Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 46x^{12} + 126x^{10} + 315x^{8} + 1134x^{6} + 3726x^{4} + 7290x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1889.6 | ||
Root | \(0.243856 - 1.71480i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1889 |
Dual form | 2736.2.dc.d.449.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11928 | + | 0.646214i | 0.500555 | + | 0.288996i | 0.728943 | − | 0.684575i | \(-0.240012\pi\) |
−0.228388 | + | 0.973570i | \(0.573345\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.567493 | 0.214492 | 0.107246 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107246 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.19868i | − | 1.56746i | −0.621101 | − | 0.783731i | \(-0.713314\pi\) | ||
0.621101 | − | 0.783731i | \(-0.286686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.03362 | + | 3.48351i | −1.67343 | + | 0.966153i | −0.707727 | + | 0.706486i | \(0.750279\pi\) |
−0.965698 | + | 0.259666i | \(0.916387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.318772 | + | 0.184043i | 0.0773136 | + | 0.0446370i | 0.538158 | − | 0.842844i | \(-0.319120\pi\) |
−0.460845 | + | 0.887481i | \(0.652454\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16481 | − | 4.20038i | −0.267227 | − | 0.963634i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.57542 | + | 3.79632i | −1.37107 | + | 0.791587i | −0.991063 | − | 0.133397i | \(-0.957412\pi\) |
−0.380007 | + | 0.924984i | \(0.624078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.66481 | − | 2.88354i | −0.332963 | − | 0.576709i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70169 | + | 6.41151i | 0.687386 | + | 1.19059i | 0.972681 | + | 0.232147i | \(0.0745751\pi\) |
−0.285295 | + | 0.958440i | \(0.592092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.51621i | 1.17035i | 0.810908 | + | 0.585173i | \(0.198973\pi\) | ||||
−0.810908 | + | 0.585173i | \(0.801027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.635181 | + | 0.366722i | 0.107365 | + | 0.0619873i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89784i | 0.805200i | 0.915376 | + | 0.402600i | \(0.131893\pi\) | ||||
−0.915376 | + | 0.402600i | \(0.868107\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.62146 | + | 9.73666i | −0.877925 | + | 1.52061i | −0.0243116 | + | 0.999704i | \(0.507739\pi\) |
−0.853614 | + | 0.520907i | \(0.825594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44856 | − | 4.24103i | 0.373402 | − | 0.646751i | −0.616684 | − | 0.787211i | \(-0.711525\pi\) |
0.990086 | + | 0.140459i | \(0.0448578\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.37592 | + | 4.25849i | −1.07589 | + | 0.621165i | −0.929784 | − | 0.368105i | \(-0.880007\pi\) |
−0.146104 | + | 0.989269i | \(0.546673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67795 | −0.953993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.03905 | + | 5.26380i | 0.417446 | + | 0.723038i | 0.995682 | − | 0.0928318i | \(-0.0295919\pi\) |
−0.578236 | + | 0.815870i | \(0.696259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.35946 | − | 5.81875i | 0.452989 | − | 0.784601i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.03905 | + | 5.26380i | −0.395651 | + | 0.685288i | −0.993184 | − | 0.116557i | \(-0.962814\pi\) |
0.597533 | + | 0.801844i | \(0.296148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.52983 | + | 2.64974i | 0.195875 | + | 0.339265i | 0.947187 | − | 0.320682i | \(-0.103912\pi\) |
−0.751312 | + | 0.659947i | \(0.770579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00438 | −1.11686 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.10959 | + | 0.640619i | −0.135557 | + | 0.0782641i | −0.566245 | − | 0.824237i | \(-0.691604\pi\) |
0.430688 | + | 0.902501i | \(0.358271\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.67423 | − | 6.36396i | 0.436051 | − | 0.755263i | −0.561329 | − | 0.827592i | \(-0.689710\pi\) |
0.997381 | + | 0.0723293i | \(0.0230432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.43630 | − | 12.8800i | 0.870353 | − | 1.50750i | 0.00872085 | − | 0.999962i | \(-0.497224\pi\) |
0.861632 | − | 0.507533i | \(-0.169443\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.95021i | − | 0.336208i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.12651 | − | 4.69184i | −0.914304 | − | 0.527874i | −0.0324907 | − | 0.999472i | \(-0.510344\pi\) |
−0.881814 | + | 0.471598i | \(0.843677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3503i | 1.46539i | 0.680559 | + | 0.732693i | \(0.261737\pi\) | ||||
−0.680559 | + | 0.732693i | \(0.738263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.237863 | + | 0.411990i | 0.0257998 | + | 0.0446866i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.953953 | + | 1.65229i | 0.101119 | + | 0.175143i | 0.912146 | − | 0.409866i | \(-0.134424\pi\) |
−0.811027 | + | 0.585009i | \(0.801091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.42404 | + | 1.97687i | −0.358936 | + | 0.207232i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.41060 | − | 5.45410i | 0.144724 | − | 0.559579i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.75279 | + | 2.16668i | 0.381038 | + | 0.219993i | 0.678270 | − | 0.734813i | \(-0.262730\pi\) |
−0.297232 | + | 0.954805i | \(0.596063\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.21759 | − | 1.85768i | 0.320162 | − | 0.184846i | −0.331303 | − | 0.943525i | \(-0.607488\pi\) |
0.651465 | + | 0.758679i | \(0.274155\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.14872i | 0.408785i | 0.978889 | + | 0.204393i | \(0.0655219\pi\) | ||||
−0.978889 | + | 0.204393i | \(0.934478\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.98601 | 0.772037 | 0.386019 | − | 0.922491i | \(-0.373850\pi\) | ||||
