Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(127,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("560.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.x (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(1.19252 - 0.760198i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.127 |
Dual form | 560.2.x.a.463.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.95272 | − | 1.95272i | −1.12740 | − | 1.12740i | −0.990598 | − | 0.136803i | \(-0.956317\pi\) |
−0.136803 | − | 0.990598i | \(-0.543683\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.432320 | + | 2.19388i | 0.193340 | + | 0.981132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.62620i | 1.54207i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.68840i | − | 0.509071i | −0.967063 | − | 0.254536i | \(-0.918077\pi\) | ||
0.967063 | − | 0.254536i | \(-0.0819226\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.19388 | − | 4.19388i | 1.16317 | − | 1.16317i | 0.179395 | − | 0.983777i | \(-0.442586\pi\) |
0.983777 | − | 0.179395i | \(-0.0574141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.43982 | − | 5.12822i | 0.888158 | − | 1.32410i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.32924 | − | 1.32924i | −0.322387 | − | 0.322387i | 0.527295 | − | 0.849682i | \(-0.323206\pi\) |
−0.849682 | + | 0.527295i | \(0.823206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.35101 | 1.45702 | 0.728510 | − | 0.685035i | \(-0.240213\pi\) | ||||
0.728510 | + | 0.685035i | \(0.240213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.76156 | 0.602621 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12822 | − | 5.12822i | −1.06931 | − | 1.06931i | −0.997412 | − | 0.0718953i | \(-0.977095\pi\) |
−0.0718953 | − | 0.997412i | \(-0.522905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62620 | + | 1.89692i | −0.925240 | + | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.17550 | − | 3.17550i | 0.611126 | − | 0.611126i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.35548i | − | 0.994488i | −0.867611 | − | 0.497244i | \(-0.834345\pi\) | ||
0.867611 | − | 0.497244i | \(-0.165655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.528636i | 0.0949458i | 0.998873 | + | 0.0474729i | \(0.0151168\pi\) | ||||
−0.998873 | + | 0.0474729i | \(0.984883\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.29696 | + | 3.29696i | −0.573927 | + | 0.573927i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.85700 | − | 1.24561i | −0.313891 | − | 0.210546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.76156 | − | 5.76156i | −0.947194 | − | 0.947194i | 0.0514799 | − | 0.998674i | \(-0.483606\pi\) |
−0.998674 | + | 0.0514799i | \(0.983606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.3789 | −2.62272 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.658473 | 0.102836 | 0.0514181 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514181 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.91118 | + | 2.91118i | 0.443952 | + | 0.443952i | 0.893338 | − | 0.449386i | \(-0.148357\pi\) |
−0.449386 | + | 0.893338i | \(0.648357\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.1493 | + | 2.00000i | −1.51297 | + | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.83236 | − | 8.83236i | 1.28833 | − | 1.28833i | 0.352532 | − | 0.935800i | \(-0.385321\pi\) |
0.935800 | − | 0.352532i | \(-0.114679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.19124i | 0.726919i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.38776 | − | 7.38776i | 1.01479 | − | 1.01479i | 0.0148972 | − | 0.999889i | \(-0.495258\pi\) |
0.999889 | − | 0.0148972i | \(-0.00474210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.70414 | − | 0.729929i | 0.499466 | − | 0.0984236i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.4017 | − | 12.4017i | −1.64265 | − | 1.64265i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.97421 | −0.387209 | −0.193605 | − | 0.981080i | \(-0.562018\pi\) | ||||
−0.193605 | + | 0.981080i | \(0.562018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.77551 | 1.12359 | 0.561794 | − | 0.827277i | \(-0.310111\pi\) | ||||
0.561794 | + | 0.827277i | \(0.310111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.27122 | − | 3.27122i | −0.412134 | − | 0.412134i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.0140 | + | 7.38776i | 1.36611 | + | 0.916338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.37104 | − | 4.37104i | 0.534008 | − | 0.534008i | −0.387755 | − | 0.921763i | \(-0.626749\pi\) |
0.921763 | + | 0.387755i | \(0.126749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.0279i | 2.41108i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.81086i | 0.926979i | 0.886102 | + | 0.463489i | \(0.153403\pi\) | ||||
−0.886102 | + | 0.463489i | \(0.846597\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.896916 | + | 0.896916i | −0.104976 | + | 0.104976i | −0.757644 | − | 0.652668i | \(-0.773650\pi\) |
0.652668 | + | 0.757644i | \(0.273650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.7378 | + | 5.32951i | 1.47083 | + | 0.615399i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19388 | + | 1.19388i | 0.136055 | + | 0.136055i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0021 | −1.46285 | −0.731426 | − | 0.681921i | \(-0.761145\pi\) | ||||
−0.731426 | + | 0.681921i | \(0.761145\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.47689 | 0.164098 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.65685 | − | 5.65685i | −0.620920 | − | 0.620920i | 0.324846 | − | 0.945767i | \(-0.394687\pi\) |
−0.945767 | + | 0.324846i | \(0.894687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.34153 | − | 3.49084i | 0.253974 | − | 0.378635i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4577 | + | 10.4577i | −1.12119 | + | 1.12119i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.27072i | − | 0.664695i | −0.943157 | − | 0.332347i | \(-0.892159\pi\) | ||
0.943157 | − | 0.332347i | \(-0.107841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.93104i | 0.621742i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.03228 | − | 1.03228i | 0.107042 | − | 0.107042i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.74567 | + | 13.9333i | 0.281700 | + | 1.42953i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3109 | + | 10.3109i | 1.04691 | + | 1.04691i | 0.998844 | + | 0.0480708i | \(0.0153073\pi\) |
0.0480708 | + | 0.998844i | \(0.484693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.81086 | 0.785021 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.387755 | −0.0385831 | −0.0192915 | − | 0.999814i | \(-0.506141\pi\) | ||||
−0.0192915 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.32951 | + | 5.32951i | 0.525132 | + | 0.525132i | 0.919117 | − | 0.393985i | \(-0.128904\pi\) |
−0.393985 | + | 0.919117i | \(0.628904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.19388 | + | 6.05852i | 0.116511 | + | 0.591251i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.91118 | + | 2.91118i | −0.281435 | + | 0.281435i | −0.833681 | − | 0.552246i | \(-0.813771\pi\) |
0.552246 | + | 0.833681i | \(0.313771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.14931i | − | 0.301649i | −0.988561 | − | 0.150825i | \(-0.951807\pi\) | ||
0.988561 | − | 0.150825i | \(-0.0481929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.5014i | 2.13574i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.55539 | + | 7.55539i | −0.710751 | + | 0.710751i | −0.966692 | − | 0.255941i | \(-0.917615\pi\) |
