Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(31,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bb (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: | \(7.28235666434\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-1.62241 + 0.606458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.31 |
Dual form | 912.2.bb.e.559.3 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.33641 | + | 2.31473i | 0.597662 | + | 1.03518i | 0.993165 | + | 0.116716i | \(0.0372367\pi\) |
−0.395504 | + | 0.918464i | \(0.629430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.93569i | − | 1.48755i | −0.668430 | − | 0.743775i | \(-0.733033\pi\) | ||
0.668430 | − | 0.743775i | \(-0.266967\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.20364i | − | 0.664421i | −0.943205 | − | 0.332211i | \(-0.892205\pi\) | ||
0.943205 | − | 0.332211i | \(-0.107795\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | 1.33641 | − | 2.31473i | 0.345060 | − | 0.597662i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.571993 | − | 0.990721i | −0.138729 | − | 0.240285i | 0.788287 | − | 0.615308i | \(-0.210968\pi\) |
−0.927016 | + | 0.375023i | \(0.877635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24482 | − | 0.990721i | −0.973828 | − | 0.227287i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.40841 | + | 1.96784i | −0.743775 | + | 0.429419i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.19243 | + | 1.84315i | 0.665667 | + | 0.384323i | 0.794433 | − | 0.607352i | \(-0.207768\pi\) |
−0.128766 | + | 0.991675i | \(0.541102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.07199 | + | 1.85675i | −0.214399 | + | 0.371349i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.10083 | − | 1.21292i | −0.390114 | − | 0.225233i | 0.292095 | − | 0.956389i | \(-0.405648\pi\) |
−0.682210 | + | 0.731157i | \(0.738981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.67282 | 0.659659 | 0.329829 | − | 0.944041i | \(-0.393009\pi\) | ||||
0.329829 | + | 0.944041i | \(0.393009\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.90841 | + | 1.10182i | −0.332211 | + | 0.191802i | ||||
\(34\) | 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 | ||||||||
\(39\) | 4.15788i | 0.665794i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.01847 | − | 4.62947i | 1.25227 | − | 0.723001i | 0.280714 | − | 0.959791i | \(-0.409429\pi\) |
0.971561 | + | 0.236790i | \(0.0760954\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −2.67282 | −0.398441 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.6336 | − | 6.13932i | −1.55107 | − | 0.895512i | −0.998055 | − | 0.0623432i | \(-0.980143\pi\) |
−0.553018 | − | 0.833169i | \(-0.686524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.48963 | −1.21280 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.571993 | + | 0.990721i | −0.0800951 | + | 0.138729i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.09159 | + | 2.36228i | 0.562024 | + | 0.324485i | 0.753957 | − | 0.656923i | \(-0.228142\pi\) |
−0.191934 | + | 0.981408i | \(0.561476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.10083 | − | 2.94497i | 0.687796 | − | 0.397099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.26442 | + | 4.17148i | 0.167476 | + | 0.552526i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.33641 | − | 2.31473i | −0.173986 | − | 0.301353i | 0.765824 | − | 0.643050i | \(-0.222331\pi\) |
−0.939810 | + | 0.341698i | \(0.888998\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 3.40841 | + | 1.96784i | 0.429419 | + | 0.247925i | ||||
\(64\) | 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 | ||||||||
\(69\) | − | 3.68630i | − | 0.443778i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.24482 | − | 10.8163i | −0.741123 | − | 1.28366i | −0.951984 | − | 0.306147i | \(-0.900960\pi\) |
0.210861 | − | 0.977516i | \(-0.432373\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 2.14399 | 0.247566 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.98144i | − | 0.217492i | −0.994070 | − | 0.108746i | \(-0.965317\pi\) | ||
0.994070 | − | 0.108746i | \(-0.0346835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.52884 | − | 2.64802i | 0.165826 | − | 0.287218i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.42583i | 0.260076i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.9269 | + | 7.46334i | 1.37025 | + | 0.791112i | 0.990959 | − | 0.134167i | \(-0.0428358\pi\) |
0.379287 | + | 0.925279i | \(0.376169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.18206 | + | 14.1717i | −0.857713 | + | 1.48560i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.83641 | − | 3.18076i | −0.190427 | − | 0.329829i | ||||
\(94\) | 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 | ||||||||
\(99\) | 1.90841 | + | 1.10182i | 0.191802 | + | 0.110737i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.10083 | + | 8.83490i | −0.507552 | + | 0.879105i | 0.492410 | + | 0.870363i | \(0.336116\pi\) |
−0.999962 | + | 0.00874190i | \(0.997217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4504 | 1.62091 | 0.810455 | − | 0.585802i | \(-0.199220\pi\) | ||||
0.810455 | + | 0.585802i | \(0.199220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.11007 | − | 5.25970i | −0.889051 | − | 0.513294i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.85601 | −0.469449 | −0.234724 | − | 0.972062i | \(-0.575419\pi\) | ||||
−0.234724 | + | 0.972062i | \(0.575419\pi\) | |||||||
