Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(5183,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.5183");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.c (of order \(2\), degree \(1\), not 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: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2592) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5183.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.5183 |
Dual form | 5184.2.c.i.5183.6 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.517638i | − 0.231495i | −0.993279 | − | 0.115747i | \(-0.963074\pi\) | ||||
0.993279 | − | 0.115747i | \(-0.0369263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.73205i | − 1.03262i | −0.856402 | − | 0.516309i | \(-0.827306\pi\) | ||||
0.856402 | − | 0.516309i | \(-0.172694\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.378937 | 0.114254 | 0.0571270 | − | 0.998367i | \(-0.481806\pi\) | ||||
0.0571270 | + | 0.998367i | \(0.481806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.34607i | 0.811540i | 0.913975 | + | 0.405770i | \(0.132997\pi\) | ||||
−0.913975 | + | 0.405770i | \(0.867003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.73205i | − 1.08561i | −0.839860 | − | 0.542803i | \(-0.817363\pi\) | ||||
0.839860 | − | 0.542803i | \(-0.182637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.41421 | −0.294884 | −0.147442 | − | 0.989071i | \(-0.547104\pi\) | ||||
−0.147442 | + | 0.989071i | \(0.547104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73205 | 0.946410 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.83083i | − 1.26845i | −0.773147 | − | 0.634227i | \(-0.781319\pi\) | ||||
0.773147 | − | 0.634227i | \(-0.218681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.535898i | − 0.0962502i | −0.998841 | − | 0.0481251i | \(-0.984675\pi\) | ||||
0.998841 | − | 0.0481251i | \(-0.0153246\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.26795 | 0.701647 | 0.350823 | − | 0.936442i | \(-0.385902\pi\) | ||||
0.350823 | + | 0.936442i | \(0.385902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.27792i | 0.824272i | 0.911122 | + | 0.412136i | \(0.135217\pi\) | ||||
−0.911122 | + | 0.412136i | \(0.864783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.26795i | 0.803355i | 0.915781 | + | 0.401677i | \(0.131573\pi\) | ||||
−0.915781 | + | 0.401677i | \(0.868427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.52056 | 1.38872 | 0.694358 | − | 0.719630i | \(-0.255688\pi\) | ||||
0.694358 | + | 0.719630i | \(0.255688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.464102 | −0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.44949i | − 0.336463i | −0.985747 | − | 0.168232i | \(-0.946194\pi\) | ||||
0.985747 | − | 0.168232i | \(-0.0538057\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.196152i | − 0.0264492i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.6617 | −1.77860 | −0.889298 | − | 0.457327i | \(-0.848807\pi\) | ||||
−0.889298 | + | 0.457327i | \(0.848807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.19615 | −1.17745 | −0.588723 | − | 0.808335i | \(-0.700369\pi\) | ||||
−0.588723 | + | 0.808335i | \(0.700369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.27551i | − 0.158208i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.1244i | − 1.35906i | −0.733649 | − | 0.679528i | \(-0.762185\pi\) | ||||
0.733649 | − | 0.679528i | \(-0.237815\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.1112 | 1.91204 | 0.956021 | − | 0.293298i | \(-0.0947529\pi\) | ||||
0.956021 | + | 0.293298i | \(0.0947529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2679 | −1.20177 | −0.600886 | − | 0.799335i | \(-0.705186\pi\) | ||||
−0.600886 | + | 0.799335i | \(0.705186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.03528i | − 0.117981i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 14.5885i | − 1.64133i | −0.571410 | − | 0.820665i | \(-0.693603\pi\) | ||||
0.571410 | − | 0.820665i | \(-0.306397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.757875 | 0.0831876 | 0.0415938 | − | 0.999135i | \(-0.486756\pi\) | ||||
0.0415938 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73205 | 0.187867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.20925i | 0.234180i | 0.993121 | + | 0.117090i | \(0.0373567\pi\) | ||||
−0.993121 | + | 0.117090i | \(0.962643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 6.73205i | − 0.705711i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44949 | −0.251312 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3923 | 1.46132 | 0.730659 | − | 0.682743i | \(-0.239213\pi\) | ||||
0.730659 | + | 0.682743i | \(0.239213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.48477i | 0.346747i | 0.984856 | + | 0.173374i | \(0.0554668\pi\) | ||||
−0.984856 | + | 0.173374i | \(0.944533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000i | 0.394132i | 0.980390 | + | 0.197066i | \(0.0631413\pi\) | ||||
−0.980390 | + | 0.197066i | \(0.936859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.69213 | 0.646953 | 0.323476 | − | 0.946236i | \(-0.395148\pi\) | ||||
