Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1755,2,Mod(1,1755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1755, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1755.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1755 = 3^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1755.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.0137455547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1755.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.732051 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.46410 | −0.732051 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73205 | 1.41058 | 0.705291 | − | 0.708918i | \(-0.250816\pi\) | ||||
0.705291 | + | 0.708918i | \(0.250816\pi\) | |||||||
\(8\) | 2.53590 | 0.896575 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.732051 | −0.231495 | ||||||||
\(11\) | 1.46410 | 0.441443 | 0.220722 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220722 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.07180 | 0.267949 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | −1.46410 | −0.327383 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.07180 | −0.228508 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.732051 | 0.143567 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.46410 | −1.03262 | ||||||||
\(29\) | −4.19615 | −0.779206 | −0.389603 | − | 0.920983i | \(-0.627388\pi\) | ||||
−0.389603 | + | 0.920983i | \(0.627388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.732051 | 0.131480 | 0.0657401 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657401 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(32\) | −5.85641 | −1.03528 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.92820 | −0.502183 | ||||||||
\(35\) | 3.73205 | 0.630832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.19615 | −0.196646 | −0.0983231 | − | 0.995155i | \(-0.531348\pi\) | ||||
−0.0983231 | + | 0.995155i | \(0.531348\pi\) | |||||||
\(38\) | −4.39230 | −0.712526 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.53590 | 0.400961 | ||||||||
\(41\) | 1.73205 | 0.270501 | 0.135250 | − | 0.990811i | \(-0.456816\pi\) | ||||
0.135250 | + | 0.990811i | \(0.456816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.19615 | 0.944904 | 0.472452 | − | 0.881356i | \(-0.343369\pi\) | ||||
0.472452 | + | 0.881356i | \(0.343369\pi\) | |||||||
\(44\) | −2.14359 | −0.323159 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.19615 | 0.323805 | ||||||||
\(47\) | −5.26795 | −0.768409 | −0.384205 | − | 0.923248i | \(-0.625524\pi\) | ||||
−0.384205 | + | 0.923248i | \(0.625524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | −0.732051 | −0.103528 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.46410 | 0.203034 | ||||||||
\(53\) | −1.53590 | −0.210972 | −0.105486 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105486 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.46410 | 0.197419 | ||||||||
\(56\) | 9.46410 | 1.26469 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.07180 | 0.403347 | ||||||||
\(59\) | −7.73205 | −1.00663 | −0.503314 | − | 0.864104i | \(-0.667886\pi\) | ||||
−0.503314 | + | 0.864104i | \(0.667886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | −0.535898 | −0.0680592 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.19615 | 0.879150 | 0.439575 | − | 0.898206i | \(-0.355129\pi\) | ||||
0.439575 | + | 0.898206i | \(0.355129\pi\) | |||||||
\(68\) | −5.85641 | −0.710194 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.73205 | −0.326543 | ||||||||
\(71\) | 2.66025 | 0.315714 | 0.157857 | − | 0.987462i | \(-0.449541\pi\) | ||||
0.157857 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.1962 | −1.31041 | −0.655205 | − | 0.755451i | \(-0.727418\pi\) | ||||
−0.655205 | + | 0.755451i | \(0.727418\pi\) | |||||||
\(74\) | 0.875644 | 0.101792 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.78461 | −1.00766 | ||||||||
\(77\) | 5.46410 | 0.622692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.00000 | 1.01258 | 0.506290 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506290 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(80\) | 1.07180 | 0.119831 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.26795 | −0.140022 | ||||||||
\(83\) | −8.92820 | −0.979998 | −0.489999 | − | 0.871723i | \(-0.663003\pi\) | ||||
−0.489999 | + | 0.871723i | \(0.663003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | −4.53590 | −0.489119 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.71281 | 0.395787 | ||||||||
\(89\) | −1.19615 | −0.126792 | −0.0633960 | − | 0.997988i | \(-0.520193\pi\) | ||||
−0.0633960 | + | 0.997988i | \(0.520193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.73205 | −0.391225 | ||||||||
\(92\) | 4.39230 | 0.457929 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.85641 | 0.397758 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3923 | 1.46132 | 0.730659 | − | 0.682743i | \(-0.239213\pi\) | ||||
0.730659 | + | 0.682743i | \(0.239213\pi\) | |||||||
\(98\) | −5.07180 | −0.512329 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.46410 | −0.146410 | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1244 | 1.09612 | 0.548058 | − | 0.836441i | \(-0.315367\pi\) | ||||
0.548058 | + | 0.836441i | \(0.315367\pi\) | |||||||
\(104\) | −2.53590 | −0.248665 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.12436 | 0.109207 | ||||||||
\(107\) | 6.39230 | 0.617967 | 0.308984 | − | 0.951067i | \(-0.400011\pi\) | ||||
0.308984 | + | 0.951067i | \(0.400011\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.92820 | 0.472036 | 0.236018 | − | 0.971749i | \(-0.424158\pi\) | ||||
0.236018 | + | 0.971749i | \(0.424158\pi\) | |||||||
\(110\) | −1.07180 | −0.102192 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | −20.8564 | −1.96201 | −0.981003 | − | 0.193993i | \(-0.937856\pi\) | ||||
−0.981003 | + | 0.193993i | \(0.937856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | 6.14359 | 0.570418 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.66025 | 0.521069 | ||||||||
\(119\) | 14.9282 | 1.36847 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | −2.14359 | −0.194072 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.07180 | −0.0962502 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.0000 | 1.95218 | 0.976092 | − | 0.217357i | \(-0.0697436\pi\) | ||||
