Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(37,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bb (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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.2702336256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 2773.2 | ||
Root | \(1.52274 + 1.63746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.2773 |
Dual form | 3420.2.bb.c.37.1 |
$q$-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 \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | −1.63746 | + | 1.52274i | −0.732294 | + | 0.680989i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.42815 | + | 2.42815i | −0.917753 | + | 0.917753i | −0.996866 | − | 0.0791130i | \(-0.974791\pi\) |
0.0791130 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.50958 | −1.96271 | −0.981356 | − | 0.192201i | \(-0.938437\pi\) | ||||
−0.981356 | + | 0.192201i | \(0.938437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.57882 | + | 5.57882i | −1.35306 | + | 1.35306i | −0.470850 | + | 0.882213i | \(0.656053\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890i | 1.00000i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.35890 | + | 2.35890i | 0.491864 | + | 0.491864i | 0.908893 | − | 0.417029i | \(-0.136929\pi\) |
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.362541 | − | 4.98684i | 0.0725083 | − | 0.997368i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.278560 | − | 7.67341i | 0.0470852 | − | 1.29704i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.07621 | + | 3.07621i | 0.469118 | + | 0.469118i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.432511 | + | 0.901629i | \(0.642372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.08143 | − | 8.08143i | 1.17880 | − | 1.17880i | 0.198747 | − | 0.980051i | \(-0.436313\pi\) |
0.980051 | − | 0.198747i | \(-0.0636872\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.79178i | − | 0.684540i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.6592 | − | 9.91238i | 1.43728 | − | 1.33658i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8109 | −1.38420 | −0.692099 | − | 0.721803i | \(-0.743314\pi\) | ||||
−0.692099 | + | 0.721803i | \(0.743314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9447 | − | 10.9447i | −1.28098 | − | 1.28098i | −0.940111 | − | 0.340868i | \(-0.889279\pi\) |
−0.340868 | − | 0.940111i | \(-0.610721\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.8062 | − | 15.8062i | 1.80128 | − | 1.80128i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.3589 | + | 12.3589i | 1.35657 | + | 1.35657i | 0.878114 | + | 0.478451i | \(0.158802\pi\) |
0.478451 | + | 0.878114i | \(0.341198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.640009 | − | 17.6302i | 0.0694187 | − | 1.91226i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.63746 | − | 7.13752i | −0.680989 | − | 0.732294i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.4356 | −1.73491 | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||||
−0.867453 | + | 0.497519i | \(0.834245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.45458 | − | 0.270616i | −0.695143 | − | 0.0252350i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 27.0924i | − | 2.48355i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.3746 | 2.85224 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.00000 | + | 8.71780i | 0.626099 | + | 0.779744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.3746 | 1.95488 | 0.977438 | − | 0.211221i | \(-0.0677440\pi\) | ||||
0.977438 | + | 0.211221i | \(0.0677440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5840 | − | 10.5840i | −0.917753 | − | 0.917753i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.23211 | + | 1.23211i | −0.105266 | + | 0.105266i | −0.757778 | − | 0.652512i | \(-0.773715\pi\) |
0.652512 | + | 0.757778i | \(0.273715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.3746i | − | 1.21924i | −0.792695 | − | 0.609618i | \(-0.791323\pi\) | ||
0.792695 | − | 0.609618i | \(-0.208677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 24.3746i | 1.99684i | 0.0561570 | + | 0.998422i | \(0.482115\pi\) | ||||
−0.0561570 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.282202 | − | 0.282202i | 0.0225222 | − | 0.0225222i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) |
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.4555 | −0.902820 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.64110 | + | 7.64110i | 0.598497 | + | 0.598497i | 0.939913 | − | 0.341415i | \(-0.110906\pi\) |
