Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,12,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("225.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(172.877215626\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 78.0000 | 1.72357 | 0.861786 | − | 0.507271i | \(-0.169346\pi\) | ||||
0.861786 | + | 0.507271i | \(0.169346\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4036.00 | 1.97070 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27760.0 | 0.624281 | 0.312141 | − | 0.950036i | \(-0.398954\pi\) | ||||
0.312141 | + | 0.950036i | \(0.398954\pi\) | |||||||
\(8\) | 155064. | 1.67308 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.592384\pi\) | ||||
−0.286175 | + | 0.958177i | \(0.592384\pi\) | |||||||
\(14\) | 2.16528e6 | 1.07599 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.82926e6 | 0.912968 | ||||||||
\(17\) | 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 | \(-0.859298\pi\) | ||||
−0.903886 | + | 0.427773i | \(0.859298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.97512e7 | −2.05816 | ||||||||
\(23\) | 1.53124e7 | 0.496066 | 0.248033 | − | 0.968752i | \(-0.420216\pi\) | ||||
0.248033 | + | 0.968752i | \(0.420216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.97647e7 | −0.986487 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.12039e8 | 1.23027 | ||||||||
\(29\) | −1.07513e7 | −0.0973353 | −0.0486677 | − | 0.998815i | \(-0.515498\pi\) | ||||
−0.0486677 | + | 0.998815i | \(0.515498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.09374e7 | −0.319556 | −0.159778 | − | 0.987153i | \(-0.551078\pi\) | ||||
−0.159778 | + | 0.987153i | \(0.551078\pi\) | |||||||
\(32\) | −1.88885e7 | −0.0995112 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.40580e8 | 0.908081 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.64741e8 | −1.57595 | −0.787976 | − | 0.615706i | \(-0.788871\pi\) | ||||
−0.787976 | + | 0.615706i | \(0.788871\pi\) | |||||||
\(38\) | −1.52189e9 | −3.11583 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.98833e8 | −1.21162 | −0.605812 | − | 0.795608i | \(-0.707152\pi\) | ||||
−0.605812 | + | 0.795608i | \(0.707152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.57947e8 | 0.993722 | 0.496861 | − | 0.867830i | \(-0.334486\pi\) | ||||
0.496861 | + | 0.867830i | \(0.334486\pi\) | |||||||
\(44\) | −2.57431e9 | −2.35326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.19436e9 | 0.855005 | ||||||||
\(47\) | −1.55574e9 | −0.989462 | −0.494731 | − | 0.869046i | \(-0.664733\pi\) | ||||
−0.494731 | + | 0.869046i | \(0.664733\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.20671e9 | −0.610273 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.09244e9 | −1.12793 | ||||||||
\(53\) | 3.79242e9 | 1.24566 | 0.622829 | − | 0.782358i | \(-0.285983\pi\) | ||||
0.622829 | + | 0.782358i | \(0.285983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.30458e9 | 1.04447 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.38598e8 | −0.167765 | ||||||||
\(59\) | −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 | \(0.377564\pi\) | |||||||
\(62\) | −3.97312e9 | −0.550779 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.31563e9 | −1.08448 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.29240e9 | −0.478896 | −0.239448 | − | 0.970909i | \(-0.576966\pi\) | ||||
−0.239448 | + | 0.970909i | \(0.576966\pi\) | |||||||
\(68\) | 1.24485e10 | 1.03828 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.629043\pi\) | ||||
−0.394386 | + | 0.918945i | \(0.629043\pi\) | |||||||
\(74\) | −5.18498e10 | −2.71627 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.87480e10 | −3.56258 | ||||||||
\(77\) | −1.77063e10 | −0.745469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.72054e9 | 0.136037 | 0.0680185 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680185 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.01090e10 | −2.08832 | ||||||||
\(83\) | 8.76845e9 | 0.244339 | 0.122170 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122170 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.47199e10 | 1.71275 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.89054e10 | −1.99786 | ||||||||
\(89\) | 2.54728e10 | 0.483539 | 0.241769 | − | 0.970334i | \(-0.422272\pi\) | ||||
0.241769 | + | 0.970334i | \(0.422272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.12701e10 | −0.357307 | ||||||||
\(92\) | 6.18007e10 | 0.977598 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.21348e11 | −1.70541 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.90925e10 | 0.462220 | 0.231110 | − | 0.972928i | \(-0.425764\pi\) | ||||
0.231110 | + | 0.972928i | \(0.425764\pi\) | |||||||
\(98\) | −9.41233e10 | −1.05185 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.31078e9 | −0.0881492 | −0.0440746 | − | 0.999028i | \(-0.514034\pi\) | ||||
−0.0440746 | + | 0.999028i | \(0.514034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.85751e10 | −0.412865 | −0.206433 | − | 0.978461i | \(-0.566185\pi\) | ||||
−0.206433 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(104\) | −1.18812e11 | −0.957586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.95809e11 | 2.14698 | ||||||||
\(107\) | 2.25596e11 | 1.55496 | 0.777482 | − | 0.628906i | \(-0.216497\pi\) | ||||
0.777482 | + | 0.628906i | \(0.216497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.94512e10 | −0.432348 | −0.216174 | − | 0.976355i | \(-0.569358\pi\) | ||||