0.976092 | + | 0.217357i | \(0.0697436\pi\) | |||||||
\(128\) | 10.1436 | 0.896575 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.732051 | 0.0642051 | ||||||||
\(131\) | 3.66025 | 0.319798 | 0.159899 | − | 0.987133i | \(-0.448883\pi\) | ||||
0.159899 | + | 0.987133i | \(0.448883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.3923 | 1.94166 | ||||||||
\(134\) | −5.26795 | −0.455081 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.1436 | 0.869806 | ||||||||
\(137\) | 19.3205 | 1.65066 | 0.825331 | − | 0.564649i | \(-0.190988\pi\) | ||||
0.825331 | + | 0.564649i | \(0.190988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.8564 | 1.68420 | 0.842099 | − | 0.539323i | \(-0.181320\pi\) | ||||
0.842099 | + | 0.539323i | \(0.181320\pi\) | |||||||
\(140\) | −5.46410 | −0.461801 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.94744 | −0.163426 | ||||||||
\(143\) | −1.46410 | −0.122434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.19615 | −0.348471 | ||||||||
\(146\) | 8.19615 | 0.678318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.75129 | 0.143955 | ||||||||
\(149\) | −8.66025 | −0.709476 | −0.354738 | − | 0.934966i | \(-0.615430\pi\) | ||||
−0.354738 | + | 0.934966i | \(0.615430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.58846 | −0.698919 | −0.349459 | − | 0.936952i | \(-0.613635\pi\) | ||||
−0.349459 | + | 0.936952i | \(0.613635\pi\) | |||||||
\(152\) | 15.2154 | 1.23413 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 0.732051 | 0.0587997 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.7321 | −0.856511 | −0.428255 | − | 0.903658i | \(-0.640872\pi\) | ||||
−0.428255 | + | 0.903658i | \(0.640872\pi\) | |||||||
\(158\) | −6.58846 | −0.524150 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.85641 | −0.462990 | ||||||||
\(161\) | −11.1962 | −0.882380 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.39230 | −0.344032 | −0.172016 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172016 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(164\) | −2.53590 | −0.198020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.53590 | 0.507284 | ||||||||
\(167\) | 2.53590 | 0.196234 | 0.0981169 | − | 0.995175i | \(-0.468718\pi\) | ||||
0.0981169 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.92820 | −0.224583 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.07180 | −0.691718 | ||||||||
\(173\) | 23.3205 | 1.77303 | 0.886513 | − | 0.462704i | \(-0.153121\pi\) | ||||
0.886513 | + | 0.462704i | \(0.153121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.73205 | 0.282117 | ||||||||
\(176\) | 1.56922 | 0.118284 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.875644 | 0.0656323 | ||||||||
\(179\) | −8.53590 | −0.638003 | −0.319002 | − | 0.947754i | \(-0.603348\pi\) | ||||
−0.319002 | + | 0.947754i | \(0.603348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.07180 | 0.302654 | 0.151327 | − | 0.988484i | \(-0.451645\pi\) | ||||
0.151327 | + | 0.988484i | \(0.451645\pi\) | |||||||
\(182\) | 2.73205 | 0.202513 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.60770 | −0.560847 | ||||||||
\(185\) | −1.19615 | −0.0879429 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.85641 | 0.428263 | ||||||||
\(188\) | 7.71281 | 0.562515 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.39230 | −0.318651 | ||||||||
\(191\) | −13.2679 | −0.960035 | −0.480018 | − | 0.877259i | \(-0.659370\pi\) | ||||
−0.480018 | + | 0.877259i | \(0.659370\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.66025 | −0.335452 | −0.167726 | − | 0.985834i | \(-0.553642\pi\) | ||||
−0.167726 | + | 0.985834i | \(0.553642\pi\) | |||||||
\(194\) | −10.5359 | −0.756433 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.1436 | −0.724542 | ||||||||
\(197\) | 7.26795 | 0.517820 | 0.258910 | − | 0.965901i | \(-0.416637\pi\) | ||||
0.258910 | + | 0.965901i | \(0.416637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.3205 | −1.72404 | −0.862018 | − | 0.506878i | \(-0.830799\pi\) | ||||
−0.862018 | + | 0.506878i | \(0.830799\pi\) | |||||||
\(200\) | 2.53590 | 0.179315 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.78461 | −0.618083 | ||||||||
\(203\) | −15.6603 | −1.09913 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.73205 | 0.120972 | ||||||||
\(206\) | −8.14359 | −0.567391 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.07180 | −0.0743157 | ||||||||
\(209\) | 8.78461 | 0.607644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8564 | −1.16044 | −0.580221 | − | 0.814459i | \(-0.697034\pi\) | ||||
−0.580221 | + | 0.814459i | \(0.697034\pi\) | |||||||
\(212\) | 2.24871 | 0.154442 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.67949 | −0.319883 | ||||||||
\(215\) | 6.19615 | 0.422574 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.73205 | 0.185464 | ||||||||
\(218\) | −3.60770 | −0.244344 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.14359 | −0.144521 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.12436 | −0.142257 | −0.0711287 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711287 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(224\) | −21.8564 | −1.46034 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.2679 | 1.01561 | ||||||||
\(227\) | 13.6603 | 0.906663 | 0.453331 | − | 0.891342i | \(-0.350235\pi\) | ||||
0.453331 | + | 0.891342i | \(0.350235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 2.19615 | 0.144810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6410 | −0.698617 | ||||||||
\(233\) | 5.00000 | 0.327561 | 0.163780 | − | 0.986497i | \(-0.447631\pi\) | ||||
0.163780 | + | 0.986497i | \(0.447631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.26795 | −0.343643 | ||||||||
\(236\) | 11.3205 | 0.736902 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.9282 | −0.708370 | ||||||||
\(239\) | 18.1244 | 1.17237 | 0.586184 | − | 0.810178i | \(-0.300630\pi\) | ||||
0.586184 | + | 0.810178i | \(0.300630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0526 | −1.16287 | −0.581434 | − | 0.813594i | \(-0.697508\pi\) | ||||
−0.581434 | + | 0.813594i | \(0.697508\pi\) | |||||||
\(242\) | 6.48334 | 0.416765 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.28719 | −0.274459 | ||||||||
\(245\) | 6.92820 | 0.442627 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 1.85641 | 0.117882 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.732051 | −0.0462990 | ||||||||
