Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.3 | ||
Root | \(2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.y.1849.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 2.00000i | − 1.15470i | −0.816497 | − | 0.577350i | \(-0.804087\pi\) | ||||
0.816497 | − | 0.577350i | \(-0.195913\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | − 6.74456i | − 1.87061i | −0.353849 | − | 0.935303i | \(-0.615127\pi\) | ||||
0.353849 | − | 0.935303i | \(-0.384873\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 6.74456i | − 1.63580i | −0.575363 | − | 0.817898i | \(-0.695139\pi\) | ||||
0.575363 | − | 0.817898i | \(-0.304861\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | 6.74456 | 1.54731 | 0.773654 | − | 0.633608i | \(-0.218427\pi\) | ||||
0.773654 | + | 0.633608i | \(0.218427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | 6.74456i | 1.40634i | 0.711022 | + | 0.703169i | \(0.248232\pi\) | ||||
−0.711022 | + | 0.703169i | \(0.751768\pi\) | |||||||
\(24\) | −2.00000 | −0.408248 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.74456 | 1.32272 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | −8.74456 | −1.62382 | −0.811912 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74456 | 0.852149 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 6.74456 | 1.15668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.744563i | 0.122405i | 0.998125 | + | 0.0612027i | \(0.0194936\pi\) | ||||
−0.998125 | + | 0.0612027i | \(0.980506\pi\) | |||||||
\(38\) | 6.74456i | 1.09411i | ||||||||
\(39\) | −13.4891 | −2.15999 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.74456 | −0.994432 | ||||||||
\(47\) | 4.74456i | 0.692066i | 0.938222 | + | 0.346033i | \(0.112471\pi\) | ||||
−0.938222 | + | 0.346033i | \(0.887529\pi\) | |||||||
\(48\) | − 2.00000i | − 0.288675i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.4891 | −1.88886 | ||||||||
\(52\) | 6.74456i | 0.935303i | ||||||||
\(53\) | 12.7446i | 1.75060i | 0.483580 | + | 0.875300i | \(0.339336\pi\) | ||||
−0.483580 | + | 0.875300i | \(0.660664\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | − 13.4891i | − 1.78668i | ||||||||
\(58\) | − 8.74456i | − 1.14822i | ||||||||
\(59\) | 8.74456 | 1.13845 | 0.569223 | − | 0.822183i | \(-0.307244\pi\) | ||||
0.569223 | + | 0.822183i | \(0.307244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.25544 | 0.160742 | 0.0803711 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803711 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(62\) | 4.74456i | 0.602560i | ||||||||
\(63\) | − 1.00000i | − 0.125988i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | − 4.00000i | − 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 6.74456i | 0.817898i | ||||||||
\(69\) | 13.4891 | 1.62390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 10.7446i | − 1.25756i | −0.777585 | − | 0.628778i | \(-0.783555\pi\) | ||||
0.777585 | − | 0.628778i | \(-0.216445\pi\) | |||||||
\(74\) | −0.744563 | −0.0865536 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.74456 | −0.773654 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | − 13.4891i | − 1.52734i | ||||||||
\(79\) | −6.74456 | −0.758823 | −0.379411 | − | 0.925228i | \(-0.623873\pi\) | ||||
−0.379411 | + | 0.925228i | \(0.623873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − 4.00000i | − 0.441726i | ||||||||
\(83\) | − 8.00000i | − 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 17.4891i | 1.87503i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | −15.4891 | −1.64184 | −0.820922 | − | 0.571040i | \(-0.806540\pi\) | ||||
−0.820922 | + | 0.571040i | \(0.806540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.74456 | 0.707022 | ||||||||
\(92\) | − 6.74456i | − 0.703169i | ||||||||
\(93\) | − 9.48913i | − 0.983976i | ||||||||
\(94\) | −4.74456 | −0.489364 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | − 16.7446i | − 1.70015i | −0.526659 | − | 0.850076i | \(-0.676556\pi\) | ||||
0.526659 | − | 0.850076i | \(-0.323444\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.74456 | 0.273094 | 0.136547 | − | 0.990634i | \(-0.456399\pi\) | ||||
0.136547 | + | 0.990634i | \(0.456399\pi\) | |||||||
\(102\) | − 13.4891i | − 1.33562i | ||||||||
\(103\) | 0.744563i | 0.0733639i | 0.999327 | + | 0.0366820i | \(0.0116789\pi\) | ||||
−0.999327 | + | 0.0366820i | \(0.988321\pi\) | |||||||
\(104\) | −6.74456 | −0.661359 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.7446 | −1.23786 | ||||||||
\(107\) | − 12.0000i | − 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 4.00000i | 0.384900i | ||||||||
\(109\) | 18.2337 | 1.74647 | 0.873235 | − | 0.487299i | \(-0.162018\pi\) | ||||
0.873235 | + | 0.487299i | \(0.162018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48913 | 0.141342 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − 10.0000i | − 0.940721i | −0.882474 | − | 0.470360i | \(-0.844124\pi\) | ||||
0.882474 | − | 0.470360i | \(-0.155876\pi\) | |||||||
\(114\) | 13.4891 | 1.26337 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.74456 | 0.811912 | ||||||||
\(117\) | 6.74456i | 0.623535i | ||||||||
\(118\) | 8.74456i | 0.805002i | ||||||||
\(119\) | 6.74456 | 0.618273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.25544i | 0.113662i | ||||||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | −4.74456 | −0.426074 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.74456 | −0.239794 | −0.119897 | − | 0.992786i | \(-0.538256\pi\) | ||||
−0.119897 | + | 0.992786i | \(0.538256\pi\) | |||||||
\(132\) | − 2.00000i | − 0.174078i | ||||||||
\(133\) | 6.74456i | 0.584828i | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.74456 | −0.578341 | ||||||||
\(137\) | 3.48913i | 0.298096i | 0.988830 | + | 0.149048i | \(0.0476209\pi\) | ||||
−0.988830 | + | 0.149048i | \(0.952379\pi\) | |||||||
\(138\) | 13.4891i | 1.14827i | ||||||||
\(139\) | −14.7446 | −1.25062 | −0.625309 | − | 0.780377i | \(-0.715027\pi\) | ||||
−0.625309 | + | 0.780377i | \(0.715027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.48913 | 0.799129 | ||||||||