0.386019 | + | 0.922491i | \(0.373850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7920 | − | 6.23075i | −1.03368 | − | 0.596797i | −0.115645 | − | 0.993291i | \(-0.536894\pi\) |
−0.918038 | + | 0.396493i | \(0.870227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.47237 | 0.420726 | 0.210363 | − | 0.977623i | \(-0.432535\pi\) | ||||
0.210363 | + | 0.977623i | \(0.432535\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.81294 | −0.915061 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.180901 | + | 0.104443i | 0.0165832 | + | 0.00957429i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0263 | −1.45693 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.7654i | − | 0.962891i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8089 | + | 6.81787i | −1.04787 | + | 0.604988i | −0.922052 | − | 0.387065i | \(-0.873489\pi\) |
−0.125818 | + | 0.992053i | \(0.540155\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.37592 | + | 4.25849i | 0.644437 | + | 0.372066i | 0.786322 | − | 0.617817i | \(-0.211983\pi\) |
−0.141885 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.661024 | − | 2.38369i | −0.0573180 | − | 0.206692i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.72914 | + | 2.15302i | −0.318602 | + | 0.183945i | −0.650769 | − | 0.759276i | \(-0.725553\pi\) |
0.332167 | + | 0.943220i | \(0.392220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.05523 | + | 5.29181i | 0.259141 | + | 0.448846i | 0.966012 | − | 0.258497i | \(-0.0832272\pi\) |
−0.706871 | + | 0.707343i | \(0.749894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.1097 | + | 31.3669i | 1.51441 | + | 2.62303i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.56832i | 0.794606i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.5249 | − | 8.96330i | −1.27185 | − | 0.734302i | −0.296513 | − | 0.955029i | \(-0.595824\pi\) |
−0.975336 | + | 0.220727i | \(0.929157\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.59574i | − | 0.699512i | −0.936841 | − | 0.349756i | \(-0.886265\pi\) | ||
0.936841 | − | 0.349756i | \(-0.113735\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.21087 | + | 7.29344i | −0.338225 | + | 0.585823i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.829630 | − | 1.43696i | 0.0662117 | − | 0.114682i | −0.831019 | − | 0.556244i | \(-0.812242\pi\) |
0.897231 | + | 0.441562i | \(0.145575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.73150 | + | 2.15438i | −0.294083 | + | 0.169789i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.1777 | −1.18881 | −0.594405 | − | 0.804166i | \(-0.702612\pi\) | ||||
−0.594405 | + | 0.804166i | \(0.702612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.22919 | − | 10.7893i | −0.482029 | − | 0.834900i | 0.517758 | − | 0.855527i | \(-0.326767\pi\) |
−0.999787 | + | 0.0206277i | \(0.993434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.7697 | − | 30.7781i | 1.36690 | − | 2.36754i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.23855 | − | 3.87728i | 0.170194 | − | 0.294784i | −0.768294 | − | 0.640098i | \(-0.778894\pi\) |
0.938488 | + | 0.345313i | \(0.112227\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.944770 | − | 1.63639i | −0.0714179 | − | 0.123699i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.9167 | −1.48864 | −0.744321 | − | 0.667822i | \(-0.767227\pi\) | ||||
−0.744321 | + | 0.667822i | \(0.767227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5336 | − | 7.81364i | 1.00595 | − | 0.580783i | 0.0959439 | − | 0.995387i | \(-0.469413\pi\) |
0.910002 | + | 0.414603i | \(0.136080\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.16505 | + | 5.48203i | −0.232699 | + | 0.403047i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.956782 | − | 1.65720i | 0.0699668 | − | 0.121186i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8749i | 1.00395i | 0.864882 | + | 0.501975i | \(0.167393\pi\) | ||||
−0.864882 | + | 0.501975i | \(0.832607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.73610 | − | 4.46644i | −0.556857 | − | 0.321501i | 0.195026 | − | 0.980798i | \(-0.437521\pi\) |
−0.751883 | + | 0.659297i | \(0.770854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.7967i | 1.98043i | 0.139546 | + | 0.990216i | \(0.455436\pi\) | ||||
−0.139546 | + | 0.990216i | \(0.544564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5795 | − | 20.0563i | −0.820849 | − | 1.42175i | −0.905051 | − | 0.425304i | \(-0.860167\pi\) |
0.0842013 | − | 0.996449i | \(-0.473166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.10068 | + | 3.63848i | 0.147439 | + | 0.255371i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5839 | + | 7.26534i | −0.878900 | + | 0.507433i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.8364 | + | 6.05550i | −1.51046 | + | 0.418868i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1938 | + | 9.92682i | 1.18367 | + | 0.683390i | 0.956860 | − | 0.290549i | \(-0.0938380\pi\) |
0.226807 | + | 0.973940i | \(0.427171\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.48123 | − | 3.16459i | 0.373817 | − | 0.215823i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.69790i | 0.251030i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.56447 | −0.172505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.45210 | − | 3.14777i | −0.365100 | − | 0.210790i | 0.306216 | − | 0.951962i | \(-0.400937\pi\) |
−0.671315 | + | 0.741172i | \(0.734270\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.27036 | −0.0843168 | −0.0421584 | − | 0.999111i | \(-0.513423\pi\) | ||||
−0.0421584 | + | 0.999111i | \(0.513423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.33721 | −0.154447 | −0.0772237 | − | 0.997014i | \(-0.524606\pi\) | ||||
−0.0772237 | + | 0.997014i | \(0.524606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2677 | + | 8.23749i | 0.934711 | + | 0.539656i | 0.888298 | − | 0.459267i | \(-0.151888\pi\) |