\(251\) | −25.5167 | −1.61060 | −0.805299 | − | 0.592869i | \(-0.797995\pi\) | ||||
−0.805299 | + | 0.592869i | \(0.797995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.39230 | −0.276142 | ||||||||
\(254\) | −16.1051 | −1.01052 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7128 | −0.732051 | ||||||||
\(257\) | 23.3923 | 1.45917 | 0.729586 | − | 0.683889i | \(-0.239713\pi\) | ||||
0.729586 | + | 0.683889i | \(0.239713\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.46410 | −0.277386 | ||||||||
\(260\) | 1.46410 | 0.0907997 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.67949 | −0.165540 | ||||||||
\(263\) | 13.9282 | 0.858850 | 0.429425 | − | 0.903103i | \(-0.358716\pi\) | ||||
0.429425 | + | 0.903103i | \(0.358716\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.53590 | −0.0943495 | ||||||||
\(266\) | −16.3923 | −1.00508 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5359 | −0.643582 | ||||||||
\(269\) | 13.5167 | 0.824125 | 0.412063 | − | 0.911156i | \(-0.364808\pi\) | ||||
0.412063 | + | 0.911156i | \(0.364808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1244 | 1.04023 | 0.520115 | − | 0.854096i | \(-0.325889\pi\) | ||||
0.520115 | + | 0.854096i | \(0.325889\pi\) | |||||||
\(272\) | 4.28719 | 0.259949 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.1436 | −0.854446 | ||||||||
\(275\) | 1.46410 | 0.0882886 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.66025 | −0.0997550 | −0.0498775 | − | 0.998755i | \(-0.515883\pi\) | ||||
−0.0498775 | + | 0.998755i | \(0.515883\pi\) | |||||||
\(278\) | −14.5359 | −0.871805 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.46410 | 0.565588 | ||||||||
\(281\) | −31.0526 | −1.85244 | −0.926220 | − | 0.376983i | \(-0.876962\pi\) | ||||
−0.926220 | + | 0.376983i | \(0.876962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.19615 | 0.249435 | 0.124718 | − | 0.992192i | \(-0.460197\pi\) | ||||
0.124718 | + | 0.992192i | \(0.460197\pi\) | |||||||
\(284\) | −3.89488 | −0.231119 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.07180 | 0.0633767 | ||||||||
\(287\) | 6.46410 | 0.381564 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 3.07180 | 0.180382 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.3923 | 0.959287 | ||||||||
\(293\) | 6.39230 | 0.373442 | 0.186721 | − | 0.982413i | \(-0.440214\pi\) | ||||
0.186721 | + | 0.982413i | \(0.440214\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.73205 | −0.450177 | ||||||||
\(296\) | −3.03332 | −0.176308 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.33975 | 0.367252 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1244 | 1.33287 | ||||||||
\(302\) | 6.28719 | 0.361787 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.43078 | 0.368831 | ||||||||
\(305\) | 2.92820 | 0.167668 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5167 | −1.51339 | −0.756693 | − | 0.653771i | \(-0.773186\pi\) | ||||
−0.756693 | + | 0.653771i | \(0.773186\pi\) | |||||||
\(308\) | −8.00000 | −0.455842 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.535898 | −0.0304370 | ||||||||
\(311\) | 3.32051 | 0.188289 | 0.0941444 | − | 0.995559i | \(-0.469988\pi\) | ||||
0.0941444 | + | 0.995559i | \(0.469988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.80385 | −0.441100 | −0.220550 | − | 0.975376i | \(-0.570785\pi\) | ||||
−0.220550 | + | 0.975376i | \(0.570785\pi\) | |||||||
\(314\) | 7.85641 | 0.443363 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.1769 | −0.741259 | ||||||||
\(317\) | 13.8564 | 0.778253 | 0.389127 | − | 0.921184i | \(-0.372777\pi\) | ||||
0.389127 | + | 0.921184i | \(0.372777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.14359 | −0.343975 | ||||||||
\(320\) | 2.14359 | 0.119831 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.19615 | 0.456754 | ||||||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 3.21539 | 0.178084 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.39230 | 0.242524 | ||||||||
\(329\) | −19.6603 | −1.08390 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 13.0718 | 0.717408 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.85641 | −0.101578 | ||||||||
\(335\) | 7.19615 | 0.393168 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3923 | −1.11084 | −0.555420 | − | 0.831570i | \(-0.687442\pi\) | ||||
−0.555420 | + | 0.831570i | \(0.687442\pi\) | |||||||
\(338\) | −0.732051 | −0.0398183 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.85641 | −0.317608 | ||||||||
\(341\) | 1.07180 | 0.0580410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 15.7128 | 0.847178 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.0718 | −0.917785 | ||||||||
\(347\) | −6.85641 | −0.368071 | −0.184036 | − | 0.982920i | \(-0.558916\pi\) | ||||
−0.184036 | + | 0.982920i | \(0.558916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | −2.73205 | −0.146034 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.57437 | −0.457016 | ||||||||
\(353\) | −31.5167 | −1.67746 | −0.838731 | − | 0.544546i | \(-0.816702\pi\) | ||||
−0.838731 | + | 0.544546i | \(0.816702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.66025 | 0.141192 | ||||||||
\(356\) | 1.75129 | 0.0928181 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.24871 | 0.330255 | ||||||||
\(359\) | −28.9090 | −1.52576 | −0.762878 | − | 0.646542i | \(-0.776215\pi\) | ||||
−0.762878 | + | 0.646542i | \(0.776215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −2.98076 | −0.156665 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.46410 | 0.286397 | ||||||||
\(365\) | −11.1962 | −0.586033 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.7846 | 1.60694 | 0.803472 | − | 0.595343i | \(-0.202984\pi\) | ||||
0.803472 | + | 0.595343i | \(0.202984\pi\) | |||||||
\(368\) | −3.21539 | −0.167614 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.875644 | 0.0455226 | ||||||||
\(371\) | −5.73205 | −0.297593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.875644 | 0.0453391 | 0.0226696 | − | 0.999743i | \(-0.492783\pi\) | ||||
0.0226696 | + | 0.999743i | \(0.492783\pi\) | |||||||
\(374\) | −4.28719 | −0.221685 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.3590 | −0.688937 | ||||||||
\(377\) | 4.19615 | 0.216113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6077 | −0.801713 | −0.400857 | − | 0.916141i | \(-0.631287\pi\) | ||||