\(108\) | 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 | ||||||||
\(111\) | −8.70166 | + | 5.02391i | −0.825925 | + | 0.476848i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.4823i | − | 1.36238i | −0.732107 | − | 0.681189i | \(-0.761463\pi\) | ||
0.732107 | − | 0.681189i | \(-0.238537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.85282i | 0.918780i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.60083 | − | 2.07894i | 0.332897 | − | 0.192198i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.89917 | + | 2.25119i | −0.357436 | + | 0.206366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.14399 | 0.558544 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.01847 | − | 4.62947i | −0.723001 | − | 0.417425i | ||||
\(124\) | 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 | ||||||||
\(129\) | 0.490764 | + | 0.283343i | 0.0432094 | + | 0.0249470i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7160 | − | 6.18687i | 0.936260 | − | 0.540550i | 0.0474737 | − | 0.998872i | \(-0.484883\pi\) |
0.888786 | + | 0.458323i | \(0.151550\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.89917 | + | 16.7063i | −0.338101 | + | 1.44862i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.33641 | + | 2.31473i | 0.115020 | + | 0.199221i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.71598 | − | 8.16832i | 0.402913 | − | 0.697866i | −0.591163 | − | 0.806552i | \(-0.701331\pi\) |
0.994076 | + | 0.108686i | \(0.0346643\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 12.2786i | 1.03405i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.58123 | + | 7.93492i | −0.383102 | + | 0.663551i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.48382i | − | 0.538452i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.24482 | + | 7.35224i | 0.350107 | + | 0.606402i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.15322 | + | 14.1218i | 0.667938 | + | 1.15690i | 0.978480 | + | 0.206343i | \(0.0661562\pi\) |
−0.310542 | + | 0.950560i | \(0.600510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.05767 | −0.574345 | −0.287173 | − | 0.957879i | \(-0.592715\pi\) | ||||
−0.287173 | + | 0.957879i | \(0.592715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.14399 | 0.0924858 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | − | 4.72457i | − | 0.374683i | ||||||
\(160\) | 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 | ||||||||
\(165\) | −5.10083 | − | 2.94497i | −0.397099 | − | 0.229265i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.192425 | − | 0.333290i | 0.0148903 | − | 0.0257908i | −0.858484 | − | 0.512840i | \(-0.828593\pi\) |
0.873375 | + | 0.487049i | \(0.161927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.14399 | + | 3.71349i | 0.164922 | + | 0.285653i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.98040 | − | 3.18076i | 0.227917 | − | 0.243239i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.34960 | − | 5.39799i | 0.710837 | − | 0.410402i | −0.100534 | − | 0.994934i | \(-0.532055\pi\) |
0.811371 | + | 0.584532i | \(0.198722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.30757 | + | 4.21903i | 0.552401 | + | 0.318929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.33641 | + | 2.31473i | −0.100451 | + | 0.173986i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.03920 | 0.0776737 | 0.0388368 | − | 0.999246i | \(-0.487635\pi\) | ||||
0.0388368 | + | 0.999246i | \(0.487635\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | 12.8353 | 0.948811 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | − | 3.93569i | − | 0.286279i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.2621i | 1.90026i | 0.311851 | + | 0.950131i | \(0.399051\pi\) | ||||
−0.311851 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | −9.62438 | + | 5.55664i | −0.689217 | + | 0.397919i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.9322 | 1.99008 | 0.995042 | − | 0.0994560i | \(-0.0317103\pi\) | ||||
0.995042 | + | 0.0994560i | \(0.0317103\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | −3.47116 | −0.244837 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | −3.19243 | + | 1.84315i | −0.221889 | + | 0.128108i | ||||
\(208\) | 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 | ||||||||
\(213\) | −6.24482 | + | 10.8163i | −0.427888 | + | 0.741123i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.31173 | − | 0.757326i | −0.0894590 | − | 0.0516492i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.4551i | − | 0.981275i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.35601 | − | 2.34868i | 0.0916309 | − | 0.158709i | ||||
\(220\) | 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 | ||||||||
\(225\) | −1.07199 | − | 1.85675i | −0.0714662 | − | 0.123783i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1832 | −0.941371 | −0.470686 | − | 0.882301i | \(-0.655993\pi\) | ||||
−0.470686 | + | 0.882301i | \(0.655993\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5473 | −1.09348 | −0.546738 | − | 0.837303i | \(-0.684131\pi\) | ||||
−0.546738 | + | 0.837303i | \(0.684131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.33641 | + | 7.51089i | 0.285315 | + | 0.494180i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.1193 | + | 22.7233i | 0.859474 | + | 1.48865i | 0.872431 | + | 0.488737i | \(0.162542\pi\) |
