Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.20 | ||
Character | \(\chi\) | \(=\) | 252.53 |
Dual form | 252.9.bk.a.233.20 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 724.791 | − | 418.458i | 1.15966 | − | 0.669533i | 0.208441 | − | 0.978035i | \(-0.433161\pi\) |
0.951224 | + | 0.308502i | \(0.0998277\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 613.419 | + | 2321.32i | 0.255485 | + | 0.966813i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18278.5 | + | 10553.1i | 1.24845 | + | 0.720792i | 0.970800 | − | 0.239890i | \(-0.0771114\pi\) |
0.277649 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48972.6 | −1.71467 | −0.857333 | − | 0.514762i | \(-0.827880\pi\) | ||||
−0.857333 | + | 0.514762i | \(0.827880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −57253.8 | − | 33055.5i | −0.685502 | − | 0.395775i | 0.116423 | − | 0.993200i | \(-0.462857\pi\) |
−0.801925 | + | 0.597425i | \(0.796191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −124724. | − | 216028.i | −0.957050 | − | 1.65766i | −0.729606 | − | 0.683867i | \(-0.760297\pi\) |
−0.227443 | − | 0.973791i | \(-0.573037\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −31876.4 | + | 18403.9i | −0.113909 | + | 0.0657655i | −0.555872 | − | 0.831268i | \(-0.687616\pi\) |
0.441963 | + | 0.897033i | \(0.354282\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 154902. | − | 268298.i | 0.396548 | − | 0.686842i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 159982.i | − | 0.226193i | −0.993584 | − | 0.113096i | \(-0.963923\pi\) | ||
0.993584 | − | 0.113096i | \(-0.0360769\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 458407. | − | 793984.i | 0.496369 | − | 0.859736i | −0.503622 | − | 0.863924i | \(-0.668000\pi\) |
0.999991 | + | 0.00418771i | \(0.00133299\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41597e6 | + | 1.42578e6i | 0.943590 | + | 0.950124i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −670147. | − | 1.16073e6i | −0.357571 | − | 0.619332i | 0.629983 | − | 0.776609i | \(-0.283062\pi\) |
−0.987555 | + | 0.157277i | \(0.949728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.76061e6i | − | 0.623056i | −0.950237 | − | 0.311528i | \(-0.899159\pi\) | ||
0.950237 | − | 0.311528i | \(-0.100841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.70210e6 | −0.790364 | −0.395182 | − | 0.918603i | \(-0.629318\pi\) | ||||
−0.395182 | + | 0.918603i | \(0.629318\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.31980e6 | − | 4.22609e6i | 1.50006 | − | 0.866058i | 0.500056 | − | 0.865993i | \(-0.333313\pi\) |
1.00000 | 6.49340e-5i | \(-2.06691e-5\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.01224e6 | + | 2.84788e6i | −0.869455 | + | 0.494012i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.99457e6 | − | 2.88361e6i | −0.632986 | − | 0.365455i | 0.148921 | − | 0.988849i | \(-0.452420\pi\) |
−0.781908 | + | 0.623394i | \(0.785753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.76642e7 | 1.93038 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.25134e6 | − | 2.45451e6i | −0.350847 | − | 0.202561i | 0.314211 | − | 0.949353i | \(-0.398260\pi\) |
−0.665058 | + | 0.746792i | \(0.731593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.36663e6 | + | 7.56322e6i | 0.315375 | + | 0.546245i | 0.979517 | − | 0.201361i | \(-0.0645365\pi\) |
−0.664143 | + | 0.747606i | \(0.731203\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.54949e7 | + | 2.04930e7i | −1.98844 | + | 1.14803i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.27203e6 | + | 2.20322e6i | −0.0631245 | + | 0.109335i | −0.895860 | − | 0.444335i | \(-0.853440\pi\) |
0.832736 | + | 0.553670i | \(0.186773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.62638e6i | − | 0.339465i | −0.985490 | − | 0.169733i | \(-0.945710\pi\) | ||
0.985490 | − | 0.169733i | \(-0.0542904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.18886e6 | − | 3.79121e6i | 0.0770772 | − | 0.133502i | −0.824910 | − | 0.565263i | \(-0.808775\pi\) |
0.901988 | + | 0.431762i | \(0.142108\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.32848e7 | + | 4.89038e7i | −0.377912 | + | 1.39117i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.66903e7 | + | 2.89084e7i | 0.428505 | + | 0.742192i | 0.996741 | − | 0.0806739i | \(-0.0257072\pi\) |
−0.568236 | + | 0.822866i | \(0.692374\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.92393e7i | − | 0.826815i | −0.910546 | − | 0.413408i | \(-0.864338\pi\) | ||
0.910546 | − | 0.413408i | \(-0.135662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53294e7 | −1.05994 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.08755e7 | − | 5.24670e7i | 1.44839 | − | 0.836231i | 0.450008 | − | 0.893024i | \(-0.351421\pi\) |
0.998386 | + | 0.0567936i | \(0.0180877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00407e7 | − | 1.13681e8i | −0.438071 | − | 1.65776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.80797e8 | − | 1.04383e8i | −2.21971 | − | 1.28155i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.61722e8 | 1.82676 | 0.913381 | − | 0.407107i | \(-0.133462\pi\) | ||||
0.913381 | + | 0.407107i | \(0.133462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46479e6 | − | 1.42305e6i | −0.0236861 | − | 0.0136752i | 0.488110 | − | 0.872782i | \(-0.337686\pi\) |
−0.511796 | + | 0.859107i | \(0.671020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.03776e7 | − | 1.21898e8i | −0.625296 | − | 1.08304i | −0.988484 | − | 0.151328i | \(-0.951645\pi\) |
0.363188 | − | 0.931716i | \(-0.381688\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.08663e8 | − | 6.27366e7i | 0.828984 | − | 0.478614i | −0.0245206 | − | 0.999699i | \(-0.507806\pi\) |
0.853505 | + | 0.521085i | \(0.174473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.22834e7 | − | 1.42519e8i | 0.582916 | − | 1.00964i | −0.412215 | − | 0.911087i | \(-0.635245\pi\) |
