Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.31955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 1.31955 | 0.761843 | 0.380922 | − | 0.924607i | \(-0.375607\pi\) | ||||
0.380922 | + | 0.924607i | \(0.375607\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.319551 | −0.142907 | −0.0714537 | − | 0.997444i | \(-0.522764\pi\) | ||||
−0.0714537 | + | 0.997444i | \(0.522764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93923 | 0.732962 | 0.366481 | − | 0.930426i | \(-0.380562\pi\) | ||||
0.366481 | + | 0.930426i | \(0.380562\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.25879 | −0.419595 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.25879 | −0.982561 | −0.491280 | − | 0.871001i | \(-0.663471\pi\) | ||||
−0.491280 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.25879 | 1.18117 | 0.590587 | − | 0.806974i | \(-0.298896\pi\) | ||||
0.590587 | + | 0.806974i | \(0.298896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.421664 | −0.108873 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.55892 | 0.558402 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.61968 | −1.17179 | −0.585893 | − | 0.810389i | \(-0.699256\pi\) | ||||
−0.585893 | + | 0.810389i | \(0.699256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89789 | −0.979577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.61968 | −1.08151 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.55892 | −1.21796 | −0.608980 | − | 0.793185i | \(-0.708421\pi\) | ||||
−0.608980 | + | 0.793185i | \(0.708421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.93923 | −1.24632 | −0.623162 | − | 0.782093i | \(-0.714152\pi\) | ||||
−0.623162 | + | 0.782093i | \(0.714152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.30013 | −0.748557 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.619684 | −0.104746 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.57834 | −1.24587 | −0.622935 | − | 0.782273i | \(-0.714060\pi\) | ||||
−0.622935 | + | 0.782273i | \(0.714060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.61968 | 0.899870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.30013 | −0.671568 | −0.335784 | − | 0.941939i | \(-0.609001\pi\) | ||||
−0.335784 | + | 0.941939i | \(0.609001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.13726 | 1.08842 | 0.544211 | − | 0.838949i | \(-0.316829\pi\) | ||||
0.544211 | + | 0.838949i | \(0.316829\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.402246 | 0.0599633 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.31955 | −0.921801 | −0.460901 | − | 0.887452i | \(-0.652474\pi\) | ||||
−0.460901 | + | 0.887452i | \(0.652474\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23937 | −0.462767 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.95865 | 0.554322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.31955 | −0.730696 | −0.365348 | − | 0.930871i | \(-0.619050\pi\) | ||||
−0.365348 | + | 0.930871i | \(0.619050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.04135 | 0.140415 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.31955 | −0.174779 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.74121 | −0.226687 | −0.113343 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113343 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.19802 | 0.281428 | 0.140714 | − | 0.990050i | \(-0.455060\pi\) | ||||
0.140714 | + | 0.990050i | \(0.455060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.44108 | −0.307547 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.36090 | −0.168799 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.68045 | 1.06049 | 0.530243 | − | 0.847846i | \(-0.322101\pi\) | ||||
0.530243 | + | 0.847846i | \(0.322101\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.41546 | −0.892716 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.15667 | 1.08670 | 0.543349 | − | 0.839507i | \(-0.317156\pi\) | ||||
0.543349 | + | 0.839507i | \(0.317156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.9136 | 1.86255 | 0.931274 | − | 0.364320i | \(-0.118699\pi\) | ||||
0.931274 | + | 0.364320i | \(0.118699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.46301 | −0.746284 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.31955 | −0.720180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.93923 | −0.780725 | −0.390362 | − | 0.920661i | \(-0.627650\pi\) | ||||
−0.390362 | + | 0.920661i | \(0.627650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.63910 | −0.404345 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1178 | 1.65940 | 0.829699 | − | 0.558211i | \(-0.188512\pi\) | ||||
0.829699 | + | 0.558211i | \(0.188512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.958652 | −0.103980 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.65483 | −0.927895 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.69987 | −0.604185 | −0.302092 | − | 0.953279i | \(-0.597685\pi\) | ||||
−0.302092 | + | 0.953279i | \(0.597685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.25879 | 0.865756 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.15667 | −0.949503 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.319551 | 0.0327852 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1178 | 1.73805 | 0.869027 | − | 0.494765i | \(-0.164746\pi\) | ||||
0.869027 | + | 0.494765i | \(0.164746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.10211 | 0.412278 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36090 | 0.732437 | 0.366218 | − | 0.930529i | \(-0.380652\pi\) | ||||
0.366218 | + | 0.930529i | \(0.380652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1178 | −1.48960 | −0.744802 | − | 0.667285i | \(-0.767456\pi\) | ||||
−0.744802 | + | 0.667285i | \(0.767456\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.817705 | −0.0797998 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1373 | −1.17335 | −0.586676 | − | 0.809821i | \(-0.699564\pi\) | ||||
−0.586676 | + | 0.809821i | \(0.699564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.07649 | 0.869370 | 0.434685 | − | 0.900583i | \(-0.356860\pi\) | ||||
0.434685 | + | 0.900583i | \(0.356860\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.81770 | −0.453212 | −0.226606 | − | 0.973987i | \(-0.572763\pi\) | ||||
