Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(649,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.649");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(106.203438010\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.649 |
Dual form | 1800.4.f.s.649.2 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 18.0000i | − 0.971909i | −0.873984 | − | 0.485954i | \(-0.838472\pi\) | ||||
0.873984 | − | 0.485954i | \(-0.161528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.0000 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 12.0000i | − 0.256015i | −0.991773 | − | 0.128008i | \(-0.959142\pi\) | ||||
0.991773 | − | 0.128008i | \(-0.0408582\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 102.000i | − 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −164.000 | −1.98022 | −0.990110 | − | 0.140293i | \(-0.955195\pi\) | ||||
−0.990110 | + | 0.140293i | \(0.955195\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 48.0000i | − 0.435161i | −0.976042 | − | 0.217580i | \(-0.930184\pi\) | ||||
0.976042 | − | 0.217580i | \(-0.0698164\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −146.000 | −0.934880 | −0.467440 | − | 0.884025i | \(-0.654824\pi\) | ||||
−0.467440 | + | 0.884025i | \(0.654824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 100.000 | 0.579372 | 0.289686 | − | 0.957122i | \(-0.406449\pi\) | ||||
0.289686 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 328.000i | 1.45737i | 0.684846 | + | 0.728687i | \(0.259869\pi\) | ||||
−0.684846 | + | 0.728687i | \(0.740131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −288.000 | −1.09703 | −0.548513 | − | 0.836142i | \(-0.684806\pi\) | ||||
−0.548513 | + | 0.836142i | \(0.684806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 120.000i | − 0.425577i | −0.977098 | − | 0.212789i | \(-0.931745\pi\) | ||||
0.977098 | − | 0.212789i | \(-0.0682546\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.0000i | 0.0496562i | 0.999692 | + | 0.0248281i | \(0.00790384\pi\) | ||||
−0.999692 | + | 0.0248281i | \(0.992096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.0000 | 0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 126.000i | 0.326555i | 0.986580 | + | 0.163278i | \(0.0522066\pi\) | ||||
−0.986580 | + | 0.163278i | \(0.947793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −642.000 | −1.41663 | −0.708316 | − | 0.705896i | \(-0.750545\pi\) | ||||
−0.708316 | + | 0.705896i | \(0.750545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 602.000 | 1.26358 | 0.631789 | − | 0.775141i | \(-0.282321\pi\) | ||||
0.631789 | + | 0.775141i | \(0.282321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 436.000i | 0.795013i | 0.917599 | + | 0.397507i | \(0.130124\pi\) | ||||
−0.917599 | + | 0.397507i | \(0.869876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 652.000 | 1.08983 | 0.544917 | − | 0.838490i | \(-0.316561\pi\) | ||||
0.544917 | + | 0.838490i | \(0.316561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1062.00i | − 1.70271i | −0.524591 | − | 0.851354i | \(-0.675782\pi\) | ||||
0.524591 | − | 0.851354i | \(-0.324218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 612.000i | − 0.905765i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −388.000 | −0.552575 | −0.276287 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276287 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 444.000i | 0.587173i | 0.955933 | + | 0.293586i | \(0.0948488\pi\) | ||||
−0.955933 | + | 0.293586i | \(0.905151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 820.000 | 0.976627 | 0.488314 | − | 0.872668i | \(-0.337612\pi\) | ||||
0.488314 | + | 0.872668i | \(0.337612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −216.000 | −0.248824 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 766.000i | − 0.801809i | −0.916120 | − | 0.400905i | \(-0.868696\pi\) | ||||
0.916120 | − | 0.400905i | \(-0.131304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −798.000 | −0.786178 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 402.000i | 0.384565i | 0.981340 | + | 0.192283i | \(0.0615891\pi\) | ||||
−0.981340 | + | 0.192283i | \(0.938411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1444.00i | 1.30464i | 0.757943 | + | 0.652321i | \(0.226205\pi\) | ||||
−0.757943 | + | 0.652321i | \(0.773795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 198.000 | 0.173990 | 0.0869952 | − | 0.996209i | \(-0.472274\pi\) | ||||