0.995132 | − | 0.0985545i | \(-0.0314219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.12894e6i | − | 0.00692399i | −0.999994 | − | 0.00346200i | \(-0.998898\pi\) | ||
0.999994 | − | 0.00346200i | \(-0.00110199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.54025e7 | + | 2.66779e7i | −0.0880643 | + | 0.152532i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.16118e7 | − | 1.53181e8i | 0.207505 | − | 0.763867i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.15557e8 | + | 2.00151e8i | 0.539084 | + | 0.933720i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.76409e7i | 0.277057i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −219505. | −0.000843781 | −0.000421891 | − | 1.00000i | \(-0.500134\pi\) | ||||
−0.000421891 | 1.00000i | \(0.500134\pi\) | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.81811e8 | + | 1.04969e8i | −0.617355 | + | 0.356430i | −0.775839 | − | 0.630932i | \(-0.782673\pi\) |
0.158483 | + | 0.987362i | \(0.449340\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.24961e8 | − | 4.22039e8i | 1.35813 | − | 1.34879i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.07778e8 | − | 2.93166e8i | −1.44142 | − | 0.832206i | −0.443479 | − | 0.896285i | \(-0.646256\pi\) |
−0.997945 | + | 0.0640783i | \(0.979589\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.51220e8 | −0.672968 | −0.336484 | − | 0.941689i | \(-0.609238\pi\) | ||||
−0.336484 | + | 0.941689i | \(0.609238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.95148e8 | − | 5.16814e8i | −2.14067 | − | 1.23592i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.69457e7 | − | 1.15953e8i | −0.151443 | − | 0.262308i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.90996e8 | + | 4.56682e8i | −1.60483 | + | 0.926550i | −0.614330 | + | 0.789049i | \(0.710574\pi\) |
−0.990502 | + | 0.137501i | \(0.956093\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.18270e8 | − | 3.78056e8i | 0.419843 | − | 0.727190i | −0.576080 | − | 0.817393i | \(-0.695418\pi\) |
0.995923 | + | 0.0902034i | \(0.0287517\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.67297e8i | − | 1.32934i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.29821e6 | − | 2.24857e6i | 0.00213672 | − | 0.00370090i | −0.864955 | − | 0.501849i | \(-0.832653\pi\) |
0.867092 | + | 0.498148i | \(0.165987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.22748e7 | − | 6.27061e7i | −0.0926849 | − | 0.0933268i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.04833e8 | + | 3.54781e8i | 0.290168 | + | 0.502585i | 0.973849 | − | 0.227195i | \(-0.0729556\pi\) |
−0.683682 | + | 0.729780i | \(0.739622\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.09139e9i | − | 1.40318i | −0.712580 | − | 0.701590i | \(-0.752474\pi\) | ||
0.712580 | − | 0.701590i | \(-0.247526\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58258e9 | 1.94008 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.56035e8 | + | 1.47822e8i | −0.285834 | + | 0.165027i | −0.636062 | − | 0.771638i | \(-0.719438\pi\) |
0.350227 | + | 0.936665i | \(0.386104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.17824e8 | + | 1.94997e8i | 0.765360 | + | 0.207911i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.47767e9 | + | 8.53134e8i | 1.43935 | + | 0.831008i | 0.997804 | − | 0.0662313i | \(-0.0210975\pi\) |
0.441544 | + | 0.897240i | \(0.354431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.61028e8 | −0.615893 | −0.307946 | − | 0.951404i | \(-0.599642\pi\) | ||||
−0.307946 | + | 0.951404i | \(0.599642\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.71432e8 | − | 5.60856e8i | −0.829326 | − | 0.478812i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.97678e8 | − | 1.20841e9i | −0.570543 | − | 0.988210i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.40735e9 | + | 8.12534e8i | −1.05747 | + | 0.610531i | −0.924732 | − | 0.380620i | \(-0.875711\pi\) |
−0.132740 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.11822e8 | − | 1.05971e9i | 0.440957 | − | 0.763759i | −0.556804 | − | 0.830644i | \(-0.687973\pi\) |
0.997761 | + | 0.0668847i | \(0.0213060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.83505e9i | − | 1.88233i | −0.337945 | − | 0.941166i | \(-0.609732\pi\) | ||
0.337945 | − | 0.941166i | \(-0.390268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.37050e9 | − | 2.37377e9i | 0.873908 | − | 1.51365i | 0.0159865 | − | 0.999872i | \(-0.494911\pi\) |
0.857921 | − | 0.513781i | \(-0.171756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.71369e8 | − | 9.81358e7i | 0.218686 | − | 0.0577888i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.36741e8 | − | 1.27607e9i | −0.417157 | − | 0.722537i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.26490e9i | − | 2.75934i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.66306e9 | −0.839034 | −0.419517 | − | 0.907748i | \(-0.637800\pi\) | ||||
−0.419517 | + | 0.907748i | \(0.637800\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.95845e9 | + | 1.13071e9i | −0.916557 | + | 0.529174i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.12429e9 | + | 5.77064e8i | 0.958019 | + | 0.260247i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.80387e9 | + | 1.61881e9i | 1.17541 | + | 0.678622i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.57119e9 | −1.44409 | −0.722044 | − | 0.691847i | \(-0.756797\pi\) | ||||
−0.722044 | + | 0.691847i | \(0.756797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.24886e9 | − | 1.29838e9i | −0.846952 | − | 0.488988i | 0.0126690 | − | 0.999920i | \(-0.495967\pi\) |
−0.859621 | + | 0.510932i | \(0.829301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.50800e7 | + | 7.80808e7i | 0.0163924 | + | 0.0283924i | 0.874105 | − | 0.485737i | \(-0.161449\pi\) |
−0.857713 | + | 0.514129i | \(0.828115\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00270e9 | + | 1.73361e9i | −1.01880 | + | 0.588204i | −0.913756 | − | 0.406264i | \(-0.866831\pi\) |
