Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,16,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(22.8309608160\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | −6252.00 | −1.65048 | −0.825239 | − | 0.564784i | \(-0.808959\pi\) | ||||
−0.825239 | + | 0.564784i | \(0.808959\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 90510.0 | 0.518109 | 0.259055 | − | 0.965863i | \(-0.416589\pi\) | ||||
0.259055 | + | 0.965863i | \(0.416589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −56.0000 | −2.57012e−5 0 | −1.28506e−5 | − | 1.00000i | \(-0.500004\pi\) | ||||
−1.28506e−5 | 1.00000i | \(0.500004\pi\) | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47386e7 | 1.72408 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.58899e7 | 1.48364 | 0.741819 | − | 0.670600i | \(-0.233963\pi\) | ||||
0.741819 | + | 0.670600i | \(0.233963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.97821e7 | −0.264239 | −0.132119 | − | 0.991234i | \(-0.542178\pi\) | ||||
−0.132119 | + | 0.991234i | \(0.542178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.65869e8 | −0.855128 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.35581e9 | −0.801370 | −0.400685 | − | 0.916216i | \(-0.631228\pi\) | ||||
−0.400685 | + | 0.916216i | \(0.631228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.78359e9 | −0.971074 | −0.485537 | − | 0.874216i | \(-0.661376\pi\) | ||||
−0.485537 | + | 0.874216i | \(0.661376\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 350112. | 4.24192e−5 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.16088e10 | 0.710936 | 0.355468 | − | 0.934689i | \(-0.384322\pi\) | ||||
0.355468 | + | 0.934689i | \(0.384322\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.23255e10 | −0.731563 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.49563e10 | −1.19507 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89591e10 | −0.311745 | −0.155873 | − | 0.987777i | \(-0.549819\pi\) | ||||
−0.155873 | + | 0.987777i | \(0.549819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.53685e11 | −1.65609 | −0.828043 | − | 0.560665i | \(-0.810546\pi\) | ||||
−0.828043 | + | 0.560665i | \(0.810546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.99504e11 | −2.44871 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.06856e6 | −1.33160e−5 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.17641e11 | 1.41596 | 0.707978 | − | 0.706234i | \(-0.249607\pi\) | ||||
0.707978 | + | 0.706234i | \(0.249607\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.73758e11 | 0.436120 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.82333e11 | −0.547164 | −0.273582 | − | 0.961849i | \(-0.588209\pi\) | ||||
−0.273582 | + | 0.961849i | \(0.588209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.66946e11 | −0.205868 | −0.102934 | − | 0.994688i | \(-0.532823\pi\) | ||||
−0.102934 | + | 0.994688i | \(0.532823\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23909e12 | 0.893260 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.95742e11 | −0.200315 | −0.100158 | − | 0.994972i | \(-0.531935\pi\) | ||||
−0.100158 | + | 0.994972i | \(0.531935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.74756e12 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.47655e12 | 1.32264 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.29934e13 | 1.51933 | 0.759666 | − | 0.650313i | \(-0.225362\pi\) | ||||
0.759666 | + | 0.650313i | \(0.225362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.67900e12 | 0.768687 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.36550e13 | 1.60274 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.20904e12 | −0.481753 | −0.240876 | − | 0.970556i | \(-0.577435\pi\) | ||||
−0.240876 | + | 0.970556i | \(0.577435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.23386e13 | −1.72490 | −0.862448 | − | 0.506145i | \(-0.831070\pi\) | ||||
−0.862448 | + | 0.506145i | \(0.831070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.38536e9 | −4.43107e−5 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.41088e12 | −0.136905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00298e13 | −0.605329 | −0.302664 | − | 0.953097i | \(-0.597876\pi\) | ||||
−0.302664 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.25785e13 | −1.17338 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.15329e14 | −1.50487 | −0.752436 | − | 0.658665i | \(-0.771121\pi\) | ||||
−0.752436 | + | 0.658665i | \(0.771121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.37873e13 | 0.463903 | 0.231951 | − | 0.972727i | \(-0.425489\pi\) | ||||
0.231951 | + | 0.972727i | \(0.425489\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.39579e14 | 1.20743 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.36984e9 | −3.81312e−5 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96038e13 | −0.466370 | −0.233185 | − | 0.972432i | \(-0.574915\pi\) | ||||
−0.233185 | + | 0.972432i | \(0.574915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.11352e13 | 0.248360 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.41707e12 | 0.0138219 | 0.00691095 | − | 0.999976i | \(-0.497800\pi\) | ||||
0.00691095 | + | 0.999976i | \(0.497800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.22715e14 | −0.415198 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.81052e14 | 0.514529 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.77306e14 | −0.904209 | −0.452105 | − | 0.891965i | \(-0.649327\pi\) | ||||
