Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,12,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
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: | yes |
Analytic conductor: | \(36.8804726669\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5370.00 | −0.768492 | −0.384246 | − | 0.923231i | \(-0.625539\pi\) | ||||
−0.384246 | + | 0.923231i | \(0.625539\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27760.0 | 0.624281 | 0.312141 | − | 0.950036i | \(-0.398954\pi\) | ||||
0.312141 | + | 0.950036i | \(0.398954\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −637836. | −1.19412 | −0.597062 | − | 0.802195i | \(-0.703665\pi\) | ||||
−0.597062 | + | 0.802195i | \(0.703665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 766214. | 0.572350 | 0.286175 | − | 0.958177i | \(-0.407616\pi\) | ||||
0.286175 | + | 0.958177i | \(0.407616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30491e6 | −0.443689 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.08435e6 | 0.526860 | 0.263430 | − | 0.964679i | \(-0.415146\pi\) | ||||
0.263430 | + | 0.964679i | \(0.415146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.95114e7 | 1.80777 | 0.903886 | − | 0.427773i | \(-0.140702\pi\) | ||||
0.903886 | + | 0.427773i | \(0.140702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.74568e6 | 0.360429 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.53124e7 | −0.496066 | −0.248033 | − | 0.968752i | \(-0.579784\pi\) | ||||
−0.248033 | + | 0.968752i | \(0.579784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.99912e7 | −0.409420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.07513e7 | 0.0973353 | 0.0486677 | − | 0.998815i | \(-0.484502\pi\) | ||||
0.0486677 | + | 0.998815i | \(0.484502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09374e7 | 0.319556 | 0.159778 | − | 0.987153i | \(-0.448922\pi\) | ||||
0.159778 | + | 0.987153i | \(0.448922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.54994e8 | −0.689428 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.49071e8 | −0.479755 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.64741e8 | 1.57595 | 0.787976 | − | 0.615706i | \(-0.211129\pi\) | ||||
0.787976 | + | 0.615706i | \(0.211129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.86190e8 | 0.330446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.98833e8 | 1.21162 | 0.605812 | − | 0.795608i | \(-0.292848\pi\) | ||||
0.605812 | + | 0.795608i | \(0.292848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.57947e8 | 0.993722 | 0.496861 | − | 0.867830i | \(-0.334486\pi\) | ||||
0.496861 | + | 0.867830i | \(0.334486\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.17093e8 | −0.256164 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.55574e9 | 0.989462 | 0.494731 | − | 0.869046i | \(-0.335267\pi\) | ||||
0.494731 | + | 0.869046i | \(0.335267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.20671e9 | −0.610273 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.49498e8 | 0.304183 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.79242e9 | 1.24566 | 0.622829 | − | 0.782358i | \(-0.285983\pi\) | ||||
0.622829 | + | 0.782358i | \(0.285983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.42518e9 | 0.917674 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.74127e9 | 1.04372 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.55307e8 | −0.101122 | −0.0505612 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505612 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.95042e9 | 0.750461 | 0.375230 | − | 0.926932i | \(-0.377564\pi\) | ||||
0.375230 | + | 0.926932i | \(0.377564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.63920e9 | 0.208094 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.11457e9 | −0.439846 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.29240e9 | −0.478896 | −0.239448 | − | 0.970909i | \(-0.576966\pi\) | ||||
−0.239448 | + | 0.970909i | \(0.576966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.72090e9 | −0.286404 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.48311e10 | 0.975556 | 0.487778 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487778 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.39710e10 | 0.788773 | 0.394386 | − | 0.918945i | \(-0.370957\pi\) | ||||
0.394386 | + | 0.918945i | \(0.370957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.85787e9 | −0.236379 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.77063e10 | −0.745469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.72054e9 | −0.136037 | −0.0680185 | − | 0.997684i | \(-0.521668\pi\) | ||||
−0.0680185 | + | 0.997684i | \(0.521668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.76845e9 | −0.244339 | −0.122170 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122170 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.65630e10 | −0.404888 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.61256e9 | 0.0561966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.54728e10 | −0.483539 | −0.241769 | − | 0.970334i | \(-0.577728\pi\) | ||||
−0.241769 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.12701e10 | 0.357307 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.23778e10 | 0.184496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.04776e11 | −1.38926 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.90925e10 | −0.462220 | −0.231110 | − | 0.972928i | \(-0.574236\pi\) | ||||
−0.231110 | + | 0.972928i | \(0.574236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.76636e10 | −0.398041 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.31078e9 | 0.0881492 | 0.0440746 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440746 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.85751e10 | −0.412865 | −0.206433 | − | 0.978461i | \(-0.566185\pi\) | ||||
−0.206433 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.62243e10 | −0.276987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.25596e11 | −1.55496 | −0.777482 | − | 0.628906i | \(-0.783503\pi\) | ||||
−0.777482 | + | 0.628906i | \(0.783503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.94512e10 | −0.432348 | −0.216174 | − | 0.976355i | \(-0.569358\pi\) | ||||
−0.216174 | + | 0.976355i | \(0.569358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.61532e11 | 0.909876 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.59665e11 | −1.83640 | −0.918198 | − | 0.396122i | \(-0.870356\pi\) | ||||