0.0464127 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0076 | −0.718055 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.22455i | 0.467317i | 0.972319 | + | 0.233659i | \(0.0750698\pi\) | ||||
−0.972319 | + | 0.233659i | \(0.924930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.53918 | + | 3.19804i | −0.356810 | + | 0.206004i | −0.667680 | − | 0.744448i | \(-0.732713\pi\) |
0.310871 | + | 0.950452i | \(0.399379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.47447 | − | 4.31539i | −0.477526 | − | 0.275700i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.6601 | + | 21.2859i | 1.37820 | + | 1.35439i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.24080 | + | 5.33518i | −0.583274 | + | 0.336753i | −0.762433 | − | 0.647067i | \(-0.775996\pi\) |
0.179159 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7358 | + | 34.1835i | 1.24078 | + | 2.14910i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.61211 | − | 16.6487i | −0.599587 | − | 1.03851i | −0.992882 | − | 0.119103i | \(-0.961998\pi\) |
0.393295 | − | 0.919412i | \(-0.371335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.77949i | 0.172709i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.62360 | − | 4.40149i | −0.470091 | − | 0.271407i | 0.246187 | − | 0.969222i | \(-0.420822\pi\) |
−0.716278 | + | 0.697815i | \(0.754156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.85552i | 0.482561i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.57542 | − | 11.3890i | 0.400910 | − | 0.694397i | −0.592926 | − | 0.805257i | \(-0.702027\pi\) |
0.993836 | + | 0.110860i | \(0.0353606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00000 | − | 1.73205i | 0.0607457 | − | 0.105215i | −0.834053 | − | 0.551684i | \(-0.813985\pi\) |
0.894799 | + | 0.446469i | \(0.147319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.9906 | + | 8.65484i | −0.903969 | + | 0.521907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.3372 | −1.04169 | −0.520846 | − | 0.853651i | \(-0.674383\pi\) | ||||
−0.520846 | + | 0.853651i | \(0.674383\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.86674 | + | 11.8935i | 0.409635 | + | 0.709509i | 0.994849 | − | 0.101370i | \(-0.0323226\pi\) |
−0.585214 | + | 0.810879i | \(0.698989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.38929 | + | 7.60247i | −0.260916 | + | 0.451920i | −0.966486 | − | 0.256721i | \(-0.917358\pi\) |
0.705569 | + | 0.708641i | \(0.250691\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.19014 | + | 5.52548i | −0.188308 | + | 0.326159i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.43226 | − | 14.6051i | −0.496015 | − | 0.859123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.3394 | 1.07140 | 0.535700 | − | 0.844409i | \(-0.320048\pi\) | ||||
0.535700 | + | 0.844409i | \(0.320048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.80308 | + | 3.92776i | −0.396090 | + | 0.228683i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.4490 | − | 45.8111i | 1.52959 | − | 2.64932i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38954 | − | 2.40675i | 0.0800918 | − | 0.138723i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.95439i | 0.226428i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0784 | + | 11.0149i | 1.08886 | + | 0.628654i | 0.933273 | − | 0.359168i | \(-0.116940\pi\) |
0.155588 | + | 0.987822i | \(0.450273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.2852i | − | 1.09356i | −0.837276 | − | 0.546780i | \(-0.815853\pi\) | ||
0.837276 | − | 0.546780i | \(-0.184147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.53766 | + | 11.3236i | 0.369531 | + | 0.640046i | 0.989492 | − | 0.144586i | \(-0.0461852\pi\) |
−0.619962 | + | 0.784632i | \(0.712852\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0434 | + | 20.8598i | 0.676427 | + | 1.17161i | 0.976050 | + | 0.217548i | \(0.0698057\pi\) |
−0.299623 | + | 0.954058i | \(0.596861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.3314 | − | 19.2439i | 1.86620 | − | 1.07745i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.401741 | − | 1.55334i | 0.0223535 | − | 0.0864302i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0897 | + | 11.5988i | 1.11438 | + | 0.643386i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.18578 | + | 2.41666i | −0.230770 | + | 0.133235i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.91609i | − | 0.490072i | −0.969514 | − | 0.245036i | \(-0.921200\pi\) | ||
0.969514 | − | 0.245036i | \(-0.0787999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.65591 | −0.0904720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4778 | − | 7.78138i | −0.734180 | − | 0.423879i | 0.0857694 | − | 0.996315i | \(-0.472665\pi\) |
−0.819949 | + | 0.572436i | \(0.805998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.8757 | 1.83447 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.76214 | −0.419116 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.33896 | − | 4.23715i | −0.393976 | − | 0.227462i | 0.289905 | − | 0.957055i | \(-0.406376\pi\) |
−0.683881 | + | 0.729593i | \(0.739709\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.72700 | −0.199502 | −0.0997510 | − | 0.995012i | \(-0.531805\pi\) | ||||
−0.0997510 | + | 0.995012i | \(0.531805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.08071i | 0.217194i | 0.994086 | + | 0.108597i | \(0.0346359\pi\) | ||||
−0.994086 | + | 0.108597i | \(0.965364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.22496 | − | 4.74868i | 0.436536 | − | 0.252034i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5822 | − | 8.99636i | −0.822395 | − | 0.474810i | 0.0288467 | − | 0.999584i | \(-0.490817\pi\) |