−0.452105 | + | 0.891965i | \(0.649327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.34780e9 | 6.79124e−6 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.58604e15 | 2.73333 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.42453e14 | −0.503123 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.66982e14 | −0.209837 | −0.104919 | − | 0.994481i | \(-0.533458\pi\) | ||||
−0.104919 | + | 0.994481i | \(0.533458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.37218e15 | 2.55790 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.06802e13 | 0.0563167 | 0.0281583 | − | 0.999603i | \(-0.491036\pi\) | ||||
0.0281583 | + | 0.999603i | \(0.491036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.87676e14 | −0.470825 | −0.235412 | − | 0.971896i | \(-0.575644\pi\) | ||||
−0.235412 | + | 0.971896i | \(0.575644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.16886e10 | 2.19778e−5 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.56968e14 | −0.395518 | −0.197759 | − | 0.980251i | \(-0.563366\pi\) | ||||
−0.197759 | + | 0.980251i | \(0.563366\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.09023e15 | −1.09520 | −0.547602 | − | 0.836739i | \(-0.684459\pi\) | ||||
−0.547602 | + | 0.836739i | \(0.684459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.11189e15 | −2.33700 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.63296e15 | −0.652959 | −0.326480 | − | 0.945204i | \(-0.605862\pi\) | ||||
−0.326480 | + | 0.945204i | \(0.605862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.05072e15 | 0.368342 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.47893e15 | −0.455567 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.59256e10 | 2.05962e−5 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.01763e15 | 1.20118 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.26595e15 | 0.903082 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.78283e15 | −0.897139 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.51334e15 | −1.08462 | −0.542308 | − | 0.840180i | \(-0.682449\pi\) | ||||
−0.542308 | + | 0.840180i | \(0.682449\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.29414e15 | 0.339780 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.12636e16 | 1.48642 | 0.743212 | − | 0.669056i | \(-0.233301\pi\) | ||||
0.743212 | + | 0.669056i | \(0.233301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.11881e11 | 2.49577e−5 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.87920e15 | −0.619177 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.10328e15 | 0.481332 | 0.240666 | − | 0.970608i | \(-0.422634\pi\) | ||||
0.240666 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.76682e15 | −0.234083 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.34978e15 | 0.330616 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.73251e15 | −0.392034 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.62109e15 | −0.161518 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.96818e16 | 1.65048 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.68469e16 | 1.34896 | 0.674478 | − | 0.738295i | \(-0.264369\pi\) | ||||
0.674478 | + | 0.738295i | \(0.264369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.65479e16 | 1.66164 | 0.830818 | − | 0.556544i | \(-0.187873\pi\) | ||||
0.830818 | + | 0.556544i | \(0.187873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.35409e16 | −1.38162 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29611e16 | −0.858033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.99685e16 | 1.01723 | 0.508613 | − | 0.860995i | \(-0.330158\pi\) | ||||
0.508613 | + | 0.860995i | \(0.330158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.12346e16 | −2.50762 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.50095e11 | −1.82719e−5 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.29497e16 | 1.10041 | 0.550203 | − | 0.835031i | \(-0.314550\pi\) | ||||
0.550203 | + | 0.835031i | \(0.314550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.42611e16 | −1.26870 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.10064e15 | −0.151678 | −0.0758392 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758392 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.76120e16 | −0.930178 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.36008e16 | −1.67421 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.69309e16 | −0.933259 | −0.466629 | − | 0.884453i | \(-0.654532\pi\) | ||||
−0.466629 | + | 0.884453i | \(0.654532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.25023e12 | 1.88020e−5 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.75749e16 | 0.795122 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.65655e15 | 0.0337225 | 0.0168613 | − | 0.999858i | \(-0.494633\pi\) | ||||
0.0168613 | + | 0.999858i | \(0.494633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.17648e16 | 0.604569 | 0.302284 | − | 0.953218i | \(-0.402251\pi\) | ||||
0.302284 | + | 0.953218i | \(0.402251\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.64701e17 | 2.84690 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.40047e16 | 0.733620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.30009e17 | −1.18894 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.63756e12 | 3.07147e−5 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.36753e16 | −0.418817 | −0.209408 | − | 0.977828i | \(-0.567154\pi\) | ||||