−0.918198 | + | 0.396122i | \(0.870356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.22274e10 | 0.381222 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.52442e10 | 0.190783 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.56217e10 | 0.328909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.21523e11 | 0.425931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.18417e11 | 0.699532 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.69560e11 | 1.08313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.50273e11 | −0.672192 | −0.336096 | − | 0.941828i | \(-0.609107\pi\) | ||||
−0.336096 | + | 0.941828i | \(0.609107\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.32781e11 | 0.573726 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.78918e10 | 0.221694 | 0.110847 | − | 0.993837i | \(-0.464644\pi\) | ||||
0.110847 | + | 0.993837i | \(0.464644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.41637e11 | 1.12856 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.70536e10 | −0.147896 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.55015e11 | −0.274416 | −0.137208 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137208 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.12627e12 | 1.84102 | 0.920512 | − | 0.390715i | \(-0.127772\pi\) | ||||
0.920512 | + | 0.390715i | \(0.127772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.78045e11 | 0.571266 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.88719e11 | −0.683457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.77343e10 | −0.0748014 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.93230e11 | −0.352341 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.38458e12 | −1.54452 | −0.772261 | − | 0.635306i | \(-0.780874\pi\) | ||||
−0.772261 | + | 0.635306i | \(0.780874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.98601e11 | 0.724196 | 0.362098 | − | 0.932140i | \(-0.382061\pi\) | ||||
0.362098 | + | 0.932140i | \(0.382061\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.82128e11 | 0.175620 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.73534e11 | −0.245576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13127e12 | 1.78316 | 0.891580 | − | 0.452863i | \(-0.149597\pi\) | ||||
0.891580 | + | 0.452863i | \(0.149597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.21557e11 | 0.719181 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.25071e11 | −0.309684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.63564e11 | 0.111342 | 0.0556708 | − | 0.998449i | \(-0.482270\pi\) | ||||
0.0556708 | + | 0.998449i | \(0.482270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.32319e11 | 0.529819 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.80943e9 | 0.00524816 | 0.00262408 | − | 0.999997i | \(-0.499165\pi\) | ||||
0.00262408 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20508e12 | −0.672416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.15213e12 | 0.602591 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.30852e11 | −0.358571 | −0.179286 | − | 0.983797i | \(-0.557379\pi\) | ||||
−0.179286 | + | 0.983797i | \(0.557379\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.54956e11 | −0.255593 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.34940e11 | −0.0583830 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.92371e12 | −1.59590 | −0.797950 | − | 0.602724i | \(-0.794082\pi\) | ||||
−0.797950 | + | 0.602724i | \(0.794082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.27931e12 | 0.872110 | 0.436055 | − | 0.899920i | \(-0.356375\pi\) | ||||
0.436055 | + | 0.899920i | \(0.356375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.20295e12 | 0.433279 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.56966e12 | −1.21111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.96731e12 | −0.629136 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.98326e11 | 0.120143 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.38709e12 | −0.964147 | −0.482073 | − | 0.876131i | \(-0.660116\pi\) | ||||
−0.482073 | + | 0.876131i | \(0.660116\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.92921e12 | −1.32499 | −0.662494 | − | 0.749067i | \(-0.730502\pi\) | ||||
−0.662494 | + | 0.749067i | \(0.730502\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.99840e11 | −0.253945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.35785e12 | 1.52667 | 0.763337 | − | 0.646001i | \(-0.223560\pi\) | ||||
0.763337 | + | 0.646001i | \(0.223560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.78554e12 | 0.859875 | 0.429938 | − | 0.902859i | \(-0.358536\pi\) | ||||
0.429938 | + | 0.902859i | \(0.358536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28605e12 | −0.276491 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.98455e11 | 0.0607646 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.82674e12 | −0.931123 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.04180e11 | −0.165355 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.24451e13 | −2.15870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.79494e11 | −0.0295458 | −0.0147729 | − | 0.999891i | \(-0.504703\pi\) | ||||
−0.0147729 | + | 0.999891i | \(0.504703\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.60395e12 | 0.563237 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.14418e12 | −0.763668 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41402e12 | 0.199493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.39495e12 | 0.455398 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.36328e12 | 0.301548 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.22568e12 | −0.270263 | −0.135132 | − | 0.990828i | \(-0.543146\pi\) | ||||
−0.135132 | + | 0.990828i | \(0.543146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.18046e12 | −0.136473 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.15848e11 | 0.0457923 | 0.0228961 | − | 0.999738i | \(-0.492711\pi\) | ||||
0.0228961 | + | 0.999738i | \(0.492711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.81248e13 | 1.90186 | 0.950928 | − | 0.309414i | \(-0.100133\pi\) | ||||
0.950928 | + | 0.309414i | \(0.100133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.30264e12 | −0.430397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.87641e10 | −0.00179007 | −0.000895033 | − | 1.00000i | \(-0.500285\pi\) | ||||
−0.000895033 | 1.00000i | \(0.500285\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.35433e12 | −0.760394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.04092e11 | −0.0785410 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.76252e13 | 1.46200 | 0.730999 | − | 0.682379i | \(-0.239054\pi\) | ||||