−0.216174 | + | 0.976355i | \(0.569358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.06300e11 | 0.569949 | ||||||||
\(113\) | −3.59665e11 | −1.83640 | −0.918198 | − | 0.396122i | \(-0.870356\pi\) | ||||
−0.918198 | + | 0.396122i | \(0.870356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.33921e10 | −0.191819 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.33139e10 | −0.174292 | ||||||||
\(119\) | 8.56217e10 | 0.328909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.21523e11 | 0.425931 | ||||||||
\(122\) | 3.86133e11 | 1.29347 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.05583e11 | −0.629751 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.50273e11 | −0.672192 | −0.336096 | − | 0.941828i | \(-0.609107\pi\) | ||||
−0.336096 | + | 0.941828i | \(0.609107\pi\) | |||||||
\(128\) | −6.87936e11 | −1.76967 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | −4.12807e11 | −0.825412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.78272e11 | 0.881477 | ||||||||
\(137\) | −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 | \(-0.872228\pi\) | ||||
−0.920512 | + | 0.390715i | \(0.872228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.15682e12 | 1.68144 | ||||||||
\(143\) | 4.88719e11 | 0.683457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.08974e12 | −1.35951 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.68289e12 | −3.10573 | ||||||||
\(149\) | 1.38458e12 | 1.54452 | 0.772261 | − | 0.635306i | \(-0.219126\pi\) | ||||
0.772261 | + | 0.635306i | \(0.219126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.98601e11 | −0.724196 | −0.362098 | − | 0.932140i | \(-0.617939\pi\) | ||||
−0.362098 | + | 0.932140i | \(0.617939\pi\) | |||||||
\(152\) | −3.02552e12 | −3.02454 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.38109e12 | −1.28487 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.13127e12 | −1.78316 | −0.891580 | − | 0.452863i | \(-0.850403\pi\) | ||||
−0.891580 | + | 0.452863i | \(0.850403\pi\) | |||||||
\(158\) | 2.90202e11 | 0.234470 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | \(0.482270\pi\) | |||||||
\(164\) | −3.62769e12 | −2.38775 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.83939e11 | 0.421137 | ||||||||
\(167\) | −8.80943e9 | −0.00524816 | −0.00262408 | − | 0.999997i | \(-0.500835\pi\) | ||||
−0.00262408 | + | 0.999997i | \(0.500835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20508e12 | −0.672416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.86627e12 | 1.95833 | ||||||||
\(173\) | −7.30852e11 | −0.358571 | −0.179286 | − | 0.983797i | \(-0.557379\pi\) | ||||
−0.179286 | + | 0.983797i | \(0.557379\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.44244e12 | −1.09020 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.98688e12 | 0.833414 | ||||||||
\(179\) | −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 | \(0.356375\pi\) | |||||||
\(182\) | −1.65907e12 | −0.615845 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.37440e12 | 0.829956 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.96731e12 | −0.629136 | ||||||||
\(188\) | −6.27897e12 | −1.94994 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.269498\pi\) | ||||
0.662494 | + | 0.749067i | \(0.269498\pi\) | |||||||
\(194\) | 3.04921e12 | 0.796670 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.87028e12 | −1.20267 | ||||||||
\(197\) | 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 | \(-0.641464\pi\) | ||||
−0.429938 | + | 0.902859i | \(0.641464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.26241e11 | −0.151932 | ||||||||
\(203\) | −2.98455e11 | −0.0607646 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.78885e12 | −0.711604 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.93404e12 | −0.522537 | ||||||||
\(209\) | 1.24451e13 | 2.15870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79494e11 | 0.0295458 | 0.0147729 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147729 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(212\) | 1.53062e13 | 2.45482 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.75965e13 | 2.68009 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.41402e12 | −0.199493 | ||||||||
\(218\) | −5.41719e12 | −0.745184 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(0.543146\pi\) | |||||||
\(224\) | −5.24344e11 | −0.0621230 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.80538e13 | −3.16516 | ||||||||
\(227\) | −4.15848e11 | −0.0457923 | −0.0228961 | − | 0.999738i | \(-0.507289\pi\) | ||||
−0.0228961 | + | 0.999738i | \(0.507289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.81248e13 | 1.90186 | 0.950928 | − | 0.309414i | \(-0.100133\pi\) | ||||
0.950928 | + | 0.309414i | \(0.100133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.66713e12 | −0.162850 | ||||||||
\(233\) | −1.87641e10 | −0.00179007 | −0.000895033 | − | 1.00000i | \(-0.500285\pi\) | ||||
−0.000895033 | 1.00000i | \(0.500285\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.24122e12 | −0.199282 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.67849e12 | 0.566898 | ||||||||
\(239\) | 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 | \(0.511227\pi\) | |||||||
\(242\) | 9.47880e12 | 0.734123 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.99799e13 | 1.47894 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.49499e13 | 1.03468 | ||||||||
\(248\) | −7.89856e12 | −0.534643 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(254\) | −1.95213e13 | −1.15857 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.45806e13 | −1.96568 | ||||||||