−0.226606 | + | 0.973987i | \(0.572763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.79577 | 0.167457 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.36090 | −0.495615 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.81770 | 0.533308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.380316 | −0.0345742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.67424 | −0.511629 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.16288 | 0.282896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7350 | −1.66246 | −0.831232 | − | 0.555926i | \(-0.812364\pi\) | ||||
−0.831232 | + | 0.555926i | \(0.812364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.41797 | 0.829206 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4155 | −1.08474 | −0.542372 | − | 0.840139i | \(-0.682474\pi\) | ||||
−0.542372 | + | 0.840139i | \(0.682474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.93923 | −0.168153 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.79577 | 0.154556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.2782 | 1.04900 | 0.524499 | − | 0.851411i | \(-0.324253\pi\) | ||||
0.524499 | + | 0.851411i | \(0.324253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2588 | −1.12460 | −0.562298 | − | 0.826935i | \(-0.690083\pi\) | ||||
−0.562298 | + | 0.826935i | \(0.690083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.33897 | −0.702268 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8785 | −1.16058 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.09591 | 0.174056 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.27451 | −0.352556 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.55892 | −0.619251 | −0.309625 | − | 0.950859i | \(-0.600204\pi\) | ||||
−0.309625 | + | 0.950859i | \(0.600204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.396041 | 0.0322294 | 0.0161147 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161147 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.77636 | −0.305300 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.21744 | 0.178109 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0351 | −0.880700 | −0.440350 | − | 0.897826i | \(-0.645146\pi\) | ||||
−0.440350 | + | 0.897826i | \(0.645146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.01942 | −0.556676 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8979 | −0.858874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.03514 | 0.237731 | 0.118865 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118865 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.37411 | 0.106974 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.97438 | −0.771841 | −0.385920 | − | 0.922532i | \(-0.626116\pi\) | ||||
−0.385920 | + | 0.922532i | \(0.626116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.13726 | 0.395173 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.25879 | 0.0962617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.75694 | −0.133578 | −0.0667888 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667888 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.49815 | −0.717993 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.29762 | −0.172700 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.30013 | 0.321407 | 0.160704 | − | 0.987003i | \(-0.448624\pi\) | ||||
0.160704 | + | 0.987003i | \(0.448624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4349 | 1.07294 | 0.536468 | − | 0.843921i | \(-0.319758\pi\) | ||||
0.536468 | + | 0.843921i | \(0.319758\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.90040 | 0.214404 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.42166 | 0.178044 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.77636 | −0.714918 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.8979 | −0.792705 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7350 | −1.71741 | −0.858703 | − | 0.512474i | \(-0.828729\pi\) | ||||
−0.858703 | + | 0.512474i | \(0.828729\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6962 | −1.48974 | −0.744872 | − | 0.667208i | \(-0.767489\pi\) | ||||
−0.744872 | + | 0.667208i | \(0.767489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.79577 | −0.128598 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.7569 | 1.12264 | 0.561318 | − | 0.827600i | \(-0.310295\pi\) | ||||
0.561318 | + | 0.827600i | \(0.310295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.85654 | −0.698712 | −0.349356 | − | 0.936990i | \(-0.613600\pi\) | ||||
−0.349356 | + | 0.936990i | \(0.613600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.4543 | 0.807924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.7193 | −0.892719 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.37411 | 0.0959721 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.07398 | 0.491675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.25879 | 0.225415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.1373 | 0.835563 | 0.417782 | − | 0.908548i | \(-0.362808\pi\) | ||||
0.417782 | + | 0.908548i | \(0.362808\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0827 | 0.827893 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.28072 | −0.155544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.4568 | −0.913508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.9988 | 1.41897 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7764 | 0.859431 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.5746 | 1.24385 | 0.621925 | − | 0.783077i | \(-0.286351\pi\) | ||||
0.621925 | + | 0.783077i | \(0.286351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.16539 | 0.411026 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2939 | −1.41333 | −0.706664 | − | 0.707549i | \(-0.749801\pi\) | ||||
−0.706664 | + | 0.707549i | \(0.749801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4762 | 0.758370 | 0.379185 | − | 0.925321i | \(-0.376204\pi\) | ||||
0.379185 | + | 0.925321i | \(0.376204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.33897 | −0.548664 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.6548 | −1.15661 | −0.578303 | − | 0.815822i | \(-0.696285\pi\) | ||||
−0.578303 | + | 0.815822i | \(0.696285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.01942 | 0.131732 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.15667 | −0.594790 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.5432 | −0.746667 | −0.373334 | − | 0.927697i | \(-0.621785\pi\) | ||||