0.323476 | + | 0.946236i | \(0.395148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.92820 | 0.950949 | 0.475475 | − | 0.879729i | \(-0.342276\pi\) | ||||
0.475475 | + | 0.879729i | \(0.342276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.83032i | 0.172182i | 0.996287 | + | 0.0860908i | \(0.0274375\pi\) | ||||
−0.996287 | + | 0.0860908i | \(0.972562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.732051i | 0.0682641i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.14162 | 0.838011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8564 | −0.986946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.03768i | − 0.450584i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.12436i | − 0.277242i | −0.990346 | − | 0.138621i | \(-0.955733\pi\) | ||||
0.990346 | − | 0.138621i | \(-0.0442669\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.6975 | −1.72097 | −0.860487 | − | 0.509472i | \(-0.829841\pi\) | ||||
−0.860487 | + | 0.509472i | \(0.829841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.9282 | −1.12102 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.0082i | 1.88029i | 0.340773 | + | 0.940146i | \(0.389311\pi\) | ||||
−0.340773 | + | 0.940146i | \(0.610689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 8.39230i | − 0.711826i | −0.934519 | − | 0.355913i | \(-0.884170\pi\) | ||||
0.934519 | − | 0.355913i | \(-0.115830\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.933740 | 0.0780833 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.53590 | −0.293640 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20.2151i | − 1.65608i | −0.560665 | − | 0.828042i | \(-0.689455\pi\) | ||||
0.560665 | − | 0.828042i | \(-0.310545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 14.9282i | − 1.21484i | −0.794381 | − | 0.607420i | \(-0.792205\pi\) | ||||
0.794381 | − | 0.607420i | \(-0.207795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.277401 | −0.0222814 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.66025 | 0.531546 | 0.265773 | − | 0.964036i | \(-0.414373\pi\) | ||||
0.265773 | + | 0.964036i | \(0.414373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.86370i | 0.304502i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 22.3923i | − 1.75390i | −0.480581 | − | 0.876950i | \(-0.659574\pi\) | ||||
0.480581 | − | 0.876950i | \(-0.340426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.4553 | −1.58288 | −0.791440 | − | 0.611246i | \(-0.790668\pi\) | ||||
−0.791440 | + | 0.611246i | \(0.790668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.17398i | − 0.0892558i | −0.999004 | − | 0.0446279i | \(-0.985790\pi\) | ||||
0.999004 | − | 0.0446279i | \(-0.0142102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 12.9282i | − 0.977280i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0716 | −0.902272 | −0.451136 | − | 0.892455i | \(-0.648981\pi\) | ||||
−0.451136 | + | 0.892455i | \(0.648981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3205 | −0.841447 | −0.420723 | − | 0.907189i | \(-0.638224\pi\) | ||||
−0.420723 | + | 0.907189i | \(0.638224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.20925i | − 0.162428i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.26795i | 0.0927216i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6574 | 0.771140 | 0.385570 | − | 0.922679i | \(-0.374005\pi\) | ||||
0.385570 | + | 0.922679i | \(0.374005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.53590 | −0.110556 | −0.0552782 | − | 0.998471i | \(-0.517605\pi\) | ||||
−0.0552782 | + | 0.998471i | \(0.517605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.1093i | − 1.21898i | −0.792792 | − | 0.609492i | \(-0.791373\pi\) | ||||
0.792792 | − | 0.609492i | \(-0.208627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000i | 0.567105i | 0.958957 | + | 0.283552i | \(0.0915130\pi\) | ||||
−0.958957 | + | 0.283552i | \(0.908487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.6622 | −1.30983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.73205 | 0.190815 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1.79315i | − 0.124035i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 5.12436i | − 0.352775i | −0.984321 | − | 0.176388i | \(-0.943559\pi\) | ||||
0.984321 | − | 0.176388i | \(-0.0564412\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.72689 | 0.185972 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.46410 | −0.0993897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.24504i | 0.554622i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.7321i | − 1.38832i | −0.719820 | − | 0.694160i | \(-0.755776\pi\) | ||||
0.719820 | − | 0.694160i | \(-0.244224\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.2485 | 1.47668 | 0.738342 | − | 0.674427i | \(-0.235609\pi\) | ||||
0.738342 | + | 0.674427i | \(0.235609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0000 | −0.726900 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3.24453i | − 0.212556i | −0.994336 | − | 0.106278i | \(-0.966107\pi\) | ||||
