Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(609,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1216.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.c (of order \(2\), degree \(1\), 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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.3 | ||
Root | \(-0.396143 - 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.609 |
Dual form | 1216.2.c.h.609.6 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.37228i | − 1.36964i | −0.728714 | − | 0.684819i | \(-0.759881\pi\) | ||||
0.728714 | − | 0.684819i | \(-0.240119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.792287i | − 0.354322i | −0.984182 | − | 0.177161i | \(-0.943309\pi\) | ||||
0.984182 | − | 0.177161i | \(-0.0566913\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.31662 | 1.25357 | 0.626783 | − | 0.779194i | \(-0.284371\pi\) | ||||
0.626783 | + | 0.779194i | \(0.284371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.62772 | −0.875906 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.37228i | 1.01678i | 0.861127 | + | 0.508391i | \(0.169759\pi\) | ||||
−0.861127 | + | 0.508391i | \(0.830241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.10891i | − 1.13961i | −0.821781 | − | 0.569804i | \(-0.807019\pi\) | ||||
0.821781 | − | 0.569804i | \(-0.192981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.87953 | −0.485292 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 7.86797i | − 1.71693i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.52434 | 0.526361 | 0.263180 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263180 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.37228 | 0.874456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 0.883156i | − 0.169963i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.98844i | − 1.11203i | −0.831174 | − | 0.556013i | \(-0.812331\pi\) | ||||
0.831174 | − | 0.556013i | \(-0.187669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.46410 | −0.622171 | −0.311086 | − | 0.950382i | \(-0.600693\pi\) | ||||
−0.311086 | + | 0.950382i | \(0.600693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.62772i | − 0.444166i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.16915i | − 0.521005i | −0.965473 | − | 0.260502i | \(-0.916112\pi\) | ||||
0.965473 | − | 0.260502i | \(-0.0838882\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.74749 | −1.56085 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.37228i | 1.42926i | 0.699503 | + | 0.714630i | \(0.253405\pi\) | ||||
−0.699503 | + | 0.714630i | \(0.746595\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.08191i | 0.310352i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.30506 | −1.35728 | −0.678642 | − | 0.734470i | \(-0.737431\pi\) | ||||
−0.678642 | + | 0.734470i | \(0.737431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 11.8614i | − 1.66093i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.45254i | 1.29841i | 0.760615 | + | 0.649203i | \(0.224898\pi\) | ||||
−0.760615 | + | 0.649203i | \(0.775102\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.67181 | 0.360267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.37228 | −0.314216 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.37228i | 0.569223i | 0.958643 | + | 0.284611i | \(0.0918645\pi\) | ||||
−0.958643 | + | 0.284611i | \(0.908135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.55134i | − 0.582740i | −0.956610 | − | 0.291370i | \(-0.905889\pi\) | ||||
0.956610 | − | 0.291370i | \(-0.0941110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.71516 | −1.09801 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.25544 | −0.403787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.37228i | − 1.02284i | −0.859332 | − | 0.511418i | \(-0.829120\pi\) | ||||
0.859332 | − | 0.511418i | \(-0.170880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 5.98844i | − 0.720923i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.63325 | −0.787222 | −0.393611 | − | 0.919277i | \(-0.628774\pi\) | ||||
−0.393611 | + | 0.919277i | \(0.628774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4891 | −1.69582 | −0.847912 | − | 0.530137i | \(-0.822140\pi\) | ||||
−0.847912 | + | 0.530137i | \(0.822140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 10.3723i | − 1.19769i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.1846i | 1.27460i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5615 | 1.52578 | 0.762891 | − | 0.646527i | \(-0.223779\pi\) | ||||
0.762891 | + | 0.646527i | \(0.223779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.97825 | −1.10869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.00000i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.96143i | − 0.429678i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.2063 | −1.52307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.48913 | 0.793846 | 0.396923 | − | 0.917852i | \(-0.370078\pi\) | ||||
0.396923 | + | 0.917852i | \(0.370078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 13.6277i | − 1.42857i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21782i | 0.852149i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.792287 | −0.0812869 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.74456 | 0.887876 | 0.443938 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443938 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 8.86141i | − 0.890605i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 13.8564i | − 1.37876i | −0.724398 | − | 0.689382i | \(-0.757882\pi\) | ||||
0.724398 | − | 0.689382i | \(-0.242118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.34363 | −0.526523 | −0.263262 | − | 0.964724i | \(-0.584798\pi\) | ||||
−0.263262 | + | 0.964724i | \(0.584798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.23369 | −0.608346 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.62772i | 0.737399i | 0.929549 | + | 0.368700i | \(0.120197\pi\) | ||||
−0.929549 | + | 0.368700i | \(0.879803\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 12.6217i | − 1.20894i | −0.796628 | − | 0.604469i | \(-0.793385\pi\) | ||||
