Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(737,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bj (of order \(4\), degree \(2\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.3 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.737 |
Dual form | 2880.2.bj.c.1313.3 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 2.22474 | + | 0.224745i | 0.994936 | + | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | − | 1.41421i | −0.534522 | − | 0.534522i | 0.387392 | − | 0.921915i | \(-0.373376\pi\) |
−0.921915 | + | 0.387392i | \(0.873376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.317837 | − | 0.317837i | −0.0881522 | − | 0.0881522i | 0.661656 | − | 0.749808i | \(-0.269854\pi\) |
−0.749808 | + | 0.661656i | \(0.769854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.04989 | − | 2.04989i | 0.497171 | − | 0.497171i | −0.413385 | − | 0.910556i | \(-0.635654\pi\) |
0.910556 | + | 0.413385i | \(0.135654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89898 | 0.665072 | 0.332536 | − | 0.943091i | \(-0.392096\pi\) | ||||
0.332536 | + | 0.943091i | \(0.392096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.449490 | − | 0.449490i | −0.0937251 | − | 0.0937251i | 0.658690 | − | 0.752415i | \(-0.271111\pi\) |
−0.752415 | + | 0.658690i | \(0.771111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | + | 1.00000i | 0.979796 | + | 0.200000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.55051i | 0.659313i | 0.944101 | + | 0.329657i | \(0.106933\pi\) | ||||
−0.944101 | + | 0.329657i | \(0.893067\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.09978 | −0.736342 | −0.368171 | − | 0.929758i | \(-0.620016\pi\) | ||||
−0.368171 | + | 0.929758i | \(0.620016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.82843 | − | 3.46410i | −0.478091 | − | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.97469 | − | 5.97469i | 0.982233 | − | 0.982233i | −0.0176117 | − | 0.999845i | \(-0.505606\pi\) |
0.999845 | + | 0.0176117i | \(0.00560626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.41421i | − | 0.220863i | −0.993884 | − | 0.110432i | \(-0.964777\pi\) | ||
0.993884 | − | 0.110432i | \(-0.0352233\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.89898 | − | 2.89898i | −0.442090 | − | 0.442090i | 0.450624 | − | 0.892714i | \(-0.351202\pi\) |
−0.892714 | + | 0.450624i | \(0.851202\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.44949 | − | 6.44949i | 0.940755 | − | 0.940755i | −0.0575858 | − | 0.998341i | \(-0.518340\pi\) |
0.998341 | + | 0.0575858i | \(0.0183403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.00000i | − | 0.428571i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.89898 | − | 2.89898i | 0.398205 | − | 0.398205i | −0.479394 | − | 0.877600i | \(-0.659144\pi\) |
0.877600 | + | 0.479394i | \(0.159144\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.70674 | − | 0.778539i | −1.03918 | − | 0.104978i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.29253i | 0.819217i | 0.912261 | + | 0.409609i | \(0.134335\pi\) | ||||
−0.912261 | + | 0.409609i | \(0.865665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.2207i | − | 1.69274i | −0.532594 | − | 0.846371i | \(-0.678783\pi\) | ||
0.532594 | − | 0.846371i | \(-0.321217\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.635674 | − | 0.778539i | −0.0788457 | − | 0.0965659i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.8990i | − | 1.53083i | −0.643539 | − | 0.765414i | \(-0.722534\pi\) | ||
0.643539 | − | 0.765414i | \(-0.277466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.89898 | + | 7.89898i | −0.924506 | + | 0.924506i | −0.997344 | − | 0.0728382i | \(-0.976794\pi\) |
0.0728382 | + | 0.997344i | \(0.476794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89898 | + | 4.89898i | 0.558291 | + | 0.558291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.1421i | − | 1.59111i | −0.605878 | − | 0.795557i | \(-0.707178\pi\) | ||
0.605878 | − | 0.795557i | \(-0.292822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.12096 | − | 9.12096i | 1.00115 | − | 1.00115i | 0.00115564 | − | 0.999999i | \(-0.499632\pi\) |
0.999999 | − | 0.00115564i | \(-0.000367851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.02118 | − | 4.09978i | 0.544623 | − | 0.444683i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.24264 | −0.449719 | −0.224860 | − | 0.974391i | \(-0.572192\pi\) | ||||
−0.224860 | + | 0.974391i | \(0.572192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.898979i | 0.0942387i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.44949 | + | 0.651531i | 0.661704 | + | 0.0668456i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.89898 | − | 7.89898i | −0.802020 | − | 0.802020i | 0.181391 | − | 0.983411i | \(-0.441940\pi\) |
−0.983411 | + | 0.181391i | \(0.941940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.34847 | 0.930207 | 0.465104 | − | 0.885256i | \(-0.346017\pi\) | ||||
0.465104 | + | 0.885256i | \(0.346017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.97809 | + | 8.97809i | −0.884638 | + | 0.884638i | −0.994002 | − | 0.109364i | \(-0.965119\pi\) |
0.109364 | + | 0.994002i | \(0.465119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.12096 | + | 9.12096i | 0.881756 | + | 0.881756i | 0.993713 | − | 0.111957i | \(-0.0357119\pi\) |
−0.111957 | + | 0.993713i | \(0.535712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.02118 | 0.480942 | 0.240471 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240471 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.02118 | + | 5.02118i | 0.472353 | + | 0.472353i | 0.902675 | − | 0.430322i | \(-0.141600\pi\) |