−0.0129574 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 32.8187i | − | 2.14085i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.50924 | + | 6.07817i | −0.227949 | + | 0.394820i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.26047i | 0.0815327i | 0.999169 | + | 0.0407664i | \(0.0129799\pi\) | ||||
−0.999169 | + | 0.0407664i | \(0.987020\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 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 | ||||||||
\(249\) | −1.71598 | + | 0.990721i | −0.108746 | + | 0.0627844i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6521 | + | 14.2329i | 1.55603 | + | 0.898372i | 0.997631 | + | 0.0687973i | \(0.0219162\pi\) |
0.558396 | + | 0.829575i | \(0.311417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.06163 | − | 7.03494i | 0.255352 | − | 0.442283i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.05767 | −0.191479 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4764 | + | 6.04858i | 0.653503 | + | 0.377300i | 0.789797 | − | 0.613368i | \(-0.210186\pi\) |
−0.136294 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.5450 | −2.45721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.10083 | − | 1.21292i | 0.130038 | − | 0.0750776i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.11930 | + | 0.646229i | −0.0690191 | + | 0.0398482i | −0.534112 | − | 0.845413i | \(-0.679354\pi\) |
0.465093 | + | 0.885262i | \(0.346021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6279i | 0.775728i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.9267i | − | 0.913497i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.5420 | + | 14.1693i | −1.49635 | + | 0.863920i | −0.999991 | − | 0.00419513i | \(-0.998665\pi\) |
−0.496363 | + | 0.868115i | \(0.665331\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 16.3641 | 0.990402 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | −1.83641 | + | 3.18076i | −0.109943 | + | 0.190427i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8445 | − | 9.14784i | −0.945205 | − | 0.545714i | −0.0536166 | − | 0.998562i | \(-0.517075\pi\) |
−0.891588 | + | 0.452847i | \(0.850408\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | −7.96608 | + | 8.50161i | −0.471870 | + | 0.503592i | ||||
\(286\) | 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 | ||||||||
\(291\) | −2.91764 | − | 1.68450i | −0.171035 | − | 0.0987472i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.6512i | − | 1.14804i | −0.818842 | − | 0.574019i | \(-0.805384\pi\) | ||
0.818842 | − | 0.574019i | \(-0.194616\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.57199 | − | 6.18687i | 0.207969 | − | 0.360214i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.20364i | − | 0.127868i | ||||||
\(298\) | 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 | ||||||||
\(303\) | 10.2017 | 0.586070 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | −8.22522 | − | 14.2465i | −0.467916 | − | 0.810455i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.1868i | 1.65503i | 0.561444 | + | 0.827515i | \(0.310246\pi\) | ||||
−0.561444 | + | 0.827515i | \(0.689754\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 10.5194i | 0.592701i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.37562 | − | 1.37156i | −0.133428 | − | 0.0770346i | 0.431800 | − | 0.901969i | \(-0.357879\pi\) |
−0.565228 | + | 0.824935i | \(0.691212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.67282 | + | 4.62947i | −0.149649 | + | 0.259200i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.42801 | + | 4.20543i | 0.135518 | + | 0.234724i | ||||
\(322\) | 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 | ||||||||
\(327\) | 12.7345 | + | 7.35224i | 0.704217 | + | 0.406580i | ||||
\(328\) | 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 | ||||||||
\(333\) | 8.70166 | + | 5.02391i | 0.476848 | + | 0.275308i | ||||
\(334\) | 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 | ||||||||
\(339\) | −12.5420 | + | 7.24114i | −0.681189 | + | 0.393285i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.09357i | − | 0.438291i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.86273i | 0.316558i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.53279 | − | 4.92641i | 0.459390 | − | 0.265229i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.542026 | − | 0.312939i | 0.0290975 | − | 0.0167994i | −0.485381 | − | 0.874303i | \(-0.661319\pi\) |
0.514478 | + | 0.857503i | \(0.327986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.79834 | 0.363907 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.60083 | − | 2.07894i | −0.192198 | − | 0.110966i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0185 | 1.06548 | 0.532738 | − | 0.846280i | \(-0.321163\pi\) | ||||
0.532738 | + | 0.846280i | \(0.321163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6913 | − | 28.9102i | 0.885882 | − | 1.53439i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.89917 | + | 2.25119i | 0.206366 | + | 0.119145i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.7882 | − | 8.53796i | 0.780490 | − | 0.450616i | −0.0561140 | − | 0.998424i | \(-0.517871\pi\) |
0.836604 | + | 0.547808i | \(0.184538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0369 | + | 8.41086i | 0.896681 | + | 0.442677i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.07199 | − | 5.32085i | −0.161238 | − | 0.279272i | ||||
\(364\) | 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 | ||||||||
\(369\) | 9.25893i | 0.482001i | ||||||||
\(370\) | 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 | ||||||||