0.796628 | − | 0.604469i | \(-0.206615\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.51811 | −0.713587 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25544 | −0.306246 | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||||
−0.153123 | + | 0.988207i | \(0.548933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.00000i | − 0.186501i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.7971i | 0.998189i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.5831 | 1.52017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.372281 | −0.0338438 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 7.42554i | − 0.664160i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.9051 | −1.67755 | −0.838777 | − | 0.544475i | \(-0.816729\pi\) | ||||
−0.838777 | + | 0.544475i | \(0.816729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.2337 | 1.95757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.37228i | − 0.119897i | −0.998201 | − | 0.0599484i | \(-0.980906\pi\) | ||||
0.998201 | − | 0.0599484i | \(-0.0190936\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.31662i | − 0.287588i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.699713 | −0.0602217 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00000 | 0.427179 | 0.213589 | − | 0.976924i | \(-0.431485\pi\) | ||||
0.213589 | + | 0.976924i | \(0.431485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.37228i | 0.794947i | 0.917614 | + | 0.397473i | \(0.130113\pi\) | ||||
−0.917614 | + | 0.397473i | \(0.869887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.0742i | 1.85899i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.8564 | 1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.74456 | −0.394014 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 9.48913i | − 0.782650i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.2819i | 1.74348i | 0.489965 | + | 0.871742i | \(0.337010\pi\) | ||||
−0.489965 | + | 0.871742i | \(0.662990\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.3692 | −1.82038 | −0.910189 | − | 0.414193i | \(-0.864064\pi\) | ||||
−0.910189 | + | 0.414193i | \(0.864064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.1386 | −1.06219 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74456i | 0.220449i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.28962i | 0.102923i | 0.998675 | + | 0.0514615i | \(0.0163879\pi\) | ||||
−0.998675 | + | 0.0514615i | \(0.983612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.4241 | 1.77835 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.37228 | 0.659828 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.744563i | 0.0583186i | 0.999575 | + | 0.0291593i | \(0.00928302\pi\) | ||||
−0.999575 | + | 0.0291593i | \(0.990717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 6.33830i | − 0.493436i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1947 | 1.56271 | 0.781356 | − | 0.624085i | \(-0.214528\pi\) | ||||
0.781356 | + | 0.624085i | \(0.214528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.88316 | −0.298704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.62772i | 0.200947i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.75372i | − 0.361419i | −0.983537 | − | 0.180709i | \(-0.942161\pi\) | ||||
0.983537 | − | 0.180709i | \(-0.0578393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.5012 | 1.09619 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3723 | 0.779628 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783i | 1.71748i | 0.512416 | + | 0.858738i | \(0.328751\pi\) | ||||
−0.512416 | + | 0.858738i | \(0.671249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 11.6819i | − 0.868311i | −0.900838 | − | 0.434155i | \(-0.857047\pi\) | ||||
0.900838 | − | 0.434155i | \(-0.142953\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7971 | −0.798142 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.51087 | −0.184603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8614i | 1.23303i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.92910i | − 0.213060i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7089 | 0.991943 | 0.495972 | − | 0.868339i | \(-0.334812\pi\) | ||||
0.495972 | + | 0.868339i | \(0.334812\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7446 | 1.06134 | 0.530668 | − | 0.847580i | \(-0.321941\pi\) | ||||
0.530668 | + | 0.847580i | \(0.321941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.72281i | 0.553042i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.1947i | 1.43881i | 0.694589 | + | 0.719406i | \(0.255586\pi\) | ||||
−0.694589 | + | 0.719406i | \(0.744414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.78073 | 0.480673 | 0.240336 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240336 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8614 | −1.40092 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 19.8614i | − 1.39400i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.63325 | −0.461043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.37228 | 0.233266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.37228i | 0.576372i | 0.957575 | + | 0.288186i | \(0.0930521\pi\) | ||||
−0.957575 | + | 0.288186i | \(0.906948\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.7359i | 1.07821i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.42554 | 0.506417 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4891 | −0.779933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.3723i | 2.32266i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 20.5446i | − 1.38198i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4891 | −0.765942 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.11684i | − 0.206872i | −0.994636 | − | 0.103436i | \(-0.967016\pi\) | ||||
0.994636 | − | 0.103436i | \(-0.0329837\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.96143i | − 0.261779i | −0.991397 | − | 0.130889i | \(-0.958217\pi\) | ||||
0.991397 | − | 0.130889i | \(-0.0417833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.5330 | 1.74574 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.1168 | −1.84200 | −0.920998 | − | 0.389568i | \(-0.872624\pi\) | ||||
