Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.6 | ||
Root | \(0.500000 - 1.56488i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.a.5615.5 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.12976 | 0.505246 | 0.252623 | − | 0.967565i | \(-0.418707\pi\) | ||||
0.252623 | + | 0.967565i | \(0.418707\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.86182i | 1.16438i | 0.813052 | + | 0.582191i | \(0.197804\pi\) | ||||
−0.813052 | + | 0.582191i | \(0.802196\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.08658i | − 1.41076i | −0.708828 | − | 0.705381i | \(-0.750776\pi\) | ||||
0.708828 | − | 0.705381i | \(-0.249224\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.00000i | − 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.99158 | −1.83339 | −0.916697 | − | 0.399583i | \(-0.869155\pi\) | ||||
−0.916697 | + | 0.399583i | \(0.869155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.68044 | 1.60148 | 0.800741 | − | 0.599010i | \(-0.204439\pi\) | ||||
0.800741 | + | 0.599010i | \(0.204439\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.72363 | −0.744726 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.73205 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.08658i | − 0.733971i | −0.930227 | − | 0.366985i | \(-0.880390\pi\) | ||||
0.930227 | − | 0.366985i | \(-0.119610\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.12976i | 0.190965i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.28273i | 1.36167i | 0.732436 | + | 0.680836i | \(0.238383\pi\) | ||||
−0.732436 | + | 0.680836i | \(0.761617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.41249i | − 1.31381i | −0.753973 | − | 0.656905i | \(-0.771865\pi\) | ||||
0.753973 | − | 0.656905i | \(-0.228135\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0148 | 1.52724 | 0.763620 | − | 0.645666i | \(-0.223420\pi\) | ||||
0.763620 | + | 0.645666i | \(0.223420\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.93662 | 0.282485 | 0.141243 | − | 0.989975i | \(-0.454890\pi\) | ||||
0.141243 | + | 0.989975i | \(0.454890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.72363 | −1.06092 | −0.530461 | − | 0.847709i | \(-0.677981\pi\) | ||||
−0.530461 | + | 0.847709i | \(0.677981\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.36294i | 0.588299i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 10.9916i | − 1.43098i | −0.698622 | − | 0.715491i | \(-0.746203\pi\) | ||||
0.698622 | − | 0.715491i | \(-0.253797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.4641i | − 1.46783i | −0.679243 | − | 0.733914i | \(-0.737692\pi\) | ||||
0.679243 | − | 0.733914i | \(-0.262308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 5.74663i | − 0.712782i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.08658 | −0.621424 | −0.310712 | − | 0.950504i | \(-0.600567\pi\) | ||||
−0.310712 | + | 0.950504i | \(0.600567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6804 | −1.62357 | −0.811785 | − | 0.583957i | \(-0.801504\pi\) | ||||
−0.811785 | + | 0.583957i | \(0.801504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.63706 | −0.308644 | −0.154322 | − | 0.988021i | \(-0.549319\pi\) | ||||
−0.154322 | + | 0.988021i | \(0.549319\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.86182 | −0.440095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.17295i | 0.807020i | 0.914975 | + | 0.403510i | \(0.132210\pi\) | ||||
−0.914975 | + | 0.403510i | \(0.867790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.9052i | − 1.63606i | −0.575177 | − | 0.818029i | \(-0.695067\pi\) | ||||
0.575177 | − | 0.818029i | \(-0.304933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.25953i | − 0.245080i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 12.6889i | − 1.34502i | −0.740090 | − | 0.672508i | \(-0.765217\pi\) | ||||
0.740090 | − | 0.672508i | \(-0.234783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.08658 | 0.533218 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.02861 | −0.926316 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.17315 | 0.423719 | 0.211860 | − | 0.977300i | \(-0.432048\pi\) | ||||
0.211860 | + | 0.977300i | \(0.432048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.37753i | 0.529863i | 0.964267 | + | 0.264932i | \(0.0853494\pi\) | ||||
−0.964267 | + | 0.264932i | \(0.914651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8418i | 1.24147i | 0.784022 | + | 0.620733i | \(0.213165\pi\) | ||||
−0.784022 | + | 0.620733i | \(0.786835\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.0782i | − 1.25266i | −0.779558 | − | 0.626330i | \(-0.784556\pi\) | ||||
0.779558 | − | 0.626330i | \(-0.215444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.05496i | 0.663675i | 0.943337 | + | 0.331837i | \(0.107669\pi\) | ||||