−0.400857 | + | 0.916141i | \(0.631287\pi\) | |||||||
\(380\) | −8.78461 | −0.450641 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.71281 | 0.496951 | ||||||||
\(383\) | −3.80385 | −0.194368 | −0.0971838 | − | 0.995266i | \(-0.530983\pi\) | ||||
−0.0971838 | + | 0.995266i | \(0.530983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.46410 | 0.278476 | ||||||||
\(386\) | 3.41154 | 0.173643 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.0718 | −1.06976 | ||||||||
\(389\) | −20.2487 | −1.02665 | −0.513325 | − | 0.858194i | \(-0.671587\pi\) | ||||
−0.513325 | + | 0.858194i | \(0.671587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 17.5692 | 0.887380 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.32051 | −0.268043 | ||||||||
\(395\) | 9.00000 | 0.452839 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1962 | 1.16418 | 0.582091 | − | 0.813124i | \(-0.302235\pi\) | ||||
0.582091 | + | 0.813124i | \(0.302235\pi\) | |||||||
\(398\) | 17.8038 | 0.892426 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.07180 | 0.0535898 | ||||||||
\(401\) | −22.1244 | −1.10484 | −0.552419 | − | 0.833567i | \(-0.686295\pi\) | ||||
−0.552419 | + | 0.833567i | \(0.686295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.732051 | −0.0364660 | ||||||||
\(404\) | −17.5692 | −0.874101 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.4641 | 0.568954 | ||||||||
\(407\) | −1.75129 | −0.0868082 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3205 | 1.15312 | 0.576562 | − | 0.817053i | \(-0.304394\pi\) | ||||
0.576562 | + | 0.817053i | \(0.304394\pi\) | |||||||
\(410\) | −1.26795 | −0.0626195 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.2872 | −0.802412 | ||||||||
\(413\) | −28.8564 | −1.41993 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.92820 | −0.438268 | ||||||||
\(416\) | 5.85641 | 0.287134 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.43078 | −0.314540 | ||||||||
\(419\) | −35.7128 | −1.74469 | −0.872343 | − | 0.488895i | \(-0.837400\pi\) | ||||
−0.872343 | + | 0.488895i | \(0.837400\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.07180 | 0.149710 | 0.0748551 | − | 0.997194i | \(-0.476151\pi\) | ||||
0.0748551 | + | 0.997194i | \(0.476151\pi\) | |||||||
\(422\) | 12.3397 | 0.600689 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.89488 | −0.189152 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9282 | 0.528853 | ||||||||
\(428\) | −9.35898 | −0.452384 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.53590 | −0.218740 | ||||||||
\(431\) | 26.3923 | 1.27127 | 0.635636 | − | 0.771989i | \(-0.280738\pi\) | ||||
0.635636 | + | 0.771989i | \(0.280738\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.875644 | 0.0420808 | 0.0210404 | − | 0.999779i | \(-0.493302\pi\) | ||||
0.0210404 | + | 0.999779i | \(0.493302\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.21539 | −0.345555 | ||||||||
\(437\) | −18.0000 | −0.861057 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.9282 | −1.33294 | −0.666470 | − | 0.745532i | \(-0.732196\pi\) | ||||
−0.666470 | + | 0.745532i | \(0.732196\pi\) | |||||||
\(440\) | 3.71281 | 0.177001 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.92820 | 0.139280 | ||||||||
\(443\) | −17.7128 | −0.841561 | −0.420781 | − | 0.907162i | \(-0.638244\pi\) | ||||
−0.420781 | + | 0.907162i | \(0.638244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.19615 | −0.0567031 | ||||||||
\(446\) | 1.55514 | 0.0736378 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 24.1244 | 1.13850 | 0.569249 | − | 0.822165i | \(-0.307234\pi\) | ||||
0.569249 | + | 0.822165i | \(0.307234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.53590 | 0.119411 | ||||||||
\(452\) | 30.5359 | 1.43629 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | −3.73205 | −0.174961 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.1962 | 1.45929 | 0.729647 | − | 0.683824i | \(-0.239684\pi\) | ||||
0.729647 | + | 0.683824i | \(0.239684\pi\) | |||||||
\(458\) | 7.32051 | 0.342065 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.39230 | 0.204792 | ||||||||
\(461\) | −0.411543 | −0.0191675 | −0.00958373 | − | 0.999954i | \(-0.503051\pi\) | ||||
−0.00958373 | + | 0.999954i | \(0.503051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4449 | −1.36842 | −0.684209 | − | 0.729286i | \(-0.739853\pi\) | ||||
−0.684209 | + | 0.729286i | \(0.739853\pi\) | |||||||
\(464\) | −4.49742 | −0.208788 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.66025 | −0.169558 | ||||||||
\(467\) | −29.0000 | −1.34196 | −0.670980 | − | 0.741475i | \(-0.734126\pi\) | ||||
−0.670980 | + | 0.741475i | \(0.734126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.8564 | 1.24011 | ||||||||
\(470\) | 3.85641 | 0.177883 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.6077 | −0.902517 | ||||||||
\(473\) | 9.07180 | 0.417122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | −21.8564 | −1.00179 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.2679 | −0.606862 | ||||||||
\(479\) | −18.8038 | −0.859170 | −0.429585 | − | 0.903026i | \(-0.641340\pi\) | ||||
−0.429585 | + | 0.903026i | \(0.641340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.19615 | 0.0545399 | ||||||||
\(482\) | 13.2154 | 0.601945 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.9667 | 0.589395 | ||||||||
\(485\) | 14.3923 | 0.653521 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3923 | −0.924064 | −0.462032 | − | 0.886863i | \(-0.652879\pi\) | ||||
−0.462032 | + | 0.886863i | \(0.652879\pi\) | |||||||
\(488\) | 7.42563 | 0.336142 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.07180 | −0.229120 | ||||||||
\(491\) | 14.5359 | 0.655996 | 0.327998 | − | 0.944678i | \(-0.393626\pi\) | ||||
0.327998 | + | 0.944678i | \(0.393626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.7846 | −0.755941 | ||||||||
\(494\) | 4.39230 | 0.197619 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.784610 | 0.0352300 | ||||||||
\(497\) | 9.92820 | 0.445341 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.1244 | 1.93051 | 0.965256 | − | 0.261307i | \(-0.0841536\pi\) | ||||
0.965256 | + | 0.261307i | \(0.0841536\pi\) | |||||||
\(500\) | −1.46410 | −0.0654766 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.6795 | 0.833707 | ||||||||