0.0869952 | + | 0.996209i | \(0.472274\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2010.00i | 1.67332i | 0.547724 | + | 0.836659i | \(0.315494\pi\) | ||||
−0.547724 | + | 0.836659i | \(0.684506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1836.00 | −1.41433 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −175.000 | −0.131480 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 866.000i | − 0.605079i | −0.953137 | − | 0.302540i | \(-0.902166\pi\) | ||||
0.953137 | − | 0.302540i | \(-0.0978345\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2098.00 | −1.39926 | −0.699630 | − | 0.714505i | \(-0.746652\pi\) | ||||
−0.699630 | + | 0.714505i | \(0.746652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2952.00i | 1.92459i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 886.000i | 0.552526i | 0.961082 | + | 0.276263i | \(0.0890961\pi\) | ||||
−0.961082 | + | 0.276263i | \(0.910904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 500.000 | 0.305104 | 0.152552 | − | 0.988295i | \(-0.451251\pi\) | ||||
0.152552 | + | 0.988295i | \(0.451251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 408.000i | − 0.238592i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2302.00 | −1.26569 | −0.632843 | − | 0.774280i | \(-0.718112\pi\) | ||||
−0.632843 | + | 0.774280i | \(0.718112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2384.00 | −1.28482 | −0.642408 | − | 0.766363i | \(-0.722064\pi\) | ||||
−0.642408 | + | 0.766363i | \(0.722064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1452.00i | 0.738103i | 0.929409 | + | 0.369052i | \(0.120317\pi\) | ||||
−0.929409 | + | 0.369052i | \(0.879683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −864.000 | −0.422936 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 604.000i | − 0.290239i | −0.989414 | − | 0.145119i | \(-0.953643\pi\) | ||||
0.989414 | − | 0.145119i | \(-0.0463566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 664.000i | − 0.307676i | −0.988096 | − | 0.153838i | \(-0.950837\pi\) | ||||
0.988096 | − | 0.153838i | \(-0.0491634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2053.00 | 0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4118.00i | 1.80974i | 0.425684 | + | 0.904872i | \(0.360034\pi\) | ||||
−0.425684 | + | 0.904872i | \(0.639966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1746.00 | −0.729062 | −0.364531 | − | 0.931191i | \(-0.618771\pi\) | ||||
−0.364531 | + | 0.931191i | \(0.618771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1270.00 | −0.521538 | −0.260769 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260769 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3468.00i | − 1.35618i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2676.00 | 1.01376 | 0.506881 | − | 0.862016i | \(-0.330798\pi\) | ||||
0.506881 | + | 0.862016i | \(0.330798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3146.00i | 1.17334i | 0.809827 | + | 0.586668i | \(0.199561\pi\) | ||||
−0.809827 | + | 0.586668i | \(0.800439\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3674.00i | − 1.32874i | −0.747404 | − | 0.664370i | \(-0.768700\pi\) | ||||
0.747404 | − | 0.664370i | \(-0.231300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1392.00 | 0.495861 | 0.247930 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247930 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2628.00i | 0.908618i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5576.00 | −1.84545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −540.000 | −0.176185 | −0.0880927 | − | 0.996112i | \(-0.528077\pi\) | ||||
−0.0880927 | + | 0.996112i | \(0.528077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 1800.00i | − 0.563097i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1224.00 | −0.372557 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4166.00i | − 1.25101i | −0.780219 | − | 0.625507i | \(-0.784892\pi\) | ||||
0.780219 | − | 0.625507i | \(-0.215108\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5024.00i | − 1.46896i | −0.678629 | − | 0.734481i | \(-0.737425\pi\) | ||||
0.678629 | − | 0.734481i | \(-0.262575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4454.00 | −1.28528 | −0.642639 | − | 0.766169i | \(-0.722160\pi\) | ||||
−0.642639 | + | 0.766169i | \(0.722160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1526.00i | 0.429063i | 0.976717 | + | 0.214531i | \(0.0688224\pi\) | ||||