\(142\) | − 4.00000i | − 0.335673i | ||||||||
\(143\) | 6.74456i | 0.564009i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.7446 | 0.889226 | ||||||||
\(147\) | 2.00000i | 0.164957i | ||||||||
\(148\) | − 0.744563i | − 0.0612027i | ||||||||
\(149\) | 0.744563 | 0.0609969 | 0.0304985 | − | 0.999535i | \(-0.490291\pi\) | ||||
0.0304985 | + | 0.999535i | \(0.490291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.25544 | −0.753197 | −0.376598 | − | 0.926377i | \(-0.622906\pi\) | ||||
−0.376598 | + | 0.926377i | \(0.622906\pi\) | |||||||
\(152\) | − 6.74456i | − 0.547056i | ||||||||
\(153\) | 6.74456i | 0.545266i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.4891 | 1.07999 | ||||||||
\(157\) | 0.510875i | 0.0407722i | 0.999792 | + | 0.0203861i | \(0.00648955\pi\) | ||||
−0.999792 | + | 0.0203861i | \(0.993510\pi\) | |||||||
\(158\) | − 6.74456i | − 0.536569i | ||||||||
\(159\) | 25.4891 | 2.02142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.74456 | −0.531546 | ||||||||
\(162\) | − 11.0000i | − 0.864242i | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | − 2.00000i | − 0.154303i | ||||||||
\(169\) | −32.4891 | −2.49916 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.74456 | −0.515770 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | − 20.2337i | − 1.53834i | −0.639045 | − | 0.769169i | \(-0.720670\pi\) | ||||
0.639045 | − | 0.769169i | \(-0.279330\pi\) | |||||||
\(174\) | −17.4891 | −1.32585 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | − 17.4891i | − 1.31456i | ||||||||
\(178\) | − 15.4891i | − 1.16096i | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4891 | −1.44862 | −0.724308 | − | 0.689477i | \(-0.757840\pi\) | ||||
−0.724308 | + | 0.689477i | \(0.757840\pi\) | |||||||
\(182\) | 6.74456i | 0.499940i | ||||||||
\(183\) | − 2.51087i | − 0.185609i | ||||||||
\(184\) | 6.74456 | 0.497216 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.48913 | 0.695776 | ||||||||
\(187\) | 6.74456i | 0.493211i | ||||||||
\(188\) | − 4.74456i | − 0.346033i | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 2.00000i | 0.144338i | ||||||||
\(193\) | 2.00000i | 0.143963i | 0.997406 | + | 0.0719816i | \(0.0229323\pi\) | ||||
−0.997406 | + | 0.0719816i | \(0.977068\pi\) | |||||||
\(194\) | 16.7446 | 1.20219 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 1.00000i | 0.0710669i | ||||||||
\(199\) | −3.25544 | −0.230772 | −0.115386 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115386 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 2.74456i | 0.193107i | ||||||||
\(203\) | − 8.74456i | − 0.613748i | ||||||||
\(204\) | 13.4891 | 0.944428 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.744563 | −0.0518761 | ||||||||
\(207\) | − 6.74456i | − 0.468780i | ||||||||
\(208\) | − 6.74456i | − 0.467651i | ||||||||
\(209\) | −6.74456 | −0.466531 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | − 12.7446i | − 0.875300i | ||||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 4.74456i | 0.322082i | ||||||||
\(218\) | 18.2337i | 1.23494i | ||||||||
\(219\) | −21.4891 | −1.45210 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −45.4891 | −3.05993 | ||||||||
\(222\) | 1.48913i | 0.0999435i | ||||||||
\(223\) | − 15.2554i | − 1.02158i | −0.859706 | − | 0.510790i | \(-0.829353\pi\) | ||||
0.859706 | − | 0.510790i | \(-0.170647\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.0000 | 0.665190 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | 13.4891i | 0.893339i | ||||||||
\(229\) | 6.00000 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | −0.131590 | ||||||||
\(232\) | 8.74456i | 0.574109i | ||||||||
\(233\) | 24.9783i | 1.63638i | 0.574948 | + | 0.818190i | \(0.305022\pi\) | ||||
−0.574948 | + | 0.818190i | \(0.694978\pi\) | |||||||
\(234\) | −6.74456 | −0.440906 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.74456 | −0.569223 | ||||||||
\(237\) | 13.4891i | 0.876213i | ||||||||
\(238\) | 6.74456i | 0.437185i | ||||||||
\(239\) | 14.7446 | 0.953746 | 0.476873 | − | 0.878972i | \(-0.341770\pi\) | ||||
0.476873 | + | 0.878972i | \(0.341770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 10.0000i | 0.641500i | ||||||||
\(244\) | −1.25544 | −0.0803711 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.00000 | −0.510061 | ||||||||
\(247\) | − 45.4891i | − 2.89440i | ||||||||
\(248\) | − 4.74456i | − 0.301280i | ||||||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.2337 | −1.65586 | −0.827928 | − | 0.560835i | \(-0.810480\pi\) | ||||
−0.827928 | + | 0.560835i | \(0.810480\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | − 6.74456i | − 0.424027i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 10.2337i | − 0.638360i | −0.947694 | − | 0.319180i | \(-0.896593\pi\) | ||||
0.947694 | − | 0.319180i | \(-0.103407\pi\) | |||||||
\(258\) | − 8.00000i | − 0.498058i | ||||||||
\(259\) | −0.744563 | −0.0462649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.74456 | 0.541275 | ||||||||
\(262\) | − 2.74456i | − 0.169560i | ||||||||
\(263\) | − 26.9783i | − 1.66355i | −0.555113 | − | 0.831775i | \(-0.687325\pi\) | ||||
0.555113 | − | 0.831775i | \(-0.312675\pi\) | |||||||
\(264\) | 2.00000 | 0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.74456 | −0.413536 | ||||||||
\(267\) | 30.9783i | 1.89584i | ||||||||
\(268\) | 4.00000i | 0.244339i | ||||||||
\(269\) | −20.9783 | −1.27907 | −0.639533 | − | 0.768763i | \(-0.720872\pi\) | ||||
−0.639533 | + | 0.768763i | \(0.720872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9783 | 0.909864 | 0.454932 | − | 0.890526i | \(-0.349664\pi\) | ||||
0.454932 | + | 0.890526i | \(0.349664\pi\) | |||||||
\(272\) | − 6.74456i | − 0.408949i | ||||||||
\(273\) | − 13.4891i | − 0.816399i | ||||||||
\(274\) | −3.48913 | −0.210786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.4891 | −0.811950 | ||||||||
\(277\) | 15.4891i | 0.930651i | 0.885140 | + | 0.465326i | \(0.154063\pi\) | ||||
−0.885140 | + | 0.465326i | \(0.845937\pi\) | |||||||
\(278\) | − 14.7446i | − 0.884320i | ||||||||