\(503\) | 22.3923 | 0.998424 | 0.499212 | − | 0.866480i | \(-0.333623\pi\) | ||||
0.499212 | + | 0.866480i | \(0.333623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 3.21539 | 0.142942 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.2102 | −1.42910 | ||||||||
\(509\) | −15.4641 | −0.685434 | −0.342717 | − | 0.939439i | \(-0.611347\pi\) | ||||
−0.342717 | + | 0.939439i | \(0.611347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.7846 | −1.84844 | ||||||||
\(512\) | −11.7128 | −0.517638 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.1244 | −0.755323 | ||||||||
\(515\) | 11.1244 | 0.490198 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.71281 | −0.339209 | ||||||||
\(518\) | 3.26795 | 0.143585 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.53590 | −0.111207 | ||||||||
\(521\) | 9.46410 | 0.414630 | 0.207315 | − | 0.978274i | \(-0.433528\pi\) | ||||
0.207315 | + | 0.978274i | \(0.433528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.5167 | 1.37813 | 0.689064 | − | 0.724701i | \(-0.258022\pi\) | ||||
0.689064 | + | 0.724701i | \(0.258022\pi\) | |||||||
\(524\) | −5.35898 | −0.234108 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1962 | −0.444573 | ||||||||
\(527\) | 2.92820 | 0.127555 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 1.12436 | 0.0488389 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.7846 | −1.42139 | ||||||||
\(533\) | −1.73205 | −0.0750234 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.39230 | 0.276363 | ||||||||
\(536\) | 18.2487 | 0.788224 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.89488 | −0.426599 | ||||||||
\(539\) | 10.1436 | 0.436916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.1244 | −0.822220 | −0.411110 | − | 0.911586i | \(-0.634859\pi\) | ||||
−0.411110 | + | 0.911586i | \(0.634859\pi\) | |||||||
\(542\) | −12.5359 | −0.538463 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.4256 | −1.00437 | ||||||||
\(545\) | 4.92820 | 0.211101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53590 | −0.108427 | −0.0542136 | − | 0.998529i | \(-0.517265\pi\) | ||||
−0.0542136 | + | 0.998529i | \(0.517265\pi\) | |||||||
\(548\) | −28.2872 | −1.20837 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.07180 | −0.0457016 | ||||||||
\(551\) | −25.1769 | −1.07257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.5885 | 1.42833 | ||||||||
\(554\) | 1.21539 | 0.0516370 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29.0718 | −1.23292 | ||||||||
\(557\) | 26.3397 | 1.11605 | 0.558025 | − | 0.829824i | \(-0.311559\pi\) | ||||
0.558025 | + | 0.829824i | \(0.311559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.19615 | −0.262069 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.7321 | 0.958894 | ||||||||
\(563\) | 42.3205 | 1.78360 | 0.891798 | − | 0.452433i | \(-0.149444\pi\) | ||||
0.891798 | + | 0.452433i | \(0.149444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.8564 | −0.877436 | ||||||||
\(566\) | −3.07180 | −0.129117 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.74613 | 0.283061 | ||||||||
\(569\) | −5.26795 | −0.220844 | −0.110422 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110422 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.0000 | 1.12991 | 0.564957 | − | 0.825120i | \(-0.308893\pi\) | ||||
0.564957 | + | 0.825120i | \(0.308893\pi\) | |||||||
\(572\) | 2.14359 | 0.0896281 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.73205 | −0.197512 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.7846 | −1.53136 | −0.765682 | − | 0.643220i | \(-0.777598\pi\) | ||||
−0.765682 | + | 0.643220i | \(0.777598\pi\) | |||||||
\(578\) | 0.732051 | 0.0304493 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.14359 | 0.255099 | ||||||||
\(581\) | −33.3205 | −1.38237 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.24871 | −0.0931321 | ||||||||
\(584\) | −28.3923 | −1.17488 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.67949 | −0.193308 | ||||||||
\(587\) | −38.6410 | −1.59489 | −0.797443 | − | 0.603395i | \(-0.793814\pi\) | ||||
−0.797443 | + | 0.603395i | \(0.793814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.39230 | 0.180982 | ||||||||
\(590\) | 5.66025 | 0.233029 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.28203 | −0.0526912 | ||||||||
\(593\) | 34.9282 | 1.43433 | 0.717165 | − | 0.696904i | \(-0.245440\pi\) | ||||
0.717165 | + | 0.696904i | \(0.245440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9282 | 0.611997 | ||||||||
\(596\) | 12.6795 | 0.519372 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.19615 | −0.0898074 | ||||||||
\(599\) | −6.05256 | −0.247301 | −0.123650 | − | 0.992326i | \(-0.539460\pi\) | ||||
−0.123650 | + | 0.992326i | \(0.539460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7128 | 0.926475 | 0.463237 | − | 0.886234i | \(-0.346688\pi\) | ||||
0.463237 | + | 0.886234i | \(0.346688\pi\) | |||||||
\(602\) | −16.9282 | −0.689942 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.5744 | 0.511644 | ||||||||
\(605\) | −8.85641 | −0.360064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.3205 | −1.51479 | −0.757396 | − | 0.652955i | \(-0.773529\pi\) | ||||
−0.757396 | + | 0.652955i | \(0.773529\pi\) | |||||||
\(608\) | −35.1384 | −1.42505 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.14359 | −0.0867916 | ||||||||
\(611\) | 5.26795 | 0.213118 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4641 | 0.624589 | 0.312295 | − | 0.949985i | \(-0.398902\pi\) | ||||
0.312295 | + | 0.949985i | \(0.398902\pi\) | |||||||
\(614\) | 19.4115 | 0.783386 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.8564 | 0.558291 | ||||||||
\(617\) | −3.46410 | −0.139459 | −0.0697297 | − | 0.997566i | \(-0.522214\pi\) | ||||
−0.0697297 | + | 0.997566i | \(0.522214\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.1962 | −0.892139 | −0.446069 | − | 0.894998i | \(-0.647177\pi\) | ||||
−0.446069 | + | 0.894998i | \(0.647177\pi\) | |||||||
\(620\) | −1.07180 | −0.0430444 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.43078 | −0.0974654 | ||||||||
\(623\) | −4.46410 | −0.178850 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.71281 | 0.228330 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.7128 | 0.627009 | ||||||||
\(629\) | −4.78461 | −0.190775 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.26795 | −0.368951 | −0.184476 | − | 0.982837i | \(-0.559059\pi\) | ||||