−0.943337 | + | 0.331837i | \(0.892331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.67709 | 0.809143 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.91362 | −0.355784 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.85565 | −0.881516 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.63706i | − 0.411472i | −0.978608 | − | 0.205736i | \(-0.934041\pi\) | ||||
0.978608 | − | 0.205736i | \(-0.0659589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.36930i | 0.731229i | 0.930766 | + | 0.365615i | \(0.119141\pi\) | ||||
−0.930766 | + | 0.365615i | \(0.880859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.99158i | − 0.692958i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.9366i | − 1.19069i | −0.803472 | − | 0.595343i | \(-0.797016\pi\) | ||||
0.803472 | − | 0.595343i | \(-0.202984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9832 | 1.18604 | 0.593018 | − | 0.805189i | \(-0.297936\pi\) | ||||
0.593018 | + | 0.805189i | \(0.297936\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.6434 | 1.64266 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.34610 | −0.443970 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.7700 | 1.78347 | 0.891735 | − | 0.452558i | \(-0.149488\pi\) | ||||
0.891735 | + | 0.452558i | \(0.149488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0464i | 1.30584i | 0.757428 | + | 0.652919i | \(0.226456\pi\) | ||||
−0.757428 | + | 0.652919i | \(0.773544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.61687i | − 0.370836i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 5.49572i | − 0.438606i | −0.975657 | − | 0.219303i | \(-0.929622\pi\) | ||||
0.975657 | − | 0.219303i | \(-0.0703783\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68044i | 0.605304i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.62247 | −0.127082 | −0.0635410 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635410 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.70905 | −0.673926 | −0.336963 | − | 0.941518i | \(-0.609400\pi\) | ||||
−0.336963 | + | 0.941518i | \(0.609400\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8732 | −0.990250 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.53891 | −0.117001 | −0.0585005 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0585005 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.72363i | − 0.281480i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 26.7386i | − 1.99854i | −0.0382400 | − | 0.999269i | \(-0.512175\pi\) | ||||
0.0382400 | − | 0.999269i | \(-0.487825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10135i | 0.230522i | 0.993335 | + | 0.115261i | \(0.0367704\pi\) | ||||
−0.993335 | + | 0.115261i | \(0.963230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.35753i | 0.687980i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.72363 | 0.564808 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8132 | −0.999489 | −0.499745 | − | 0.866173i | \(-0.666573\pi\) | ||||
−0.499745 | + | 0.866173i | \(0.666573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.05496 | 0.507827 | 0.253913 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253913 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.362748 | −0.0258448 | −0.0129224 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129224 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 7.70029i | − 0.545859i | −0.962034 | − | 0.272930i | \(-0.912007\pi\) | ||||
0.962034 | − | 0.272930i | \(-0.0879926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.73205i | − 0.332125i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 9.50414i | − 0.663798i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 30.8620i | − 2.13477i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5191 | 0.999533 | 0.499767 | − | 0.866160i | \(-0.333419\pi\) | ||||
0.499767 | + | 0.866160i | \(0.333419\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3143 | 0.771632 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.08658 | 0.277415 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1732 | −0.684320 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2743i | 1.29070i | 0.763886 | + | 0.645352i | \(0.223289\pi\) | ||||
−0.763886 | + | 0.645352i | \(0.776711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 23.2341i | − 1.54210i | −0.636773 | − | 0.771052i | \(-0.719731\pi\) | ||||
0.636773 | − | 0.771052i | \(-0.280269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.4641i | − 0.889733i | −0.895597 | − | 0.444866i | \(-0.853251\pi\) | ||||
0.895597 | − | 0.444866i | \(-0.146749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 17.4641i | − 1.14411i | −0.820215 | − | 0.572056i | \(-0.806146\pi\) | ||||
0.820215 | − | 0.572056i | \(-0.193854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.18793 | 0.142725 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.82724 | 0.118194 | 0.0590972 | − | 0.998252i | \(-0.481178\pi\) | ||||
0.0590972 | + | 0.998252i | \(0.481178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.5193 | −1.38618 | −0.693089 | − | 0.720852i | \(-0.743751\pi\) | ||||