−0.373334 | + | 0.927697i | \(0.621785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.57834 | 0.616995 | 0.308497 | − | 0.951225i | \(-0.400174\pi\) | ||||
0.308497 | + | 0.951225i | \(0.400174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.0571 | 0.773462 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03514 | 0.0661328 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.25879 | −0.270980 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.9488 | 1.26420 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.223643 | 0.0141162 | 0.00705811 | − | 0.999975i | \(-0.497753\pi\) | ||||
0.00705811 | + | 0.999975i | \(0.497753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.3133 | 1.15135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.26499 | −0.0792168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0826952 | −0.00515838 | −0.00257919 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00257919 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.6962 | −0.913176 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.25627 | 0.511050 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.04135 | −0.0642122 | −0.0321061 | − | 0.999484i | \(-0.510221\pi\) | ||||
−0.0321061 | + | 0.999484i | \(0.510221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.69987 | 0.104422 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.52126 | −0.460294 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8528 | 0.844623 | 0.422312 | − | 0.906451i | \(-0.361219\pi\) | ||||
0.422312 | + | 0.906451i | \(0.361219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2976 | 0.747027 | 0.373514 | − | 0.927625i | \(-0.378153\pi\) | ||||
0.373514 | + | 0.927625i | \(0.378153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.8979 | 0.659570 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.9612 | 0.962494 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6804 | 0.701810 | 0.350905 | − | 0.936411i | \(-0.385874\pi\) | ||||
0.350905 | + | 0.936411i | \(0.385874\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.73501 | 0.522951 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.23937 | 0.0739345 | 0.0369673 | − | 0.999316i | \(-0.488230\pi\) | ||||
0.0369673 | + | 0.999316i | \(0.488230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6585 | 0.871359 | 0.435679 | − | 0.900102i | \(-0.356508\pi\) | ||||
0.435679 | + | 0.900102i | \(0.356508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.421664 | 0.0249772 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.33897 | −0.492234 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.5879 | 1.32412 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.0157 | −1.16933 | −0.584666 | − | 0.811274i | \(-0.698774\pi\) | ||||
−0.584666 | + | 0.811274i | \(0.698774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.556406 | 0.0323952 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.3133 | 1.06265 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9330 | −1.38408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.8408 | 0.797771 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.71308 | 0.558002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.702379 | −0.0402181 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.4180 | −1.10824 | −0.554121 | − | 0.832436i | \(-0.686946\pi\) | ||||
−0.554121 | + | 0.832436i | \(0.686946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.9488 | −1.13485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.8565 | −1.69301 | −0.846505 | − | 0.532382i | \(-0.821297\pi\) | ||||
−0.846505 | + | 0.532382i | \(0.821297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4543 | −0.986575 | −0.493288 | − | 0.869866i | \(-0.664205\pi\) | ||||
−0.493288 | + | 0.869866i | \(0.664205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.780049 | 0.0439508 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5370 | 0.647982 | 0.323991 | − | 0.946060i | \(-0.394975\pi\) | ||||
0.323991 | + | 0.946060i | \(0.394975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.3741 | 1.19672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.0157 | −0.893911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.8591 | −1.15705 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.9769 | 0.662324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.2551 | −0.675645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3196 | 0.622179 | 0.311089 | − | 0.950381i | \(-0.399306\pi\) | ||||
0.311089 | + | 0.950381i | \(0.399306\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.53950 | 0.522761 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.77384 | −0.151551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.51757 | 0.246088 | 0.123044 | − | 0.992401i | \(-0.460734\pi\) | ||||
0.123044 | + | 0.992401i | \(0.460734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.35721 | −0.345276 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6135 | 1.22459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8565 | −1.07215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.36962 | 0.127576 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.6937 | 0.949846 | 0.474923 | − | 0.880027i | \(-0.342476\pi\) | ||||
0.474923 | + | 0.880027i | \(0.342476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7193 | 0.627319 | 0.313659 | − | 0.949536i | \(-0.398445\pi\) | ||||
0.313659 | + | 0.949536i | \(0.398445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.9330 | −1.27745 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.37662 | −0.499067 | −0.249534 | − | 0.968366i | \(-0.580277\pi\) | ||||
−0.249534 | + | 0.968366i | \(0.580277\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.92602 | −0.155297 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.67676 | 0.406297 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.4568 | −1.50189 | −0.750946 | − | 0.660363i | \(-0.770402\pi\) | ||||
−0.750946 | + | 0.660363i | \(0.770402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.501846 | −0.0263401 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.08521 | −0.266172 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.60027 | 0.448930 | 0.224465 | − | 0.974482i | \(-0.427937\pi\) | ||||