−0.105043 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53688e9 | − | 6.12605e9i | 1.15971 | − | 2.00867i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.68372e9i | 1.43549i | 0.696307 | + | 0.717744i | \(0.254825\pi\) | ||||
−0.696307 | + | 0.717744i | \(0.745175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.42738e9 | + | 4.20435e9i | −0.719565 | + | 1.24632i | 0.241607 | + | 0.970374i | \(0.422325\pi\) |
−0.961172 | + | 0.275949i | \(0.911008\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.44110e9 | + | 4.16153e9i | −0.677520 | + | 1.15502i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.10804e9 | + | 1.05794e10i | 1.64102 | + | 2.84233i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.48552e9i | 0.374269i | 0.982334 | + | 0.187134i | \(0.0599200\pi\) | ||||
−0.982334 | + | 0.187134i | \(0.940080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.76873e8 | −0.189613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.04194e9 | − | 3.48832e9i | 1.38498 | − | 0.799619i | 0.392237 | − | 0.919864i | \(-0.371701\pi\) |
0.992744 | + | 0.120245i | \(0.0383679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.28334e9 | − | 2.26764e9i | 0.507424 | − | 0.503935i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.32456e9 | − | 4.22883e9i | −1.53094 | − | 0.883889i | −0.999319 | − | 0.0369072i | \(-0.988249\pi\) |
−0.531622 | − | 0.846982i | \(-0.678417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.82669e9 | −0.978736 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.46192e9 | + | 2.57609e9i | 0.852142 | + | 0.491985i | 0.861373 | − | 0.507973i | \(-0.169605\pi\) |
−0.00923072 | + | 0.999957i | \(0.502938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.08632e9 | + | 3.61361e9i | 0.386815 | + | 0.669984i | 0.992019 | − | 0.126087i | \(-0.0402417\pi\) |
−0.605204 | + | 0.796071i | \(0.706908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.66276e9 | − | 3.26939e9i | 0.990141 | − | 0.571658i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.85814e8 | + | 1.53428e9i | −0.150461 | + | 0.260606i | −0.931397 | − | 0.364005i | \(-0.881409\pi\) |
0.780936 | + | 0.624611i | \(0.214742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.30429e9i | − | 0.209193i | −0.994515 | − | 0.104597i | \(-0.966645\pi\) | ||
0.994515 | − | 0.104597i | \(-0.0333552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55119e9 | + | 6.15084e9i | −0.553641 | + | 0.958934i | 0.444367 | + | 0.895845i | \(0.353429\pi\) |
−0.998008 | + | 0.0630890i | \(0.979905\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.08693e9 | − | 1.07999e9i | 0.602379 | − | 0.159181i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.30254e9 | − | 2.25607e9i | −0.186725 | − | 0.323416i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.34050e9i | 0.588938i | 0.955661 | + | 0.294469i | \(0.0951428\pi\) | ||||
−0.955661 | + | 0.294469i | \(0.904857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.10844e9 | −0.542486 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.56107e9 | − | 9.01286e8i | 0.195316 | − | 0.112766i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65752e9 | − | 6.27243e9i | −0.201926 | − | 0.764134i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.32978e9 | + | 3.65450e9i | 0.731458 | + | 0.422307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.58360e9 | −0.516004 | −0.258002 | − | 0.966144i | \(-0.583064\pi\) | ||||
−0.258002 | + | 0.966144i | \(0.583064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.28259e10 | + | 7.40504e9i | 1.37103 | + | 0.791564i | 0.991058 | − | 0.133435i | \(-0.0426006\pi\) |
0.379971 | + | 0.924998i | \(0.375934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.92619e9 | − | 6.80037e9i | −0.409067 | − | 0.708525i | 0.585719 | − | 0.810514i | \(-0.300812\pi\) |
−0.994785 | + | 0.101990i | \(0.967479\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.40674e9 | + | 2.54423e9i | −0.436396 | + | 0.251953i | −0.702068 | − | 0.712110i | \(-0.747740\pi\) |
0.265672 | + | 0.964064i | \(0.414406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.68831e9 | − | 2.92424e9i | 0.163038 | − | 0.282390i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.64912e10i | 1.51510i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.58594e9 | + | 1.31392e10i | −0.679948 | + | 1.17771i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.43002e10 | + | 1.43992e10i | 1.22056 | + | 1.22901i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70894e9 | + | 8.15612e9i | 0.392294 | + | 0.679472i | 0.992752 | − | 0.120184i | \(-0.0383484\pi\) |
−0.600458 | + | 0.799656i | \(0.705015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.12916e9i | 0.169056i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.01405e10 | −0.786216 | −0.393108 | − | 0.919492i | \(-0.628600\pi\) | ||||
−0.393108 | + | 0.919492i | \(0.628600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.67580e10 | − | 9.67525e9i | 1.23938 | − | 0.715558i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.68543e9 | − | 9.88805e9i | −0.699749 | − | 0.714388i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.83864e9 | + | 4.52564e9i | 0.540658 | + | 0.312149i | 0.745346 | − | 0.666678i | \(-0.232284\pi\) |
−0.204688 | + | 0.978827i | \(0.565618\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.27218e10 | 1.53159 | 0.765794 | − | 0.643086i | \(-0.222346\pi\) | ||||
0.765794 | + | 0.643086i | \(0.222346\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.37058e10 | − | 7.91307e9i | −0.882687 | − | 0.509620i | −0.0111437 | − | 0.999938i | \(-0.503547\pi\) |
−0.871543 | + | 0.490318i | \(0.836881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.60978e9 | − | 6.25232e9i | −0.227283 | − | 0.393666i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.05475e10 | + | 6.08960e9i | −0.634997 | + | 0.366616i | −0.782685 | − | 0.622418i | \(-0.786150\pi\) |