−0.693089 | + | 0.720852i | \(0.743751\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.12976 | −0.0721780 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.6498i | 2.58648i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.15818i | − 0.0731035i | −0.999332 | − | 0.0365517i | \(-0.988363\pi\) | ||||
0.999332 | − | 0.0365517i | \(-0.0116374\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.6604i | 1.86474i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0812i | 0.691224i | 0.938377 | + | 0.345612i | \(0.112329\pi\) | ||||
−0.938377 | + | 0.345612i | \(0.887671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.28273 | −0.514664 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7354 | 0.661973 | 0.330987 | − | 0.943635i | \(-0.392619\pi\) | ||||
0.330987 | + | 0.943635i | \(0.392619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.72589 | −0.536027 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.75204 | −0.350708 | −0.175354 | − | 0.984505i | \(-0.556107\pi\) | ||||
−0.175354 | + | 0.984505i | \(0.556107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.33735i | − 0.0812380i | −0.999175 | − | 0.0406190i | \(-0.987067\pi\) | ||||
0.999175 | − | 0.0406190i | \(-0.0129330\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 14.3800i | − 0.867145i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.13537i | 0.188386i | 0.995554 | + | 0.0941930i | \(0.0300271\pi\) | ||||
−0.995554 | + | 0.0941930i | \(0.969973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 13.3839i | − 0.798416i | −0.916860 | − | 0.399208i | \(-0.869285\pi\) | ||||
0.916860 | − | 0.399208i | \(-0.130715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.8104 | −1.29649 | −0.648247 | − | 0.761430i | \(-0.724498\pi\) | ||||
−0.648247 | + | 0.761430i | \(0.724498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.41249 | 0.496574 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.6982 | 1.79341 | 0.896705 | − | 0.442629i | \(-0.145954\pi\) | ||||
0.896705 | + | 0.442629i | \(0.145954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 12.4179i | − 0.722998i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 39.0671i | − 2.25931i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0148i | 0.577242i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 12.9517i | − 0.741614i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.10977 | −0.519922 | −0.259961 | − | 0.965619i | \(-0.583710\pi\) | ||||
−0.259961 | + | 0.965619i | \(0.583710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.5275 | −1.56094 | −0.780470 | − | 0.625193i | \(-0.785020\pi\) | ||||
−0.780470 | + | 0.625193i | \(0.785020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.36294 | 0.303131 | 0.151566 | − | 0.988447i | \(-0.451568\pi\) | ||||
0.151566 | + | 0.988447i | \(0.451568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.30832 | −0.410476 | −0.205238 | − | 0.978712i | \(-0.565797\pi\) | ||||
−0.205238 | + | 0.978712i | \(0.565797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 18.2743i | − 1.02316i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.9832i | 0.889327i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.9405i | 1.05063i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.93662i | 0.106769i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5823 | −0.581655 | −0.290828 | − | 0.956775i | \(-0.593931\pi\) | ||||
−0.290828 | + | 0.956775i | \(0.593931\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.74663 | −0.313972 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.29095 | −0.233743 | −0.116872 | − | 0.993147i | \(-0.537287\pi\) | ||||
−0.116872 | + | 0.993147i | \(0.537287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7816 | 0.854622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 10.3405i | − 0.555107i | −0.960710 | − | 0.277554i | \(-0.910476\pi\) | ||||
0.960710 | − | 0.277554i | \(-0.0895236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.1182i | 0.595143i | 0.954700 | + | 0.297572i | \(0.0961767\pi\) | ||||
−0.954700 | + | 0.297572i | \(0.903823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 23.3407i | − 1.24230i | −0.783692 | − | 0.621150i | \(-0.786666\pi\) | ||||
0.783692 | − | 0.621150i | \(-0.213334\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.4557 | −0.820302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3923 | −1.18182 | −0.590910 | − | 0.806737i | \(-0.701231\pi\) | ||||
−0.590910 | + | 0.806737i | \(0.701231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.8654 | 2.36133 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.97925 | −0.155941 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.93696i | 0.101109i | 0.998721 | + | 0.0505543i | \(0.0160988\pi\) | ||||