0.224465 | + | 0.974482i | \(0.427937\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.41295 | 0.281787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3159 | −0.535573 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0157 | −0.622151 | −0.311075 | − | 0.950385i | \(-0.600689\pi\) | ||||
−0.311075 | + | 0.950385i | \(0.600689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.17358 | 0.215523 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.9330 | −1.43862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5370 | 1.20901 | 0.604507 | − | 0.796600i | \(-0.293370\pi\) | ||||
0.604507 | + | 0.796600i | \(0.293370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.7218 | −1.26654 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0571 | −0.616088 | −0.308044 | − | 0.951372i | \(-0.599674\pi\) | ||||
−0.308044 | + | 0.951372i | \(0.599674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.01942 | 0.102919 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.98427 | −0.456696 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3986 | −0.882142 | −0.441071 | − | 0.897472i | \(-0.645401\pi\) | ||||
−0.441071 | + | 0.897472i | \(0.645401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.8591 | −0.852599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.3828 | −0.826404 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.21744 | 0.111571 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8371 | 0.744654 | 0.372327 | − | 0.928102i | \(-0.378560\pi\) | ||||
0.372327 | + | 0.928102i | \(0.378560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.55892 | −0.128106 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.81770 | −0.140709 | −0.0703547 | − | 0.997522i | \(-0.522413\pi\) | ||||
−0.0703547 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.5527 | −1.47213 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.16288 | 0.0577839 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.6962 | 1.22414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.33528 | 0.164919 | 0.0824594 | − | 0.996594i | \(-0.473723\pi\) | ||||
0.0824594 | + | 0.996594i | \(0.473723\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2017 | 0.799172 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.37662 | −0.166153 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.83092 | −0.237140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4956 | −0.856765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.2357 | 0.988577 | 0.494289 | − | 0.869298i | \(-0.335429\pi\) | ||||
0.494289 | + | 0.869298i | \(0.335429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.83712 | 0.284484 | 0.142242 | − | 0.989832i | \(-0.454569\pi\) | ||||
0.142242 | + | 0.989832i | \(0.454569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.95496 | 0.386783 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.6937 | −0.712747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.26248 | 0.206276 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.3133 | −0.884177 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1955 | −0.635605 | −0.317803 | − | 0.948157i | \(-0.602945\pi\) | ||||
−0.317803 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9781 | 0.815914 | 0.407957 | − | 0.913001i | \(-0.366241\pi\) | ||||
0.407957 | + | 0.913001i | \(0.366241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.76566 | 0.132603 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.61968 | 0.268826 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.38283 | 0.304636 | 0.152318 | − | 0.988332i | \(-0.451326\pi\) | ||||
0.152318 | + | 0.988332i | \(0.451326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.07767 | 0.194175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3766 | 0.873100 | 0.436550 | − | 0.899680i | \(-0.356200\pi\) | ||||
0.436550 | + | 0.899680i | \(0.356200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.82140 | 0.0863425 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.97438 | −0.471772 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.7569 | 1.49870 | 0.749351 | − | 0.662173i | \(-0.230365\pi\) | ||||
0.749351 | + | 0.662173i | \(0.230365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0132 | 0.659856 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.522596 | 0.0245537 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.63910 | −0.123723 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.9173 | 1.44625 | 0.723125 | − | 0.690717i | \(-0.242705\pi\) | ||||
0.723125 | + | 0.690717i | \(0.242705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.8591 | −0.786913 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2369 | 1.12882 | 0.564411 | − | 0.825494i | \(-0.309103\pi\) | ||||
0.564411 | + | 0.825494i | \(0.309103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5941 | 0.957087 | 0.478544 | − | 0.878064i | \(-0.341165\pi\) | ||||
0.478544 | + | 0.878064i | \(0.341165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.92602 | 0.135691 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.85905 | −0.0860267 | −0.0430133 | − | 0.999074i | \(-0.513696\pi\) | ||||
−0.0430133 | + | 0.999074i | \(0.513696\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.8334 | 0.777296 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5614 | −0.670955 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.2588 | −1.06944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89789 | 0.224730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.69617 | 0.306597 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.91361 | 0.315891 | 0.157946 | − | 0.987448i | \(-0.449513\pi\) | ||||
0.157946 | + | 0.987448i | \(0.449513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.2745 | −1.47159 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.3803 | −0.654327 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.47002 | −0.248381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.5527 | −1.79230 | −0.896152 | − | 0.443747i | \(-0.853649\pi\) | ||||
−0.896152 | + | 0.443747i | \(0.853649\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00502 | 0.181113 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7958 | −0.532336 | −0.266168 | − | 0.963927i | \(-0.585758\pi\) | ||||