0.147688 | + | 0.989034i | \(0.452817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26202e10 | + | 3.91793e10i | −1.33189 | + | 2.30690i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.66378e9i | − | 0.206423i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.23886e9 | − | 1.08060e10i | 0.343907 | − | 0.595664i | −0.641248 | − | 0.767334i | \(-0.721583\pi\) |
0.985155 | + | 0.171670i | \(0.0549162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.63003e9 | − | 1.33628e10i | 0.191608 | − | 0.705348i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.61759e9 | − | 7.99790e9i | −0.238550 | − | 0.413181i | 0.721748 | − | 0.692156i | \(-0.243339\pi\) |
−0.960299 | + | 0.278974i | \(0.910006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.83473e9i | 0.387845i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.45607e9 | −0.409838 | −0.204919 | − | 0.978779i | \(-0.565693\pi\) | ||||
−0.204919 | + | 0.978779i | \(0.565693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.65796e10 | + | 1.53458e10i | −1.23525 | + | 0.713170i | −0.968119 | − | 0.250491i | \(-0.919408\pi\) |
−0.267128 | + | 0.963661i | \(0.586075\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.08355e10 | + | 4.10041e10i | 0.493182 | + | 1.86631i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.61072e10 | + | 2.08465e10i | 1.57687 | + | 0.910406i | 0.995293 | + | 0.0969156i | \(0.0308977\pi\) |
0.581578 | + | 0.813491i | \(0.302436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43340e9 | 0.104113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.41939e10 | + | 1.39684e10i | 0.993844 | + | 0.573796i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.55350e10 | + | 2.69073e10i | 0.625386 | + | 1.08320i | 0.988466 | + | 0.151442i | \(0.0483916\pi\) |
−0.363081 | + | 0.931758i | \(0.618275\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.39090e10 | − | 8.03037e9i | 0.537921 | − | 0.310569i | −0.206315 | − | 0.978486i | \(-0.566147\pi\) |
0.744236 | + | 0.667917i | \(0.232814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.24494e10 | + | 3.88835e10i | −0.851107 | + | 1.47416i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.82886e10i | − | 1.03094i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.40215e9 | − | 4.16065e9i | 0.0858434 | − | 0.148685i | −0.819907 | − | 0.572497i | \(-0.805975\pi\) |
0.905750 | + | 0.423812i | \(0.139308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.08985e9 | − | 1.13743e10i | 0.106203 | − | 0.390955i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.64200e10 | − | 2.84403e10i | −0.553580 | − | 0.958829i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.03712e10i | 1.30983i | 0.755702 | + | 0.654915i | \(0.227296\pi\) | ||||
−0.755702 | + | 0.654915i | \(0.772704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.59449e10 | 1.46254 | 0.731271 | − | 0.682087i | \(-0.238927\pi\) | ||||
0.731271 | + | 0.682087i | \(0.238927\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.77374e10 | + | 1.02407e10i | −0.543670 | + | 0.313888i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.48781e10 | + | 1.47757e10i | −0.447543 | + | 0.444465i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.51461e10 | − | 2.02916e10i | −1.01852 | − | 0.588041i | −0.104843 | − | 0.994489i | \(-0.533434\pi\) |
−0.913674 | + | 0.406448i | \(0.866767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.67077e10 | 0.475297 | 0.237648 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237648 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.95149e9 | + | 4.59080e9i | 0.218033 | + | 0.125882i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.49785e10 | − | 4.32640e10i | −0.672524 | − | 1.16485i | −0.977186 | − | 0.212386i | \(-0.931877\pi\) |
0.304661 | − | 0.952461i | \(-0.401457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.84406e9 | + | 4.52877e9i | −0.203670 | + | 0.117589i | −0.598366 | − | 0.801223i | \(-0.704183\pi\) |
0.394696 | + | 0.918812i | \(0.370850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.39105e10 | − | 7.60552e10i | 1.11977 | − | 1.93949i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.89084e10i | 0.465231i | 0.972569 | + | 0.232615i | \(0.0747284\pi\) | ||||
−0.972569 | + | 0.232615i | \(0.925272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85799e10 | − | 3.21814e10i | 0.449094 | − | 0.777854i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.93439e10 | − | 6.98241e10i | −1.61794 | − | 1.62915i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.46303e10 | − | 5.99814e10i | −0.793946 | − | 1.37516i | −0.923506 | − | 0.383584i | \(-0.874690\pi\) |
0.129560 | − | 0.991572i | \(-0.458644\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.87667e10i | − | 0.636922i | −0.947936 | − | 0.318461i | \(-0.896834\pi\) | ||
0.947936 | − | 0.318461i | \(-0.103166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.38852e10 | −0.302154 | −0.151077 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151077 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.31919e10 | + | 7.61637e9i | −0.277358 | + | 0.160133i | −0.632227 | − | 0.774783i | \(-0.717859\pi\) |
0.354869 | + | 0.934916i | \(0.384526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.89466e9 | − | 1.60129e9i | −0.121834 | − | 0.0330962i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.93904e10 | − | 2.85156e10i | −0.986729 | − | 0.569688i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.72796e10 | −1.51807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.30795e10 | + | 2.48720e10i | 0.818331 | + | 0.472464i | 0.849841 | − | 0.527040i | \(-0.176698\pi\) |
−0.0315095 | + | 0.999503i | \(0.510031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.28188e10 | + | 5.68439e10i | 0.613116 | + | 1.06195i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.17214e11 | − | 6.76738e10i | 2.11843 | − | 1.22308i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.22486e10 | − | 5.58563e10i | 0.573318 | − | 0.993016i | −0.422904 | − | 0.906174i | \(-0.638989\pi\) |