−0.430322 | + | 0.902675i | \(0.641600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.898979 | − | 1.10102i | −0.0838303 | − | 0.102671i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.79796 | −0.531498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6742 | + | 3.32577i | 0.954733 | + | 0.297465i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8065 | − | 11.8065i | −1.04766 | − | 1.04766i | −0.998806 | − | 0.0488531i | \(-0.984443\pi\) |
−0.0488531 | − | 0.998806i | \(-0.515557\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.73545 | 0.413738 | 0.206869 | − | 0.978369i | \(-0.433673\pi\) | ||||
0.206869 | + | 0.978369i | \(0.433673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.09978 | − | 4.09978i | −0.355496 | − | 0.355496i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2207 | + | 13.2207i | −1.12952 | + | 1.12952i | −0.139269 | + | 0.990255i | \(0.544475\pi\) |
−0.990255 | + | 0.139269i | \(0.955525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.7980 | −1.00069 | −0.500345 | − | 0.865826i | \(-0.666793\pi\) | ||||
−0.500345 | + | 0.865826i | \(0.666793\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.10102 | + | 1.10102i | 0.0920720 | + | 0.0920720i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.797959 | + | 7.89898i | −0.0662669 | + | 0.655975i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4495i | 1.34759i | 0.738916 | + | 0.673797i | \(0.235338\pi\) | ||||
−0.738916 | + | 0.673797i | \(0.764662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2419 | −1.48451 | −0.742253 | − | 0.670120i | \(-0.766243\pi\) | ||||
−0.742253 | + | 0.670120i | \(0.766243\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.12096 | − | 0.921404i | −0.732613 | − | 0.0740089i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2672 | − | 12.2672i | 0.979031 | − | 0.979031i | −0.0207539 | − | 0.999785i | \(-0.506607\pi\) |
0.999785 | + | 0.0207539i | \(0.00660663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.27135i | 0.100196i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7980 | + | 15.7980i | 1.23739 | + | 1.23739i | 0.961063 | + | 0.276328i | \(0.0891177\pi\) |
0.276328 | + | 0.961063i | \(0.410882\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.44949 | − | 8.44949i | 0.653841 | − | 0.653841i | −0.300075 | − | 0.953916i | \(-0.597012\pi\) |
0.953916 | + | 0.300075i | \(0.0970116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.7980i | − | 0.984458i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.44949 | − | 6.44949i | 0.490346 | − | 0.490346i | −0.418069 | − | 0.908415i | \(-0.637293\pi\) |
0.908415 | + | 0.418069i | \(0.137293\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.51399 | − | 8.34242i | −0.416818 | − | 0.630627i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.84961i | 0.586707i | 0.956004 | + | 0.293354i | \(0.0947713\pi\) | ||||
−0.956004 | + | 0.293354i | \(0.905229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2207i | − | 0.982689i | −0.870965 | − | 0.491345i | \(-0.836506\pi\) | ||
0.870965 | − | 0.491345i | \(-0.163494\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.6349 | − | 11.9494i | 1.07598 | − | 0.878536i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.10102 | + | 7.10102i | −0.519278 | + | 0.519278i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.79796i | − | 0.419526i | −0.977752 | − | 0.209763i | \(-0.932731\pi\) | ||
0.977752 | − | 0.209763i | \(-0.0672692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.797959 | − | 0.797959i | 0.0574383 | − | 0.0574383i | −0.677804 | − | 0.735242i | \(-0.737068\pi\) |
0.735242 | + | 0.677804i | \(0.237068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.55051 | + | 1.55051i | 0.110469 | + | 0.110469i | 0.760181 | − | 0.649712i | \(-0.225110\pi\) |
−0.649712 | + | 0.760181i | \(0.725110\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.19955i | 0.581251i | 0.956837 | + | 0.290625i | \(0.0938633\pi\) | ||||
−0.956837 | + | 0.290625i | \(0.906137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.02118 | − | 5.02118i | 0.352418 | − | 0.352418i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.317837 | − | 3.14626i | 0.0221987 | − | 0.219745i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0424 | −0.694645 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.79796i | − | 0.536834i | −0.963303 | − | 0.268417i | \(-0.913500\pi\) | ||
0.963303 | − | 0.268417i | \(-0.0865004\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.79796 | − | 7.10102i | −0.395418 | − | 0.484286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.79796 | + | 5.79796i | 0.393591 | + | 0.393591i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.30306 | −0.0876534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.89949 | − | 9.89949i | 0.662919 | − | 0.662919i | −0.293148 | − | 0.956067i | \(-0.594703\pi\) |
0.956067 | + | 0.293148i | \(0.0947028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.09978 | − | 4.09978i | −0.272112 | − | 0.272112i | 0.557838 | − | 0.829950i | \(-0.311631\pi\) |
−0.829950 | + | 0.557838i | \(0.811631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1920 | + | 16.1920i | 1.06077 | + | 1.06077i | 0.998030 | + | 0.0627452i | \(0.0199855\pi\) |
0.0627452 | + | 0.998030i | \(0.480014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.7980 | − | 12.8990i | 1.03055 | − | 0.841437i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4949 | 1.58444 | 0.792222 | − | 0.610234i | \(-0.208924\pi\) | ||||
0.792222 | + | 0.610234i | \(0.208924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7980 | 1.01764 | 0.508818 | − | 0.860874i | \(-0.330083\pi\) | ||||
