Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,12,Mod(1,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, 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("20.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.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: | \(15.3668636112\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46729}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 11682 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-107.584\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.1 |
$q$-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 | ||||||||
\(3\) | 542.338 | 1.28856 | 0.644278 | − | 0.764792i | \(-0.277158\pi\) | ||||
0.644278 | + | 0.764792i | \(0.277158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3125.00 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49659.5 | 1.11677 | 0.558384 | − | 0.829582i | \(-0.311422\pi\) | ||||
0.558384 | + | 0.829582i | \(0.311422\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 116983. | 0.660374 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19451.8 | −0.0364166 | −0.0182083 | − | 0.999834i | \(-0.505796\pi\) | ||||
−0.0182083 | + | 0.999834i | \(0.505796\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −759548. | −0.567371 | −0.283685 | − | 0.958917i | \(-0.591557\pi\) | ||||
−0.283685 | + | 0.958917i | \(0.591557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.69481e6 | 0.576259 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.35438e6 | 0.402167 | 0.201084 | − | 0.979574i | \(-0.435554\pi\) | ||||
0.201084 | + | 0.979574i | \(0.435554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.62826e7 | 1.50861 | 0.754307 | − | 0.656522i | \(-0.227973\pi\) | ||||
0.754307 | + | 0.656522i | \(0.227973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.69322e7 | 1.43902 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.07894e7 | 0.997466 | 0.498733 | − | 0.866756i | \(-0.333799\pi\) | ||||
0.498733 | + | 0.866756i | \(0.333799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.26290e7 | −0.437626 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.24708e8 | −1.12903 | −0.564514 | − | 0.825424i | \(-0.690936\pi\) | ||||
−0.564514 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.87600e8 | 1.80426 | 0.902130 | − | 0.431464i | \(-0.142003\pi\) | ||||
0.902130 | + | 0.431464i | \(0.142003\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.05494e7 | −0.0469248 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.55186e8 | 0.499434 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.80788e8 | −1.61400 | −0.806998 | − | 0.590554i | \(-0.798909\pi\) | ||||
−0.806998 | + | 0.590554i | \(0.798909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.11932e8 | −0.731088 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.20702e7 | −0.0432305 | −0.0216152 | − | 0.999766i | \(-0.506881\pi\) | ||||
−0.0216152 | + | 0.999766i | \(0.506881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.32076e9 | −1.37008 | −0.685040 | − | 0.728505i | \(-0.740215\pi\) | ||||
−0.685040 | + | 0.728505i | \(0.740215\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.65573e8 | 0.295328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20253e9 | −1.40082 | −0.700411 | − | 0.713740i | \(-0.747000\pi\) | ||||
−0.700411 | + | 0.713740i | \(0.747000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.88739e8 | 0.247172 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.27687e9 | 0.518215 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.55551e9 | 1.49630 | 0.748151 | − | 0.663528i | \(-0.230942\pi\) | ||||
0.748151 | + | 0.663528i | \(0.230942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.07867e7 | −0.0162860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.83065e9 | 1.94393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.70865e9 | −0.311148 | −0.155574 | − | 0.987824i | \(-0.549723\pi\) | ||||
−0.155574 | + | 0.987824i | \(0.549723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.50342e9 | −0.985888 | −0.492944 | − | 0.870061i | \(-0.664079\pi\) | ||||
−0.492944 | + | 0.870061i | \(0.664079\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.80933e9 | 0.737485 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.37359e9 | −0.253736 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.87165e7 | 0.00621798 | 0.00310899 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00310899 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.66983e10 | 1.28529 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.55089e10 | −1.67792 | −0.838958 | − | 0.544196i | \(-0.816835\pi\) | ||||
−0.838958 | + | 0.544196i | \(0.816835\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.19267e10 | 0.673358 | 0.336679 | − | 0.941620i | \(-0.390696\pi\) | ||||
0.336679 | + | 0.941620i | \(0.390696\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.29627e9 | 0.257711 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.65964e8 | −0.0406689 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.68170e9 | −0.354000 | −0.177000 | − | 0.984211i | \(-0.556639\pi\) | ||||
−0.177000 | + | 0.984211i | \(0.556639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.84192e10 | −1.22428 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.07710e10 | −0.300142 | −0.150071 | − | 0.988675i | \(-0.547950\pi\) | ||||
−0.150071 | + | 0.988675i | \(0.547950\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.35742e9 | 0.179855 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.76338e10 | −1.45481 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.08101e10 | −1.34416 | −0.672079 | − | 0.740480i | \(-0.734598\pi\) | ||||
−0.672079 | + | 0.740480i | \(0.734598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.77188e10 | −0.633622 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.55976e11 | 2.32489 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.08830e10 | 0.674673 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.53217e10 | −0.181160 | −0.0905800 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905800 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.27553e9 | −0.0240486 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.01154e11 | 1.90441 | 0.952207 | − | 0.305453i | \(-0.0988078\pi\) | ||||
0.952207 | + | 0.305453i | \(0.0988078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.24282e11 | 1.05634 | 0.528168 | − | 0.849140i | \(-0.322879\pi\) | ||||
0.528168 | + | 0.849140i | \(0.322879\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.41632e10 | 0.643548 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.78965e11 | −1.23355 | −0.616774 | − | 0.787140i | \(-0.711561\pi\) | ||||