0.996222 | − | 0.0868413i | \(-0.0276773\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.21476e9i | 0.124135i | 0.998072 | + | 0.0620677i | \(0.0197695\pi\) | ||||
−0.998072 | + | 0.0620677i | \(0.980231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.28828e9 | + | 9.15957e9i | −0.0895214 | + | 0.155056i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.00246e10 | − | 5.29158e9i | 0.328199 | − | 0.0867281i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.75926e9 | − | 8.24328e9i | −0.0767604 | − | 0.132953i | 0.825090 | − | 0.565001i | \(-0.191124\pi\) |
−0.901850 | + | 0.432048i | \(0.857791\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 2.93889e10i | − | 0.459104i | −0.973296 | − | 0.229552i | \(-0.926274\pi\) | ||
0.973296 | − | 0.229552i | \(-0.0737260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.38194e9 | −0.0366239 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.43159e10 | + | 1.40388e10i | −0.362259 | + | 0.209150i | −0.670071 | − | 0.742297i | \(-0.733736\pi\) |
0.307812 | + | 0.951447i | \(0.400403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.01433e10 | + | 2.75543e9i | 0.148763 | + | 0.0404116i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.02018e11 | − | 5.89001e10i | −1.45027 | − | 0.837312i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.78394e11 | 2.49699 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.67202e10 | − | 5.00680e10i | −1.17698 | − | 0.679530i | −0.221667 | − | 0.975122i | \(-0.571150\pi\) |
−0.955314 | + | 0.295592i | \(0.904483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.91195e10 | + | 6.77569e10i | 0.522861 | + | 0.905622i | 0.999646 | + | 0.0266019i | \(0.00846865\pi\) |
−0.476785 | + | 0.879020i | \(0.658198\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.24911e10 | + | 3.03058e10i | −0.680524 | + | 0.392901i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.84781e10 | + | 6.66460e10i | −0.491350 | + | 0.851043i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.62216e10i | 1.06833i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.25052e10 | − | 9.09417e10i | 0.640896 | − | 1.11006i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.21670e11 | − | 8.39655e8i | −1.44155 | − | 0.00994823i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.48762e10 | − | 7.77278e10i | −0.523874 | − | 0.907376i | −0.999614 | − | 0.0277901i | \(-0.991153\pi\) |
0.475740 | − | 0.879586i | \(-0.342180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.37729e11i | − | 1.56113i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.66942e11 | 1.86473 | 0.932366 | − | 0.361516i | \(-0.117741\pi\) | ||||
0.932366 | + | 0.361516i | \(0.117741\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.45605e10 | + | 1.99535e10i | −0.374950 | + | 0.216478i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.68675e10 | + | 5.64764e10i | −0.608084 | + | 0.603902i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.62662e10 | − | 4.40323e10i | −0.792340 | − | 0.457458i | 0.0484458 | − | 0.998826i | \(-0.484573\pi\) |
−0.840786 | + | 0.541368i | \(0.817907\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.32329e11 | 1.35521 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.58868e10 | − | 1.49458e10i | −0.257659 | − | 0.148759i | 0.365607 | − | 0.930769i | \(-0.380861\pi\) |
−0.623266 | + | 0.782010i | \(0.714195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.72413e8 | − | 8.18244e8i | −0.00463584 | − | 0.00802951i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.42108e10 | + | 2.55251e10i | −0.421774 | + | 0.243511i | −0.695836 | − | 0.718201i | \(-0.744966\pi\) |
0.274062 | + | 0.961712i | \(0.411633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00852e10 | − | 6.94296e10i | 0.377085 | − | 0.653131i | −0.613551 | − | 0.789655i | \(-0.710260\pi\) |
0.990637 | + | 0.136524i | \(0.0435930\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.14032e10i | 0.104317i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.03022e11 | + | 1.78440e11i | −0.929453 | + | 1.60986i | −0.145215 | + | 0.989400i | \(0.546387\pi\) |
−0.784238 | + | 0.620460i | \(0.786946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.10868e10 | − | 2.40701e10i | 0.799376 | − | 0.211239i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.08623e10 | − | 1.05417e11i | −0.526834 | − | 0.912504i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.93891e10i | − | 0.752891i | −0.926439 | − | 0.376446i | \(-0.877146\pi\) | ||
0.926439 | − | 0.376446i | \(-0.122854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.28697e11 | −1.90020 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.30044e11 | − | 7.50812e10i | 1.05165 | − | 0.607173i | 0.128542 | − | 0.991704i | \(-0.458970\pi\) |
0.923112 | + | 0.384531i | \(0.125637\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.39401e10 | − | 1.28437e11i | −0.270798 | − | 1.02476i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.89741e10 | − | 5.13692e10i | −0.691124 | − | 0.399021i | 0.112909 | − | 0.993605i | \(-0.463983\pi\) |
−0.804033 | + | 0.594585i | \(0.797317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.05848e9 | −0.0694316 | −0.0347158 | − | 0.999397i | \(-0.511053\pi\) | ||||
−0.0347158 | + | 0.999397i | \(0.511053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.67510e11 | + | 9.67118e10i | 1.25031 | + | 0.721868i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.29946e10 | − | 1.43751e11i | −0.611357 | − | 1.05890i | −0.991012 | − | 0.133774i | \(-0.957290\pi\) |
0.379654 | − | 0.925128i | \(-0.376043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.58469e11 | + | 2.06962e11i | −2.57210 | + | 1.48500i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.93003e10 | − | 3.34291e10i | 0.136685 | − | 0.236746i | −0.789555 | − | 0.613680i | \(-0.789688\pi\) |
0.926240 | + | 0.376934i | \(0.123022\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.21113e11i | − | 1.52571i | −0.646568 | − | 0.762856i | \(-0.723796\pi\) | ||