\(257\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.63556e12 | 0.382106 | ||||||||
\(263\) | 1.65956e13 | 0.813272 | 0.406636 | − | 0.913590i | \(-0.366702\pi\) | ||||
0.406636 | + | 0.913590i | \(0.366702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.22477e13 | −1.94515 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.13601e13 | −0.943762 | ||||||||
\(269\) | −2.85236e13 | −1.23471 | −0.617357 | − | 0.786683i | \(-0.711797\pi\) | ||||
−0.617357 | + | 0.786683i | \(0.711797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.33800e13 | 0.971658 | 0.485829 | − | 0.874054i | \(-0.338518\pi\) | ||||
0.485829 | + | 0.874054i | \(0.338518\pi\) | |||||||
\(272\) | 1.18108e13 | 0.481006 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.20911e13 | −0.472976 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.03641e13 | 1.11872 | 0.559361 | − | 0.828924i | \(-0.311047\pi\) | ||||
0.559361 | + | 0.828924i | \(0.311047\pi\) | |||||||
\(278\) | −8.78487e13 | −3.17314 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.59749e13 | −0.543942 | −0.271971 | − | 0.962306i | \(-0.587675\pi\) | ||||
−0.271971 | + | 0.962306i | \(0.587675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.87045e13 | −0.939993 | −0.469997 | − | 0.882668i | \(-0.655745\pi\) | ||||
−0.469997 | + | 0.882668i | \(0.655745\pi\) | |||||||
\(284\) | 5.98583e13 | 1.92253 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.81201e13 | 1.17799 | ||||||||
\(287\) | −2.49516e13 | −0.756394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47587e13 | −0.722419 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.63870e13 | −1.55444 | ||||||||
\(293\) | 4.81754e13 | 1.30333 | 0.651663 | − | 0.758508i | \(-0.274071\pi\) | ||||
0.651663 | + | 0.758508i | \(0.274071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.03077e14 | −2.63669 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.07997e14 | 2.66209 | ||||||||
\(299\) | −1.17325e13 | −0.283923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.65926e13 | 0.620362 | ||||||||
\(302\) | −5.44909e13 | −1.24820 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.47143e13 | −1.65044 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.57350e13 | −0.538597 | −0.269298 | − | 0.963057i | \(-0.586792\pi\) | ||||
−0.269298 | + | 0.963057i | \(0.586792\pi\) | |||||||
\(308\) | −7.14627e13 | −1.46910 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.537840\pi\) | ||||
−0.118597 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(314\) | −1.66239e14 | −3.07341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.50161e13 | 0.268089 | ||||||||
\(317\) | −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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.31555e13 | 0.533764 | ||||||||
\(323\) | −6.01801e13 | −0.952443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.27580e13 | 0.191905 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.39377e14 | −2.02714 | ||||||||
\(329\) | −4.31874e13 | −0.617703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.40115e13 | −0.470513 | −0.235256 | − | 0.971933i | \(-0.575593\pi\) | ||||
−0.235256 | + | 0.971933i | \(0.575593\pi\) | |||||||
\(332\) | 3.53895e13 | 0.481520 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.87135e11 | −0.00904558 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.99439e13 | 0.751244 | 0.375622 | − | 0.926773i | \(-0.377429\pi\) | ||||
0.375622 | + | 0.926773i | \(0.377429\pi\) | |||||||
\(338\) | −9.39960e13 | −1.15896 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24897e13 | 0.381590 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.83888e13 | −1.00526 | ||||||||
\(344\) | 1.48543e14 | 1.66257 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.70064e13 | −0.618024 | ||||||||
\(347\) | 9.78685e13 | 1.04431 | 0.522157 | − | 0.852850i | \(-0.325128\pi\) | ||||
0.522157 | + | 0.852850i | \(0.325128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.42790e14 | −1.47624 | −0.738120 | − | 0.674670i | \(-0.764286\pi\) | ||||
−0.738120 | + | 0.674670i | \(0.764286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.20478e13 | 0.118829 | ||||||||
\(353\) | 1.44246e14 | 1.40069 | 0.700346 | − | 0.713804i | \(-0.253029\pi\) | ||||
0.700346 | + | 0.713804i | \(0.253029\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.02808e14 | 0.952911 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.06050e14 | −2.75065 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 1.77786e14 | 1.50314 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.58461e13 | −0.704147 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.60110e14 | 1.25532 | 0.627659 | − | 0.778488i | \(-0.284013\pi\) | ||||
0.627659 | + | 0.778488i | \(0.284013\pi\) | |||||||
\(368\) | 5.86351e13 | 0.452892 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.05277e14 | 0.777641 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.47258e13 | 0.249031 | 0.124516 | − | 0.992218i | \(-0.460262\pi\) | ||||
0.124516 | + | 0.992218i | \(0.460262\pi\) | |||||||
\(374\) | −1.53450e14 | −1.08436 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.41239e14 | −1.65545 | ||||||||
\(377\) | 8.23777e12 | 0.0557099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46500e14 | −0.962327 | −0.481163 | − | 0.876631i | \(-0.659786\pi\) | ||||
−0.481163 | + | 0.876631i | \(0.659786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.64193e14 | −1.66178 | ||||||||