−0.998721 | + | 0.0505543i | \(0.983901\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 7.72363i | − 0.400991i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 15.1246i | − 0.783120i | −0.920153 | − | 0.391560i | \(-0.871936\pi\) | ||||
0.920153 | − | 0.391560i | \(-0.128064\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0699i | 1.23966i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.15837 | −0.316334 | −0.158167 | − | 0.987412i | \(-0.550558\pi\) | ||||
−0.158167 | + | 0.987412i | \(0.550558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.8822 | −0.760445 | −0.380222 | − | 0.924895i | \(-0.624153\pi\) | ||||
−0.380222 | + | 0.924895i | \(0.624153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.36294 | −0.222356 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.82685 | −0.0926250 | −0.0463125 | − | 0.998927i | \(-0.514747\pi\) | ||||
−0.0463125 | + | 0.998927i | \(0.514747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 15.3609i | − 0.776833i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.10375i | 0.407744i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.18999i | − 0.109912i | −0.998489 | − | 0.0549562i | \(-0.982498\pi\) | ||||
0.998489 | − | 0.0549562i | \(-0.0175019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 3.59071i | − 0.179312i | −0.995973 | − | 0.0896558i | \(-0.971423\pi\) | ||||
0.995973 | − | 0.0896558i | \(-0.0285767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.7867 | −1.03546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.9864 | −1.58551 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.3588 | −1.74838 | −0.874191 | − | 0.485583i | \(-0.838607\pi\) | ||||
−0.874191 | + | 0.485583i | \(0.838607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.9916 | 0.540860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 16.8394i | − 0.826612i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.44952i | − 0.119667i | −0.998208 | − | 0.0598334i | \(-0.980943\pi\) | ||||
0.998208 | − | 0.0598334i | \(-0.0190569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.26589i | − 0.305381i | −0.988274 | − | 0.152690i | \(-0.951206\pi\) | ||||
0.988274 | − | 0.152690i | \(-0.0487937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.44726i | 0.361245i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4641 | 0.554787 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.01177 | −0.145072 | −0.0725359 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725359 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00020 | −0.336408 | −0.168204 | − | 0.985752i | \(-0.553797\pi\) | ||||
−0.168204 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −61.3789 | −2.93615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.33735i | 0.0638281i | 0.999491 | + | 0.0319140i | \(0.0101603\pi\) | ||||
−0.999491 | + | 0.0319140i | \(0.989840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.90821i | 0.0906618i | 0.998972 | + | 0.0453309i | \(0.0144342\pi\) | ||||
−0.998972 | + | 0.0453309i | \(0.985566\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 14.3354i | − 0.679565i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 10.0695i | − 0.475211i | −0.971362 | − | 0.237606i | \(-0.923637\pi\) | ||||
0.971362 | − | 0.237606i | \(-0.0763625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4875 | 1.52978 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.74663 | 0.269406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3205 | 0.482773 | 0.241387 | − | 0.970429i | \(-0.422398\pi\) | ||||
0.241387 | + | 0.970429i | \(0.422398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.9420 | 0.835644 | 0.417822 | − | 0.908529i | \(-0.362794\pi\) | ||||
0.417822 | + | 0.908529i | \(0.362794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 21.6664i | − 1.00692i | −0.864017 | − | 0.503462i | \(-0.832059\pi\) | ||||
0.864017 | − | 0.503462i | \(-0.167941\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 18.3525i | − 0.849251i | −0.905369 | − | 0.424625i | \(-0.860406\pi\) | ||||
0.905369 | − | 0.424625i | \(-0.139594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5.08658i | − 0.234876i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 38.6752i | 1.77829i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.7577 | 1.36538 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.6518 | −0.669459 | −0.334730 | − | 0.942314i | \(-0.608645\pi\) | ||||
−0.334730 | + | 0.942314i | \(0.608645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.1307 | 1.92100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.71468 | 0.214083 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.60789i | − 0.299432i | −0.988729 | − | 0.149716i | \(-0.952164\pi\) | ||||
0.988729 | − | 0.149716i | \(-0.0478360\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.08323i | 0.319662i | 0.987144 | + | 0.159831i | \(0.0510949\pi\) | ||||