−0.976717 | + | 0.214531i | \(0.931178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6828.00 | −1.84798 | −0.923989 | − | 0.382420i | \(-0.875091\pi\) | ||||
−0.923989 | + | 0.382420i | \(0.875091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5782.00 | 1.54544 | 0.772721 | − | 0.634746i | \(-0.218895\pi\) | ||||
0.772721 | + | 0.634746i | \(0.218895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1968.00i | 0.506967i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6394.00 | −1.60791 | −0.803956 | − | 0.594689i | \(-0.797275\pi\) | ||||
−0.803956 | + | 0.594689i | \(0.797275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1632.00i | − 0.405545i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1862.00i | 0.451939i | 0.974134 | + | 0.225970i | \(0.0725550\pi\) | ||||
−0.974134 | + | 0.225970i | \(0.927445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5904.00 | 1.41644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6504.00i | 1.52492i | 0.647036 | + | 0.762460i | \(0.276008\pi\) | ||||
−0.647036 | + | 0.762460i | \(0.723992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8298.00 | −1.88081 | −0.940405 | − | 0.340056i | \(-0.889554\pi\) | ||||
−0.940405 | + | 0.340056i | \(0.889554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1848.00 | 0.414236 | 0.207118 | − | 0.978316i | \(-0.433592\pi\) | ||||
0.207118 | + | 0.978316i | \(0.433592\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2824.00i | 0.612555i | 0.951942 | + | 0.306277i | \(0.0990835\pi\) | ||||
−0.951942 | + | 0.306277i | \(0.900916\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1940.00 | −0.411853 | −0.205927 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205927 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6548.00i | − 1.37540i | −0.725995 | − | 0.687700i | \(-0.758620\pi\) | ||||
0.725995 | − | 0.687700i | \(-0.241380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5184.00i | 1.06621i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5491.00 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6566.00i | − 1.30918i | −0.755984 | − | 0.654590i | \(-0.772841\pi\) | ||||
0.755984 | − | 0.654590i | \(-0.227159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −576.000 | −0.111408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2160.00 | −0.413622 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8432.00i | 1.56756i | 0.621041 | + | 0.783778i | \(0.286710\pi\) | ||||
−0.621041 | + | 0.783778i | \(0.713290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4916.00 | −0.896337 | −0.448168 | − | 0.893949i | \(-0.647924\pi\) | ||||
−0.448168 | + | 0.893949i | \(0.647924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10106.0i | 1.82500i | 0.409077 | + | 0.912500i | \(0.365851\pi\) | ||||
−0.409077 | + | 0.912500i | \(0.634149\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3382.00i | 0.599218i | 0.954062 | + | 0.299609i | \(0.0968562\pi\) | ||||
−0.954062 | + | 0.299609i | \(0.903144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4964.00 | −0.871256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16728.0i | 2.88164i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 288.000 | 0.0482613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6460.00 | −1.07273 | −0.536365 | − | 0.843986i | \(-0.680203\pi\) | ||||
−0.536365 | + | 0.843986i | \(0.680203\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5294.00i | 0.855735i | 0.903842 | + | 0.427867i | \(0.140735\pi\) | ||||
−0.903842 | + | 0.427867i | \(0.859265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3400.00 | 0.539942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6516.00i | − 1.02575i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 12096.0i | − 1.87132i | −0.352906 | − | 0.935659i | \(-0.614806\pi\) | ||||
0.352906 | − | 0.935659i | \(-0.385194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 862.000 | 0.132211 | 0.0661057 | − | 0.997813i | \(-0.478943\pi\) | ||||
0.0661057 | + | 0.997813i | \(0.478943\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6878.00i | 1.03705i | 0.855062 | + | 0.518525i | \(0.173519\pi\) | ||||
−0.855062 | + | 0.518525i | \(0.826481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6216.00 | −0.913838 | −0.456919 | − | 0.889508i | \(-0.651047\pi\) | ||||
−0.456919 | + | 0.889508i | \(0.651047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20037.0 | 2.92127 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 13274.0i | − 1.88800i | −0.329941 | − | 0.944002i | \(-0.607029\pi\) | ||||