−0.851242 | + | 0.524774i | \(0.824150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2864 | + | 9.78534i | −0.857180 | + | 0.515018i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.6465 | − | 9.61088i | 0.871319 | − | 0.503056i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.68238 | + | 8.11012i | 0.244418 | + | 0.423345i | 0.961968 | − | 0.273162i | \(-0.0880697\pi\) |
−0.717550 | + | 0.696507i | \(0.754736\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72464 | + | 2.98717i | 0.0895389 | + | 0.155086i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.5873i | − | 0.548189i | −0.961703 | − | 0.274094i | \(-0.911622\pi\) | ||
0.961703 | − | 0.274094i | \(-0.0883781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −44.6691 | − | 25.7897i | −2.30058 | − | 1.32824i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.3186i | − | 0.786865i | −0.919354 | − | 0.393432i | \(-0.871288\pi\) | ||
0.919354 | − | 0.393432i | \(-0.128712\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.3940 | − | 19.7350i | 0.582207 | − | 1.00841i | −0.413010 | − | 0.910726i | \(-0.635523\pi\) |
0.995217 | − | 0.0976857i | \(-0.0311440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.90647 | − | 3.30210i | 0.0971626 | − | 0.168291i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.9670 | − | 16.7241i | 1.46869 | − | 0.847947i | 0.469303 | − | 0.883037i | \(-0.344505\pi\) |
0.999384 | + | 0.0350897i | \(0.0111717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.79475 | −0.141336 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.06387 | − | 10.5029i | −0.305106 | − | 0.528460i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8033 | + | 20.4440i | −0.592393 | + | 1.02605i | 0.401517 | + | 0.915852i | \(0.368483\pi\) |
−0.993909 | + | 0.110202i | \(0.964850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.52315 | + | 6.10227i | −0.175938 | + | 0.304733i | −0.940485 | − | 0.339834i | \(-0.889629\pi\) |
0.764548 | + | 0.644567i | \(0.222962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.6993 | − | 39.3164i | −1.13073 | − | 1.95849i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.4623 | 1.26212 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8592 | + | 6.26957i | −0.536953 | + | 0.310010i | −0.743843 | − | 0.668354i | \(-0.766999\pi\) |
0.206890 | + | 0.978364i | \(0.433666\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.72464 | + | 2.98717i | −0.0848640 | + | 0.146989i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.62715 | + | 14.9427i | −0.423490 | + | 0.733507i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.58347i | − | 0.321624i | −0.986985 | − | 0.160812i | \(-0.948589\pi\) | ||
0.986985 | − | 0.160812i | \(-0.0514112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.01114 | + | 0.583781i | 0.0492798 | + | 0.0284517i | 0.524437 | − | 0.851449i | \(-0.324276\pi\) |
−0.475158 | + | 0.879901i | \(0.657609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.22559i | − | 0.0594499i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.868167 | + | 1.50371i | 0.0420136 | + | 0.0727696i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8530 | − | 20.5300i | −0.570940 | − | 0.988897i | −0.996470 | − | 0.0839526i | \(-0.973246\pi\) |
0.425530 | − | 0.904944i | \(-0.360088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.9098 | − | 15.5364i | 1.29320 | − | 0.746630i | 0.313980 | − | 0.949430i | \(-0.398337\pi\) |
0.979220 | + | 0.202800i | \(0.0650041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.6051 | + | 23.1973i | 1.12919 | + | 1.10968i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2663 | − | 6.50459i | −0.537711 | − | 0.310447i | 0.206440 | − | 0.978459i | \(-0.433812\pi\) |
−0.744151 | + | 0.668012i | \(0.767146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.1466 | + | 10.4770i | −0.862172 | + | 0.497775i | −0.864739 | − | 0.502221i | \(-0.832516\pi\) |
0.00256685 | + | 0.999997i | \(0.499183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.46583i | 0.116892i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.3017 | −1.24125 | −0.620626 | − | 0.784107i | \(-0.713122\pi\) | ||||
−0.620626 | + | 0.784107i | \(0.713122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.6178 | + | 29.2242i | 2.38350 | + | 1.37611i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.10992 | −0.239557 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5839 | 0.682208 | 0.341104 | − | 0.940026i | \(-0.389199\pi\) | ||||
0.341104 | + | 0.940026i | \(0.389199\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0887 | + | 11.0209i | 0.889050 | + | 0.513293i | 0.873632 | − | 0.486588i | \(-0.161759\pi\) |
0.0154182 | + | 0.999881i | \(0.495092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.59279 | 0.0740234 | 0.0370117 | − | 0.999315i | \(-0.488216\pi\) | ||||
0.0370117 | + | 0.999315i | \(0.488216\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 27.9641i | − | 1.29402i | −0.762480 | − | 0.647011i | \(-0.776019\pi\) | ||
0.762480 | − | 0.647011i | \(-0.223981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.629681 | + | 0.363547i | −0.0290760 | + | 0.0167870i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.0478 | − | 12.7293i | −1.01376 | − | 0.585293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.1728 | + | 10.3517i | −0.466759 | + | 0.474966i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9582 | + | 9.79083i | −0.774841 | + | 0.447354i | −0.834599 | − | 0.550859i | \(-0.814300\pi\) |
0.0597581 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0617 | − | 29.5517i | −0.777946 | − | 1.34744i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.80027 | + | 4.85021i | 0.127154 | + | 0.220237i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.40254i | 0.290127i | 0.989422 | + | 0.145063i | \(0.0463386\pi\) | ||||