−0.266168 | + | 0.963927i | \(0.585758\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6768 | −0.886197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.31083 | −0.0589176 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7569 | 0.796508 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.01573 | 0.0454701 | 0.0227351 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227351 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.1617 | −0.588021 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.0897 | −1.92127 | −0.960637 | − | 0.277805i | \(-0.910393\pi\) | ||||
−0.960637 | + | 0.277805i | \(0.910393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.35218 | −0.104671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.77887 | 0.301060 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.1881 | 1.55969 | 0.779843 | − | 0.625975i | \(-0.215299\pi\) | ||||
0.779843 | + | 0.625975i | \(0.215299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.8602 | 1.36518 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.61968 | 0.248115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.83092 | 0.212876 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.5941 | 0.905726 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.31837 | −0.101765 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.2174 | 0.622877 | 0.311439 | − | 0.950266i | \(-0.399189\pi\) | ||||
0.311439 | + | 0.950266i | \(0.399189\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.38032 | −0.191538 | −0.0957689 | − | 0.995404i | \(-0.530531\pi\) | ||||
−0.0957689 | + | 0.995404i | \(0.530531\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.5333 | −0.546998 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.8177 | −0.906833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.58085 | 0.373080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.19182 | 0.0951167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.3133 | −0.793239 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.87847 | 0.167681 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.67424 | 0.244862 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5564 | 0.454697 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9198 | 0.641453 | 0.320727 | − | 0.947172i | \(-0.396073\pi\) | ||||
0.320727 | + | 0.947172i | \(0.396073\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0476 | 0.817409 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.90040 | −0.124239 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −46.0703 | −1.96982 | −0.984912 | − | 0.173058i | \(-0.944635\pi\) | ||||
−0.984912 | + | 0.173058i | \(0.944635\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.76684 | −0.118086 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55892 | 0.279419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4568 | −0.572242 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.19551 | 0.135642 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.2295 | −1.87406 | −0.937031 | − | 0.349245i | \(-0.886438\pi\) | ||||
−0.937031 | + | 0.349245i | \(0.886438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.3960 | 1.28562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.9004 | −0.544655 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.61348 | −0.110145 | −0.0550725 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550725 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.53950 | 0.0647673 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.05707 | −0.296369 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4312 | 1.39905 | 0.699526 | − | 0.714607i | \(-0.253395\pi\) | ||||
0.699526 | + | 0.714607i | \(0.253395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.3196 | −1.30839 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.5246 | 1.14785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6742 | 0.527636 | 0.263818 | − | 0.964573i | \(-0.415018\pi\) | ||||
0.263818 | + | 0.964573i | \(0.415018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.3097 | −1.13495 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3170 | 1.21628 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3353 | 0.717954 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.71308 | 0.0708271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5721 | 0.890377 | 0.445189 | − | 0.895437i | \(-0.353137\pi\) | ||||
0.445189 | + | 0.895437i | \(0.353137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93923 | 0.285926 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.7921 | 0.855272 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.76063 | −0.195496 | −0.0977479 | − | 0.995211i | \(-0.531164\pi\) | ||||
−0.0977479 | + | 0.995211i | \(0.531164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85905 | −0.0762137 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.0062 | −0.532309 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.9268 | 1.67222 | 0.836112 | − | 0.548558i | \(-0.184823\pi\) | ||||
0.836112 | + | 0.548558i | \(0.184823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.5139 | −1.04073 | −0.520366 | − | 0.853943i | \(-0.674205\pi\) | ||||
−0.520366 | + | 0.853943i | \(0.674205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9268 | −0.444975 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.121530 | 0.00494091 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.1955 | 1.34736 | 0.673682 | − | 0.739021i | \(-0.264712\pi\) | ||||
0.673682 | + | 0.739021i | \(0.264712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.7837 | −0.680112 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.9136 | −1.08881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3159 | 1.58795 | 0.793976 | − | 0.607949i | \(-0.208007\pi\) | ||||
0.793976 | + | 0.607949i | \(0.208007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.81321 | 0.0731157 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.45932 | 0.0990084 | 0.0495042 | − | 0.998774i | \(-0.484236\pi\) | ||||
0.0495042 | + | 0.998774i | \(0.484236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.5139 | −1.82936 | −0.914679 | − | 0.404182i | \(-0.867556\pi\) | ||||
−0.914679 | + | 0.404182i | \(0.867556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.5808 | 1.26730 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.0534 | −0.442844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4787 | 0.939149 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.30013 | 0.171731 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.7350 | −0.906504 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.6329 | −0.980620 | −0.490310 | − | 0.871548i | \(-0.663116\pi\) | ||||