0.730999 | + | 0.682379i | \(0.239054\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.90117e11 | −0.0705267 | −0.0352633 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352633 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.48003e12 | 0.468990 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.49499e13 | 1.03468 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.13073e12 | −0.141069 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.42280e13 | 1.53502 | 0.767508 | − | 0.641040i | \(-0.221497\pi\) | ||||
0.767508 | + | 0.641040i | \(0.221497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.76677e12 | 0.592364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.02480e12 | −0.233762 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.80492e12 | 0.434246 | 0.217123 | − | 0.976144i | \(-0.430333\pi\) | ||||
0.217123 | + | 0.976144i | \(0.430333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.84532e13 | 0.983837 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.34851e11 | 0.0324451 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.65956e13 | −0.813272 | −0.406636 | − | 0.913590i | \(-0.633298\pi\) | ||||
−0.406636 | + | 0.913590i | \(0.633298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.03653e13 | −0.957278 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.18988e12 | −0.279171 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.85236e13 | 1.23471 | 0.617357 | − | 0.786683i | \(-0.288203\pi\) | ||||
0.617357 | + | 0.786683i | \(0.288203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.33800e13 | −0.971658 | −0.485829 | − | 0.874054i | \(-0.661482\pi\) | ||||
−0.485829 | + | 0.874054i | \(0.661482\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.16863e12 | 0.206291 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.27511e13 | 0.488898 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.03641e13 | −1.11872 | −0.559361 | − | 0.828924i | \(-0.688953\pi\) | ||||
−0.559361 | + | 0.828924i | \(0.688953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00780e12 | 0.106519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.59749e13 | 0.543942 | 0.271971 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271971 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.87045e13 | −0.939993 | −0.469997 | − | 0.882668i | \(-0.655745\pi\) | ||||
−0.469997 | + | 0.882668i | \(0.655745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.54606e13 | −0.802089 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.49516e13 | 0.756394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47587e13 | −0.722419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.49948e12 | −0.266863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.81754e13 | 1.30333 | 0.651663 | − | 0.758508i | \(-0.274071\pi\) | ||||
0.651663 | + | 0.758508i | \(0.274071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.98200e12 | 0.0777117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.15225e12 | −0.229809 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.17325e13 | −0.283923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65926e13 | 0.620362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.26252e12 | 0.0508930 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.65838e13 | −0.576723 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.57350e13 | −0.538597 | −0.269298 | − | 0.963057i | \(-0.586792\pi\) | ||||
−0.269298 | + | 0.963057i | \(0.586792\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.18037e13 | −0.238368 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.46043e13 | −0.674446 | −0.337223 | − | 0.941425i | \(-0.609488\pi\) | ||||
−0.337223 | + | 0.941425i | \(0.609488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.26066e13 | 0.237194 | 0.118597 | − | 0.992942i | \(-0.462160\pi\) | ||||
0.118597 | + | 0.992942i | \(0.462160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.80251e12 | −0.159918 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.18243e13 | −1.43568 | −0.717838 | − | 0.696210i | \(-0.754868\pi\) | ||||
−0.717838 | + | 0.696210i | \(0.754868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.85754e12 | −0.116230 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.48198e13 | −0.897758 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.01801e13 | 0.952443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53176e13 | −0.234332 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.68766e13 | −0.249616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.31874e13 | 0.617703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.40115e13 | 0.470513 | 0.235256 | − | 0.971933i | \(-0.424407\pi\) | ||||
0.235256 | + | 0.971933i | \(0.424407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.92523e13 | 0.525317 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.84202e13 | 0.368028 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.99439e13 | −0.751244 | −0.375622 | − | 0.926773i | \(-0.622571\pi\) | ||||
−0.375622 | + | 0.926773i | \(0.622571\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.73985e13 | −1.06024 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.24897e13 | −0.381590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.83888e13 | −1.00526 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.99813e13 | 0.220099 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.78685e13 | −1.04431 | −0.522157 | − | 0.852850i | \(-0.674872\pi\) | ||||
−0.522157 | + | 0.852850i | \(0.674872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.42790e14 | −1.47624 | −0.738120 | − | 0.674670i | \(-0.764286\pi\) | ||||
−0.738120 | + | 0.674670i | \(0.764286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.09943e13 | 0.110149 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.44246e14 | 1.40069 | 0.700346 | − | 0.713804i | \(-0.253029\pi\) | ||||
0.700346 | + | 0.713804i | \(0.253029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.96429e13 | −0.749707 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.08061e13 | 0.189896 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.24349e14 | 1.10059 | 0.550293 | − | 0.834972i | \(-0.314516\pi\) | ||||
0.550293 | + | 0.834972i | \(0.314516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.64205e14 | 2.26804 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.95301e13 | 0.245911 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.50243e13 | −0.606165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.60110e14 | 1.25532 | 0.627659 | − | 0.778488i | \(-0.284013\pi\) | ||||
0.627659 | + | 0.778488i | \(0.284013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.30752e13 | 0.403875 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.05277e14 | 0.777641 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.47258e13 | −0.249031 | −0.124516 | − | 0.992218i | \(-0.539738\pi\) | ||||