−0.209408 | + | 0.977828i | \(0.567154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.14450e17 | 0.825913 | 0.412957 | − | 0.910751i | \(-0.364496\pi\) | ||||
0.412957 | + | 0.910751i | \(0.364496\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.38288e16 | 0.225958 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.07130e17 | −1.28158 | −0.640790 | − | 0.767716i | \(-0.721393\pi\) | ||||
−0.640790 | + | 0.767716i | \(0.721393\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.59838e16 | 0.206399 | 0.103200 | − | 0.994661i | \(-0.467092\pi\) | ||||
0.103200 | + | 0.994661i | \(0.467092\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.87746e17 | 0.999081 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.62171e12 | 8.01222e−6 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.17580e16 | −0.283491 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.87187e17 | 1.22571 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.62809e17 | −1.44072 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.02699e16 | −0.333753 | −0.166876 | − | 0.985978i | \(-0.553368\pi\) | ||||
−0.166876 | + | 0.985978i | \(0.553368\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.21035e17 | 2.48376 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.32122e16 | −0.106662 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42064e13 | 4.25633e−5 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.73758e17 | −0.765661 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.10535e16 | 0.211753 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.22894e17 | 0.788449 | 0.394225 | − | 0.919014i | \(-0.371013\pi\) | ||||
0.394225 | + | 0.919014i | \(0.371013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.52302e17 | −1.26127 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.84856e17 | −1.67724 | −0.838621 | − | 0.544715i | \(-0.816638\pi\) | ||||
−0.838621 | + | 0.544715i | \(0.816638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.84092e17 | −1.56892 | −0.784460 | − | 0.620180i | \(-0.787060\pi\) | ||||
−0.784460 | + | 0.620180i | \(0.787060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.35722e13 | 6.29347e−5 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.17048e17 | −1.26002 | −0.630012 | − | 0.776586i | \(-0.716950\pi\) | ||||
−0.630012 | + | 0.776586i | \(0.716950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.29716e16 | −0.103785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.97683e17 | 0.769733 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.93110e17 | −1.00651 | −0.503255 | − | 0.864138i | \(-0.667864\pi\) | ||||
−0.503255 | + | 0.864138i | \(0.667864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.65566e17 | 1.31721 | 0.658604 | − | 0.752490i | \(-0.271147\pi\) | ||||
0.658604 | + | 0.752490i | \(0.271147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.12355e17 | 0.785157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.29702e17 | −0.518109 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.26191e17 | 0.256595 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.13635e16 | −0.0228127 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.46641e17 | 0.851425 | 0.425712 | − | 0.904859i | \(-0.360024\pi\) | ||||
0.425712 | + | 0.904859i | \(0.360024\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.11317e18 | 1.05477 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.67213e17 | 0.685274 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.40156e18 | 1.18063 | 0.590314 | − | 0.807174i | \(-0.299004\pi\) | ||||
0.590314 | + | 0.807174i | \(0.299004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.57879e13 | −3.63917e−5 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.16408e17 | −0.537473 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.38804e18 | −0.983412 | −0.491706 | − | 0.870761i | \(-0.663626\pi\) | ||||
−0.491706 | + | 0.870761i | \(0.663626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.17603e18 | 0.787181 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.35892e18 | 1.49238 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.85472e18 | −1.70774 | −0.853870 | − | 0.520486i | \(-0.825751\pi\) | ||||
−0.853870 | + | 0.520486i | \(0.825751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.76158e18 | 0.996858 | 0.498429 | − | 0.866931i | \(-0.333910\pi\) | ||||
0.498429 | + | 0.866931i | \(0.333910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.09304e13 | −1.12088e−5 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.14079e18 | −1.08537 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.96897e17 | 0.190581 | 0.0952905 | − | 0.995450i | \(-0.469622\pi\) | ||||
0.0952905 | + | 0.995450i | \(0.469622\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.27582e18 | −2.85522 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.36756e17 | 0.145217 | 0.0726086 | − | 0.997361i | \(-0.476868\pi\) | ||||
0.0726086 | + | 0.997361i | \(0.476868\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.56529e18 | 1.86668 | 0.933340 | − | 0.358992i | \(-0.116880\pi\) | ||||
0.933340 | + | 0.358992i | \(0.116880\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.14102e18 | 0.830393 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.82107e13 | 1.40628e−5 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.02419e18 | −0.357805 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.04397e18 | 0.346331 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.51076e17 | 0.268201 | 0.134101 | − | 0.990968i | \(-0.457185\pi\) | ||||
