Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
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([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.954288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1855.1 | ||
Root | \(-1.62241 - 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1855 |
Dual form | 2736.2.bm.n.559.1 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −1.33641 | − | 2.31473i | −0.597662 | − | 1.03518i | −0.993165 | − | 0.116716i | \(-0.962763\pi\) |
0.395504 | − | 0.918464i | \(-0.370570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.93569i | − | 1.48755i | −0.668430 | − | 0.743775i | \(-0.733033\pi\) | ||
0.668430 | − | 0.743775i | \(-0.266967\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20364i | 0.664421i | 0.943205 | + | 0.332211i | \(0.107795\pi\) | ||||
−0.943205 | + | 0.332211i | \(0.892205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60083 | − | 2.07894i | −0.998691 | − | 0.576594i | −0.0908300 | − | 0.995866i | \(-0.528952\pi\) |
−0.907861 | + | 0.419272i | \(0.862285\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.571993 | + | 0.990721i | 0.138729 | + | 0.240285i | 0.927016 | − | 0.375023i | \(-0.122365\pi\) |
−0.788287 | + | 0.615308i | \(0.789032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24482 | − | 0.990721i | −0.973828 | − | 0.227287i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.19243 | − | 1.84315i | −0.665667 | − | 0.384323i | 0.128766 | − | 0.991675i | \(-0.458898\pi\) |
−0.794433 | + | 0.607352i | \(0.792232\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.07199 | + | 1.85675i | −0.214399 | + | 0.371349i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.10083 | + | 1.21292i | 0.390114 | + | 0.225233i | 0.682210 | − | 0.731157i | \(-0.261019\pi\) |
−0.292095 | + | 0.956389i | \(0.594352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.67282 | 0.659659 | 0.329829 | − | 0.944041i | \(-0.393009\pi\) | ||||
0.329829 | + | 0.944041i | \(0.393009\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.11007 | + | 5.25970i | −1.53988 | + | 0.889051i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.0478i | − | 1.65185i | −0.563780 | − | 0.825925i | \(-0.690653\pi\) | ||
0.563780 | − | 0.825925i | \(-0.309347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.01847 | + | 4.62947i | −1.25227 | + | 0.723001i | −0.971561 | − | 0.236790i | \(-0.923905\pi\) |
−0.280714 | + | 0.959791i | \(0.590571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.490764 | + | 0.283343i | −0.0748409 | + | 0.0432094i | −0.536953 | − | 0.843612i | \(-0.680425\pi\) |
0.462113 | + | 0.886821i | \(0.347092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.6336 | + | 6.13932i | 1.55107 | + | 0.895512i | 0.998055 | + | 0.0623432i | \(0.0198573\pi\) |
0.553018 | + | 0.833169i | \(0.313476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.48963 | −1.21280 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.09159 | − | 2.36228i | −0.562024 | − | 0.324485i | 0.191934 | − | 0.981408i | \(-0.438524\pi\) |
−0.753957 | + | 0.656923i | \(0.771858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.10083 | − | 2.94497i | 0.687796 | − | 0.397099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.33641 | + | 2.31473i | 0.173986 | + | 0.301353i | 0.939810 | − | 0.341698i | \(-0.111002\pi\) |
−0.765824 | + | 0.643050i | \(0.777669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.41764 | + | 11.1157i | −0.821695 | + | 1.42322i | 0.0827247 | + | 0.996572i | \(0.473638\pi\) |
−0.904419 | + | 0.426645i | \(0.859696\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.1133i | 1.37843i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73558 | − | 3.00612i | 0.212035 | − | 0.367255i | −0.740316 | − | 0.672259i | \(-0.765324\pi\) |
0.952351 | + | 0.305003i | \(0.0986576\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.24482 | + | 10.8163i | 0.741123 | + | 1.28366i | 0.951984 | + | 0.306147i | \(0.0990400\pi\) |
−0.210861 | + | 0.977516i | \(0.567627\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.35601 | + | 2.34868i | 0.158709 | + | 0.274893i | 0.934404 | − | 0.356216i | \(-0.115933\pi\) |
−0.775694 | + | 0.631109i | \(0.782600\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.67282 | 0.988360 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50924 | − | 6.07817i | −0.394820 | − | 0.683848i | 0.598258 | − | 0.801303i | \(-0.295860\pi\) |
−0.993078 | + | 0.117455i | \(0.962526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.98144i | 0.217492i | 0.994070 | + | 0.108746i | \(0.0346835\pi\) | ||||
−0.994070 | + | 0.108746i | \(0.965317\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.52884 | − | 2.64802i | 0.165826 | − | 0.287218i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9269 | − | 7.46334i | −1.37025 | − | 0.791112i | −0.379287 | − | 0.925279i | \(-0.623831\pi\) |
−0.990959 | + | 0.134167i | \(0.957164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.18206 | + | 14.1717i | −0.857713 | + | 1.48560i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.37957 | + | 11.1496i | 0.346736 | + | 1.14393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.91764 | − | 1.68450i | 0.296242 | − | 0.171035i | −0.344512 | − | 0.938782i | \(-0.611956\pi\) |
0.640753 | + | 0.767747i | \(0.278622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.10083 | − | 8.83490i | 0.507552 | − | 0.879105i | −0.492410 | − | 0.870363i | \(-0.663884\pi\) |
0.999962 | − | 0.00874190i | \(-0.00278267\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4504 | 1.62091 | 0.810455 | − | 0.585802i | \(-0.199220\pi\) | ||||
0.810455 | + | 0.585802i | \(0.199220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.85601 | 0.469449 | 0.234724 | − | 0.972062i | \(-0.424581\pi\) | ||||