0.329941 | − | 0.944002i | \(-0.392971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2268.00 | 0.317382 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1300.00i | − 0.180460i | −0.995921 | − | 0.0902298i | \(-0.971240\pi\) | ||||
0.995921 | − | 0.0902298i | \(-0.0287602\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1752.00i | 0.239344i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13324.0 | −1.80583 | −0.902913 | − | 0.429824i | \(-0.858576\pi\) | ||||
−0.902913 | + | 0.429824i | \(0.858576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 6192.00i | − 0.826100i | −0.910708 | − | 0.413050i | \(-0.864463\pi\) | ||||
0.910708 | − | 0.413050i | \(-0.135537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2022.00 | −0.263546 | −0.131773 | − | 0.991280i | \(-0.542067\pi\) | ||||
−0.131773 | + | 0.991280i | \(0.542067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4896.00 | −0.633252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7856.00i | 0.993152i | 0.867993 | + | 0.496576i | \(0.165410\pi\) | ||||
−0.867993 | + | 0.496576i | \(0.834590\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1148.00 | 0.142964 | 0.0714818 | − | 0.997442i | \(-0.477227\pi\) | ||||
0.0714818 | + | 0.997442i | \(0.477227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1200.00i | − 0.148328i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11152.0i | 1.35819i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6310.00 | 0.762859 | 0.381430 | − | 0.924398i | \(-0.375432\pi\) | ||||
0.381430 | + | 0.924398i | \(0.375432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11556.0i | 1.37684i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13362.0 | 1.55794 | 0.778969 | − | 0.627062i | \(-0.215743\pi\) | ||||
0.778969 | + | 0.627062i | \(0.215743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5146.00 | −0.595726 | −0.297863 | − | 0.954609i | \(-0.596274\pi\) | ||||
−0.297863 | + | 0.954609i | \(0.596274\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10836.0i | − 1.22808i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6368.00 | −0.711684 | −0.355842 | − | 0.934546i | \(-0.615806\pi\) | ||||
−0.355842 | + | 0.934546i | \(0.615806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6138.00i | 0.681232i | 0.940202 | + | 0.340616i | \(0.110636\pi\) | ||||
−0.940202 | + | 0.340616i | \(0.889364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7872.00i | 0.861714i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4424.00 | 0.480970 | 0.240485 | − | 0.970653i | \(-0.422693\pi\) | ||||
0.240485 | + | 0.970653i | \(0.422693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 488.000i | 0.0523377i | 0.999658 | + | 0.0261688i | \(0.00833075\pi\) | ||||
−0.999658 | + | 0.0261688i | \(0.991669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16884.0 | −1.77462 | −0.887311 | − | 0.461172i | \(-0.847429\pi\) | ||||
−0.887311 | + | 0.461172i | \(0.847429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9792.00 | −1.02237 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 5398.00i | − 0.552533i | −0.961081 | − | 0.276267i | \(-0.910903\pi\) | ||||
0.961081 | − | 0.276267i | \(-0.0890973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6122.00 | −0.618503 | −0.309252 | − | 0.950980i | \(-0.600079\pi\) | ||||
−0.309252 | + | 0.950980i | \(0.600079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8162.00i | − 0.819266i | −0.912250 | − | 0.409633i | \(-0.865657\pi\) | ||||
0.912250 | − | 0.409633i | \(-0.134343\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2660.00i | − 0.263576i | −0.991278 | − | 0.131788i | \(-0.957928\pi\) | ||||
0.991278 | − | 0.131788i | \(-0.0420719\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7848.00 | 0.772680 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4080.00i | − 0.396614i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9788.00 | −0.933664 | −0.466832 | − | 0.884346i | \(-0.654605\pi\) | ||||
−0.466832 | + | 0.884346i | \(0.654605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3936.00 | 0.373111 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4714.00i | 0.438628i | 0.975654 | + | 0.219314i | \(0.0703819\pi\) | ||||
−0.975654 | + | 0.219314i | \(0.929618\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6690.00 | −0.614899 | −0.307450 | − | 0.951564i | \(-0.599476\pi\) | ||||