−0.920998 | + | 0.389568i | \(0.872624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37228i | 0.480915i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 32.1716i | − 2.08977i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.1012 | 1.55898 | 0.779490 | − | 0.626415i | \(-0.215478\pi\) | ||||
0.779490 | + | 0.626415i | \(0.215478\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.0217i | 1.34855i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.16915i | − 0.202469i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.10891 | −0.261444 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.9783 | 1.20270 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 10.8614i | − 0.685566i | −0.939415 | − | 0.342783i | \(-0.888630\pi\) | ||||
0.939415 | − | 0.342783i | \(-0.111370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.51278i | 0.535194i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.39764 | −0.588503 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2337 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 10.5109i | − 0.653114i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.7359i | 0.974030i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1561 | 1.48953 | 0.744766 | − | 0.667326i | \(-0.232561\pi\) | ||||
0.744766 | + | 0.667326i | \(0.232561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.48913 | 0.460053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 17.7663i | − 1.08728i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.51278i | 0.519033i | 0.965739 | + | 0.259517i | \(0.0835632\pi\) | ||||
−0.965739 | + | 0.259517i | \(0.916437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.57301 | 0.460028 | 0.230014 | − | 0.973187i | \(-0.426123\pi\) | ||||
0.230014 | + | 0.973187i | \(0.426123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −32.3288 | −1.95663 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.7446i | 0.889131i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13.0641i | − 0.784947i | −0.919763 | − | 0.392473i | \(-0.871619\pi\) | ||||
0.919763 | − | 0.392473i | \(-0.128381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.10268 | 0.544963 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.2337 | −1.68428 | −0.842140 | − | 0.539258i | \(-0.818705\pi\) | ||||
−0.842140 | + | 0.539258i | \(0.818705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.3723i | − 1.38934i | −0.719330 | − | 0.694669i | \(-0.755551\pi\) | ||||
0.719330 | − | 0.694669i | \(-0.244449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.87953i | 0.111334i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 20.7446i | − 1.21607i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.0627i | 1.63944i | 0.572765 | + | 0.819719i | \(0.305871\pi\) | ||||
−0.572765 | + | 0.819719i | \(0.694129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | 0.201688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.97825 | 0.172816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 10.3723i | − 0.599845i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.0843i | 1.79167i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.8713 | −1.88841 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.60597 | −0.206477 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.7446i | 1.52639i | 0.646167 | + | 0.763196i | \(0.276371\pi\) | ||||
−0.646167 | + | 0.763196i | \(0.723629\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.6766i | 0.721146i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2164 | 1.31648 | 0.658240 | − | 0.752808i | \(-0.271301\pi\) | ||||
0.658240 | + | 0.752808i | \(0.271301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1168 | 1.19359 | 0.596797 | − | 0.802392i | \(-0.296440\pi\) | ||||
0.596797 | + | 0.802392i | \(0.296440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.90491i | 0.389047i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2603i | 1.02560i | 0.858508 | + | 0.512800i | \(0.171392\pi\) | ||||
−0.858508 | + | 0.512800i | \(0.828608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1947 | 1.13069 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0951 | 1.00997 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.00000i | − 0.278207i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 17.9653i | − 0.996537i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.9422 | −1.65581 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.8614 | −1.70144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 17.8614i | − 0.981752i | −0.871230 | − | 0.490876i | \(-0.836677\pi\) | ||||
0.871230 | − | 0.490876i | \(-0.163323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.32763i | 0.456351i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.63325 | −0.362413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7446 | −1.34792 | −0.673961 | − | 0.738767i | \(-0.735408\pi\) | ||||
−0.673961 | + | 0.738767i | \(0.735408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.72281i | 0.419446i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 11.6819i | − 0.632612i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.94987 | −0.537243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.74456 | −0.255439 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8832i | 1.06738i | 0.845679 | + | 0.533692i | \(0.179196\pi\) | ||||
−0.845679 | + | 0.533692i | \(0.820804\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1615i | 1.23981i | 0.784679 | + | 0.619903i | \(0.212828\pi\) | ||||
−0.784679 | + | 0.619903i | \(0.787172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.62881 | −0.193692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1168 | 1.12394 | 0.561968 | − | 0.827159i | \(-0.310044\pi\) | ||||
0.561968 | + | 0.827159i | \(0.310044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.25544i | 0.278930i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 39.3398i | − 2.08208i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.5831 | −0.875224 | −0.437612 | − | 0.899164i | \(-0.644176\pi\) | ||||
−0.437612 | + | 0.899164i | \(0.644176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.883156i | 0.0463537i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4795i | 0.600867i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.5870 | −1.59663 | −0.798314 | − | 0.602241i | \(-0.794275\pi\) | ||||