\(375\) | −3.81681 | − | 6.61091i | −0.197099 | − | 0.341386i | ||||
\(376\) | 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 | ||||||||
\(381\) | 11.6336 | 0.596008 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.23558 | − | 9.06829i | −0.267526 | − | 0.463368i | 0.700697 | − | 0.713459i | \(-0.252873\pi\) |
−0.968222 | + | 0.250091i | \(0.919539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5905 | − | 20.0753i | −0.590705 | − | 1.02313i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.566686i | − | 0.0288063i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.25405 | + | 2.17208i | −0.0635830 | + | 0.110129i | −0.896065 | − | 0.443924i | \(-0.853586\pi\) |
0.832482 | + | 0.554053i | \(0.186919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4.21707i | − | 0.213267i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.7160 | − | 6.18687i | −0.540550 | − | 0.312087i | ||||
\(394\) | 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 | ||||||||
\(399\) | 16.4176 | − | 4.97636i | 0.821910 | − | 0.249129i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.97399 | + | 5.75848i | −0.498077 | + | 0.287565i | −0.727919 | − | 0.685663i | \(-0.759512\pi\) |
0.229842 | + | 0.973228i | \(0.426179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2252 | − | 7.63558i | −0.658795 | − | 0.380355i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.33641 | − | 2.31473i | 0.0664068 | − | 0.115020i | ||||
\(406\) | 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 | ||||||||
\(411\) | −9.43196 | −0.465244 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | − | 13.7341i | − | 0.672562i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.2053i | − | 1.32907i | −0.747259 | − | 0.664533i | \(-0.768630\pi\) | ||
0.747259 | − | 0.664533i | \(-0.231370\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 10.6336 | − | 6.13932i | 0.517024 | − | 0.298504i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.45269 | 0.118973 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.7478 | + | 25.2578i | 2.11711 | + | 1.22231i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.16246 | 0.442368 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6336 | − | 18.4180i | 0.512203 | − | 0.887162i | −0.487696 | − | 0.873013i | \(-0.662163\pi\) |
0.999900 | − | 0.0141492i | \(-0.00450397\pi\) | |||||||
\(432\) | 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 | ||||||||
\(435\) | −5.61515 | + | 3.24191i | −0.269226 | + | 0.155438i | ||||
\(436\) | 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 | ||||||||
\(441\) | 4.24482 | − | 7.35224i | 0.202134 | − | 0.350107i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.5513 | + | 18.2161i | 1.49905 | + | 0.865474i | 0.999999 | − | 0.00110093i | \(-0.000350438\pi\) |
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.8964i | 1.89127i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.15322 | − | 14.1218i | 0.385634 | − | 0.667938i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 28.9509i | − | 1.36628i | −0.730289 | − | 0.683138i | \(-0.760615\pi\) | ||
0.730289 | − | 0.683138i | \(-0.239385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2017 | − | 17.6698i | −0.480377 | − | 0.832038i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.52884 | + | 6.11213i | 0.165799 | + | 0.287173i | ||||
\(454\) | 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 | ||||||||
\(459\) | −0.571993 | − | 0.990721i | −0.0266984 | − | 0.0462429i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1677 | − | 31.4674i | −0.846156 | − | 1.46559i | −0.884613 | − | 0.466325i | \(-0.845578\pi\) |
0.0384575 | − | 0.999260i | \(-0.487756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.6264i | − | 1.37685i | −0.725306 | − | 0.688427i | \(-0.758302\pi\) | ||
0.725306 | − | 0.688427i | \(-0.241698\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.90841 | − | 8.50161i | 0.227622 | − | 0.394253i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.4879i | 1.41081i | 0.708803 | + | 0.705407i | \(0.249236\pi\) | ||||
−0.708803 | + | 0.705407i | \(0.750764\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.8311 | − | 6.83071i | −0.546311 | − | 0.315413i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.66246 | − | 9.80766i | 0.260912 | − | 0.451913i | ||||
\(472\) | 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 | ||||||||
\(477\) | −4.09159 | + | 2.36228i | −0.187341 | + | 0.108162i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.5882 | − | 11.8866i | −0.940699 | − | 0.543113i | −0.0505196 | − | 0.998723i | \(-0.516088\pi\) |
−0.890179 | + | 0.455610i | \(0.849421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.8888 | + | 36.1805i | −0.952447 | + | 1.64969i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.5081 | −0.660142 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | −0.793256 | + | 0.457986i | −0.0358723 | + | 0.0207109i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.5513 | − | 16.4841i | 1.28850 | − | 0.743916i | 0.310114 | − | 0.950699i | \(-0.399633\pi\) |
0.978387 | + | 0.206783i | \(0.0662996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.77512i | 0.124985i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.88993i | 0.264733i | ||||||||
\(496\) | 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 | ||||||||