0.255941 | + | 0.966692i | \(0.417615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.03365 | − | 13.4677i | 0.842392 | − | 1.25587i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19.4017 | + | 19.4017i | 1.79369 | + | 1.79369i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.87982 | 0.172323 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.14931 | 0.740847 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.28581 | − | 1.28581i | −0.115938 | − | 0.115938i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.16160 | − | 9.32924i | −0.551110 | − | 0.834432i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.43982 | − | 3.43982i | 0.305235 | − | 0.305235i | −0.537823 | − | 0.843058i | \(-0.680753\pi\) |
0.843058 | + | 0.537823i | \(0.180753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 11.3694i | − | 1.00102i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.87964i | 0.601077i | 0.953770 | + | 0.300539i | \(0.0971664\pi\) | ||||
−0.953770 | + | 0.300539i | \(0.902834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.49084 | + | 4.49084i | −0.389405 | + | 0.389405i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.33950 | + | 5.59383i | 0.717750 | + | 0.481440i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.62620 | − | 6.62620i | −0.566114 | − | 0.566114i | 0.364923 | − | 0.931038i | \(-0.381095\pi\) |
−0.931038 | + | 0.364923i | \(0.881095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.9985 | 1.61143 | 0.805717 | − | 0.592301i | \(-0.201780\pi\) | ||||
0.805717 | + | 0.592301i | \(0.201780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.4942 | −2.90493 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.08093 | − | 7.08093i | −0.592137 | − | 0.592137i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7493 | − | 2.31528i | 0.975724 | − | 0.192274i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.95272 | + | 1.95272i | −0.161057 | + | 0.161057i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.52311i | 0.288625i | 0.989532 | + | 0.144312i | \(0.0460970\pi\) | ||||
−0.989532 | + | 0.144312i | \(0.953903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.20275i | 0.260636i | 0.991472 | + | 0.130318i | \(0.0415998\pi\) | ||||
−0.991472 | + | 0.130318i | \(0.958400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.14931 | − | 6.14931i | 0.497142 | − | 0.497142i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.15976 | + | 0.228540i | −0.0931543 | + | 0.0183568i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.08476 | − | 8.08476i | −0.645234 | − | 0.645234i | 0.306603 | − | 0.951837i | \(-0.400808\pi\) |
−0.951837 | + | 0.306603i | \(0.900808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −28.8524 | −2.28814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.25240 | 0.571569 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.50501 | + | 8.50501i | 0.666164 | + | 0.666164i | 0.956826 | − | 0.290662i | \(-0.0938754\pi\) |
−0.290662 | + | 0.956826i | \(0.593875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.65847 | − | 5.80779i | −0.674061 | − | 0.452136i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.5859 | + | 15.5859i | −1.20608 | + | 1.20608i | −0.233790 | + | 0.972287i | \(0.575113\pi\) |
−0.972287 | + | 0.233790i | \(0.924887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.1772i | − | 1.70594i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 29.3810i | 2.24682i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.80612 | + | 5.80612i | −0.441431 | + | 0.441431i | −0.892493 | − | 0.451062i | \(-0.851045\pi\) |
0.451062 | + | 0.892493i | \(0.351045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.92989 | − | 4.61254i | 0.145886 | − | 0.348675i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.80779 | + | 5.80779i | 0.436540 | + | 0.436540i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9870 | −1.56864 | −0.784322 | − | 0.620354i | \(-0.786989\pi\) | ||||
−0.784322 | + | 0.620354i | \(0.786989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.13536 | −0.381708 | −0.190854 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190854 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.1361 | − | 17.1361i | −1.26674 | − | 1.26674i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1493 | − | 15.1310i | 0.746192 | − | 1.11245i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.24428 | + | 2.24428i | −0.164118 | + | 0.164118i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.49084i | 0.326660i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.0136i | − | 0.796917i | −0.917186 | − | 0.398459i | \(-0.869545\pi\) | ||
0.917186 | − | 0.398459i | \(-0.130455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1955 | + | 13.1955i | −0.949836 | + | 0.949836i | −0.998801 | − | 0.0489647i | \(-0.984408\pi\) |
0.0489647 | + | 0.998801i | \(0.484408\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.08093 | − | 35.9333i | −0.507076 | − | 2.57324i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.640151 | − | 0.640151i | −0.0456089 | − | 0.0456089i | 0.683935 | − | 0.729543i | \(-0.260267\pi\) |
−0.729543 | + | 0.683935i | \(0.760267\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3495 | 1.79698 | 0.898490 | − | 0.438994i | \(-0.144665\pi\) | ||||
0.898490 | + | 0.438994i | \(0.144665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.0708 | −1.20408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.78690 | + | 3.78690i | 0.265788 | + | 0.265788i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.284672 | + | 1.44461i | 0.0198823 | + | 0.100896i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.7242 | − | 23.7242i | 1.64894 | − | 1.64894i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.7230i | − | 0.741727i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.8817i | 1.36872i | 0.729146 | + | 0.684358i | \(0.239917\pi\) | ||||
−0.729146 | + | 0.684358i | \(0.760083\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.2524 | − | 15.2524i | 1.04508 | − | 1.04508i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.12822 | + | 7.64535i | −0.349742 | + | 0.521408i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.373802 | − | 0.373802i | −0.0253753 | − | 0.0253753i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.50285 | 0.236700 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.1493 | −0.749984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.88394 | − | 2.88394i | −0.193123 | − | 0.193123i | 0.603921 | − | 0.797044i | \(-0.293604\pi\) |
−0.797044 | + | 0.603921i | \(0.793604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.77551 | − | 21.4017i | −0.585034 | − | 1.42678i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7493 | − | 10.7493i | 0.713456 | − | 0.713456i | −0.253801 | − | 0.967257i | \(-0.581681\pi\) |
0.967257 | + | 0.253801i | \(0.0816808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8925i | 0.851964i | 0.904732 | + | 0.425982i | \(0.140071\pi\) | ||||
−0.904732 | + | 0.425982i | \(0.859929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4.66261i | − | 0.306777i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.67243 | + | 7.67243i | −0.502637 | + | 0.502637i | −0.912257 | − | 0.409619i | \(-0.865662\pi\) |
0.409619 | + | 0.912257i | \(0.365662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.1955 | + | 15.5587i | 1.51311 | + | 1.01494i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3894 | + | 25.3894i | 1.64922 | + | 1.64922i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.62531 | −0.622610 | −0.311305 | − | 0.950310i | \(-0.600766\pi\) | ||||
