Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 13x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Root | \(3.12250 - 1.80278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.116 |
Dual form | 637.2.r.b.324.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −3.12250 | + | 1.80278i | −1.39642 | + | 0.806226i | −0.994016 | − | 0.109235i | \(-0.965160\pi\) |
−0.402408 | + | 0.915460i | \(0.631827\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.60555i | − | 1.00000i | ||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12250 | + | 1.80278i | −0.716350 | + | 0.413585i | −0.813408 | − | 0.581694i | \(-0.802390\pi\) |
0.0970575 | + | 0.995279i | \(0.469057\pi\) | |||||||
\(20\) | − | 7.21110i | − | 1.61245i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | − | 6.92820i | 0.800000 | − | 1.38564i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.36750 | − | 5.40833i | −1.68245 | − | 0.971364i | −0.960024 | − | 0.279918i | \(-0.909693\pi\) |
−0.722428 | − | 0.691446i | \(-0.756974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.21110i | − | 1.12619i | −0.826394 | − | 0.563093i | \(-0.809611\pi\) | ||
0.826394 | − | 0.563093i | \(-0.190389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000 | 1.37249 | 0.686244 | − | 0.727372i | \(-0.259258\pi\) | ||||
0.686244 | + | 0.727372i | \(0.259258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.36750 | − | 5.40833i | −1.39642 | − | 0.806226i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.12250 | + | 1.80278i | −0.455463 | + | 0.262962i | −0.710135 | − | 0.704066i | \(-0.751366\pi\) |
0.254671 | + | 0.967028i | \(0.418033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.24500 | + | 3.60555i | 0.866025 | + | 0.500000i | ||||
\(53\) | −5.50000 | + | 9.52628i | −0.755483 | + | 1.30854i | 0.189651 | + | 0.981852i | \(0.439264\pi\) |
−0.945134 | + | 0.326683i | \(0.894069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4900 | + | 7.21110i | 1.62606 | + | 0.938806i | 0.985253 | + | 0.171103i | \(0.0547329\pi\) |
0.640806 | + | 0.767703i | \(0.278600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 6.50000 | + | 11.2583i | 0.806226 | + | 1.39642i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.36750 | − | 5.40833i | −1.09638 | − | 0.632997i | −0.161114 | − | 0.986936i | \(-0.551509\pi\) |
−0.935269 | + | 0.353939i | \(0.884842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.21110i | − | 0.827170i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.50000 | − | 12.9904i | −0.843816 | − | 1.46153i | −0.886646 | − | 0.462450i | \(-0.846971\pi\) |
0.0428296 | − | 0.999082i | \(-0.486363\pi\) | |||||||
\(80\) | 12.4900 | + | 7.21110i | 1.39642 | + | 0.806226i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.0278i | 1.97880i | 0.145204 | + | 0.989402i | \(0.453616\pi\) | ||||
−0.145204 | + | 0.989402i | \(0.546384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.12250 | + | 1.80278i | −0.330984 | + | 0.191094i | −0.656278 | − | 0.754519i | \(-0.727870\pi\) |
0.325294 | + | 0.945613i | \(0.394537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.50000 | − | 11.2583i | 0.666886 | − | 1.15508i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0278i | 1.83044i | 0.402953 | + | 0.915221i | \(0.367984\pi\) | ||||
−0.402953 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.00000 | + | 13.8564i | 0.800000 | + | 1.38564i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.0000 | −1.78737 | −0.893685 | − | 0.448695i | \(-0.851889\pi\) | ||||
−0.893685 | + | 0.448695i | \(0.851889\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.12250 | + | 1.80278i | 0.291175 | + | 0.168110i | ||||
\(116\) | 5.00000 | − | 8.66025i | 0.464238 | − | 0.804084i | ||||
\(117\) | 9.36750 | − | 5.40833i | 0.866025 | − | 0.500000i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | − | 9.52628i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.7350 | − | 10.8167i | 1.68245 | − | 0.971364i | ||||
\(125\) | 10.8167i | 0.967471i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | − | 10.3923i | 0.500000 | − | 0.866025i | ||||
\(145\) | 15.6125 | − | 9.01388i | 1.29655 | − | 0.748562i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 39.0000 | 3.13256 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(164\) | 12.4900 | + | 7.21110i | 0.975305 | + | 0.563093i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0278i | 1.39503i | 0.716570 | + | 0.697515i | \(0.245711\pi\) | ||||