−0.989422 | + | 0.145063i | \(0.953661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4305 | + | 15.8370i | 1.23792 | + | 0.714713i | 0.968668 | − | 0.248357i | \(-0.0798907\pi\) |
0.269251 | + | 0.963070i | \(0.413224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.72508i | 0.122731i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.08510 | − | 3.61150i | 0.0935296 | − | 0.161998i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6526 | − | 27.1110i | 0.700704 | − | 1.21366i | −0.267515 | − | 0.963554i | \(-0.586202\pi\) |
0.968219 | − | 0.250102i | \(-0.0804642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.6512 | + | 7.30415i | −0.564087 | + | 0.325676i | −0.754784 | − | 0.655973i | \(-0.772259\pi\) |
0.190697 | + | 0.981649i | \(0.438925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.80183 | 0.213679 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.73838 | + | 11.6712i | 0.298673 | + | 0.517317i | 0.975833 | − | 0.218519i | \(-0.0701226\pi\) |
−0.677159 | + | 0.735836i | \(0.736789\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.22004 | − | 7.30933i | 0.186684 | − | 0.323346i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.68096 | + | 4.64355i | −0.118137 | + | 0.204619i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.1385 | + | 38.3451i | 0.973651 | + | 1.68641i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.9855 | −1.48893 | −0.744466 | − | 0.667660i | \(-0.767296\pi\) | ||||
−0.744466 | + | 0.667660i | \(0.767296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3345 | + | 14.0496i | −1.06408 | + | 0.614344i | −0.926557 | − | 0.376155i | \(-0.877246\pi\) |
−0.137519 | + | 0.990499i | \(0.543913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.19927 | + | 2.07719i | −0.0522408 | + | 0.0904837i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.3241 | − | 30.0062i | 0.753221 | − | 1.30462i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 78.3298i | − | 3.39284i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.93855 | + | 5.16067i | 0.386447 | + | 0.223115i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.7165i | 1.49535i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.28083 | + | 12.6108i | 0.313027 | + | 0.542179i | 0.979016 | − | 0.203782i | \(-0.0653235\pi\) |
−0.665989 | + | 0.745962i | \(0.731990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.05279 | − | 13.9478i | −0.344944 | − | 0.597460i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.2049 | − | 14.5520i | 1.07768 | − | 0.622200i | 0.147412 | − | 0.989075i | \(-0.452906\pi\) |
0.930270 | + | 0.366875i | \(0.119572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.6190 | − | 23.0167i | 0.963602 | − | 0.980545i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.61174 | − | 2.66259i | −0.196111 | − | 0.113225i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.81683 | − | 2.20365i | 0.161724 | − | 0.0933717i | −0.416953 | − | 0.908928i | \(-0.636902\pi\) |
0.578678 | + | 0.815556i | \(0.303569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.1184i | 1.44305i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.6092 | 1.07930 | 0.539650 | − | 0.841889i | \(-0.318557\pi\) | ||||
0.539650 | + | 0.841889i | \(0.318557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00582 | + | 2.89011i | 0.210596 | + | 0.121588i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.5543 | 1.07129 | 0.535646 | − | 0.844442i | \(-0.320068\pi\) | ||||
0.535646 | + | 0.844442i | \(0.320068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.73586 | −0.198190 | −0.0990949 | − | 0.995078i | \(-0.531595\pi\) | ||||
−0.0990949 | + | 0.995078i | \(0.531595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.8937 | + | 12.6403i | 0.913031 | + | 0.527139i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.68553 | 0.153431 | 0.0767154 | − | 0.997053i | \(-0.475557\pi\) | ||||
0.0767154 | + | 0.997053i | \(0.475557\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.57620i | 0.314314i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.3648 | − | 15.7991i | 1.13333 | − | 0.654331i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.2610 | + | 20.9353i | 1.49665 | + | 0.864093i | 0.999993 | − | 0.00385243i | \(-0.00122627\pi\) |
0.496660 | + | 0.867945i | \(0.334560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3706 | − | 7.59018i | 1.12779 | − | 0.312748i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.3479 | − | 22.7175i | 1.61582 | − | 0.932896i | 0.627840 | − | 0.778343i | \(-0.283939\pi\) |
0.987984 | − | 0.154554i | \(-0.0493940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.134985 | + | 0.233801i | 0.00553386 | + | 0.00958492i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.87586 | − | 8.44524i | −0.199222 | − | 0.345063i | 0.749054 | − | 0.662509i | \(-0.230508\pi\) |
−0.948277 | + | 0.317446i | \(0.897175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 23.4702i | − | 0.957371i | −0.877986 | − | 0.478686i | \(-0.841113\pi\) | ||
0.877986 | − | 0.478686i | \(-0.158887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.9378 | − | 10.3564i | −0.729276 | − | 0.421048i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.5195i | 1.48228i | 0.671351 | + | 0.741139i | \(0.265714\pi\) | ||||
−0.671351 | + | 0.741139i | \(0.734286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6690 | − | 51.3882i | 1.20028 | − | 2.07894i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.29576 | + | 10.9046i | −0.254283 | + | 0.440432i | −0.964701 | − | 0.263349i | \(-0.915173\pi\) |
0.710417 | + | 0.703781i | \(0.248506\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.9375 | − | 14.9750i | 1.04420 | − | 0.602872i | 0.123183 | − | 0.992384i | \(-0.460690\pi\) |
0.921021 | + | 0.389512i | \(0.127356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.39512 | 0.297235 | 0.148618 | − | 0.988895i | \(-0.452518\pi\) | ||||