−0.616774 | + | 0.787140i | \(0.711561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.15715e10 | 0.507800 | 0.253900 | − | 0.967230i | \(-0.418287\pi\) | ||||
0.253900 | + | 0.967230i | \(0.418287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.69217e11 | −2.07972 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.55934e11 | 1.30676 | 0.653381 | − | 0.757029i | \(-0.273350\pi\) | ||||
0.653381 | + | 0.757029i | \(0.273350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.62169e10 | 0.446080 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.88545e10 | −0.374677 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.16917e11 | 0.449128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.84933e11 | −0.998674 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.73929e10 | −0.0557048 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.05176e10 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.21115e11 | 0.862461 | 0.431231 | − | 0.902242i | \(-0.358080\pi\) | ||||
0.431231 | + | 0.902242i | \(0.358080\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.16296e11 | −1.76542 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.42126e11 | −1.45421 | −0.727107 | − | 0.686524i | \(-0.759136\pi\) | ||||
−0.727107 | + | 0.686524i | \(0.759136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.08584e11 | 1.68477 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.01966e11 | −0.195713 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.79216e11 | −0.848336 | −0.424168 | − | 0.905583i | \(-0.639433\pi\) | ||||
−0.424168 | + | 0.905583i | \(0.639433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.77838e11 | 1.10801 | 0.554006 | − | 0.832513i | \(-0.313099\pi\) | ||||
0.554006 | + | 0.832513i | \(0.313099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.19451e12 | −1.80504 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.47745e10 | 0.0206617 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.89712e11 | −0.504917 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.65062e11 | 0.318494 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.05810e11 | −0.787342 | −0.393671 | − | 0.919251i | \(-0.628795\pi\) | ||||
−0.393671 | + | 0.919251i | \(0.628795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.42190e11 | 0.665718 | 0.332859 | − | 0.942977i | \(-0.391987\pi\) | ||||
0.332859 | + | 0.942977i | \(0.391987\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.75423e11 | 0.265581 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.98749e11 | 0.806890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.25437e12 | 1.04949 | 0.524743 | − | 0.851261i | \(-0.324161\pi\) | ||||
0.524743 | + | 0.851261i | \(0.324161\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.47062e12 | 1.92807 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.52899e12 | 1.11394 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.85578e10 | −0.0398615 | −0.0199307 | − | 0.999801i | \(-0.506345\pi\) | ||||
−0.0199307 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.29669e10 | −0.0209854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.63528e12 | −0.974206 | −0.487103 | − | 0.873344i | \(-0.661946\pi\) | ||||
−0.487103 | + | 0.873344i | \(0.661946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.21525e12 | −0.678090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.90479e12 | 0.996250 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.99007e12 | −0.976371 | −0.488186 | − | 0.872740i | \(-0.662341\pi\) | ||||
−0.488186 | + | 0.872740i | \(0.662341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.84956e11 | 0.223354 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.26664e11 | −0.400931 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.71716e12 | −1.10515 | −0.552577 | − | 0.833462i | \(-0.686356\pi\) | ||||
−0.552577 | + | 0.833462i | \(0.686356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.72114e12 | 1.04116 | 0.520582 | − | 0.853812i | \(-0.325715\pi\) | ||||
0.520582 | + | 0.853812i | \(0.325715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.52705e12 | −1.27037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.12746e12 | −0.721801 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.57967e10 | −0.0146455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62034e12 | −0.488727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.22323e12 | 0.632850 | 0.316425 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316425 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.75455e11 | 0.100924 | 0.0504618 | − | 0.998726i | \(-0.483931\pi\) | ||||
0.0504618 | + | 0.998726i | \(0.483931\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.28729e12 | −0.326953 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.51030e11 | −0.0842907 | −0.0421453 | − | 0.999111i | \(-0.513419\pi\) | ||||
−0.0421453 | + | 0.999111i | \(0.513419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.02056e12 | 0.913260 | 0.456630 | − | 0.889657i | \(-0.349056\pi\) | ||||
0.456630 | + | 0.889657i | \(0.349056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.72675e10 | 0.00801221 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.19293e12 | −1.26086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00219e11 | −0.0193333 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.60185e12 | 0.658701 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.16725e11 | −0.0549386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.85562e11 | 0.0963872 | 0.0481936 | − | 0.998838i | \(-0.484654\pi\) | ||||
0.0481936 | + | 0.998838i | \(0.484654\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.38344e13 | −2.16209 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.12736e12 | −0.612719 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42821e13 | 2.01494 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.46832e12 | 0.867659 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.78826e12 | −0.228178 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.67568e12 | 0.932052 | 0.466026 | − | 0.884771i | \(-0.345685\pi\) | ||||
0.466026 | + | 0.884771i | \(0.345685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.14242e12 | 0.132075 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.03622e12 | 0.884931 | 0.442466 | − | 0.896785i | \(-0.354104\pi\) | ||||
0.442466 | + | 0.896785i | \(0.354104\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.30248e13 | 1.36671 | 0.683354 | − | 0.730087i | \(-0.260521\pi\) | ||||