−0.716570 | + | 0.697515i | \(0.754289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.36750 | − | 5.40833i | −0.716350 | − | 0.413585i | ||||
\(172\) | −9.00000 | + | 15.5885i | −0.686244 | + | 1.18861i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5000 | + | 21.6506i | −0.934294 | + | 1.61824i | −0.158406 | + | 0.987374i | \(0.550635\pi\) |
−0.775888 | + | 0.630870i | \(0.782698\pi\) | |||||||
\(180\) | 18.7350 | − | 10.8167i | 1.39642 | − | 0.806226i | ||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 7.21110i | − | 0.525924i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.0000 | + | 17.3205i | 0.723575 | + | 1.25327i | 0.959558 | + | 0.281511i | \(0.0908356\pi\) |
−0.235983 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.0000 | + | 22.5167i | 0.907959 | + | 1.57263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50000 | − | 2.59808i | 0.104257 | − | 0.180579i | ||||
\(208\) | −12.4900 | + | 7.21110i | −0.866025 | + | 0.500000i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | −11.0000 | − | 19.0526i | −0.755483 | − | 1.30854i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.1025 | + | 16.2250i | −1.91657 | + | 1.10653i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0278i | 1.20723i | 0.797277 | + | 0.603614i | \(0.206273\pi\) | ||||
−0.797277 | + | 0.603614i | \(0.793727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 24.0000 | 1.60000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4900 | + | 7.21110i | 0.828990 | + | 0.478618i | 0.853507 | − | 0.521082i | \(-0.174471\pi\) |
−0.0245166 | + | 0.999699i | \(0.507805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7350 | − | 10.8167i | 1.23804 | − | 0.714785i | 0.269349 | − | 0.963043i | \(-0.413191\pi\) |
0.968694 | + | 0.248258i | \(0.0798581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5000 | − | 25.1147i | −0.949927 | − | 1.64532i | −0.745573 | − | 0.666424i | \(-0.767824\pi\) |
−0.204354 | − | 0.978897i | \(-0.565509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.50000 | − | 11.2583i | 0.424013 | − | 0.734412i | ||||
\(236\) | −24.9800 | + | 14.4222i | −1.62606 | + | 0.938806i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.36750 | − | 5.40833i | −0.603414 | − | 0.348381i | 0.166970 | − | 0.985962i | \(-0.446602\pi\) |
−0.770383 | + | 0.637581i | \(0.779935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.50000 | + | 11.2583i | 0.413585 | + | 0.716350i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −26.0000 | −1.61245 | ||||||||
\(261\) | −7.50000 | − | 12.9904i | −0.464238 | − | 0.804084i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5000 | − | 26.8468i | 0.955771 | − | 1.65544i | 0.223177 | − | 0.974778i | \(-0.428357\pi\) |
0.732594 | − | 0.680666i | \(-0.238309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 39.6611i | − | 2.43636i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.9800 | + | 14.4222i | −1.51743 | + | 0.876087i | −0.517636 | + | 0.855601i | \(0.673188\pi\) |
−0.999790 | + | 0.0204858i | \(0.993479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 32.4500i | − | 1.94273i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.7350 | − | 10.8167i | 1.09638 | − | 0.632997i | ||||
\(293\) | 18.0278i | 1.05319i | 0.850115 | + | 0.526596i | \(0.176532\pi\) | ||||
−0.850115 | + | 0.526596i | \(0.823468\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −52.0000 | −3.02756 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.12250 | + | 1.80278i | −0.180579 | + | 0.104257i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.4900 | + | 7.21110i | 0.716350 | + | 0.413585i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.4500i | − | 1.85202i | −0.377503 | − | 0.926009i | \(-0.623217\pi\) | ||
0.377503 | − | 0.926009i | \(-0.376783\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.0000 | 1.68763 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −24.9800 | + | 14.4222i | −1.39642 | + | 0.806226i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −9.00000 | − | 15.5885i | −0.500000 | − | 0.866025i | ||||
\(325\) | −24.9800 | − | 14.4222i | −1.38564 | − | 0.800000i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −31.2250 | − | 18.0278i | −1.71369 | − | 0.989402i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.0000 | + | 27.7128i | −0.858925 | + | 1.48770i | 0.0140303 | + | 0.999902i | \(0.495534\pi\) |