0.234724 | + | 0.972062i | \(0.424581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7345 | + | 7.35224i | −1.21974 | + | 0.704217i | −0.964862 | − | 0.262757i | \(-0.915368\pi\) |
−0.254877 | + | 0.966973i | \(0.582035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4823i | 1.36238i | 0.732107 | + | 0.681189i | \(0.238537\pi\) | ||||
−0.732107 | + | 0.681189i | \(0.761463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.85282i | 0.918780i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.89917 | − | 2.25119i | 0.357436 | − | 0.206366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.14399 | 0.558544 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.63362 | −0.682772 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.81681 | + | 10.0750i | −0.516158 | + | 0.894013i | 0.483666 | + | 0.875253i | \(0.339305\pi\) |
−0.999824 | + | 0.0187598i | \(0.994028\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7160 | + | 6.18687i | −0.936260 | + | 0.540550i | −0.888786 | − | 0.458323i | \(-0.848450\pi\) |
−0.0474737 | + | 0.998872i | \(0.515117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.89917 | + | 16.7063i | −0.338101 | + | 1.44862i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.71598 | + | 8.16832i | −0.402913 | + | 0.697866i | −0.994076 | − | 0.108686i | \(-0.965336\pi\) |
0.591163 | + | 0.806552i | \(0.298669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8941 | + | 6.86705i | 1.00884 | + | 0.582456i | 0.910853 | − | 0.412731i | \(-0.135425\pi\) |
0.0979905 | + | 0.995187i | \(0.468759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.58123 | − | 7.93492i | 0.383102 | − | 0.663551i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.48382i | − | 0.538452i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.15322 | − | 14.1218i | −0.667938 | − | 1.15690i | −0.978480 | − | 0.206343i | \(-0.933844\pi\) |
0.310542 | − | 0.950560i | \(-0.399490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.05767 | −0.574345 | −0.287173 | − | 0.957879i | \(-0.592715\pi\) | ||||
−0.287173 | + | 0.957879i | \(0.592715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.90841 | − | 8.50161i | −0.394253 | − | 0.682866i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.66246 | + | 9.80766i | 0.451913 | + | 0.782737i | 0.998505 | − | 0.0546625i | \(-0.0174083\pi\) |
−0.546592 | + | 0.837399i | \(0.684075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.25405 | + | 12.5644i | −0.571699 | + | 0.990212i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.915973i | − | 0.0717445i | −0.999356 | − | 0.0358723i | \(-0.988579\pi\) | ||
0.999356 | − | 0.0358723i | \(-0.0114209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.192425 | + | 0.333290i | −0.0148903 | + | 0.0257908i | −0.873375 | − | 0.487049i | \(-0.838073\pi\) |
0.858484 | + | 0.512840i | \(0.171407\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.14399 | + | 3.71349i | 0.164922 | + | 0.285653i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.34960 | + | 5.39799i | −0.710837 | + | 0.410402i | −0.811371 | − | 0.584532i | \(-0.801278\pi\) |
0.100534 | + | 0.994934i | \(0.467945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.30757 | + | 4.21903i | 0.552401 | + | 0.318929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.03920 | −0.0776737 | −0.0388368 | − | 0.999246i | \(-0.512365\pi\) | ||||
−0.0388368 | + | 0.999246i | \(0.512365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.73445 | − | 3.88814i | −0.500568 | − | 0.289003i | 0.228380 | − | 0.973572i | \(-0.426657\pi\) |
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23.2580 | + | 13.4280i | −1.70996 | + | 0.987247i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.18319 | + | 1.26047i | −0.159651 | + | 0.0921743i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 26.2621i | − | 1.90026i | −0.311851 | − | 0.950131i | \(-0.600949\pi\) | ||
0.311851 | − | 0.950131i | \(-0.399051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.23445 | − | 4.75416i | 0.592729 | − | 0.342212i | −0.173447 | − | 0.984843i | \(-0.555491\pi\) |
0.766176 | + | 0.642631i | \(0.222157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.9322 | −1.99008 | −0.995042 | − | 0.0994560i | \(-0.968290\pi\) | ||||
−0.995042 | + | 0.0994560i | \(0.968290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.87562 | − | 3.96964i | −0.487399 | − | 0.281400i | 0.236096 | − | 0.971730i | \(-0.424132\pi\) |
−0.723495 | + | 0.690330i | \(0.757466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.77365 | − | 8.26821i | 0.335045 | − | 0.580315i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.4320 | + | 12.3737i | 1.49687 | + | 0.864220i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.18319 | − | 9.35403i | 0.151014 | − | 0.647032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.32605 | + | 7.49293i | 0.297817 | + | 0.515835i | 0.975636 | − | 0.219394i | \(-0.0704081\pi\) |
−0.677819 | + | 0.735229i | \(0.737075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.31173 | + | 0.757326i | 0.0894590 | + | 0.0516492i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.4551i | − | 0.981275i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.75656i | − | 0.319961i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.18206 | + | 12.4397i | 0.480946 | + | 0.833023i | 0.999761 | − | 0.0218634i | \(-0.00695988\pi\) |
−0.518815 | + | 0.854887i | \(0.673627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.1832 | 0.941371 | 0.470686 | − | 0.882301i | \(-0.344007\pi\) | ||||
0.470686 | + | 0.882301i | \(0.344007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5473 | −1.09348 | −0.546738 | − | 0.837303i | \(-0.684131\pi\) | ||||