0.646568 | − | 0.762856i | \(-0.276204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.39023e10 | − | 1.10682e11i | 0.435265 | − | 0.753902i | −0.562052 | − | 0.827102i | \(-0.689988\pi\) |
0.997317 | + | 0.0732002i | \(0.0233212\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.77537e11 | + | 1.78767e11i | 1.17852 | + | 1.18668i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.88133e10 | + | 1.53829e11i | 0.582047 | + | 1.00814i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.86081e10i | 0.566071i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.26478e11 | −0.797806 | −0.398903 | − | 0.916993i | \(-0.630609\pi\) | ||||
−0.398903 | + | 0.916993i | \(0.630609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.59095e8 | + | 9.18537e7i | −0.000978504 | + | 0.000564939i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.45462e11 | − | 1.39468e11i | 1.49083 | − | 0.847066i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.09854e11 | + | 1.21159e11i | 1.24304 | + | 0.717669i | 0.969712 | − | 0.244252i | \(-0.0785423\pi\) |
0.273328 | + | 0.961921i | \(0.411876\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.70210e11 | 0.995730 | 0.497865 | − | 0.867255i | \(-0.334117\pi\) | ||||
0.497865 | + | 0.867255i | \(0.334117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.28533e10 | − | 3.05149e10i | −0.301617 | − | 0.174138i | 0.341552 | − | 0.939863i | \(-0.389047\pi\) |
−0.643169 | + | 0.765724i | \(0.722381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.18055e10 | − | 8.97298e10i | −0.292010 | − | 0.505775i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.38832e11 | − | 8.01548e10i | 0.763550 | − | 0.440836i | −0.0670191 | − | 0.997752i | \(-0.521349\pi\) |
0.830569 | + | 0.556916i | \(0.188016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.78499e10 | + | 1.52161e11i | −0.477283 | + | 0.826679i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.13989e11i | − | 0.604393i | −0.953246 | − | 0.302197i | \(-0.902280\pi\) | ||
0.953246 | − | 0.302197i | \(-0.0977199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.48808e10 | + | 9.50563e10i | −0.287484 | + | 0.497938i | −0.973209 | − | 0.229924i | \(-0.926152\pi\) |
0.685724 | + | 0.727861i | \(0.259486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.31402e11 | − | 4.83718e11i | 0.671919 | − | 2.47347i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.94429e9 | + | 5.09965e9i | 0.0148757 | + | 0.0257654i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.84326e11i | 0.909278i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.43979e11 | 1.67676 | 0.838382 | − | 0.545083i | \(-0.183502\pi\) | ||||
0.838382 | + | 0.545083i | \(0.183502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.16116e9 | − | 1.82510e9i | 0.0150484 | − | 0.00868823i | −0.492457 | − | 0.870337i | \(-0.663901\pi\) |
0.507505 | + | 0.861649i | \(0.330568\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.92032e10 | + | 3.75408e11i | 0.466709 | + | 1.76614i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.03296e11 | + | 1.17373e11i | 0.934213 | + | 0.539368i | 0.888142 | − | 0.459570i | \(-0.151996\pi\) |
0.0460716 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.90710e11 | −2.22876 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.44597e11 | + | 1.41218e11i | 1.08536 | + | 0.626633i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.53270e11 | − | 2.65472e11i | −0.672273 | − | 1.16441i | −0.977258 | − | 0.212053i | \(-0.931985\pi\) |
0.304985 | − | 0.952357i | \(-0.401348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.82082e11 | + | 1.05125e11i | −0.780417 | + | 0.450574i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.81978e10 | + | 1.00802e11i | −0.246590 | + | 0.427107i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.37987e11i | 1.81380i | 0.421347 | + | 0.906900i | \(0.361557\pi\) | ||||
−0.421347 | + | 0.906900i | \(0.638443\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.67166e11 | + | 2.89540e11i | −0.684427 | + | 1.18546i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.79140e9 | − | 6.59448e9i | 0.00716991 | − | 0.0263938i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.20872e11 | + | 3.82561e11i | 0.874089 | + | 1.51397i | 0.857731 | + | 0.514100i | \(0.171874\pi\) |
0.0163580 | + | 0.999866i | \(0.494793\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.37459e10i | 0.130576i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.65060e11 | −3.30995 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.51748e11 | + | 8.76116e10i | −0.567815 | + | 0.327828i | −0.756276 | − | 0.654253i | \(-0.772983\pi\) |
0.188461 | + | 0.982081i | \(0.439650\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39792e11 | − | 2.38143e11i | 0.887348 | − | 0.881245i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.29228e10 | − | 2.47815e10i | −0.155359 | − | 0.0896964i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.98686e10 | −0.142723 | −0.0713614 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713614 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.54705e11 | + | 8.93192e10i | 0.541796 | + | 0.312806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.30870e11 | + | 2.26673e11i | 0.453339 | + | 0.785206i | 0.998591 | − | 0.0530658i | \(-0.0168993\pi\) |
−0.545252 | + | 0.838272i | \(0.683566\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.65017e10 | + | 2.68478e10i | −0.157615 | + | 0.0909993i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.42907e11 | − | 2.47523e11i | 0.479155 | − | 0.829921i | −0.520559 | − | 0.853826i | \(-0.674276\pi\) |
0.999714 | + | 0.0239043i | \(0.00760970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.26170e11i | 1.07026i | 0.844770 | + | 0.535130i | \(0.179737\pi\) | ||||
−0.844770 | + | 0.535130i | \(0.820263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.82204e11 | + | 6.61998e11i | −1.24071 | + | 2.14897i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.12287e11 | + | 2.13757e11i | 0.674523 | + | 0.679194i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.19607e11 | + | 2.07165e11i | 0.376007 | + | 0.651263i | 0.990477 | − | 0.137677i | \(-0.0439636\pi\) |