\(279\) | −4.74456 | −0.284050 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0000 | 0.835170 | 0.417585 | − | 0.908638i | \(-0.362877\pi\) | ||||
0.417585 | + | 0.908638i | \(0.362877\pi\) | |||||||
\(282\) | 9.48913i | 0.565069i | ||||||||
\(283\) | − 28.0000i | − 1.66443i | −0.554455 | − | 0.832214i | \(-0.687073\pi\) | ||||
0.554455 | − | 0.832214i | \(-0.312927\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.74456 | −0.398814 | ||||||||
\(287\) | − 4.00000i | − 0.236113i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −28.4891 | −1.67583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −33.4891 | −1.96317 | ||||||||
\(292\) | 10.7446i | 0.628778i | ||||||||
\(293\) | − 13.2554i | − 0.774391i | −0.921998 | − | 0.387195i | \(-0.873444\pi\) | ||||
0.921998 | − | 0.387195i | \(-0.126556\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.744563 | 0.0432768 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | 0.744563i | 0.0431314i | ||||||||
\(299\) | 45.4891 | 2.63070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | − 9.25544i | − 0.532591i | ||||||||
\(303\) | − 5.48913i | − 0.315342i | ||||||||
\(304\) | 6.74456 | 0.386827 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.74456 | −0.385561 | ||||||||
\(307\) | − 1.48913i | − 0.0849889i | −0.999097 | − | 0.0424944i | \(-0.986470\pi\) | ||||
0.999097 | − | 0.0424944i | \(-0.0135305\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | 1.48913 | 0.0847134 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.7446 | −1.17632 | −0.588158 | − | 0.808746i | \(-0.700147\pi\) | ||||
−0.588158 | + | 0.808746i | \(0.700147\pi\) | |||||||
\(312\) | 13.4891i | 0.763671i | ||||||||
\(313\) | 2.23369i | 0.126256i | 0.998005 | + | 0.0631278i | \(0.0201076\pi\) | ||||
−0.998005 | + | 0.0631278i | \(0.979892\pi\) | |||||||
\(314\) | −0.510875 | −0.0288303 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.74456 | 0.379411 | ||||||||
\(317\) | 2.23369i | 0.125456i | 0.998031 | + | 0.0627282i | \(0.0199801\pi\) | ||||
−0.998031 | + | 0.0627282i | \(0.980020\pi\) | |||||||
\(318\) | 25.4891i | 1.42936i | ||||||||
\(319\) | 8.74456 | 0.489602 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | − 6.74456i | − 0.375860i | ||||||||
\(323\) | − 45.4891i | − 2.53108i | ||||||||
\(324\) | 11.0000 | 0.611111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | − 36.4674i | − 2.01665i | ||||||||
\(328\) | 4.00000i | 0.220863i | ||||||||
\(329\) | −4.74456 | −0.261576 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9783 | 0.823279 | 0.411640 | − | 0.911347i | \(-0.364956\pi\) | ||||
0.411640 | + | 0.911347i | \(0.364956\pi\) | |||||||
\(332\) | 8.00000i | 0.439057i | ||||||||
\(333\) | − 0.744563i | − 0.0408018i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 26.0000i | 1.41631i | 0.706057 | + | 0.708155i | \(0.250472\pi\) | ||||
−0.706057 | + | 0.708155i | \(0.749528\pi\) | |||||||
\(338\) | − 32.4891i | − 1.76718i | ||||||||
\(339\) | −20.0000 | −1.08625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.74456 | −0.256932 | ||||||||
\(342\) | − 6.74456i | − 0.364704i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.2337 | 1.08777 | ||||||||
\(347\) | − 22.9783i | − 1.23354i | −0.787145 | − | 0.616769i | \(-0.788441\pi\) | ||||
0.787145 | − | 0.616769i | \(-0.211559\pi\) | |||||||
\(348\) | − 17.4891i | − 0.937516i | ||||||||
\(349\) | −30.7446 | −1.64572 | −0.822859 | − | 0.568245i | \(-0.807623\pi\) | ||||
−0.822859 | + | 0.568245i | \(0.807623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.9783 | −1.43999 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | − 8.74456i | − 0.465426i | −0.972545 | − | 0.232713i | \(-0.925240\pi\) | ||||
0.972545 | − | 0.232713i | \(-0.0747603\pi\) | |||||||
\(354\) | 17.4891 | 0.929537 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.4891 | 0.820922 | ||||||||
\(357\) | − 13.4891i | − 0.713920i | ||||||||
\(358\) | 4.00000i | 0.211407i | ||||||||
\(359\) | 1.25544 | 0.0662594 | 0.0331297 | − | 0.999451i | \(-0.489453\pi\) | ||||
0.0331297 | + | 0.999451i | \(0.489453\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4891 | 1.39416 | ||||||||
\(362\) | − 19.4891i | − 1.02433i | ||||||||
\(363\) | − 2.00000i | − 0.104973i | ||||||||
\(364\) | −6.74456 | −0.353511 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.51087 | 0.131246 | ||||||||
\(367\) | − 8.74456i | − 0.456462i | −0.973607 | − | 0.228231i | \(-0.926706\pi\) | ||||
0.973607 | − | 0.228231i | \(-0.0732942\pi\) | |||||||
\(368\) | 6.74456i | 0.351585i | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.7446 | −0.661665 | ||||||||
\(372\) | 9.48913i | 0.491988i | ||||||||
\(373\) | 16.9783i | 0.879100i | 0.898218 | + | 0.439550i | \(0.144862\pi\) | ||||
−0.898218 | + | 0.439550i | \(0.855138\pi\) | |||||||
\(374\) | −6.74456 | −0.348753 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.74456 | 0.244682 | ||||||||
\(377\) | 58.9783i | 3.03753i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 37.4891 | 1.92569 | 0.962844 | − | 0.270060i | \(-0.0870435\pi\) | ||||
0.962844 | + | 0.270060i | \(0.0870435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 16.0000i | − 0.818631i | ||||||||
\(383\) | − 19.7228i | − 1.00779i | −0.863765 | − | 0.503894i | \(-0.831900\pi\) | ||||
0.863765 | − | 0.503894i | \(-0.168100\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 16.7446i | 0.850076i | ||||||||
\(389\) | 7.48913 | 0.379714 | 0.189857 | − | 0.981812i | \(-0.439198\pi\) | ||||
0.189857 | + | 0.981812i | \(0.439198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.4891 | 2.30048 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 5.48913i | 0.276890i | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 35.4891i | 1.78115i | 0.454838 | + | 0.890574i | \(0.349697\pi\) | ||||
−0.454838 | + | 0.890574i | \(0.650303\pi\) | |||||||
\(398\) | − 3.25544i | − 0.163180i | ||||||||
\(399\) | 13.4891 | 0.675301 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.4891 | 1.17299 | 0.586495 | − | 0.809953i | \(-0.300507\pi\) | ||||
0.586495 | + | 0.809953i | \(0.300507\pi\) | |||||||
\(402\) | − 8.00000i | − 0.399004i | ||||||||