−0.546738 | + | 0.837303i | \(0.684131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1193 | − | 22.7233i | −0.859474 | − | 1.48865i | −0.872431 | − | 0.488737i | \(-0.837458\pi\) |
0.0129574 | − | 0.999916i | \(-0.495875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 32.8187i | − | 2.14085i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.26047i | − | 0.0815327i | −0.999169 | − | 0.0407664i | \(-0.987020\pi\) | ||
0.999169 | − | 0.0407664i | \(-0.0129799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1336 | − | 10.4695i | −1.16809 | − | 0.674397i | −0.214860 | − | 0.976645i | \(-0.568930\pi\) |
−0.953229 | + | 0.302248i | \(0.902263\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.3456 | + | 19.6512i | 0.724847 | + | 1.25547i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2252 | + | 12.3921i | 0.841500 | + | 0.788493i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.6521 | − | 14.2329i | −1.55603 | − | 0.898372i | −0.997631 | − | 0.0687973i | \(-0.978084\pi\) |
−0.558396 | − | 0.829575i | \(-0.688583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.06163 | − | 7.03494i | 0.255352 | − | 0.442283i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4764 | − | 6.04858i | −0.653503 | − | 0.377300i | 0.136294 | − | 0.990668i | \(-0.456481\pi\) |
−0.789797 | + | 0.613368i | \(0.789814\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.5450 | −2.45721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.11930 | − | 0.646229i | 0.0690191 | − | 0.0398482i | −0.465093 | − | 0.885262i | \(-0.653979\pi\) |
0.534112 | + | 0.845413i | \(0.320646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6279i | 0.775728i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.5420 | − | 14.1693i | 1.49635 | − | 0.863920i | 0.496363 | − | 0.868115i | \(-0.334669\pi\) |
0.999991 | + | 0.00419513i | \(0.00133536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2017 | + | 7.62198i | −0.801944 | + | 0.463002i | −0.844150 | − | 0.536106i | \(-0.819895\pi\) |
0.0422066 | + | 0.999109i | \(0.486561\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.09159 | − | 2.36228i | −0.246732 | − | 0.142451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8353 | −0.951450 | −0.475725 | − | 0.879594i | \(-0.657814\pi\) | ||||
−0.475725 | + | 0.879594i | \(0.657814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8445 | + | 9.14784i | 0.945205 | + | 0.545714i | 0.891588 | − | 0.452847i | \(-0.149592\pi\) |
0.0536166 | + | 0.998562i | \(0.482925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4218 | + | 14.6773i | −1.51117 | + | 0.872474i | −0.511254 | + | 0.859430i | \(0.670819\pi\) |
−0.999915 | + | 0.0130439i | \(0.995848\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.2201 | + | 31.5582i | 1.07550 | + | 1.86282i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.84565 | − | 13.5891i | 0.461509 | − | 0.799356i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6512i | 1.14804i | 0.818842 | + | 0.574019i | \(0.194616\pi\) | ||||
−0.818842 | + | 0.574019i | \(0.805384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.57199 | − | 6.18687i | 0.207969 | − | 0.360214i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.66359 | + | 13.2737i | 0.443197 | + | 0.767639i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11515 | + | 1.93150i | 0.0642761 | + | 0.111330i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.3064 | 1.96438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.59046 | − | 6.21887i | −0.204919 | − | 0.354929i | 0.745188 | − | 0.666854i | \(-0.232360\pi\) |
−0.950107 | + | 0.311925i | \(0.899026\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.1868i | − | 1.65503i | −0.561444 | − | 0.827515i | \(-0.689754\pi\) | ||
0.561444 | − | 0.827515i | \(-0.310246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.24482 | − | 12.5484i | 0.409501 | − | 0.709277i | −0.585333 | − | 0.810793i | \(-0.699036\pi\) |
0.994834 | + | 0.101516i | \(0.0323694\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.37562 | + | 1.37156i | 0.133428 | + | 0.0770346i | 0.565228 | − | 0.824935i | \(-0.308788\pi\) |
−0.431800 | + | 0.901969i | \(0.642121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.67282 | + | 4.62947i | −0.149649 | + | 0.259200i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.44648 | − | 4.77212i | −0.0804842 | − | 0.265528i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.72013 | − | 4.45722i | 0.428236 | − | 0.247242i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.1625 | − | 41.8506i | 1.33212 | − | 2.30730i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0761 | 0.553835 | 0.276918 | − | 0.960894i | \(-0.410687\pi\) | ||||
0.276918 | + | 0.960894i | \(0.410687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.27781 | −0.506901 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.76555 | − | 2.17404i | 0.205123 | − | 0.118428i | −0.393920 | − | 0.919145i | \(-0.628881\pi\) |
0.599043 | + | 0.800717i | \(0.295548\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.09357i | 0.438291i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.86273i | 0.316558i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.542026 | + | 0.312939i | −0.0290975 | + | 0.0167994i | −0.514478 | − | 0.857503i | \(-0.672014\pi\) |
0.485381 | + | 0.874303i | \(0.338681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.79834 | 0.363907 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.0185 | −1.06548 | −0.532738 | − | 0.846280i | \(-0.678837\pi\) | ||||
−0.532738 | + | 0.846280i | \(0.678837\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6913 | − | 28.9102i | 0.885882 | − | 1.53439i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.7882 | + | 8.53796i | −0.780490 | + | 0.450616i | −0.836604 | − | 0.547808i | \(-0.815462\pi\) |