\(501\) | −0.384851 | −0.0171939 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.8521 | − | 7.42014i | −0.573045 | − | 0.330848i | 0.185320 | − | 0.982678i | \(-0.440668\pi\) |
−0.758365 | + | 0.651831i | \(0.774001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.2672 | −1.21338 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.14399 | − | 3.71349i | 0.0952178 | − | 0.164922i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8168 | + | 14.3280i | 1.09999 | + | 0.635077i | 0.936217 | − | 0.351422i | \(-0.114302\pi\) |
0.163769 | + | 0.986499i | \(0.447635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24369 | − | 5.33684i | 0.408917 | − | 0.236088i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.24482 | − | 0.990721i | −0.187413 | − | 0.0437414i | ||||
\(514\) | 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 | ||||||||
\(519\) | −9.34960 | − | 5.39799i | −0.410402 | − | 0.236946i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 0.911178i | − | 0.0399194i | −0.999801 | − | 0.0199597i | \(-0.993646\pi\) | ||
0.999801 | − | 0.0199597i | \(-0.00635380\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | − | 8.43806i | − | 0.368267i | ||||||
\(526\) | 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 | ||||||||
\(531\) | 2.67282 | 0.115991 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.4975 | −1.66751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.48963 | − | 11.2404i | −0.280571 | − | 0.485964i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.519602 | − | 0.899976i | −0.0224225 | − | 0.0388368i | ||||
\(538\) | 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 | ||||||||
\(543\) | 7.77627i | 0.333712i | ||||||||
\(544\) | 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 | ||||||||
\(549\) | −6.41764 | − | 11.1157i | −0.273898 | − | 0.474406i | ||||
\(550\) | 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 | ||||||||
\(555\) | −23.2580 | − | 13.4280i | −0.987247 | − | 0.569988i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.514319 | + | 0.890827i | −0.0217924 | + | 0.0377455i | −0.876716 | − | 0.481008i | \(-0.840271\pi\) |
0.854924 | + | 0.518754i | \(0.173604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.35621 | 0.0996572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.18319 | + | 1.26047i | 0.0921743 | + | 0.0532169i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.29588 | 0.181050 | 0.0905249 | − | 0.995894i | \(-0.471146\pi\) | ||||
0.0905249 | + | 0.995894i | \(0.471146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.5226 | − | 19.3543i | 1.41031 | − | 0.814241i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.40841 | + | 1.96784i | −0.143140 | + | 0.0826417i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9992i | 1.08995i | 0.838454 | + | 0.544973i | \(0.183460\pi\) | ||||
−0.838454 | + | 0.544973i | \(0.816540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.2310i | − | 1.47437i | −0.675691 | − | 0.737185i | \(-0.736154\pi\) | ||
0.675691 | − | 0.737185i | \(-0.263846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.7437 | − | 13.1311i | 0.950131 | − | 0.548558i | ||||
\(574\) | 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 | ||||||||
\(579\) | −8.23445 | − | 4.75416i | −0.342212 | − | 0.197576i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.79834 | −0.323530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.20561 | − | 9.01639i | 0.215594 | − | 0.373421i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.62438 | + | 5.55664i | 0.397919 | + | 0.229739i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.84452 | + | 5.68373i | −0.406327 | + | 0.234593i | −0.689210 | − | 0.724561i | \(-0.742042\pi\) |
0.282884 | + | 0.959154i | \(0.408709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.5905 | − | 3.63875i | −0.642394 | − | 0.149932i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.9661 | − | 24.1900i | −0.574488 | − | 0.995042i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9269 | − | 22.3900i | 0.530843 | − | 0.919447i | −0.468509 | − | 0.883459i | \(-0.655209\pi\) |
0.999352 | − | 0.0359886i | \(-0.0114580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4218 | − | 6.01702i | −0.427252 | − | 0.246674i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.93928i | 0.324933i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.56276 | + | 4.43883i | −0.104711 | + | 0.181366i | −0.913620 | − | 0.406569i | \(-0.866725\pi\) |
0.808909 | + | 0.587934i | \(0.200059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7822i | 0.521398i | 0.965420 | + | 0.260699i | \(0.0839530\pi\) | ||||
−0.965420 | + | 0.260699i | \(0.916047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.73558 | + | 3.00612i | 0.0706783 | + | 0.122418i | ||||
\(604\) | 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 | ||||||||
\(609\) | 9.54731 | 0.386876 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | − | 24.7475i | − | 0.997915i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1717 | + | 17.6179i | −0.409497 | + | 0.709270i | −0.994833 | − | 0.101521i | \(-0.967629\pi\) |
0.585336 | + | 0.810791i | \(0.300962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.1402i | − | 0.528150i | −0.964502 | − | 0.264075i | \(-0.914933\pi\) | ||
0.964502 | − | 0.264075i | \(-0.0850667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.19243 | + | 1.84315i | 0.128108 | + | 0.0739630i | ||||
\(622\) | 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 | ||||||||