0.994336 | − | 0.106278i | \(-0.0338934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4.92820i | − 0.321481i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.24316 | −0.597890 | −0.298945 | − | 0.954270i | \(-0.596635\pi\) | ||||
−0.298945 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.12436 | 0.523336 | 0.261668 | − | 0.965158i | \(-0.415727\pi\) | ||||
0.261668 | + | 0.965158i | \(0.415727\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.240237i | 0.0153482i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 11.6603i | − 0.741924i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3533 | 0.969090 | 0.484545 | − | 0.874766i | \(-0.338985\pi\) | ||||
0.484545 | + | 0.874766i | \(0.338985\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.535898 | −0.0336916 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3514i | 1.01997i | 0.860183 | + | 0.509986i | \(0.170349\pi\) | ||||
−0.860183 | + | 0.509986i | \(0.829651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 11.6603i | − 0.724533i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3490 | 0.761471 | 0.380736 | − | 0.924684i | \(-0.375671\pi\) | ||||
0.380736 | + | 0.924684i | \(0.375671\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.26795 | −0.0778895 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4176i | 0.940031i | 0.882658 | + | 0.470015i | \(0.155752\pi\) | ||||
−0.882658 | + | 0.470015i | \(0.844248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 16.7321i | − 1.01640i | −0.861239 | − | 0.508200i | \(-0.830311\pi\) | ||||
0.861239 | − | 0.508200i | \(-0.169689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.79315 | 0.108131 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9282 | −0.896949 | −0.448474 | − | 0.893796i | \(-0.648032\pi\) | ||||
−0.448474 | + | 0.893796i | \(0.648032\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.10394i | − 0.244821i | −0.992480 | − | 0.122410i | \(-0.960938\pi\) | ||||
0.992480 | − | 0.122410i | \(-0.0390624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 15.3205i | − 0.910710i | −0.890310 | − | 0.455355i | \(-0.849512\pi\) | ||||
0.890310 | − | 0.455355i | \(-0.150488\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4195 | 0.851158 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.80385 | 0.341403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.5539i | 0.674989i | 0.941328 | + | 0.337494i | \(0.109579\pi\) | ||||
−0.941328 | + | 0.337494i | \(0.890421\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.07180i | 0.411736i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.48477 | −0.201529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.3923 | 0.829559 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.76028i | 0.272573i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000i | 1.02731i | 0.857996 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0754 | −0.571321 | −0.285661 | − | 0.958331i | \(-0.592213\pi\) | ||||
−0.285661 | + | 0.958331i | \(0.592213\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.32051 | −0.357256 | −0.178628 | − | 0.983917i | \(-0.557166\pi\) | ||||
−0.178628 | + | 0.983917i | \(0.557166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 19.5588i | − 1.09853i | −0.835649 | − | 0.549265i | \(-0.814908\pi\) | ||||
0.835649 | − | 0.549265i | \(-0.185092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 2.58846i | − 0.144926i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.8338 | 0.881013 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.6603 | 0.646795 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 26.0106i | − 1.43401i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 18.1962i | − 1.00015i | −0.865982 | − | 0.500075i | \(-0.833306\pi\) | ||||
0.865982 | − | 0.500075i | \(-0.166694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.75839 | −0.314614 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.92820 | 0.486350 | 0.243175 | − | 0.969982i | \(-0.421811\pi\) | ||||
0.243175 | + | 0.969982i | \(0.421811\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 0.203072i | − 0.0109970i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 17.8564i | − 0.964155i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.86422 | −0.475856 | −0.237928 | − | 0.971283i | \(-0.576468\pi\) | ||||
−0.237928 | + | 0.971283i | \(0.576468\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.8564 | 1.59818 | 0.799088 | − | 0.601214i | \(-0.205316\pi\) | ||||
0.799088 | + | 0.601214i | \(0.205316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 30.8081i | − 1.63975i | −0.572543 | − | 0.819875i | \(-0.694043\pi\) | ||||
0.572543 | − | 0.819875i | \(-0.305957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.33975i | − 0.442628i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.44949 | 0.129279 | 0.0646396 | − | 0.997909i | \(-0.479410\pi\) | ||||
0.0646396 | + | 0.997909i | \(0.479410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.39230 | −0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.31508i | 0.278204i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.4641i | 1.01602i | 0.861352 | + | 0.508009i | \(0.169618\pi\) | ||||