0.134101 | + | 0.990968i | \(0.457185\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.33510e17 | −0.249601 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.22866e18 | −1.77305 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.94002e17 | −0.187857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.05490e13 | 5.29104e−6 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.79373e17 | −0.0929494 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.83207e18 | −0.893685 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.96999e18 | −0.881560 | −0.440780 | − | 0.897615i | \(-0.645298\pi\) | ||||
−0.440780 | + | 0.897615i | \(0.645298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.67415e18 | 0.777085 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.18666e18 | −0.642144 | −0.321072 | − | 0.947055i | \(-0.604043\pi\) | ||||
−0.321072 | + | 0.947055i | \(0.604043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.59866e18 | 0.307024 | 0.153512 | − | 0.988147i | \(-0.450942\pi\) | ||||
0.153512 | + | 0.988147i | \(0.450942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.25389e14 | −2.29578e−5 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.92262e18 | −0.859512 | −0.429756 | − | 0.902945i | \(-0.641400\pi\) | ||||
−0.429756 | + | 0.902945i | \(0.641400\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.77689e18 | −0.462517 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.10736e18 | 0.652793 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12985e18 | 0.778190 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.33467e18 | 0.193307 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.30681e19 | 1.80761 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.89615e13 | 5.14833e−6 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.42897e18 | 0.811767 | 0.405883 | − | 0.913925i | \(-0.366964\pi\) | ||||
0.405883 | + | 0.913925i | \(0.366964\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.02273e19 | 2.44122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.71800e18 | −0.313627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.44912e19 | 1.59912 | 0.799560 | − | 0.600586i | \(-0.205066\pi\) | ||||
0.799560 | + | 0.600586i | \(0.205066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.02092e19 | 1.07769 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.43259e19 | −2.45703 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.31727e14 | 5.14023e−5 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.56908e18 | −0.607941 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.11500e19 | −1.87430 | −0.937149 | − | 0.348929i | \(-0.886546\pi\) | ||||
−0.937149 | + | 0.348929i | \(0.886546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.04783e19 | −0.889409 | −0.444705 | − | 0.895677i | \(-0.646691\pi\) | ||||
−0.444705 | + | 0.895677i | \(0.646691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.88323e18 | 0.315784 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.39442e19 | 1.08663 | 0.543316 | − | 0.839528i | \(-0.317168\pi\) | ||||
0.543316 | + | 0.839528i | \(0.317168\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.04384e19 | −0.779689 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.74687e14 | −3.39935e−5 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.03027e19 | 0.707528 | 0.353764 | − | 0.935335i | \(-0.384902\pi\) | ||||
0.353764 | + | 0.935335i | \(0.384902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.65550e17 | −0.0570148 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.13702e19 | −1.98252 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.96319e18 | 0.240353 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.17900e19 | 0.686310 | 0.343155 | − | 0.939279i | \(-0.388504\pi\) | ||||
0.343155 | + | 0.939279i | \(0.388504\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.68800e19 | −0.943352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.27629e14 | −3.90486e−5 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.32551e19 | −1.71413 | −0.857063 | − | 0.515212i | \(-0.827713\pi\) | ||||
−0.857063 | + | 0.515212i | \(0.827713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.99022e19 | 1.48071 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.73124e18 | 0.0823752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.27237e18 | 0.286839 | 0.143419 | − | 0.989662i | \(-0.454190\pi\) | ||||
0.143419 | + | 0.989662i | \(0.454190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.07214e19 | 1.79013 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.27919e19 | −1.38604 | −0.693020 | − | 0.720918i | \(-0.743720\pi\) | ||||
−0.693020 | + | 0.720918i | \(0.743720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.86024e14 | −1.97561e−5 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.07772e18 | −0.354931 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.69074e19 | 1.01216 | 0.506081 | − | 0.862486i | \(-0.331094\pi\) | ||||