\(627\) | 9.19243 | − | 2.78632i | 0.367110 | − | 0.111275i | ||||
\(628\) | 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 | ||||||||
\(633\) | 4.32605 | − | 7.49293i | 0.171945 | − | 0.297817i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.0946 | −1.23395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.5697 | + | 17.6494i | 1.21122 | + | 0.699296i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4896 | 0.494082 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.9714 | − | 18.4587i | 1.26279 | − | 0.729074i | 0.289179 | − | 0.957275i | \(-0.406618\pi\) |
0.973614 | + | 0.228201i | \(0.0732844\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | 1.51465i | 0.0596394i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.5387i | 1.04335i | 0.853146 | + | 0.521673i | \(0.174692\pi\) | ||||
−0.853146 | + | 0.521673i | \(0.825308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.10083 | + | 2.94497i | −0.200225 | + | 0.115600i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5185 | + | 7.22754i | −0.490638 | + | 0.283270i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.23860 | −0.0876033 | −0.0438017 | − | 0.999040i | \(-0.513947\pi\) | ||||
−0.0438017 | + | 0.999040i | \(0.513947\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.6419 | + | 16.5364i | 1.11913 | + | 0.646132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.71203 | −0.105806 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.43724 | − | 5.95348i | 0.133896 | − | 0.231915i | −0.791279 | − | 0.611455i | \(-0.790585\pi\) |
0.925175 | + | 0.379540i | \(0.123918\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 4.11930 | − | 2.37828i | 0.159980 | − | 0.0923647i | ||||
\(664\) | 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 | ||||||||
\(669\) | 7.18206 | − | 12.4397i | 0.277674 | − | 0.480946i | ||||
\(670\) | 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 | ||||||||
\(675\) | −1.07199 | + | 1.85675i | −0.0412610 | + | 0.0714662i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.1650i | − | 0.544405i | −0.962240 | − | 0.272202i | \(-0.912248\pi\) | ||
0.962240 | − | 0.272202i | \(-0.0877520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.62967 | − | 11.4829i | −0.254423 | − | 0.440674i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.09159 | + | 12.2830i | 0.271751 | + | 0.470686i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.8952 | −0.914325 | −0.457163 | − | 0.889383i | \(-0.651134\pi\) | ||||
−0.457163 | + | 0.889383i | \(0.651134\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.2100 | 0.963223 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.27365 | + | 14.3304i | 0.315660 | + | 0.546738i | ||||
\(688\) | 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 | ||||||||
\(693\) | 4.33641 | − | 7.51089i | 0.164727 | − | 0.285315i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.7088i | 1.39245i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.17302 | − | 5.29605i | −0.347453 | − | 0.200602i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1193 | − | 22.7233i | 0.496218 | − | 0.859474i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2109 | + | 24.6140i | 0.536738 | + | 0.929658i | 0.999077 | + | 0.0429544i | \(0.0136770\pi\) |
−0.462339 | + | 0.886703i | \(0.652990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.95458 | + | 42.6511i | −0.375444 | + | 1.60862i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.4218 | + | 16.4093i | −1.07043 | + | 0.618011i | ||||
\(706\) | 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 | ||||||||
\(711\) | 7.01847 | 0.263213 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.7252 | + | 6.76956i | 0.439113 | + | 0.253522i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.4896 | −0.915860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.09159 | − | 0.630233i | 0.0407664 | − | 0.0235365i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.844517 | + | 0.487582i | −0.0314952 | + | 0.0181837i | −0.515665 | − | 0.856790i | \(-0.672455\pi\) |
0.484170 | + | 0.874974i | \(0.339122\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 64.7438i | − | 2.41118i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.9389i | 0.778726i | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | −11.3456 | + | 19.6512i | −0.418491 | + | 0.724847i | ||||
\(736\) | 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 | ||||||||
\(741\) | 4.11930 | − | 17.6494i | 0.151326 | − | 0.648368i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.1101 | + | 41.7599i | 0.884513 | + | 1.53202i | 0.846271 | + | 0.532752i | \(0.178842\pi\) |
0.0382412 | + | 0.999269i | \(0.487824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.7921 | + | 37.7451i | −0.798402 | + | 1.38287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.71598 | + | 0.990721i | 0.0627844 | + | 0.0362486i | ||||
\(748\) | 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 | ||||||||
\(753\) | − | 28.4658i | − | 1.03735i | ||||||
\(754\) | 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 | ||||||||
\(759\) | −8.12325 | −0.294855 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.5496 | −0.672421 | −0.336211 | − | 0.941787i | \(-0.609145\pi\) | ||||
−0.336211 | + | 0.941787i | \(0.609145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9361 | + | 50.1188i | 1.04756 | + | 1.81442i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.52884 | + | 2.64802i | 0.0552752 | + | 0.0957395i | ||||
