Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3182656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 25x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.3 | ||
Root | \(1.46962 + 1.46962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.g.1217.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.31955i | − 0.761843i | −0.924607 | − | 0.380922i | \(-0.875607\pi\) | ||||
0.924607 | − | 0.380922i | \(-0.124393\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.319551i | − 0.142907i | −0.997444 | − | 0.0714537i | \(-0.977236\pi\) | ||||
0.997444 | − | 0.0714537i | \(-0.0227638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.93923 | −0.732962 | −0.366481 | − | 0.930426i | \(-0.619438\pi\) | ||||
−0.366481 | + | 0.930426i | \(0.619438\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.25879 | 0.419595 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.25879i | − 0.982561i | −0.871001 | − | 0.491280i | \(-0.836529\pi\) | ||||
0.871001 | − | 0.491280i | \(-0.163471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.25879i | − 1.18117i | −0.806974 | − | 0.590587i | \(-0.798896\pi\) | ||||
0.806974 | − | 0.590587i | \(-0.201104\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.55892i | 0.558402i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.61968 | 1.17179 | 0.585893 | − | 0.810389i | \(-0.300744\pi\) | ||||
0.585893 | + | 0.810389i | \(0.300744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89789 | 0.979577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.61968i | − 1.08151i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.55892i | 1.21796i | 0.793185 | + | 0.608980i | \(0.208421\pi\) | ||||
−0.793185 | + | 0.608980i | \(0.791579\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 0.619684i | 0.104746i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.57834i | − 1.24587i | −0.782273 | − | 0.622935i | \(-0.785940\pi\) | ||||
0.782273 | − | 0.622935i | \(-0.214060\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.61968 | −0.899870 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.30013 | 0.671568 | 0.335784 | − | 0.941939i | \(-0.390999\pi\) | ||||
0.335784 | + | 0.941939i | \(0.390999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.13726i | 1.08842i | 0.838949 | + | 0.544211i | \(0.183171\pi\) | ||||
−0.838949 | + | 0.544211i | \(0.816829\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 0.402246i | − 0.0599633i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | − 3.95865i | − 0.554322i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.31955i | − 0.730696i | −0.930871 | − | 0.365348i | \(-0.880950\pi\) | ||||
0.930871 | − | 0.365348i | \(-0.119050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.04135 | −0.140415 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.31955 | 0.174779 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.74121i | − 0.226687i | −0.993556 | − | 0.113343i | \(-0.963844\pi\) | ||||
0.993556 | − | 0.113343i | \(-0.0361560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.19802i | − 0.281428i | −0.990050 | − | 0.140714i | \(-0.955060\pi\) | ||||
0.990050 | − | 0.140714i | \(-0.0449398\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.44108 | −0.307547 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.36090 | −0.168799 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.68045i | − 1.06049i | −0.847846 | − | 0.530243i | \(-0.822101\pi\) | ||||
0.847846 | − | 0.530243i | \(-0.177899\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 7.41546i | − 0.892716i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.15667 | −1.08670 | −0.543349 | − | 0.839507i | \(-0.682844\pi\) | ||||
−0.543349 | + | 0.839507i | \(0.682844\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.9136 | −1.86255 | −0.931274 | − | 0.364320i | \(-0.881301\pi\) | ||||
−0.931274 | + | 0.364320i | \(0.881301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 6.46301i | − 0.746284i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.31955i | 0.720180i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | − 15.1178i | − 1.65940i | −0.558211 | − | 0.829699i | \(-0.688512\pi\) | ||||
0.558211 | − | 0.829699i | \(-0.311488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 0.958652i | − 0.103980i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.65483 | 0.927895 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.69987 | 0.604185 | 0.302092 | − | 0.953279i | \(-0.402315\pi\) | ||||
0.302092 | + | 0.953279i | \(0.402315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.25879i | 0.865756i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.15667i | 0.949503i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 4.10211i | − 0.412278i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36090i | 0.732437i | 0.930529 | + | 0.366218i | \(0.119348\pi\) | ||||
−0.930529 | + | 0.366218i | \(0.880652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1178 | 1.48960 | 0.744802 | − | 0.667285i | \(-0.232544\pi\) | ||||
0.744802 | + | 0.667285i | \(0.232544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.817705 | 0.0797998 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.1373i | − 1.17335i | −0.809821 | − | 0.586676i | \(-0.800436\pi\) | ||||
0.809821 | − | 0.586676i | \(-0.199564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 9.07649i | − 0.869370i | −0.900583 | − | 0.434685i | \(-0.856860\pi\) | ||||