−0.798314 | + | 0.602241i | \(0.794275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.3505i | 1.62764i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8935i | 1.28894i | 0.764631 | + | 0.644469i | \(0.222921\pi\) | ||||
−0.764631 | + | 0.644469i | \(0.777079\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.6155 | −0.909659 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.6060 | −1.26727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.3505i | − 0.788504i | −0.919002 | − | 0.394252i | \(-0.871004\pi\) | ||||
0.919002 | − | 0.394252i | \(-0.128996\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.8482i | 2.29764i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.92287 | −0.404840 | −0.202420 | − | 0.979299i | \(-0.564881\pi\) | ||||
−0.202420 | + | 0.979299i | \(0.564881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.86141 | 0.451619 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 24.6277i | − 1.25190i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12.1793i | − 0.617513i | −0.951141 | − | 0.308756i | \(-0.900087\pi\) | ||||
0.951141 | − | 0.308756i | \(-0.0999128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.6217 | 0.638306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.25544 | −0.164215 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 10.7446i | − 0.540618i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9.30506i | − 0.467008i | −0.972356 | − | 0.233504i | \(-0.924981\pi\) | ||||
0.972356 | − | 0.233504i | \(-0.0750192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.86797 | −0.393891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.7228 | −1.08479 | −0.542393 | − | 0.840125i | \(-0.682482\pi\) | ||||
−0.542393 | + | 0.840125i | \(0.682482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.2337i | 0.709030i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.90564i | 0.392834i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6873 | 0.529748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 11.8614i | − 0.585080i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.5012i | 0.713558i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.33830 | 0.311135 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.2337 | 1.08879 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.2337i | 1.67243i | 0.548405 | + | 0.836213i | \(0.315235\pi\) | ||||
−0.548405 | + | 0.836213i | \(0.684765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.9855i | 1.75383i | 0.480647 | + | 0.876914i | \(0.340402\pi\) | ||||
−0.480647 | + | 0.876914i | \(0.659598\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.4511 | 1.18885 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.8614 | 1.06043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 15.0951i | − 0.730503i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 32.8713i | − 1.58704i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3870 | −0.548491 | −0.274246 | − | 0.961660i | \(-0.588428\pi\) | ||||
−0.274246 | + | 0.961660i | \(0.588428\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4891 | 1.03270 | 0.516351 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516351 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.2554i | 0.539657i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.52434i | − 0.120755i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.92820 | 0.330665 | 0.165333 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165333 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5109 | −0.500518 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10.3505i | − 0.491769i | −0.969299 | − | 0.245884i | \(-0.920922\pi\) | ||||
0.969299 | − | 0.245884i | \(-0.0790783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.93354i | − 0.281277i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 50.4868 | 2.38794 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.5109 | 0.684811 | 0.342405 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342405 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.0660i | 2.49326i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7971 | −0.506174 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.0000 | 1.45012 | 0.725059 | − | 0.688686i | \(-0.241812\pi\) | ||||
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.41578i | − 0.206111i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1846i | 0.520918i | 0.965485 | + | 0.260459i | \(0.0838739\pi\) | ||||
−0.965485 | + | 0.260459i | \(0.916126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.31040 | −0.386217 | −0.193108 | − | 0.981177i | \(-0.561857\pi\) | ||||
−0.193108 | + | 0.981177i | \(0.561857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.51087 | 0.301935 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 28.1168i | − 1.30109i | −0.759467 | − | 0.650546i | \(-0.774540\pi\) | ||||
0.759467 | − | 0.650546i | \(-0.225460\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 27.7677i | − 1.28219i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.05934 | 0.140967 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.6060 | −1.45324 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.37228i | − 0.200614i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 24.8386i | − 1.13728i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.1514 | −0.646592 | −0.323296 | − | 0.946298i | \(-0.604791\pi\) | ||||
−0.323296 | + | 0.946298i | \(0.604791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0217 | −0.593741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 19.8614i | − 0.903725i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 6.92820i | − 0.314594i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.2974 | −1.32759 | −0.663796 | − | 0.747914i | \(-0.731056\pi\) | ||||
−0.663796 | + | 0.747914i | \(0.731056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.76631 | 0.0798754 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 14.9783i | − 0.675959i | −0.941153 | − | 0.337979i | \(-0.890257\pi\) | ||||
0.941153 | − | 0.337979i | \(-0.109743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 29.9422i | − 1.34853i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.02078 | −0.315560 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.0000 | −0.986835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.37228i | − 0.0614317i | −0.999528 | − | 0.0307159i | \(-0.990221\pi\) | ||||