\(766\) | 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 | ||||||||
\(771\) | − | 12.0972i | − | 0.435668i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.981529 | − | 0.566686i | −0.0353031 | − | 0.0203823i | 0.482245 | − | 0.876037i | \(-0.339822\pi\) |
−0.517548 | + | 0.855654i | \(0.673155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.93724 | + | 6.81950i | −0.141430 | + | 0.244964i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.7725 | + | 34.2470i | 0.709335 | + | 1.22860i | ||||
\(778\) | 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 | ||||||||
\(783\) | −2.10083 | − | 1.21292i | −0.0750776 | − | 0.0433460i | ||||
\(784\) | 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 | ||||||||
\(789\) | 1.11930 | + | 0.646229i | 0.0398482 | + | 0.0230064i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.9977 | −2.02661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.2177 | − | 26.6838i | 1.64124 | − | 0.947569i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.9361 | − | 6.31397i | 0.387864 | − | 0.223933i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.2972i | − | 0.364746i | −0.983229 | − | 0.182373i | \(-0.941622\pi\) | ||
0.983229 | − | 0.182373i | \(-0.0583778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0466i | 0.496933i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9269 | + | 7.46334i | −0.456749 | + | 0.263704i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.17565 | − | 2.98816i | 0.182645 | − | 0.105450i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.7776 | 1.36673 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5420 | + | 14.1693i | 0.863920 | + | 0.498785i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.1338 | −0.918816 | −0.459408 | − | 0.888225i | \(-0.651938\pi\) | ||||
−0.459408 | + | 0.888225i | \(0.651938\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 13.2017 | + | 7.62198i | 0.463002 | + | 0.267315i | ||||
\(814\) | 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 | ||||||||
\(819\) | −8.18206 | − | 14.1717i | −0.285904 | − | 0.495201i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.89917 | + | 6.75356i | −0.136082 | + | 0.235701i | −0.926010 | − | 0.377498i | \(-0.876784\pi\) |
0.789928 | + | 0.613199i | \(0.210118\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | − | 4.72457i | − | 0.164488i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.99605 | − | 3.45726i | 0.0694094 | − | 0.120221i | −0.829232 | − | 0.558904i | \(-0.811222\pi\) |
0.898641 | + | 0.438684i | \(0.144555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.8873i | − | 1.76739i | −0.468063 | − | 0.883695i | \(-0.655048\pi\) | ||
0.468063 | − | 0.883695i | \(-0.344952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.91764 | + | 13.7138i | 0.274660 | + | 0.475725i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.85601 | + | 8.41086i | 0.168251 | + | 0.291419i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02864 | 0.0355975 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.67282 | 0.126951 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.3117 | − | 43.8412i | −0.873858 | − | 1.51357i | −0.857974 | − | 0.513692i | \(-0.828277\pi\) |
−0.0158834 | − | 0.999874i | \(-0.505056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5577 | − | 20.0185i | −0.398540 | − | 0.690292i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.2957i | 0.630136i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.73050 | + | 9.92551i | −0.197135 | + | 0.341448i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24.1808i | − | 0.830862i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.4218 | + | 14.6773i | 0.872474 | + | 0.503723i | ||||
\(850\) | 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 | ||||||||
\(855\) | 11.3456 | + | 2.64802i | 0.388013 | + | 0.0905605i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6521 | − | 14.2329i | 0.842099 | − | 0.486186i | −0.0158779 | − | 0.999874i | \(-0.505054\pi\) |
0.857977 | + | 0.513688i | \(0.171721\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −18.2201 | + | 31.5582i | −0.620940 | + | 1.07550i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.5922 | 1.34773 | 0.673866 | − | 0.738853i | \(-0.264632\pi\) | ||||
0.673866 | + | 0.738853i | \(0.264632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.9898 | + | 14.4279i | 0.849680 | + | 0.490563i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6913 | −0.532904 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 3.36900i | 0.114023i | ||||||||
\(874\) | 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 | ||||||||
\(879\) | −17.0185 | + | 9.82562i | −0.574019 | + | 0.331410i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.9815 | 0.942722 | 0.471361 | − | 0.881940i | \(-0.343763\pi\) | ||||
0.471361 | + | 0.881940i | \(0.343763\pi\) | |||||||
\(882\) | 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 | ||||||||
\(885\) | −7.14399 | −0.240142 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.09555 | + | 3.62960i | −0.0703616 | + | 0.121870i | −0.899060 | − | 0.437826i | \(-0.855749\pi\) |
0.828698 | + | 0.559696i | \(0.189082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.6521 | + | 22.8931i | 1.32989 | + | 0.767811i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.90841 | + | 1.10182i | −0.0639340 | + | 0.0369123i | ||||