−0.311305 | + | 0.950310i | \(0.600766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.56934 | −0.552000 | −0.276000 | − | 0.961158i | \(-0.589009\pi\) | ||||
−0.276000 | + | 0.961158i | \(0.589009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.4104 | − | 12.4104i | −0.796130 | − | 0.796130i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.19388 | − | 0.432320i | 0.140162 | − | 0.0276199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6353 | − | 26.6353i | 1.69477 | − | 1.69477i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.0925i | 1.40005i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.82237i | − | 0.367505i | −0.982973 | − | 0.183752i | \(-0.941176\pi\) | ||
0.982973 | − | 0.183752i | \(-0.0588244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.65847 | + | 8.65847i | −0.544354 | + | 0.544354i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.3890 | + | 2.24428i | −0.713204 | + | 0.140542i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.1493 | + | 20.1493i | 1.25688 | + | 1.25688i | 0.952575 | + | 0.304305i | \(0.0984242\pi\) |
0.304305 | + | 0.952575i | \(0.401576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.14807 | 0.506297 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.7755 | 1.53357 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0358 | + | 22.0358i | 1.35878 | + | 1.35878i | 0.875420 | + | 0.483363i | \(0.160585\pi\) |
0.483363 | + | 0.875420i | \(0.339415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.4017 | + | 13.0140i | 1.19184 | + | 0.799441i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2449 | + | 12.2449i | −0.749378 | + | 0.749378i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000i | 0.365826i | 0.983129 | + | 0.182913i | \(0.0585527\pi\) | ||||
−0.983129 | + | 0.182913i | \(0.941447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 32.6318i | − | 1.98224i | −0.132978 | − | 0.991119i | \(-0.542454\pi\) | ||
0.132978 | − | 0.991119i | \(-0.457546\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.5816 | − | 11.5816i | 0.700952 | − | 0.700952i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.20275 | + | 7.81086i | 0.193133 | + | 0.471013i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.03228 | − | 6.03228i | −0.362444 | − | 0.362444i | 0.502268 | − | 0.864712i | \(-0.332499\pi\) |
−0.864712 | + | 0.502268i | \(0.832499\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.44557 | −0.146413 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.56165 | 0.331780 | 0.165890 | − | 0.986144i | \(-0.446950\pi\) | ||||
0.165890 | + | 0.986144i | \(0.446950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.1719 | − | 17.1719i | −1.02076 | − | 1.02076i | −0.999780 | − | 0.0209810i | \(-0.993321\pi\) |
−0.0209810 | − | 0.999780i | \(-0.506679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.8463 | − | 32.5693i | 1.29406 | − | 1.92924i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.465611 | + | 0.465611i | −0.0274842 | + | 0.0274842i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.4663i | − | 0.792133i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 40.2686i | − | 2.36059i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4280 | + | 18.4280i | −1.07657 | + | 1.07657i | −0.0797582 | + | 0.996814i | \(0.525415\pi\) |
−0.996814 | + | 0.0797582i | \(0.974585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.28581 | − | 6.52505i | −0.0748628 | − | 0.379903i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.36151 | − | 5.36151i | −0.311106 | − | 0.311106i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −43.0142 | −2.48758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.11704 | −0.237302 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.757176 | + | 0.757176i | 0.0434986 | + | 0.0434986i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.79383 | + | 19.2524i | 0.217234 | + | 1.10239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8209 | + | 10.8209i | −0.617579 | + | 0.617579i | −0.944910 | − | 0.327331i | \(-0.893851\pi\) |
0.327331 | + | 0.944910i | \(0.393851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 20.8140i | − | 1.18407i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.9111i | − | 0.618713i | −0.950946 | − | 0.309356i | \(-0.899886\pi\) | ||
0.950946 | − | 0.309356i | \(-0.100114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3109 | + | 14.3109i | −0.808901 | + | 0.808901i | −0.984468 | − | 0.175567i | \(-0.943824\pi\) |
0.175567 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.76243 | − | 8.59086i | 0.324676 | − | 0.484040i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.50479 | + | 5.50479i | 0.309180 | + | 0.309180i | 0.844591 | − | 0.535411i | \(-0.179843\pi\) |
−0.535411 | + | 0.844591i | \(0.679843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.04218 | −0.506265 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3694 | 0.634580 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.44199 | − | 8.44199i | −0.469725 | − | 0.469725i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4463 | + | 27.3571i | −0.634925 | + | 1.51750i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.14971 | + | 6.14971i | −0.340080 | + | 0.340080i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.4908i | 0.688642i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.91972i | − | 0.160482i | −0.996775 | − | 0.0802410i | \(-0.974431\pi\) | ||
0.996775 | − | 0.0802410i | \(-0.0255690\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.6541 | − | 26.6541i | 1.46064 | − | 1.46064i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4792 | + | 7.69984i | 0.627177 | + | 0.420687i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.01395 | − | 1.01395i | −0.0552336 | − | 0.0552336i | 0.678950 | − | 0.734184i | \(-0.262435\pi\) |
−0.734184 | + | 0.678950i | \(0.762435\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.5071 | 1.60260 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.892548 | 0.0483342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −43.9388 | + | 8.65847i | −2.36558 | + | 0.466157i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9964 | − | 13.9964i | 0.751364 | − | 0.751364i | −0.223370 | − | 0.974734i | \(-0.571706\pi\) |
0.974734 | + | 0.223370i | \(0.0717058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.3232i | − | 0.659646i | −0.944043 | − | 0.329823i | \(-0.893011\pi\) | ||
0.944043 | − | 0.329823i | \(-0.106989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 26.6353i | − | 1.42169i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0585 | + | 13.0585i | −0.695035 | + | 0.695035i | −0.963335 | − | 0.268300i | \(-0.913538\pi\) |
0.268300 | + | 0.963335i | \(0.413538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.1361 | + | 3.37680i | −0.909489 | + | 0.179222i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.67076 | − | 3.67076i | −0.194277 | − | 0.194277i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.42256 | −0.338970 | −0.169485 | − | 0.985533i | \(-0.554210\pi\) | ||||
−0.169485 | + | 0.985533i | \(0.554210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.3353 | 1.12291 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.9133 | − | 15.9133i | −0.835231 | − | 0.835231i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.35548 | − | 1.57997i | −0.123291 | − | 0.0826994i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.895444 | − | 0.895444i | 0.0467418 | − | 0.0467418i | −0.683350 | − | 0.730091i | \(-0.739477\pi\) |