−0.490310 | + | 0.871548i | \(0.663116\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0157 | 0.636568 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.98679 | 0.237578 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.7958 | −0.546608 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.5263 | −0.455973 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.2357 | 1.19424 | 0.597119 | − | 0.802153i | \(-0.296312\pi\) | ||||
0.597119 | + | 0.802153i | \(0.296312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4945 | −0.926531 | −0.463266 | − | 0.886220i | \(-0.653322\pi\) | ||||
−0.463266 | + | 0.886220i | \(0.653322\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.00952 | −0.118500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.0959 | −1.22251 | −0.611253 | − | 0.791435i | \(-0.709334\pi\) | ||||
−0.611253 | + | 0.791435i | \(0.709334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.67424 | 0.222734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.7569 | −0.695949 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9550 | 0.859164 | 0.429582 | − | 0.903028i | \(-0.358661\pi\) | ||||
0.429582 | + | 0.903028i | \(0.358661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.96737 | 0.155018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0318 | −0.781516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.2976 | 1.25814 | 0.629068 | − | 0.777350i | \(-0.283437\pi\) | ||||
0.629068 | + | 0.777350i | \(0.283437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5808 | −0.761607 | −0.380803 | − | 0.924656i | \(-0.624353\pi\) | ||||
−0.380803 | + | 0.924656i | \(0.624353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.8591 | 0.654751 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.619684 | 0.0240303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.8591 | 1.42719 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.5102 | 0.947619 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.16288 | −0.276520 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.8309 | 1.57392 | 0.786958 | − | 0.617006i | \(-0.211655\pi\) | ||||
0.786958 | + | 0.617006i | \(0.211655\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.5246 | 1.05942 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.43739 | 0.170543 | 0.0852714 | − | 0.996358i | \(-0.472824\pi\) | ||||
0.0852714 | + | 0.996358i | \(0.472824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1955 | 1.27393 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.0984 | −1.07673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.8785 | 0.531045 | 0.265522 | − | 0.964105i | \(-0.414456\pi\) | ||||
0.265522 | + | 0.964105i | \(0.414456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.92351 | −0.149910 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.1435 | 0.577759 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6548 | −0.863080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.4543 | −1.38679 | −0.693393 | − | 0.720559i | \(-0.743885\pi\) | ||||
−0.693393 | + | 0.720559i | \(0.743885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.95496 | 0.302184 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.23686 | 0.160713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9004 | −0.488637 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2964 | −0.881152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.11784 | 0.117759 | 0.0588796 | − | 0.998265i | \(-0.481247\pi\) | ||||
0.0588796 | + | 0.998265i | \(0.481247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.57834 | 0.285822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.66472 | 0.100359 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.2745 | 0.536848 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3133 | −0.913107 | −0.456553 | − | 0.889696i | \(-0.650916\pi\) | ||||
−0.456553 | + | 0.889696i | \(0.650916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.73501 | 0.327588 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.9963 | 1.46042 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.43488 | 0.165855 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2318 | −0.568843 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0608 | −0.673553 | −0.336776 | − | 0.941585i | \(-0.609337\pi\) | ||||
−0.336776 | + | 0.941585i | \(0.609337\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.3170 | −1.09182 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.6391 | 0.470053 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.1248 | 1.19309 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4531 | −1.01818 | −0.509090 | − | 0.860713i | \(-0.670018\pi\) | ||||
−0.509090 | + | 0.860713i | \(0.670018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8272 | 0.993601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4118 | 0.791943 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.6003 | −0.834760 | −0.417380 | − | 0.908732i | \(-0.637052\pi\) | ||||
−0.417380 | + | 0.908732i | \(0.637052\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.36592 | 0.0503828 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.2877 | −1.04199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.13356 | 0.225627 | 0.112813 | − | 0.993616i | \(-0.464014\pi\) | ||||
0.112813 | + | 0.993616i | \(0.464014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.61968 | −0.206444 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.817705 | 0.0299987 | 0.0149993 | − | 0.999888i | \(-0.495225\pi\) | ||||
0.0149993 | + | 0.999888i | \(0.495225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41546 | 0.0884956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.0301 | −0.696276 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.5370 | −0.860023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.6003 | 1.04364 | 0.521819 | − | 0.853056i | \(-0.325254\pi\) | ||||
0.521819 | + | 0.853056i | \(0.325254\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.295108 | 0.0107543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.126555 | −0.00460582 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9901 | −0.835589 | −0.417795 | − | 0.908541i | \(-0.637197\pi\) | ||||