−0.861352 | + | 0.508009i | \(0.830382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.69213 | −0.347438 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2487 | −0.841326 | −0.420663 | − | 0.907217i | \(-0.638203\pi\) | ||||
−0.420663 | + | 0.907217i | \(0.638203\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 16.8319i | − 0.866885i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.39230i | − 0.328351i | −0.986431 | − | 0.164175i | \(-0.947504\pi\) | ||||
0.986431 | − | 0.164175i | \(-0.0524963\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.8738 | −1.27099 | −0.635497 | − | 0.772104i | \(-0.719205\pi\) | ||||
−0.635497 | + | 0.772104i | \(0.719205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.535898 | −0.0273119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.3591i | 1.69137i | 0.533679 | + | 0.845687i | \(0.320809\pi\) | ||||
−0.533679 | + | 0.845687i | \(0.679191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.73205i | − 0.239310i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.55154 | −0.379959 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.58846 | 0.481231 | 0.240615 | − | 0.970621i | \(-0.422651\pi\) | ||||
0.240615 | + | 0.970621i | \(0.422651\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.24453i | 0.162024i | 0.996713 | + | 0.0810120i | \(0.0258152\pi\) | ||||
−0.996713 | + | 0.0810120i | \(0.974185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.32051i | − 0.0657792i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.61729 | 0.0801659 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1962 | 1.24587 | 0.622935 | − | 0.782274i | \(-0.285940\pi\) | ||||
0.622935 | + | 0.782274i | \(0.285940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.3244i | 1.83661i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 0.392305i | − 0.0192575i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.7028 | −1.59764 | −0.798818 | − | 0.601573i | \(-0.794541\pi\) | ||||
−0.798818 | + | 0.601573i | \(0.794541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8564 | 0.919005 | 0.459503 | − | 0.888176i | \(-0.348028\pi\) | ||||
0.459503 | + | 0.888176i | \(0.348028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.8338i | 0.768050i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.1244i | 1.21585i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.48528 | −0.408722 | −0.204361 | − | 0.978896i | \(-0.565512\pi\) | ||||
−0.204361 | + | 0.978896i | \(0.565512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.1769 | 1.35410 | 0.677048 | − | 0.735939i | \(-0.263259\pi\) | ||||
0.677048 | + | 0.735939i | \(0.263259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.69213i | 0.320128i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.535898i | 0.0255770i | 0.999918 | + | 0.0127885i | \(0.00407082\pi\) | ||||
−0.999918 | + | 0.0127885i | \(0.995929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.8439 | 1.75051 | 0.875253 | − | 0.483666i | \(-0.160695\pi\) | ||||
0.875253 | + | 0.483666i | \(0.160695\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.14359 | 0.0542115 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.9053i | 1.31693i | 0.752610 | + | 0.658467i | \(0.228795\pi\) | ||||
−0.752610 | + | 0.658467i | \(0.771205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000i | 0.0941763i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.48477 | −0.163368 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1962 | −0.617290 | −0.308645 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308645 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 20.9358i | − 0.975078i | −0.873101 | − | 0.487539i | \(-0.837895\pi\) | ||||
0.873101 | − | 0.487539i | \(-0.162105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.39230i | − 0.111180i | −0.998454 | − | 0.0555899i | \(-0.982296\pi\) | ||||
0.998454 | − | 0.0555899i | \(-0.0177039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.8695 | 1.01200 | 0.506001 | − | 0.862533i | \(-0.331123\pi\) | ||||
0.506001 | + | 0.862533i | \(0.331123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.3923 | −1.40339 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.99622i | 0.0917864i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 22.3923i | − 1.02743i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.00429 | −0.137270 | −0.0686348 | − | 0.997642i | \(-0.521864\pi\) | ||||
−0.0686348 | + | 0.997642i | \(0.521864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5167 | 0.479518 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 7.45001i | − 0.338287i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.0718i | − 1.04548i | −0.852491 | − | 0.522741i | \(-0.824909\pi\) | ||||
0.852491 | − | 0.522741i | \(-0.175091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.8396 | 1.52716 | 0.763580 | − | 0.645714i | \(-0.223440\pi\) | ||||