0.148618 | + | 0.988895i | \(0.452518\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.541361 | + | 0.937665i | 0.0216892 | + | 0.0375668i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.36729 | + | 2.36822i | −0.0546917 | + | 0.0947288i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.901414 | + | 1.56130i | −0.0359417 | + | 0.0622529i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.08910 | − | 14.0107i | −0.322022 | − | 0.557759i | 0.658883 | − | 0.752245i | \(-0.271029\pi\) |
−0.980905 | + | 0.194487i | \(0.937696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.6232 | −0.699356 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.2922 | − | 23.2627i | 1.59644 | − | 0.921703i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0432 | + | 26.0555i | −0.594169 | + | 1.02913i | 0.399494 | + | 0.916736i | \(0.369186\pi\) |
−0.993664 | + | 0.112396i | \(0.964148\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1523 | + | 29.7087i | −0.676421 | + | 1.17160i | 0.299631 | + | 0.954055i | \(0.403137\pi\) |
−0.976051 | + | 0.217540i | \(0.930197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.64279i | 0.103899i | 0.998650 | + | 0.0519494i | \(0.0165435\pi\) | ||||
−0.998650 | + | 0.0519494i | \(0.983457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3648 | + | 15.7991i | 1.07416 | + | 0.620168i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 5.11932i | − | 0.200334i | −0.994971 | − | 0.100167i | \(-0.968062\pi\) | ||
0.994971 | − | 0.100167i | \(-0.0319378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.50379 | + | 9.53285i | 0.215051 | + | 0.372479i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.54797 | − | 11.3414i | −0.255073 | − | 0.441799i | 0.709843 | − | 0.704360i | \(-0.248766\pi\) |
−0.964915 | + | 0.262562i | \(0.915433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.92165 | + | 2.26416i | −0.152534 | + | 0.0880658i | −0.574325 | − | 0.818628i | \(-0.694735\pi\) |
0.421790 | + | 0.906694i | \(0.361402\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.800503 | − | 3.09516i | 0.0310422 | − | 0.120025i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.6803 | − | 28.1056i | −1.88491 | − | 1.08825i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.7752 | − | 7.95310i | 0.531784 | − | 0.307026i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.7011i | 0.759423i | 0.925105 | + | 0.379712i | \(0.123977\pi\) | ||||
−0.925105 | + | 0.379712i | \(0.876023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.1374 | 0.581777 | 0.290889 | − | 0.956757i | \(-0.406049\pi\) | ||||
0.290889 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.12968 | + | 1.22957i | 0.0817297 | + | 0.0471866i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.68384 | −0.294014 | −0.147007 | − | 0.989135i | \(-0.546964\pi\) | ||||
−0.147007 | + | 0.989135i | \(0.546964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.56524 | −0.212637 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.6730 | − | 21.1732i | −1.39713 | − | 0.806633i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.59504 | −0.174804 | −0.0874019 | − | 0.996173i | \(-0.527856\pi\) | ||||
−0.0874019 | + | 0.996173i | \(0.527856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.89733i | 0.299563i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.58393 | + | 2.06919i | −0.135751 | + | 0.0783760i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.0953 | − | 20.2623i | −1.32553 | − | 0.765296i | −0.340927 | − | 0.940090i | \(-0.610741\pi\) |
−0.984605 | + | 0.174793i | \(0.944074\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.5728 | − | 5.70508i | 0.775918 | − | 0.215171i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.82596 | − | 1.05422i | 0.0686723 | − | 0.0396480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.07280 | − | 8.78634i | −0.190513 | − | 0.329978i | 0.754907 | − | 0.655831i | \(-0.227682\pi\) |
−0.945420 | + | 0.325853i | \(0.894348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.7376 | − | 42.8468i | −0.926431 | − | 1.60463i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.8109i | 1.75063i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9443 | + | 10.3602i | 0.669211 | + | 0.386369i | 0.795778 | − | 0.605589i | \(-0.207062\pi\) |
−0.126567 | + | 0.991958i | \(0.540396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.35437i | 0.0876811i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.3252 | − | 21.3479i | 0.457748 | − | 0.792843i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.64321 | + | 13.2384i | −0.283471 | + | 0.490986i | −0.972237 | − | 0.233997i | \(-0.924819\pi\) |
0.688766 | + | 0.724983i | \(0.258153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.56107 | − | 0.901282i | 0.0577381 | − | 0.0333351i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.6289 | 0.909689 | 0.454845 | − | 0.890571i | \(-0.349695\pi\) | ||||
0.454845 | + | 0.890571i | \(0.349695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.33038 | + | 5.76838i | 0.122676 | + | 0.212481i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.955908 | + | 1.65568i | −0.0351636 | + | 0.0609052i | −0.883072 | − | 0.469238i | \(-0.844529\pi\) |
0.847908 | + | 0.530143i | \(0.177862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.9492 | + | 38.0172i | −0.805239 | + | 1.39471i | 0.110891 | + | 0.993833i | \(0.464630\pi\) |
−0.916130 | + | 0.400882i | \(0.868704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.5844 | − | 20.0648i | −0.424420 | − | 0.735118i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.53200 | 0.165596 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.4632 | + | 10.6598i | −0.673733 | + | 0.388980i | −0.797490 | − | 0.603333i | \(-0.793839\pi\) |