\(383\) | 6.43419e13 | 0.398933 | 0.199467 | − | 0.979905i | \(-0.436079\pi\) | ||||
0.199467 | + | 0.979905i | \(0.436079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84478e14 | 2.28371 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.57777e14 | 0.910899 | ||||||||
\(389\) | 3.98900e13 | 0.227061 | 0.113530 | − | 0.993535i | \(-0.463784\pi\) | ||||
0.113530 | + | 0.993535i | \(0.463784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.72287e13 | 0.261357 | ||||||||
\(392\) | −1.87117e14 | −1.02103 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.95912e14 | 2.63133 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.06552e14 | −0.542268 | −0.271134 | − | 0.962542i | \(-0.587399\pi\) | ||||
−0.271134 | + | 0.962542i | \(0.587399\pi\) | |||||||
\(398\) | −2.95272e14 | −1.48206 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.41445e13 | −0.164447 | −0.0822236 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822236 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.90289e13 | 0.182898 | ||||||||
\(404\) | −3.75783e13 | −0.173716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.32795e13 | −0.104732 | ||||||||
\(407\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.96049e14 | −0.813635 | ||||||||
\(413\) | −1.54153e13 | −0.0631288 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.44726e13 | 0.0569553 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.70716e14 | 3.72068 | ||||||||
\(419\) | 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 | \(0.593985\pi\) | |||||||
\(422\) | 1.40005e13 | 0.0509244 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.88067e14 | 2.08408 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.37424e14 | 0.468499 | ||||||||
\(428\) | 9.10504e14 | 3.06437 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.462262\pi\) | ||||
0.118280 | + | 0.992980i | \(0.462262\pi\) | |||||||
\(434\) | −1.10294e14 | −0.343841 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.80305e14 | −0.852030 | ||||||||
\(437\) | −2.98766e14 | −0.896773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.68335e14 | −1.07817 | −0.539086 | − | 0.842250i | \(-0.681230\pi\) | ||||
−0.539086 | + | 0.842250i | \(0.681230\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.84335e14 | −0.519740 | ||||||||
\(443\) | −1.11248e14 | −0.309793 | −0.154896 | − | 0.987931i | \(-0.549504\pi\) | ||||
−0.154896 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.73603e14 | −0.465818 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.58602e14 | −0.677022 | ||||||||
\(449\) | 8.83314e13 | 0.228434 | 0.114217 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114217 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.73308e14 | 1.44683 | ||||||||
\(452\) | −1.45161e15 | −3.61899 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.24361e13 | −0.0789263 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.42094e12 | 0.0221083 | 0.0110541 | − | 0.999939i | \(-0.496481\pi\) | ||||
0.0110541 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(458\) | 1.41373e15 | 3.27799 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.97134e14 | 1.55941 | 0.779706 | − | 0.626146i | \(-0.215369\pi\) | ||||
0.779706 | + | 0.626146i | \(0.215369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.87941e14 | 0.410513 | 0.205256 | − | 0.978708i | \(-0.434197\pi\) | ||||
0.205256 | + | 0.978708i | \(0.434197\pi\) | |||||||
\(464\) | −4.11694e13 | −0.0888640 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.46360e12 | −0.00308531 | ||||||||
\(467\) | 3.20007e14 | 0.666678 | 0.333339 | − | 0.942807i | \(-0.391825\pi\) | ||||
0.333339 | + | 0.942807i | \(0.391825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.46917e14 | −0.298966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.61081e13 | −0.169185 | ||||||||
\(473\) | −6.11013e14 | −1.18663 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.45569e14 | 0.648181 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.37477e15 | 2.51986 | ||||||||
\(479\) | 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 | ||||||||
\(482\) | −6.94291e13 | −0.121558 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.90467e14 | 0.839384 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.76546e14 | −0.292045 | −0.146022 | − | 0.989281i | \(-0.546647\pi\) | ||||
−0.146022 | + | 0.989281i | \(0.546647\pi\) | |||||||
\(488\) | 7.67632e14 | 1.25558 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(494\) | 1.16609e15 | 1.78334 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.95053e14 | −0.291745 | ||||||||
\(497\) | 4.11711e14 | 0.609021 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.01209e14 | 0.869907 | 0.434953 | − | 0.900453i | \(-0.356765\pi\) | ||||
0.434953 | + | 0.900453i | \(0.356765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.88979e15 | 2.64571 | ||||||||
\(503\) | 1.09203e15 | 1.51221 | 0.756103 | − | 0.654453i | \(-0.227101\pi\) | ||||
0.756103 | + | 0.654453i | \(0.227101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.61808e14 | −1.02098 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.01010e15 | −1.32469 | ||||||||
\(509\) | −8.76371e14 | −1.13695 | −0.568474 | − | 0.822702i | \(-0.692466\pi\) | ||||
−0.568474 | + | 0.822702i | \(0.692466\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.87835e14 | −0.492416 | ||||||||