−0.184476 | + | 0.982837i | \(0.559059\pi\) | |||||||
\(632\) | 22.8231 | 0.907854 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.1436 | −0.402854 | ||||||||
\(635\) | 22.0000 | 0.873043 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.92820 | −0.274505 | ||||||||
\(638\) | 4.49742 | 0.178055 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.1436 | 0.400961 | ||||||||
\(641\) | −0.143594 | −0.00567160 | −0.00283580 | − | 0.999996i | \(-0.500903\pi\) | ||||
−0.00283580 | + | 0.999996i | \(0.500903\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.3205 | −1.55065 | −0.775325 | − | 0.631563i | \(-0.782414\pi\) | ||||
−0.775325 | + | 0.631563i | \(0.782414\pi\) | |||||||
\(644\) | 16.3923 | 0.645947 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.5692 | −0.691252 | ||||||||
\(647\) | −44.4641 | −1.74806 | −0.874032 | − | 0.485868i | \(-0.838504\pi\) | ||||
−0.874032 | + | 0.485868i | \(0.838504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.3205 | −0.444369 | ||||||||
\(650\) | 0.732051 | 0.0287134 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.43078 | 0.251849 | ||||||||
\(653\) | −40.8564 | −1.59883 | −0.799417 | − | 0.600776i | \(-0.794858\pi\) | ||||
−0.799417 | + | 0.600776i | \(0.794858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.66025 | 0.143018 | ||||||||
\(656\) | 1.85641 | 0.0724805 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.3923 | 0.561070 | ||||||||
\(659\) | −44.4449 | −1.73133 | −0.865663 | − | 0.500627i | \(-0.833103\pi\) | ||||
−0.865663 | + | 0.500627i | \(0.833103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1051 | 1.79328 | 0.896641 | − | 0.442759i | \(-0.146000\pi\) | ||||
0.896641 | + | 0.442759i | \(0.146000\pi\) | |||||||
\(662\) | 8.78461 | 0.341424 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.6410 | −0.878642 | ||||||||
\(665\) | 22.3923 | 0.868336 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5885 | 0.487427 | ||||||||
\(668\) | −3.71281 | −0.143653 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.26795 | −0.203519 | ||||||||
\(671\) | 4.28719 | 0.165505 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6077 | −0.987104 | −0.493552 | − | 0.869716i | \(-0.664302\pi\) | ||||
−0.493552 | + | 0.869716i | \(0.664302\pi\) | |||||||
\(674\) | 14.9282 | 0.575013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.46410 | −0.0563116 | ||||||||
\(677\) | 36.0000 | 1.38359 | 0.691796 | − | 0.722093i | \(-0.256820\pi\) | ||||
0.691796 | + | 0.722093i | \(0.256820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.7128 | 2.06131 | ||||||||
\(680\) | 10.1436 | 0.388989 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.784610 | −0.0300443 | ||||||||
\(683\) | 33.1769 | 1.26948 | 0.634740 | − | 0.772726i | \(-0.281107\pi\) | ||||
0.634740 | + | 0.772726i | \(0.281107\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3205 | 0.738199 | ||||||||
\(686\) | 0.196152 | 0.00748913 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.64102 | 0.253186 | ||||||||
\(689\) | 1.53590 | 0.0585131 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5359 | −0.629055 | −0.314528 | − | 0.949248i | \(-0.601846\pi\) | ||||
−0.314528 | + | 0.949248i | \(0.601846\pi\) | |||||||
\(692\) | −34.1436 | −1.29794 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.01924 | 0.190528 | ||||||||
\(695\) | 19.8564 | 0.753196 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.92820 | 0.262424 | ||||||||
\(698\) | −13.1769 | −0.498754 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.46410 | −0.206524 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.17691 | −0.270682 | ||||||||
\(704\) | 3.13844 | 0.118284 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.0718 | 0.868319 | ||||||||
\(707\) | 44.7846 | 1.68430 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.3731 | 1.85424 | 0.927122 | − | 0.374759i | \(-0.122275\pi\) | ||||
0.927122 | + | 0.374759i | \(0.122275\pi\) | |||||||
\(710\) | −1.94744 | −0.0730862 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.03332 | −0.113679 | ||||||||
\(713\) | −2.19615 | −0.0822466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46410 | −0.0547543 | ||||||||
\(716\) | 12.4974 | 0.467051 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.1628 | 0.789790 | ||||||||
\(719\) | 24.0526 | 0.897009 | 0.448505 | − | 0.893781i | \(-0.351957\pi\) | ||||
0.448505 | + | 0.893781i | \(0.351957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.5167 | 1.54616 | ||||||||
\(722\) | −12.4449 | −0.463150 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.96152 | −0.221558 | ||||||||
\(725\) | −4.19615 | −0.155841 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.8038 | −0.586132 | −0.293066 | − | 0.956092i | \(-0.594676\pi\) | ||||
−0.293066 | + | 0.956092i | \(0.594676\pi\) | |||||||
\(728\) | −9.46410 | −0.350763 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.19615 | 0.303353 | ||||||||
\(731\) | 24.7846 | 0.916692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.3923 | 1.41805 | 0.709026 | − | 0.705182i | \(-0.249135\pi\) | ||||
0.709026 | + | 0.705182i | \(0.249135\pi\) | |||||||
\(734\) | −22.5359 | −0.831815 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.5692 | 0.647610 | ||||||||
\(737\) | 10.5359 | 0.388095 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2679 | 0.708783 | 0.354391 | − | 0.935097i | \(-0.384688\pi\) | ||||
0.354391 | + | 0.935097i | \(0.384688\pi\) | |||||||
\(740\) | 1.75129 | 0.0643787 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.19615 | 0.154046 | ||||||||
\(743\) | −19.8564 | −0.728461 | −0.364230 | − | 0.931309i | \(-0.618668\pi\) | ||||
−0.364230 | + | 0.931309i | \(0.618668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.66025 | −0.317287 | ||||||||
\(746\) | −0.641016 | −0.0234693 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.57437 | −0.313510 | ||||||||
\(749\) | 23.8564 | 0.871694 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.5359 | −0.895328 | −0.447664 | − | 0.894202i | \(-0.647744\pi\) | ||||
−0.447664 | + | 0.894202i | \(0.647744\pi\) | |||||||
\(752\) | −5.64617 | −0.205895 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.07180 | −0.111868 | ||||||||
\(755\) | −8.58846 | −0.312566 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.784610 | −0.0285171 | −0.0142586 | − | 0.999898i | \(-0.504539\pi\) | ||||