−0.124516 | + | 0.992218i | \(0.539738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.98031e13 | 0.625344 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.23777e12 | 0.0557099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.46500e14 | 0.962327 | 0.481163 | − | 0.876631i | \(-0.340214\pi\) | ||||
0.481163 | + | 0.876631i | \(0.340214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.08164e13 | −0.388090 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.43419e13 | −0.398933 | −0.199467 | − | 0.979905i | \(-0.563921\pi\) | ||||
−0.199467 | + | 0.979905i | \(0.563921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.50830e13 | 0.572887 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.65658e13 | 0.331241 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.98900e13 | −0.227061 | −0.113530 | − | 0.993535i | \(-0.536216\pi\) | ||||
−0.113530 | + | 0.993535i | \(0.536216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.72287e13 | −0.261357 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.37877e13 | 0.127995 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.99793e13 | 0.104543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.06552e14 | 0.542268 | 0.271134 | − | 0.962542i | \(-0.412601\pi\) | ||||
0.271134 | + | 0.962542i | \(0.412601\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.31618e14 | 0.651573 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.41445e13 | 0.164447 | 0.0822236 | − | 0.996614i | \(-0.473798\pi\) | ||||
0.0822236 | + | 0.996614i | \(0.473798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.90289e13 | 0.182898 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.87240e13 | −0.0853880 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.23996e14 | −1.88188 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.33349e13 | 0.230427 | 0.115213 | − | 0.993341i | \(-0.463245\pi\) | ||||
0.115213 | + | 0.993341i | \(0.463245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.76686e13 | −0.158434 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.54153e13 | −0.0631288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.70866e13 | 0.187773 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.73682e14 | 1.06292 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.01288e14 | 0.383159 | 0.191580 | − | 0.981477i | \(-0.438639\pi\) | ||||
0.191580 | + | 0.981477i | \(0.438639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.57928e14 | −0.581981 | −0.290991 | − | 0.956726i | \(-0.593985\pi\) | ||||
−0.290991 | + | 0.956726i | \(0.593985\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.18650e13 | 0.329821 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.16600e13 | −0.215707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37424e14 | 0.468499 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.18759e14 | −0.394594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.13171e14 | −1.66202 | −0.831012 | − | 0.556254i | \(-0.812238\pi\) | ||||
−0.831012 | + | 0.556254i | \(0.812238\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.49248e13 | −0.236560 | −0.118280 | − | 0.992980i | \(-0.537738\pi\) | ||||
−0.118280 | + | 0.992980i | \(0.537738\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.40294e13 | −0.0431866 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.98766e14 | −0.896773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.68335e14 | 1.07817 | 0.539086 | − | 0.842250i | \(-0.318770\pi\) | ||||
0.539086 | + | 0.842250i | \(0.318770\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.12550e13 | −0.203424 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.11248e14 | 0.309793 | 0.154896 | − | 0.987931i | \(-0.450496\pi\) | ||||
0.154896 | + | 0.987931i | \(0.450496\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.36789e14 | 0.371595 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.36453e14 | −0.891730 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.83314e13 | −0.228434 | −0.114217 | − | 0.993456i | \(-0.536436\pi\) | ||||
−0.114217 | + | 0.993456i | \(0.536436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.73308e14 | −1.44683 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.69760e14 | 0.418115 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.14220e14 | −0.274588 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.42094e12 | −0.0221083 | −0.0110541 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110541 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.42571e13 | 0.101394 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.97134e14 | −1.55941 | −0.779706 | − | 0.626146i | \(-0.784631\pi\) | ||||
−0.779706 | + | 0.626146i | \(0.784631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.87941e14 | 0.410513 | 0.205256 | − | 0.978708i | \(-0.434197\pi\) | ||||
0.205256 | + | 0.978708i | \(0.434197\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.64687e13 | −0.141784 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.20007e14 | −0.666678 | −0.333339 | − | 0.942807i | \(-0.608175\pi\) | ||||
−0.333339 | + | 0.942807i | \(0.608175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.46917e14 | −0.298966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.17899e14 | 1.02951 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.11013e14 | −1.18663 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.90057e14 | −0.740139 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.23938e14 | 0.415219 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.50382e14 | 0.272491 | 0.136245 | − | 0.990675i | \(-0.456496\pi\) | ||||
0.136245 | + | 0.990675i | \(0.456496\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.09334e14 | 0.901996 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.03292e14 | −0.178796 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.09927e14 | 0.355212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.76546e14 | −0.292045 | −0.146022 | − | 0.989281i | \(-0.546647\pi\) | ||||
−0.146022 | + | 0.989281i | \(0.546647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.97462e13 | 0.0642831 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.60958e14 | 1.36155 | 0.680775 | − | 0.732492i | \(-0.261643\pi\) | ||||
0.680775 | + | 0.732492i | \(0.261643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.31607e13 | 0.0512821 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.02253e14 | 0.305891 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.11711e14 | 0.609021 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.01209e14 | −0.869907 | −0.434953 | − | 0.900453i | \(-0.643235\pi\) | ||||