\(512\) | −1.28839e15 | −1.61832 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.08784e14 | 0.748455 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.92308e14 | 1.18154 | ||||||||
\(518\) | −1.43935e15 | −1.69571 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.71989e14 | 0.424544 | 0.212272 | − | 0.977211i | \(-0.431914\pi\) | ||||
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.73507e14 | 1.08788 | 0.543939 | − | 0.839125i | \(-0.316932\pi\) | ||||
0.543939 | + | 0.839125i | \(0.316932\pi\) | |||||||
\(524\) | 3.95091e14 | 0.436893 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.29445e15 | 1.40173 | ||||||||
\(527\) | −1.57109e14 | −0.168361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.18341e14 | −0.753919 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.18605e15 | −2.22405 | ||||||||
\(533\) | 6.88699e14 | 0.693473 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.20661e14 | −0.801230 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.22484e15 | −2.12812 | ||||||||
\(539\) | 7.69683e14 | 0.728741 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.74606e15 | 1.61985 | 0.809925 | − | 0.586533i | \(-0.199508\pi\) | ||||
0.809925 | + | 0.586533i | \(0.199508\pi\) | |||||||
\(542\) | 1.82364e15 | 1.67472 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.82588e13 | −0.0524285 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.74624e14 | −0.152467 | −0.0762333 | − | 0.997090i | \(-0.524289\pi\) | ||||
−0.0762333 | + | 0.997090i | \(0.524289\pi\) | |||||||
\(548\) | −6.25639e14 | −0.540793 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.09772e14 | 0.175960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03282e14 | 0.0849254 | ||||||||
\(554\) | 2.36840e15 | 1.92820 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.54561e15 | −3.62811 | ||||||||
\(557\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.24604e15 | −0.937523 | ||||||||
\(563\) | −9.75798e14 | −0.727049 | −0.363525 | − | 0.931585i | \(-0.618427\pi\) | ||||
−0.363525 | + | 0.931585i | \(0.618427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.23895e15 | −1.62015 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.29977e15 | 1.63218 | ||||||||
\(569\) | −1.92427e15 | −1.35254 | −0.676269 | − | 0.736655i | \(-0.736404\pi\) | ||||
−0.676269 | + | 0.736655i | \(0.736404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61132e15 | 1.11092 | 0.555461 | − | 0.831543i | \(-0.312542\pi\) | ||||
0.555461 | + | 0.831543i | \(0.312542\pi\) | |||||||
\(572\) | 1.97247e15 | 1.34689 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.94623e15 | −1.30370 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.53250e15 | 1.64848 | 0.824239 | − | 0.566242i | \(-0.191603\pi\) | ||||
0.824239 | + | 0.566242i | \(0.191603\pi\) | |||||||
\(578\) | −1.93118e15 | −1.24514 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.43412e14 | 0.152536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41894e15 | −1.48747 | ||||||||
\(584\) | −2.16640e15 | −1.31968 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.75768e15 | 2.24638 | ||||||||
\(587\) | −3.11508e15 | −1.84484 | −0.922421 | − | 0.386186i | \(-0.873792\pi\) | ||||
−0.922421 | + | 0.386186i | \(0.873792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.93860e14 | 0.577685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.54547e15 | −1.43879 | ||||||||
\(593\) | −2.20723e15 | −1.23608 | −0.618040 | − | 0.786146i | \(-0.712073\pi\) | ||||
−0.618040 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.58817e15 | 3.04379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.15138e14 | −0.489362 | ||||||||
\(599\) | −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 | \(0.634399\pi\) | |||||||
\(602\) | 2.07422e15 | 1.06924 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.81956e15 | −1.42718 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.05592e14 | 0.249036 | 0.124518 | − | 0.992217i | \(-0.460262\pi\) | ||||
0.124518 | + | 0.992217i | \(0.460262\pi\) | |||||||
\(608\) | 3.68541e14 | 0.179894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.19203e15 | 0.566319 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.98375e15 | 0.925665 | 0.462832 | − | 0.886446i | \(-0.346833\pi\) | ||||
0.462832 | + | 0.886446i | \(0.346833\pi\) | |||||||
\(614\) | −2.00733e15 | −0.928310 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.74561e15 | −1.24723 | ||||||||
\(617\) | −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 | \(-0.432792\pi\) | ||||
0.209574 | + | 0.977793i | \(0.432792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.69913e15 | −1.16246 | ||||||||
\(623\) | 7.07124e14 | 0.301864 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.83314e14 | −0.408821 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.60181e15 | −3.51408 | ||||||||
\(629\) | −2.05030e15 | −0.830306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00593e15 | 0.400318 | 0.200159 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200159 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(632\) | 5.76922e14 | 0.227601 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.38230e15 | −2.47449 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.24597e14 | 0.349290 | ||||||||
\(638\) | 5.34888e14 | 0.200332 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.13144e15 | −0.412966 | −0.206483 | − | 0.978450i | \(-0.566202\pi\) | ||||
−0.206483 | + | 0.978450i | \(0.566202\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.68306e14 | 0.311539 | 0.155769 | − | 0.987793i | \(-0.450214\pi\) | ||||