0.506081 | + | 0.862486i | \(0.331094\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.57394e19 | −0.569723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.04201e19 | −2.45331 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.20494e18 | −0.241631 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.98326e18 | 0.225491 | 0.112746 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.32468e15 | −4.11922e−5 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.22571e19 | 0.367118 | 0.183559 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183559 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51659e19 | 0.437602 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.62825e18 | 0.128678 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.84036e19 | 2.10077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.13285e19 | 1.06739 | 0.533697 | − | 0.845676i | \(-0.320802\pi\) | ||||
0.533697 | + | 0.845676i | \(0.320802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.19057e19 | −0.794428 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.15706e14 | 1.23816e−5 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.09279e17 | 0.00716126 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.72982e19 | 0.386349 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.58312e19 | 1.41849 | 0.709246 | − | 0.704961i | \(-0.249036\pi\) | ||||
0.709246 | + | 0.704961i | \(0.249036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.81572e18 | −0.141709 | −0.0708543 | − | 0.997487i | \(-0.522573\pi\) | ||||
−0.0708543 | + | 0.997487i | \(0.522573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.72117e19 | −0.345359 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.02693e19 | 0.586253 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.37096e15 | 4.43319e−5 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.58396e19 | 0.647044 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.43444e19 | 0.424444 | 0.212222 | − | 0.977222i | \(-0.431930\pi\) | ||||
0.212222 | + | 0.977222i | \(0.431930\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.73209e19 | 0.628483 | 0.314241 | − | 0.949343i | \(-0.398250\pi\) | ||||
0.314241 | + | 0.949343i | \(0.398250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.63870e19 | 0.266582 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.39231e19 | −0.690371 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.88153e19 | −1.34898 | −0.674488 | − | 0.738286i | \(-0.735635\pi\) | ||||
−0.674488 | + | 0.738286i | \(0.735635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.17448e20 | −1.72408 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.24463e19 | 0.460402 | 0.230201 | − | 0.973143i | \(-0.426062\pi\) | ||||
0.230201 | + | 0.973143i | \(0.426062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.41500e19 | −0.468479 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.67847e20 | −2.22642 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.40615e20 | 1.80378 | 0.901892 | − | 0.431961i | \(-0.142178\pi\) | ||||
0.901892 | + | 0.431961i | \(0.142178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.54289e19 | −0.811794 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.28498e20 | −2.74249 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.03009e14 | 3.51861e−6 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.10893e20 | −1.24605 | −0.623023 | − | 0.782204i | \(-0.714096\pi\) | ||||
−0.623023 | + | 0.782204i | \(0.714096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.80687e19 | 0.957694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.96124e19 | 0.311686 | 0.155843 | − | 0.987782i | \(-0.450191\pi\) | ||||
0.155843 | + | 0.987782i | \(0.450191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33021e20 | 1.35538 | 0.677692 | − | 0.735346i | \(-0.262980\pi\) | ||||
0.677692 | + | 0.735346i | \(0.262980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.43553e20 | 1.41616 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.07393e18 | 0.0675747 | 0.0337873 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337873 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.68167e15 | 1.55576e−5 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.87363e20 | −1.67891 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.51864e19 | −0.305433 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.44707e19 | 0.710402 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.21438e20 | 2.61944 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.30964e19 | −0.103427 | −0.0517136 | − | 0.998662i | \(-0.516468\pi\) | ||||
−0.0517136 | + | 0.998662i | \(0.516468\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.88803e19 | −0.374150 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.06440e15 | 3.01573e−5 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.51136e19 | −0.108719 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.82232e19 | −0.615340 | −0.307670 | − | 0.951493i | \(-0.599549\pi\) | ||||
−0.307670 | + | 0.951493i | \(0.599549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.68521e20 | −1.81619 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.32523e20 | 1.52530 | 0.762651 | − | 0.646811i | \(-0.223898\pi\) | ||||
0.762651 | + | 0.646811i | \(0.223898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.92632e19 | 0.249824 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.14706e20 | 1.32527 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.45841e15 | 3.86770e−5 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.91680e20 | −1.11384 | −0.556919 | − | 0.830567i | \(-0.688017\pi\) | ||||