0.900583 | − | 0.434685i | \(-0.143140\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 1.79577i | − 0.167457i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5.36090i | − 0.495615i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.81770 | −0.533308 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.380316 | 0.0345742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.67424i | − 0.511629i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.16288i | − 0.282896i | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 12.4155i | 1.08474i | 0.840139 | + | 0.542372i | \(0.182474\pi\) | ||||
−0.840139 | + | 0.542372i | \(0.817526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.93923i | − 0.168153i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.79577 | −0.154556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.2782 | −1.04900 | −0.524499 | − | 0.851411i | \(-0.675747\pi\) | ||||
−0.524499 | + | 0.851411i | \(0.675747\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 13.2588i | − 1.12460i | −0.826935 | − | 0.562298i | \(-0.809917\pi\) | ||||
0.826935 | − | 0.562298i | \(-0.190083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.33897i | 0.702268i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8785 | −1.16058 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.09591 | 0.174056 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.27451i | 0.352556i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.55892i | − 0.619251i | −0.950859 | − | 0.309625i | \(-0.899796\pi\) | ||||
0.950859 | − | 0.309625i | \(-0.100204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.396041 | −0.0322294 | −0.0161147 | − | 0.999870i | \(-0.505130\pi\) | ||||
−0.0161147 | + | 0.999870i | \(0.505130\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.77636 | 0.305300 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.21744i | 0.178109i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0351i | 0.880700i | 0.897826 | + | 0.440350i | \(0.145146\pi\) | ||||
−0.897826 | + | 0.440350i | \(0.854854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.01942 | −0.556676 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8979 | −0.858874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3.03514i | − 0.237731i | −0.992910 | − | 0.118865i | \(-0.962074\pi\) | ||||
0.992910 | − | 0.118865i | \(-0.0379257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.37411i | 0.106974i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.97438 | 0.771841 | 0.385920 | − | 0.922532i | \(-0.373884\pi\) | ||||
0.385920 | + | 0.922532i | \(0.373884\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.13726 | −0.395173 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.25879i | 0.0962617i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.75694i | 0.133578i | 0.997767 | + | 0.0667888i | \(0.0212754\pi\) | ||||
−0.997767 | + | 0.0667888i | \(0.978725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.49815 | −0.717993 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.29762 | −0.172700 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.30013i | − 0.321407i | −0.987003 | − | 0.160704i | \(-0.948624\pi\) | ||||
0.987003 | − | 0.160704i | \(-0.0513763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4349i | 1.07294i | 0.843921 | + | 0.536468i | \(0.180242\pi\) | ||||
−0.843921 | + | 0.536468i | \(0.819758\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.90040 | −0.214404 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42166 | −0.178044 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.77636i | − 0.714918i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.8979i | 0.792705i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 1.79577i | 0.128598i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.7569i | 1.12264i | 0.827600 | + | 0.561318i | \(0.189705\pi\) | ||||
−0.827600 | + | 0.561318i | \(0.810295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.85654 | 0.698712 | 0.349356 | − | 0.936990i | \(-0.386400\pi\) | ||||
0.349356 | + | 0.936990i | \(0.386400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.4543 | −0.807924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 12.7193i | − 0.892719i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.37411i | − 0.0959721i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.07398 | 0.491675 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.25879 | 0.225415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 12.1373i | − 0.835563i | −0.908548 | − | 0.417782i | \(-0.862808\pi\) | ||||
0.908548 | − | 0.417782i | \(-0.137192\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0827i | 0.827893i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.28072 | 0.155544 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.4568 | 0.913508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.9988i | 1.41897i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 12.7764i | − 0.859431i | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 21.2939i | 1.41333i | 0.707549 | + | 0.706664i | \(0.249801\pi\) | ||||
−0.707549 | + | 0.706664i | \(0.750199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4762i | 0.758370i | 0.925321 | + | 0.379185i | \(0.123796\pi\) | ||||
−0.925321 | + | 0.379185i | \(0.876204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.33897 | 0.548664 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.6548 | 1.15661 | 0.578303 | − | 0.815822i | \(-0.303715\pi\) | ||||