0.730091 | + | 0.683350i | \(0.239477\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.04623i | 0.158580i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4479i | 0.542426i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.6541 | − | 20.6541i | 1.06943 | − | 1.06943i | 0.0720263 | − | 0.997403i | \(-0.477053\pi\) |
0.997403 | − | 0.0720263i | \(-0.0229465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.18549 | + | 30.2492i | −0.319417 | + | 1.56206i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.4602 | − | 22.4602i | −1.15676 | − | 1.15676i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5586 | 1.21013 | 0.605063 | − | 0.796178i | \(-0.293148\pi\) | ||||
0.605063 | + | 0.796178i | \(0.293148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4340 | −0.688244 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.58808 | + | 6.58808i | 0.336635 | + | 0.336635i | 0.855099 | − | 0.518464i | \(-0.173496\pi\) |
−0.518464 | + | 0.855099i | \(0.673496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.10308 | + | 3.13536i | −0.107183 | + | 0.159793i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.4677 | + | 13.4677i | −0.684603 | + | 0.684603i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 26.2234i | − | 1.32958i | −0.747030 | − | 0.664791i | \(-0.768521\pi\) | ||
0.747030 | − | 0.664791i | \(-0.231479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6332i | 0.689462i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.4340 | − | 13.4340i | 0.677655 | − | 0.677655i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.62108 | − | 28.5250i | −0.282827 | − | 1.43525i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.35714 | − | 7.35714i | −0.369244 | − | 0.369244i | 0.497957 | − | 0.867202i | \(-0.334084\pi\) |
−0.867202 | + | 0.497957i | \(0.834084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.5387 | 0.878031 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.33716 | −0.416338 | −0.208169 | − | 0.978093i | \(-0.566750\pi\) | ||||
−0.208169 | + | 0.978093i | \(0.566750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.21703 | + | 2.21703i | 0.110438 | + | 0.110438i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.638488 | + | 3.24011i | 0.0317267 | + | 0.161002i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.72780 | + | 9.72780i | −0.482189 | + | 0.482189i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8463i | 0.783550i | 0.920061 | + | 0.391775i | \(0.128139\pi\) | ||||
−0.920061 | + | 0.391775i | \(0.871861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.8782i | 1.27648i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.10308 | − | 2.10308i | 0.103486 | − | 0.103486i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.96487 | − | 14.8560i | 0.489156 | − | 0.729253i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.0987 | − | 37.0987i | −1.81673 | − | 1.81673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7048 | 0.669523 | 0.334761 | − | 0.942303i | \(-0.391344\pi\) | ||||
0.334761 | + | 0.942303i | \(0.391344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7678 | −0.671002 | −0.335501 | − | 0.942040i | \(-0.608906\pi\) | ||||
−0.335501 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.8602 | + | 40.8602i | 1.98669 | + | 1.98669i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.67076 | + | 3.62786i | 0.420594 | + | 0.175977i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.20522 | + | 6.20522i | −0.300292 | + | 0.300292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.6541i | 1.33515i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 22.8015i | − | 1.09831i | −0.835721 | − | 0.549154i | \(-0.814950\pi\) | ||
0.835721 | − | 0.549154i | \(-0.185050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.98605 | + | 8.98605i | −0.431842 | + | 0.431842i | −0.889255 | − | 0.457413i | \(-0.848776\pi\) |
0.457413 | + | 0.889255i | \(0.348776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.4641 | − | 18.4219i | −1.31680 | − | 0.883262i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.5693 | − | 32.5693i | −1.55800 | − | 1.55800i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1361 | 0.817860 | 0.408930 | − | 0.912566i | \(-0.365902\pi\) | ||||
0.408930 | + | 0.912566i | \(0.365902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.62620 | 0.220295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2650 | + | 10.2650i | 0.487703 | + | 0.487703i | 0.907581 | − | 0.419877i | \(-0.137927\pi\) |
−0.419877 | + | 0.907581i | \(0.637927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.7572 | − | 2.71096i | 0.652153 | − | 0.128512i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.87964 | − | 6.87964i | 0.325396 | − | 0.325396i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1772i | 1.47134i | 0.677338 | + | 0.735672i | \(0.263133\pi\) | ||||
−0.677338 | + | 0.735672i | \(0.736867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.11177i | − | 0.0523510i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.25406 | − | 6.25406i | 0.293841 | − | 0.293841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.0120 | + | 2.56411i | −0.610011 | + | 0.120207i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.72302 | − | 3.72302i | −0.174156 | − | 0.174156i | 0.614647 | − | 0.788802i | \(-0.289299\pi\) |
−0.788802 | + | 0.614647i | \(0.789299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.44199 | −0.394038 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3815 | 0.623238 | 0.311619 | − | 0.950207i | \(-0.399129\pi\) | ||||
0.311619 | + | 0.950207i | \(0.399129\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9248 | + | 13.9248i | 0.647140 | + | 0.647140i | 0.952301 | − | 0.305161i | \(-0.0987102\pi\) |
−0.305161 | + | 0.952301i | \(0.598710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.71096 | + | 1.81841i | 0.125718 | + | 0.0843268i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6805 | − | 11.6805i | 0.540510 | − | 0.540510i | −0.383169 | − | 0.923678i | \(-0.625167\pi\) |
0.923678 | + | 0.383169i | \(0.125167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.18159i | 0.285439i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.5745i | 1.45488i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.91524 | − | 4.91524i | 0.226003 | − | 0.226003i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.3810 | + | 12.0473i | −1.34809 | + | 0.552769i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.1772 | + | 34.1772i | 1.56487 | + | 1.56487i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.0845 | −1.05476 | −0.527379 | − | 0.849630i | \(-0.676825\pi\) | ||||
−0.527379 | + | 0.849630i | \(0.676825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.3265 | −2.20350 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.1619 | − | 14.1619i | −0.644387 | − | 0.644387i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.1633 | + | 27.0785i | −0.824751 | + | 1.22957i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.19700 | + | 4.19700i | −0.190184 | + | 0.190184i | −0.795776 | − | 0.605592i | \(-0.792937\pi\) |
0.605592 | + | 0.795776i | \(0.292937\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 33.2158i | − | 1.50207i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2529i | 0.733481i | 0.930323 | + | 0.366740i | \(0.119526\pi\) | ||||