−0.614470 | + | 0.788940i | \(0.710630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.65348e11i | − | 1.12440i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.21959e11 | 1.58947 | 0.794736 | − | 0.606955i | \(-0.207609\pi\) | ||||
0.794736 | + | 0.606955i | \(0.207609\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.55548e11 | + | 1.47541e11i | −0.761963 | + | 0.439920i | −0.830000 | − | 0.557763i | \(-0.811660\pi\) |
0.0680370 | + | 0.997683i | \(0.478326\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.81306e11 | + | 1.03582e11i | 1.12506 | + | 0.305624i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.08199e11 | + | 1.20204e11i | 0.601585 | + | 0.347325i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.58950e11 | −0.740475 | −0.370237 | − | 0.928937i | \(-0.620724\pi\) | ||||
−0.370237 | + | 0.928937i | \(0.620724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.21275e11 | + | 3.00958e11i | 1.45999 | + | 0.842924i | 0.999010 | − | 0.0444875i | \(-0.0141655\pi\) |
0.460978 | + | 0.887412i | \(0.347499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.42016e11 | − | 2.45979e11i | −0.393669 | − | 0.681854i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.80340e11 | + | 2.19590e11i | −1.03281 | + | 0.596296i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.10352e10 | − | 1.57678e11i | 0.244684 | − | 0.423805i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.17299e9i | − | 0.00572240i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.00655e10 | − | 1.74339e10i | 0.0262382 | − | 0.0454460i | −0.852608 | − | 0.522551i | \(-0.824980\pi\) |
0.878846 | + | 0.477105i | \(0.158314\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.62063e9 | − | 6.92512e8i | 0.00669421 | − | 0.00176897i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.13845e11 | − | 3.70390e11i | −0.540762 | − | 0.936628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.96631e11i | − | 1.47868i | −0.673335 | − | 0.739338i | \(-0.735139\pi\) | ||
0.673335 | − | 0.739338i | \(-0.264861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.58782e11 | −1.37106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.00182e10 | − | 4.61985e10i | 0.192454 | − | 0.111113i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.13761e10 | − | 1.93894e10i | −0.169969 | − | 0.0461722i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.39044e11 | + | 3.11217e11i | 1.25843 | + | 0.726557i | 0.972770 | − | 0.231773i | \(-0.0744527\pi\) |
0.285664 | + | 0.958330i | \(0.407786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.09734e11 | −0.947151 | −0.473575 | − | 0.880753i | \(-0.657037\pi\) | ||||
−0.473575 | + | 0.880753i | \(0.657037\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.96922e11 | + | 1.71428e11i | 0.672994 | + | 0.388553i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.37015e11 | + | 5.83728e11i | 0.756417 | + | 1.31015i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.95045e10 | + | 3.43549e10i | −0.130972 | + | 0.0756165i | −0.564054 | − | 0.825738i | \(-0.690759\pi\) |
0.433083 | + | 0.901354i | \(0.357426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.63746e11 | − | 6.30026e11i | 0.792864 | − | 1.37328i | −0.131323 | − | 0.991340i | \(-0.541922\pi\) |
0.924187 | − | 0.381941i | \(-0.124744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.93292e11i | 0.627016i | 0.949586 | + | 0.313508i | \(0.101504\pi\) | ||||
−0.949586 | + | 0.313508i | \(0.898496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.61801e11 | + | 6.26659e11i | −0.766041 | + | 1.32682i | 0.173653 | + | 0.984807i | \(0.444443\pi\) |
−0.939694 | + | 0.342016i | \(0.888890\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.81108e11 | + | 2.63005e9i | 0.791531 | + | 0.00546240i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.56700e11 | − | 7.91028e11i | −0.939476 | − | 1.62722i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.46491e11i | − | 1.91015i | −0.296356 | − | 0.955077i | \(-0.595772\pi\) | ||
0.296356 | − | 0.955077i | \(-0.404228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.74652e11 | 0.948837 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.14704e12 | − | 6.62245e11i | 2.24985 | − | 1.29895i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.93730e11 | + | 3.91022e11i | −0.765005 | + | 0.759744i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.27238e10 | + | 2.46666e10i | 0.0814613 | + | 0.0470317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74752e11 | 0.330086 | 0.165043 | − | 0.986286i | \(-0.447224\pi\) | ||||
0.165043 | + | 0.986286i | \(0.447224\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.00768e11 | + | 2.89118e11i | 0.928353 | + | 0.535985i | 0.886290 | − | 0.463130i | \(-0.153274\pi\) |
0.0420626 | + | 0.999115i | \(0.486607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.02744e10 | − | 1.77957e10i | −0.0188704 | − | 0.0326846i | 0.856436 | − | 0.516253i | \(-0.172674\pi\) |
−0.875306 | + | 0.483569i | \(0.839340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.06769e11 | + | 2.92583e11i | −0.913623 | + | 0.527481i | −0.881595 | − | 0.472006i | \(-0.843530\pi\) |
−0.0320281 | + | 0.999487i | \(0.510197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.23714e11 | + | 2.14280e11i | −0.220981 | + | 0.382751i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.04539e11i | 1.23545i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.22946e10 | − | 1.07897e11i | 0.108237 | − | 0.187473i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.57016e11 | + | 4.14922e10i | −0.267862 | + | 0.0707838i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.83203e10 | − | 1.01014e11i | −0.0985874 | − | 0.170758i | 0.812513 | − | 0.582943i | \(-0.198099\pi\) |