0.578303 | + | 0.815822i | \(0.303715\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.01942i | 0.131732i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.15667i | 0.594790i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 12.0571i | − 0.773462i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03514i | 0.0661328i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.25879 | 0.270980 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.9488 | −1.26420 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.223643i | 0.0141162i | 0.999975 | + | 0.00705811i | \(0.00224668\pi\) | ||||
−0.999975 | + | 0.00705811i | \(0.997753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 18.3133i | − 1.15135i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 14.6962i | 0.913176i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.25627i | 0.511050i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.04135 | 0.0642122 | 0.0321061 | − | 0.999484i | \(-0.489779\pi\) | ||||
0.0321061 | + | 0.999484i | \(0.489779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.69987 | −0.104422 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 7.52126i | − 0.460294i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 13.8528i | − 0.844623i | −0.906451 | − | 0.422312i | \(-0.861219\pi\) | ||||
0.906451 | − | 0.422312i | \(-0.138781\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 15.9612i | − 0.962494i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6804i | 0.701810i | 0.936411 | + | 0.350905i | \(0.114126\pi\) | ||||
−0.936411 | + | 0.350905i | \(0.885874\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.73501 | −0.522951 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.23937 | −0.0739345 | −0.0369673 | − | 0.999316i | \(-0.511770\pi\) | ||||
−0.0369673 | + | 0.999316i | \(0.511770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6585i | 0.871359i | 0.900102 | + | 0.435679i | \(0.143492\pi\) | ||||
−0.900102 | + | 0.435679i | \(0.856508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 0.421664i | − 0.0249772i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.33897 | −0.492234 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 22.5879i | − 1.32412i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 20.0157i | − 1.16933i | −0.811274 | − | 0.584666i | \(-0.801226\pi\) | ||||
0.811274 | − | 0.584666i | \(-0.198774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.556406 | −0.0323952 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.3133 | −1.06265 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 23.9330i | − 1.38408i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 13.8408i | − 0.797771i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.71308 | 0.558002 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.702379 | −0.0402181 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.4180i | 1.10824i | 0.832436 | + | 0.554121i | \(0.186946\pi\) | ||||
−0.832436 | + | 0.554121i | \(0.813054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 19.9488i | − 1.13485i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.8565 | 1.69301 | 0.846505 | − | 0.532382i | \(-0.178703\pi\) | ||||
0.846505 | + | 0.532382i | \(0.178703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4543 | 0.986575 | 0.493288 | − | 0.869866i | \(-0.335795\pi\) | ||||
0.493288 | + | 0.869866i | \(0.335795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.780049i | 0.0439508i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 11.5370i | − 0.647982i | −0.946060 | − | 0.323991i | \(-0.894975\pi\) | ||||
0.946060 | − | 0.323991i | \(-0.105025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.3741 | 1.19672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.0157 | −0.893911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00000i | 0.166924i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 20.8591i | − 1.15705i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.9769 | −0.662324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.2551 | 0.675645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3196i | 0.622179i | 0.950381 | + | 0.311089i | \(0.100694\pi\) | ||||
−0.950381 | + | 0.311089i | \(0.899306\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 9.53950i | − 0.522761i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 6.35721i | 0.345276i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.6135i | 1.22459i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8565 | 1.07215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.36962 | −0.127576 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.6937i | 0.949846i | 0.880027 | + | 0.474923i | \(0.157524\pi\) | ||||
−0.880027 | + | 0.474923i | \(0.842476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11.7193i | − 0.627319i | −0.949536 | − | 0.313659i | \(-0.898445\pi\) | ||||
0.949536 | − | 0.313659i | \(-0.101555\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 2.92602i | 0.155297i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.67676i | 0.406297i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.4568 | 1.50189 | 0.750946 | − | 0.660363i | \(-0.229598\pi\) | ||||
0.750946 | + | 0.660363i | \(0.229598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 0.501846i | − 0.0263401i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.08521i | 0.266172i | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 10.3159i | 0.535573i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.0157i | − 0.622151i | −0.950385 | − | 0.311075i | \(-0.899311\pi\) | ||||