−0.987144 | + | 0.159831i | \(0.948905\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.46410i | 0.426242i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 13.6804i | − 0.613652i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.13297 | 0.319316 | 0.159658 | − | 0.987172i | \(-0.448961\pi\) | ||||
0.159658 | + | 0.987172i | \(0.448961\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.7321 | 0.656870 | 0.328435 | − | 0.944527i | \(-0.393479\pi\) | ||||
0.328435 | + | 0.944527i | \(0.393479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.25953 | −0.100548 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.21955 | 0.275677 | 0.137838 | − | 0.990455i | \(-0.455985\pi\) | ||||
0.137838 | + | 0.990455i | \(0.455985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2.63706i | − 0.116657i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.07534i | 0.267711i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.47888i | 0.328921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0897i | 0.880147i | 0.897962 | + | 0.440073i | \(0.145048\pi\) | ||||
−0.897962 | + | 0.440073i | \(0.854952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5885 | −1.11891 | −0.559453 | − | 0.828862i | \(-0.688989\pi\) | ||||
−0.559453 | + | 0.828862i | \(0.688989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.17315 | −0.356028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.9892 | 1.56475 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −42.7908 | −1.85347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.5082i | 0.627246i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.86182i | − 0.166340i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.7932i | 1.10894i | 0.832205 | + | 0.554469i | \(0.187078\pi\) | ||||
−0.832205 | + | 0.554469i | \(0.812922\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 14.7752i | − 0.632902i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.41771 | 0.0606167 | 0.0303084 | − | 0.999541i | \(-0.490351\pi\) | ||||
0.0303084 | + | 0.999541i | \(0.490351\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.8166 | 1.61104 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.17295 | −0.305025 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.36275 | −0.184856 | −0.0924278 | − | 0.995719i | \(-0.529463\pi\) | ||||
−0.0924278 | + | 0.995719i | \(0.529463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 50.9409i | − 2.15457i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4007i | 1.07051i | 0.844690 | + | 0.535256i | \(0.179785\pi\) | ||||
−0.844690 | + | 0.535256i | \(0.820215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.97044i | 0.335319i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 24.9746i | − 1.04699i | −0.852029 | − | 0.523495i | \(-0.824628\pi\) | ||||
0.852029 | − | 0.523495i | \(-0.175372\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.02956 | 0.336026 | 0.168013 | − | 0.985785i | \(-0.446265\pi\) | ||||
0.168013 | + | 0.985785i | \(0.446265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.5991 | −1.19267 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7808 | −0.906748 | −0.453374 | − | 0.891320i | \(-0.649780\pi\) | ||||
−0.453374 | + | 0.891320i | \(0.649780\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9052 | 0.618372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 29.8272i | − 1.23532i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2913i | 0.548592i | 0.961645 | + | 0.274296i | \(0.0884449\pi\) | ||||
−0.961645 | + | 0.274296i | \(0.911555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.6582i | 1.34566i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 0.746075i | − 0.0306376i | −0.999883 | − | 0.0153188i | \(-0.995124\pi\) | ||||
0.999883 | − | 0.0153188i | \(-0.00487632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.25953 | 0.0926317 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.1595 | 1.72259 | 0.861296 | − | 0.508104i | \(-0.169654\pi\) | ||||
0.861296 | + | 0.508104i | \(0.169654\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6371 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.42147 | −0.179758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.5950i | 1.81006i | 0.425352 | + | 0.905028i | \(0.360150\pi\) | ||||
−0.425352 | + | 0.905028i | \(0.639850\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 9.85078i | − 0.398520i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6859i | 0.673935i | 0.941516 | + | 0.336968i | \(0.109401\pi\) | ||||
−0.941516 | + | 0.336968i | \(0.890599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.1225i | − 1.21269i | −0.795203 | − | 0.606343i | \(-0.792636\pi\) | ||||
0.795203 | − | 0.606343i | \(-0.207364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.5002 | −1.30629 | −0.653147 | − | 0.757231i | \(-0.726552\pi\) | ||||