−0.417795 | + | 0.908541i | \(0.637197\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.1654 | 0.877148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.6669 | 1.69167 | 0.845836 | − | 0.533443i | \(-0.179102\pi\) | ||||
0.845836 | + | 0.533443i | \(0.179102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6014 | 0.637215 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.20674 | 0.0436297 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.41546 | −0.267757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.674244 | −0.0243139 | −0.0121569 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121569 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.109120 | −0.00392988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −51.5684 | −1.85479 | −0.927394 | − | 0.374086i | \(-0.877956\pi\) | ||||
−0.927394 | + | 0.374086i | \(0.877956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.9876 | 1.22087 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.3923 | −0.695697 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.30013 | 0.154068 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8396 | −1.06775 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.8591 | 1.31724 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.52629 | 0.125859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.2902 | 1.43619 | 0.718096 | − | 0.695944i | \(-0.245014\pi\) | ||||
0.718096 | + | 0.695944i | \(0.245014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.37411 | −0.0489196 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.34266 | −0.332187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.36090 | 0.332415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.24306 | 0.0795532 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0728 | 0.569328 | 0.284664 | − | 0.958627i | \(-0.408118\pi\) | ||||
0.284664 | + | 0.958627i | \(0.408118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.9587 | −0.670709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.17491 | 0.253513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51.8591 | −1.83007 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.48243 | 0.122739 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.2795 | 0.643470 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.7094 | 1.53674 | 0.768370 | − | 0.640006i | \(-0.221068\pi\) | ||||
0.768370 | + | 0.640006i | \(0.221068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.30265 | 0.221316 | 0.110658 | − | 0.993859i | \(-0.464704\pi\) | ||||
0.110658 | + | 0.993859i | \(0.464704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.2273 | 0.569117 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.969882 | −0.0339735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.13726 | −0.249701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.3960 | −0.363267 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.1505 | 1.71536 | 0.857682 | − | 0.514181i | \(-0.171904\pi\) | ||||
0.857682 | + | 0.514181i | \(0.171904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.9231 | 1.56592 | 0.782961 | − | 0.622071i | \(-0.213708\pi\) | ||||
0.782961 | + | 0.622071i | \(0.213708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.0616 | 0.733270 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.3547 | −1.54236 | −0.771182 | − | 0.636615i | \(-0.780334\pi\) | ||||
−0.771182 | + | 0.636615i | \(0.780334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.4857 | −1.16301 | −0.581504 | − | 0.813544i | \(-0.697536\pi\) | ||||
−0.581504 | + | 0.813544i | \(0.697536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4129 | 0.534669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.71810 | −0.336712 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.18732 | 0.110302 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.9963 | 1.34791 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9136 | −0.583923 | −0.291961 | − | 0.956430i | \(-0.594308\pi\) | ||||
−0.291961 | + | 0.956430i | \(0.594308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0194 | 0.483428 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.63541 | 0.0563265 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.64161 | −0.0564732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.737522 | −0.0253416 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.3427 | 0.663838 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.5879 | 1.45989 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.1530 | −1.51177 | −0.755885 | − | 0.654705i | \(-0.772793\pi\) | ||||
−0.755885 | + | 0.654705i | \(0.772793\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.402246 | −0.0137565 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.3887 | −1.58461 | −0.792303 | − | 0.610128i | \(-0.791118\pi\) | ||||
−0.792303 | + | 0.610128i | \(0.791118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.3378 | 1.17159 | 0.585795 | − | 0.810459i | \(-0.300782\pi\) | ||||
0.585795 | + | 0.810459i | \(0.300782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.0037 | −0.375005 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0132 | 0.817419 | 0.408710 | − | 0.912664i | \(-0.365979\pi\) | ||||
0.408710 | + | 0.912664i | \(0.365979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.561431 | 0.0190892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.5564 | −0.358514 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6135 | 0.767110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.9682 | 1.25262 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.5477 | −0.729279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.13356 | 0.207352 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.7325 | −1.51051 | −0.755255 | − | 0.655432i | \(-0.772487\pi\) | ||||
−0.755255 | + | 0.655432i | \(0.772487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.4118 | −0.890847 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6073 | −0.829040 | −0.414520 | − | 0.910040i | \(-0.636051\pi\) | ||||
−0.414520 | + | 0.910040i | \(0.636051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.9806 | −0.941622 | −0.470811 | − | 0.882234i | \(-0.656039\pi\) | ||||