0.0561140 | + | 0.998424i | \(0.482129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0369 | + | 8.41086i | 0.896681 | + | 0.442677i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.62438 | − | 6.27762i | 0.189709 | − | 0.328586i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5277 | + | 14.7384i | 1.33254 | + | 0.769340i | 0.985688 | − | 0.168582i | \(-0.0539187\pi\) |
0.346848 | + | 0.937921i | \(0.387252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.29721 | + | 16.1032i | −0.482687 | + | 0.836038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.6745i | − | 1.38116i | −0.723258 | − | 0.690578i | \(-0.757356\pi\) | ||
0.723258 | − | 0.690578i | \(-0.242644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.04316 | − | 8.73500i | −0.259736 | − | 0.449876i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.80890 | 0.349750 | 0.174875 | − | 0.984591i | \(-0.444048\pi\) | ||||
0.174875 | + | 0.984591i | \(0.444048\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.23558 | + | 9.06829i | 0.267526 | + | 0.463368i | 0.968222 | − | 0.250091i | \(-0.0804606\pi\) |
−0.700697 | + | 0.713459i | \(0.747127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5905 | − | 20.0753i | −0.590705 | − | 1.02313i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.25405 | − | 2.17208i | 0.0635830 | − | 0.110129i | −0.832482 | − | 0.554053i | \(-0.813081\pi\) |
0.896065 | + | 0.443924i | \(0.146414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.21707i | − | 0.213267i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.37957 | + | 16.2459i | −0.471937 | + | 0.817419i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.54316 | − | 7.86898i | −0.228014 | − | 0.394933i | 0.729205 | − | 0.684295i | \(-0.239890\pi\) |
−0.957220 | + | 0.289363i | \(0.906557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.97399 | − | 5.75848i | 0.498077 | − | 0.287565i | −0.229842 | − | 0.973228i | \(-0.573821\pi\) |
0.727919 | + | 0.685663i | \(0.240488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2252 | − | 7.63558i | −0.658795 | − | 0.380355i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.1417 | 1.09752 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.1664 | + | 9.33368i | 0.799378 | + | 0.461521i | 0.843253 | − | 0.537516i | \(-0.180637\pi\) |
−0.0438759 | + | 0.999037i | \(0.513971\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.11007 | − | 5.25970i | 0.448277 | − | 0.258813i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.58651 | − | 2.64802i | 0.225143 | − | 0.129986i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.2053i | 1.32907i | 0.747259 | + | 0.664533i | \(0.231370\pi\) | ||||
−0.747259 | + | 0.664533i | \(0.768630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.11930 | + | 0.646229i | −0.0545514 | + | 0.0314953i | −0.527028 | − | 0.849848i | \(-0.676694\pi\) |
0.472476 | + | 0.881343i | \(0.343360\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.45269 | −0.118973 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.7478 | + | 25.2578i | 2.11711 | + | 1.22231i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6336 | + | 18.4180i | −0.512203 | + | 0.887162i | 0.487696 | + | 0.873013i | \(0.337837\pi\) |
−0.999900 | + | 0.0141492i | \(0.995496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.3890 | + | 19.2771i | 1.60457 | + | 0.926401i | 0.990556 | + | 0.137108i | \(0.0437807\pi\) |
0.614017 | + | 0.789293i | \(0.289553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7252 | + | 10.9866i | 0.560893 | + | 0.525562i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3692 | − | 21.4241i | −0.590350 | − | 1.02252i | −0.994185 | − | 0.107684i | \(-0.965656\pi\) |
0.403835 | − | 0.914832i | \(-0.367677\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.5513 | − | 18.2161i | −1.49905 | − | 0.865474i | −0.499046 | − | 0.866575i | \(-0.666316\pi\) |
−0.999999 | + | 0.00110093i | \(0.999650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.8964i | 1.89127i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9509i | 1.36628i | 0.730289 | + | 0.683138i | \(0.239385\pi\) | ||||
−0.730289 | + | 0.683138i | \(0.760615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2017 | − | 17.6698i | −0.480377 | − | 0.832038i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.7384 | 2.05049 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2224 | −0.665295 | −0.332648 | − | 0.943051i | \(-0.607942\pi\) | ||||
−0.332648 | + | 0.943051i | \(0.607942\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1677 | + | 31.4674i | 0.846156 | + | 1.46559i | 0.884613 | + | 0.466325i | \(0.154422\pi\) |
−0.0384575 | + | 0.999260i | \(0.512244\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.6264i | − | 1.37685i | −0.725306 | − | 0.688427i | \(-0.758302\pi\) | ||
0.725306 | − | 0.688427i | \(-0.241698\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 30.4879i | − | 1.41081i | −0.708803 | − | 0.705407i | \(-0.750764\pi\) | ||
0.708803 | − | 0.705407i | \(-0.249236\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.8311 | − | 6.83071i | −0.546311 | − | 0.315413i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.624385 | − | 1.08147i | −0.0287092 | − | 0.0497259i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.38993 | − | 6.81950i | 0.293190 | − | 0.312900i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.5882 | + | 11.8866i | 0.940699 | + | 0.543113i | 0.890179 | − | 0.455610i | \(-0.150579\pi\) |
0.0505196 | + | 0.998723i | \(0.483912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.8888 | + | 36.1805i | −0.952447 | + | 1.64969i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.79834 | − | 4.50237i | −0.354104 | − | 0.204442i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2880 | −0.466193 | −0.233096 | − | 0.972454i | \(-0.574886\pi\) | ||||