−0.556919 | + | 0.830567i | \(0.688017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.43932e19 | 0.250342 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.64372e20 | −1.44696 | −0.723478 | − | 0.690348i | \(-0.757458\pi\) | ||||
−0.723478 | + | 0.690348i | \(0.757458\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.49217e18 | 0.0291782 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.97670e20 | 1.53524 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.35342e20 | 0.677718 | 0.338859 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338859 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.45209e15 | −1.19228e−5 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.45768e20 | 1.16050 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.31906e19 | −0.243939 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.67146e19 | −0.297195 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.55932e20 | 1.54032 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.16387e20 | 0.489352 | 0.244676 | − | 0.969605i | \(-0.421318\pi\) | ||||
0.244676 | + | 0.969605i | \(0.421318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.37253e20 | −0.969280 | −0.484640 | − | 0.874714i | \(-0.661049\pi\) | ||||
−0.484640 | + | 0.874714i | \(0.661049\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.81643e15 | −3.10323e−5 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.43950e20 | 1.32714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.31870e20 | −0.494571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27819e20 | −0.830578 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.07913e19 | 0.144582 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.94622e19 | −0.204921 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.66087e19 | −0.0556583 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.55243e20 | −1.48364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.01502e20 | −0.638706 | −0.319353 | − | 0.947636i | \(-0.603466\pi\) | ||||
−0.319353 | + | 0.947636i | \(0.603466\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.23634e20 | −0.997827 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.89187e20 | −0.567435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.12934e20 | 0.621355 | 0.310677 | − | 0.950515i | \(-0.399444\pi\) | ||||
0.310677 | + | 0.950515i | \(0.399444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.04740e21 | −2.97385 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09569e20 | 0.302728 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.45781e15 | 1.19863e−5 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.62677e20 | −1.21082 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.73616e20 | 0.696991 | 0.348495 | − | 0.937310i | \(-0.386693\pi\) | ||||
0.348495 | + | 0.937310i | \(0.386693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.19368e19 | 0.0543982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.12816e20 | 1.96232 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.23411e20 | 0.525159 | 0.262580 | − | 0.964910i | \(-0.415427\pi\) | ||||
0.262580 | + | 0.964910i | \(0.415427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.47799e20 | −0.338304 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.86357e15 | −6.38315e−6 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.24953e20 | −1.13967 | −0.569834 | − | 0.821760i | \(-0.692993\pi\) | ||||
−0.569834 | + | 0.821760i | \(0.692993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.54331e20 | 0.326348 | 0.163174 | − | 0.986597i | \(-0.447827\pi\) | ||||
0.163174 | + | 0.986597i | \(0.447827\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.35578e20 | 0.691248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.59173e20 | −0.520094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.19413e20 | 1.40656 | 0.703282 | − | 0.710911i | \(-0.251717\pi\) | ||||
0.703282 | + | 0.710911i | \(0.251717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.15539e20 | −1.36315 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.91356e14 | −3.55239e−7 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.24593e21 | 2.25414 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.33858e20 | −0.236034 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.31990e20 | 0.742485 | 0.371243 | − | 0.928536i | \(-0.378932\pi\) | ||||
0.371243 | + | 0.928536i | \(0.378932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.59842e20 | 1.60818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.29498e21 | 2.11522 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.19124e20 | −0.667471 | −0.333736 | − | 0.942667i | \(-0.608309\pi\) | ||||
−0.333736 | + | 0.942667i | \(0.608309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.87203e15 | 1.06711e−5 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.24970e20 | −0.340658 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.18808e20 | −0.470791 | −0.235396 | − | 0.971900i | \(-0.575639\pi\) | ||||
−0.235396 | + | 0.971900i | \(0.575639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.85641e20 | −1.41958 | −0.709791 | − | 0.704413i | \(-0.751210\pi\) | ||||
−0.709791 | + | 0.704413i | \(0.751210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.42895e20 | −1.04363 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.54146e20 | 0.622344 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.08297e21 | −1.44777 | −0.723886 | − | 0.689920i | \(-0.757646\pi\) | ||||