−0.653147 | + | 0.757231i | \(0.726552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.6889 | 0.508368 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.48359 | 0.299343 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.5655 | 0.660508 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8734i | 0.751340i | 0.926754 | + | 0.375670i | \(0.122587\pi\) | ||||
−0.926754 | + | 0.375670i | \(0.877413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.23878i | − 0.207895i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.08658i | 0.201537i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.1417i | 0.519067i | 0.965734 | + | 0.259534i | \(0.0835688\pi\) | ||||
−0.965734 | + | 0.259534i | \(0.916431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3121 | −0.446105 | −0.223053 | − | 0.974806i | \(-0.571602\pi\) | ||||
−0.223053 | + | 0.974806i | \(0.571602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.1038 | −0.397219 | −0.198610 | − | 0.980079i | \(-0.563643\pi\) | ||||
−0.198610 | + | 0.980079i | \(0.563643\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.4475 | 1.66621 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2661 | 0.714807 | 0.357404 | − | 0.933950i | \(-0.383662\pi\) | ||||
0.357404 | + | 0.933950i | \(0.383662\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.45534i | 0.369451i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 37.9781i | − 1.47942i | −0.672927 | − | 0.739709i | \(-0.734963\pi\) | ||||
0.672927 | − | 0.739709i | \(-0.265037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.98899i | − 0.349631i | −0.984601 | − | 0.174816i | \(-0.944067\pi\) | ||||
0.984601 | − | 0.174816i | \(-0.0559329\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 9.02861i | − 0.350114i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.3442 | −1.40725 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.2722 | 1.70911 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4937 | 0.828520 | 0.414260 | − | 0.910159i | \(-0.364040\pi\) | ||||
0.414260 | + | 0.910159i | \(0.364040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5920 | −0.522383 | −0.261192 | − | 0.965287i | \(-0.584115\pi\) | ||||
−0.261192 | + | 0.965287i | \(0.584115\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.17315i | 0.160151i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13.0200i | − 0.498196i | −0.968478 | − | 0.249098i | \(-0.919866\pi\) | ||||
0.968478 | − | 0.249098i | \(-0.0801342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 15.7451i | − 0.601590i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.2868i | 1.49671i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.07556 | 0.307209 | 0.153604 | − | 0.988132i | \(-0.450912\pi\) | ||||
0.153604 | + | 0.988132i | \(0.450912\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.7977 | 0.599240 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.8250 | −0.637292 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.91978 | −0.374665 | −0.187333 | − | 0.982297i | \(-0.559984\pi\) | ||||
−0.187333 | + | 0.982297i | \(0.559984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 66.1921i | − 2.49648i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.00000i | − 0.0752177i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 33.4709i | − 1.25702i | −0.777800 | − | 0.628512i | \(-0.783664\pi\) | ||||
0.777800 | − | 0.628512i | \(-0.216336\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 31.3867i | − 1.17544i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.1924 | 0.829950 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.1075 | 1.08553 | 0.542764 | − | 0.839886i | \(-0.317378\pi\) | ||||
0.542764 | + | 0.839886i | \(0.317378\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.37753 | −0.200270 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.6204 | 0.654406 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.39230i | 0.0887257i | 0.999015 | + | 0.0443628i | \(0.0141258\pi\) | ||||
−0.999015 | + | 0.0443628i | \(0.985874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 20.0296i | − 0.740820i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.3315i | 0.750962i | 0.926830 | + | 0.375481i | \(0.122522\pi\) | ||||
−0.926830 | + | 0.375481i | \(0.877478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 19.6434i | − 0.723574i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.5823 | −1.34570 | −0.672851 | − | 0.739778i | \(-0.734930\pi\) | ||||
−0.672851 | + | 0.739778i | \(0.734930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.9864 | 0.513110 | 0.256555 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256555 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.5950 | 0.901091 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.8418 | −0.469230 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 47.5657i | − 1.73570i | −0.496830 | − | 0.867848i | \(-0.665503\pi\) | ||||