0.123757 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.55469 | − | 9.62100i | 0.202156 | − | 0.350144i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.43453 | + | 7.68084i | −0.161176 | + | 0.279165i | −0.935291 | − | 0.353880i | \(-0.884862\pi\) |
0.774115 | + | 0.633045i | \(0.218195\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.98326i | 0.253143i | 0.991957 | + | 0.126571i | \(0.0403973\pi\) | ||||
−0.991957 | + | 0.126571i | \(0.959603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.12436 | − | 3.53590i | −0.221717 | − | 0.128008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 42.3463i | − | 1.52904i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7022 | + | 41.0535i | 0.854724 | + | 1.48043i | 0.876901 | + | 0.480672i | \(0.159607\pi\) |
−0.0221765 | + | 0.999754i | \(0.507060\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.0383 | − | 36.4394i | −0.756695 | − | 1.31063i | −0.944527 | − | 0.328433i | \(-0.893479\pi\) |
0.187832 | − | 0.982201i | \(-0.439854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.7898 | − | 10.8483i | 0.674949 | − | 0.389682i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.4457 | + | 12.2709i | 1.69992 | + | 0.439650i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.0842 | − | 19.1012i | −1.18385 | − | 0.683494i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.85717 | − | 1.07224i | 0.0662852 | − | 0.0382698i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.3759i | − | 1.29666i | −0.761360 | − | 0.648330i | \(-0.775468\pi\) | ||
0.761360 | − | 0.648330i | \(-0.224532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.53804 | 0.0902423 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.4608 | − | 10.6584i | −0.655563 | − | 0.378490i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.4903 | 1.29255 | 0.646277 | − | 0.763103i | \(-0.276325\pi\) | ||||
0.646277 | + | 0.763103i | \(0.276325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.13499 | −0.110908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −66.9592 | − | 38.6589i | −2.36294 | − | 1.36424i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.56877 | −0.196273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.2246i | 0.570426i | 0.958464 | + | 0.285213i | \(0.0920644\pi\) | ||||
−0.958464 | + | 0.285213i | \(0.907936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8200 | − | 9.71103i | 0.590630 | − | 0.341001i | −0.174716 | − | 0.984619i | \(-0.555901\pi\) |
0.765347 | + | 0.643618i | \(0.222568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9880 | − | 9.80804i | −0.595065 | − | 0.343561i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.6661 | − | 5.34487i | −0.723014 | − | 0.186993i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.0185 | + | 15.0218i | −0.908052 | + | 0.524264i | −0.879804 | − | 0.475337i | \(-0.842326\pi\) |
−0.0282484 | + | 0.999601i | \(0.508993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4360 | − | 21.5399i | −0.433493 | − | 0.750833i | 0.563678 | − | 0.825995i | \(-0.309386\pi\) |
−0.997171 | + | 0.0751621i | \(0.976053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9634 | + | 20.7213i | 0.416010 | + | 0.720550i | 0.995534 | − | 0.0944052i | \(-0.0300949\pi\) |
−0.579524 | + | 0.814955i | \(0.696762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 9.30883i | − | 0.323309i | −0.986847 | − | 0.161655i | \(-0.948317\pi\) | ||
0.986847 | − | 0.161655i | \(-0.0516830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.12875 | − | 1.22903i | −0.0737567 | − | 0.0425834i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.1016i | − | 0.557218i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.9788 | + | 24.2120i | −0.482601 | + | 0.835890i | −0.999800 | − | 0.0199750i | \(-0.993641\pi\) |
0.517199 | + | 0.855865i | \(0.326975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9050 | + | 22.3520i | −0.444998 | + | 0.770760i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.7784 | − | 22.9661i | 1.36842 | − | 0.790057i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.09479 | −0.312501 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.5938 | − | 32.2053i | −0.637386 | − | 1.10398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.9441 | − | 24.1519i | 0.477438 | − | 0.826947i | −0.522228 | − | 0.852806i | \(-0.674899\pi\) |
0.999666 | + | 0.0258593i | \(0.00823219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.5128 | + | 30.3330i | −0.598225 | + | 1.03616i | 0.394858 | + | 0.918742i | \(0.370794\pi\) |
−0.993083 | + | 0.117415i | \(0.962539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0062 | + | 41.5800i | 0.819081 | + | 1.41869i | 0.906360 | + | 0.422506i | \(0.138850\pi\) |
−0.0872788 | + | 0.996184i | \(0.527817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.42220 | 0.150533 | 0.0752667 | − | 0.997163i | \(-0.476019\pi\) | ||||
0.0752667 | + | 0.997163i | \(0.476019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.01111 | − | 2.89317i | 0.170383 | − | 0.0983706i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.3914 | + | 42.2471i | −0.827422 | + | 1.43314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.46321 | − | 7.73051i | 0.151230 | − | 0.261938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 6.10931i | − | 0.206532i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4386 | − | 15.2643i | −0.892768 | − | 0.515440i | −0.0179213 | − | 0.999839i | \(-0.505705\pi\) |
−0.874847 | + | 0.484399i | \(0.839038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4912i | 1.46526i | 0.680629 | + | 0.732629i | \(0.261707\pi\) | ||||
−0.680629 | + | 0.732629i | \(0.738293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0588 | + | 33.0108i | 0.641379 | + | 1.11090i | 0.985125 | + | 0.171838i | \(0.0549706\pi\) |