−0.930323 | + | 0.366740i | \(0.880474\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.11870 | + | 7.11870i | −0.320610 | + | 0.320610i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.37680 | + | 17.1361i | 0.151776 | + | 0.770209i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.52311 | − | 5.52311i | −0.247746 | − | 0.247746i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3043 | 1.17754 | 0.588771 | − | 0.808300i | \(-0.299612\pi\) | ||||
0.588771 | + | 0.808300i | \(0.299612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60.8699 | 2.71946 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.2664 | + | 13.2664i | 0.591521 | + | 0.591521i | 0.938042 | − | 0.346521i | \(-0.112637\pi\) |
−0.346521 | + | 0.938042i | \(0.612637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.167635 | − | 0.850688i | −0.00745964 | − | 0.0378551i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43.3058 | + | 43.3058i | −1.92328 | + | 1.92328i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 33.3449i | − | 1.47798i | −0.673714 | − | 0.738992i | \(-0.735302\pi\) | ||
0.673714 | − | 0.738992i | \(-0.264698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.26843i | − | 0.0561121i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.1676 | − | 20.1676i | 0.890423 | − | 0.890423i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.38824 | + | 13.9964i | −0.413695 | + | 0.616753i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.9125 | − | 14.9125i | −0.655852 | − | 0.655852i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.6754 | 0.995340 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 44.9850 | 1.97083 | 0.985414 | − | 0.170172i | \(-0.0544322\pi\) | ||||
0.985414 | + | 0.170172i | \(0.0544322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9391 | + | 12.9391i | 0.565787 | + | 0.565787i | 0.930945 | − | 0.365159i | \(-0.118985\pi\) |
−0.365159 | + | 0.930945i | \(0.618985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.7755 | + | 5.23844i | −0.557569 | + | 0.228624i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.702682 | − | 0.702682i | 0.0306093 | − | 0.0306093i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.5972i | 1.28684i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 13.7593i | − | 0.597102i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.76156 | − | 2.76156i | 0.119616 | − | 0.119616i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.64535 | − | 5.12822i | −0.330537 | − | 0.221712i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.9817 | + | 40.9817i | 1.76849 | + | 1.76849i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.68840 | −0.0727244 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.3188 | 1.26052 | 0.630258 | − | 0.776386i | \(-0.282949\pi\) | ||||
0.630258 | + | 0.776386i | \(0.282949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0279 | + | 10.0279i | 0.430338 | + | 0.430338i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.90921 | − | 1.36151i | 0.295958 | − | 0.0583208i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7357 | + | 21.7357i | −0.929350 | + | 0.929350i | −0.997664 | − | 0.0683141i | \(-0.978238\pi\) |
0.0683141 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.5972i | 1.73265i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.0127i | − | 1.44899i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.19388 | − | 9.19388i | 0.390963 | − | 0.390963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −49.3652 | + | 9.72780i | −2.09544 | + | 0.412922i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.0847616 | + | 0.0847616i | 0.00359146 | + | 0.00359146i | 0.708900 | − | 0.705309i | \(-0.249192\pi\) |
−0.705309 | + | 0.708900i | \(0.749192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.4183 | 1.03278 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.76488 | 0.370054 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.22279 | + | 1.22279i | 0.0515343 | + | 0.0515343i | 0.732404 | − | 0.680870i | \(-0.238398\pi\) |
−0.680870 | + | 0.732404i | \(0.738398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.8420 | − | 13.3093i | −0.834757 | − | 0.559924i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.04432 | + | 1.04432i | −0.0438571 | + | 0.0438571i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.1108i | 0.801166i | 0.916261 | + | 0.400583i | \(0.131192\pi\) | ||||
−0.916261 | + | 0.400583i | \(0.868808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.3237i | 1.18531i | 0.805456 | + | 0.592656i | \(0.201921\pi\) | ||||
−0.805456 | + | 0.592656i | \(0.798079\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.5065 | + | 21.5065i | −0.898445 | + | 0.898445i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.4520 | + | 13.9964i | 1.39504 | + | 0.583688i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.10475 | + | 8.10475i | 0.337405 | + | 0.337405i | 0.855390 | − | 0.517985i | \(-0.173318\pi\) |
−0.517985 | + | 0.855390i | \(0.673318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 51.5343 | 2.14169 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4735 | − | 12.4735i | −0.516598 | − | 0.516598i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −34.1772 | + | 50.9527i | −1.41305 | + | 2.10664i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.53080 | + | 5.53080i | −0.228281 | + | 0.228281i | −0.811974 | − | 0.583693i | \(-0.801607\pi\) |
0.583693 | + | 0.811974i | \(0.301607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35737i | 0.138338i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.50007i | 0.102839i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.24636 | − | 4.24636i | 0.174377 | − | 0.174377i | −0.614522 | − | 0.788899i | \(-0.710651\pi\) |
0.788899 | + | 0.614522i | \(0.210651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.812687 | + | 4.12411i | 0.0333169 | + | 0.169072i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.5004 | − | 49.5004i | −2.02592 | − | 2.02592i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.0293 | −1.43126 | −0.715630 | − | 0.698480i | \(-0.753860\pi\) | ||||
−0.715630 | + | 0.698480i | \(0.753860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5573 | 1.00171 | 0.500856 | − | 0.865531i | \(-0.333019\pi\) | ||||
0.500856 | + | 0.865531i | \(0.333019\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2213 | + | 20.2213i | 0.823475 | + | 0.823475i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.52311 | + | 17.8786i | 0.143235 | + | 0.726868i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.99570 | − | 3.99570i | 0.162181 | − | 0.162181i | −0.621351 | − | 0.783532i | \(-0.713416\pi\) |
0.783532 | + | 0.621351i | \(0.213416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 14.7895i | − | 0.599299i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 74.0836i | − | 2.99710i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.7110 | + | 15.7110i | −0.634560 | + | 0.634560i | −0.949208 | − | 0.314649i | \(-0.898113\pi\) |
0.314649 | + | 0.949208i | \(0.398113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.26503 | − | 3.37680i | 0.0913348 | − | 0.136166i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4725 | + | 16.4725i | 0.663159 | + | 0.663159i | 0.956123 | − | 0.292965i | \(-0.0946418\pi\) |
−0.292965 | + | 0.956123i | \(0.594642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0788 | −0.646262 | −0.323131 | − | 0.946354i | \(-0.604735\pi\) | ||||