0.683354 | + | 0.730087i | \(0.260521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.23879e11 | −0.0524041 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.09159e13 | 1.04136 | 0.520680 | − | 0.853752i | \(-0.325678\pi\) | ||||
0.520680 | + | 0.853752i | \(0.325678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88289e12 | −0.626467 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.25075e12 | −0.456148 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.18735e13 | −0.984895 | −0.492447 | − | 0.870342i | \(-0.663898\pi\) | ||||
−0.492447 | + | 0.870342i | \(0.663898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.34520e13 | 1.85818 | 0.929088 | − | 0.369859i | \(-0.120594\pi\) | ||||
0.929088 | + | 0.369859i | \(0.120594\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.50561e13 | −1.13993 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.52731e12 | 0.110539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23674e13 | −0.855944 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.84153e12 | −0.386750 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.53634e13 | −0.973378 | −0.486689 | − | 0.873575i | \(-0.661796\pi\) | ||||
−0.486689 | + | 0.873575i | \(0.661796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.98908e11 | −0.0363243 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.99021e12 | 0.231753 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.42146e12 | −0.190362 | −0.0951809 | − | 0.995460i | \(-0.530343\pi\) | ||||
−0.0951809 | + | 0.995460i | \(0.530343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.38076e13 | −1.80246 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.45887e13 | −0.745581 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.19978e13 | 0.587954 | 0.293977 | − | 0.955812i | \(-0.405021\pi\) | ||||
0.293977 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.42360e13 | 0.669167 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.84030e13 | −1.73202 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.54949e13 | 0.670734 | 0.335367 | − | 0.942088i | \(-0.391140\pi\) | ||||
0.335367 | + | 0.942088i | \(0.391140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.54301e13 | 1.05686 | 0.528430 | − | 0.848977i | \(-0.322781\pi\) | ||||
0.528430 | + | 0.848977i | \(0.322781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.04563e13 | −0.816456 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.89959e11 | −0.00728331 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.18585e12 | 0.0805345 | 0.0402672 | − | 0.999189i | \(-0.487179\pi\) | ||||
0.0402672 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.36444e13 | 1.19149 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.08522e13 | −0.710013 | −0.355007 | − | 0.934864i | \(-0.615521\pi\) | ||||
−0.355007 | + | 0.934864i | \(0.615521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.16150e13 | 1.69025 | 0.845124 | − | 0.534570i | \(-0.179526\pi\) | ||||
0.845124 | + | 0.534570i | \(0.179526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.75958e13 | 0.869353 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.59259e12 | −0.0482784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.87288e13 | −0.838262 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.30953e12 | −0.233435 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.44670e13 | 0.391387 | 0.195693 | − | 0.980665i | \(-0.437304\pi\) | ||||
0.195693 | + | 0.980665i | \(0.437304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.33952e12 | −0.139149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.34692e11 | 0.0159369 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.33860e13 | −0.565933 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.55881e13 | −1.53006 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.09094e14 | 2.45394 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.03232e13 | −0.440902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.67889e13 | −0.351368 | −0.175684 | − | 0.984447i | \(-0.556214\pi\) | ||||
−0.175684 | + | 0.984447i | \(0.556214\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.74026e13 | 1.36115 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98233e13 | 0.386361 | 0.193181 | − | 0.981163i | \(-0.438120\pi\) | ||||
0.193181 | + | 0.981163i | \(0.438120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.94059e13 | 0.365123 | 0.182561 | − | 0.983194i | \(-0.441561\pi\) | ||||
0.182561 | + | 0.983194i | \(0.441561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.81542e13 | 0.329813 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.63212e13 | 1.69004 | 0.845018 | − | 0.534737i | \(-0.179589\pi\) | ||||
0.845018 | + | 0.534737i | \(0.179589\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.42579e12 | 0.0411153 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.70592e13 | −1.58949 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.83353e13 | 0.606715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.41746e12 | −0.113474 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.42393e13 | 0.654328 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.09376e14 | −1.56439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.14888e14 | −1.58936 | −0.794679 | − | 0.607030i | \(-0.792361\pi\) | ||||
−0.794679 | + | 0.607030i | \(0.792361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.96409e13 | −1.06584 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.14739e11 | 0.00278077 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.51535e13 | −1.19251 | −0.596253 | − | 0.802797i | \(-0.703344\pi\) | ||||
−0.596253 | + | 0.802797i | \(0.703344\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.38803e14 | 1.68383 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.59432e12 | −0.0657050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.39225e13 | −0.840735 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.21821e13 | 0.574799 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.79048e14 | −1.91054 | −0.955272 | − | 0.295727i | \(-0.904438\pi\) | ||||
−0.955272 | + | 0.295727i | \(0.904438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.42818e14 | −1.47654 | −0.738268 | − | 0.674507i | \(-0.764356\pi\) | ||||
−0.738268 | + | 0.674507i | \(0.764356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.47833e13 | 0.248296 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.34518e13 | 0.810354 | 0.405177 | − | 0.914238i | \(-0.367210\pi\) | ||||
0.405177 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.97152e13 | −0.750387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.34086e13 | 0.578726 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.10422e14 | 0.977322 | 0.488661 | − | 0.872474i | \(-0.337486\pi\) | ||||