0.496830 | − | 0.867848i | \(-0.334497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1287i | 0.659769i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 41.3844i | − 1.50414i | −0.659082 | − | 0.752071i | \(-0.729055\pi\) | ||||
0.659082 | − | 0.752071i | \(-0.270945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 19.8335i | − 0.718966i | −0.933152 | − | 0.359483i | \(-0.882953\pi\) | ||||
0.933152 | − | 0.359483i | \(-0.117047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0782 | 0.473461 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −55.9095 | −2.01878 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.2739 | −0.731096 | −0.365548 | − | 0.930792i | \(-0.619118\pi\) | ||||
−0.365548 | + | 0.930792i | \(0.619118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.271102 | 0.00975088 | 0.00487544 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487544 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.2169i | 0.546607i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 67.2291i | 2.40873i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 52.8313i | − 1.89045i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.20887i | − 0.221604i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.0760 | 1.78501 | 0.892507 | − | 0.451033i | \(-0.148944\pi\) | ||||
0.892507 | + | 0.451033i | \(0.148944\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.05496 | −0.250845 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.3130 | −2.07076 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.1762 | 0.962629 | 0.481314 | − | 0.876548i | \(-0.340160\pi\) | ||||
0.481314 | + | 0.876548i | \(0.340160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 3.87325i | − 0.137026i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10.1838i | − 0.359379i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.67709i | 0.305827i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.5566i | 1.17979i | 0.807480 | + | 0.589894i | \(0.200831\pi\) | ||||
−0.807480 | + | 0.589894i | \(0.799169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.54206 | 0.124379 | 0.0621893 | − | 0.998064i | \(-0.480192\pi\) | ||||
0.0621893 | + | 0.998064i | \(0.480192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.83301 | −0.0642077 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −80.0339 | −2.80003 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.0847 | 1.08486 | 0.542431 | − | 0.840100i | \(-0.317504\pi\) | ||||
0.542431 | + | 0.840100i | \(0.317504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.2323i | 1.26298i | 0.775385 | + | 0.631489i | \(0.217556\pi\) | ||||
−0.775385 | + | 0.631489i | \(0.782444\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.4991i | 1.86034i | 0.367123 | + | 0.930172i | \(0.380343\pi\) | ||||
−0.367123 | + | 0.930172i | \(0.619657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.2003i | 1.60460i | 0.596920 | + | 0.802301i | \(0.296391\pi\) | ||||
−0.596920 | + | 0.802301i | \(0.703609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.83918 | −0.340499 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.0211 | −1.00192 | −0.500960 | − | 0.865470i | \(-0.667020\pi\) | ||||
−0.500960 | + | 0.865470i | \(0.667020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5437 | −0.500320 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.91362i | − 0.134474i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.6150i | 2.18069i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.8777i | 1.74202i | 0.491266 | + | 0.871009i | \(0.336534\pi\) | ||||
−0.491266 | + | 0.871009i | \(0.663466\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 22.3553i | − 0.763642i | −0.924236 | − | 0.381821i | \(-0.875297\pi\) | ||||
0.924236 | − | 0.381821i | \(-0.124703\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.4134 | −1.51537 | −0.757684 | − | 0.652622i | \(-0.773669\pi\) | ||||
−0.757684 | + | 0.652622i | \(0.773669\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.80145 | 0.299605 | 0.149802 | − | 0.988716i | \(-0.452136\pi\) | ||||
0.149802 | + | 0.988716i | \(0.452136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.73860 | −0.0591143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.7006 | −0.939679 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.8732i | 0.876681i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 9.85565i | − 0.333182i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5280i | 0.862020i | 0.902347 | + | 0.431010i | \(0.141843\pi\) | ||||
−0.902347 | + | 0.431010i | \(0.858157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.0812i | 1.38406i | 0.721869 | + | 0.692030i | \(0.243283\pi\) | ||||
−0.721869 | + | 0.692030i | \(0.756717\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.80145 | −0.0942763 | −0.0471381 | − | 0.998888i | \(-0.515010\pi\) | ||||
−0.0471381 | + | 0.998888i | \(0.515010\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.4366 | 1.52561 | 0.762806 | − | 0.646628i | \(-0.223821\pi\) | ||||