−0.434953 | + | 0.900453i | \(0.643235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.14069e12 | 0.00303003 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09203e15 | −1.51221 | −0.756103 | − | 0.654453i | \(-0.772899\pi\) | ||||
−0.756103 | + | 0.654453i | \(0.772899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.99989e13 | −0.0677420 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.92834e14 | −0.388219 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.76371e14 | 1.13695 | 0.568474 | − | 0.822702i | \(-0.307534\pi\) | ||||
0.568474 | + | 0.822702i | \(0.307534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.87835e14 | 0.492416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.79967e14 | 0.347906 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.60848e14 | 0.317284 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.92308e14 | −1.18154 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.77597e14 | −0.207021 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.71989e14 | −0.424544 | −0.212272 | − | 0.977211i | \(-0.568086\pi\) | ||||
−0.212272 | + | 0.977211i | \(0.568086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.73507e14 | 1.08788 | 0.543939 | − | 0.839125i | \(-0.316932\pi\) | ||||
0.543939 | + | 0.839125i | \(0.316932\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.34854e14 | −0.147567 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.57109e14 | 0.168361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.18341e14 | −0.753919 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.27903e13 | −0.0337074 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.88699e14 | 0.693473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21145e15 | 1.19498 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.53463e14 | −0.921393 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.69683e14 | 0.728741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.74606e15 | 1.61985 | 0.809925 | − | 0.586533i | \(-0.199508\pi\) | ||||
0.809925 | + | 0.586533i | \(0.199508\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.53872e14 | 0.503513 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.72953e14 | 0.332256 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.74624e14 | −0.152467 | −0.0762333 | − | 0.997090i | \(-0.524289\pi\) | ||||
−0.0762333 | + | 0.997090i | \(0.524289\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.92317e14 | 0.250154 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09772e14 | 0.175960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.03282e14 | −0.0849254 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.67427e14 | −0.699232 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.58365e15 | 1.25157 | 0.625785 | − | 0.779995i | \(-0.284779\pi\) | ||||
0.625785 | + | 0.779995i | \(0.284779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.33993e14 | 0.568757 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.78057e14 | −0.363232 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.75798e14 | 0.727049 | 0.363525 | − | 0.931585i | \(-0.381573\pi\) | ||||
0.363525 | + | 0.931585i | \(0.381573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.93140e15 | 1.41125 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.67931e13 | 0.0693646 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.92427e15 | 1.35254 | 0.676269 | − | 0.736655i | \(-0.263596\pi\) | ||||
0.676269 | + | 0.736655i | \(0.263596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.61132e15 | −1.11092 | −0.555461 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.23063e14 | −0.556650 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.06113e14 | 0.203099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.53250e15 | −1.64848 | −0.824239 | − | 0.566242i | \(-0.808397\pi\) | ||||
−0.824239 | + | 0.566242i | \(0.808397\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.19780e15 | −0.764982 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.43412e14 | −0.152536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41894e15 | −1.48747 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.42961e14 | −0.146615 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.11508e15 | 1.84484 | 0.922421 | − | 0.386186i | \(-0.126208\pi\) | ||||
0.922421 | + | 0.386186i | \(0.126208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.93860e14 | 0.577685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.54496e15 | 0.881425 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.20723e15 | −1.23608 | −0.618040 | − | 0.786146i | \(-0.712073\pi\) | ||||
−0.618040 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.59788e14 | −0.252764 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.19885e14 | 0.496449 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.41159e15 | −1.80763 | −0.903813 | − | 0.427927i | \(-0.859244\pi\) | ||||
−0.903813 | + | 0.427927i | \(0.859244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.57545e15 | −0.819588 | −0.409794 | − | 0.912178i | \(-0.634399\pi\) | ||||
−0.409794 | + | 0.912178i | \(0.634399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.12511e14 | −0.159632 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.52579e14 | −0.327325 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.05592e14 | 0.249036 | 0.124518 | − | 0.992217i | \(-0.460262\pi\) | ||||
0.124518 | + | 0.992217i | \(0.460262\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.25246e13 | 0.0350825 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.19203e15 | 0.566319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.98375e15 | −0.925665 | −0.462832 | − | 0.886446i | \(-0.653167\pi\) | ||||
−0.462832 | + | 0.886446i | \(0.653167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.17290e15 | −0.537584 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.93099e15 | −0.869382 | −0.434691 | − | 0.900580i | \(-0.643142\pi\) | ||||
−0.434691 | + | 0.900580i | \(0.643142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.47689e14 | −0.419148 | −0.209574 | − | 0.977793i | \(-0.567208\pi\) | ||||
−0.209574 | + | 0.977793i | \(0.567208\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.19716e14 | −0.0954679 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.07124e14 | −0.301864 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00840e15 | −0.422955 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.02415e15 | −1.24633 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.05030e15 | 0.830306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00593e15 | −0.400318 | −0.200159 | − | 0.979763i | \(-0.564146\pi\) | ||||