−0.343747 | + | 0.939062i | \(0.611696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.77728 | − | 10.0065i | −0.193982 | − | 0.335987i | 0.752584 | − | 0.658496i | \(-0.228807\pi\) |
−0.946566 | + | 0.322509i | \(0.895474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.70146 | + | 3.86909i | −0.224760 | + | 0.129765i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.4789 | + | 26.0213i | 0.886081 | + | 0.870771i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.2922 | − | 12.8704i | −0.745147 | − | 0.430211i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.7788 | + | 24.1210i | −1.39340 | + | 0.804480i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.23727i | 0.0745343i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.1971 | 0.671375 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.0561 | + | 17.9303i | 1.03120 | + | 0.595365i | 0.917329 | − | 0.398131i | \(-0.130341\pi\) |
0.113873 | + | 0.993495i | \(0.463674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0217 | 1.39224 | 0.696121 | − | 0.717925i | \(-0.254908\pi\) | ||||
0.696121 | + | 0.717925i | \(0.254908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.4040 | 2.29694 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.18578 | + | 2.41666i | 0.138227 | + | 0.0798052i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.57457 | 0.282849 | 0.141425 | − | 0.989949i | \(-0.454832\pi\) | ||||
0.141425 | + | 0.989949i | \(0.454832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.1970i | 1.68517i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1231 | − | 8.15400i | 0.464366 | − | 0.268102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.20113 | + | 3.58022i | 0.203452 | + | 0.117463i | 0.598265 | − | 0.801298i | \(-0.295857\pi\) |
−0.394812 | + | 0.918762i | \(0.629190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.77858 | + | 28.0499i | 0.254933 | + | 0.919300i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14181 | − | 1.23657i | 0.0700445 | − | 0.0404402i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.73610 | − | 4.73906i | −0.0893844 | − | 0.154818i | 0.817867 | − | 0.575408i | \(-0.195157\pi\) |
−0.907251 | + | 0.420589i | \(0.861823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.9764 | − | 24.2079i | −0.455618 | − | 0.789154i | 0.543105 | − | 0.839665i | \(-0.317249\pi\) |
−0.998724 | + | 0.0505105i | \(0.983915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 85.3635i | − | 2.77982i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.45438 | − | 2.57174i | −0.144748 | − | 0.0835702i | 0.425877 | − | 0.904781i | \(-0.359966\pi\) |
−0.570625 | + | 0.821211i | \(0.693299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 103.618i | 3.36357i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.85765 | − | 13.6099i | 0.254534 | − | 0.440866i | −0.710235 | − | 0.703965i | \(-0.751411\pi\) |
0.964769 | + | 0.263099i | \(0.0847445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.96613 | + | 15.5298i | −0.290137 | + | 0.502532i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.11626 | + | 1.22182i | −0.0683375 | + | 0.0394547i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.4610 | −0.369711 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.77255 | − | 9.99835i | −0.185825 | − | 0.321858i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.83027 | − | 11.8304i | 0.219647 | − | 0.380439i | −0.735053 | − | 0.678009i | \(-0.762843\pi\) |
0.954700 | + | 0.297570i | \(0.0961762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.857770 | − | 1.48570i | 0.0275271 | − | 0.0476784i | −0.851934 | − | 0.523650i | \(-0.824570\pi\) |
0.879461 | + | 0.475971i | \(0.157903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.73382 | + | 3.00307i | 0.0555837 | + | 0.0962738i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0857 | 0.994519 | 0.497259 | − | 0.867602i | \(-0.334340\pi\) | ||||
0.497259 | + | 0.867602i | \(0.334340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.58975 | − | 4.95930i | 0.274530 | − | 0.158500i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.745601 | − | 1.29142i | 0.0237810 | − | 0.0411898i | −0.853890 | − | 0.520454i | \(-0.825763\pi\) |
0.877671 | + | 0.479264i | \(0.159096\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9626 | + | 31.1121i | −0.572336 | + | 0.991315i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.1821i | 1.18232i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.1101 | + | 21.4255i | 1.17884 | + | 0.680604i | 0.955746 | − | 0.294193i | \(-0.0950508\pi\) |
0.223095 | + | 0.974797i | \(0.428384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 29.9314i | − | 0.948888i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.82963 | + | 17.0254i | 0.311308 | + | 0.539200i | 0.978646 | − | 0.205554i | \(-0.0658998\pi\) |
−0.667338 | + | 0.744755i | \(0.732566\pi\) | |||||||
\(998\) | 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 | 2736.2.dc.d.1889.6 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.d.1889.3 | 16 | ||
4.3 | odd | 2 | 684.2.bk.a.521.6 | yes | 16 | ||
12.11 | even | 2 | 684.2.bk.a.521.3 | yes | 16 | ||
19.12 | odd | 6 | inner | 2736.2.dc.d.449.3 | 16 | ||
57.50 | even | 6 | inner | 2736.2.dc.d.449.6 | 16 | ||
76.31 | even | 6 | 684.2.bk.a.449.3 | ✓ | 16 | ||
228.107 | odd | 6 | 684.2.bk.a.449.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.bk.a.449.3 | ✓ | 16 | 76.31 | even | 6 | ||
684.2.bk.a.449.6 | yes | 16 | 228.107 | odd | 6 | ||
684.2.bk.a.521.3 | yes | 16 | 12.11 | even | 2 | ||
684.2.bk.a.521.6 | yes | 16 | 4.3 | odd | 2 | ||
2736.2.dc.d.449.3 | 16 | 19.12 | odd | 6 | inner | ||
2736.2.dc.d.449.6 | 16 | 57.50 | even | 6 | inner | ||
2736.2.dc.d.1889.3 | 16 | 3.2 | odd | 2 | inner | ||
2736.2.dc.d.1889.6 | 16 | 1.1 | even | 1 | trivial |