\(403\) | − 32.0000i | − 1.59403i | ||||||||
\(404\) | −2.74456 | −0.136547 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.74456 | 0.433985 | ||||||||
\(407\) | − 0.744563i | − 0.0369066i | ||||||||
\(408\) | 13.4891i | 0.667811i | ||||||||
\(409\) | 21.4891 | 1.06257 | 0.531284 | − | 0.847194i | \(-0.321710\pi\) | ||||
0.531284 | + | 0.847194i | \(0.321710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.97825 | 0.344212 | ||||||||
\(412\) | − 0.744563i | − 0.0366820i | ||||||||
\(413\) | 8.74456i | 0.430292i | ||||||||
\(414\) | 6.74456 | 0.331477 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.74456 | 0.330679 | ||||||||
\(417\) | 29.4891i | 1.44409i | ||||||||
\(418\) | − 6.74456i | − 0.329887i | ||||||||
\(419\) | 0.744563 | 0.0363743 | 0.0181871 | − | 0.999835i | \(-0.494211\pi\) | ||||
0.0181871 | + | 0.999835i | \(0.494211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.51087 | 0.219847 | 0.109923 | − | 0.993940i | \(-0.464939\pi\) | ||||
0.109923 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(422\) | − 12.0000i | − 0.584151i | ||||||||
\(423\) | − 4.74456i | − 0.230689i | ||||||||
\(424\) | 12.7446 | 0.618931 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 1.25544i | 0.0607549i | ||||||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 13.4891 | 0.651261 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.2554 | −0.831165 | −0.415583 | − | 0.909555i | \(-0.636422\pi\) | ||||
−0.415583 | + | 0.909555i | \(0.636422\pi\) | |||||||
\(432\) | − 4.00000i | − 0.192450i | ||||||||
\(433\) | − 36.7446i | − 1.76583i | −0.469532 | − | 0.882915i | \(-0.655577\pi\) | ||||
0.469532 | − | 0.882915i | \(-0.344423\pi\) | |||||||
\(434\) | −4.74456 | −0.227746 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.2337 | −0.873235 | ||||||||
\(437\) | 45.4891i | 2.17604i | ||||||||
\(438\) | − 21.4891i | − 1.02679i | ||||||||
\(439\) | −14.9783 | −0.714873 | −0.357436 | − | 0.933937i | \(-0.616349\pi\) | ||||
−0.357436 | + | 0.933937i | \(0.616349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − 45.4891i | − 2.16370i | ||||||||
\(443\) | 29.4891i | 1.40107i | 0.713618 | + | 0.700535i | \(0.247055\pi\) | ||||
−0.713618 | + | 0.700535i | \(0.752945\pi\) | |||||||
\(444\) | −1.48913 | −0.0706708 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.2554 | 0.722366 | ||||||||
\(447\) | − 1.48913i | − 0.0704332i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | 4.97825 | 0.234938 | 0.117469 | − | 0.993077i | \(-0.462522\pi\) | ||||
0.117469 | + | 0.993077i | \(0.462522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 10.0000i | 0.470360i | ||||||||
\(453\) | 18.5109i | 0.869717i | ||||||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4891 | −0.631686 | ||||||||
\(457\) | 3.48913i | 0.163214i | 0.996665 | + | 0.0816072i | \(0.0260053\pi\) | ||||
−0.996665 | + | 0.0816072i | \(0.973995\pi\) | |||||||
\(458\) | 6.00000i | 0.280362i | ||||||||
\(459\) | −26.9783 | −1.25924 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7228 | 1.57063 | 0.785314 | − | 0.619098i | \(-0.212502\pi\) | ||||
0.785314 | + | 0.619098i | \(0.212502\pi\) | |||||||
\(462\) | − 2.00000i | − 0.0930484i | ||||||||
\(463\) | − 1.25544i | − 0.0583451i | −0.999574 | − | 0.0291726i | \(-0.990713\pi\) | ||||
0.999574 | − | 0.0291726i | \(-0.00928723\pi\) | |||||||
\(464\) | −8.74456 | −0.405956 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.9783 | −1.15710 | ||||||||
\(467\) | 16.9783i | 0.785660i | 0.919611 | + | 0.392830i | \(0.128504\pi\) | ||||
−0.919611 | + | 0.392830i | \(0.871496\pi\) | |||||||
\(468\) | − 6.74456i | − 0.311768i | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.02175 | 0.0470797 | ||||||||
\(472\) | − 8.74456i | − 0.402501i | ||||||||
\(473\) | 4.00000i | 0.183920i | ||||||||
\(474\) | −13.4891 | −0.619576 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.74456 | −0.309137 | ||||||||
\(477\) | − 12.7446i | − 0.583533i | ||||||||
\(478\) | 14.7446i | 0.674401i | ||||||||
\(479\) | 41.4891 | 1.89569 | 0.947843 | − | 0.318737i | \(-0.103259\pi\) | ||||
0.947843 | + | 0.318737i | \(0.103259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.02175 | 0.228972 | ||||||||
\(482\) | 20.0000i | 0.910975i | ||||||||
\(483\) | 13.4891i | 0.613776i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | 9.25544i | 0.419404i | 0.977765 | + | 0.209702i | \(0.0672494\pi\) | ||||
−0.977765 | + | 0.209702i | \(0.932751\pi\) | |||||||
\(488\) | − 1.25544i | − 0.0568310i | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9783 | 1.39803 | 0.699014 | − | 0.715108i | \(-0.253622\pi\) | ||||
0.699014 | + | 0.715108i | \(0.253622\pi\) | |||||||
\(492\) | − 8.00000i | − 0.360668i | ||||||||
\(493\) | 58.9783i | 2.65625i | ||||||||
\(494\) | 45.4891 | 2.04665 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.74456 | 0.213037 | ||||||||
\(497\) | − 4.00000i | − 0.179425i | ||||||||
\(498\) | − 16.0000i | − 0.716977i | ||||||||
\(499\) | 13.4891 | 0.603856 | 0.301928 | − | 0.953331i | \(-0.402370\pi\) | ||||
0.301928 | + | 0.953331i | \(0.402370\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 26.2337i | − 1.17087i | ||||||||
\(503\) | − 6.51087i | − 0.290306i | −0.989409 | − | 0.145153i | \(-0.953633\pi\) | ||||
0.989409 | − | 0.145153i | \(-0.0463674\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.74456 | 0.299832 | ||||||||
\(507\) | 64.9783i | 2.88579i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.4891 | 1.57303 | 0.786514 | − | 0.617573i | \(-0.211884\pi\) | ||||
0.786514 | + | 0.617573i | \(0.211884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.7446 | 0.475311 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 26.9783i | − 1.19112i | ||||||||
\(514\) | 10.2337 | 0.451389 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | − 4.74456i | − 0.208666i | ||||||||
\(518\) | − 0.744563i | − 0.0327142i | ||||||||
\(519\) | −40.4674 | −1.77632 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00000 | −0.0876216 | −0.0438108 | − | 0.999040i | \(-0.513950\pi\) | ||||
−0.0438108 | + | 0.999040i | \(0.513950\pi\) | |||||||