−0.341415 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2285 | + | 12.9891i | 0.848792 | + | 0.981882i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.3158 | − | 36.3158i | 2.65567 | − | 2.65567i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3746 | −0.750679 | −0.375339 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375339 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7178 | − | 19.7178i | 1.40483 | − | 1.40483i | 0.621117 | − | 0.783718i | \(-0.286679\pi\) |
0.783718 | − | 0.621117i | \(-0.213321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.1123i | − | 1.07128i | −0.844446 | − | 0.535641i | \(-0.820070\pi\) | ||
0.844446 | − | 0.535641i | \(-0.179930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 28.3746i | − | 1.96271i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.72144 | − | 0.352907i | −0.662997 | − | 0.0240681i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.37459i | 0.553408i | 0.960955 | + | 0.276704i | \(0.0892422\pi\) | ||||
−0.960955 | + | 0.276704i | \(0.910758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.6573 | − | 20.6573i | −1.35330 | − | 1.35330i | −0.881939 | − | 0.471364i | \(-0.843762\pi\) |
−0.471364 | − | 0.881939i | \(-0.656238\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.927111 | + | 25.5389i | −0.0604781 | + | 1.66597i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.9260i | 0.706745i | 0.935483 | + | 0.353373i | \(0.114965\pi\) | ||||
−0.935483 | + | 0.353373i | \(0.885035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.29662 | + | 7.84634i | 0.466164 | + | 0.501284i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.3746 | −1.91723 | −0.958613 | − | 0.284711i | \(-0.908102\pi\) | ||||
−0.958613 | + | 0.284711i | \(0.908102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.3554 | − | 15.3554i | −0.965388 | − | 0.965388i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.92900 | − | 1.92900i | −0.118947 | − | 0.118947i | 0.645128 | − | 0.764075i | \(-0.276804\pi\) |
−0.764075 | + | 0.645128i | \(0.776804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1534 | −1.58871 | −0.794353 | − | 0.607457i | \(-0.792190\pi\) | ||||
−0.794353 | + | 0.607457i | \(0.792190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.35999 | + | 32.4622i | −0.142313 | + | 1.95754i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7417 | + | 21.7417i | −1.30633 | + | 1.30633i | −0.382288 | + | 0.924043i | \(0.624864\pi\) |
−0.924043 | + | 0.382288i | \(0.875136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6049 | − | 14.6049i | −0.868174 | − | 0.868174i | 0.124096 | − | 0.992270i | \(-0.460397\pi\) |
−0.992270 | + | 0.124096i | \(0.960397\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 45.2465i | − | 2.66156i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.9390 | −0.861069 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.7025 | − | 16.4622i | 1.01364 | − | 0.942623i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1314 | 1.59519 | 0.797594 | − | 0.603195i | \(-0.206106\pi\) | ||||
0.797594 | + | 0.603195i | \(0.206106\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.4356 | + | 14.4356i | 0.815948 | + | 0.815948i | 0.985518 | − | 0.169570i | \(-0.0542379\pi\) |
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.3175 | − | 24.3175i | −1.35306 | − | 1.35306i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.2458i | 2.16369i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.36188 | − | 5.36188i | −0.289514 | − | 0.289514i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.74865 | − | 9.74865i | 0.523335 | − | 0.523335i | −0.395242 | − | 0.918577i | \(-0.629339\pi\) |
0.918577 | + | 0.395242i | \(0.129339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.8492i | 1.97249i | 0.165277 | + | 0.986247i | \(0.447148\pi\) | ||||
−0.165277 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4356 | − | 24.4356i | −1.30058 | − | 1.30058i | −0.928003 | − | 0.372572i | \(-0.878476\pi\) |
−0.372572 | − | 0.928003i | \(-0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.3746i | 1.81422i | 0.420892 | + | 0.907111i | \(0.361717\pi\) | ||||
−0.420892 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.5874 | + | 1.25559i | 1.81039 | + | 0.0657205i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.0767 | − | 27.0767i | 1.41339 | − | 1.41339i | 0.682598 | − | 0.730794i | \(-0.260850\pi\) |
0.730794 | − | 0.682598i | \(-0.239150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.81331 | + | 49.9507i | −0.0924146 | + | 2.54572i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.39449i | − | 0.324213i | −0.986773 | − | 0.162107i | \(-0.948171\pi\) | ||