0.763580 | + | 0.645714i | \(0.223440\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8564 | 1.02940 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 44.0165i | − 1.97441i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4449i | 1.00477i | 0.864644 | + | 0.502385i | \(0.167544\pi\) | ||||
−0.864644 | + | 0.502385i | \(0.832456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9743 | −0.667673 | −0.333836 | − | 0.942631i | \(-0.608343\pi\) | ||||
−0.333836 | + | 0.942631i | \(0.608343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.80385 | 0.0802702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 2.65256i | − 0.117573i | −0.998271 | − | 0.0587864i | \(-0.981277\pi\) | ||||
0.998271 | − | 0.0587864i | \(-0.0187231\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0526i | 1.24097i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07055 | 0.0912394 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60770 | 0.158666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 29.9759i | − 1.31327i | −0.754210 | − | 0.656634i | \(-0.771980\pi\) | ||||
0.754210 | − | 0.656634i | \(-0.228020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.80385i | 0.253785i | 0.991917 | + | 0.126892i | \(0.0405003\pi\) | ||||
−0.991917 | + | 0.126892i | \(0.959500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.79315 | 0.0781109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.0053i | 0.563323i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 3.46410i | − 0.149766i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.175865 | −0.00757506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | −0.300954 | −0.150477 | − | 0.988614i | \(-0.548081\pi\) | ||||
−0.150477 | + | 0.988614i | \(0.548081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 5.13922i | − 0.220140i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 33.3205i | − 1.42468i | −0.701834 | − | 0.712341i | \(-0.747635\pi\) | ||||
0.701834 | − | 0.712341i | \(-0.252365\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.3238 | −1.37704 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −39.8564 | −1.69487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 19.1798i | − 0.812675i | −0.913723 | − | 0.406337i | \(-0.866806\pi\) | ||||
0.913723 | − | 0.406337i | \(-0.133194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.9808i | 0.549028i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.3292 | 1.91040 | 0.955198 | − | 0.295967i | \(-0.0956418\pi\) | ||||
0.955198 | + | 0.295967i | \(0.0956418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.947441 | 0.0398591 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.9783i | 1.42444i | 0.701954 | + | 0.712222i | \(0.252311\pi\) | ||||
−0.701954 | + | 0.712222i | \(0.747689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 12.1436i | − 0.508194i | −0.967179 | − | 0.254097i | \(-0.918222\pi\) | ||||
0.967179 | − | 0.254097i | \(-0.0817782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.69213 | −0.279081 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5359 | 0.480246 | 0.240123 | − | 0.970743i | \(-0.422812\pi\) | ||||
0.240123 | + | 0.970743i | \(0.422812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.07055i | − 0.0859010i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 0.928203i | − 0.0384422i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0053 | 0.536787 | 0.268394 | − | 0.963309i | \(-0.413507\pi\) | ||||
0.268394 | + | 0.963309i | \(0.413507\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.53590 | −0.104490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 25.3915i | − 1.04270i | −0.853342 | − | 0.521351i | \(-0.825428\pi\) | ||||
0.853342 | − | 0.521351i | \(-0.174572\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.73205i | − 0.193995i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.277401 | 0.0113343 | 0.00566716 | − | 0.999984i | \(-0.498196\pi\) | ||||
0.00566716 | + | 0.999984i | \(0.498196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7846 | −1.54127 | −0.770633 | − | 0.637279i | \(-0.780060\pi\) | ||||
−0.770633 | + | 0.637279i | \(0.780060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.61969i | 0.228473i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.26795i | − 0.132642i | −0.997798 | − | 0.0663210i | \(-0.978874\pi\) | ||||
0.997798 | − | 0.0663210i | \(-0.0211261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4596 | 0.949075 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3923 | −1.38909 | −0.694546 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694546 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 7.86611i | − 0.316678i | −0.987385 | − | 0.158339i | \(-0.949386\pi\) | ||||
0.987385 | − | 0.158339i | \(-0.0506138\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.92820i | 0.358855i | 0.983771 | + | 0.179427i | \(0.0574245\pi\) | ||||