−0.872955 | + | 0.487800i | \(0.837799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.4500i | − | 1.73701i | −0.495683 | − | 0.868503i | \(-0.665082\pi\) | ||
0.495683 | − | 0.868503i | \(-0.334918\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.2250 | − | 18.0278i | −1.66194 | − | 0.959521i | −0.971788 | − | 0.235854i | \(-0.924211\pi\) |
−0.690150 | − | 0.723666i | \(-0.742456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 7.21110i | − | 0.382188i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.0000 | 2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 18.7350 | − | 10.8167i | 0.975305 | − | 0.563093i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.00000 | + | 5.19615i | 0.155334 | + | 0.269047i | 0.933181 | − | 0.359408i | \(-0.117021\pi\) |
−0.777847 | + | 0.628454i | \(0.783688\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0278i | 0.928477i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 13.0000 | + | 22.5167i | 0.666886 | + | 1.15508i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.9800 | + | 14.4222i | −1.27642 | + | 0.736940i | −0.976188 | − | 0.216927i | \(-0.930397\pi\) |
−0.300230 | + | 0.953867i | \(0.597063\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.5000 | + | 23.3827i | 0.686244 | + | 1.18861i | ||||
\(388\) | −31.2250 | − | 18.0278i | −1.58521 | − | 0.915221i | ||||
\(389\) | 5.00000 | − | 8.66025i | 0.253510 | − | 0.439092i | −0.710980 | − | 0.703213i | \(-0.751748\pi\) |
0.964490 | + | 0.264120i | \(0.0850816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.8375 | + | 27.0416i | 2.35665 | + | 1.36061i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.12250 | + | 1.80278i | −0.156714 | + | 0.0904787i | −0.576306 | − | 0.817234i | \(-0.695506\pi\) |
0.419592 | + | 0.907713i | \(0.362173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −32.0000 | −1.60000 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.5000 | + | 33.7750i | −0.971364 | + | 1.68245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 32.4500i | − | 1.61245i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3475 | + | 19.8305i | 1.69837 | + | 0.980557i | 0.947305 | + | 0.320333i | \(0.103795\pi\) |
0.751069 | + | 0.660224i | \(0.229539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.5000 | − | 56.2917i | −1.59536 | − | 2.76325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.36750 | − | 5.40833i | −0.455463 | − | 0.262962i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0000 | 0.773389 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.12250 | + | 1.80278i | 0.149369 | + | 0.0862385i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.5000 | + | 35.5070i | 0.973984 | + | 1.68699i | 0.683247 | + | 0.730188i | \(0.260567\pi\) |
0.290738 | + | 0.956803i | \(0.406099\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.50000 | − | 11.2583i | 0.308130 | − | 0.533696i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 19.0000 | − | 32.9090i | 0.893685 | − | 1.54791i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.24500 | + | 3.60555i | −0.291175 | + | 0.168110i | ||||
\(461\) | − | 7.21110i | − | 0.335855i | −0.985799 | − | 0.167927i | \(-0.946293\pi\) | ||
0.985799 | − | 0.167927i | \(-0.0537074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 10.0000 | + | 17.3205i | 0.464238 | + | 0.804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 21.6333i | 1.00000i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8444i | 1.32347i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −33.0000 | −1.51097 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.3475 | + | 19.8305i | 1.56938 | + | 0.906080i | 0.996241 | + | 0.0866194i | \(0.0276064\pi\) |
0.573135 | + | 0.819461i | \(0.305727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | −32.5000 | − | 56.2917i | −1.47575 | − | 2.55607i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −40.0000 | −1.80517 | −0.902587 | − | 0.430507i | \(-0.858335\pi\) | ||||
−0.902587 | + | 0.430507i | \(0.858335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.2666i | 1.94273i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(500\) | −18.7350 | − | 10.8167i | −0.837854 | − | 0.483735i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000 | − | 20.7846i | 0.532414 | − | 0.922168i | ||||
\(509\) | −3.12250 | + | 1.80278i | −0.138402 | + | 0.0799066i | −0.567602 | − | 0.823303i | \(-0.692129\pi\) |