0.950385 | − | 0.311075i | \(-0.100689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.17358 | −0.215523 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.9330 | 1.43862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5370i | 1.20901i | 0.796600 | + | 0.604507i | \(0.206630\pi\) | ||||
−0.796600 | + | 0.604507i | \(0.793370\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.7218i | 1.26654i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 8.98427i | 0.456696i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 17.3986i | − 0.882142i | −0.897472 | − | 0.441071i | \(-0.854599\pi\) | ||||
0.897472 | − | 0.441071i | \(-0.145401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8591 | 0.852599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.3828 | 0.826404 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.21744i | 0.111571i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.8371i | − 0.744654i | −0.928102 | − | 0.372327i | \(-0.878560\pi\) | ||||
0.928102 | − | 0.372327i | \(-0.121440\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 29.5527i | 1.47213i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.16288i | 0.0577839i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.6962 | −1.22414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.33528 | −0.164919 | −0.0824594 | − | 0.996594i | \(-0.526277\pi\) | ||||
−0.0824594 | + | 0.996594i | \(0.526277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.2017i | 0.799172i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.37662i | 0.166153i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.83092 | −0.237140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.4956 | −0.856765 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 20.2357i | − 0.988577i | −0.869298 | − | 0.494289i | \(-0.835429\pi\) | ||||
0.869298 | − | 0.494289i | \(-0.164571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.83712i | 0.284484i | 0.989832 | + | 0.142242i | \(0.0454311\pi\) | ||||
−0.989832 | + | 0.142242i | \(0.954569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.95496 | −0.386783 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6937 | 0.712747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.26248i | 0.206276i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.3133i | 0.884177i | ||||||||
\(430\) | 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 | ||||||||
\(435\) | − 2.76566i | − 0.132603i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.61968i | 0.268826i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.38283 | −0.304636 | −0.152318 | − | 0.988332i | \(-0.548674\pi\) | ||||
−0.152318 | + | 0.988332i | \(0.548674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.07767 | −0.194175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3766i | 0.873100i | 0.899680 | + | 0.436550i | \(0.143800\pi\) | ||||
−0.899680 | + | 0.436550i | \(0.856200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.82140i | − 0.0863425i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 14.0132i | − 0.659856i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.522596i | 0.0245537i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.63910 | 0.123723 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.9173 | −1.44625 | −0.723125 | − | 0.690717i | \(-0.757295\pi\) | ||||
−0.723125 | + | 0.690717i | \(0.757295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 16.8591i | − 0.786913i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 24.2369i | − 1.12882i | −0.825494 | − | 0.564411i | \(-0.809103\pi\) | ||||
0.825494 | − | 0.564411i | \(-0.190897\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | 1.85905i | 0.0860267i | 0.999074 | + | 0.0430133i | \(0.0136958\pi\) | ||||
−0.999074 | + | 0.0430133i | \(0.986304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.8334i | 0.777296i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.5614 | 0.670955 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.2588 | 1.06944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89789i | 0.224730i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.69617i | − 0.306597i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 14.3803i | 0.654327i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5.47002i | − 0.248381i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.5527 | 1.79230 | 0.896152 | − | 0.443747i | \(-0.146351\pi\) | ||||
0.896152 | + | 0.443747i | \(0.146351\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00502 | −0.181113 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 11.7958i | − 0.532336i | −0.963927 | − | 0.266168i | \(-0.914242\pi\) | ||||
0.963927 | − | 0.266168i | \(-0.0857576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.6768i | 0.886197i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.31083 | −0.0589176 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7569 | 0.796508 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.01573i | − 0.0454701i | −0.999742 | − | 0.0227351i | \(-0.992763\pi\) | ||||
0.999742 | − | 0.0227351i | \(-0.00723742\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 13.1617i | − 0.588021i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 43.0897 | 1.92127 | 0.960637 | − | 0.277805i | \(-0.0896070\pi\) | ||||