0.508818 | + | 0.860874i | \(0.330083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.674235 | − | 6.67423i | 0.0430753 | − | 0.426401i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.921404 | − | 0.921404i | −0.0586275 | − | 0.0586275i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.6062 | −1.11130 | −0.555648 | − | 0.831418i | \(-0.687530\pi\) | ||||
−0.555648 | + | 0.831418i | \(0.687530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.55708 | + | 1.55708i | 0.0978927 | + | 0.0978927i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.02118 | + | 5.02118i | −0.313213 | + | 0.313213i | −0.846153 | − | 0.532940i | \(-0.821087\pi\) |
0.532940 | + | 0.846153i | \(0.321087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8990 | −1.05005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4495 | − | 12.4495i | −0.767668 | − | 0.767668i | 0.210027 | − | 0.977696i | \(-0.432645\pi\) |
−0.977696 | + | 0.210027i | \(0.932645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.10102 | − | 5.79796i | 0.436212 | − | 0.356166i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 16.4495i | − | 1.00294i | −0.865174 | − | 0.501472i | \(-0.832792\pi\) | ||
0.865174 | − | 0.501472i | \(-0.167208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0424 | 0.610030 | 0.305015 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305015 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.9706 | − | 3.46410i | −1.02336 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.14626 | − | 3.14626i | 0.189041 | − | 0.189041i | −0.606241 | − | 0.795281i | \(-0.707323\pi\) |
0.795281 | + | 0.606241i | \(0.207323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.8557i | − | 1.66173i | −0.556474 | − | 0.830865i | \(-0.687846\pi\) | ||
0.556474 | − | 0.830865i | \(-0.312154\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8990 | + | 12.8990i | 0.766765 | + | 0.766765i | 0.977536 | − | 0.210771i | \(-0.0675974\pi\) |
−0.210771 | + | 0.977536i | \(0.567597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | + | 2.00000i | −0.118056 | + | 0.118056i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.59592i | 0.505642i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3485 | + | 15.3485i | −0.896667 | + | 0.896667i | −0.995140 | − | 0.0984726i | \(-0.968604\pi\) |
0.0984726 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.41421 | + | 13.9993i | −0.0823387 | + | 0.815069i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.285729i | 0.0165241i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.19955i | 0.472614i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.97129 | − | 29.4128i | 0.170136 | − | 1.68417i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.89898 | + | 2.89898i | −0.165453 | + | 0.165453i | −0.784978 | − | 0.619524i | \(-0.787326\pi\) |
0.619524 | + | 0.784978i | \(0.287326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.10102i | 0.402662i | 0.979523 | + | 0.201331i | \(0.0645267\pi\) | ||||
−0.979523 | + | 0.201331i | \(0.935473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | + | 5.00000i | −0.282617 | + | 0.282617i | −0.834152 | − | 0.551535i | \(-0.814042\pi\) |
0.551535 | + | 0.834152i | \(0.314042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.10102 | + | 5.10102i | 0.286502 | + | 0.286502i | 0.835695 | − | 0.549193i | \(-0.185065\pi\) |
−0.549193 | + | 0.835695i | \(0.685065\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.2993i | − | 0.688630i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.94258 | − | 5.94258i | 0.330654 | − | 0.330654i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.23924 | − | 1.87492i | −0.0687407 | − | 0.104002i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.2419 | −1.00571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.8990i | − | 1.25864i | −0.777146 | − | 0.629321i | \(-0.783333\pi\) | ||
0.777146 | − | 0.629321i | \(-0.216667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.10102 | − | 2.10102i | −0.114450 | − | 0.114450i | 0.647562 | − | 0.762012i | \(-0.275788\pi\) |
−0.762012 | + | 0.647562i | \(0.775788\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2020 | 0.769084 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1421 | + | 14.1421i | −0.763604 | + | 0.763604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0424 | + | 10.0424i | 0.539102 | + | 0.539102i | 0.923265 | − | 0.384163i | \(-0.125510\pi\) |
−0.384163 | + | 0.923265i | \(0.625510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.02118 | 0.268778 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.2918 | + | 20.2918i | 1.08002 | + | 1.08002i | 0.996506 | + | 0.0835172i | \(0.0266153\pi\) |
0.0835172 | + | 0.996506i | \(0.473385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.89898 | − | 28.6969i | 0.153862 | − | 1.52308i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4949 | −1.29279 | −0.646396 | − | 0.763002i | \(-0.723724\pi\) | ||||
−0.646396 | + | 0.763002i | \(0.723724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5959 | −0.557680 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.3485 | + | 15.7980i | −1.01275 | + | 0.826903i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.33562 | + | 2.33562i | 0.121918 | + | 0.121918i | 0.765433 | − | 0.643515i | \(-0.222525\pi\) |
−0.643515 | + | 0.765433i | \(0.722525\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.19955 | −0.425700 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70334 | − | 4.70334i | −0.243530 | − | 0.243530i | 0.574779 | − | 0.818309i | \(-0.305088\pi\) |
−0.818309 | + | 0.574779i | \(0.805088\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.12848 | − | 1.12848i | 0.0581199 | − | 0.0581199i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.202041 | −0.0103782 | −0.00518908 | − | 0.999987i | \(-0.501652\pi\) | ||||