−0.983771 | + | 0.179427i | \(0.942576\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.03579 | 0.241819 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0526 | 0.842102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.2808i | 0.569414i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.61729 | −0.0641800 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14359 | −0.0453108 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 4.55721i | − 0.179999i | −0.995942 | − | 0.0899994i | \(-0.971313\pi\) | ||||
0.995942 | − | 0.0899994i | \(-0.0286865\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00000i | 0.157745i | 0.996885 | + | 0.0788723i | \(0.0251319\pi\) | ||||
−0.996885 | + | 0.0788723i | \(0.974868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.1218 | −1.65598 | −0.827989 | − | 0.560744i | \(-0.810515\pi\) | ||||
−0.827989 | + | 0.560744i | \(0.810515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.17691 | −0.203212 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 45.4307i | 1.77784i | 0.458062 | + | 0.888920i | \(0.348544\pi\) | ||||
−0.458062 | + | 0.888920i | \(0.651456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1962i | 0.398397i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.62587 | −0.297062 | −0.148531 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148531 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.5167 | −1.42033 | −0.710167 | − | 0.704034i | \(-0.751380\pi\) | ||||
−0.710167 | + | 0.704034i | \(0.751380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.69213i | 0.259510i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.66025i | 0.374047i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.48477 | −0.134528 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.32051 | −0.166543 | −0.0832717 | − | 0.996527i | \(-0.526537\pi\) | ||||
−0.0832717 | + | 0.996527i | \(0.526537\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 44.4698i | 1.70911i | 0.519360 | + | 0.854556i | \(0.326170\pi\) | ||||
−0.519360 | + | 0.854556i | \(0.673830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 39.3205i | − 1.50898i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.0764 | −0.768202 | −0.384101 | − | 0.923291i | \(-0.625489\pi\) | ||||
−0.384101 | + | 0.923291i | \(0.625489\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3923 | 0.435278 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 6.03579i | − 0.229945i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5885i | 1.08756i | 0.839229 | + | 0.543778i | \(0.183007\pi\) | ||||
−0.839229 | + | 0.543778i | \(0.816993\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.34418 | −0.164784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.6603 | −0.668930 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.1146i | 1.13741i | 0.822541 | + | 0.568706i | \(0.192556\pi\) | ||||
−0.822541 | + | 0.568706i | \(0.807444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 20.1962i | − 0.761712i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.52056 | 0.358057 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | 0.488225 | 0.244113 | − | 0.969747i | \(-0.421503\pi\) | ||||
0.244113 | + | 0.969747i | \(0.421503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.757875i | 0.0283826i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.483340i | − 0.0180759i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.4916 | 1.17444 | 0.587220 | − | 0.809427i | \(-0.300222\pi\) | ||||
0.587220 | + | 0.809427i | \(0.300222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9282 | 0.406988 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 32.3238i | − 1.20048i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.9090i | 1.48014i | 0.672529 | + | 0.740071i | \(0.265208\pi\) | ||||
−0.672529 | + | 0.740071i | \(0.734792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.6269 | −0.651955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.67949 | −0.172841 | −0.0864205 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864205 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 4.21543i | − 0.155278i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.0000i | 1.17714i | 0.808447 | + | 0.588570i | \(0.200309\pi\) | ||||
−0.808447 | + | 0.588570i | \(0.799691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.3959 | 1.81216 | 0.906081 | − | 0.423105i | \(-0.139060\pi\) | ||||
0.906081 | + | 0.423105i | \(0.139060\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.4641 | −0.383375 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 18.2832i | − 0.668055i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.5885i | 1.48109i | 0.672005 | + | 0.740547i | \(0.265433\pi\) | ||||
−0.672005 | + | 0.740547i | \(0.734567\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.72741 | −0.281229 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7846 | −0.610047 | −0.305024 | − | 0.952345i | \(-0.598664\pi\) | ||||
−0.305024 | + | 0.952345i | \(0.598664\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 34.6346i | − 1.25550i | −0.778413 | − | 0.627752i | \(-0.783975\pi\) | ||||