−0.200159 | + | 0.979763i | \(0.564146\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.36170e13 | −0.0170583 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.34397e15 | 0.516574 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.24597e14 | −0.349290 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.75761e14 | 0.325185 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.13144e15 | 0.412966 | 0.206483 | − | 0.978450i | \(-0.433798\pi\) | ||||
0.206483 | + | 0.978450i | \(0.433798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.68306e14 | 0.311539 | 0.155769 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155769 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.25003e15 | −0.440904 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.37636e15 | 0.477265 | 0.238633 | − | 0.971110i | \(-0.423301\pi\) | ||||
0.238633 | + | 0.971110i | \(0.423301\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.54195e14 | 0.120753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.43607e14 | 0.115177 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.55276e15 | 0.841370 | 0.420685 | − | 0.907207i | \(-0.361790\pi\) | ||||
0.420685 | + | 0.907207i | \(0.361790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.25679e14 | −0.170370 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.24974e14 | 0.262924 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.26792e14 | −0.290478 | −0.145239 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145239 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.90332e15 | −0.586683 | −0.293342 | − | 0.956008i | \(-0.594767\pi\) | ||||
−0.293342 | + | 0.956008i | \(0.594767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.74276e14 | 0.174099 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.90859e15 | −0.867288 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64627e14 | −0.0482847 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.40841e14 | −0.156037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15756e15 | −0.896143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.92990e15 | 1.37643 | 0.688217 | − | 0.725505i | \(-0.258394\pi\) | ||||
0.688217 | + | 0.725505i | \(0.258394\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.86852e14 | −0.0787930 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.30293e14 | 0.116286 | 0.0581429 | − | 0.998308i | \(-0.481482\pi\) | ||||
0.0581429 | + | 0.998308i | \(0.481482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.08521e15 | −0.288555 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.01051e14 | 0.0264382 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.81244e15 | 0.981498 | 0.490749 | − | 0.871301i | \(-0.336723\pi\) | ||||
0.490749 | + | 0.871301i | \(0.336723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.32429e14 | 0.210887 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.40432e15 | 1.09804 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.90580e15 | 0.712952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.03729e15 | −0.974901 | −0.487450 | − | 0.873151i | \(-0.662073\pi\) | ||||
−0.487450 | + | 0.873151i | \(0.662073\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.04554e15 | −0.248490 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.04805e15 | −1.41481 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.77232e15 | 0.638356 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.55967e12 | −0.00103350 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.71267e15 | −1.05152 | −0.525761 | − | 0.850632i | \(-0.676219\pi\) | ||||
−0.525761 | + | 0.850632i | \(0.676219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.29700e16 | 2.84896 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.03010e15 | −0.439013 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.58467e14 | 0.0550299 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.66706e14 | 0.181684 | 0.0908422 | − | 0.995865i | \(-0.471044\pi\) | ||||
0.0908422 | + | 0.995865i | \(0.471044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.19694e14 | −0.0453457 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.79972e14 | −0.158521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.62442e15 | 0.525231 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.28293e15 | 0.844085 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.62666e13 | −0.00509795 | −0.00254897 | − | 0.999997i | \(-0.500811\pi\) | ||||
−0.00254897 | + | 0.999997i | \(0.500811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.34844e15 | −0.257744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.16298e14 | −0.0407186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.14931e14 | −0.0398511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.68018e15 | 1.03734 | 0.518672 | − | 0.854973i | \(-0.326427\pi\) | ||||
0.518672 | + | 0.854973i | \(0.326427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.95465e15 | 0.523552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.62312e15 | −0.283320 | −0.141660 | − | 0.989915i | \(-0.545244\pi\) | ||||
−0.141660 | + | 0.989915i | \(0.545244\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.57465e15 | 0.270771 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.37568e15 | 0.571861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.64794e15 | −0.608840 | −0.304420 | − | 0.952538i | \(-0.598463\pi\) | ||||
−0.304420 | + | 0.952538i | \(0.598463\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.63283e15 | 0.597372 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.76045e15 | −1.09531 | −0.547655 | − | 0.836704i | \(-0.684479\pi\) | ||||
−0.547655 | + | 0.836704i | \(0.684479\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.43520e15 | 1.18695 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.17768e14 | −0.0814465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.26254e15 | −0.970734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.64833e13 | −0.00404532 | −0.00202266 | − | 0.999998i | \(-0.500644\pi\) | ||||
−0.00202266 | + | 0.999998i | \(0.500644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.88741e15 | 0.886242 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.75149e15 | −0.556539 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.37364e15 | 1.07809 | 0.539045 | − | 0.842277i | \(-0.318785\pi\) | ||||
0.539045 | + | 0.842277i | \(0.318785\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.37333e15 | 0.342001 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.20983e15 | 0.881991 | 0.440996 | − | 0.897509i | \(-0.354625\pi\) | ||||