0.429200 | + | 0.903209i | \(0.358796\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43.2666i | 1.87761i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0000 | −1.12619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9800 | + | 14.4222i | 1.07998 | + | 0.623526i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0000 | 1.58201 | 0.791003 | − | 0.611812i | \(-0.209559\pi\) | ||||
0.791003 | + | 0.611812i | \(0.209559\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.6125 | − | 9.01388i | 0.665115 | − | 0.384004i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 32.4500i | − | 1.37249i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 59.3275 | − | 34.2527i | 2.49593 | − | 1.44102i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.500000 | − | 0.866025i | −0.0209611 | − | 0.0363057i | 0.855355 | − | 0.518043i | \(-0.173339\pi\) |
−0.876316 | + | 0.481737i | \(0.840006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50000 | − | 2.59808i | 0.0627730 | − | 0.108726i | −0.832931 | − | 0.553377i | \(-0.813339\pi\) |
0.895704 | + | 0.444651i | \(0.146672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | −31.2250 | − | 18.0278i | −1.29991 | − | 0.750505i | −0.319524 | − | 0.947578i | \(-0.603523\pi\) |
−0.980389 | + | 0.197073i | \(0.936856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 36.0555i | 1.49712i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.5000 | + | 33.7750i | −0.806226 | + | 1.39642i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0278i | 0.744085i | 0.928216 | + | 0.372043i | \(0.121342\pi\) | ||||
−0.928216 | + | 0.372043i | \(0.878658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.0000 | 1.60697 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.5925 | − | 23.4361i | 1.66693 | − | 0.962405i | 0.697657 | − | 0.716432i | \(-0.254226\pi\) |
0.969277 | − | 0.245973i | \(-0.0791073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.50000 | + | 9.52628i | −0.224724 | + | 0.389233i | −0.956237 | − | 0.292595i | \(-0.905481\pi\) |
0.731513 | + | 0.681828i | \(0.238815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.3475 | + | 19.8305i | 1.39642 | + | 0.806226i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.50000 | + | 11.2583i | 0.262962 | + | 0.455463i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4900 | + | 7.21110i | 0.502015 | + | 0.289839i | 0.729545 | − | 0.683932i | \(-0.239732\pi\) |
−0.227530 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(620\) | −39.0000 | + | 67.5500i | −1.56628 | + | 2.71287i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.4700 | − | 21.6333i | 1.48695 | − | 0.858492i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.50000 | − | 14.7224i | 0.335730 | − | 0.581501i | −0.647895 | − | 0.761730i | \(-0.724350\pi\) |
0.983625 | + | 0.180229i | \(0.0576838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.2666i | 1.70627i | 0.521691 | + | 0.853134i | \(0.325301\pi\) | ||||
−0.521691 | + | 0.853134i | \(0.674699\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | + | 29.4449i | 0.665261 | + | 1.15227i | 0.979214 | + | 0.202828i | \(0.0650132\pi\) |
−0.313953 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.9800 | + | 14.4222i | −0.975305 | + | 0.563093i | ||||
\(657\) | − | 32.4500i | − | 1.26599i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.0000 | −0.740135 | −0.370067 | − | 0.929005i | \(-0.620665\pi\) | ||||
−0.370067 | + | 0.929005i | \(0.620665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.36750 | − | 5.40833i | −0.364353 | − | 0.210360i | 0.306635 | − | 0.951827i | \(-0.400797\pi\) |
−0.670989 | + | 0.741468i | \(0.734130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.50000 | + | 4.33013i | 0.0968004 | + | 0.167663i | ||||
\(668\) | −31.2250 | − | 18.0278i | −1.20813 | − | 0.697515i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.0000 | 1.96591 | 0.982953 | − | 0.183858i | \(-0.0588587\pi\) | ||||
0.982953 | + | 0.183858i | \(0.0588587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | − | 22.5167i | 0.500000 | − | 0.866025i | ||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 18.7350 | − | 10.8167i | 0.716350 | − | 0.413585i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.0000 | − | 31.1769i | −0.686244 | − | 1.18861i | ||||
\(689\) | 34.3475 | + | 19.8305i | 1.30854 | + | 0.755483i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.5925 | − | 23.4361i | 1.54421 | − | 0.891551i | 0.545645 | − | 0.838016i | \(-0.316285\pi\) |