0.488661 | + | 0.872474i | \(0.337486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.48632e14 | 1.27592 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.54530e14 | −1.28685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.72711e13 | 0.301135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.35584e13 | 0.498322 | 0.249161 | − | 0.968462i | \(-0.419845\pi\) | ||||
0.249161 | + | 0.968462i | \(0.419845\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.75167e12 | −0.0285483 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.26224e14 | 1.67102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.93761e13 | 0.497521 | 0.248760 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248760 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.65508e13 | 0.115252 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.47216e13 | 0.640577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.64902e13 | −0.502447 | −0.251224 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251224 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.74153e14 | 1.11133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.21465e14 | 0.753110 | 0.376555 | − | 0.926394i | \(-0.377109\pi\) | ||||
0.376555 | + | 0.926394i | \(0.377109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.01864e12 | −0.0181877 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.54506e14 | −0.904766 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.85195e14 | −1.62338 | −0.811688 | − | 0.584092i | \(-0.801451\pi\) | ||||
−0.811688 | + | 0.584092i | \(0.801451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.24898e13 | 0.401148 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.48249e14 | −1.87383 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.02553e13 | −0.158313 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.43169e14 | 0.728618 | 0.364309 | − | 0.931278i | \(-0.381305\pi\) | ||||
0.364309 | + | 0.931278i | \(0.381305\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.38526e14 | 2.17092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.83730e14 | 1.84812 | 0.924062 | − | 0.382242i | \(-0.124848\pi\) | ||||
0.924062 | + | 0.382242i | \(0.124848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.18446e14 | −1.02368 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.20060e14 | −0.547515 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.32425e13 | 0.0587762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.42103e13 | −0.104598 | −0.0522988 | − | 0.998631i | \(-0.516655\pi\) | ||||
−0.0522988 | + | 0.998631i | \(0.516655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.59897e14 | −1.09313 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.48506e13 | −0.347480 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.36594e13 | −0.134228 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.67617e14 | 1.42773 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.87208e14 | 0.708187 | 0.354093 | − | 0.935210i | \(-0.384790\pi\) | ||||
0.354093 | + | 0.935210i | \(0.384790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.90015e14 | −1.06873 | −0.534366 | − | 0.845253i | \(-0.679449\pi\) | ||||
−0.534366 | + | 0.845253i | \(0.679449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.57659e14 | −0.925067 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.29919e13 | 0.0804334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.22956e14 | −1.10101 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.01279e12 | 0.0266237 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.21836e14 | −0.394595 | −0.197298 | − | 0.980344i | \(-0.563217\pi\) | ||||
−0.197298 | + | 0.980344i | \(0.563217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.62337e13 | −0.209120 | −0.104560 | − | 0.994519i | \(-0.533343\pi\) | ||||
−0.104560 | + | 0.994519i | \(0.533343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.11356e14 | −0.650613 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.01331e14 | 1.50479 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.40333e13 | −0.0410776 | −0.0205388 | − | 0.999789i | \(-0.506538\pi\) | ||||
−0.0205388 | + | 0.999789i | \(0.506538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71743e13 | 0.163226 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.34013e14 | −1.20860 | −0.604299 | − | 0.796758i | \(-0.706547\pi\) | ||||
−0.604299 | + | 0.796758i | \(0.706547\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.21282e14 | −0.601126 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.82788e14 | −1.01453 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.80839e14 | −0.984888 | −0.492444 | − | 0.870344i | \(-0.663896\pi\) | ||||
−0.492444 | + | 0.870344i | \(0.663896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.23821e11 | 0.00157431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.48284e14 | 0.857814 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.17871e14 | −0.283364 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.71367e14 | 1.10617 | 0.553083 | − | 0.833126i | \(-0.313451\pi\) | ||||
0.553083 | + | 0.833126i | \(0.313451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.68210e13 | −0.175999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.27142e14 | −0.731782 | −0.365891 | − | 0.930658i | \(-0.619236\pi\) | ||||
−0.365891 | + | 0.930658i | \(0.619236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.66836e14 | 1.01969 | 0.509846 | − | 0.860266i | \(-0.329702\pi\) | ||||
0.509846 | + | 0.860266i | \(0.329702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87426e14 | 1.03972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.78595e13 | −0.0580404 | −0.0290202 | − | 0.999579i | \(-0.509239\pi\) | ||||
−0.0290202 | + | 0.999579i | \(0.509239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.41243e12 | 0.00694404 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.80291e14 | 1.35232 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.56910e13 | 0.0498936 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.59009e14 | 0.301723 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.32918e14 | 0.988120 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.05624e14 | 1.09738 | 0.548691 | − | 0.836025i | \(-0.315126\pi\) | ||||
0.548691 | + | 0.836025i | \(0.315126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17092e14 | 0.915734 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.29227e14 | 1.43537 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.78803e13 | −0.0810172 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.89431e14 | −1.30588 | −0.652942 | − | 0.757408i | \(-0.726466\pi\) | ||||