−0.307450 | + | 0.951564i | \(0.599476\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14892.0i | 1.36045i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 11736.0i | − 1.05922i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20636.0 | 1.85129 | 0.925646 | − | 0.378392i | \(-0.123523\pi\) | ||||
0.925646 | + | 0.378392i | \(0.123523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 15952.0i | − 1.41404i | −0.707191 | − | 0.707022i | \(-0.750038\pi\) | ||||
0.707191 | − | 0.707022i | \(-0.249962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2230.00 | 0.194191 | 0.0970953 | − | 0.995275i | \(-0.469045\pi\) | ||||
0.0970953 | + | 0.995275i | \(0.469045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19116.0 | −1.65488 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 544.000i | 0.0462768i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1260.00 | 0.105953 | 0.0529766 | − | 0.998596i | \(-0.483129\pi\) | ||||
0.0529766 | + | 0.998596i | \(0.483129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2900.00i | − 0.242463i | −0.992624 | − | 0.121231i | \(-0.961316\pi\) | ||||
0.992624 | − | 0.121231i | \(-0.0386843\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 10200.0i | − 0.843110i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9863.00 | 0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3456.00i | 0.280855i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 646.000 | 0.0516237 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19554.0 | 1.55396 | 0.776980 | − | 0.629526i | \(-0.216751\pi\) | ||||
0.776980 | + | 0.629526i | \(0.216751\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2664.00i | 0.208235i | 0.994565 | + | 0.104117i | \(0.0332018\pi\) | ||||
−0.994565 | + | 0.104117i | \(0.966798\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23944.0 | 1.85127 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6984.00i | 0.537052i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11358.0i | − 0.864011i | −0.901871 | − | 0.432005i | \(-0.857806\pi\) | ||||
0.901871 | − | 0.432005i | \(-0.142194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1440.00 | −0.108954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2440.00i | 0.182653i | 0.995821 | + | 0.0913266i | \(0.0291107\pi\) | ||||
−0.995821 | + | 0.0913266i | \(0.970889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24156.0 | 1.77974 | 0.889870 | − | 0.456214i | \(-0.150795\pi\) | ||||
0.889870 | + | 0.456214i | \(0.150795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2220.00 | −0.162704 | −0.0813521 | − | 0.996685i | \(-0.525924\pi\) | ||||
−0.0813521 | + | 0.996685i | \(0.525924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 5782.00i | − 0.417171i | −0.978004 | − | 0.208586i | \(-0.933114\pi\) | ||||
0.978004 | − | 0.208586i | \(-0.0668860\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7992.00 | 0.570678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4284.00i | 0.304331i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1684.00i | 0.118409i | 0.998246 | + | 0.0592045i | \(0.0188564\pi\) | ||||
−0.998246 | + | 0.0592045i | \(0.981144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16400.0 | −1.14728 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 15246.0i | − 1.05578i | −0.849312 | − | 0.527891i | \(-0.822983\pi\) | ||||
0.849312 | − | 0.527891i | \(-0.177017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9016.00 | −0.614998 | −0.307499 | − | 0.951548i | \(-0.599492\pi\) | ||||
−0.307499 | + | 0.951548i | \(0.599492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18682.0 | −1.26798 | −0.633989 | − | 0.773342i | \(-0.718584\pi\) | ||||
−0.633989 | + | 0.773342i | \(0.718584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 22022.0i | − 1.47256i | −0.676676 | − | 0.736281i | \(-0.736580\pi\) | ||||
0.676676 | − | 0.736281i | \(-0.263420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 192.000 | 0.0127127 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22808.0i | 1.50278i | 0.659856 | + | 0.751392i | \(0.270617\pi\) | ||||
−0.659856 | + | 0.751392i | \(0.729383\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 9422.00i | − 0.614774i | −0.951585 | − | 0.307387i | \(-0.900545\pi\) | ||||
0.951585 | − | 0.307387i | \(-0.0994546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4172.00 | −0.270900 | −0.135450 | − | 0.990784i | \(-0.543248\pi\) | ||||