0.998566 | − | 0.0535342i | \(-0.0170486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.5000 | − | 38.9711i | 0.843816 | − | 1.46153i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.8167i | 0.405087i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.0000 | − | 43.3013i | −0.934294 | − | 1.61824i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 43.2666i | 1.61245i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0000 | + | 34.6410i | −0.742781 | + | 1.28654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.8375 | + | 27.0416i | −1.72998 | + | 0.998806i | −0.840560 | + | 0.541718i | \(0.817774\pi\) |
−0.889422 | + | 0.457087i | \(0.848893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −46.8375 | + | 27.0416i | −1.71369 | + | 0.989402i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5000 | + | 23.3827i | 0.492622 | + | 0.853246i | 0.999964 | − | 0.00849853i | \(-0.00270520\pi\) |
−0.507342 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(752\) | 12.4900 | + | 7.21110i | 0.455463 | + | 0.262962i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.0000 | −1.70824 | −0.854122 | − | 0.520073i | \(-0.825905\pi\) | ||||
−0.854122 | + | 0.520073i | \(0.825905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.5925 | − | 23.4361i | 1.47148 | − | 0.849557i | 0.471990 | − | 0.881604i | \(-0.343536\pi\) |
0.999486 | + | 0.0320465i | \(0.0102025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −40.0000 | −1.44715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.0000 | − | 45.0333i | 0.938806 | − | 1.62606i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.4500i | − | 1.17018i | −0.810970 | − | 0.585088i | \(-0.801060\pi\) | ||
0.810970 | − | 0.585088i | \(-0.198940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.2250 | − | 18.0278i | −1.12308 | − | 0.648413i | −0.180898 | − | 0.983502i | \(-0.557900\pi\) |
−0.942187 | + | 0.335089i | \(0.891234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −74.9400 | + | 43.2666i | −2.69192 | + | 1.55418i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.0000 | + | 22.5167i | 0.465773 | + | 0.806743i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.3475 | + | 19.8305i | 1.22436 | + | 0.706882i | 0.965844 | − | 0.259126i | \(-0.0834344\pi\) |
0.258512 | + | 0.966008i | \(0.416768\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.36750 | − | 5.40833i | −0.330984 | − | 0.191094i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5000 | − | 26.8468i | 0.544951 | − | 0.943883i | −0.453659 | − | 0.891175i | \(-0.649882\pi\) |
0.998610 | − | 0.0527074i | \(-0.0167851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2666i | 1.51930i | 0.650334 | + | 0.759648i | \(0.274629\pi\) | ||||
−0.650334 | + | 0.759648i | \(0.725371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.1025 | + | 16.2250i | −0.983182 | + | 0.567640i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −52.0000 | −1.81592 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | + | 3.46410i | −0.0697156 | + | 0.120751i | −0.898776 | − | 0.438408i | \(-0.855543\pi\) |
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 3.00000 | + | 5.19615i | 0.104257 | + | 0.180579i | ||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 28.8444i | − | 1.00000i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.5000 | − | 56.2917i | −1.12471 | − | 1.94805i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 57.6888i | − | 1.99164i | −0.0913415 | − | 0.995820i | \(-0.529115\pi\) | ||
0.0913415 | − | 0.995820i | \(-0.470885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.00000 | − | 8.66025i | 0.172107 | − | 0.298098i | ||||
\(845\) | 40.5925 | − | 23.4361i | 1.39642 | − | 0.806226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 44.0000 | 1.51097 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0278i | 0.617259i | 0.951182 | + | 0.308629i | \(0.0998703\pi\) | ||||
−0.951182 | + | 0.308629i | \(0.900130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39.0000 | 1.33377 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | − | 64.8999i | − | 2.21307i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −46.8375 | + | 27.0416i | −1.58521 | + | 0.915221i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.2250 | − | 18.0278i | −1.04549 | − | 0.603614i | ||||