−0.233096 | + | 0.972454i | \(0.574886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.5513 | + | 16.4841i | −1.28850 | + | 0.743916i | −0.978387 | − | 0.206783i | \(-0.933700\pi\) |
−0.310114 | + | 0.950699i | \(0.600367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.77512i | 0.124985i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.5697 | − | 24.5776i | 1.90951 | − | 1.10246i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.2067 | + | 8.20227i | −0.635981 | + | 0.367184i | −0.783065 | − | 0.621940i | \(-0.786345\pi\) |
0.147084 | + | 0.989124i | \(0.453011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.8521 | + | 7.42014i | 0.573045 | + | 0.330848i | 0.758365 | − | 0.651831i | \(-0.225999\pi\) |
−0.185320 | + | 0.982678i | \(0.559332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.2672 | −1.21338 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.8168 | − | 14.3280i | −1.09999 | − | 0.635077i | −0.163769 | − | 0.986499i | \(-0.552365\pi\) |
−0.936217 | + | 0.351422i | \(0.885698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24369 | − | 5.33684i | 0.408917 | − | 0.236088i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.9846 | − | 38.0784i | −0.968755 | − | 1.67793i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.5288 | + | 23.4326i | −0.594998 | + | 1.03057i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.911178i | 0.0399194i | 0.999801 | + | 0.0199597i | \(0.00635380\pi\) | ||||
−0.999801 | + | 0.0199597i | \(0.993646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.12043 | − | 8.86885i | 0.223901 | − | 0.387808i | −0.732088 | − | 0.681210i | \(-0.761454\pi\) |
0.955989 | + | 0.293402i | \(0.0947875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.10083 | + | 3.63875i | 0.0915136 | + | 0.158506i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.70561 | − | 8.15036i | −0.204592 | − | 0.354364i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.4975 | 1.66751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.48963 | − | 11.2404i | −0.280571 | − | 0.485964i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 18.7081i | − | 0.805813i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6233 | − | 33.9885i | 0.843670 | − | 1.46128i | −0.0431020 | − | 0.999071i | \(-0.513724\pi\) |
0.886772 | − | 0.462208i | \(-0.152943\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.0369 | + | 19.6512i | 1.45798 | + | 0.841767i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.81794 | − | 10.0770i | 0.248757 | − | 0.430860i | −0.714424 | − | 0.699713i | \(-0.753311\pi\) |
0.963181 | + | 0.268853i | \(0.0866446\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.71598 | − | 7.22994i | −0.328712 | − | 0.308006i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.9218 | + | 13.8113i | −1.01726 | + | 0.587314i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.514319 | − | 0.890827i | 0.0217924 | − | 0.0377455i | −0.854924 | − | 0.518754i | \(-0.826396\pi\) |
0.876716 | + | 0.481008i | \(0.159729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.35621 | 0.0996572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.29588 | −0.181050 | −0.0905249 | − | 0.995894i | \(-0.528854\pi\) | ||||
−0.0905249 | + | 0.995894i | \(0.528854\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.5226 | − | 19.3543i | 1.41031 | − | 0.814241i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 25.9992i | − | 1.08995i | −0.838454 | − | 0.544973i | \(-0.816540\pi\) | ||
0.838454 | − | 0.544973i | \(-0.183460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.2310i | − | 1.47437i | −0.675691 | − | 0.737185i | \(-0.736154\pi\) | ||
0.675691 | − | 0.737185i | \(-0.263846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.84452 | − | 3.95168i | 0.285436 | − | 0.164797i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.51037 | 0.395922 | 0.197961 | − | 0.980210i | \(-0.436568\pi\) | ||||
0.197961 | + | 0.980210i | \(0.436568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.79834 | 0.323530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.20561 | − | 9.01639i | 0.215594 | − | 0.373421i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.84452 | − | 5.68373i | 0.406327 | − | 0.234593i | −0.282884 | − | 0.959154i | \(-0.591291\pi\) |
0.689210 | + | 0.724561i | \(0.257958\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.5905 | − | 3.63875i | −0.642394 | − | 0.149932i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.9269 | + | 22.3900i | −0.530843 | + | 0.919447i | 0.468509 | + | 0.883459i | \(0.344791\pi\) |
−0.999352 | + | 0.0359886i | \(0.988542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4218 | − | 6.01702i | −0.427252 | − | 0.246674i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.56276 | − | 4.43883i | 0.104711 | − | 0.181366i | −0.808909 | − | 0.587934i | \(-0.799941\pi\) |
0.913620 | + | 0.406569i | \(0.133275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7822i | 0.521398i | 0.965420 | + | 0.260699i | \(0.0839530\pi\) | ||||
−0.965420 | + | 0.260699i | \(0.916047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.21090 | − | 14.2217i | −0.333820 | − | 0.578194i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.7882 | −1.29024 | −0.645121 | − | 0.764080i | \(-0.723193\pi\) | ||||
−0.645121 | + | 0.764080i | \(0.723193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.5266 | − | 44.2133i | −1.03269 | − | 1.78868i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.1664 | − | 36.6613i | −0.854903 | − | 1.48074i | −0.876735 | − | 0.480974i | \(-0.840283\pi\) |
0.0218315 | − | 0.999762i | \(-0.493050\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1717 | − | 17.6179i | 0.409497 | − | 0.709270i | −0.585336 | − | 0.810791i | \(-0.699038\pi\) |