−0.470811 | + | 0.882234i | \(0.656039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.734207 | 0.0246801 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.3060 | −1.55480 | −0.777401 | − | 0.629005i | \(-0.783462\pi\) | ||||
−0.777401 | + | 0.629005i | \(0.783462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.3316 | −1.21852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.8591 | 0.397293 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.31955 | 0.211476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37411 | −0.0459315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.5808 | −1.05445 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.5139 | 1.51797 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.9587 | −0.531660 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.2637 | 0.607776 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.61268 | −0.153331 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.99380 | −0.232225 | −0.116113 | − | 0.993236i | \(-0.537043\pi\) | ||||
−0.116113 | + | 0.993236i | \(0.537043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.26579 | −0.307327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.19182 | 0.0726181 | 0.0363090 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363090 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.2658 | −1.63046 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.926825 | −0.0306399 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0765 | −0.795076 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.3716 | −0.968880 | −0.484440 | − | 0.874825i | \(-0.660977\pi\) | ||||
−0.484440 | + | 0.874825i | \(0.660977\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.6230 | −0.844307 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.9963 | 1.28358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.1178 | 1.22043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.0301 | 0.625031 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.7288 | 0.712899 | 0.356449 | − | 0.934315i | \(-0.383987\pi\) | ||||
0.356449 | + | 0.934315i | \(0.383987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23937 | 0.106166 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.3972 | −1.28981 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.12404 | 0.102167 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.917305 | −0.0299670 | −0.0149835 | − | 0.999888i | \(-0.504770\pi\) | ||||
−0.0149835 | + | 0.999888i | \(0.504770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.0318 | −0.751615 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.3716 | −0.631496 | −0.315748 | − | 0.948843i | \(-0.602255\pi\) | ||||
−0.315748 | + | 0.948843i | \(0.602255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.1654 | 0.786933 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.48243 | 0.113283 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7532 | 1.51928 | 0.759638 | − | 0.650346i | \(-0.225376\pi\) | ||||
0.759638 | + | 0.650346i | \(0.225376\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.7727 | 2.19999 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.2236 | 0.493660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7313 | −0.444801 | −0.222400 | − | 0.974955i | \(-0.571389\pi\) | ||||
−0.222400 | + | 0.974955i | \(0.571389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.58454 | 0.245430 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.2042 | 0.911713 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.8103 | 0.768875 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1530 | 0.553322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.2782 | 0.492333 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.61348 | 0.212895 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.47371 | 0.272496 | 0.136248 | − | 0.990675i | \(-0.456496\pi\) | ||||
0.136248 | + | 0.990675i | \(0.456496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.95865 | −0.127170 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −59.1054 | −1.89678 | −0.948392 | − | 0.317101i | \(-0.897291\pi\) | ||||
−0.948392 | + | 0.317101i | \(0.897291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.7119 | −0.824286 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.5246 | −0.881492 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.9268 | −1.24538 | −0.622690 | − | 0.782469i | \(-0.713960\pi\) | ||||
−0.622690 | + | 0.782469i | \(0.713960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.5746 | 0.593648 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4254 | −0.364784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.5089 | 1.64288 | 0.821439 | − | 0.570297i | \(-0.193172\pi\) | ||||
0.821439 | + | 0.570297i | \(0.193172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.03514 | −0.160433 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.1712 | −0.514736 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.1091 | −1.27540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9707 | 0.920284 | 0.460142 | − | 0.887845i | \(-0.347798\pi\) | ||||
0.460142 | + | 0.887845i | \(0.347798\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.9367 | 0.474003 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.14967 | 0.0998511 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.9111 | −0.883953 | −0.441977 | − | 0.897027i | \(-0.645723\pi\) | ||||
−0.441977 | + | 0.897027i | \(0.645723\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 42.5879 | 1.34742 |
(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 | 4864.2.a.bf.1.2 | 3 | ||
4.3 | odd | 2 | 4864.2.a.bd.1.2 | 3 | |||
8.3 | odd | 2 | 4864.2.a.be.1.2 | 3 | |||
8.5 | even | 2 | 4864.2.a.bc.1.2 | 3 | |||
16.3 | odd | 4 | 2432.2.c.f.1217.3 | ✓ | 6 | ||
16.5 | even | 4 | 2432.2.c.g.1217.3 | yes | 6 | ||
16.11 | odd | 4 | 2432.2.c.f.1217.4 | yes | 6 | ||
16.13 | even | 4 | 2432.2.c.g.1217.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.f.1217.3 | ✓ | 6 | 16.3 | odd | 4 | ||
2432.2.c.f.1217.4 | yes | 6 | 16.11 | odd | 4 | ||
2432.2.c.g.1217.3 | yes | 6 | 16.5 | even | 4 | ||
2432.2.c.g.1217.4 | yes | 6 | 16.13 | even | 4 | ||
4864.2.a.bc.1.2 | 3 | 8.5 | even | 2 | |||
4864.2.a.bd.1.2 | 3 | 4.3 | odd | 2 | |||
4864.2.a.be.1.2 | 3 | 8.3 | odd | 2 | |||
4864.2.a.bf.1.2 | 3 | 1.1 | even | 1 | trivial |