0.999528 | − | 0.0307159i | \(-0.00977870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 47.9075i | − 2.14035i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.4294 | 0.955491 | 0.477745 | − | 0.878498i | \(-0.341454\pi\) | ||||
0.477745 | + | 0.878498i | \(0.341454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9783 | −0.488526 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.21194i | 0.409117i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 24.5437i | − 1.08788i | −0.839124 | − | 0.543939i | \(-0.816932\pi\) | ||||
0.839124 | − | 0.543939i | \(-0.183068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.0550 | −2.12583 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.883156 | −0.0389923 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.23369i | 0.186559i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 31.3793i | − 1.38006i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2772 | −0.495013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.2337 | −1.76267 | −0.881335 | − | 0.472492i | \(-0.843355\pi\) | ||||
−0.881335 | + | 0.472492i | \(0.843355\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 19.6277i | − 0.858260i | −0.903243 | − | 0.429130i | \(-0.858820\pi\) | ||||
0.903243 | − | 0.429130i | \(-0.141180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 34.4010i | − 1.50138i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3205 | −0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6277 | −0.722944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 11.4891i | − 0.498586i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.04334 | 0.261276 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.5109 | 2.35232 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.4891i | 0.581018i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 33.5538i | − 1.44259i | −0.692628 | − | 0.721295i | \(-0.743547\pi\) | ||||
0.692628 | − | 0.721295i | \(-0.256453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.7128 | −1.18927 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4891i | 1.08984i | 0.838489 | + | 0.544918i | \(0.183439\pi\) | ||||
−0.838489 | + | 0.544918i | \(0.816561\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9596i | 0.510425i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.98844 | −0.255116 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.9783 | 1.91267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.95650i | 0.252839i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.5051i | 1.20780i | 0.797060 | + | 0.603900i | \(0.206387\pi\) | ||||
−0.797060 | + | 0.603900i | \(0.793613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.5099 | 1.62879 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | 1.68880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9.48913i | − 0.399919i | −0.979804 | − | 0.199959i | \(-0.935919\pi\) | ||||
0.979804 | − | 0.199959i | \(-0.0640811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.57924i | 0.108509i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −33.0941 | −1.38982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9783 | 0.795610 | 0.397805 | − | 0.917470i | \(-0.369772\pi\) | ||||
0.397805 | + | 0.917470i | \(0.369772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.97825i | − 0.124636i | −0.998056 | − | 0.0623180i | \(-0.980151\pi\) | ||||
0.998056 | − | 0.0623180i | \(-0.0198493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 32.5214i | − 1.35860i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.0371 | 0.460280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.4674 | −1.47653 | −0.738263 | − | 0.674513i | \(-0.764354\pi\) | ||||
−0.738263 | + | 0.674513i | \(0.764354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 34.9783i | − 1.45365i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.5330i | 1.10077i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.8766 | −1.32020 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.55437 | 0.353680 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.13859i | − 0.129544i | −0.997900 | − | 0.0647718i | \(-0.979368\pi\) | ||||
0.997900 | − | 0.0647718i | \(-0.0206319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.46410i | 0.142736i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 47.9075 | 1.97065 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.9783 | −1.68278 | −0.841388 | − | 0.540432i | \(-0.818261\pi\) | ||||
−0.841388 | + | 0.540432i | \(0.818261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 13.1386i | − 0.538630i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 16.0858i | − 0.658348i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0564 | 1.35065 | 0.675325 | − | 0.737520i | \(-0.264003\pi\) | ||||
0.675325 | + | 0.737520i | \(0.264003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.4674 | 1.89544 | 0.947722 | − | 0.319097i | \(-0.103380\pi\) | ||||
0.947722 | + | 0.319097i | \(0.103380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.0000i | 0.895909i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.294954i | 0.0119916i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.62792 | −0.309608 | −0.154804 | − | 0.987945i | \(-0.549475\pi\) | ||||
−0.154804 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −47.1168 | −1.90927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.2337i | 1.54677i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 35.1383i | − 1.41922i | −0.704592 | − | 0.709612i | \(-0.748870\pi\) | ||||
0.704592 | − | 0.709612i | \(-0.251130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.8397 | 1.36233 | 0.681167 | − | 0.732128i | \(-0.261473\pi\) | ||||
0.681167 | + | 0.732128i | \(0.261473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2337i | 0.732874i | 0.930443 | + | 0.366437i | \(0.119422\pi\) | ||||