0.778413 | − | 0.627752i | \(-0.216025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 27.1244i | − 0.981968i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.6637 | −1.21553 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.0333 | 1.80425 | 0.902124 | − | 0.431477i | \(-0.142007\pi\) | ||||
0.902124 | + | 0.431477i | \(0.142007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 53.1209i | − 1.91063i | −0.295594 | − | 0.955314i | \(-0.595517\pi\) | ||||
0.295594 | − | 0.955314i | \(-0.404483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.53590i | − 0.0910922i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.9754 | 0.894836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.10512 | 0.218458 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 3.44760i | − 0.123050i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2679i | 0.758121i | 0.925372 | + | 0.379060i | \(0.123753\pi\) | ||||
−0.925372 | + | 0.379060i | \(0.876247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.00052 | 0.177798 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.6603 | −0.804689 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.58493i | − 0.339516i | −0.985486 | − | 0.169758i | \(-0.945701\pi\) | ||||
0.985486 | − | 0.169758i | \(-0.0542985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.8564i | 1.12700i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.89091 | −0.137307 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 23.2466i | − 0.817307i | −0.912690 | − | 0.408653i | \(-0.865999\pi\) | ||||
0.912690 | − | 0.408653i | \(-0.134001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6410i | 0.795034i | 0.917595 | + | 0.397517i | \(0.130128\pi\) | ||||
−0.917595 | + | 0.397517i | \(0.869872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5911 | −0.406019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9282 | 0.872127 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.7372i | 1.56134i | 0.624944 | + | 0.780669i | \(0.285122\pi\) | ||||
−0.624944 | + | 0.780669i | \(0.714878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3923i | 0.850262i | 0.905132 | + | 0.425131i | \(0.139772\pi\) | ||||
−0.905132 | + | 0.425131i | \(0.860228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.5259 | −0.783302 | −0.391651 | − | 0.920114i | \(-0.628096\pi\) | ||||
−0.391651 | + | 0.920114i | \(0.628096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.7128 | 1.37928 | 0.689642 | − | 0.724151i | \(-0.257768\pi\) | ||||
0.689642 | + | 0.724151i | \(0.257768\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.55291i | − 0.0538053i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5885i | 0.366429i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.6718 | 1.19700 | 0.598502 | − | 0.801122i | \(-0.295763\pi\) | ||||
0.598502 | + | 0.801122i | \(0.295763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6603 | −0.608974 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.58630i | 0.123373i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6603i | 1.01914i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.03579 | −0.206904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.5692 | −1.35482 | −0.677412 | − | 0.735604i | \(-0.736899\pi\) | ||||
−0.677412 | + | 0.735604i | \(0.736899\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.9072i | 0.919133i | 0.888143 | + | 0.459567i | \(0.151995\pi\) | ||||
−0.888143 | + | 0.459567i | \(0.848005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4641i | 1.48298i | 0.670966 | + | 0.741488i | \(0.265880\pi\) | ||||
−0.670966 | + | 0.741488i | \(0.734120\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.0502 | −1.02292 | −0.511461 | − | 0.859307i | \(-0.670895\pi\) | ||||
−0.511461 | + | 0.859307i | \(0.670895\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.607695 | −0.0206623 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 5.52811i | − 0.187528i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 27.4115i | − 0.928805i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.7632 | −0.465281 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.1244 | 0.679551 | 0.339776 | − | 0.940507i | \(-0.389649\pi\) | ||||
0.339776 | + | 0.940507i | \(0.389649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.7033i | 1.27026i | 0.772407 | + | 0.635128i | \(0.219053\pi\) | ||||
−0.772407 | + | 0.635128i | \(0.780947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.3205i | 1.18863i | 0.804232 | + | 0.594315i | \(0.202577\pi\) | ||||
−0.804232 | + | 0.594315i | \(0.797423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.79744 | 0.161082 | 0.0805412 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805412 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.53590 | −0.286285 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 45.0518i | − 1.50760i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.24871i | 0.208871i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.66063 | −0.122089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.19615 | 0.273053 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.85993i | 0.194791i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.4641i | 0.646295i | 0.946349 | + | 0.323147i | \(0.104741\pi\) | ||||