\(522\) | 8.74456i | 0.382739i | ||||||||
\(523\) | 17.4891i | 0.764746i | 0.924008 | + | 0.382373i | \(0.124893\pi\) | ||||
−0.924008 | + | 0.382373i | \(0.875107\pi\) | |||||||
\(524\) | 2.74456 | 0.119897 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.9783 | 1.17631 | ||||||||
\(527\) | − 32.0000i | − 1.39394i | ||||||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | −22.4891 | −0.977788 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.74456 | −0.379482 | ||||||||
\(532\) | − 6.74456i | − 0.292414i | ||||||||
\(533\) | 26.9783i | 1.16856i | ||||||||
\(534\) | −30.9783 | −1.34056 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | − 8.00000i | − 0.345225i | ||||||||
\(538\) | − 20.9783i | − 0.904437i | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.76631 | 0.0759397 | 0.0379698 | − | 0.999279i | \(-0.487911\pi\) | ||||
0.0379698 | + | 0.999279i | \(0.487911\pi\) | |||||||
\(542\) | 14.9783i | 0.643371i | ||||||||
\(543\) | 38.9783i | 1.67272i | ||||||||
\(544\) | 6.74456 | 0.289171 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.4891 | 0.577281 | ||||||||
\(547\) | 14.9783i | 0.640424i | 0.947346 | + | 0.320212i | \(0.103754\pi\) | ||||
−0.947346 | + | 0.320212i | \(0.896246\pi\) | |||||||
\(548\) | − 3.48913i | − 0.149048i | ||||||||
\(549\) | −1.25544 | −0.0535808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58.9783 | −2.51256 | ||||||||
\(552\) | − 13.4891i | − 0.574135i | ||||||||
\(553\) | − 6.74456i | − 0.286808i | ||||||||
\(554\) | −15.4891 | −0.658070 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.7446 | 0.625309 | ||||||||
\(557\) | − 0.978251i | − 0.0414498i | −0.999785 | − | 0.0207249i | \(-0.993403\pi\) | ||||
0.999785 | − | 0.0207249i | \(-0.00659741\pi\) | |||||||
\(558\) | − 4.74456i | − 0.200853i | ||||||||
\(559\) | −26.9783 | −1.14106 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4891 | 0.569511 | ||||||||
\(562\) | 14.0000i | 0.590554i | ||||||||
\(563\) | − 5.48913i | − 0.231339i | −0.993288 | − | 0.115670i | \(-0.963099\pi\) | ||||
0.993288 | − | 0.115670i | \(-0.0369014\pi\) | |||||||
\(564\) | −9.48913 | −0.399564 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28.0000 | 1.17693 | ||||||||
\(567\) | − 11.0000i | − 0.461957i | ||||||||
\(568\) | 4.00000i | 0.167836i | ||||||||
\(569\) | −16.5109 | −0.692172 | −0.346086 | − | 0.938203i | \(-0.612489\pi\) | ||||
−0.346086 | + | 0.938203i | \(0.612489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4891 | −0.731897 | −0.365949 | − | 0.930635i | \(-0.619255\pi\) | ||||
−0.365949 | + | 0.930635i | \(0.619255\pi\) | |||||||
\(572\) | − 6.74456i | − 0.282004i | ||||||||
\(573\) | 32.0000i | 1.33682i | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 8.74456i | − 0.364041i | −0.983295 | − | 0.182020i | \(-0.941736\pi\) | ||||
0.983295 | − | 0.182020i | \(-0.0582637\pi\) | |||||||
\(578\) | − 28.4891i | − 1.18499i | ||||||||
\(579\) | 4.00000 | 0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | − 33.4891i | − 1.38817i | ||||||||
\(583\) | − 12.7446i | − 0.527826i | ||||||||
\(584\) | −10.7446 | −0.444613 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2554 | 0.547577 | ||||||||
\(587\) | − 4.97825i | − 0.205474i | −0.994709 | − | 0.102737i | \(-0.967240\pi\) | ||||
0.994709 | − | 0.102737i | \(-0.0327601\pi\) | |||||||
\(588\) | − 2.00000i | − 0.0824786i | ||||||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.0000 | 0.822690 | ||||||||
\(592\) | 0.744563i | 0.0306013i | ||||||||
\(593\) | 40.2337i | 1.65220i | 0.563524 | + | 0.826100i | \(0.309445\pi\) | ||||
−0.563524 | + | 0.826100i | \(0.690555\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.744563 | −0.0304985 | ||||||||
\(597\) | 6.51087i | 0.266472i | ||||||||
\(598\) | 45.4891i | 1.86019i | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.4891 | −1.36605 | −0.683025 | − | 0.730395i | \(-0.739336\pi\) | ||||
−0.683025 | + | 0.730395i | \(0.739336\pi\) | |||||||
\(602\) | 4.00000i | 0.163028i | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 9.25544 | 0.376598 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.48913 | 0.222980 | ||||||||
\(607\) | 8.00000i | 0.324710i | 0.986732 | + | 0.162355i | \(0.0519090\pi\) | ||||
−0.986732 | + | 0.162355i | \(0.948091\pi\) | |||||||
\(608\) | 6.74456i | 0.273528i | ||||||||
\(609\) | −17.4891 | −0.708695 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | − 6.74456i | − 0.272633i | ||||||||
\(613\) | − 11.4891i | − 0.464041i | −0.972711 | − | 0.232021i | \(-0.925466\pi\) | ||||
0.972711 | − | 0.232021i | \(-0.0745337\pi\) | |||||||
\(614\) | 1.48913 | 0.0600962 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | − 10.0000i | − 0.402585i | −0.979531 | − | 0.201292i | \(-0.935486\pi\) | ||||
0.979531 | − | 0.201292i | \(-0.0645141\pi\) | |||||||
\(618\) | 1.48913i | 0.0599014i | ||||||||
\(619\) | −0.744563 | −0.0299265 | −0.0149632 | − | 0.999888i | \(-0.504763\pi\) | ||||
−0.0149632 | + | 0.999888i | \(0.504763\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.9783 | 1.08260 | ||||||||
\(622\) | − 20.7446i | − 0.831781i | ||||||||
\(623\) | − 15.4891i | − 0.620559i | ||||||||
\(624\) | −13.4891 | −0.539997 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.23369 | −0.0892761 | ||||||||
\(627\) | 13.4891i | 0.538704i | ||||||||
\(628\) | − 0.510875i | − 0.0203861i | ||||||||
\(629\) | 5.02175 | 0.200230 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.97825 | −0.118562 | −0.0592811 | − | 0.998241i | \(-0.518881\pi\) | ||||
−0.0592811 | + | 0.998241i | \(0.518881\pi\) | |||||||
\(632\) | 6.74456i | 0.268284i | ||||||||
\(633\) | 24.0000i | 0.953914i | ||||||||
\(634\) | −2.23369 | −0.0887111 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −25.4891 | −1.01071 | ||||||||
\(637\) | 6.74456i | 0.267229i | ||||||||
\(638\) | 8.74456i | 0.346201i | ||||||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4891 | 0.453793 | 0.226897 | − | 0.973919i | \(-0.427142\pi\) | ||||
0.226897 | + | 0.973919i | \(0.427142\pi\) | |||||||
\(642\) | − 24.0000i | − 0.947204i | ||||||||