−0.00518908 | + | 0.999987i | \(0.501652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.1464 | + | 25.1464i | 1.28492 | + | 1.28492i | 0.937831 | + | 0.347091i | \(0.112831\pi\) |
0.347091 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.79796 | + | 12.0000i | 0.499350 | + | 0.611577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 16.4495i | − | 0.834022i | −0.908901 | − | 0.417011i | \(-0.863078\pi\) | ||
0.908901 | − | 0.417011i | \(-0.136922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.84281 | −0.0931948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.17837 | − | 31.4626i | 0.159921 | − | 1.58306i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4094 | + | 26.4094i | −1.32545 | + | 1.32545i | −0.416153 | + | 0.909295i | \(0.636622\pi\) |
−0.909295 | + | 0.416153i | \(0.863378\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.62815i | − | 0.430869i | −0.976518 | − | 0.215435i | \(-0.930883\pi\) | ||
0.976518 | − | 0.215435i | \(-0.0691168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.30306 | + | 1.30306i | 0.0649101 | + | 0.0649101i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.6969 | + | 20.6969i | −1.02591 | + | 1.02591i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.2020i | − | 0.504458i | −0.967668 | − | 0.252229i | \(-0.918836\pi\) | ||
0.967668 | − | 0.252229i | \(-0.0811637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.89898 | − | 8.89898i | 0.437890 | − | 0.437890i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3417 | − | 18.2419i | 1.09671 | − | 0.895460i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.1913i | 1.47494i | 0.675379 | + | 0.737471i | \(0.263980\pi\) | ||||
−0.675379 | + | 0.737471i | \(0.736020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.4838i | 1.77811i | 0.457798 | + | 0.889056i | \(0.348638\pi\) | ||||
−0.457798 | + | 0.889056i | \(0.651362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0922 | − | 7.99247i | 0.586560 | − | 0.387692i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.6969 | + | 18.6969i | −0.904808 | + | 0.904808i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.6969i | 0.900600i | 0.892877 | + | 0.450300i | \(0.148683\pi\) | ||||
−0.892877 | + | 0.450300i | \(0.851317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0000 | + | 15.0000i | −0.720854 | + | 0.720854i | −0.968779 | − | 0.247925i | \(-0.920251\pi\) |
0.247925 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.30306 | − | 1.30306i | −0.0623339 | − | 0.0623339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.4838i | 1.74128i | 0.491923 | + | 0.870639i | \(0.336294\pi\) | ||||
−0.491923 | + | 0.870639i | \(0.663706\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.3417 | − | 22.3417i | 1.06149 | − | 1.06149i | 0.0635040 | − | 0.997982i | \(-0.479772\pi\) |
0.997982 | − | 0.0635040i | \(-0.0202276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.43879 | − | 0.953512i | −0.447442 | − | 0.0452008i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.7839 | −1.64155 | −0.820776 | − | 0.571250i | \(-0.806459\pi\) | ||||
−0.820776 | + | 0.571250i | \(0.806459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.89898i | 0.230684i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.202041 | + | 2.00000i | −0.00947183 | + | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8990 | − | 17.8990i | −0.837279 | − | 0.837279i | 0.151221 | − | 0.988500i | \(-0.451679\pi\) |
−0.988500 | + | 0.151221i | \(0.951679\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9444 | −0.975477 | −0.487739 | − | 0.872990i | \(-0.662178\pi\) | ||||
−0.487739 | + | 0.872990i | \(0.662178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2200 | − | 27.2200i | 1.26502 | − | 1.26502i | 0.316392 | − | 0.948628i | \(-0.397528\pi\) |
0.948628 | − | 0.316392i | \(-0.102472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.3205 | + | 17.3205i | 0.801498 | + | 0.801498i | 0.983330 | − | 0.181832i | \(-0.0582027\pi\) |
−0.181832 | + | 0.983330i | \(0.558203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0424 | + | 10.0424i | 0.461748 | + | 0.461748i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.2020 | + | 2.89898i | 0.651634 | + | 0.133014i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8990 | 0.589369 | 0.294685 | − | 0.955595i | \(-0.404785\pi\) | ||||
0.294685 | + | 0.955595i | \(0.404785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.79796 | −0.173172 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.7980 | − | 19.3485i | −0.717348 | − | 0.878569i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7347 | + | 18.7347i | 0.848951 | + | 0.848951i | 0.990002 | − | 0.141051i | \(-0.0450482\pi\) |
−0.141051 | + | 0.990002i | \(0.545048\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.40669 | −0.424518 | −0.212259 | − | 0.977213i | \(-0.568082\pi\) | ||||
−0.212259 | + | 0.977213i | \(0.568082\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.27815 | + | 7.27815i | 0.327791 | + | 0.327791i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.2419 | + | 18.2419i | −0.818262 | + | 0.818262i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1010 | −0.765547 | −0.382773 | − | 0.923842i | \(-0.625031\pi\) | ||||
−0.382773 | + | 0.923842i | \(0.625031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.4495 | − | 26.4495i | −1.17932 | − | 1.17932i | −0.979917 | − | 0.199408i | \(-0.936098\pi\) |