0.994833 | + | 0.101521i | \(0.0323709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.1402i | − | 0.528150i | −0.964502 | − | 0.264075i | \(-0.914933\pi\) | ||
0.964502 | − | 0.264075i | \(-0.0850667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.3734 | + | 50.8761i | −1.17682 | + | 2.03831i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5616 | + | 26.9535i | 0.622465 | + | 1.07814i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.95458 | − | 5.74728i | 0.396915 | − | 0.229159i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.57312 | + | 2.06294i | 0.142244 | + | 0.0821245i | 0.569433 | − | 0.822038i | \(-0.307163\pi\) |
−0.427189 | + | 0.904162i | \(0.640496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.0946 | 1.23395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.5697 | + | 17.6494i | 1.21122 | + | 0.699296i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.9714 | + | 18.4587i | −1.26279 | + | 0.729074i | −0.973614 | − | 0.228201i | \(-0.926716\pi\) |
−0.289179 | + | 0.957275i | \(0.593382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.62854 | − | 3.82699i | 0.261404 | − | 0.150922i | −0.363571 | − | 0.931567i | \(-0.618443\pi\) |
0.624975 | + | 0.780645i | \(0.285109\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 26.5387i | − | 1.04335i | −0.853146 | − | 0.521673i | \(-0.825308\pi\) | ||
0.853146 | − | 0.521673i | \(-0.174692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.10083 | + | 2.94497i | −0.200225 | + | 0.115600i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.23860 | 0.0876033 | 0.0438017 | − | 0.999040i | \(-0.486053\pi\) | ||||
0.0438017 | + | 0.999040i | \(0.486053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.6419 | + | 16.5364i | 1.11913 | + | 0.646132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.43724 | + | 5.95348i | −0.133896 | + | 0.231915i | −0.925175 | − | 0.379540i | \(-0.876082\pi\) |
0.791279 | + | 0.611455i | \(0.209415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2386 | + | 18.6130i | 1.25394 | + | 0.723960i | 0.971889 | − | 0.235440i | \(-0.0756531\pi\) |
0.282047 | + | 0.959400i | \(0.408986\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 43.8815 | − | 13.3009i | 1.70165 | − | 0.515788i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.47116 | − | 7.74428i | −0.173124 | − | 0.299860i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.4949 | − | 14.1421i | −0.945616 | − | 0.545952i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 40.4406i | − | 1.55887i | −0.626482 | − | 0.779436i | \(-0.715506\pi\) | ||
0.626482 | − | 0.779436i | \(-0.284494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.1650i | 0.544405i | 0.962240 | + | 0.272202i | \(0.0877520\pi\) | ||||
−0.962240 | + | 0.272202i | \(0.912248\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.62967 | − | 11.4829i | −0.254423 | − | 0.440674i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.8952 | 0.914325 | 0.457163 | − | 0.889383i | \(-0.348866\pi\) | ||||
0.457163 | + | 0.889383i | \(0.348866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2100 | 0.963223 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.82209 | + | 17.0124i | 0.374192 | + | 0.648119i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0166i | 0.723427i | 0.932289 | + | 0.361714i | \(0.117808\pi\) | ||||
−0.932289 | + | 0.361714i | \(0.882192\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 36.7088i | − | 1.39245i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.17302 | − | 5.29605i | −0.347453 | − | 0.200602i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2109 | − | 24.6140i | −0.536738 | − | 0.929658i | −0.999077 | − | 0.0429544i | \(-0.986323\pi\) |
0.462339 | − | 0.886703i | \(-0.347010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.95458 | + | 42.6511i | −0.375444 | + | 1.60862i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.7714 | − | 20.0753i | −1.30771 | − | 0.755008i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8681 | − | 24.0202i | 0.520826 | − | 0.902098i | −0.478880 | − | 0.877880i | \(-0.658957\pi\) |
0.999707 | − | 0.0242175i | \(-0.00770943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.7252 | − | 6.76956i | −0.439113 | − | 0.253522i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.4896 | −0.915860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.844517 | − | 0.487582i | 0.0314952 | − | 0.0181837i | −0.484170 | − | 0.874974i | \(-0.660878\pi\) |
0.515665 | + | 0.856790i | \(0.327545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 64.7438i | − | 2.41118i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.50415 | + | 2.60047i | −0.167280 | + | 0.0965792i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6924 | − | 13.1015i | 0.841615 | − | 0.485907i | −0.0161975 | − | 0.999869i | \(-0.505156\pi\) |
0.857813 | + | 0.513962i | \(0.171823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.561428 | − | 0.324141i | −0.0207652 | − | 0.0119888i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.2751 | 1.00743 | 0.503715 | − | 0.863870i | \(-0.331966\pi\) | ||||
0.503715 | + | 0.863870i | \(0.331966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.62438 | + | 3.82459i | 0.244012 | + | 0.140881i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.2908 | + | 12.2922i | −0.783195 | + | 0.452178i | −0.837561 | − | 0.546343i | \(-0.816019\pi\) |
0.0543667 | + | 0.998521i | \(0.482686\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.1101 | − | 41.7599i | −0.884513 | − | 1.53202i | −0.846271 | − | 0.532752i | \(-0.821158\pi\) |
−0.0382412 | − | 0.999269i | \(-0.512176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.7921 | + | 37.7451i | −0.798402 | + | 1.38287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.1118i | − | 0.698328i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.2437 | + | 28.1349i | −0.592741 | + | 1.02666i | 0.401121 | + | 0.916025i | \(0.368621\pi\) |