\(893\) | 6.50000 | − | 11.2583i | 0.217514 | − | 0.376746i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 90.1388i | − | 3.01301i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.8375 | + | 27.0416i | 1.56212 | + | 0.901889i | ||||
\(900\) | −24.0000 | + | 41.5692i | −0.800000 | + | 1.38564i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5000 | + | 45.8993i | −0.879918 | + | 1.52406i | −0.0284883 | + | 0.999594i | \(0.509069\pi\) |
−0.851430 | + | 0.524469i | \(0.824264\pi\) | |||||||
\(908\) | −24.9800 | + | 14.4222i | −0.828990 | + | 0.478618i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0000 | 1.22586 | 0.612932 | − | 0.790135i | \(-0.289990\pi\) | ||||
0.612932 | + | 0.790135i | \(0.289990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.2666i | 1.42957i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0000 | + | 17.3205i | 0.329870 | + | 0.571351i | 0.982486 | − | 0.186338i | \(-0.0596619\pi\) |
−0.652616 | + | 0.757689i | \(0.726329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.12250 | + | 1.80278i | −0.102446 | + | 0.0591472i | −0.550348 | − | 0.834936i | \(-0.685505\pi\) |
0.447902 | + | 0.894083i | \(0.352171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 58.0000 | 1.89985 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.0000 | + | 22.5167i | 0.424013 | + | 0.734412i | ||||
\(941\) | −53.0825 | − | 30.6472i | −1.73044 | − | 0.999070i | −0.886782 | − | 0.462188i | \(-0.847065\pi\) |
−0.843657 | − | 0.536882i | \(-0.819602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.24500 | + | 3.60555i | −0.203365 | + | 0.117413i | ||||
\(944\) | − | 57.6888i | − | 1.87761i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5000 | + | 33.7750i | −0.632997 | + | 1.09638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −61.0000 | −1.97598 | −0.987992 | − | 0.154506i | \(-0.950622\pi\) | ||||
−0.987992 | + | 0.154506i | \(0.950622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62.4500 | − | 36.0555i | −2.02083 | − | 1.16673i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.0000 | + | 74.4782i | 1.38710 | + | 2.40252i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000 | − | 20.7846i | 0.386695 | − | 0.669775i | ||||
\(964\) | 18.7350 | − | 10.8167i | 0.603414 | − | 0.348381i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.0825 | − | 30.6472i | −1.69307 | − | 0.977493i | −0.952017 | − | 0.306045i | \(-0.900994\pi\) |
−0.741051 | − | 0.671449i | \(-0.765672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −26.0000 | −0.827170 | ||||||||
\(989\) | −4.50000 | − | 7.79423i | −0.143092 | − | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.0000 | + | 51.9615i | −0.952981 | + | 1.65061i | −0.214060 | + | 0.976820i | \(0.568669\pi\) |
−0.738921 | + | 0.673792i | \(0.764664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.r.b.116.1 | 4 | ||
7.2 | even | 3 | inner | 637.2.r.b.324.2 | 4 | ||
7.3 | odd | 6 | 637.2.c.b.246.2 | yes | 2 | ||
7.4 | even | 3 | 637.2.c.b.246.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 637.2.r.b.324.1 | 4 | ||
7.6 | odd | 2 | inner | 637.2.r.b.116.2 | 4 | ||
13.12 | even | 2 | inner | 637.2.r.b.116.2 | 4 | ||
91.12 | odd | 6 | inner | 637.2.r.b.324.2 | 4 | ||
91.18 | odd | 12 | 8281.2.a.u.1.1 | 2 | |||
91.25 | even | 6 | 637.2.c.b.246.2 | yes | 2 | ||
91.31 | even | 12 | 8281.2.a.u.1.2 | 2 | |||
91.38 | odd | 6 | 637.2.c.b.246.1 | ✓ | 2 | ||
91.51 | even | 6 | inner | 637.2.r.b.324.1 | 4 | ||
91.60 | odd | 12 | 8281.2.a.u.1.2 | 2 | |||
91.73 | even | 12 | 8281.2.a.u.1.1 | 2 | |||
91.90 | odd | 2 | CM | 637.2.r.b.116.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.b.246.1 | ✓ | 2 | 7.4 | even | 3 | ||
637.2.c.b.246.1 | ✓ | 2 | 91.38 | odd | 6 | ||
637.2.c.b.246.2 | yes | 2 | 7.3 | odd | 6 | ||
637.2.c.b.246.2 | yes | 2 | 91.25 | even | 6 | ||
637.2.r.b.116.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.r.b.116.1 | 4 | 91.90 | odd | 2 | CM | ||
637.2.r.b.116.2 | 4 | 7.6 | odd | 2 | inner | ||
637.2.r.b.116.2 | 4 | 13.12 | even | 2 | inner | ||
637.2.r.b.324.1 | 4 | 7.5 | odd | 6 | inner | ||
637.2.r.b.324.1 | 4 | 91.51 | even | 6 | inner | ||
637.2.r.b.324.2 | 4 | 7.2 | even | 3 | inner | ||
637.2.r.b.324.2 | 4 | 91.12 | odd | 6 | inner | ||
8281.2.a.u.1.1 | 2 | 91.18 | odd | 12 | |||
8281.2.a.u.1.1 | 2 | 91.73 | even | 12 | |||
8281.2.a.u.1.2 | 2 | 91.31 | even | 12 | |||
8281.2.a.u.1.2 | 2 | 91.60 | odd | 12 |