−0.0142586 | + | 0.999898i | \(0.504539\pi\) | |||||||
\(758\) | 11.4256 | 0.414997 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.2154 | 0.551920 | ||||||||
\(761\) | 37.0526 | 1.34315 | 0.671577 | − | 0.740935i | \(-0.265617\pi\) | ||||
0.671577 | + | 0.740935i | \(0.265617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.3923 | 0.665846 | ||||||||
\(764\) | 19.4256 | 0.702794 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.78461 | 0.100612 | ||||||||
\(767\) | 7.73205 | 0.279188 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.80385 | −0.0650484 | −0.0325242 | − | 0.999471i | \(-0.510355\pi\) | ||||
−0.0325242 | + | 0.999471i | \(0.510355\pi\) | |||||||
\(770\) | −4.00000 | −0.144150 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.82309 | 0.245568 | ||||||||
\(773\) | 46.7846 | 1.68273 | 0.841363 | − | 0.540471i | \(-0.181754\pi\) | ||||
0.841363 | + | 0.540471i | \(0.181754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.732051 | 0.0262960 | ||||||||
\(776\) | 36.4974 | 1.31018 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.8231 | 0.531433 | ||||||||
\(779\) | 10.3923 | 0.372343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.89488 | 0.139370 | ||||||||
\(782\) | 8.78461 | 0.314137 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.42563 | 0.265201 | ||||||||
\(785\) | −10.7321 | −0.383043 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.4115 | −0.656301 | −0.328150 | − | 0.944626i | \(-0.606425\pi\) | ||||
−0.328150 | + | 0.944626i | \(0.606425\pi\) | |||||||
\(788\) | −10.6410 | −0.379071 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.58846 | −0.234407 | ||||||||
\(791\) | −77.8372 | −2.76757 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.92820 | −0.103984 | ||||||||
\(794\) | −16.9808 | −0.602625 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.6077 | 1.26208 | ||||||||
\(797\) | −37.6410 | −1.33331 | −0.666657 | − | 0.745365i | \(-0.732275\pi\) | ||||
−0.666657 | + | 0.745365i | \(0.732275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.0718 | −0.745467 | ||||||||
\(800\) | −5.85641 | −0.207055 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.1962 | 0.571906 | ||||||||
\(803\) | −16.3923 | −0.578472 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1962 | −0.394613 | ||||||||
\(806\) | 0.535898 | 0.0188762 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.4308 | 1.07055 | ||||||||
\(809\) | −51.2295 | −1.80113 | −0.900566 | − | 0.434719i | \(-0.856848\pi\) | ||||
−0.900566 | + | 0.434719i | \(0.856848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5359 | 1.14249 | 0.571245 | − | 0.820780i | \(-0.306461\pi\) | ||||
0.571245 | + | 0.820780i | \(0.306461\pi\) | |||||||
\(812\) | 22.9282 | 0.804622 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.28203 | 0.0449352 | ||||||||
\(815\) | −4.39230 | −0.153856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.1769 | 1.30066 | ||||||||
\(818\) | −17.0718 | −0.596901 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.53590 | −0.0885574 | ||||||||
\(821\) | −8.12436 | −0.283542 | −0.141771 | − | 0.989899i | \(-0.545280\pi\) | ||||
−0.141771 | + | 0.989899i | \(0.545280\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.5359 | −1.06441 | −0.532207 | − | 0.846614i | \(-0.678637\pi\) | ||||
−0.532207 | + | 0.846614i | \(0.678637\pi\) | |||||||
\(824\) | 28.2102 | 0.982750 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.1244 | 0.735010 | ||||||||
\(827\) | −1.46410 | −0.0509118 | −0.0254559 | − | 0.999676i | \(-0.508104\pi\) | ||||
−0.0254559 | + | 0.999676i | \(0.508104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.6077 | −0.854661 | −0.427330 | − | 0.904096i | \(-0.640546\pi\) | ||||
−0.427330 | + | 0.904096i | \(0.640546\pi\) | |||||||
\(830\) | 6.53590 | 0.226864 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.14359 | −0.0743157 | ||||||||
\(833\) | 27.7128 | 0.960192 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.53590 | 0.0877584 | ||||||||
\(836\) | −12.8616 | −0.444826 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.1436 | 0.903115 | ||||||||
\(839\) | −38.2487 | −1.32049 | −0.660246 | − | 0.751049i | \(-0.729548\pi\) | ||||
−0.660246 | + | 0.751049i | \(0.729548\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3923 | −0.392838 | ||||||||
\(842\) | −2.24871 | −0.0774957 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.6795 | 0.849503 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.0526 | −1.13570 | ||||||||
\(848\) | −1.64617 | −0.0565297 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.92820 | −0.100437 | ||||||||
\(851\) | 3.58846 | 0.123011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.5885 | −0.739175 | −0.369587 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369587 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.2102 | 0.554054 | ||||||||
\(857\) | 11.7846 | 0.402555 | 0.201277 | − | 0.979534i | \(-0.435491\pi\) | ||||
0.201277 | + | 0.979534i | \(0.435491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7128 | −0.706712 | −0.353356 | − | 0.935489i | \(-0.614960\pi\) | ||||
−0.353356 | + | 0.935489i | \(0.614960\pi\) | |||||||
\(860\) | −9.07180 | −0.309346 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.3205 | −0.658059 | ||||||||
\(863\) | 23.0718 | 0.785373 | 0.392687 | − | 0.919672i | \(-0.371546\pi\) | ||||
0.392687 | + | 0.919672i | \(0.371546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3205 | 0.792921 | ||||||||
\(866\) | −0.641016 | −0.0217826 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | −0.135769 | ||||||||
\(869\) | 13.1769 | 0.446996 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.19615 | −0.243832 | ||||||||
\(872\) | 12.4974 | 0.423216 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.1769 | 0.445716 | ||||||||
\(875\) | 3.73205 | 0.126166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3731 | 1.63344 | 0.816721 | − | 0.577032i | \(-0.195789\pi\) | ||||
0.816721 | + | 0.577032i | \(0.195789\pi\) | |||||||
\(878\) | 20.4449 | 0.689981 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.56922 | 0.0528984 | ||||||||
\(881\) | 23.8564 | 0.803743 | 0.401871 | − | 0.915696i | \(-0.368360\pi\) | ||||