−0.652942 | + | 0.757408i | \(0.726466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.17581e13 | −0.0513637 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.81410e14 | −0.286889 | −0.143444 | − | 0.989658i | \(-0.545818\pi\) | ||||
−0.143444 | + | 0.989658i | \(0.545818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.93609e14 | −0.454058 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.11103e12 | −0.0107548 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26676e15 | −1.87384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.89614e14 | 0.708436 | 0.354218 | − | 0.935163i | \(-0.384747\pi\) | ||||
0.354218 | + | 0.935163i | \(0.384747\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.86873e14 | −1.25532 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.37938e14 | 0.329488 | 0.164744 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164744 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.28607e14 | 0.851680 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.59074e14 | −0.873757 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.23454e14 | −1.06830 | −0.534148 | − | 0.845391i | \(-0.679368\pi\) | ||||
−0.534148 | + | 0.845391i | \(0.679368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.92276e14 | 0.751985 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.31285e14 | −0.660210 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.88380e14 | 0.472408 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.28430e13 | 0.0510131 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.07929e15 | −1.25811 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.50125e14 | −1.08436 | −0.542180 | − | 0.840263i | \(-0.682401\pi\) | ||||
−0.542180 | + | 0.840263i | \(0.682401\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.61137e15 | 1.80067 | 0.900337 | − | 0.435194i | \(-0.143320\pi\) | ||||
0.900337 | + | 0.435194i | \(0.143320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.63010e14 | 0.287804 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.77118e14 | 0.725614 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.82246e12 | −0.00506130 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.99883e14 | −0.205474 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.43588e13 | 0.0245277 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.59264e14 | −0.551660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.47362e15 | −1.42405 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.50683e12 | −0.00900114 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.03512e15 | −0.960294 | −0.480147 | − | 0.877188i | \(-0.659417\pi\) | ||||
−0.480147 | + | 0.877188i | \(0.659417\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.47578e15 | 1.34160 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.54911e14 | 0.227095 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.24788e14 | 0.458198 | 0.229099 | − | 0.973403i | \(-0.426422\pi\) | ||||
0.229099 | + | 0.973403i | \(0.426422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.60791e14 | −0.651055 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.03056e15 | −1.70327 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.80789e14 | −0.395336 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.15380e15 | −0.930081 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.26339e15 | 1.78878 | 0.894388 | − | 0.447292i | \(-0.147612\pi\) | ||||
0.894388 | + | 0.447292i | \(0.147612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00318e15 | 0.777344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.48373e13 | −0.0188716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.47720e14 | 0.482604 | 0.241302 | − | 0.970450i | \(-0.422426\pi\) | ||||
0.241302 | + | 0.970450i | \(0.422426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.99794e14 | 0.584402 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.90788e15 | −1.36724 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.63615e14 | 0.185290 | 0.0926451 | − | 0.995699i | \(-0.470468\pi\) | ||||
0.0926451 | + | 0.995699i | \(0.470468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.94491e14 | −0.134091 | −0.0670457 | − | 0.997750i | \(-0.521357\pi\) | ||||
−0.0670457 | + | 0.997750i | \(0.521357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.20574e15 | 0.815461 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.00678e14 | 0.199493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.85826e14 | 0.511516 | 0.255758 | − | 0.966741i | \(-0.417675\pi\) | ||||
0.255758 | + | 0.966741i | \(0.417675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.03624e14 | 0.130046 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.34883e14 | −0.335189 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.86126e13 | −0.0544902 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.77670e14 | −0.167561 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.69825e15 | 1.00576 | 0.502878 | − | 0.864357i | \(-0.332274\pi\) | ||||
0.502878 | + | 0.864357i | \(0.332274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.68286e15 | 2.72193 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.90377e14 | −0.108613 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.57747e15 | −0.883406 | −0.441703 | − | 0.897161i | \(-0.645625\pi\) | ||||
−0.441703 | + | 0.897161i | \(0.645625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.65366e14 | 0.200856 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.18050e15 | 1.17679 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.36133e14 | 0.125115 | 0.0625573 | − | 0.998041i | \(-0.480074\pi\) | ||||
0.0625573 | + | 0.998041i | \(0.480074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.87143e15 | 1.49379 | 0.746893 | − | 0.664944i | \(-0.231545\pi\) | ||||
0.746893 | + | 0.664944i | \(0.231545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.03868e12 | 0.00410619 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.90417e14 | −0.446621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.22001e14 | −0.454144 | −0.227072 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227072 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.35866e15 | −1.62469 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.67292e15 | 0.794785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.25894e14 | −0.198732 | −0.0993662 | − | 0.995051i | \(-0.531682\pi\) | ||||
