 0.640970i | \(0.778532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1232.00 | −0.0440779 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4928.00 | 0.175739 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8250.00 | −0.293252 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14696.0 | −0.520690 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8760.00 | 0.309372 | 0.154686 | − | 0.987964i | \(-0.450563\pi\) | ||||
0.154686 | + | 0.987964i | \(0.450563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7040.00 | −0.247030 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 63360.0 | 2.21614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49632.0 | −1.73042 | −0.865212 | − | 0.501407i | \(-0.832816\pi\) | ||||
−0.865212 | + | 0.501407i | \(0.832816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 96.0000 | 0.00333636 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36900.0 | 1.27833 | 0.639163 | − | 0.769071i | \(-0.279281\pi\) | ||||
0.639163 | + | 0.769071i | \(0.279281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14400.0 | −0.497273 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33340.0 | 1.14404 | 0.572019 | − | 0.820240i | \(-0.306160\pi\) | ||||
0.572019 | + | 0.820240i | \(0.306160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28160.0 | 0.963237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19560.0 | 0.666957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5610.00 | 0.190688 | 0.0953440 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953440 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13920.0 | −0.471666 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38368.0 | 1.29599 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48609.0 | 1.63167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1100.00 | 0.0368089 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53800.0 | 1.79470 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25160.0 | 0.836702 | 0.418351 | − | 0.908285i | \(-0.362608\pi\) | ||||
0.418351 | + | 0.908285i | \(0.362608\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28800.0 | 0.954788 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1060.00 | 0.0350330 | 0.0175165 | − | 0.999847i | \(-0.494424\pi\) | ||||
0.0175165 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −48400.0 | −1.58979 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38770.0 | −1.26956 | −0.634781 | − | 0.772692i | \(-0.718910\pi\) | ||||
−0.634781 | + | 0.772692i | \(0.718910\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14080.0 | 0.459651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7502.00 | −0.244159 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24296.0 | −0.788324 | −0.394162 | − | 0.919041i | \(-0.628965\pi\) | ||||
−0.394162 | + | 0.919041i | \(0.628965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 106200. | 3.43534 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26400.0 | −0.848808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1672.00 | 0.0535952 | 0.0267976 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267976 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32432.0 | 1.03645 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61600.0 | 1.96266 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45628.0 | −1.44940 | −0.724701 | − | 0.689064i | \(-0.758022\pi\) | ||||
−0.724701 | + | 0.689064i | \(0.758022\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4560.00 | −0.144416 |
(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 | 784.4.a.f.1.1 | 1 | ||
4.3 | odd | 2 | 196.4.a.c.1.1 | yes | 1 | ||
7.6 | odd | 2 | 784.4.a.m.1.1 | 1 | |||
12.11 | even | 2 | 1764.4.a.a.1.1 | 1 | |||
28.3 | even | 6 | 196.4.e.e.177.1 | 2 | |||
28.11 | odd | 6 | 196.4.e.b.177.1 | 2 | |||
28.19 | even | 6 | 196.4.e.e.165.1 | 2 | |||
28.23 | odd | 6 | 196.4.e.b.165.1 | 2 | |||
28.27 | even | 2 | 196.4.a.a.1.1 | ✓ | 1 | ||
84.11 | even | 6 | 1764.4.k.p.1549.1 | 2 | |||
84.23 | even | 6 | 1764.4.k.p.361.1 | 2 | |||
84.47 | odd | 6 | 1764.4.k.a.361.1 | 2 | |||
84.59 | odd | 6 | 1764.4.k.a.1549.1 | 2 | |||
84.83 | odd | 2 | 1764.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.4.a.a.1.1 | ✓ | 1 | 28.27 | even | 2 | ||
196.4.a.c.1.1 | yes | 1 | 4.3 | odd | 2 | ||
196.4.e.b.165.1 | 2 | 28.23 | odd | 6 | |||
196.4.e.b.177.1 | 2 | 28.11 | odd | 6 | |||
196.4.e.e.165.1 | 2 | 28.19 | even | 6 | |||
196.4.e.e.177.1 | 2 | 28.3 | even | 6 | |||
784.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
784.4.a.m.1.1 | 1 | 7.6 | odd | 2 | |||
1764.4.a.a.1.1 | 1 | 12.11 | even | 2 | |||
1764.4.a.m.1.1 | 1 | 84.83 | odd | 2 | |||
1764.4.k.a.361.1 | 2 | 84.47 | odd | 6 | |||
1764.4.k.a.1549.1 | 2 | 84.59 | odd | 6 | |||
1764.4.k.p.361.1 | 2 | 84.23 | even | 6 | |||
1764.4.k.p.1549.1 | 2 | 84.11 | even | 6 |