−0.199408 | − | 0.979917i | \(-0.563902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.7980 | + | 2.10102i | 0.925497 | + | 0.0934942i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.04541i | 0.356606i | 0.983976 | + | 0.178303i | \(0.0570608\pi\) | ||||
−0.983976 | + | 0.178303i | \(0.942939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3417 | 0.988338 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.9917 | + | 17.9562i | −0.969072 | + | 0.791244i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.3417 | + | 22.3417i | −0.982586 | + | 0.982586i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8133i | 0.780416i | 0.920727 | + | 0.390208i | \(0.127597\pi\) | ||||
−0.920727 | + | 0.390208i | \(0.872403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8990 | + | 12.8990i | 0.564033 | + | 0.564033i | 0.930451 | − | 0.366418i | \(-0.119416\pi\) |
−0.366418 | + | 0.930451i | \(0.619416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.40408 | + | 8.40408i | −0.366088 | + | 0.366088i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.5959i | − | 0.982431i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.449490 | + | 0.449490i | −0.0194696 | + | 0.0194696i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2419 | + | 22.3417i | 0.788667 | + | 0.965915i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3923i | 0.447628i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.02118i | − | 0.215877i | −0.994158 | − | 0.107939i | \(-0.965575\pi\) | ||
0.994158 | − | 0.107939i | \(-0.0344250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1708 | + | 1.12848i | 0.478506 | + | 0.0483390i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.0000 | + | 10.0000i | −0.427569 | + | 0.427569i | −0.887800 | − | 0.460230i | \(-0.847767\pi\) |
0.460230 | + | 0.887800i | \(0.347767\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2929i | 0.438490i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | + | 20.0000i | −0.850487 | + | 0.850487i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.5959 | − | 21.5959i | −0.915048 | − | 0.915048i | 0.0816155 | − | 0.996664i | \(-0.473992\pi\) |
−0.996664 | + | 0.0816155i | \(0.973992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.84281i | 0.0779424i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.3840 | − | 32.3840i | 1.36482 | − | 1.36482i | 0.497174 | − | 0.867651i | \(-0.334371\pi\) |
0.867651 | − | 0.497174i | \(-0.165629\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0424 | + | 12.2993i | 0.422485 | + | 0.517437i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.39983 | 0.100606 | 0.0503031 | − | 0.998734i | \(-0.483981\pi\) | ||||
0.0503031 | + | 0.998734i | \(0.483981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.69694i | 0.363956i | 0.983303 | + | 0.181978i | \(0.0582499\pi\) | ||||
−0.983303 | + | 0.181978i | \(0.941750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.75255 | − | 2.65153i | −0.0730864 | − | 0.110576i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5959 | − | 16.5959i | −0.690897 | − | 0.690897i | 0.271532 | − | 0.962429i | \(-0.412470\pi\) |
−0.962429 | + | 0.271532i | \(0.912470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.7980 | −1.07028 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0424 | + | 10.0424i | −0.415912 | + | 0.415912i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2631 | + | 23.2631i | 0.960171 | + | 0.960171i | 0.999237 | − | 0.0390661i | \(-0.0124383\pi\) |
−0.0390661 | + | 0.999237i | \(0.512438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8852 | −0.489720 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2631 | + | 23.2631i | 0.955301 | + | 0.955301i | 0.999043 | − | 0.0437422i | \(-0.0139280\pi\) |
−0.0437422 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.8990 | − | 1.30306i | −0.528807 | − | 0.0534203i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.6969 | 0.763936 | 0.381968 | − | 0.924176i | \(-0.375246\pi\) | ||||
0.381968 | + | 0.924176i | \(0.375246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.7980 | 1.05232 | 0.526160 | − | 0.850385i | \(-0.323631\pi\) | ||||
0.526160 | + | 0.850385i | \(0.323631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.22474 | + | 0.224745i | 0.0904487 | + | 0.00913718i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7279 | + | 12.7279i | 0.516610 | + | 0.516610i | 0.916544 | − | 0.399934i | \(-0.130967\pi\) |
−0.399934 | + | 0.916544i | \(0.630967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.09978 | −0.165859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9815 | + | 11.9815i | 0.483928 | + | 0.483928i | 0.906384 | − | 0.422456i | \(-0.138832\pi\) |
−0.422456 | + | 0.906384i | \(0.638832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2918 | + | 20.2918i | −0.816917 | + | 0.816917i | −0.985660 | − | 0.168743i | \(-0.946029\pi\) |
0.168743 | + | 0.985660i | \(0.446029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5959 | 0.707240 | 0.353620 | − | 0.935389i | \(-0.384951\pi\) | ||||
0.353620 | + | 0.935389i | \(0.384951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000 | + | 6.00000i | 0.240385 | + | 0.240385i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | + | 9.79796i | 0.920000 | + | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 24.4949i | − | 0.976676i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.3417 | 0.889409 | 0.444704 | − | 0.895677i | \(-0.353309\pi\) | ||||
0.444704 | + | 0.895677i | \(0.353309\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.6130 | − | 28.9199i | −0.937055 | − | 1.14765i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.953512 | + | 0.953512i | −0.0377795 | + | 0.0377795i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 13.7135i | − | 0.541652i | −0.962628 | − | 0.270826i | \(-0.912703\pi\) | ||