0.155769 | + | 0.987793i | \(0.450214\pi\) | |||||||
\(644\) | 1.71559e15 | 0.610296 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.69405e15 | −1.64160 | ||||||||
\(647\) | −1.37636e15 | −0.477265 | −0.238633 | − | 0.971110i | \(-0.576699\pi\) | ||||
−0.238633 | + | 0.971110i | \(0.576699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.54195e14 | 0.120753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.60146e14 | 0.219421 | ||||||||
\(653\) | 2.55276e15 | 0.841370 | 0.420685 | − | 0.907207i | \(-0.361790\pi\) | ||||
0.420685 | + | 0.907207i | \(0.361790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.44187e15 | −1.10617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.36862e15 | −1.06466 | ||||||||
\(659\) | −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 | \(0.594767\pi\) | |||||||
\(662\) | −2.65289e15 | −0.810963 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.35967e15 | 0.408799 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64627e14 | −0.0482847 | ||||||||
\(668\) | −3.55548e13 | −0.0103426 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15756e15 | −0.896143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.92990e15 | −1.37643 | −0.688217 | − | 0.725505i | \(-0.741606\pi\) | ||||
−0.688217 | + | 0.725505i | \(0.741606\pi\) | |||||||
\(674\) | 4.67563e15 | 1.29482 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.86369e15 | −1.32513 | ||||||||
\(677\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.53420e15 | 0.657698 | ||||||||
\(683\) | −3.81244e15 | −0.981498 | −0.490749 | − | 0.871301i | \(-0.663277\pi\) | ||||
−0.490749 | + | 0.871301i | \(0.663277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.89433e15 | −1.73264 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.66823e15 | 0.907236 | ||||||||
\(689\) | −2.90580e15 | −0.712952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.03729e15 | 0.974901 | 0.487450 | − | 0.873151i | \(-0.337927\pi\) | ||||
0.487450 | + | 0.873151i | \(0.337927\pi\) | |||||||
\(692\) | −2.94972e15 | −0.706638 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.63374e15 | 1.79995 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.77232e15 | −0.638356 | ||||||||
\(698\) | −1.11376e16 | −2.54441 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.71267e15 | 1.05152 | 0.525761 | − | 0.850632i | \(-0.323781\pi\) | ||||
0.525761 | + | 0.850632i | \(0.323781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.29700e16 | 2.84896 | ||||||||
\(704\) | 5.94185e15 | 1.29501 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.12512e16 | 2.41419 | ||||||||
\(707\) | −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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.94991e15 | 0.808997 | ||||||||
\(713\) | −7.79972e14 | −0.158521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.58361e16 | −3.14505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.69924e15 | 1.89694 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 2.06080e16 | 3.90913 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.19929e15 | 1.71867 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.68018e15 | 1.03734 | 0.518672 | − | 0.854973i | \(-0.326427\pi\) | ||||
0.518672 | + | 0.854973i | \(0.326427\pi\) | |||||||
\(728\) | −3.29823e15 | −0.597803 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.95465e15 | 0.523552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.62312e15 | 0.283320 | 0.141660 | − | 0.989915i | \(-0.454756\pi\) | ||||
0.141660 | + | 0.989915i | \(0.454756\pi\) | |||||||
\(734\) | 1.24885e16 | 2.16363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.89227e14 | −0.0493641 | ||||||||
\(737\) | 3.37568e15 | 0.571861 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.64794e15 | 0.608840 | 0.304420 | − | 0.952538i | \(-0.401537\pi\) | ||||
0.304420 | + | 0.952538i | \(0.401537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.21164e15 | 1.34032 | ||||||||
\(743\) | 6.76045e15 | 1.09531 | 0.547655 | − | 0.836704i | \(-0.315521\pi\) | ||||
0.547655 | + | 0.836704i | \(0.315521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.70861e15 | 0.429224 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.94007e15 | −1.23984 | ||||||||
\(749\) | 6.26254e15 | 0.970734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.64833e13 | 0.00404532 | 0.00202266 | − | 0.999998i | \(-0.499356\pi\) | ||||
0.00202266 | + | 0.999998i | \(0.499356\pi\) | |||||||
\(752\) | −5.95734e15 | −0.903347 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.42546e14 | 0.0960200 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.37364e15 | −1.07809 | −0.539045 | − | 0.842277i | \(-0.681215\pi\) | ||||
−0.539045 | + | 0.842277i | \(0.681215\pi\) | |||||||
\(758\) | −1.14270e16 | −1.65864 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.20983e15 | −0.881991 | −0.440996 | − | 0.897509i | \(-0.645375\pi\) | ||||
−0.440996 | + | 0.897509i | \(0.645375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.92796e15 | −0.269907 | ||||||||
\(764\) | −1.36703e16 | −1.90005 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.01866e15 | 0.687591 | ||||||||
\(767\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.98943e16 | 2.61116 | ||||||||
\(773\) | −2.95047e15 | −0.384507 | −0.192254 | − | 0.981345i | \(-0.561580\pi\) | ||||