0.986773 | − | 0.162107i | \(-0.0518289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.3198 | −1.33105 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.5136 | − | 25.5136i | 1.28049 | − | 1.28049i | 0.340099 | − | 0.940389i | \(-0.389539\pi\) |
0.940389 | − | 0.340099i | \(-0.110461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.0565 | − | 1.41783i | −1.91721 | − | 0.0695984i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.71780i | − | 0.425892i | −0.977064 | − | 0.212946i | \(-0.931694\pi\) | ||
0.977064 | − | 0.212946i | \(-0.0683059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.7981 | + | 29.8432i | 1.25139 | + | 1.44761i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26.2505 | − | 26.2505i | 1.27035 | − | 1.27035i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.2822 | + | 10.2822i | −0.491864 | + | 0.491864i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3915 | + | 25.3915i | 1.20639 | + | 1.20639i | 0.972189 | + | 0.234198i | \(0.0752464\pi\) |
0.234198 | + | 0.972189i | \(0.424754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.43161 | − | 4.43161i | 0.207302 | − | 0.207302i | −0.595818 | − | 0.803120i | \(-0.703172\pi\) |
0.803120 | + | 0.595818i | \(0.203172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.374586 | −0.0174462 | −0.00872311 | − | 0.999962i | \(-0.502777\pi\) | ||||
−0.00872311 | + | 0.999962i | \(0.502777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3967 | + | 30.3967i | 1.41266 | + | 1.41266i | 0.739511 | + | 0.673145i | \(0.235057\pi\) |
0.673145 | + | 0.739511i | \(0.264943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.89236 | + | 4.89236i | −0.226392 | + | 0.226392i | −0.811183 | − | 0.584792i | \(-0.801176\pi\) |
0.584792 | + | 0.811183i | \(0.301176\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.0249 | − | 20.0249i | −0.920744 | − | 0.920744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.7371 | + | 1.58028i | 0.997368 | + | 0.0725083i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00000i | 0.182765i | 0.995816 | + | 0.0913823i | \(0.0291285\pi\) | ||||
−0.995816 | + | 0.0913823i | \(0.970871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.00000 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.3746i | 1.71788i | 0.512074 | + | 0.858941i | \(0.328877\pi\) | ||||
−0.512074 | + | 0.858941i | \(0.671123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6411 | − | 17.6411i | −0.786578 | − | 0.786578i | 0.194354 | − | 0.980932i | \(-0.437739\pi\) |
−0.980932 | + | 0.194354i | \(0.937739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.5501 | − | 26.5498i | 1.27046 | − | 1.18145i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53.1506 | 2.35124 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −52.6067 | + | 52.6067i | −2.31364 | + | 2.31364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 11.8712i | − | 0.516139i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.1924i | 1.34355i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.2657 | −1.77415 | −0.887075 | − | 0.461625i | \(-0.847267\pi\) | ||||
−0.887075 | + | 0.461625i | \(0.847267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.8993 | + | 32.8993i | −1.39399 | + | 1.39399i | −0.577838 | + | 0.816152i | \(0.696103\pi\) |
−0.816152 | + | 0.577838i | \(0.803897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.1534 | −1.09449 | −0.547243 | − | 0.836974i | \(-0.684323\pi\) | ||||
−0.547243 | + | 0.836974i | \(0.684323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.6186 | − | 10.9083i | 0.526234 | − | 0.454906i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.72603 | − | 6.72603i | 0.280008 | − | 0.280008i | −0.553104 | − | 0.833112i | \(-0.686557\pi\) |
0.833112 | + | 0.553104i | \(0.186557\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60.0184 | −2.48998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.0301 | − | 34.0301i | 1.40457 | − | 1.40457i | 0.619862 | − | 0.784711i | \(-0.287189\pi\) |
0.784711 | − | 0.619862i | \(-0.212811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.4356 | − | 34.4356i | −1.41410 | − | 1.41410i | −0.715994 | − | 0.698106i | \(-0.754026\pi\) |
−0.698106 | − | 0.715994i | \(-0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.2546 | + | 44.3627i | 1.69127 | + | 1.81869i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −51.3746 | + | 47.7753i | −2.08867 | + | 1.94234i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.9778 | + | 27.9778i | 1.13001 | + | 1.13001i | 0.990174 | + | 0.139837i | \(0.0446580\pi\) |