−0.946349 | + | 0.323147i | \(0.895259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.3591 | −1.10524 | −0.552618 | − | 0.833434i | \(-0.686371\pi\) | ||||
−0.552618 | + | 0.833434i | \(0.686371\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.287187 | 0.00950451 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 53.8144i | 1.77711i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4449i | 0.674414i | 0.941431 | + | 0.337207i | \(0.109482\pi\) | ||||
−0.941431 | + | 0.337207i | \(0.890518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.6995 | 1.30673 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.1962 | 0.664045 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 17.9687i | − 0.589533i | −0.955569 | − | 0.294767i | \(-0.904758\pi\) | ||||
0.955569 | − | 0.294767i | \(-0.0952419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.19615i | 0.0719760i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.656339 | 0.0214646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.3923 | −0.437508 | −0.218754 | − | 0.975780i | \(-0.570199\pi\) | ||||
−0.218754 | + | 0.975780i | \(0.570199\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6384i | 1.06398i | 0.846750 | + | 0.531991i | \(0.178556\pi\) | ||||
−0.846750 | + | 0.531991i | \(0.821444\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 7.46410i | − 0.243065i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.8406 | −1.42463 | −0.712314 | − | 0.701861i | \(-0.752353\pi\) | ||||
−0.712314 | + | 0.701861i | \(0.752353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.3013 | −0.821314 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 29.9387i | − 0.969810i | −0.874567 | − | 0.484905i | \(-0.838854\pi\) | ||||
0.874567 | − | 0.484905i | \(-0.161146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 5.51666i | − 0.178515i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 60.1276 | 1.94162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7128 | 0.990736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.795040i | 0.0255932i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.6603i | 1.78991i | 0.446153 | + | 0.894957i | \(0.352794\pi\) | ||||
−0.446153 | + | 0.894957i | \(0.647206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.6584 | 0.662960 | 0.331480 | − | 0.943462i | \(-0.392452\pi\) | ||||
0.331480 | + | 0.943462i | \(0.392452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.9282 | −0.735044 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5297i | 0.656802i | 0.944538 | + | 0.328401i | \(0.106510\pi\) | ||||
−0.944538 | + | 0.328401i | \(0.893490\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.837169i | 0.0267560i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.5627 | −1.22996 | −0.614980 | − | 0.788543i | \(-0.710836\pi\) | ||||
−0.614980 | + | 0.788543i | \(0.710836\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.85641 | −0.282189 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 7.45001i | − 0.236896i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4449i | 1.03065i | 0.856996 | + | 0.515323i | \(0.172328\pi\) | ||||
−0.856996 | + | 0.515323i | \(0.827672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.14110 | 0.131282 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.19615 | −0.227904 | −0.113952 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113952 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5184.2.c.i.5183.3 | 8 | ||
3.2 | odd | 2 | inner | 5184.2.c.i.5183.5 | 8 | ||
4.3 | odd | 2 | inner | 5184.2.c.i.5183.4 | 8 | ||
8.3 | odd | 2 | 2592.2.c.a.2591.6 | yes | 8 | ||
8.5 | even | 2 | 2592.2.c.a.2591.5 | yes | 8 | ||
12.11 | even | 2 | inner | 5184.2.c.i.5183.6 | 8 | ||
24.5 | odd | 2 | 2592.2.c.a.2591.3 | ✓ | 8 | ||
24.11 | even | 2 | 2592.2.c.a.2591.4 | yes | 8 | ||
72.5 | odd | 6 | 2592.2.s.f.1727.2 | 8 | |||
72.11 | even | 6 | 2592.2.s.f.863.3 | 8 | |||
72.13 | even | 6 | 2592.2.s.f.1727.3 | 8 | |||
72.29 | odd | 6 | 2592.2.s.b.863.3 | 8 | |||
72.43 | odd | 6 | 2592.2.s.f.863.2 | 8 | |||
72.59 | even | 6 | 2592.2.s.b.1727.2 | 8 | |||
72.61 | even | 6 | 2592.2.s.b.863.2 | 8 | |||
72.67 | odd | 6 | 2592.2.s.b.1727.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2592.2.c.a.2591.3 | ✓ | 8 | 24.5 | odd | 2 | ||
2592.2.c.a.2591.4 | yes | 8 | 24.11 | even | 2 | ||
2592.2.c.a.2591.5 | yes | 8 | 8.5 | even | 2 | ||
2592.2.c.a.2591.6 | yes | 8 | 8.3 | odd | 2 | ||
2592.2.s.b.863.2 | 8 | 72.61 | even | 6 | |||
2592.2.s.b.863.3 | 8 | 72.29 | odd | 6 | |||
2592.2.s.b.1727.2 | 8 | 72.59 | even | 6 | |||
2592.2.s.b.1727.3 | 8 | 72.67 | odd | 6 | |||
2592.2.s.f.863.2 | 8 | 72.43 | odd | 6 | |||
2592.2.s.f.863.3 | 8 | 72.11 | even | 6 | |||
2592.2.s.f.1727.2 | 8 | 72.5 | odd | 6 | |||
2592.2.s.f.1727.3 | 8 | 72.13 | even | 6 | |||
5184.2.c.i.5183.3 | 8 | 1.1 | even | 1 | trivial | ||
5184.2.c.i.5183.4 | 8 | 4.3 | odd | 2 | inner | ||
5184.2.c.i.5183.5 | 8 | 3.2 | odd | 2 | inner | ||
5184.2.c.i.5183.6 | 8 | 12.11 | even | 2 | inner |