\(643\) | − 46.4674i | − 1.83249i | −0.400613 | − | 0.916247i | \(-0.631203\pi\) | ||||
0.400613 | − | 0.916247i | \(-0.368797\pi\) | |||||||
\(644\) | 6.74456 | 0.265773 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45.4891 | 1.78975 | ||||||||
\(647\) | 8.74456i | 0.343784i | 0.985116 | + | 0.171892i | \(0.0549880\pi\) | ||||
−0.985116 | + | 0.171892i | \(0.945012\pi\) | |||||||
\(648\) | 11.0000i | 0.432121i | ||||||||
\(649\) | −8.74456 | −0.343254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.48913 | 0.371908 | ||||||||
\(652\) | − 4.00000i | − 0.156652i | ||||||||
\(653\) | − 15.7228i | − 0.615281i | −0.951503 | − | 0.307641i | \(-0.900461\pi\) | ||||
0.951503 | − | 0.307641i | \(-0.0995394\pi\) | |||||||
\(654\) | 36.4674 | 1.42599 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.00000 | −0.156174 | ||||||||
\(657\) | 10.7446i | 0.419185i | ||||||||
\(658\) | − 4.74456i | − 0.184962i | ||||||||
\(659\) | 41.4891 | 1.61619 | 0.808093 | − | 0.589054i | \(-0.200500\pi\) | ||||
0.808093 | + | 0.589054i | \(0.200500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 14.9783i | 0.582146i | ||||||||
\(663\) | 90.9783i | 3.53330i | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.744563 | 0.0288512 | ||||||||
\(667\) | − 58.9783i | − 2.28365i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.5109 | −1.17962 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.25544 | −0.0484656 | ||||||||
\(672\) | 2.00000i | 0.0771517i | ||||||||
\(673\) | − 20.9783i | − 0.808652i | −0.914615 | − | 0.404326i | \(-0.867506\pi\) | ||||
0.914615 | − | 0.404326i | \(-0.132494\pi\) | |||||||
\(674\) | −26.0000 | −1.00148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.4891 | 1.24958 | ||||||||
\(677\) | 36.2337i | 1.39257i | 0.717764 | + | 0.696287i | \(0.245166\pi\) | ||||
−0.717764 | + | 0.696287i | \(0.754834\pi\) | |||||||
\(678\) | − 20.0000i | − 0.768095i | ||||||||
\(679\) | 16.7446 | 0.642597 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.0000 | 1.53280 | ||||||||
\(682\) | − 4.74456i | − 0.181679i | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 6.74456 | 0.257885 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | − 12.0000i | − 0.457829i | ||||||||
\(688\) | − 4.00000i | − 0.152499i | ||||||||
\(689\) | 85.9565 | 3.27468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.76631 | 0.0671937 | 0.0335968 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335968 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(692\) | 20.2337i | 0.769169i | ||||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | 22.9783 | 0.872242 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17.4891 | 0.662924 | ||||||||
\(697\) | 26.9783i | 1.02187i | ||||||||
\(698\) | − 30.7446i | − 1.16370i | ||||||||
\(699\) | 49.9565 | 1.88953 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.2337 | 0.839755 | 0.419877 | − | 0.907581i | \(-0.362073\pi\) | ||||
0.419877 | + | 0.907581i | \(0.362073\pi\) | |||||||
\(702\) | − 26.9783i | − 1.01823i | ||||||||
\(703\) | 5.02175i | 0.189399i | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.74456 | 0.329106 | ||||||||
\(707\) | 2.74456i | 0.103220i | ||||||||
\(708\) | 17.4891i | 0.657282i | ||||||||
\(709\) | −0.510875 | −0.0191863 | −0.00959315 | − | 0.999954i | \(-0.503054\pi\) | ||||
−0.00959315 | + | 0.999954i | \(0.503054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.74456 | 0.252941 | ||||||||
\(712\) | 15.4891i | 0.580480i | ||||||||
\(713\) | 32.0000i | 1.19841i | ||||||||
\(714\) | 13.4891 | 0.504818 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | − 29.4891i | − 1.10129i | ||||||||
\(718\) | 1.25544i | 0.0468525i | ||||||||
\(719\) | −7.72281 | −0.288012 | −0.144006 | − | 0.989577i | \(-0.545999\pi\) | ||||
−0.144006 | + | 0.989577i | \(0.545999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.744563 | −0.0277290 | ||||||||
\(722\) | 26.4891i | 0.985823i | ||||||||
\(723\) | − 40.0000i | − 1.48762i | ||||||||
\(724\) | 19.4891 | 0.724308 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | 0.0742270 | ||||||||
\(727\) | 14.2337i | 0.527898i | 0.964537 | + | 0.263949i | \(0.0850251\pi\) | ||||
−0.964537 | + | 0.263949i | \(0.914975\pi\) | |||||||
\(728\) | − 6.74456i | − 0.249970i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.9783 | −0.997827 | ||||||||
\(732\) | 2.51087i | 0.0928046i | ||||||||
\(733\) | 16.2337i | 0.599605i | 0.954001 | + | 0.299802i | \(0.0969208\pi\) | ||||
−0.954001 | + | 0.299802i | \(0.903079\pi\) | |||||||
\(734\) | 8.74456 | 0.322768 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.74456 | −0.248608 | ||||||||
\(737\) | 4.00000i | 0.147342i | ||||||||
\(738\) | 4.00000i | 0.147242i | ||||||||
\(739\) | 30.9783 | 1.13955 | 0.569777 | − | 0.821800i | \(-0.307030\pi\) | ||||
0.569777 | + | 0.821800i | \(0.307030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −90.9783 | −3.34217 | ||||||||
\(742\) | − 12.7446i | − 0.467868i | ||||||||
\(743\) | − 26.9783i | − 0.989736i | −0.868968 | − | 0.494868i | \(-0.835216\pi\) | ||||
0.868968 | − | 0.494868i | \(-0.164784\pi\) | |||||||
\(744\) | −9.48913 | −0.347888 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.9783 | −0.621618 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | − 6.74456i | − 0.246606i | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | 4.74456i | 0.173016i | ||||||||
\(753\) | 52.4674i | 1.91202i | ||||||||
\(754\) | −58.9783 | −2.14786 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | − 19.2554i | − 0.699851i | −0.936778 | − | 0.349925i | \(-0.886207\pi\) | ||||
0.936778 | − | 0.349925i | \(-0.113793\pi\) | |||||||
\(758\) | 37.4891i | 1.36167i | ||||||||
\(759\) | −13.4891 | −0.489624 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.4891 | −1.06898 | −0.534490 | − | 0.845175i | \(-0.679496\pi\) | ||||
−0.534490 | + | 0.845175i | \(0.679496\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.2337i | 0.660104i | ||||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7228 | 0.712614 | ||||||||
\(767\) | − 58.9783i | − 2.12958i | ||||||||