−0.993861 | + | 0.110632i | \(0.964713\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.43196 | + | 16.3366i | 0.343264 | + | 0.594551i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5801 | − | 20.0573i | −0.420886 | − | 0.728996i | 0.575141 | − | 0.818055i | \(-0.304947\pi\) |
−0.996026 | + | 0.0890590i | \(0.971614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.5496 | 0.672421 | 0.336211 | − | 0.941787i | \(-0.390855\pi\) | ||||
0.336211 | + | 0.941787i | \(0.390855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9361 | + | 50.1188i | 1.04756 | + | 1.81442i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.1133i | − | 0.401277i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8249 | + | 32.6057i | −0.678844 | + | 1.17579i | 0.296486 | + | 0.955037i | \(0.404185\pi\) |
−0.975329 | + | 0.220755i | \(0.929148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.981529 | + | 0.566686i | 0.0353031 | + | 0.0203823i | 0.517548 | − | 0.855654i | \(-0.326845\pi\) |
−0.482245 | + | 0.876037i | \(0.660178\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.93724 | + | 6.81950i | −0.141430 | + | 0.244964i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.6235 | − | 11.7072i | 1.38383 | − | 0.419453i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.8353 | + | 13.7613i | −0.852893 | + | 0.492418i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.1348 | − | 26.2142i | 0.540182 | − | 0.935623i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9687 | 0.497930 | 0.248965 | − | 0.968512i | \(-0.419910\pi\) | ||||
0.248965 | + | 0.968512i | \(0.419910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.9977 | 2.02661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.2177 | − | 26.6838i | 1.64124 | − | 0.947569i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2972i | 0.364746i | 0.983229 | + | 0.182373i | \(0.0583778\pi\) | ||||
−0.983229 | + | 0.182373i | \(0.941622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0466i | 0.496933i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.17565 | + | 2.98816i | −0.182645 | + | 0.105450i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.7776 | 1.36673 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.1338 | 0.918816 | 0.459408 | − | 0.888225i | \(-0.348062\pi\) | ||||
0.459408 | + | 0.888225i | \(0.348062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0185 | + | 31.2089i | −0.632714 | + | 1.09589i | 0.354280 | + | 0.935139i | \(0.384726\pi\) |
−0.986995 | + | 0.160754i | \(0.948608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.12023 | + | 1.22412i | −0.0742685 | + | 0.0428789i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.36392 | − | 0.716528i | 0.0827031 | − | 0.0250682i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.89917 | − | 6.75356i | 0.136082 | − | 0.235701i | −0.789928 | − | 0.613199i | \(-0.789882\pi\) |
0.926010 | + | 0.377498i | \(0.123216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.8824 | + | 13.7885i | 0.832488 | + | 0.480637i | 0.854704 | − | 0.519116i | \(-0.173739\pi\) |
−0.0222159 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.99605 | + | 3.45726i | −0.0694094 | + | 0.120221i | −0.898641 | − | 0.438684i | \(-0.855445\pi\) |
0.829232 | + | 0.558904i | \(0.188778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.8873i | − | 1.76739i | −0.468063 | − | 0.883695i | \(-0.655048\pi\) | ||
0.468063 | − | 0.883695i | \(-0.344952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.85601 | − | 8.41086i | −0.168251 | − | 0.291419i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02864 | 0.0355975 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.3117 | + | 43.8412i | 0.873858 | + | 1.51357i | 0.857974 | + | 0.513692i | \(0.171723\pi\) |
0.0158834 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5577 | − | 20.0185i | −0.398540 | − | 0.690292i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.73050 | − | 9.92551i | 0.197135 | − | 0.341448i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24.1808i | − | 0.830862i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.5196 | + | 32.0769i | −0.634844 | + | 1.09958i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.3745 | + | 17.9691i | 0.355216 | + | 0.615251i | 0.987155 | − | 0.159766i | \(-0.0510741\pi\) |
−0.631939 | + | 0.775018i | \(0.717741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.6521 | + | 14.2329i | −0.842099 | + | 0.486186i | −0.857977 | − | 0.513688i | \(-0.828279\pi\) |
0.0158779 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.4453 | − | 25.0832i | −1.48234 | − | 0.855827i | −0.482537 | − | 0.875876i | \(-0.660285\pi\) |
−0.999799 | + | 0.0200484i | \(0.993618\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.5922 | −1.34773 | −0.673866 | − | 0.738853i | \(-0.735368\pi\) | ||||
−0.673866 | + | 0.738853i | \(0.735368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9898 | + | 14.4279i | 0.849680 | + | 0.490563i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3941 | − | 7.73308i | 0.454363 | − | 0.262327i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4991 | + | 7.21634i | −0.423515 | + | 0.244516i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30.0435i | 1.01566i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.5924 | + | 24.0134i | −1.40447 | + | 0.810873i | −0.994848 | − | 0.101380i | \(-0.967674\pi\) |
−0.409626 | + | 0.912253i | \(0.634341\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.9815 | −0.942722 | −0.471361 | − | 0.881940i | \(-0.656237\pi\) | ||||
−0.471361 | + | 0.881940i | \(0.656237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.3445 | − | 15.2100i | −0.886564 | − | 0.511858i | −0.0137467 | − | 0.999906i | \(-0.504376\pi\) |