0.139837 | + | 0.990174i | \(0.455342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.3699 | − | 30.3699i | 1.22264 | − | 1.22264i | 0.255956 | − | 0.966689i | \(-0.417610\pi\) |
0.966689 | − | 0.255956i | \(-0.0823901\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.0000i | − | 0.964641i | −0.875995 | − | 0.482321i | \(-0.839794\pi\) | ||
0.875995 | − | 0.482321i | \(-0.160206\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7371 | − | 3.61587i | −0.989485 | − | 0.144635i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.9643 | 1.47153 | 0.735763 | − | 0.677239i | \(-0.236824\pi\) | ||||
0.735763 | + | 0.677239i | \(0.236824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0360724 | + | 0.0360724i | 0.00142255 | + | 0.00142255i | 0.707818 | − | 0.706395i | \(-0.249680\pi\) |
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.3863 | + | 20.3863i | −0.801468 | + | 0.801468i | −0.983325 | − | 0.181857i | \(-0.941789\pi\) |
0.181857 | + | 0.983325i | \(0.441789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3368 | − | 13.3368i | −0.521908 | − | 0.521908i | 0.396239 | − | 0.918147i | \(-0.370315\pi\) |
−0.918147 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.6375 | + | 34.0706i | −1.43154 | + | 1.33125i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.4476 | + | 1.21421i | 1.29704 | + | 0.0470852i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.3746 | 2.71678 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.141349 | − | 3.89371i | 0.00540067 | − | 0.148771i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6958 | 0.406889 | 0.203445 | − | 0.979086i | \(-0.434786\pi\) | ||||
0.203445 | + | 0.979086i | \(0.434786\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.8887 | + | 23.5378i | 0.830286 | + | 0.892839i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.4356 | −0.658533 | −0.329267 | − | 0.944237i | \(-0.606802\pi\) | ||||
−0.329267 | + | 0.944237i | \(0.606802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 42.3362 | − | 42.3362i | 1.59222 | − | 1.59222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.3068i | 1.96442i | 0.187779 | + | 0.982211i | \(0.439871\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.62541i | − | 0.209793i | −0.994483 | − | 0.104896i | \(-0.966549\pi\) | ||
0.994483 | − | 0.104896i | \(-0.0334511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0919 | − | 18.0919i | 0.670990 | − | 0.670990i | −0.286954 | − | 0.957944i | \(-0.592643\pi\) |
0.957944 | + | 0.286954i | \(0.0926427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.3233 | −1.26949 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.1534 | − | 19.1534i | −0.707447 | − | 0.707447i | 0.258551 | − | 0.965998i | \(-0.416755\pi\) |
−0.965998 | + | 0.258551i | \(0.916755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.7150i | 0.872370i | 0.899857 | + | 0.436185i | \(0.143671\pi\) | ||||
−0.899857 | + | 0.436185i | \(0.856329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.1161 | − | 39.9124i | −1.35983 | − | 1.46228i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.6904 | + | 37.6904i | −1.36988 | + | 1.36988i | −0.509276 | + | 0.860603i | \(0.670087\pi\) |
−0.860603 | + | 0.509276i | \(0.829913\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.4519 | 1.64763 | 0.823816 | − | 0.566857i | \(-0.191841\pi\) | ||||
0.823816 | + | 0.566857i | \(0.191841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 44.3746i | − | 1.60019i | −0.599874 | − | 0.800094i | \(-0.704783\pi\) | ||
0.599874 | − | 0.800094i | \(-0.295217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0323746 | + | 0.891814i | −0.00115550 | + | 0.0318302i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 90.1697i | 3.18998i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 71.2453 | + | 71.2453i | 2.51419 | + | 2.51419i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.7579 | − | 17.4437i | 0.661129 | − | 0.614810i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.6630i | − | 1.14837i | −0.818726 | − | 0.574184i | \(-0.805319\pi\) | ||
0.818726 | − | 0.574184i | \(-0.194681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.1474 | − | 0.876596i | −0.845846 | − | 0.0307058i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.4089 | + | 13.4089i | −0.469118 | + | 0.469118i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.62541 | −0.266129 | −0.133064 | − | 0.991107i | \(-0.542482\pi\) | ||||