0.960637 | + | 0.277805i | \(0.0896070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.35218 | 0.104671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.77887i | 0.301060i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 35.1881i | − 1.55969i | −0.625975 | − | 0.779843i | \(-0.715299\pi\) | ||||
0.625975 | − | 0.779843i | \(-0.284701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.8602 | 1.36518 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.61968 | 0.248115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.83092i | − 0.212876i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.5941i | 0.905726i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.31837 | 0.101765 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2174 | −0.622877 | −0.311439 | − | 0.950266i | \(-0.600811\pi\) | ||||
−0.311439 | + | 0.950266i | \(0.600811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.38032i | − 0.191538i | −0.995404 | − | 0.0957689i | \(-0.969469\pi\) | ||||
0.995404 | − | 0.0957689i | \(-0.0305310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5333i | 0.546998i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.8177 | −0.906833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.58085 | 0.373080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.19182i | − 0.0951167i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 18.3133i | − 0.793239i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.87847 | −0.167681 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.67424 | −0.244862 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.5564i | 0.454697i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 14.9198i | − 0.641453i | −0.947172 | − | 0.320727i | \(-0.896073\pi\) | ||||
0.947172 | − | 0.320727i | \(-0.103927\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0476 | 0.817409 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.90040 | −0.124239 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.0703i | 1.96982i | 0.173058 | + | 0.984912i | \(0.444635\pi\) | ||||
−0.173058 | + | 0.984912i | \(0.555365\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.76684i | − 0.118086i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.55892 | −0.279419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.4568 | 0.572242 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.19551i | 0.135642i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 44.2295i | 1.87406i | 0.349245 | + | 0.937031i | \(0.386438\pi\) | ||||
−0.349245 | + | 0.937031i | \(0.613562\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.3960 | 1.28562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.9004 | −0.544655 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.61348i | 0.110145i | 0.998482 | + | 0.0550725i | \(0.0175390\pi\) | ||||
−0.998482 | + | 0.0550725i | \(0.982461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.53950i | 0.0647673i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.05707 | 0.296369 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.4312i | 1.39905i | 0.714607 | + | 0.699526i | \(0.246605\pi\) | ||||
−0.714607 | + | 0.699526i | \(0.753395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.3196i | 1.30839i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 27.3097i | 1.13495i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.3170i | 1.21628i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.3353 | −0.717954 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.71308 | −0.0708271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5721i | 0.890377i | 0.895437 | + | 0.445189i | \(0.146863\pi\) | ||||
−0.895437 | + | 0.445189i | \(0.853137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 6.93923i | − 0.285926i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 1.85905i | 0.0762137i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 13.0062i | − 0.532309i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.9268 | −1.67222 | −0.836112 | − | 0.548558i | \(-0.815177\pi\) | ||||
−0.836112 | + | 0.548558i | \(0.815177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5139 | 1.04073 | 0.520366 | − | 0.853943i | \(-0.325795\pi\) | ||||
0.520366 | + | 0.853943i | \(0.325795\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 10.9268i | − 0.444975i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 0.121530i | − 0.00494091i | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 26.9136i | 1.08881i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3159i | 1.58795i | 0.607949 | + | 0.793976i | \(0.291993\pi\) | ||||
−0.607949 | + | 0.793976i | \(0.708007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.81321 | −0.0731157 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.45932 | −0.0990084 | −0.0495042 | − | 0.998774i | \(-0.515764\pi\) | ||||
−0.0495042 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 45.5139i | − 1.82936i | −0.404182 | − | 0.914679i | \(-0.632444\pi\) | ||||
0.404182 | − | 0.914679i | \(-0.367556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 31.5808i | − 1.26730i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.0534 | −0.442844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4787 | 0.939149 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.30013i | − 0.171731i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 22.7350i | − 0.906504i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6329 | 0.980620 | 0.490310 | − | 0.871548i | \(-0.336884\pi\) | ||||