−0.930443 | + | 0.366437i | \(0.880578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.22938i | − 0.0894621i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.8386 | 0.995138 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.9783 | 0.639130 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 8.00000i | − 0.319489i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 15.8457i | − 0.631811i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8843 | −0.473107 | −0.236553 | − | 0.971619i | \(-0.576018\pi\) | ||||
−0.236553 | + | 0.971619i | \(0.576018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.8614 | 0.789420 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9783i | 0.594394i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 16.4356i | − 0.651204i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.4303 | 0.689533 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.9783 | 1.38156 | 0.690779 | − | 0.723066i | \(-0.257268\pi\) | ||||
0.690779 | + | 0.723066i | \(0.257268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.6277i | − 1.20784i | −0.797045 | − | 0.603920i | \(-0.793605\pi\) | ||||
0.797045 | − | 0.603920i | \(-0.206395\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 17.6155i | − 0.693608i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5831 | −0.651950 | −0.325975 | − | 0.945378i | \(-0.605693\pi\) | ||||
−0.325975 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.7446 | −0.578775 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.2554i | 1.06822i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.5200i | 1.85960i | 0.368064 | + | 0.929800i | \(0.380021\pi\) | ||||
−0.368064 | + | 0.929800i | \(0.619979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.08724 | −0.0424820 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.0733 | 1.48538 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1386i | 0.706579i | 0.935514 | + | 0.353290i | \(0.114937\pi\) | ||||
−0.935514 | + | 0.353290i | \(0.885063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.2549i | − 0.748930i | −0.927241 | − | 0.374465i | \(-0.877826\pi\) | ||||
0.927241 | − | 0.374465i | \(-0.122174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.7375 | −1.89281 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.62772 | −0.101899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 15.1168i | − 0.585327i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 16.4356i | − 0.635439i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3484 | 0.592519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.25544 | 0.202582 | 0.101291 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101291 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 3.86141i | − 0.148626i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.10891i | 0.157918i | 0.996878 | + | 0.0789592i | \(0.0251597\pi\) | ||||
−0.996878 | + | 0.0789592i | \(0.974840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.0024 | 1.11301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.39403 | −0.283340 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12.0000i | − 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.96143i | − 0.151359i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.39764 | −0.358542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.8397 | 1.47967 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.8614i | 0.413187i | 0.978427 | + | 0.206594i | \(0.0662378\pi\) | ||||
−0.978427 | + | 0.206594i | \(0.933762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 29.3900i | − 1.11643i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.42554 | 0.281667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 66.7011i | 2.52287i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7128i | 1.04670i | 0.852118 | + | 0.523349i | \(0.175318\pi\) | ||||
−0.852118 | + | 0.523349i | \(0.824682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.16915 | −0.119527 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4891 | 0.658679 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 45.9565i | − 1.72837i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.699713i | 0.0262783i | 0.999914 | + | 0.0131391i | \(0.00418244\pi\) | ||||
−0.999914 | + | 0.0131391i | \(0.995818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.6357 | −1.33644 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.74456 | −0.327486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 10.9783i | − 0.410563i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 57.1749i | − 2.13524i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.89587 | −0.219879 | −0.109939 | − | 0.993938i | \(-0.535066\pi\) | ||||
−0.109939 | + | 0.993938i | \(0.535066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.7228 | −0.660032 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 18.9783i | − 0.705809i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 26.1831i | − 0.972417i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6371 | 0.765389 | 0.382694 | − | 0.923875i | \(-0.374996\pi\) | ||||
0.382694 | + | 0.923875i | \(0.374996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9348 | 0.738324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.8614i | 1.73323i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5099i | 1.42239i | 0.702992 | + | 0.711197i | \(0.251847\pi\) | ||||
−0.702992 | + | 0.711197i | \(0.748153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.51811 | −0.277310 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.2337 | 1.04000 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 27.6060i | − 1.01550i | −0.861504 | − | 0.507751i | \(-0.830477\pi\) | ||||
0.861504 | − | 0.507751i | \(-0.169523\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.74749i | 0.358083i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.63325 | −0.243350 | −0.121675 | − | 0.992570i | \(-0.538827\pi\) | ||||
−0.121675 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.8614 | 0.617754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 21.0217i | − 0.769146i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.2983i | 0.924379i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.2921 | −1.10537 | −0.552686 | − | 0.833389i | \(-0.686397\pi\) | ||||