0.962628 | − | 0.270826i | \(-0.0872969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1010 | + | 17.1010i | 0.674398 | + | 0.674398i | 0.958727 | − | 0.284329i | \(-0.0917706\pi\) |
−0.284329 | + | 0.958727i | \(0.591771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.0454 | + | 18.0454i | −0.709438 | + | 0.709438i | −0.966417 | − | 0.256979i | \(-0.917273\pi\) |
0.256979 | + | 0.966417i | \(0.417273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.7980i | − | 0.855645i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.4949 | + | 30.4949i | −1.19336 | + | 1.19336i | −0.217239 | + | 0.976118i | \(0.569705\pi\) |
−0.976118 | + | 0.217239i | \(0.930295\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.5352 | + | 1.06427i | 0.411643 | + | 0.0415844i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.4332i | 1.88669i | 0.331814 | + | 0.943345i | \(0.392339\pi\) | ||||
−0.331814 | + | 0.943345i | \(0.607661\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.2631i | 0.904829i | 0.891808 | + | 0.452415i | \(0.149437\pi\) | ||||
−0.891808 | + | 0.452415i | \(0.850563\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.19955 | − | 10.0424i | −0.317965 | − | 0.389426i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.59592 | − | 1.59592i | 0.0617942 | − | 0.0617942i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.7980i | 1.76801i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.5959 | + | 16.5959i | −0.639726 | + | 0.639726i | −0.950488 | − | 0.310762i | \(-0.899416\pi\) |
0.310762 | + | 0.950488i | \(0.399416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.6969 | − | 16.6969i | −0.641715 | − | 0.641715i | 0.309262 | − | 0.950977i | \(-0.399918\pi\) |
−0.950977 | + | 0.309262i | \(0.899918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.3417i | 0.857395i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.02118 | − | 5.02118i | 0.192130 | − | 0.192130i | −0.604486 | − | 0.796616i | \(-0.706621\pi\) |
0.796616 | + | 0.604486i | \(0.206621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.3840 | + | 26.4415i | −1.23733 | + | 1.01028i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.84281 | −0.0702054 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.4949i | 0.551412i | 0.961242 | + | 0.275706i | \(0.0889116\pi\) | ||||
−0.961242 | + | 0.275706i | \(0.911088\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.2474 | − | 2.65153i | −0.995622 | − | 0.100578i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.89898 | − | 2.89898i | −0.109807 | − | 0.109807i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.55051 | 0.134101 | 0.0670505 | − | 0.997750i | \(-0.478641\pi\) | ||||
0.0670505 | + | 0.997750i | \(0.478641\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3205 | − | 17.3205i | 0.653255 | − | 0.653255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.2207 | − | 13.2207i | −0.497217 | − | 0.497217i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2843 | −1.06224 | −0.531119 | − | 0.847297i | \(-0.678228\pi\) | ||||
−0.531119 | + | 0.847297i | \(0.678228\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.84281 | + | 1.84281i | 0.0690137 | + | 0.0690137i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.20204 | + | 2.69694i | 0.0823517 | + | 0.100860i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7980 | −0.962102 | −0.481051 | − | 0.876693i | \(-0.659745\pi\) | ||||
−0.481051 | + | 0.876693i | \(0.659745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.3939 | 0.945717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.55051 | + | 17.3939i | −0.131863 | + | 0.645992i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9063 | + | 15.9063i | 0.589932 | + | 0.589932i | 0.937613 | − | 0.347681i | \(-0.113031\pi\) |
−0.347681 | + | 0.937613i | \(0.613031\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.8852 | −0.439589 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.603566 | + | 0.603566i | 0.0222932 | + | 0.0222932i | 0.718166 | − | 0.695872i | \(-0.244982\pi\) |
−0.695872 | + | 0.718166i | \(0.744982\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.2929 | −1.48220 | −0.741098 | − | 0.671396i | \(-0.765695\pi\) | ||||
−0.741098 | + | 0.671396i | \(0.765695\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.4495 | + | 26.4495i | 0.970338 | + | 0.970338i | 0.999573 | − | 0.0292349i | \(-0.00930708\pi\) |
−0.0292349 | + | 0.999573i | \(0.509307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.69694 | + | 36.5959i | −0.135445 | + | 1.34077i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 25.7980i | − | 0.942637i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3417 | 0.815260 | 0.407630 | − | 0.913147i | \(-0.366355\pi\) | ||||
0.407630 | + | 0.913147i | \(0.366355\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.5836 | − | 4.09978i | −1.47699 | − | 0.149206i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.87492 | + | 1.87492i | −0.0681450 | + | 0.0681450i | −0.740358 | − | 0.672213i | \(-0.765344\pi\) |
0.672213 | + | 0.740358i | \(0.265344\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.5563i | − | 0.563917i | −0.959427 | − | 0.281959i | \(-0.909016\pi\) | ||
0.959427 | − | 0.281959i | \(-0.0909841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.10102 | − | 7.10102i | −0.257074 | − | 0.257074i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00000 | − | 2.00000i | 0.0722158 | − | 0.0722158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.5959i | − | 1.13938i | −0.821860 | − | 0.569689i | \(-0.807064\pi\) | ||