\(768\) | − 2.00000i | − 0.0721688i | ||||||||
\(769\) | 8.00000 | 0.288487 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4674 | −0.737115 | ||||||||
\(772\) | − 2.00000i | − 0.0719816i | ||||||||
\(773\) | 51.4891i | 1.85194i | 0.377603 | + | 0.925968i | \(0.376748\pi\) | ||||
−0.377603 | + | 0.925968i | \(0.623252\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.7446 | −0.601095 | ||||||||
\(777\) | 1.48913i | 0.0534221i | ||||||||
\(778\) | 7.48913i | 0.268498i | ||||||||
\(779\) | −26.9783 | −0.966596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 45.4891i | 1.62669i | ||||||||
\(783\) | 34.9783i | 1.25002i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.48913 | −0.195791 | ||||||||
\(787\) | 5.48913i | 0.195666i | 0.995203 | + | 0.0978331i | \(0.0311911\pi\) | ||||
−0.995203 | + | 0.0978331i | \(0.968809\pi\) | |||||||
\(788\) | − 10.0000i | − 0.356235i | ||||||||
\(789\) | −53.9565 | −1.92090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | − 1.00000i | − 0.0355335i | ||||||||
\(793\) | − 8.46738i | − 0.300685i | ||||||||
\(794\) | −35.4891 | −1.25946 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.25544 | 0.115386 | ||||||||
\(797\) | − 42.4674i | − 1.50427i | −0.659008 | − | 0.752136i | \(-0.729024\pi\) | ||||
0.659008 | − | 0.752136i | \(-0.270976\pi\) | |||||||
\(798\) | 13.4891i | 0.477510i | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4891 | 0.547281 | ||||||||
\(802\) | 23.4891i | 0.829430i | ||||||||
\(803\) | 10.7446i | 0.379167i | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | 41.9565i | 1.47694i | ||||||||
\(808\) | − 2.74456i | − 0.0965534i | ||||||||
\(809\) | −34.4674 | −1.21181 | −0.605904 | − | 0.795538i | \(-0.707189\pi\) | ||||
−0.605904 | + | 0.795538i | \(0.707189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7446 | −0.658211 | −0.329105 | − | 0.944293i | \(-0.606747\pi\) | ||||
−0.329105 | + | 0.944293i | \(0.606747\pi\) | |||||||
\(812\) | 8.74456i | 0.306874i | ||||||||
\(813\) | − 29.9565i | − 1.05062i | ||||||||
\(814\) | 0.744563 | 0.0260969 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.4891 | −0.472214 | ||||||||
\(817\) | − 26.9783i | − 0.943850i | ||||||||
\(818\) | 21.4891i | 0.751350i | ||||||||
\(819\) | −6.74456 | −0.235674 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.72281 | 0.269528 | 0.134764 | − | 0.990878i | \(-0.456972\pi\) | ||||
0.134764 | + | 0.990878i | \(0.456972\pi\) | |||||||
\(822\) | 6.97825i | 0.243394i | ||||||||
\(823\) | − 7.76631i | − 0.270717i | −0.990797 | − | 0.135358i | \(-0.956781\pi\) | ||||
0.990797 | − | 0.135358i | \(-0.0432186\pi\) | |||||||
\(824\) | 0.744563 | 0.0259381 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.74456 | −0.304262 | ||||||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | 6.74456i | 0.234390i | ||||||||
\(829\) | −14.4674 | −0.502473 | −0.251236 | − | 0.967926i | \(-0.580837\pi\) | ||||
−0.251236 | + | 0.967926i | \(0.580837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.9783 | 1.07462 | ||||||||
\(832\) | 6.74456i | 0.233826i | ||||||||
\(833\) | 6.74456i | 0.233685i | ||||||||
\(834\) | −29.4891 | −1.02112 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.74456 | 0.233266 | ||||||||
\(837\) | − 18.9783i | − 0.655984i | ||||||||
\(838\) | 0.744563i | 0.0257205i | ||||||||
\(839\) | 3.25544 | 0.112390 | 0.0561951 | − | 0.998420i | \(-0.482103\pi\) | ||||
0.0561951 | + | 0.998420i | \(0.482103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | 4.51087i | 0.155455i | ||||||||
\(843\) | − 28.0000i | − 0.964371i | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.74456 | 0.163121 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 12.7446i | 0.437650i | ||||||||
\(849\) | −56.0000 | −1.92192 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.02175 | −0.172143 | ||||||||
\(852\) | − 8.00000i | − 0.274075i | ||||||||
\(853\) | 22.7446i | 0.778759i | 0.921077 | + | 0.389379i | \(0.127311\pi\) | ||||
−0.921077 | + | 0.389379i | \(0.872689\pi\) | |||||||
\(854\) | −1.25544 | −0.0429602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − 43.2119i | − 1.47609i | −0.674751 | − | 0.738046i | \(-0.735749\pi\) | ||||
0.674751 | − | 0.738046i | \(-0.264251\pi\) | |||||||
\(858\) | 13.4891i | 0.460511i | ||||||||
\(859\) | 29.2119 | 0.996698 | 0.498349 | − | 0.866976i | \(-0.333940\pi\) | ||||
0.498349 | + | 0.866976i | \(0.333940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | − 17.2554i | − 0.587723i | ||||||||
\(863\) | 40.2337i | 1.36957i | 0.728745 | + | 0.684785i | \(0.240104\pi\) | ||||
−0.728745 | + | 0.684785i | \(0.759896\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.7446 | 1.24863 | ||||||||
\(867\) | 56.9783i | 1.93508i | ||||||||
\(868\) | − 4.74456i | − 0.161041i | ||||||||
\(869\) | 6.74456 | 0.228794 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.9783 | −0.914123 | ||||||||
\(872\) | − 18.2337i | − 0.617471i | ||||||||
\(873\) | 16.7446i | 0.566718i | ||||||||
\(874\) | −45.4891 | −1.53869 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.4891 | 0.726050 | ||||||||
\(877\) | − 26.4674i | − 0.893740i | −0.894599 | − | 0.446870i | \(-0.852539\pi\) | ||||
0.894599 | − | 0.446870i | \(-0.147461\pi\) | |||||||
\(878\) | − 14.9783i | − 0.505491i | ||||||||
\(879\) | −26.5109 | −0.894190 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.4891 | −1.86948 | −0.934738 | − | 0.355338i | \(-0.884366\pi\) | ||||
−0.934738 | + | 0.355338i | \(0.884366\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | 8.00000i | 0.269221i | 0.990899 | + | 0.134611i | \(0.0429784\pi\) | ||||
−0.990899 | + | 0.134611i | \(0.957022\pi\) | |||||||
\(884\) | 45.4891 | 1.52996 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.4891 | −0.990707 | ||||||||
\(887\) | − 41.4891i | − 1.39307i | −0.717524 | − | 0.696534i | \(-0.754724\pi\) | ||||
0.717524 | − | 0.696534i | \(-0.245276\pi\) | |||||||
\(888\) | − 1.48913i | − 0.0499718i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.0000 | 0.368514 | ||||||||
\(892\) | 15.2554i | 0.510790i | ||||||||