−0.0993662 | + | 0.995051i | \(0.531682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.43527e13 | −0.0249120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.66401e15 | −1.19941 | −0.599705 | − | 0.800221i | \(-0.704715\pi\) | ||||
−0.599705 | + | 0.800221i | \(0.704715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.71903e15 | −0.760301 | −0.380151 | − | 0.924925i | \(-0.624128\pi\) | ||||
−0.380151 | + | 0.924925i | \(0.624128\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00463e15 | −0.436518 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.51639e15 | −1.50111 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.71772e14 | −0.0707914 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.60283e15 | −0.649097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.92062e13 | −0.0195821 | −0.00979103 | − | 0.999952i | \(-0.503117\pi\) | ||||
−0.00979103 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.17572e14 | 0.124200 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00348e15 | 0.385704 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.71221e14 | −0.140238 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.98411e15 | −1.10805 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.72099e15 | 1.72311 | 0.861557 | − | 0.507661i | \(-0.169490\pi\) | ||||
0.861557 | + | 0.507661i | \(0.169490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.18915e15 | −1.14423 | −0.572117 | − | 0.820172i | \(-0.693878\pi\) | ||||
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.23842e15 | −0.789522 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.51792e15 | −0.873110 | −0.436555 | − | 0.899677i | \(-0.643802\pi\) | ||||
−0.436555 | + | 0.899677i | \(0.643802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.32362e13 | 0.0113309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.74570e15 | 2.59636 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.80457e15 | −1.25396 | −0.626979 | − | 0.779036i | \(-0.715709\pi\) | ||||
−0.626979 | + | 0.779036i | \(0.715709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00664e15 | −0.650344 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.39523e15 | 0.444668 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.23977e15 | 1.01542 | 0.507709 | − | 0.861529i | \(-0.330493\pi\) | ||||
0.507709 | + | 0.861529i | \(0.330493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.71166e15 | −0.835848 | −0.417924 | − | 0.908482i | \(-0.637242\pi\) | ||||
−0.417924 | + | 0.908482i | \(0.637242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.69842e14 | −0.294020 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.52683e15 | 0.753453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.83968e15 | −1.12617 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.16281e15 | 1.20100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.26503e14 | 0.0359026 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.62755e15 | 1.01282 | 0.506409 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506409 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.18643e14 | −0.0875253 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.05118e15 | 1.09482 | 0.547412 | − | 0.836863i | \(-0.315613\pi\) | ||||
0.547412 | + | 0.836863i | \(0.315613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.60868e14 | −0.202314 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.35835e15 | 1.14028 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.56724e15 | −1.17582 | −0.587908 | − | 0.808928i | \(-0.700048\pi\) | ||||
−0.587908 | + | 0.808928i | \(0.700048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.49755e15 | −0.379388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.06384e15 | 1.76108 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.46013e15 | −0.848958 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.26218e15 | −1.51215 | −0.756077 | − | 0.654482i | \(-0.772887\pi\) | ||||
−0.756077 | + | 0.654482i | \(0.772887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.13002e14 | −0.0268567 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.11824e15 | 0.495518 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.55052e13 | −0.0173859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.92009e15 | 1.34185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.12469e15 | −0.250949 | −0.125474 | − | 0.992097i | \(-0.540045\pi\) | ||||
−0.125474 | + | 0.992097i | \(0.540045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10850e16 | −2.43490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.73285e15 | −0.807237 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.98922e15 | 2.12679 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.16576e15 | 0.873253 | 0.436626 | − | 0.899643i | \(-0.356173\pi\) | ||||
0.436626 | + | 0.899643i | \(0.356173\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.13260e15 | −0.233772 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.85503e15 | 1.79969 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.61705e13 | 0.00924019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.43944e15 | −1.26909 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.31711e14 | −0.161422 | −0.0807111 | − | 0.996738i | \(-0.525719\pi\) | ||||
−0.0807111 | + | 0.996738i | \(0.525719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.17176e15 | 1.17968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.27189e16 | 2.39436 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.21785e15 | −0.225806 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.54083e15 | 0.281395 | 0.140697 | − | 0.990053i | \(-0.455066\pi\) | ||||
0.140697 | + | 0.990053i | \(0.455066\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.35962e15 | −0.244577 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.10956e15 | −0.551001 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.81955e14 | 0.0841268 | 0.0420634 | − | 0.999115i | \(-0.486607\pi\) | ||||
0.0420634 | + | 0.999115i | \(0.486607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.28318e14 | 0.142435 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.33666e12 | −0.000226438 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.56414e15 | −0.261055 | −0.130528 | − | 0.991445i | \(-0.541667\pi\) | ||||
−0.130528 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.70731e15 | −1.10293 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.48466e14 | −0.0888610 | −0.0444305 | − | 0.999012i | \(-0.514147\pi\) | ||||
−0.0444305 | + | 0.999012i | \(0.514147\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.20566e15 | −0.352110 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.26003e15 | −0.198206 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.88729e15 | −1.37759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.51331e15 | −1.45315 | −0.726577 | − | 0.687085i | \(-0.758890\pi\) | ||||