0.821860 | − | 0.569689i | \(-0.192936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.1010 | − | 13.1010i | 0.471211 | − | 0.471211i | −0.431095 | − | 0.902306i | \(-0.641873\pi\) |
0.902306 | + | 0.431095i | \(0.141873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0847 | − | 4.09978i | −0.721464 | − | 0.147268i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4.09978i | − | 0.146890i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.6834i | 1.59890i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0484 | − | 24.5344i | 1.07247 | − | 0.875672i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.3939 | − | 37.3939i | 1.33295 | − | 1.33295i | 0.430227 | − | 0.902721i | \(-0.358434\pi\) |
0.902721 | − | 0.430227i | \(-0.141566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 14.2020i | − | 0.504966i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.20204 | + | 4.20204i | −0.149219 | + | 0.149219i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0454 | + | 18.0454i | 0.639201 | + | 0.639201i | 0.950358 | − | 0.311157i | \(-0.100717\pi\) |
−0.311157 | + | 0.950358i | \(0.600717\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.4415i | − | 0.935432i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.3629 | − | 27.3629i | 0.965615 | − | 0.965615i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.285729 | + | 2.82843i | −0.0100706 | + | 0.0996890i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.7423 | −0.412837 | −0.206419 | − | 0.978464i | \(-0.566181\pi\) | ||||
−0.206419 | + | 0.978464i | \(0.566181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 45.1918i | − | 1.58690i | −0.608635 | − | 0.793450i | \(-0.708283\pi\) | ||
0.608635 | − | 0.793450i | \(-0.291717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.5959 | + | 38.6969i | 1.10676 | + | 1.35549i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.40408 | − | 8.40408i | −0.294022 | − | 0.294022i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.55051 | 0.123914 | 0.0619568 | − | 0.998079i | \(-0.480266\pi\) | ||||
0.0619568 | + | 0.998079i | \(0.480266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.24264 | + | 4.24264i | −0.147889 | + | 0.147889i | −0.777174 | − | 0.629285i | \(-0.783348\pi\) |
0.629285 | + | 0.777174i | \(0.283348\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.1845 | + | 24.1845i | 0.840977 | + | 0.840977i | 0.988986 | − | 0.148009i | \(-0.0472864\pi\) |
−0.148009 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.0635 | 0.523178 | 0.261589 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261589 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.14966 | − | 6.14966i | −0.213073 | − | 0.213073i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.6969 | − | 16.8990i | 0.716247 | − | 0.584813i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.8990 | −1.82628 | −0.913138 | − | 0.407651i | \(-0.866348\pi\) | ||||
−0.913138 | + | 0.407651i | \(0.866348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3939 | 0.565306 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.87628 | − | 28.4722i | 0.0989469 | − | 0.979473i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41421 | − | 1.41421i | −0.0485930 | − | 0.0485930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.37113 | −0.184120 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.43879 | − | 9.43879i | −0.323178 | − | 0.323178i | 0.526807 | − | 0.849985i | \(-0.323389\pi\) |
−0.849985 | + | 0.526807i | \(0.823389\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.14966 | − | 6.14966i | 0.210069 | − | 0.210069i | −0.594228 | − | 0.804297i | \(-0.702542\pi\) |
0.804297 | + | 0.594228i | \(0.202542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.00000 | −0.204717 | −0.102359 | − | 0.994748i | \(-0.532639\pi\) | ||||
−0.102359 | + | 0.994748i | \(0.532639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.6515 | − | 14.6515i | −0.498744 | − | 0.498744i | 0.412303 | − | 0.911047i | \(-0.364725\pi\) |
−0.911047 | + | 0.412303i | \(0.864725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7980 | − | 12.8990i | 0.537147 | − | 0.438578i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.9898i | 1.66186i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.3923 | − | 19.7990i | −0.351324 | − | 0.669328i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4668 | + | 20.4668i | −0.691114 | + | 0.691114i | −0.962477 | − | 0.271363i | \(-0.912526\pi\) |
0.271363 | + | 0.962477i | \(0.412526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.0696i | − | 1.18153i | −0.806845 | − | 0.590763i | \(-0.798827\pi\) | ||
0.806845 | − | 0.590763i | \(-0.201173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59592 | − | 1.59592i | −0.0537069 | − | 0.0537069i | 0.679743 | − | 0.733450i | \(-0.262091\pi\) |
−0.733450 | + | 0.679743i | \(0.762091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.2474 | − | 14.2474i | 0.478383 | − | 0.478383i | −0.426232 | − | 0.904614i | \(-0.640159\pi\) |
0.904614 | + | 0.426232i | \(0.140159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.3939i | 1.11999i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.6969 | − | 18.6969i | 0.625669 | − | 0.625669i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.76416 | + | 17.4634i | −0.0589693 | + | 0.583736i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.5563i | − | 0.485480i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.8852i | − | 0.395952i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.97129 | − | 29.4128i | 0.0987691 | − | 0.977713i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.8990 | + | 32.8990i | −1.09239 | + | 1.09239i | −0.0971200 | + | 0.995273i | \(0.530963\pi\) |