\(893\) | 32.0000i | 1.07084i | ||||||||
\(894\) | 1.48913 | 0.0498038 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | − 90.9783i | − 3.03768i | ||||||||
\(898\) | 4.97825i | 0.166126i | ||||||||
\(899\) | −41.4891 | −1.38374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 85.9565 | 2.86363 | ||||||||
\(902\) | 4.00000i | 0.133185i | ||||||||
\(903\) | − 8.00000i | − 0.266223i | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.5109 | −0.614983 | ||||||||
\(907\) | − 14.5109i | − 0.481826i | −0.970547 | − | 0.240913i | \(-0.922553\pi\) | ||||
0.970547 | − | 0.240913i | \(-0.0774468\pi\) | |||||||
\(908\) | − 20.0000i | − 0.663723i | ||||||||
\(909\) | −2.74456 | −0.0910314 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.0000 | 0.662630 | 0.331315 | − | 0.943520i | \(-0.392508\pi\) | ||||
0.331315 | + | 0.943520i | \(0.392508\pi\) | |||||||
\(912\) | − 13.4891i | − 0.446670i | ||||||||
\(913\) | 8.00000i | 0.264761i | ||||||||
\(914\) | −3.48913 | −0.115410 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | − 2.74456i | − 0.0906334i | ||||||||
\(918\) | − 26.9783i | − 0.890415i | ||||||||
\(919\) | 55.2119 | 1.82127 | 0.910637 | − | 0.413207i | \(-0.135592\pi\) | ||||
0.910637 | + | 0.413207i | \(0.135592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.97825 | −0.0981367 | ||||||||
\(922\) | 33.7228i | 1.11060i | ||||||||
\(923\) | 26.9783i | 0.888000i | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.25544 | 0.0412562 | ||||||||
\(927\) | − 0.744563i | − 0.0244546i | ||||||||
\(928\) | − 8.74456i | − 0.287054i | ||||||||
\(929\) | 28.9783 | 0.950746 | 0.475373 | − | 0.879784i | \(-0.342313\pi\) | ||||
0.475373 | + | 0.879784i | \(0.342313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.74456 | −0.221044 | ||||||||
\(932\) | − 24.9783i | − 0.818190i | ||||||||
\(933\) | 41.4891i | 1.35829i | ||||||||
\(934\) | −16.9783 | −0.555545 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.74456 | 0.220453 | ||||||||
\(937\) | − 18.7446i | − 0.612358i | −0.951974 | − | 0.306179i | \(-0.900949\pi\) | ||||
0.951974 | − | 0.306179i | \(-0.0990506\pi\) | |||||||
\(938\) | 4.00000i | 0.130605i | ||||||||
\(939\) | 4.46738 | 0.145787 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.2337 | 0.398807 | 0.199403 | − | 0.979917i | \(-0.436100\pi\) | ||||
0.199403 | + | 0.979917i | \(0.436100\pi\) | |||||||
\(942\) | 1.02175i | 0.0332904i | ||||||||
\(943\) | − 26.9783i | − 0.878533i | ||||||||
\(944\) | 8.74456 | 0.284611 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | − 8.00000i | − 0.259965i | −0.991516 | − | 0.129983i | \(-0.958508\pi\) | ||||
0.991516 | − | 0.129983i | \(-0.0414921\pi\) | |||||||
\(948\) | − 13.4891i | − 0.438106i | ||||||||
\(949\) | −72.4674 | −2.35239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.46738 | 0.144865 | ||||||||
\(952\) | − 6.74456i | − 0.218593i | ||||||||
\(953\) | − 6.00000i | − 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 12.7446 | 0.412620 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.7446 | −0.476873 | ||||||||
\(957\) | − 17.4891i | − 0.565343i | ||||||||
\(958\) | 41.4891i | 1.34045i | ||||||||
\(959\) | −3.48913 | −0.112670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 5.02175i | 0.161908i | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | −20.0000 | −0.644157 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.4891 | −0.434005 | ||||||||
\(967\) | − 50.9783i | − 1.63935i | −0.572829 | − | 0.819675i | \(-0.694154\pi\) | ||||
0.572829 | − | 0.819675i | \(-0.305846\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | −90.9783 | −2.92264 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7228 | 0.632935 | 0.316468 | − | 0.948603i | \(-0.397503\pi\) | ||||
0.316468 | + | 0.948603i | \(0.397503\pi\) | |||||||
\(972\) | − 10.0000i | − 0.320750i | ||||||||
\(973\) | − 14.7446i | − 0.472689i | ||||||||
\(974\) | −9.25544 | −0.296563 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.25544 | 0.0401856 | ||||||||
\(977\) | 12.9783i | 0.415211i | 0.978213 | + | 0.207606i | \(0.0665670\pi\) | ||||
−0.978213 | + | 0.207606i | \(0.933433\pi\) | |||||||
\(978\) | 8.00000i | 0.255812i | ||||||||
\(979\) | 15.4891 | 0.495035 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.2337 | −0.582157 | ||||||||
\(982\) | 30.9783i | 0.988556i | ||||||||
\(983\) | − 2.23369i | − 0.0712436i | −0.999365 | − | 0.0356218i | \(-0.988659\pi\) | ||||
0.999365 | − | 0.0356218i | \(-0.0113412\pi\) | |||||||
\(984\) | 8.00000 | 0.255031 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −58.9783 | −1.87825 | ||||||||
\(987\) | 9.48913i | 0.302042i | ||||||||
\(988\) | 45.4891i | 1.44720i | ||||||||
\(989\) | 26.9783 | 0.857858 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.48913 | 0.0473036 | 0.0236518 | − | 0.999720i | \(-0.492471\pi\) | ||||
0.0236518 | + | 0.999720i | \(0.492471\pi\) | |||||||
\(992\) | 4.74456i | 0.150640i | ||||||||
\(993\) | − 29.9565i | − 0.950641i | ||||||||
\(994\) | 4.00000 | 0.126872 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | 39.2119i | 1.24185i | 0.783868 | + | 0.620927i | \(0.213244\pi\) | ||||
−0.783868 | + | 0.620927i | \(0.786756\pi\) | |||||||
\(998\) | 13.4891i | 0.426991i | ||||||||
\(999\) | 2.97825 | 0.0942277 |
(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 | 3850.2.c.y.1849.3 | 4 | ||
5.2 | odd | 4 | 3850.2.a.bc.1.1 | 2 | |||
5.3 | odd | 4 | 770.2.a.k.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 3850.2.c.y.1849.2 | 4 | ||
15.8 | even | 4 | 6930.2.a.bo.1.2 | 2 | |||
20.3 | even | 4 | 6160.2.a.r.1.2 | 2 | |||
35.13 | even | 4 | 5390.2.a.bq.1.1 | 2 | |||
55.43 | even | 4 | 8470.2.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.k.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
3850.2.a.bc.1.1 | 2 | 5.2 | odd | 4 | |||
3850.2.c.y.1849.2 | 4 | 5.4 | even | 2 | inner | ||
3850.2.c.y.1849.3 | 4 | 1.1 | even | 1 | trivial | ||
5390.2.a.bq.1.1 | 2 | 35.13 | even | 4 | |||
6160.2.a.r.1.2 | 2 | 20.3 | even | 4 | |||
6930.2.a.bo.1.2 | 2 | 15.8 | even | 4 | |||
8470.2.a.bu.1.1 | 2 | 55.43 | even | 4 |