\(892\) | 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 | ||||||||
\(897\) | −7.66359 | + | 13.2737i | −0.255880 | + | 0.443197i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.71598 | − | 4.45482i | −0.257342 | − | 0.148577i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.40484i | − | 0.180061i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.11515 | − | 1.93150i | 0.0371098 | − | 0.0642761i | ||||
\(904\) | 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 | ||||||||
\(909\) | −5.10083 | − | 8.83490i | −0.169184 | − | 0.293035i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.95854 | 0.0648892 | 0.0324446 | − | 0.999474i | \(-0.489671\pi\) | ||||
0.0324446 | + | 0.999474i | \(0.489671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.36638 | −0.144506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.1532 | + | 29.7103i | 0.567068 | + | 0.982191i | ||||
\(916\) | 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 | ||||||||
\(921\) | −3.59046 | + | 6.21887i | −0.118310 | + | 0.204919i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.9304i | 1.70931i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6562 | + | 10.7712i | 0.613414 | + | 0.354154i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.22522 | + | 14.2465i | −0.270152 | + | 0.467916i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.02997 | − | 5.24806i | −0.0994100 | − | 0.172183i | 0.812031 | − | 0.583615i | \(-0.198362\pi\) |
−0.911441 | + | 0.411432i | \(0.865029\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0369 | + | 8.41086i | 1.18106 | + | 0.275655i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.2765 | − | 14.5934i | 0.827515 | − | 0.477766i | ||||
\(934\) | 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 | ||||||||
\(939\) | −14.4896 | −0.472851 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.6706 | + | 20.5944i | 1.16283 | + | 0.671359i | 0.951980 | − | 0.306160i | \(-0.0990444\pi\) |
0.210847 | + | 0.977519i | \(0.432378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.1312 | 1.11146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.11007 | − | 5.25970i | 0.296350 | − | 0.171098i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.88900 | + | 1.09062i | −0.0613843 | + | 0.0354403i | −0.530378 | − | 0.847761i | \(-0.677950\pi\) |
0.468994 | + | 0.883201i | \(0.344617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 11.2763i | − | 0.366044i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.74312i | 0.0889519i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.7974 | + | 12.5847i | −0.706087 | + | 0.407660i | −0.809611 | − | 0.586967i | \(-0.800322\pi\) |
0.103523 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −60.7899 | + | 35.0970i | −1.96711 | + | 1.13571i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.34565 | 0.172800 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.1479 | − | 18.5606i | −1.03811 | − | 0.599354i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.5104 | −0.564851 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.42801 | − | 4.20543i | 0.0782414 | − | 0.135518i | ||||
\(964\) | 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 | ||||||||
\(969\) | 3.40954 | − | 3.63875i | 0.109530 | − | 0.116893i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3272 | + | 42.1359i | 0.780696 | + | 1.35221i | 0.931537 | + | 0.363647i | \(0.118469\pi\) |
−0.150840 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.0266 | − | 46.8114i | 0.866432 | − | 1.50070i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.72013 | − | 4.45722i | −0.247242 | − | 0.142745i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.2811i | 0.360914i | 0.983583 | + | 0.180457i | \(0.0577576\pi\) | ||||
−0.983583 | + | 0.180457i | \(0.942242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.4465 | − | 28.4861i | 0.525632 | − | 0.910421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.7045i | − | 0.469478i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.8485 | + | 34.3786i | 0.633068 | + | 1.09651i | 0.986921 | + | 0.161205i | \(0.0515379\pi\) |
−0.353853 | + | 0.935301i | \(0.615129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37.3289 | + | 64.6555i | 1.18940 | + | 2.06010i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.3249 | 1.53820 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −5.03807 | − | 8.72620i | −0.159878 | − | 0.276918i | ||||
\(994\) | 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 | ||||||||
\(999\) | − | 10.0478i | − | 0.317899i |
(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 | 912.2.bb.e.31.3 | ✓ | 6 | |
3.2 | odd | 2 | 2736.2.bm.n.1855.1 | 6 | |||
4.3 | odd | 2 | 912.2.bb.f.31.3 | yes | 6 | ||
12.11 | even | 2 | 2736.2.bm.o.1855.1 | 6 | |||
19.8 | odd | 6 | 912.2.bb.f.559.3 | yes | 6 | ||
57.8 | even | 6 | 2736.2.bm.o.559.1 | 6 | |||
76.27 | even | 6 | inner | 912.2.bb.e.559.3 | yes | 6 | |
228.179 | odd | 6 | 2736.2.bm.n.559.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.bb.e.31.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
912.2.bb.e.559.3 | yes | 6 | 76.27 | even | 6 | inner | |
912.2.bb.f.31.3 | yes | 6 | 4.3 | odd | 2 | ||
912.2.bb.f.559.3 | yes | 6 | 19.8 | odd | 6 | ||
2736.2.bm.n.559.1 | 6 | 228.179 | odd | 6 | |||
2736.2.bm.n.1855.1 | 6 | 3.2 | odd | 2 | |||
2736.2.bm.o.559.1 | 6 | 57.8 | even | 6 | |||
2736.2.bm.o.1855.1 | 6 | 12.11 | even | 2 |