−0.192254 | + | 0.981345i | \(0.561580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.06184e15 | 0.773330 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.11142e15 | 0.391355 | ||||||||
\(779\) | 1.75375e16 | 2.19034 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.45980e15 | −1.16493 | ||||||||
\(782\) | 3.68384e15 | 0.450468 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.62081e15 | −0.557160 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.35545e16 | −1.60038 | −0.800190 | − | 0.599746i | \(-0.795268\pi\) | ||||
−0.800190 | + | 0.599746i | \(0.795268\pi\) | |||||||
\(788\) | 2.56603e16 | 3.00862 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.98429e15 | −1.14643 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.79308e15 | −0.429526 | ||||||||
\(794\) | −8.31105e15 | −0.934638 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.52784e16 | −1.69456 | ||||||||
\(797\) | −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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.66327e15 | −0.283437 | ||||||||
\(803\) | 8.91121e15 | 0.941892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.04426e15 | 0.315238 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.44377e15 | −0.147481 | ||||||||
\(809\) | −9.45859e15 | −0.959643 | −0.479821 | − | 0.877366i | \(-0.659299\pi\) | ||||
−0.479821 | + | 0.877366i | \(0.659299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07996e16 | −1.08092 | −0.540461 | − | 0.841369i | \(-0.681750\pi\) | ||||
−0.540461 | + | 0.841369i | \(0.681750\pi\) | |||||||
\(812\) | −1.20456e15 | −0.119749 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.30717e16 | 3.24356 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.86909e16 | −1.79642 | ||||||||
\(818\) | 4.16012e15 | 0.397158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.10411e16 | 1.03306 | 0.516529 | − | 0.856270i | \(-0.327224\pi\) | ||||
0.516529 | + | 0.856270i | \(0.327224\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.26104e16 | −1.16420 | −0.582101 | − | 0.813117i | \(-0.697769\pi\) | ||||
−0.582101 | + | 0.813117i | \(0.697769\pi\) | |||||||
\(824\) | −7.53224e15 | −0.690756 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.20239e15 | −0.108807 | ||||||||
\(827\) | −7.86172e14 | −0.0706704 | −0.0353352 | − | 0.999376i | \(-0.511250\pi\) | ||||
−0.0353352 | + | 0.999376i | \(0.511250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.92589e15 | −0.525659 | −0.262829 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262829 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.13777e15 | 0.620704 | ||||||||
\(833\) | −3.72192e15 | −0.321528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.02283e16 | 4.25416 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.90044e15 | 0.660403 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | −1.23184e16 | −1.00309 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.24437e14 | 0.0582260 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.37348e15 | 0.265901 | ||||||||
\(848\) | 1.45222e16 | 1.13725 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.01788e16 | −0.781775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.98378e16 | 1.50409 | 0.752046 | − | 0.659110i | \(-0.229067\pi\) | ||||
0.752046 | + | 0.659110i | \(0.229067\pi\) | |||||||
\(854\) | 1.07190e16 | 0.807491 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.49818e16 | 2.60157 | ||||||||
\(857\) | 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 | \(-0.698004\pi\) | ||||
−0.582701 | + | 0.812687i | \(0.698004\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.00274e16 | −2.86462 | ||||||||
\(863\) | −4.02926e15 | −0.286527 | −0.143264 | − | 0.989685i | \(-0.545760\pi\) | ||||
−0.143264 | + | 0.989685i | \(0.545760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.84413e15 | 0.407729 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.70699e15 | −0.393142 | ||||||||
\(869\) | −2.37310e15 | −0.162445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.05511e15 | 0.274096 | ||||||||
\(872\) | −1.07694e16 | −0.723352 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.33037e16 | −1.54565 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.76958e15 | −0.635884 | −0.317942 | − | 0.948110i | \(-0.602992\pi\) | ||||
−0.317942 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(878\) | −2.87301e16 | −1.85831 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.62583e16 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66061e16 | −1.04108 | −0.520540 | − | 0.853837i | \(-0.674269\pi\) | ||||
−0.520540 | + | 0.853837i | \(0.674269\pi\) | |||||||
\(884\) | −9.53818e15 | −0.594262 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.67733e15 | −0.533950 | ||||||||
\(887\) | −1.91314e16 | −1.16995 | −0.584975 | − | 0.811051i | \(-0.698896\pi\) | ||||
−0.584975 | + | 0.811051i | \(0.698896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.94758e15 | −0.419637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.98286e15 | −0.532608 | ||||||||
\(893\) | 3.03547e16 | 1.78872 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.90971e16 | −1.10477 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.88985e15 | 0.393722 | ||||||||
\(899\) | 5.47641e14 | 0.0311041 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.16972e16 | 0.656287 | ||||||||
\(902\) | 4.47180e16 | 2.49372 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.57710e16 | −3.07243 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07252e16 | 0.580182 | 0.290091 | − | 0.956999i | \(-0.406314\pi\) | ||||