0.440996 | + | 0.897509i | \(0.354625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.92796e15 | −0.269907 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.78027e14 | −0.134963 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.25484e14 | −0.0578774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.86195e15 | −1.18832 | −0.594162 | − | 0.804346i | \(-0.702516\pi\) | ||||
−0.594162 | + | 0.804346i | \(0.702516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.89659e15 | 0.250712 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.95047e15 | −0.384507 | −0.192254 | − | 0.981345i | \(-0.561580\pi\) | ||||
−0.192254 | + | 0.981345i | \(0.561580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.01830e15 | −0.130833 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.48413e15 | 0.568019 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.75375e16 | 2.19034 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.45980e15 | −1.16493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.54269e14 | 0.0187322 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.14449e16 | −1.37034 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.35545e16 | −1.60038 | −0.800190 | − | 0.599746i | \(-0.795268\pi\) | ||||
−0.800190 | + | 0.599746i | \(0.795268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.03272e15 | −0.469543 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.98429e15 | −1.14643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79308e15 | 0.429526 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.94876e15 | −0.552685 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.59922e16 | −1.76152 | −0.880762 | − | 0.473558i | \(-0.842969\pi\) | ||||
−0.880762 | + | 0.473558i | \(0.842969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.79846e15 | 0.521308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50414e15 | −0.161180 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.91121e15 | −0.941892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.28263e15 | 0.237990 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.93123e15 | 0.712863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.45859e15 | 0.959643 | 0.479821 | − | 0.877366i | \(-0.340701\pi\) | ||||
0.479821 | + | 0.877366i | \(0.340701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.07996e16 | 1.08092 | 0.540461 | − | 0.841369i | \(-0.318250\pi\) | ||||
0.540461 | + | 0.841369i | \(0.318250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.68134e15 | −0.560987 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.78341e14 | −0.0855651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.86909e16 | 1.79642 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.25598e15 | 0.119102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.10411e16 | −1.03306 | −0.516529 | − | 0.856270i | \(-0.672776\pi\) | ||||
−0.516529 | + | 0.856270i | \(0.672776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.26104e16 | −1.16420 | −0.582101 | − | 0.813117i | \(-0.697769\pi\) | ||||
−0.582101 | + | 0.813117i | \(0.697769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.09852e15 | 0.282266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.86172e14 | 0.0706704 | 0.0353352 | − | 0.999376i | \(-0.488750\pi\) | ||||
0.0353352 | + | 0.999376i | \(0.488750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.92589e15 | −0.525659 | −0.262829 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262829 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.37848e15 | −0.645894 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.72192e15 | −0.321528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.73066e13 | −0.00403317 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.30896e14 | 0.0614986 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.10209e16 | −1.74566 | −0.872831 | − | 0.488022i | \(-0.837718\pi\) | ||||
−0.872831 | + | 0.488022i | \(0.837718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20849e16 | −0.990526 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.88189e15 | 0.314045 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.47126e15 | 0.516746 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.37348e15 | 0.265901 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.97520e15 | −0.542705 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.01788e16 | −0.781775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.98378e16 | −1.50409 | −0.752046 | − | 0.659110i | \(-0.770933\pi\) | ||||
−0.752046 | + | 0.659110i | \(0.770933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.18693e15 | −0.463086 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.96639e15 | 0.588663 | 0.294332 | − | 0.955703i | \(-0.404903\pi\) | ||||
0.294332 | + | 0.955703i | \(0.404903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59749e16 | 1.16540 | 0.582701 | − | 0.812687i | \(-0.301996\pi\) | ||||
0.582701 | + | 0.812687i | \(0.301996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.06324e15 | 0.436704 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.02926e15 | 0.286527 | 0.143264 | − | 0.989685i | \(-0.454240\pi\) | ||||
0.143264 | + | 0.989685i | \(0.454240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.92467e15 | 0.275559 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.01635e15 | −0.417089 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.37310e15 | 0.162445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.05511e15 | −0.274096 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.30837e15 | −0.154073 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.02590e16 | 0.676176 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.76958e15 | 0.635884 | 0.317942 | − | 0.948110i | \(-0.397008\pi\) | ||||
0.317942 | + | 0.948110i | \(0.397008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.17066e16 | 0.752476 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.62583e16 | 1.03207 | 0.516033 | − | 0.856569i | \(-0.327408\pi\) | ||||
0.516033 | + | 0.856569i | \(0.327408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66061e16 | −1.04108 | −0.520540 | − | 0.853837i | \(-0.674269\pi\) | ||||
−0.520540 | + | 0.853837i | \(0.674269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.24626e14 | 0.0448669 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.91314e16 | 1.16995 | 0.584975 | − | 0.811051i | \(-0.301104\pi\) | ||||