0.490310 | + | 0.871548i | \(0.336884\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0157 | −0.636568 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.98679i | 0.237578i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.7958i | 0.546608i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 23.4945i | 0.926531i | 0.886220 | + | 0.463266i | \(0.153322\pi\) | ||||
−0.886220 | + | 0.463266i | \(0.846678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.00952i | − 0.118500i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.0959 | 1.22251 | 0.611253 | − | 0.791435i | \(-0.290666\pi\) | ||||
0.611253 | + | 0.791435i | \(0.290666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.67424 | −0.222734 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 17.7569i | − 0.695949i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 21.9550i | − 0.859164i | −0.903028 | − | 0.429582i | \(-0.858661\pi\) | ||||
0.903028 | − | 0.429582i | \(-0.141339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.96737 | 0.155018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0318 | −0.781516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 32.2976i | − 1.25814i | −0.777350 | − | 0.629068i | \(-0.783437\pi\) | ||||
0.777350 | − | 0.629068i | \(-0.216563\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.5808i | − 0.761607i | −0.924656 | − | 0.380803i | \(-0.875647\pi\) | ||||
0.924656 | − | 0.380803i | \(-0.124353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.8591 | −0.654751 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.619684 | −0.0240303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.8591i | 1.42719i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 24.5102i | − 0.947619i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 27.5246i | − 1.05942i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.43739i | 0.170543i | 0.996358 | + | 0.0852714i | \(0.0271757\pi\) | ||||
−0.996358 | + | 0.0852714i | \(0.972824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.1955 | −1.27393 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.0984 | 1.07673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.8785i | 0.531045i | 0.964105 | + | 0.265522i | \(0.0855444\pi\) | ||||
−0.964105 | + | 0.265522i | \(0.914456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.92351i | 0.149910i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.1435 | 0.577759 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6548 | −0.863080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.4543i | 1.38679i | 0.720559 | + | 0.693393i | \(0.243885\pi\) | ||||
−0.720559 | + | 0.693393i | \(0.756115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.95496i | 0.302184i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.23686 | −0.160713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.9004 | 0.488637 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 23.2964i | − 0.881152i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.11784i | − 0.117759i | −0.998265 | − | 0.0588796i | \(-0.981247\pi\) | ||||
0.998265 | − | 0.0588796i | \(-0.0187528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.57834 | 0.285822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.66472 | 0.100359 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 14.2745i | − 0.536848i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 24.3133i | − 0.913107i | −0.889696 | − | 0.456553i | \(-0.849084\pi\) | ||||
0.889696 | − | 0.456553i | \(-0.150916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.73501 | −0.327588 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.9963 | −1.46042 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.43488i | 0.165855i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2318i | 0.568843i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | − 12.6391i | − 0.470053i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.1248i | 1.19309i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.4531 | 1.01818 | 0.509090 | − | 0.860713i | \(-0.329982\pi\) | ||||
0.509090 | + | 0.860713i | \(0.329982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.8272 | −0.993601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.4118i | 0.791943i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.6003i | 0.834760i | 0.908732 | + | 0.417380i | \(0.137052\pi\) | ||||
−0.908732 | + | 0.417380i | \(0.862948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.36592 | 0.0503828 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.2877 | −1.04199 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6.13356i | − 0.225627i | −0.993616 | − | 0.112813i | \(-0.964014\pi\) | ||||
0.993616 | − | 0.112813i | \(-0.0359862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 5.61968i | − 0.206444i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.817705 | −0.0299987 | −0.0149993 | − | 0.999888i | \(-0.504775\pi\) | ||||
−0.0149993 | + | 0.999888i | \(0.504775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.41546 | −0.0884956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 19.0301i | − 0.696276i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.5370i | 0.860023i | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 0.126555i | 0.00460582i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22.9901i | − 0.835589i | −0.908541 | − | 0.417795i | \(-0.862803\pi\) | ||||
0.908541 | − | 0.417795i | \(-0.137197\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.1654 | −0.877148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.6669 | −1.69167 | −0.845836 | − | 0.533443i | \(-0.820898\pi\) | ||||