−0.552686 | + | 0.833389i | \(0.686397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.7663 | −0.938977 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.7228i | 0.644999i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.6998i | 1.77002i | 0.465568 | + | 0.885012i | \(0.345850\pi\) | ||||
−0.465568 | + | 0.885012i | \(0.654150\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.1947 | 0.733021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | −0.398750 | −0.199375 | − | 0.979923i | \(-0.563891\pi\) | ||||
−0.199375 | + | 0.979923i | \(0.563891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 41.8614i | − 1.51548i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.4095i | 0.376358i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.9653 | 0.648690 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.4674 | −1.13474 | −0.567371 | − | 0.823462i | \(-0.692040\pi\) | ||||
−0.567371 | + | 0.823462i | \(0.692040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 43.2554i | − 1.55781i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9600i | 0.681943i | 0.940074 | + | 0.340972i | \(0.110756\pi\) | ||||
−0.940074 | + | 0.340972i | \(0.889244\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1460 | −0.544061 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.9348 | −0.894529 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 22.3692i | − 0.800432i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.28873 | −0.189004 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.02175 | 0.0364678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 20.6060i | − 0.734523i | −0.930118 | − | 0.367262i | \(-0.880295\pi\) | ||||
0.930118 | − | 0.367262i | \(-0.119705\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 57.3052i | − 2.04012i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7971 | −0.383899 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7011 | −0.664094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 17.7663i | − 0.630106i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 11.3321i | − 0.401402i | −0.979652 | − | 0.200701i | \(-0.935678\pi\) | ||||
0.979652 | − | 0.200701i | \(-0.0643220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.5253 | −1.64595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.6793 | −0.695334 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 48.8614i | − 1.72428i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.63325i | − 0.233791i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.1947 | 0.710887 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.97825 | 0.280500 | 0.140250 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140250 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.138593i | 0.00486667i | 0.999997 | + | 0.00243334i | \(0.000774556\pi\) | ||||
−0.999997 | + | 0.00243334i | \(0.999225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 17.9653i | − 0.630071i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.589907 | 0.0206636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.37228 | 0.327895 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.8098i | 1.25130i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.0179i | 1.29193i | 0.763366 | + | 0.645966i | \(0.223545\pi\) | ||||
−0.763366 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2704 | −0.950586 | −0.475293 | − | 0.879828i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.9783 | 1.21779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11.3505i | − 0.394697i | −0.980333 | − | 0.197348i | \(-0.936767\pi\) | ||||
0.980333 | − | 0.197348i | \(-0.0632330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1113i | 1.15000i | 0.818152 | + | 0.575002i | \(0.194999\pi\) | ||||
−0.818152 | + | 0.575002i | \(0.805001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.9918 | −1.07509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0000 | 0.692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 16.0000i | − 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.05934i | 0.105746i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.7306 | −0.577604 | −0.288802 | − | 0.957389i | \(-0.593257\pi\) | ||||
−0.288802 | + | 0.957389i | \(0.593257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.86141 | −0.236600 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 66.9783i | 2.30685i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.07657i | 0.105837i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.23472 | −0.0424254 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −55.4456 | −1.90289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.00000i | − 0.274236i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6766i | 0.434038i | 0.976167 | + | 0.217019i | \(0.0696334\pi\) | ||||
−0.976167 | + | 0.217019i | \(0.930367\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.08191 | 0.0711997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.2337 | −0.417895 | −0.208947 | − | 0.977927i | \(-0.567004\pi\) | ||||
−0.208947 | + | 0.977927i | \(0.567004\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.6060i | 1.07838i | 0.842184 | + | 0.539191i | \(0.181270\pi\) | ||||
−0.842184 | + | 0.539191i | \(0.818730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.1971 | −1.67469 | −0.837345 | − | 0.546675i | \(-0.815893\pi\) | ||||
−0.837345 | + | 0.546675i | \(0.815893\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.76631 | −0.128058 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 18.9783i | − 0.644535i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.7330i | 1.55139i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.4010 | −1.16563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.9783 | −0.777696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 24.6277i | − 0.832569i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 24.5986i | − 0.830635i | −0.909677 | − | 0.415317i | \(-0.863671\pi\) | ||||
0.909677 | − | 0.415317i | \(-0.136329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 66.5725 | 2.24544 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37228 | 0.0462333 | 0.0231167 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231167 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.1168i | 1.21543i | 0.794156 | + | 0.607714i | \(0.207913\pi\) | ||||