0.290091 | + | 0.956999i | \(0.406314\pi\) | |||||||
\(908\) | −1.67836e15 | −0.0902430 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | 7.34833e14 | 0.0381052 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.31516e16 | 3.74799 | ||||||||
\(917\) | 2.71748e15 | 0.138399 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.83551e16 | 0.923679 | 0.461839 | − | 0.886964i | \(-0.347190\pi\) | ||||
0.461839 | + | 0.886964i | \(0.347190\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.43764e16 | 2.68776 | ||||||||
\(923\) | −1.13638e16 | −0.558359 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.46594e16 | 0.707549 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.03075e14 | 0.00968596 | ||||||||
\(929\) | 1.10125e16 | 0.522155 | 0.261078 | − | 0.965318i | \(-0.415922\pi\) | ||||
0.261078 | + | 0.965318i | \(0.415922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.35446e16 | 1.10323 | ||||||||
\(932\) | −7.57317e13 | −0.00352769 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.49605e16 | 1.14907 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.36357e15 | −0.378289 | −0.189145 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189145 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(938\) | −1.14595e16 | −0.515289 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.22942e16 | −0.985028 | −0.492514 | − | 0.870305i | \(-0.663922\pi\) | ||||
−0.492514 | + | 0.870305i | \(0.663922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37633e16 | −0.601045 | ||||||||
\(944\) | −2.12642e15 | −0.0923214 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.76590e16 | −2.04524 | ||||||||
\(947\) | −3.78038e16 | −1.61291 | −0.806457 | − | 0.591293i | \(-0.798618\pi\) | ||||
−0.806457 | + | 0.591293i | \(0.798618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.07048e16 | 0.451454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.32768e16 | 0.550290 | ||||||||
\(953\) | 4.79568e15 | 0.197624 | 0.0988119 | − | 0.995106i | \(-0.468496\pi\) | ||||
0.0988119 | + | 0.995106i | \(0.468496\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.11355e16 | 2.88116 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.17298e16 | 0.469657 | ||||||||
\(959\) | −4.30321e15 | −0.171313 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28139e16 | −0.897884 | ||||||||
\(962\) | 3.97280e16 | 1.55466 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.59251e15 | −0.138987 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.37420e16 | −1.28329 | −0.641645 | − | 0.767002i | \(-0.721748\pi\) | ||||
−0.641645 | + | 0.767002i | \(0.721748\pi\) | |||||||
\(968\) | 1.88439e16 | 0.712616 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(974\) | −1.37706e16 | −0.503360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.89565e16 | 0.685147 | ||||||||
\(977\) | −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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.71547e16 | 2.34673 | ||||||||
\(983\) | −4.42687e15 | −0.153834 | −0.0769170 | − | 0.997038i | \(-0.524508\pi\) | ||||
−0.0769170 | + | 0.997038i | \(0.524508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.58653e15 | −0.0883884 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.03378e16 | 2.03904 | ||||||||
\(989\) | 1.46684e16 | 0.492951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79167e16 | −1.26016 | −0.630080 | − | 0.776530i | \(-0.716978\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(992\) | 9.62130e14 | 0.0317994 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.21135e16 | 1.04969 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.76003e13 | −0.00185183 | −0.000925915 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000925915 | 1.00000i | \(0.500295\pi\) | ||||||||
\(998\) | 4.68943e16 | 1.49935 | ||||||||
\(999\) | 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 | 225.12.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 75.12.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.12.b.a.199.2 | 2 | |||
5.3 | odd | 4 | 225.12.b.a.199.1 | 2 | |||
5.4 | even | 2 | 9.12.a.a.1.1 | 1 | |||
15.2 | even | 4 | 75.12.b.a.49.1 | 2 | |||
15.8 | even | 4 | 75.12.b.a.49.2 | 2 | |||
15.14 | odd | 2 | 3.12.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 144.12.a.l.1.1 | 1 | |||
45.4 | even | 6 | 81.12.c.e.55.1 | 2 | |||
45.14 | odd | 6 | 81.12.c.a.55.1 | 2 | |||
45.29 | odd | 6 | 81.12.c.a.28.1 | 2 | |||
45.34 | even | 6 | 81.12.c.e.28.1 | 2 | |||
60.59 | even | 2 | 48.12.a.f.1.1 | 1 | |||
105.104 | even | 2 | 147.12.a.c.1.1 | 1 | |||
120.29 | odd | 2 | 192.12.a.q.1.1 | 1 | |||
120.59 | even | 2 | 192.12.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.12.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
9.12.a.a.1.1 | 1 | 5.4 | even | 2 | |||
48.12.a.f.1.1 | 1 | 60.59 | even | 2 | |||
75.12.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
75.12.b.a.49.1 | 2 | 15.2 | even | 4 | |||
75.12.b.a.49.2 | 2 | 15.8 | even | 4 | |||
81.12.c.a.28.1 | 2 | 45.29 | odd | 6 | |||
81.12.c.a.55.1 | 2 | 45.14 | odd | 6 | |||
81.12.c.e.28.1 | 2 | 45.34 | even | 6 | |||
81.12.c.e.55.1 | 2 | 45.4 | even | 6 | |||
144.12.a.l.1.1 | 1 | 20.19 | odd | 2 | |||
147.12.a.c.1.1 | 1 | 105.104 | even | 2 | |||
192.12.a.g.1.1 | 1 | 120.59 | even | 2 | |||
192.12.a.q.1.1 | 1 | 120.29 | odd | 2 | |||
225.12.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.12.b.a.199.1 | 2 | 5.3 | odd | 4 | |||
225.12.b.a.199.2 | 2 | 5.2 | odd | 4 |