−0.323131 | + | 0.946354i | \(0.604735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.5693 | −1.30696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.43407 | + | 4.43407i | 0.177647 | + | 0.177647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | − | 17.5510i | 0.712137 | − | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.9390 | + | 20.9390i | −0.836224 | + | 0.836224i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3169i | 0.610727i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.55084i | 0.141357i | 0.997499 | + | 0.0706784i | \(0.0225164\pi\) | ||||
−0.997499 | + | 0.0706784i | \(0.977484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 38.8234 | − | 38.8234i | 1.54309 | − | 1.54309i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.03365 | + | 6.05944i | 0.358489 | + | 0.240462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.19388 | − | 4.19388i | −0.166167 | − | 0.166167i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.1346 | −1.42946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.1020 | −1.70243 | −0.851214 | − | 0.524819i | \(-0.824133\pi\) | ||||
−0.851214 | + | 0.524819i | \(0.824133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7005 | + | 17.7005i | 0.698039 | + | 0.698039i | 0.963987 | − | 0.265948i | \(-0.0856850\pi\) |
−0.265948 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.9431 | − | 4.91524i | 0.982135 | − | 0.193537i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.8875 | − | 18.8875i | 0.742544 | − | 0.742544i | −0.230523 | − | 0.973067i | \(-0.574044\pi\) |
0.973067 | + | 0.230523i | \(0.0740436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.02165i | 0.197117i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.45986i | 0.0572163i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31695 | + | 4.31695i | −0.168935 | + | 0.168935i | −0.786511 | − | 0.617576i | \(-0.788115\pi\) |
0.617576 | + | 0.786511i | \(0.288115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0931 | + | 2.97421i | −0.589736 | + | 0.116212i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.14931 | − | 4.14931i | −0.161880 | − | 0.161880i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.05369 | −0.274773 | −0.137386 | − | 0.990518i | \(-0.543870\pi\) | ||||
−0.137386 | + | 0.990518i | \(0.543870\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.2216 | 1.17548 | 0.587741 | − | 0.809049i | \(-0.300017\pi\) | ||||
0.587741 | + | 0.809049i | \(0.300017\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7714 | + | 21.7714i | 0.845533 | + | 0.845533i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.7938 | − | 7.91087i | −0.457345 | − | 0.306770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.4641 | + | 27.4641i | −1.06341 | + | 1.06341i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2630i | 0.435454i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 14.8166i | − | 0.571987i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.9248 | − | 14.9248i | 0.575310 | − | 0.575310i | −0.358298 | − | 0.933607i | \(-0.616643\pi\) |
0.933607 | + | 0.358298i | \(0.116643\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.66684 | + | 20.7142i | −0.333587 | + | 0.797289i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.37214 | + | 2.37214i | 0.0911687 | + | 0.0911687i | 0.751220 | − | 0.660052i | \(-0.229466\pi\) |
−0.660052 | + | 0.751220i | \(0.729466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.5818 | −0.559599 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.9806 | −1.60870 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.58808 | − | 6.58808i | −0.252086 | − | 0.252086i | 0.569740 | − | 0.821825i | \(-0.307044\pi\) |
−0.821825 | + | 0.569740i | \(0.807044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.6724 | − | 17.4017i | 0.445981 | − | 0.664885i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.1755 | − | 25.1755i | 0.960505 | − | 0.960505i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 61.9667i | − | 2.36074i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.45126i | − | 0.359543i | −0.983708 | − | 0.179772i | \(-0.942464\pi\) | ||
0.983708 | − | 0.179772i | \(-0.0575358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.52311 | + | 5.52311i | −0.209806 | + | 0.209806i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.21345 | + | 41.6804i | 0.311554 | + | 1.58103i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.875267 | − | 0.875267i | −0.0331531 | − | 0.0331531i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.9641 | 1.13335 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.71866 | 0.367069 | 0.183534 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183534 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.5917 | − | 36.5917i | −1.38008 | − | 1.38008i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.9125 | − | 75.6760i | −0.561638 | − | 2.85012i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.274184 | − | 0.274184i | 0.0103118 | − | 0.0103118i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.2514i | − | 1.06100i | −0.847684 | − | 0.530501i | \(-0.822004\pi\) | ||
0.847684 | − | 0.530501i | \(-0.177996\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 60.1503i | − | 2.25581i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.71096 | − | 2.71096i | 0.101526 | − | 0.101526i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.4735 | − | 18.5959i | 0.466481 | − | 0.695449i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.7955 | + | 18.7955i | 0.701931 | + | 0.701931i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.4541 | 1.43410 | 0.717048 | − | 0.697023i | \(-0.245493\pi\) | ||||
0.717048 | + | 0.697023i | \(0.245493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.53707 | −0.280695 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.7335 | + | 16.7335i | 0.622325 | + | 0.622325i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1589 | + | 24.7755i | 0.377292 | + | 0.920139i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.53080 | − | 5.53080i | 0.205126 | − | 0.205126i | −0.597066 | − | 0.802192i | \(-0.703667\pi\) |
0.802192 | + | 0.597066i | \(0.203667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.0375i | 1.63102i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.73931i | − | 0.286249i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.8986 | + | 35.8986i | −1.32594 | + | 1.32594i | −0.417070 | + | 0.908874i | \(0.636943\pi\) |
−0.908874 | + | 0.417070i | \(0.863057\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.12822 | − | 3.43982i | −0.189157 | − | 0.126880i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.38006 | − | 7.38006i | −0.271848 | − | 0.271848i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.83029 | −0.361613 | −0.180807 | − | 0.983519i | \(-0.557871\pi\) | ||||
−0.180807 | + | 0.983519i | \(0.557871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −104.022 | −3.82136 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0787 | + | 24.0787i | 0.883363 | + | 0.883363i | 0.993875 | − | 0.110511i | \(-0.0352489\pi\) |
−0.110511 | + | 0.993875i | \(0.535249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.72928 | + | 1.52311i | −0.283179 | + | 0.0558026i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.1697 | − | 26.1697i | 0.957500 | − | 0.957500i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.11704i | − | 0.150433i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0479i | 0.585595i | 0.956174 | + | 0.292798i | \(0.0945862\pi\) | ||||