0.762806 | + | 0.646628i | \(0.223821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.63706 | 0.155522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.4767 | −0.517907 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 30.2083i | − 1.00975i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.3379i | 0.644954i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4473i | 0.514623i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.50380i | 0.116470i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.5318 | −1.54506 | −0.772531 | − | 0.634977i | \(-0.781010\pi\) | ||||
−0.772531 | + | 0.634977i | \(0.781010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9174 | −0.825550 | −0.412775 | − | 0.910833i | \(-0.635440\pi\) | ||||
−0.412775 | + | 0.910833i | \(0.635440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.5611 | 1.90500 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.36930 | −0.276379 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.77228i | 0.289371i | 0.989478 | + | 0.144685i | \(0.0462170\pi\) | ||||
−0.989478 | + | 0.144685i | \(0.953783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 69.5866i | 2.29047i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 30.8418i | − 1.01407i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96002i | 0.129924i | 0.997888 | + | 0.0649620i | \(0.0206926\pi\) | ||||
−0.997888 | + | 0.0649620i | \(0.979307\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.99158 | 0.261913 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.72589 | 0.285367 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6077 | −0.379207 | −0.189603 | − | 0.981861i | \(-0.560720\pi\) | ||||
−0.189603 | + | 0.981861i | \(0.560720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.05758 | −0.0670751 | −0.0335376 | − | 0.999437i | \(-0.510677\pi\) | ||||
−0.0335376 | + | 0.999437i | \(0.510677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 64.6117i | − 2.10404i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 53.3723i | − 1.73437i | −0.497989 | − | 0.867184i | \(-0.665928\pi\) | ||||
0.497989 | − | 0.867184i | \(-0.334072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4136i | 0.435423i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.9433i | 1.48825i | 0.668040 | + | 0.744125i | \(0.267133\pi\) | ||||
−0.668040 | + | 0.744125i | \(0.732867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.6057 | −0.504988 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.9366 | 0.450037 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2999 | 0.461287 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.97044 | 0.256578 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.43455i | 0.0461319i | 0.999734 | + | 0.0230659i | \(0.00734276\pi\) | ||||
−0.999734 | + | 0.0230659i | \(0.992657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.6030i | 0.436542i | 0.975888 | + | 0.218271i | \(0.0700417\pi\) | ||||
−0.975888 | + | 0.218271i | \(0.929958\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9832i | 0.448280i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 10.3860i | − 0.332278i | −0.986102 | − | 0.166139i | \(-0.946870\pi\) | ||||
0.986102 | − | 0.166139i | \(-0.0531300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.0020 | 1.56611 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0062 | 0.638098 | 0.319049 | − | 0.947738i | \(-0.396637\pi\) | ||||
0.319049 | + | 0.947738i | \(0.396637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.409820 | −0.0130580 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76.9179 | 2.44585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7220i | 1.45241i | 0.687480 | + | 0.726203i | \(0.258717\pi\) | ||||
−0.687480 | + | 0.726203i | \(0.741283\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8.69952i | − 0.275793i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.6964i | 1.32054i | 0.751030 | + | 0.660269i | \(0.229558\pi\) | ||||
−0.751030 | + | 0.660269i | \(0.770442\pi\) | |||||||
\(998\) | 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 | 6048.2.j.a.5615.6 | 8 | ||
3.2 | odd | 2 | 6048.2.j.b.5615.4 | 8 | |||
4.3 | odd | 2 | 1512.2.j.a.323.2 | ✓ | 8 | ||
8.3 | odd | 2 | 6048.2.j.b.5615.3 | 8 | |||
8.5 | even | 2 | 1512.2.j.b.323.5 | yes | 8 | ||
12.11 | even | 2 | 1512.2.j.b.323.7 | yes | 8 | ||
24.5 | odd | 2 | 1512.2.j.a.323.4 | yes | 8 | ||
24.11 | even | 2 | inner | 6048.2.j.a.5615.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.a.323.2 | ✓ | 8 | 4.3 | odd | 2 | ||
1512.2.j.a.323.4 | yes | 8 | 24.5 | odd | 2 | ||
1512.2.j.b.323.5 | yes | 8 | 8.5 | even | 2 | ||
1512.2.j.b.323.7 | yes | 8 | 12.11 | even | 2 | ||
6048.2.j.a.5615.5 | 8 | 24.11 | even | 2 | inner | ||
6048.2.j.a.5615.6 | 8 | 1.1 | even | 1 | trivial | ||
6048.2.j.b.5615.3 | 8 | 8.3 | odd | 2 | |||
6048.2.j.b.5615.4 | 8 | 3.2 | odd | 2 |