0.401871 | + | 0.915696i | \(0.368360\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.0333 | −1.44819 | −0.724093 | − | 0.689702i | \(-0.757742\pi\) | ||||
−0.724093 | + | 0.689702i | \(0.757742\pi\) | |||||||
\(884\) | 5.85641 | 0.196972 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.9667 | 0.435624 | ||||||||
\(887\) | −5.39230 | −0.181056 | −0.0905279 | − | 0.995894i | \(-0.528855\pi\) | ||||
−0.0905279 | + | 0.995894i | \(0.528855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 82.1051 | 2.75372 | ||||||||
\(890\) | 0.875644 | 0.0293517 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.11027 | 0.104140 | ||||||||
\(893\) | −31.6077 | −1.05771 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.53590 | −0.285324 | ||||||||
\(896\) | 37.8564 | 1.26469 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.6603 | −0.589330 | ||||||||
\(899\) | −3.07180 | −0.102450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.14359 | −0.204673 | ||||||||
\(902\) | −1.85641 | −0.0618116 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −52.8897 | −1.75909 | ||||||||
\(905\) | 4.07180 | 0.135351 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.8038 | 0.391940 | 0.195970 | − | 0.980610i | \(-0.437214\pi\) | ||||
0.195970 | + | 0.980610i | \(0.437214\pi\) | |||||||
\(908\) | −20.0000 | −0.663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.73205 | 0.0905666 | ||||||||
\(911\) | −1.01924 | −0.0337689 | −0.0168844 | − | 0.999857i | \(-0.505375\pi\) | ||||
−0.0168844 | + | 0.999857i | \(0.505375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.0718 | −0.432613 | ||||||||
\(914\) | −22.8372 | −0.755386 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.6410 | 0.483753 | ||||||||
\(917\) | 13.6603 | 0.451101 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.5359 | −0.512482 | −0.256241 | − | 0.966613i | \(-0.582484\pi\) | ||||
−0.256241 | + | 0.966613i | \(0.582484\pi\) | |||||||
\(920\) | −7.60770 | −0.250818 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.301270 | 0.00992181 | ||||||||
\(923\) | −2.66025 | −0.0875633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.19615 | −0.0393292 | ||||||||
\(926\) | 21.5551 | 0.708346 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.5744 | 0.806693 | ||||||||
\(929\) | −52.0000 | −1.70606 | −0.853032 | − | 0.521858i | \(-0.825239\pi\) | ||||
−0.853032 | + | 0.521858i | \(0.825239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.5692 | 1.36238 | ||||||||
\(932\) | −7.32051 | −0.239791 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.2295 | 0.694650 | ||||||||
\(935\) | 5.85641 | 0.191525 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.3205 | −1.34988 | −0.674941 | − | 0.737872i | \(-0.735831\pi\) | ||||
−0.674941 | + | 0.737872i | \(0.735831\pi\) | |||||||
\(938\) | −19.6603 | −0.641930 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.71281 | 0.251564 | ||||||||
\(941\) | −17.8756 | −0.582729 | −0.291365 | − | 0.956612i | \(-0.594109\pi\) | ||||
−0.291365 | + | 0.956612i | \(0.594109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.19615 | −0.169210 | ||||||||
\(944\) | −8.28719 | −0.269725 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.64102 | −0.215918 | ||||||||
\(947\) | −34.0526 | −1.10656 | −0.553280 | − | 0.832996i | \(-0.686624\pi\) | ||||
−0.553280 | + | 0.832996i | \(0.686624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1962 | 0.363442 | ||||||||
\(950\) | −4.39230 | −0.142505 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 37.8564 | 1.22693 | ||||||||
\(953\) | 36.4641 | 1.18119 | 0.590594 | − | 0.806969i | \(-0.298893\pi\) | ||||
0.590594 | + | 0.806969i | \(0.298893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.2679 | −0.429341 | ||||||||
\(956\) | −26.5359 | −0.858232 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.7654 | 0.444739 | ||||||||
\(959\) | 72.1051 | 2.32840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.4641 | −0.982713 | ||||||||
\(962\) | −0.875644 | −0.0282319 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.4308 | 0.851278 | ||||||||
\(965\) | −4.66025 | −0.150019 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000 | 0.128631 | 0.0643157 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643157 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(968\) | −22.4589 | −0.721858 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.5359 | −0.338287 | ||||||||
\(971\) | 20.9808 | 0.673305 | 0.336652 | − | 0.941629i | \(-0.390705\pi\) | ||||
0.336652 | + | 0.941629i | \(0.390705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 74.1051 | 2.37570 | ||||||||
\(974\) | 14.9282 | 0.478330 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.13844 | 0.100459 | ||||||||
\(977\) | 34.7321 | 1.11118 | 0.555588 | − | 0.831457i | \(-0.312493\pi\) | ||||
0.555588 | + | 0.831457i | \(0.312493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.75129 | −0.0559714 | ||||||||
\(980\) | −10.1436 | −0.324025 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.6410 | −0.339568 | ||||||||
\(983\) | −9.51666 | −0.303534 | −0.151767 | − | 0.988416i | \(-0.548496\pi\) | ||||
−0.151767 | + | 0.988416i | \(0.548496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.26795 | 0.231576 | ||||||||
\(986\) | 12.2872 | 0.391304 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.78461 | 0.279476 | ||||||||
\(989\) | −18.5885 | −0.591079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.7128 | 1.54741 | 0.773707 | − | 0.633544i | \(-0.218400\pi\) | ||||
0.773707 | + | 0.633544i | \(0.218400\pi\) | |||||||
\(992\) | −4.28719 | −0.136118 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.26795 | −0.230525 | ||||||||
\(995\) | −24.3205 | −0.771012 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9282 | 1.04285 | 0.521423 | − | 0.853298i | \(-0.325401\pi\) | ||||
0.521423 | + | 0.853298i | \(0.325401\pi\) | |||||||
\(998\) | −31.5692 | −0.999306 | ||||||||
\(999\) | 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 | 1755.2.a.l.1.1 | yes | 2 | |
3.2 | odd | 2 | 1755.2.a.h.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 8775.2.a.t.1.2 | 2 | |||
15.14 | odd | 2 | 8775.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1755.2.a.h.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1755.2.a.l.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
8775.2.a.t.1.2 | 2 | 5.4 | even | 2 | |||
8775.2.a.bf.1.1 | 2 | 15.14 | odd | 2 |