−0.133064 | + | 0.991107i | \(0.542482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.22343 | + | 4.22343i | 0.147219 | + | 0.147219i | 0.776875 | − | 0.629655i | \(-0.216804\pi\) |
−0.629655 | + | 0.776875i | \(0.716804\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.7325 | + | 26.7325i | 0.926226 | + | 0.926226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.7956 | − | 21.2870i | −0.680989 | − | 0.732294i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −76.1821 | + | 76.1821i | −2.61765 | + | 2.61765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.1534 | − | 39.1534i | −1.34059 | − | 1.34059i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) |
−0.445112 | − | 0.895475i | \(-0.646836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.3425i | 0.523478i | 0.965139 | + | 0.261739i | \(0.0842960\pi\) | ||||
−0.965139 | + | 0.261739i | \(0.915704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.1651 | − | 4.17106i | −1.29022 | − | 0.141008i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.2848 | −1.82890 | −0.914451 | − | 0.404696i | \(-0.867377\pi\) | ||||
−0.914451 | + | 0.404696i | \(0.867377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.2495 | + | 29.2495i | 0.984324 | + | 0.984324i | 0.999879 | − | 0.0155546i | \(-0.00495139\pi\) |
−0.0155546 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.2261 | + | 35.2261i | 1.17880 | + | 1.17880i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −80.4512 | − | 80.4512i | −2.66255 | − | 2.66255i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −54.3287 | + | 54.3287i | −1.79409 | + | 1.79409i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.71780i | 0.287574i | 0.989609 | + | 0.143787i | \(0.0459280\pi\) | ||||
−0.989609 | + | 0.143787i | \(0.954072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.8712i | 1.14409i | 0.820223 | + | 0.572043i | \(0.193849\pi\) | ||||
−0.820223 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.8869 | 0.684540 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.16619 | + | 114.765i | −0.136249 | + | 3.75322i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1931 | − | 18.1931i | 0.594341 | − | 0.594341i | −0.344460 | − | 0.938801i | \(-0.611938\pi\) |
0.938801 | + | 0.344460i | \(0.111938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.5123 | − | 26.5123i | 0.861534 | − | 0.861534i | −0.129983 | − | 0.991516i | \(-0.541492\pi\) |
0.991516 | + | 0.129983i | \(0.0414921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9880 | − | 15.7978i | 0.549717 | − | 0.511204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 5.98348i | − | 0.193217i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.5123 | + | 36.5123i | −1.17416 | + | 1.17416i | −0.192947 | + | 0.981209i | \(0.561805\pi\) |
−0.981209 | + | 0.192947i | \(0.938195\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.9036 | + | 34.9036i | 1.11896 | + | 1.11896i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.26205 | + | 62.3121i | −0.0720749 | + | 1.98543i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.5130i | 0.461485i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.0120 | + | 24.7457i | 0.729531 | + | 0.784493i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.55262 | − | 8.55262i | 0.270864 | − | 0.270864i | −0.558584 | − | 0.829448i | \(-0.688655\pi\) |
0.829448 | + | 0.558584i | \(0.188655\pi\) | |||||||
\(998\) | 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 | 3420.2.bb.c.2773.2 | 8 | ||
3.2 | odd | 2 | 380.2.l.a.113.3 | yes | 8 | ||
5.2 | odd | 4 | inner | 3420.2.bb.c.37.1 | 8 | ||
15.2 | even | 4 | 380.2.l.a.37.4 | ✓ | 8 | ||
15.8 | even | 4 | 1900.2.l.a.1557.3 | 8 | |||
15.14 | odd | 2 | 1900.2.l.a.493.3 | 8 | |||
19.18 | odd | 2 | CM | 3420.2.bb.c.2773.2 | 8 | ||
57.56 | even | 2 | 380.2.l.a.113.3 | yes | 8 | ||
95.37 | even | 4 | inner | 3420.2.bb.c.37.1 | 8 | ||
285.113 | odd | 4 | 1900.2.l.a.1557.3 | 8 | |||
285.227 | odd | 4 | 380.2.l.a.37.4 | ✓ | 8 | ||
285.284 | even | 2 | 1900.2.l.a.493.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.l.a.37.4 | ✓ | 8 | 15.2 | even | 4 | ||
380.2.l.a.37.4 | ✓ | 8 | 285.227 | odd | 4 | ||
380.2.l.a.113.3 | yes | 8 | 3.2 | odd | 2 | ||
380.2.l.a.113.3 | yes | 8 | 57.56 | even | 2 | ||
1900.2.l.a.493.3 | 8 | 15.14 | odd | 2 | |||
1900.2.l.a.493.3 | 8 | 285.284 | even | 2 | |||
1900.2.l.a.1557.3 | 8 | 15.8 | even | 4 | |||
1900.2.l.a.1557.3 | 8 | 285.113 | odd | 4 | |||
3420.2.bb.c.37.1 | 8 | 5.2 | odd | 4 | inner | ||
3420.2.bb.c.37.1 | 8 | 95.37 | even | 4 | inner | ||
3420.2.bb.c.2773.2 | 8 | 1.1 | even | 1 | trivial | ||
3420.2.bb.c.2773.2 | 8 | 19.18 | odd | 2 | CM |