−0.911100 | + | 0.412185i | \(0.864766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.98286e11i | − | 0.661138i | −0.943782 | − | 0.330569i | \(-0.892759\pi\) | ||
0.943782 | − | 0.330569i | \(-0.107241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.18954e11 | −0.853663 | −0.426831 | − | 0.904331i | \(-0.640370\pi\) | ||||
−0.426831 | + | 0.904331i | \(0.640370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.34306e11 | + | 2.50747e11i | −0.701620 | + | 0.405080i | −0.807950 | − | 0.589251i | \(-0.799423\pi\) |
0.106331 | + | 0.994331i | \(0.466090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.34649e8 | − | 5.09541e8i | −0.000215573 | − | 0.000815779i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.82590e12 | − | 1.05419e12i | −2.87126 | − | 1.65772i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.42800e12 | 2.22555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.27023e11 | − | 7.33368e10i | −0.194466 | − | 0.112275i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.90639e11 | + | 3.30196e11i | 0.289276 | + | 0.501040i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.79106e11 | + | 2.76612e11i | −0.714229 | + | 0.412361i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.02133e11 | − | 6.96515e11i | 0.594211 | − | 1.02920i | −0.399447 | − | 0.916756i | \(-0.630798\pi\) |
0.993658 | − | 0.112447i | \(-0.0358688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.63450e11i | − | 0.527681i | −0.964566 | − | 0.263841i | \(-0.915011\pi\) | ||
0.964566 | − | 0.263841i | \(-0.0849893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.14097e11 | − | 7.17237e11i | 0.595962 | − | 1.03224i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.55192e11 | − | 3.57652e11i | −0.502326 | − | 0.505805i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.39421e11 | − | 4.14689e11i | −0.335660 | − | 0.581380i | 0.647952 | − | 0.761682i | \(-0.275626\pi\) |
−0.983611 | + | 0.180302i | \(0.942293\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.22456e11i | 0.582070i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.15227e11 | −0.567178 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.20034e12 | + | 6.93019e11i | −1.61155 | + | 0.930427i | −0.622535 | + | 0.782592i | \(0.713897\pi\) |
−0.989012 | + | 0.147835i | \(0.952770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.24037e12 | + | 7.27584e11i | 1.65101 | + | 0.968466i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.01134e12 | − | 5.83898e11i | −1.32328 | − | 0.763995i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.23299e11 | 0.159957 | 0.0799784 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799784 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.85157e11 | + | 3.37841e11i | 0.746301 | + | 0.430877i | 0.824356 | − | 0.566072i | \(-0.191538\pi\) |
−0.0780549 | + | 0.996949i | \(0.524871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.24020e10 | + | 5.61219e10i | 0.0409756 | + | 0.0709718i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.68682e11 | + | 5.59269e11i | −1.20443 | + | 0.695377i | −0.961537 | − | 0.274676i | \(-0.911429\pi\) |
−0.242892 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07194e11 | + | 1.85665e11i | −0.132162 | + | 0.228911i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.21309e12i | 1.47069i | 0.677694 | + | 0.735344i | \(0.262979\pi\) | ||||
−0.677694 | + | 0.735344i | \(0.737021\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.80023e11 | + | 1.17783e12i | −0.817542 | + | 1.41602i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.69051e11 | − | 1.35855e12i | 0.436327 | − | 1.60620i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.17129e9 | + | 1.06890e10i | 0.00723573 | + | 0.0125326i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.02409e12i | − | 1.18094i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.18069e11 | −0.478125 | −0.239063 | − | 0.971004i | \(-0.576840\pi\) | ||||
−0.239063 | + | 0.971004i | \(0.576840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.68325e11 | − | 2.70388e11i | 0.526830 | − | 0.304165i | −0.212895 | − | 0.977075i | \(-0.568289\pi\) |
0.739725 | + | 0.672910i | \(0.234956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.54103e11 | − | 5.83161e11i | −0.171933 | − | 0.650634i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.40623e11 | + | 1.38924e11i | 0.264095 | + | 0.152475i | 0.626201 | − | 0.779662i | \(-0.284609\pi\) |
−0.362106 | + | 0.932137i | \(0.617942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.21476e12 | 2.41100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.07349e11 | + | 4.08388e11i | 0.757565 | + | 0.437380i | 0.828421 | − | 0.560106i | \(-0.189240\pi\) |
−0.0708561 | + | 0.997487i | \(0.522573\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.18635e12 | − | 2.05482e12i | −1.26028 | − | 2.18287i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.61332e10 | − | 4.97290e10i | 0.0900296 | − | 0.0519786i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.77809e11 | + | 6.54384e11i | −0.391721 | + | 0.678481i | −0.992677 | − | 0.120801i | \(-0.961454\pi\) |
0.600955 | + | 0.799283i | \(0.294787\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.29398e12i | − | 2.34044i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.76497e11 | + | 4.78908e11i | −0.279840 | + | 0.484698i | −0.971345 | − | 0.237674i | \(-0.923615\pi\) |
0.691504 | + | 0.722372i | \(0.256948\pi\) | |||||||
\(998\) | 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 | 252.9.bk.a.53.20 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.53.3 | ✓ | 44 | |
7.2 | even | 3 | inner | 252.9.bk.a.233.3 | yes | 44 | |
21.2 | odd | 6 | inner | 252.9.bk.a.233.20 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.3 | ✓ | 44 | 3.2 | odd | 2 | inner | |
252.9.bk.a.53.20 | yes | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.233.3 | yes | 44 | 7.2 | even | 3 | inner | |
252.9.bk.a.233.20 | yes | 44 | 21.2 | odd | 6 | inner |