−0.726577 | + | 0.687085i | \(0.758890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.33215e15 | −1.25425 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.00684e15 | 0.297718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.27757e15 | −0.917834 | −0.458917 | − | 0.888479i | \(-0.651762\pi\) | ||||
−0.458917 | + | 0.888479i | \(0.651762\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.24810e14 | −0.0468059 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.56418e15 | −0.364193 | −0.182097 | − | 0.983281i | \(-0.558288\pi\) | ||||
−0.182097 | + | 0.983281i | \(0.558288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.05080e15 | 0.567095 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.60696e14 | 0.118771 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.29780e15 | 0.176536 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.83938e14 | 0.0783018 | 0.0391509 | − | 0.999233i | \(-0.487535\pi\) | ||||
0.0391509 | + | 0.999233i | \(0.487535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.85559e15 | −0.245292 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.35645e15 | 0.307094 | 0.153547 | − | 0.988141i | \(-0.450930\pi\) | ||||
0.153547 | + | 0.988141i | \(0.450930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.80859e15 | 0.360852 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.83351e16 | −2.32257 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.22185e14 | −0.0652181 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.96192e14 | 0.0611040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.06910e15 | 0.494093 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.91990e15 | 0.469344 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.54576e15 | −0.418647 | −0.209324 | − | 0.977846i | \(-0.567126\pi\) | ||||
−0.209324 | + | 0.977846i | \(0.567126\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.50684e15 | 0.757612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.27096e16 | 1.45935 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.93966e15 | 0.559364 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.72070e15 | 0.862259 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.80052e15 | 0.528771 | 0.264385 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264385 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.18557e15 | −0.563365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.28360e15 | −0.887647 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.31996e14 | −0.0245214 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.77808e15 | 0.498169 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.40345e15 | 0.864278 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.91609e14 | −0.0397316 | −0.0198658 | − | 0.999803i | \(-0.506324\pi\) | ||||
−0.0198658 | + | 0.999803i | \(0.506324\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.86491e15 | 0.587012 | 0.293506 | − | 0.955957i | \(-0.405178\pi\) | ||||
0.293506 | + | 0.955957i | \(0.405178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.37917e16 | 1.36182 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.82993e14 | −0.0178266 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.15053e16 | −2.06692 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.41247e15 | −0.418427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.66455e15 | −0.155743 | −0.0778715 | − | 0.996963i | \(-0.524812\pi\) | ||||
−0.0778715 | + | 0.996963i | \(0.524812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.67289e16 | 1.54443 | 0.772216 | − | 0.635360i | \(-0.219148\pi\) | ||||
0.772216 | + | 0.635360i | \(0.219148\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.03022e14 | −0.00938495 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.91438e16 | 1.72087 | 0.860435 | − | 0.509560i | \(-0.170192\pi\) | ||||
0.860435 | + | 0.509560i | \(0.170192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.02576e16 | 0.909906 | 0.454953 | − | 0.890515i | \(-0.349656\pi\) | ||||
0.454953 | + | 0.890515i | \(0.349656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.18547e15 | 0.103773 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.15068e15 | 0.0994043 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.11024e15 | −0.435678 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.38411e15 | −0.789592 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.89422e16 | −1.57304 | −0.786519 | − | 0.617566i | \(-0.788119\pi\) | ||||
−0.786519 | + | 0.617566i | \(0.788119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.35153e15 | 0.274704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.13089e16 | −0.914891 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.79765e15 | −0.303251 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41496e16 | −1.11529 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.79928e16 | 2.17798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.09611e16 | −1.60991 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.33491e16 | 1.01212 | 0.506059 | − | 0.862499i | \(-0.331102\pi\) | ||||
0.506059 | + | 0.862499i | \(0.331102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.95247e15 | 0.445537 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.46363e16 | 1.82046 | 0.910231 | − | 0.414101i | \(-0.135904\pi\) | ||||
0.910231 | + | 0.414101i | \(0.135904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.13423e16 | −1.55696 | −0.778482 | − | 0.627668i | \(-0.784010\pi\) | ||||
−0.778482 | + | 0.627668i | \(0.784010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.63721e14 | −0.0622094 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.98852e15 | 0.710300 | 0.355150 | − | 0.934809i | \(-0.384430\pi\) | ||||
0.355150 | + | 0.934809i | \(0.384430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.21897e15 | −0.436646 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.55807e16 | −1.08015 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.88326e14 | 0.0128915 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.21935e13 | −0.00352790 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.79238e15 | −0.119633 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.51549e15 | 0.0998868 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.31195e16 | 1.50480 | 0.752402 | − | 0.658705i | \(-0.228895\pi\) | ||||
0.752402 | + | 0.658705i | \(0.228895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.84599e15 | 0.504323 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.73216e16 | −1.73436 | −0.867180 | − | 0.497995i | \(-0.834070\pi\) | ||||