−0.794156 | + | 0.607714i | \(0.792087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 8.21782i | − 0.276239i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0333 | −1.51207 | −0.756035 | − | 0.654531i | \(-0.772866\pi\) | ||||
−0.756035 | + | 0.654531i | \(0.772866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −62.7011 | −2.10293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 33.6495i | − 1.12730i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.30506i | 0.311382i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.2054 | 0.608538 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.6060 | −0.821569 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.7446i | 0.691870i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.2627i | 1.57455i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.7408 | 2.45394 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.25544 | −0.307661 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 18.1386i | − 0.602282i | −0.953580 | − | 0.301141i | \(-0.902632\pi\) | ||||
0.953580 | − | 0.301141i | \(-0.0973675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.4107i | 1.20767i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.81306 | −0.258858 | −0.129429 | − | 0.991589i | \(-0.541314\pi\) | ||||
−0.129429 | + | 0.991589i | \(0.541314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.9783 | −0.892850 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.55437i | 0.282799i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.55134i | − 0.150299i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7677 | −0.915972 | −0.457986 | − | 0.888959i | \(-0.651429\pi\) | ||||
−0.457986 | + | 0.888959i | \(0.651429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 63.4456 | 2.09060 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.2554i | 0.897124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 13.8564i | − 0.455596i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0416 | 0.461185 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.1168 | −1.48024 | −0.740118 | − | 0.672477i | \(-0.765230\pi\) | ||||
−0.740118 | + | 0.672477i | \(0.765230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.00000i | − 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 55.0758i | − 1.80310i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3591 | 0.436888 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.9783 | 0.783335 | 0.391668 | − | 0.920107i | \(-0.371898\pi\) | ||||
0.391668 | + | 0.920107i | \(0.371898\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 50.0951i | − 1.63479i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.69349i | − 0.185602i | −0.995685 | − | 0.0928012i | \(-0.970418\pi\) | ||||
0.995685 | − | 0.0928012i | \(-0.0295821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.32069 | −0.0754919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 37.2119i | − 1.20923i | −0.796520 | − | 0.604613i | \(-0.793328\pi\) | ||||
0.796520 | − | 0.604613i | \(-0.206672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.5345i | 1.93257i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.3185 | 1.40470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.23369 | −0.266715 | −0.133358 | − | 0.991068i | \(-0.542576\pi\) | ||||
−0.133358 | + | 0.991068i | \(0.542576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 10.8614i | − 0.351467i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 47.9075i | − 1.54863i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.5831 | 0.535497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 20.0435i | − 0.645893i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 11.6819i | − 0.376054i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8642 | 1.34626 | 0.673131 | − | 0.739524i | \(-0.264949\pi\) | ||||
0.673131 | + | 0.739524i | \(0.264949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.8614 | −0.381043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000i | 0.128366i | 0.997938 | + | 0.0641831i | \(0.0204442\pi\) | ||||
−0.997938 | + | 0.0641831i | \(0.979556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.0843i | 0.996518i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.6188 | −1.36489 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.51087 | 0.144316 | 0.0721578 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721578 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.2554i | 0.807167i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1662i | 1.05892i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.22849 | 0.198658 | 0.0993290 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993290 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 73.2119i | 2.33036i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.6588i | 0.752306i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.2434 | 0.801882 | 0.400941 | − | 0.916104i | \(-0.368683\pi\) | ||||
0.400941 | + | 0.916104i | \(0.368683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.3723 | −1.34464 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 5.37228i | − 0.170313i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2997i | 0.326196i | 0.986610 | + | 0.163098i | \(0.0521486\pi\) | ||||
−0.986610 | + | 0.163098i | \(0.947851\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.79885 | −0.0885518 |
(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 | 1216.2.c.h.609.3 | ✓ | 8 | |
4.3 | odd | 2 | inner | 1216.2.c.h.609.5 | yes | 8 | |
8.3 | odd | 2 | inner | 1216.2.c.h.609.4 | yes | 8 | |
8.5 | even | 2 | inner | 1216.2.c.h.609.6 | yes | 8 | |
16.3 | odd | 4 | 4864.2.a.bl.1.1 | 4 | |||
16.5 | even | 4 | 4864.2.a.bl.1.2 | 4 | |||
16.11 | odd | 4 | 4864.2.a.bi.1.4 | 4 | |||
16.13 | even | 4 | 4864.2.a.bi.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.h.609.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1216.2.c.h.609.4 | yes | 8 | 8.3 | odd | 2 | inner | |
1216.2.c.h.609.5 | yes | 8 | 4.3 | odd | 2 | inner | |
1216.2.c.h.609.6 | yes | 8 | 8.5 | even | 2 | inner | |
4864.2.a.bi.1.3 | 4 | 16.13 | even | 4 | |||
4864.2.a.bi.1.4 | 4 | 16.11 | odd | 4 | |||
4864.2.a.bl.1.1 | 4 | 16.3 | odd | 4 | |||
4864.2.a.bl.1.2 | 4 | 16.5 | even | 4 |