−0.956174 | + | 0.292798i | \(0.905414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.3694 | + | 11.3694i | −0.414325 | + | 0.414325i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.02644 | + | 1.38461i | −0.255718 | + | 0.0503913i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6541 | + | 14.6541i | 0.532612 | + | 0.532612i | 0.921349 | − | 0.388736i | \(-0.127088\pi\) |
−0.388736 | + | 0.921349i | \(0.627088\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.8151 | 1.22741 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2707 | −0.444813 | −0.222407 | − | 0.974954i | \(-0.571391\pi\) | ||||
−0.222407 | + | 0.974954i | \(0.571391\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.22690 | + | 2.22690i | 0.0806192 | + | 0.0806192i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.1493 | + | 10.8324i | 0.583880 | + | 0.391645i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.4735 | + | 12.4735i | −0.450391 | + | 0.450391i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.2278i | − | 0.621251i | −0.950532 | − | 0.310625i | \(-0.899462\pi\) | ||
0.950532 | − | 0.310625i | \(-0.100538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 78.6918i | − | 2.83401i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.4463 | + | 13.4463i | −0.483629 | + | 0.483629i | −0.906288 | − | 0.422660i | \(-0.861097\pi\) |
0.422660 | + | 0.906288i | \(0.361097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00278 | − | 2.44557i | −0.0360208 | − | 0.0878476i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.9109 | − | 15.9109i | −0.570799 | − | 0.570799i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.18197 | 0.149835 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.1878 | 0.471898 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.0063 | − | 17.0063i | −0.607757 | − | 0.607757i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2418 | − | 21.2322i | 0.508311 | − | 0.757809i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6690 | − | 13.6690i | 0.487248 | − | 0.487248i | −0.420189 | − | 0.907437i | \(-0.638036\pi\) |
0.907437 | + | 0.420189i | \(0.138036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 86.0591i | − | 3.06379i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.6849i | − | 0.379913i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.8034 | − | 36.8034i | 1.30693 | − | 1.30693i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.4735 | − | 63.2986i | −0.442388 | − | 2.24497i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.48292 | + | 5.48292i | 0.194215 | + | 0.194215i | 0.797515 | − | 0.603300i | \(-0.206148\pi\) |
−0.603300 | + | 0.797515i | \(0.706148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4806 | −0.830683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.0096 | 1.02500 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.51435 | + | 1.51435i | 0.0534403 | + | 0.0534403i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.13536 | + | 15.9109i | 0.110507 | + | 0.560784i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7163 | − | 11.7163i | 0.412433 | − | 0.412433i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.6907i | − | 0.621974i | −0.950414 | − | 0.310987i | \(-0.899341\pi\) | ||
0.950414 | − | 0.310987i | \(-0.100659\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.95993i | 0.139052i | 0.997580 | + | 0.0695259i | \(0.0221486\pi\) | ||||
−0.997580 | + | 0.0695259i | \(0.977851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −63.7205 | + | 63.7205i | −2.23478 | + | 2.23478i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.9821 | + | 22.3359i | −0.524799 | + | 0.782391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.4890 | + | 18.4890i | 0.646846 | + | 0.646846i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.4382 | −0.958767 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.42962 | −0.154595 | −0.0772973 | − | 0.997008i | \(-0.524629\pi\) | ||||
−0.0772973 | + | 0.997008i | \(0.524629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0158 | − | 16.0158i | −0.558275 | − | 0.558275i | 0.370541 | − | 0.928816i | \(-0.379172\pi\) |
−0.928816 | + | 0.370541i | \(0.879172\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.99834 | − | 21.5065i | 0.313282 | − | 0.748759i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.0179 | − | 29.0179i | 1.00905 | − | 1.00905i | 0.00909218 | − | 0.999959i | \(-0.497106\pi\) |
0.999959 | − | 0.00909218i | \(-0.00289417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.54769i | − | 0.192679i | −0.995349 | − | 0.0963397i | \(-0.969286\pi\) | ||
0.995349 | − | 0.0963397i | \(-0.0307135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.5586i | 0.817240i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.32924 | + | 1.32924i | −0.0460553 | + | 0.0460553i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.9318 | − | 27.4555i | −1.41650 | − | 0.950138i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.67868 | + | 1.67868i | 0.0580238 | + | 0.0580238i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.9239 | −0.998565 | −0.499282 | − | 0.866439i | \(-0.666403\pi\) | ||||
−0.499282 | + | 0.866439i | \(0.666403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.318836 | 0.0109943 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.8603 | − | 10.8603i | −0.374049 | − | 0.374049i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.6541 | − | 9.58767i | 1.67375 | − | 0.329826i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.76243 | + | 5.76243i | −0.198000 | + | 0.198000i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 67.0635i | 2.30161i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.0930i | 2.02568i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.8140 | − | 23.8140i | 0.815377 | − | 0.815377i | −0.170057 | − | 0.985434i | \(-0.554395\pi\) |
0.985434 | + | 0.170057i | \(0.0543952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −64.4583 | + | 12.7020i | −2.20443 | + | 0.434400i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.9527 | + | 22.9527i | 0.784050 | + | 0.784050i | 0.980512 | − | 0.196461i | \(-0.0629450\pi\) |
−0.196461 | + | 0.980512i | \(0.562945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.6447 | −0.397313 | −0.198657 | − | 0.980069i | \(-0.563658\pi\) | ||||
−0.198657 | + | 0.980069i | \(0.563658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81841 | 0.0619713 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.7464 | − | 26.7464i | −0.910457 | − | 0.910457i | 0.0858513 | − | 0.996308i | \(-0.472639\pi\) |
−0.996308 | + | 0.0858513i | \(0.972639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2480 | − | 10.2278i | −0.518448 | − | 0.347756i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.2958 | + | 26.2958i | −0.893051 | + | 0.893051i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.9527i | 0.744695i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 36.6632i | − | 1.24229i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −47.7003 | + | 47.7003i | −1.61441 | + | 1.61441i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9537 | + | 2.23986i | 0.370302 | + | 0.0757209i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.0646 | − | 15.0646i | −0.508694 | − | 0.508694i | 0.405432 | − | 0.914125i | \(-0.367121\pi\) |