−0.135450 | + | 0.990784i | \(0.543248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 14760.0i | − 0.949192i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33456.0 | 2.12079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11572.0 | −0.730070 | −0.365035 | − | 0.930994i | \(-0.618943\pi\) | ||||
−0.365035 | + | 0.930994i | \(0.618943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 228.000i | − 0.0141816i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −936.000 | −0.0576752 | −0.0288376 | − | 0.999584i | \(-0.509181\pi\) | ||||
−0.0288376 | + | 0.999584i | \(0.509181\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15892.0i | − 0.974680i | −0.873212 | − | 0.487340i | \(-0.837967\pi\) | ||||
0.873212 | − | 0.487340i | \(-0.162033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25056.0i | 1.52249i | 0.648463 | + | 0.761247i | \(0.275412\pi\) | ||||
−0.648463 | + | 0.761247i | \(0.724588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21828.0 | −1.32022 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4054.00i | − 0.242948i | −0.992595 | − | 0.121474i | \(-0.961238\pi\) | ||||
0.992595 | − | 0.121474i | \(-0.0387622\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6758.00 | −0.399475 | −0.199738 | − | 0.979849i | \(-0.564009\pi\) | ||||
−0.199738 | + | 0.979849i | \(0.564009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25098.0 | 1.47685 | 0.738426 | − | 0.674335i | \(-0.235569\pi\) | ||||
0.738426 | + | 0.674335i | \(0.235569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7008.00i | 0.406823i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20468.0 | 1.17758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 2830.00i | − 0.162093i | −0.996710 | − | 0.0810464i | \(-0.974174\pi\) | ||||
0.996710 | − | 0.0810464i | \(-0.0258262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10654.0i | 0.604825i | 0.953177 | + | 0.302412i | \(0.0977920\pi\) | ||||
−0.953177 | + | 0.302412i | \(0.902208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13788.0 | −0.779286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 17156.0i | − 0.961136i | −0.876957 | − | 0.480568i | \(-0.840430\pi\) | ||||
0.876957 | − | 0.480568i | \(-0.159570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1512.00 | 0.0836032 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −812.000 | −0.0447032 | −0.0223516 | − | 0.999750i | \(-0.507115\pi\) | ||||
−0.0223516 | + | 0.999750i | \(0.507115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29376.0i | 1.59641i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30270.0 | −1.63093 | −0.815465 | − | 0.578806i | \(-0.803519\pi\) | ||||
−0.815465 | + | 0.578806i | \(0.803519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 53792.0i | − 2.88592i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14364.0i | 0.764093i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 394.000 | 0.0208702 | 0.0104351 | − | 0.999946i | \(-0.496678\pi\) | ||||
0.0104351 | + | 0.999946i | \(0.496678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4800.00i | − 0.252120i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37224.0 | 1.93077 | 0.965383 | − | 0.260836i | \(-0.0839982\pi\) | ||||
0.965383 | + | 0.260836i | \(0.0839982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7236.00 | 0.373762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 12614.0i | − 0.643504i | −0.946824 | − | 0.321752i | \(-0.895728\pi\) | ||||
0.946824 | − | 0.321752i | \(-0.104272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12240.0 | −0.619306 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25664.0i | 1.29321i | 0.762826 | + | 0.646604i | \(0.223811\pi\) | ||||
−0.762826 | + | 0.646604i | \(0.776189\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14824.0i | 0.740908i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18772.0 | 0.934424 | 0.467212 | − | 0.884145i | \(-0.345259\pi\) | ||||
0.467212 | + | 0.884145i | \(0.345259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19376.0i | 0.956711i | 0.878166 | + | 0.478356i | \(0.158767\pi\) | ||||
−0.878166 | + | 0.478356i | \(0.841233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25992.0 | 1.26799 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30092.0 | 1.46215 | 0.731074 | − | 0.682299i | \(-0.239020\pi\) | ||||
0.731074 | + | 0.682299i | \(0.239020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18136.0i | 0.870758i | 0.900247 | + | 0.435379i | \(0.143386\pi\) | ||||