−0.867180 | + | 0.497995i | \(0.834070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.06010e16 | −0.664604 | −0.332302 | − | 0.943173i | \(-0.607825\pi\) | ||||
−0.332302 | + | 0.943173i | \(0.607825\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.89583e15 | −0.179302 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.11039e16 | 1.29058 | 0.645288 | − | 0.763939i | \(-0.276737\pi\) | ||||
0.645288 | + | 0.763939i | \(0.276737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.59464e16 | 0.963170 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.47321e14 | 0.0445841 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.58628e16 | −2.11330 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.49112e15 | −0.494240 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.26831e16 | −0.729236 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.58659e16 | −2.03706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.07254e16 | 0.601764 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.55709e16 | −1.97157 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.50357e15 | 0.465623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.86803e15 | 0.371528 | 0.185764 | − | 0.982594i | \(-0.440524\pi\) | ||||
0.185764 | + | 0.982594i | \(0.440524\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.35317e16 | 1.25763 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.56797e15 | −0.241197 | −0.120599 | − | 0.992701i | \(-0.538481\pi\) | ||||
−0.120599 | + | 0.992701i | \(0.538481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09515e14 | 0.0109301 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.10220e16 | −0.568127 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.18877e16 | −1.62402 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.45493e16 | 1.23539 | 0.617695 | − | 0.786418i | \(-0.288067\pi\) | ||||
0.617695 | + | 0.786418i | \(0.288067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.10527e15 | −0.452757 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.93752e16 | 0.952001 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.64832e15 | −0.322799 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.45389e16 | 0.697577 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.63221e16 | −0.773909 | −0.386954 | − | 0.922099i | \(-0.626473\pi\) | ||||
−0.386954 | + | 0.922099i | \(0.626473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.95793e15 | 0.372887 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.07509e16 | 0.497848 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.43115e14 | −0.00654969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.76542e15 | 0.441696 | 0.220848 | − | 0.975308i | \(-0.429118\pi\) | ||||
0.220848 | + | 0.975308i | \(0.429118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.05245e16 | 0.470481 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.42567e16 | 1.95540 | 0.977702 | − | 0.209999i | \(-0.0673460\pi\) | ||||
0.977702 | + | 0.209999i | \(0.0673460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.87421e14 | −0.0431209 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.06357e15 | −0.218566 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.15494e16 | 0.919412 | 0.459706 | − | 0.888071i | \(-0.347955\pi\) | ||||
0.459706 | + | 0.888071i | \(0.347955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.05893e15 | −0.382044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.22386e16 | 2.17771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.05469e16 | −1.25880 | −0.629399 | − | 0.777083i | \(-0.716699\pi\) | ||||
−0.629399 | + | 0.777083i | \(0.716699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.94759e15 | 0.283019 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.31560e15 | 0.0529794 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.37976e16 | −0.947395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.73052e16 | 2.25536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.09359e16 | −0.814604 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.17330e15 | 0.0451344 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.67248e15 | −0.101641 | −0.0508204 | − | 0.998708i | \(-0.516184\pi\) | ||||
−0.0508204 | + | 0.998708i | \(0.516184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.07907e16 | 0.781786 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.05715e16 | 0.393036 | 0.196518 | − | 0.980500i | \(-0.437037\pi\) | ||||
0.196518 | + | 0.980500i | \(0.437037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.36611e16 | 1.23739 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.02277e15 | −0.146218 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.22544e16 | 0.799826 | 0.399913 | − | 0.916553i | \(-0.369040\pi\) | ||||
0.399913 | + | 0.916553i | \(0.369040\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.37738e15 | 0.0489496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.54251e15 | 0.335338 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.53819e15 | −0.192453 | −0.0962263 | − | 0.995359i | \(-0.530677\pi\) | ||||
−0.0962263 | + | 0.995359i | \(0.530677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.09697e15 | −0.0376959 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.93189e16 | −2.01581 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.06653e16 | −1.36661 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.34700e16 | −0.780024 | −0.390012 | − | 0.920810i | \(-0.627529\pi\) | ||||
−0.390012 | + | 0.920810i | \(0.627529\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.23082e16 | −2.04798 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.25642e16 | 0.408422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.95725e16 | −1.91524 | −0.957618 | − | 0.288041i | \(-0.906996\pi\) | ||||
−0.957618 | + | 0.288041i | \(0.906996\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.22135e16 | 0.706328 |
(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 | 20.12.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 180.12.a.c.1.2 | 2 | |||
4.3 | odd | 2 | 80.12.a.i.1.1 | 2 | |||
5.2 | odd | 4 | 100.12.c.c.49.1 | 4 | |||
5.3 | odd | 4 | 100.12.c.c.49.4 | 4 | |||
5.4 | even | 2 | 100.12.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.12.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
80.12.a.i.1.1 | 2 | 4.3 | odd | 2 | |||
100.12.a.c.1.1 | 2 | 5.4 | even | 2 | |||
100.12.c.c.49.1 | 4 | 5.2 | odd | 4 | |||
100.12.c.c.49.4 | 4 | 5.3 | odd | 4 | |||
180.12.a.c.1.2 | 2 | 3.2 | odd | 2 |