−0.914125 | + | 0.405432i | \(0.867121\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 71.9691 | 2.42746 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6801 | −0.999949 | −0.499974 | − | 0.866040i | \(-0.666657\pi\) | ||||
−0.499974 | + | 0.866040i | \(0.666657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2385 | − | 25.2385i | −0.849343 | − | 0.849343i | 0.140708 | − | 0.990051i | \(-0.455062\pi\) |
−0.990051 | + | 0.140708i | \(0.955062\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.2307 | + | 15.2524i | −0.343903 | + | 0.512704i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.28006 | − | 2.28006i | 0.0765569 | − | 0.0765569i | −0.667792 | − | 0.744348i | \(-0.732760\pi\) |
0.744348 | + | 0.667792i | \(0.232760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.86464i | 0.163155i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.49357i | − | 0.0835378i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 56.0943 | − | 56.0943i | 1.87713 | − | 1.87713i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.07312 | − | 46.0429i | −0.303281 | − | 1.53905i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 83.9946 | + | 83.9946i | 2.80450 | + | 2.80450i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.83110 | 0.0944224 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.6402 | −0.654308 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.03940 | + | 8.03940i | 0.267535 | + | 0.267535i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.22012 | − | 11.2663i | −0.0737993 | − | 0.374506i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.237071 | + | 0.237071i | −0.00787181 | + | 0.00787181i | −0.711032 | − | 0.703160i | \(-0.751772\pi\) |
0.703160 | + | 0.711032i | \(0.251772\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1.79383i | − | 0.0594977i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.2665i | 0.903378i | 0.892175 | + | 0.451689i | \(0.149178\pi\) | ||||
−0.892175 | + | 0.451689i | \(0.850822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.55102 | + | 9.55102i | −0.316093 | + | 0.316093i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.1862 | − | 45.0027i | 0.997924 | − | 1.48774i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.86464 | − | 4.86464i | −0.160645 | − | 0.160645i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.7500 | −0.420584 | −0.210292 | − | 0.977639i | \(-0.567441\pi\) | ||||
−0.210292 | + | 0.977639i | \(0.567441\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.2601 | 1.39252 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.7578 | + | 32.7578i | 1.07824 | + | 1.07824i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.5833 | + | 15.7249i | 1.23573 | + | 0.517032i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.6554 | + | 24.6554i | −0.809789 | + | 0.809789i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 23.8742i | − | 0.783288i | −0.920117 | − | 0.391644i | \(-0.871906\pi\) | ||
0.920117 | − | 0.391644i | \(-0.128094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.35101i | − | 0.208146i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.3063 | + | 21.3063i | −0.697538 | + | 0.697538i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.89393 | − | 3.95343i | −0.192752 | − | 0.129291i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.71699 | − | 3.71699i | −0.121429 | − | 0.121429i | 0.643781 | − | 0.765210i | \(-0.277365\pi\) |
−0.765210 | + | 0.643781i | \(0.777365\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.8903 | 1.82391 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.3940 | 0.762623 | 0.381312 | − | 0.924447i | \(-0.375473\pi\) | ||||
0.381312 | + | 0.924447i | \(0.375473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.37680 | − | 3.37680i | −0.109964 | − | 0.109964i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.85235 | + | 1.94148i | −0.320497 | + | 0.0631564i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.8223 | − | 13.8223i | 0.449165 | − | 0.449165i | −0.445912 | − | 0.895077i | \(-0.647121\pi\) |
0.895077 | + | 0.445912i | \(0.147121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.52311i | 0.244211i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.4986i | − | 0.697140i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.78177 | + | 4.78177i | −0.154897 | + | 0.154897i | −0.780301 | − | 0.625404i | \(-0.784934\pi\) |
0.625404 | + | 0.780301i | \(0.284934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.1625 | − | 4.76141i | 0.781881 | − | 0.154076i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.6568 | + | 17.6568i | 0.570764 | + | 0.570764i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.37086 | 0.302601 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7205 | 0.990985 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4677 | − | 13.4677i | −0.433991 | − | 0.433991i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.6541 | − | 23.2447i | −1.11556 | − | 0.748273i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.02573 | + | 5.02573i | −0.161617 | + | 0.161617i | −0.783282 | − | 0.621666i | \(-0.786456\pi\) |
0.621666 | + | 0.783282i | \(0.286456\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32.9696i | 1.05914i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 25.6806i | − | 0.824128i | −0.911155 | − | 0.412064i | \(-0.864808\pi\) | ||
0.911155 | − | 0.412064i | \(-0.135192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.4340 | + | 13.4340i | −0.430674 | + | 0.430674i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 75.7720 | − | 31.0694i | 2.42665 | − | 0.995017i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.5510 | + | 22.5510i | 0.721471 | + | 0.721471i | 0.968905 | − | 0.247434i | \(-0.0795873\pi\) |
−0.247434 | + | 0.968905i | \(0.579587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5875 | −0.338377 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.5693 | 0.465163 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4914 | + | 19.4914i | 0.621678 | + | 0.621678i | 0.945960 | − | 0.324282i | \(-0.105123\pi\) |
−0.324282 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12766 | − | 1.68116i | 0.0359303 | − | 0.0535663i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.3911 | − | 24.3911i | 0.776376 | − | 0.776376i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 29.8584i | − | 0.949441i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.46264i | 0.0782282i | 0.999235 | + | 0.0391141i | \(0.0124536\pi\) | ||||
−0.999235 | + | 0.0391141i | \(0.987546\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.70138 | + | 5.70138i | −0.180928 | + | 0.180928i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9591 | + | 55.6138i | 0.347427 | + | 1.76307i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.9973 | + | 24.9973i | 0.791672 | + | 0.791672i | 0.981766 | − | 0.190094i | \(-0.0608792\pi\) |
−0.190094 | + | 0.981766i | \(0.560879\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.5917 | −1.15771 |
(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 | 560.2.x.a.127.1 | ✓ | 12 | |
4.3 | odd | 2 | inner | 560.2.x.a.127.6 | yes | 12 | |
5.3 | odd | 4 | inner | 560.2.x.a.463.6 | yes | 12 | |
20.3 | even | 4 | inner | 560.2.x.a.463.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.x.a.127.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
560.2.x.a.127.6 | yes | 12 | 4.3 | odd | 2 | inner | |
560.2.x.a.463.1 | yes | 12 | 20.3 | even | 4 | inner | |
560.2.x.a.463.6 | yes | 12 | 5.3 | odd | 4 | inner |