−0.900247 | + | 0.435379i | \(0.856614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10948.0 | 0.521504 | 0.260752 | − | 0.965406i | \(-0.416029\pi\) | ||||
0.260752 | + | 0.965406i | \(0.416029\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3564.00i | − 0.169103i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7704.00i | 0.362680i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1422.00 | −0.0666822 | −0.0333411 | − | 0.999444i | \(-0.510615\pi\) | ||||
−0.0333411 | + | 0.999444i | \(0.510615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 26142.0i | − 1.21638i | −0.793791 | − | 0.608190i | \(-0.791896\pi\) | ||||
0.793791 | − | 0.608190i | \(-0.208104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47232.0 | 2.17235 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22168.0 | 1.01566 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23404.0i | 1.06005i | 0.847981 | + | 0.530027i | \(0.177818\pi\) | ||||
−0.847981 | + | 0.530027i | \(0.822182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36180.0 | 1.62631 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 7224.00i | − 0.323495i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1418.00i | 0.0630215i | 0.999503 | + | 0.0315108i | \(0.0100318\pi\) | ||||
−0.999503 | + | 0.0315108i | \(0.989968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1632.00 | 0.0722603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 36108.0i | − 1.58683i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17304.0 | 0.752010 | 0.376005 | − | 0.926618i | \(-0.377298\pi\) | ||||
0.376005 | + | 0.926618i | \(0.377298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28012.0 | −1.21287 | −0.606433 | − | 0.795135i | \(-0.707400\pi\) | ||||
−0.606433 | + | 0.795135i | \(0.707400\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19680.0i | 0.842737i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32266.0 | 1.37161 | 0.685805 | − | 0.727786i | \(-0.259450\pi\) | ||||
0.685805 | + | 0.727786i | \(0.259450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 4962.00i | − 0.210163i | −0.994464 | − | 0.105082i | \(-0.966490\pi\) | ||||
0.994464 | − | 0.105082i | \(-0.0335104\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5064.00i | 0.212929i | 0.994316 | + | 0.106465i | \(0.0339531\pi\) | ||||
−0.994316 | + | 0.106465i | \(0.966047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8174.00 | 0.342454 | 0.171227 | − | 0.985232i | \(-0.445227\pi\) | ||||
0.171227 | + | 0.985232i | \(0.445227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1938.00i | − 0.0806095i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28240.0 | 1.16204 | 0.581021 | − | 0.813889i | \(-0.302653\pi\) | ||||
0.581021 | + | 0.813889i | \(0.302653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3073.00 | −0.125999 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3150.00i | 0.127787i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15744.0 | 0.634192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10472.0i | − 0.420345i | −0.977664 | − | 0.210173i | \(-0.932597\pi\) | ||||
0.977664 | − | 0.210173i | \(-0.0674026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 32102.0i | − 1.27956i | −0.768558 | − | 0.639780i | \(-0.779025\pi\) | ||||
0.768558 | − | 0.639780i | \(-0.220975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11060.0 | 0.439304 | 0.219652 | − | 0.975578i | \(-0.429508\pi\) | ||||
0.219652 | + | 0.975578i | \(0.429508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 36088.0i | − 1.42346i | −0.702451 | − | 0.711732i | \(-0.747911\pi\) | ||||
0.702451 | − | 0.711732i | \(-0.252089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13192.0 | −0.514969 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5232.00 | 0.203536 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34508.0i | − 1.32868i | −0.747431 | − | 0.664340i | \(-0.768713\pi\) | ||||
0.747431 | − | 0.664340i | \(-0.231287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6596.00 | −0.252242 | −0.126121 | − | 0.992015i | \(-0.540253\pi\) | ||||
−0.126121 | + | 0.992015i | \(0.540253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 17620.0i | − 0.671529i | −0.941946 | − | 0.335765i | \(-0.891005\pi\) | ||||
0.941946 | − | 0.335765i | \(-0.108995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 50784.0i | − 1.92239i | −0.275870 | − | 0.961195i | \(-0.588966\pi\) | ||||