−0.995273 | + | 0.0971200i | \(0.969037\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.4949i | − | 0.811552i | −0.913973 | − | 0.405776i | \(-0.867001\pi\) | ||
0.913973 | − | 0.405776i | \(-0.132999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.5959 | + | 31.5959i | −1.04567 | + | 1.04567i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.69694 | − | 6.69694i | −0.221152 | − | 0.221152i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.3417i | 0.736984i | 0.929631 | + | 0.368492i | \(0.120126\pi\) | ||||
−0.929631 | + | 0.368492i | \(0.879874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.09978 | + | 4.09978i | −0.134946 | + | 0.134946i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.2446 | − | 23.2952i | 1.15883 | − | 0.765941i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.89949 | 0.324792 | 0.162396 | − | 0.986726i | \(-0.448078\pi\) | ||||
0.162396 | + | 0.986726i | \(0.448078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.69694i | − | 0.285031i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.3939 | + | 14.2020i | −0.568841 | + | 0.464456i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.797959 | + | 0.797959i | 0.0260682 | + | 0.0260682i | 0.720021 | − | 0.693953i | \(-0.244132\pi\) |
−0.693953 | + | 0.720021i | \(0.744132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.2474 | −1.37723 | −0.688614 | − | 0.725128i | \(-0.741780\pi\) | ||||
−0.688614 | + | 0.725128i | \(0.741780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.635674 | + | 0.635674i | −0.0207004 | + | 0.0207004i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.1421 | − | 14.1421i | −0.459558 | − | 0.459558i | 0.438953 | − | 0.898510i | \(-0.355350\pi\) |
−0.898510 | + | 0.438953i | \(0.855350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.02118 | 0.162994 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.2207 | + | 13.2207i | 0.428262 | + | 0.428262i | 0.888036 | − | 0.459774i | \(-0.152070\pi\) |
−0.459774 | + | 0.888036i | \(0.652070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.30306 | − | 12.8990i | 0.0421661 | − | 0.417401i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.3939 | 1.20751 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.1918 | −0.457801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.95459 | − | 1.59592i | 0.0629206 | − | 0.0513744i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.35680 | + | 7.35680i | 0.236579 | + | 0.236579i | 0.815432 | − | 0.578853i | \(-0.196500\pi\) |
−0.578853 | + | 0.815432i | \(0.696500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.3191 | −1.45436 | −0.727179 | − | 0.686448i | \(-0.759169\pi\) | ||||
−0.727179 | + | 0.686448i | \(0.759169\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6848 | + | 16.6848i | 0.534891 | + | 0.534891i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.1920 | + | 16.1920i | −0.518029 | + | 0.518029i | −0.916975 | − | 0.398946i | \(-0.869376\pi\) |
0.398946 | + | 0.916975i | \(0.369376\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6969 | 0.469716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.651531 | − | 0.651531i | −0.0207806 | − | 0.0207806i | 0.696640 | − | 0.717421i | \(-0.254677\pi\) |
−0.717421 | + | 0.696640i | \(0.754677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.10102 | + | 3.79796i | 0.0988067 | + | 0.121013i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.60612i | 0.0828699i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0424 | 0.319006 | 0.159503 | − | 0.987197i | \(-0.449011\pi\) | ||||
0.159503 | + | 0.987197i | \(0.449011\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.84281 | + | 18.2419i | −0.0584209 | + | 0.578307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.05329 | − | 5.05329i | 0.160039 | − | 0.160039i | −0.622545 | − | 0.782584i | \(-0.713901\pi\) |
0.782584 | + | 0.622545i | \(0.213901\pi\) | |||||||
\(998\) | 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 | 2880.2.bj.c.737.3 | yes | 8 | |
3.2 | odd | 2 | 2880.2.bj.a.737.1 | ✓ | 8 | ||
4.3 | odd | 2 | 2880.2.bj.d.737.4 | yes | 8 | ||
5.3 | odd | 4 | 2880.2.bj.d.1313.3 | yes | 8 | ||
8.3 | odd | 2 | 2880.2.bj.a.737.2 | yes | 8 | ||
8.5 | even | 2 | 2880.2.bj.b.737.1 | yes | 8 | ||
12.11 | even | 2 | 2880.2.bj.b.737.2 | yes | 8 | ||
15.8 | even | 4 | 2880.2.bj.b.1313.1 | yes | 8 | ||
20.3 | even | 4 | inner | 2880.2.bj.c.1313.4 | yes | 8 | |
24.5 | odd | 2 | 2880.2.bj.d.737.3 | yes | 8 | ||
24.11 | even | 2 | inner | 2880.2.bj.c.737.4 | yes | 8 | |
40.3 | even | 4 | 2880.2.bj.b.1313.2 | yes | 8 | ||
40.13 | odd | 4 | 2880.2.bj.a.1313.1 | yes | 8 | ||
60.23 | odd | 4 | 2880.2.bj.a.1313.2 | yes | 8 | ||
120.53 | even | 4 | inner | 2880.2.bj.c.1313.3 | yes | 8 | |
120.83 | odd | 4 | 2880.2.bj.d.1313.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.bj.a.737.1 | ✓ | 8 | 3.2 | odd | 2 | ||
2880.2.bj.a.737.2 | yes | 8 | 8.3 | odd | 2 | ||
2880.2.bj.a.1313.1 | yes | 8 | 40.13 | odd | 4 | ||
2880.2.bj.a.1313.2 | yes | 8 | 60.23 | odd | 4 | ||
2880.2.bj.b.737.1 | yes | 8 | 8.5 | even | 2 | ||
2880.2.bj.b.737.2 | yes | 8 | 12.11 | even | 2 | ||
2880.2.bj.b.1313.1 | yes | 8 | 15.8 | even | 4 | ||
2880.2.bj.b.1313.2 | yes | 8 | 40.3 | even | 4 | ||
2880.2.bj.c.737.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2880.2.bj.c.737.4 | yes | 8 | 24.11 | even | 2 | inner | |
2880.2.bj.c.1313.3 | yes | 8 | 120.53 | even | 4 | inner | |
2880.2.bj.c.1313.4 | yes | 8 | 20.3 | even | 4 | inner | |
2880.2.bj.d.737.3 | yes | 8 | 24.5 | odd | 2 | ||
2880.2.bj.d.737.4 | yes | 8 | 4.3 | odd | 2 | ||
2880.2.bj.d.1313.3 | yes | 8 | 5.3 | odd | 4 | ||
2880.2.bj.d.1313.4 | yes | 8 | 120.83 | odd | 4 |