−0.872817 | + | 0.488048i | \(0.837709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.09555 | − | 3.62960i | 0.0703616 | − | 0.121870i | −0.828698 | − | 0.559696i | \(-0.810918\pi\) |
0.899060 | + | 0.437826i | \(0.144251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.6521 | + | 22.8931i | 1.32989 | + | 0.767811i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.0554 | − | 36.5953i | −1.30694 | − | 1.22461i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.38880 | + | 2.40548i | 0.0464226 | + | 0.0804063i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.71598 | + | 4.45482i | 0.257342 | + | 0.148577i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.40484i | − | 0.180061i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7846i | 0.690904i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.38485 | + | 7.59478i | 0.145597 | + | 0.252181i | 0.929595 | − | 0.368582i | \(-0.120157\pi\) |
−0.783999 | + | 0.620762i | \(0.786823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.95854 | −0.0648892 | −0.0324446 | − | 0.999474i | \(-0.510329\pi\) | ||||
−0.0324446 | + | 0.999474i | \(0.510329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.36638 | −0.144506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.3496 | + | 42.1747i | 0.804095 | + | 1.39273i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 43.4284i | − | 1.43257i | −0.697808 | − | 0.716285i | \(-0.745841\pi\) | ||
0.697808 | − | 0.716285i | \(-0.254159\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 51.9304i | − | 1.70931i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6562 | + | 10.7712i | 0.613414 | + | 0.354154i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.02997 | + | 5.24806i | 0.0994100 | + | 0.172183i | 0.911441 | − | 0.411432i | \(-0.134971\pi\) |
−0.812031 | + | 0.583615i | \(0.801638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0369 | + | 8.41086i | 1.18106 | + | 0.275655i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.83528 | + | 3.36900i | 0.190834 | + | 0.110178i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1297 | + | 21.0092i | −0.396259 | + | 0.686341i | −0.993261 | − | 0.115899i | \(-0.963025\pi\) |
0.597002 | + | 0.802240i | \(0.296358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.6706 | − | 20.5944i | −1.16283 | − | 0.671359i | −0.210847 | − | 0.977519i | \(-0.567622\pi\) |
−0.951980 | + | 0.306160i | \(0.900956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.1312 | 1.11146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.88900 | − | 1.09062i | 0.0613843 | − | 0.0354403i | −0.468994 | − | 0.883201i | \(-0.655383\pi\) |
0.530378 | + | 0.847761i | \(0.322050\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 11.2763i | − | 0.366044i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.7974 | − | 12.5847i | 0.706087 | − | 0.407660i | −0.103523 | − | 0.994627i | \(-0.533012\pi\) |
0.809611 | + | 0.586967i | \(0.199678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −60.7899 | + | 35.0970i | −1.96711 | + | 1.13571i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.1479 | + | 18.5606i | 1.03811 | + | 0.599354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.5104 | −0.564851 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.0092 | − | 12.7070i | −0.708502 | − | 0.409054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.65548 | + | 3.84254i | −0.214026 | + | 0.123568i | −0.603181 | − | 0.797604i | \(-0.706100\pi\) |
0.389155 | + | 0.921172i | \(0.372767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.3272 | − | 42.1359i | −0.780696 | − | 1.35221i | −0.931537 | − | 0.363647i | \(-0.881531\pi\) |
0.150840 | − | 0.988558i | \(-0.451802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.0266 | − | 46.8114i | 0.866432 | − | 1.50070i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 11.2811i | − | 0.360914i | −0.983583 | − | 0.180457i | \(-0.942242\pi\) | ||
0.983583 | − | 0.180457i | \(-0.0577576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.4465 | − | 28.4861i | 0.525632 | − | 0.910421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.8485 | − | 34.3786i | −0.633068 | − | 1.09651i | −0.986921 | − | 0.161205i | \(-0.948462\pi\) |
0.353853 | − | 0.935301i | \(-0.384871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.3289 | + | 64.6555i | 1.18940 | + | 2.06010i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.08897 | 0.0664254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.78930 | − | 13.4915i | −0.247435 | − | 0.428571i | 0.715378 | − | 0.698738i | \(-0.246254\pi\) |
−0.962814 | + | 0.270167i | \(0.912921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.2203i | 0.672728i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.5185 | − | 28.6108i | 0.523145 | − | 0.906114i | −0.476492 | − | 0.879179i | \(-0.658092\pi\) |
0.999637 | − | 0.0269353i | \(-0.00857480\pi\) | |||||||
\(998\) | 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.bm.n.1855.1 | 6 | ||
3.2 | odd | 2 | 912.2.bb.e.31.3 | ✓ | 6 | ||
4.3 | odd | 2 | 2736.2.bm.o.1855.1 | 6 | |||
12.11 | even | 2 | 912.2.bb.f.31.3 | yes | 6 | ||
19.8 | odd | 6 | 2736.2.bm.o.559.1 | 6 | |||
57.8 | even | 6 | 912.2.bb.f.559.3 | yes | 6 | ||
76.27 | even | 6 | inner | 2736.2.bm.n.559.1 | 6 | ||
228.179 | odd | 6 | 912.2.bb.e.559.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.e.31.3 | ✓ | 6 | 3.2 | odd | 2 | ||
912.2.bb.e.559.3 | yes | 6 | 228.179 | odd | 6 | ||
912.2.bb.f.31.3 | yes | 6 | 12.11 | even | 2 | ||
912.2.bb.f.559.3 | yes | 6 | 57.8 | even | 6 | ||
2736.2.bm.n.559.1 | 6 | 76.27 | even | 6 | inner | ||
2736.2.bm.n.1855.1 | 6 | 1.1 | even | 1 | trivial | ||
2736.2.bm.o.559.1 | 6 | 19.8 | odd | 6 | |||
2736.2.bm.o.1855.1 | 6 | 4.3 | odd | 2 |