0.584975 | + | 0.811051i | \(0.301104\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.94758e15 | −0.419637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.22400e15 | −0.132680 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.03547e16 | 1.78872 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.10703e16 | 1.22644 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.85101e15 | −0.163923 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.47641e14 | 0.0311041 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16972e16 | 0.656287 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.46201e15 | 0.358166 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.22399e16 | −0.670209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07252e16 | 0.580182 | 0.290091 | − | 0.956999i | \(-0.406314\pi\) | ||||
0.290091 | + | 0.956999i | \(0.406314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.49792e14 | 0.0293831 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.82249e16 | 1.49032 | 0.745162 | − | 0.666883i | \(-0.232372\pi\) | ||||
0.745162 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.59284e15 | 0.291771 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.45985e15 | −0.332971 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.71748e15 | 0.138399 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.83551e16 | −0.923679 | −0.461839 | − | 0.886964i | \(-0.652810\pi\) | ||||
−0.461839 | + | 0.886964i | \(0.652810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.25361e15 | −0.310959 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.13638e16 | 0.558359 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.32890e16 | −0.645227 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.86831e15 | −0.137622 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.10125e16 | −0.522155 | −0.261078 | − | 0.965318i | \(-0.584078\pi\) | ||||
−0.261078 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.35446e16 | −1.10323 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.40884e15 | −0.389392 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.05645e16 | 0.483486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.36357e15 | 0.378289 | 0.189145 | − | 0.981949i | \(-0.439429\pi\) | ||||
0.189145 | + | 0.981949i | \(0.439429\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.06340e15 | 0.136944 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.22942e16 | 0.985028 | 0.492514 | − | 0.870305i | \(-0.336078\pi\) | ||||
0.492514 | + | 0.870305i | \(0.336078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37633e16 | −0.601045 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.13901e15 | −0.0923289 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.78038e16 | 1.61291 | 0.806457 | − | 0.591293i | \(-0.201382\pi\) | ||||
0.806457 | + | 0.591293i | \(0.201382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07048e16 | 0.451454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.98833e16 | −0.828888 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.79568e15 | 0.197624 | 0.0988119 | − | 0.995106i | \(-0.468496\pi\) | ||||
0.0988119 | + | 0.995106i | \(0.468496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.81887e16 | 0.740939 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.66638e15 | −0.0671057 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.30321e15 | −0.171313 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28139e16 | −0.897884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.33212e16 | −0.518321 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.64698e16 | 1.01824 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.37420e16 | −1.28329 | −0.641645 | − | 0.767002i | \(-0.721748\pi\) | ||||
−0.641645 | + | 0.767002i | \(0.721748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.46238e16 | 0.549893 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.58587e16 | −1.33318 | −0.666590 | − | 0.745425i | \(-0.732247\pi\) | ||||
−0.666590 | + | 0.745425i | \(0.732247\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12651e16 | 1.14932 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.72217e15 | −0.135291 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.20023e16 | −0.431366 | −0.215683 | − | 0.976463i | \(-0.569198\pi\) | ||||
−0.215683 | + | 0.976463i | \(0.569198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.62474e16 | 0.577405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.10102e15 | −0.144116 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.42687e15 | 0.153834 | 0.0769170 | − | 0.997038i | \(-0.475492\pi\) | ||||
0.0769170 | + | 0.997038i | \(0.475492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.41417e16 | −1.17324 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.04945e16 | 0.356631 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.46684e16 | −0.492951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.79167e16 | 1.26016 | 0.630080 | − | 0.776530i | \(-0.283022\pi\) | ||||
0.630080 | + | 0.776530i | \(0.283022\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.26479e15 | 0.271651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.03283e16 | −0.660807 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.76003e13 | 0.00185183 | 0.000925915 | − | 1.00000i | \(-0.499705\pi\) | ||||
0.000925915 | 1.00000i | \(0.499705\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.53830e15 | 0.303292 |
(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 | 48.12.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 144.12.a.l.1.1 | 1 | |||
4.3 | odd | 2 | 3.12.a.a.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 192.12.a.q.1.1 | 1 | |||
8.5 | even | 2 | 192.12.a.g.1.1 | 1 | |||
12.11 | even | 2 | 9.12.a.a.1.1 | 1 | |||
20.3 | even | 4 | 75.12.b.a.49.1 | 2 | |||
20.7 | even | 4 | 75.12.b.a.49.2 | 2 | |||
20.19 | odd | 2 | 75.12.a.a.1.1 | 1 | |||
28.27 | even | 2 | 147.12.a.c.1.1 | 1 | |||
36.7 | odd | 6 | 81.12.c.a.28.1 | 2 | |||
36.11 | even | 6 | 81.12.c.e.28.1 | 2 | |||
36.23 | even | 6 | 81.12.c.e.55.1 | 2 | |||
36.31 | odd | 6 | 81.12.c.a.55.1 | 2 | |||
60.23 | odd | 4 | 225.12.b.a.199.2 | 2 | |||
60.47 | odd | 4 | 225.12.b.a.199.1 | 2 | |||
60.59 | even | 2 | 225.12.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.12.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
9.12.a.a.1.1 | 1 | 12.11 | even | 2 | |||
48.12.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.12.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
75.12.b.a.49.1 | 2 | 20.3 | even | 4 | |||
75.12.b.a.49.2 | 2 | 20.7 | even | 4 | |||
81.12.c.a.28.1 | 2 | 36.7 | odd | 6 | |||
81.12.c.a.55.1 | 2 | 36.31 | odd | 6 | |||
81.12.c.e.28.1 | 2 | 36.11 | even | 6 | |||
81.12.c.e.55.1 | 2 | 36.23 | even | 6 | |||
144.12.a.l.1.1 | 1 | 3.2 | odd | 2 | |||
147.12.a.c.1.1 | 1 | 28.27 | even | 2 | |||
192.12.a.g.1.1 | 1 | 8.5 | even | 2 | |||
192.12.a.q.1.1 | 1 | 8.3 | odd | 2 | |||
225.12.a.f.1.1 | 1 | 60.59 | even | 2 | |||
225.12.b.a.199.1 | 2 | 60.47 | odd | 4 | |||
225.12.b.a.199.2 | 2 | 60.23 | odd | 4 |