0.275870 | − | 0.961195i | \(-0.411034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15588.0 | −0.588082 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2624.00i | − 0.0983301i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14600.0 | −0.541643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12852.0 | 0.475208 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16072.0i | 0.588381i | 0.955747 | + | 0.294191i | \(0.0950501\pi\) | ||||
−0.955747 | + | 0.294191i | \(0.904950\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41760.0 | −1.51874 | −0.759369 | − | 0.650660i | \(-0.774492\pi\) | ||||
−0.759369 | + | 0.650660i | \(0.774492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15096.0i | 0.547212i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37764.0i | 1.35995i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34100.0 | −1.22400 | −0.612000 | − | 0.790858i | \(-0.709635\pi\) | ||||
−0.612000 | + | 0.790858i | \(0.709635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 7824.00i | − 0.279014i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22812.0 | 0.805638 | 0.402819 | − | 0.915280i | \(-0.368030\pi\) | ||||
0.402819 | + | 0.915280i | \(0.368030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3116.00 | −0.109691 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 38982.0i | − 1.35911i | −0.733624 | − | 0.679555i | \(-0.762173\pi\) | ||||
0.733624 | − | 0.679555i | \(-0.237827\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52766.0 | 1.82797 | 0.913986 | − | 0.405745i | \(-0.132988\pi\) | ||||
0.913986 | + | 0.405745i | \(0.132988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13824.0i | 0.477382i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13608.0i | 0.466949i | 0.972363 | + | 0.233474i | \(0.0750095\pi\) | ||||
−0.972363 | + | 0.233474i | \(0.924990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12744.0 | −0.435920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 6446.00i | − 0.219104i | −0.993981 | − | 0.109552i | \(-0.965058\pi\) | ||||
0.993981 | − | 0.109552i | \(-0.0349417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15948.0 | 0.537005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19791.0 | −0.664328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 42642.0i | − 1.41807i | −0.705173 | − | 0.709035i | \(-0.749131\pi\) | ||||
0.705173 | − | 0.709035i | \(-0.250869\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19938.0 | −0.658950 | −0.329475 | − | 0.944164i | \(-0.606872\pi\) | ||||
−0.329475 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9000.00i | − 0.296533i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49754.0i | 1.62924i | 0.579992 | + | 0.814622i | \(0.303056\pi\) | ||||
−0.579992 | + | 0.814622i | \(0.696944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27880.0 | 0.910162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 7936.00i | − 0.257497i | −0.991677 | − | 0.128748i | \(-0.958904\pi\) | ||||
0.991677 | − | 0.128748i | \(-0.0410959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5760.00 | −0.185194 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33248.0 | −1.06575 | −0.532875 | − | 0.846194i | \(-0.678888\pi\) | ||||
−0.532875 | + | 0.846194i | \(0.678888\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20196.0i | − 0.641538i | −0.947157 | − | 0.320769i | \(-0.896059\pi\) | ||||
0.947157 | − | 0.320769i | \(-0.103941\pi\) | |||||||
\(998\) | 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 | 1800.4.f.s.649.1 | 2 | ||
3.2 | odd | 2 | 1800.4.f.e.649.1 | 2 | |||
5.2 | odd | 4 | 1800.4.a.be.1.1 | 1 | |||
5.3 | odd | 4 | 360.4.a.j.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 1800.4.f.s.649.2 | 2 | ||
15.2 | even | 4 | 1800.4.a.bc.1.1 | 1 | |||
15.8 | even | 4 | 360.4.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1800.4.f.e.649.2 | 2 | |||
20.3 | even | 4 | 720.4.a.z.1.1 | 1 | |||
60.23 | odd | 4 | 720.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.4.a.a.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
360.4.a.j.1.1 | yes | 1 | 5.3 | odd | 4 | ||
720.4.a.m.1.1 | 1 | 60.23 | odd | 4 | |||
720.4.a.z.1.1 | 1 | 20.3 | even | 4 | |||
1800.4.a.bc.1.1 | 1 | 15.2 | even | 4 | |||
1800.4.a.be.1.1 | 1 | 5.2 | odd | 4 | |||
1800.4.f.e.649.1 | 2 | 3.2 | odd | 2 | |||
1800.4.f.e.649.2 | 2 | 15.14 | odd | 2 | |||
1800.4.f.s.649.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.f.s.649.2 | 2 | 5.4 | even | 2 | inner |