−0.845836 | + | 0.533443i | \(0.820898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6014i | 0.637215i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1.20674i | − 0.0436297i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0.109120i | 0.00392988i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 51.5684i | − 1.85479i | −0.374086 | − | 0.927394i | \(-0.622044\pi\) | ||||
0.374086 | − | 0.927394i | \(-0.377956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.9876 | −1.22087 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.3923 | 0.695697 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.30013i | 0.154068i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.8396i | 1.06775i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.8591 | 1.31724 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.52629 | 0.125859 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 40.2902i | − 1.43619i | −0.695944 | − | 0.718096i | \(-0.745014\pi\) | ||||
0.695944 | − | 0.718096i | \(-0.254986\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.37411i | − 0.0489196i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.34266 | 0.332187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.36090 | −0.332415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.24306i | 0.0795532i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 16.0728i | − 0.569328i | −0.958627 | − | 0.284664i | \(-0.908118\pi\) | ||||
0.958627 | − | 0.284664i | \(-0.0918820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.9587 | −0.670709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.17491 | 0.253513 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 51.8591i | 1.83007i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.48243i | 0.122739i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2795 | −0.643470 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.7094 | −1.53674 | −0.768370 | − | 0.640006i | \(-0.778932\pi\) | ||||
−0.768370 | + | 0.640006i | \(0.778932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.30265i | 0.221316i | 0.993859 | + | 0.110658i | \(0.0352958\pi\) | ||||
−0.993859 | + | 0.110658i | \(0.964704\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16.2273i | − 0.569117i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.969882 | −0.0339735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.13726 | −0.249701 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3960i | 0.363267i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.1505i | 1.71536i | 0.514181 | + | 0.857682i | \(0.328096\pi\) | ||||
−0.514181 | + | 0.857682i | \(0.671904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.9231 | −1.56592 | −0.782961 | − | 0.622071i | \(-0.786292\pi\) | ||||
−0.782961 | + | 0.622071i | \(0.786292\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.0616 | −0.733270 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 44.3547i | − 1.54236i | −0.636615 | − | 0.771182i | \(-0.719666\pi\) | ||||
0.636615 | − | 0.771182i | \(-0.280334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.4857i | 1.16301i | 0.813544 | + | 0.581504i | \(0.197536\pi\) | ||||
−0.813544 | + | 0.581504i | \(0.802464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4129 | 0.534669 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.71810 | −0.336712 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.18732i | − 0.110302i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.9963i | 1.34791i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.9136 | 0.583923 | 0.291961 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291961 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0194 | −0.483428 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.63541i | 0.0563265i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.64161i | 0.0564732i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.737522 | −0.0253416 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.3427 | 0.663838 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 42.5879i | − 1.45989i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 44.1530i | − 1.51177i | −0.654705 | − | 0.755885i | \(-0.727207\pi\) | ||||
0.654705 | − | 0.755885i | \(-0.272793\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.402246 | 0.0137565 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.3887 | 1.58461 | 0.792303 | − | 0.610128i | \(-0.208882\pi\) | ||||
0.792303 | + | 0.610128i | \(0.208882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.3378i | 1.17159i | 0.810459 | + | 0.585795i | \(0.199218\pi\) | ||||
−0.810459 | + | 0.585795i | \(0.800782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.0037i | 0.375005i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 10.5564i | 0.358514i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6135i | 0.767110i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.9682 | −1.25262 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.5477 | 0.729279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.13356i | 0.207352i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.7325i | 1.51051i | 0.655432 | + | 0.755255i | \(0.272487\pi\) | ||||
−0.655432 | + | 0.755255i | \(0.727513\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 27.9806i | 0.941622i | 0.882234 | + | 0.470811i | \(0.156039\pi\) | ||||
−0.882234 | + | 0.470811i | \(0.843961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.734207i | 0.0246801i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.3060 | 1.55480 | 0.777401 | − | 0.629005i | \(-0.216538\pi\) | ||||
0.777401 | + | 0.629005i | \(0.216538\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.3316 | 1.21852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.8591i | 0.397293i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.31955i | − 0.211476i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37411 | −0.0459315 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.5808 | −1.05445 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 45.5139i | − 1.51797i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 15.9587i | − 0.531660i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.2637 | −0.607776 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.61268 | 0.153331 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 6.99380i | − 0.232225i | −0.993236 | − | 0.116113i | \(-0.962957\pi\) | ||||
0.993236 | − | 0.116113i | \(-0.0370433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.26579i | 0.307327i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0.926825i | 0.0306399i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 24.0765i | − 0.795076i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.3716 | 0.968880 | 0.484440 | − | 0.874825i | \(-0.339023\pi\) | ||||
0.484440 | + | 0.874825i | \(0.339023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.6230 | 0.844307 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.9963i | 1.28358i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 37.1178i | − 1.22043i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 3.23937i | − 0.106166i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 39.3972i | − 1.28981i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.12404 | −0.102167 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.917305 | 0.0299670 | 0.0149835 | − | 0.999888i | \(-0.495230\pi\) | ||||
0.0149835 | + | 0.999888i | \(0.495230\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 23.0318i | − 0.751615i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.3716i | 0.631496i | 0.948843 | + | 0.315748i | \(0.102255\pi\) | ||||
−0.948843 | + | 0.315748i | \(0.897745\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.1654 | 0.786933 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.48243 | 0.113283 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 46.7532i | − 1.51928i | −0.650346 | − | 0.759638i | \(-0.725376\pi\) | ||||
0.650346 | − | 0.759638i | \(-0.274624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.7727i | 2.19999i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.2236 | −0.493660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7313 | 0.444801 | 0.222400 | − | 0.974955i | \(-0.428611\pi\) | ||||
0.222400 | + | 0.974955i | \(0.428611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.58454i | 0.245430i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 28.2042i | − 0.911713i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.8103 | 0.768875 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1530 | 0.553322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 15.2782i | − 0.492333i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.61348i | 0.212895i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.47371 | −0.272496 | −0.136248 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136248 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.95865 | 0.127170 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 59.1054i | − 1.89678i | −0.317101 | − | 0.948392i | \(-0.602709\pi\) | ||||
0.317101 | − | 0.948392i | \(-0.397291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.7119i | 0.824286i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 18.5746i | − 0.593648i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 11.4254i | − 0.364784i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.5089 | −1.64288 | −0.821439 | − | 0.570297i | \(-0.806828\pi\) | ||||
−0.821439 | + | 0.570297i | \(0.806828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.03514 | 0.160433 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 16.1712i | − 0.514736i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.1091i | 1.27540i | ||||||||
\(990\) | 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 | ||||||||
\(995\) | − 3.14967i | − 0.0998511i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 27.9111i | − 0.883953i | −0.897027 | − | 0.441977i | \(-0.854277\pi\) | ||||
0.897027 | − | 0.441977i | \(-0.145723\pi\) | |||||||
\(998\) | 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 | 2432.2.c.g.1217.3 | yes | 6 | |
4.3 | odd | 2 | 2432.2.c.f.1217.4 | yes | 6 | ||
8.3 | odd | 2 | 2432.2.c.f.1217.3 | ✓ | 6 | ||
8.5 | even | 2 | inner | 2432.2.c.g.1217.4 | yes | 6 | |
16.3 | odd | 4 | 4864.2.a.bd.1.2 | 3 | |||
16.5 | even | 4 | 4864.2.a.bc.1.2 | 3 | |||
16.11 | odd | 4 | 4864.2.a.be.1.2 | 3 | |||
16.13 | even | 4 | 4864.2.a.bf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.f.1217.3 | ✓ | 6 | 8.3 | odd | 2 | ||
2432.2.c.f.1217.4 | yes | 6 | 4.3 | odd | 2 | ||
2432.2.c.g.1217.3 | yes | 6 | 1.1 | even | 1 | trivial | |
2432.2.c.g.1217.4 | yes | 6 | 8.5 | even | 2 | inner | |
4864.2.a.bc.1.2 | 3 | 16.5 | even | 4 | |||
4864.2.a.bd.1.2 | 3 | 16.3 | odd | 4 | |||
4864.2.a.be.1.2 | 3 | 16.11 | odd | 4 | |||
4864.2.a.bf.1.2 | 3 | 16.13 | even | 4 |