−0.723886 | + | 0.689920i | \(0.757646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01389e16 | −1.32240e−5 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.15929e19 | 0.0529310 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.47488e21 | 1.83148 | 0.915742 | − | 0.401767i | \(-0.131604\pi\) | ||||
0.915742 | + | 0.401767i | \(0.131604\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.86111e20 | 0.467895 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.86048e20 | −0.220032 | −0.110016 | − | 0.993930i | \(-0.535090\pi\) | ||||
−0.110016 | + | 0.993930i | \(0.535090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.44499e20 | −0.628517 | −0.314258 | − | 0.949337i | \(-0.601756\pi\) | ||||
−0.314258 | + | 0.949337i | \(0.601756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.54068e20 | −0.849618 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.11291e16 | 2.32392e−5 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.48427e20 | 0.266746 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.26828e21 | 2.37788 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.10857e21 | −1.13471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34412e20 | 0.134344 | 0.0671721 | − | 0.997741i | \(-0.478602\pi\) | ||||
0.0671721 | + | 0.997741i | \(0.478602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.64367e20 | 0.550851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.89522e20 | −0.561949 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.83819e20 | 0.264239 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.85307e21 | −2.59451 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.15011e20 | −0.190997 | −0.0954983 | − | 0.995430i | \(-0.530444\pi\) | ||||
−0.0954983 | + | 0.995430i | \(0.530444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.36705e21 | 1.18632 | 0.593160 | − | 0.805085i | \(-0.297880\pi\) | ||||
0.593160 | + | 0.805085i | \(0.297880\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.07643e20 | 0.176043 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.14998e20 | −0.0952597 | −0.0476298 | − | 0.998865i | \(-0.515167\pi\) | ||||
−0.0476298 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.83054e20 | −0.714746 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.88183e16 | −7.02498e−5 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.23391e21 | −0.953751 | −0.476876 | − | 0.878971i | \(-0.658231\pi\) | ||||
−0.476876 | + | 0.878971i | \(0.658231\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.01947e21 | 0.770131 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.08324e21 | 0.799804 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.63082e21 | −1.17697 | −0.588485 | − | 0.808508i | \(-0.700275\pi\) | ||||
−0.588485 | + | 0.808508i | \(0.700275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.38740e21 | −0.978793 | −0.489397 | − | 0.872061i | \(-0.662783\pi\) | ||||
−0.489397 | + | 0.872061i | \(0.662783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.06746e20 | −0.349494 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.91774e16 | 1.29308e−5 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.36182e20 | −0.221631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.01873e21 | −1.30132 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.05985e21 | −2.55912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.33937e21 | −0.825631 | −0.412816 | − | 0.910815i | \(-0.635455\pi\) | ||||
−0.412816 | + | 0.910815i | \(0.635455\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.45018e21 | 0.874268 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.99408e21 | 1.17579 | 0.587893 | − | 0.808938i | \(-0.299957\pi\) | ||||
0.587893 | + | 0.808938i | \(0.299957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.35100e15 | 5.39306e−6 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.90692e21 | 2.76825 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.25180e21 | 0.690845 | 0.345422 | − | 0.938447i | \(-0.387736\pi\) | ||||
0.345422 | + | 0.938447i | \(0.387736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.61898e20 | 0.249383 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.90214e21 | 2.58947 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.76772e20 | −0.401466 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.46431e21 | 0.740539 | 0.370269 | − | 0.928924i | \(-0.379265\pi\) | ||||
0.370269 | + | 0.928924i | \(0.379265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.32842e17 | −6.57411e−5 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.50425e20 | −0.121281 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.25117e20 | 0.438481 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.48298e21 | 2.07964 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.97987e20 | −0.135305 | −0.0676523 | − | 0.997709i | \(-0.521551\pi\) | ||||
−0.0676523 | + | 0.997709i | \(0.521551\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.09362e21 | −1.37500 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.93698e20 | 0.171295 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.39809e15 | −1.44740e−6 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.21881e21 | 0.508264 | 0.254132 | − | 0.967169i | \(-0.418210\pi\) | ||||
0.254132 | + | 0.967169i | \(0.418210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.96929e21 | −0.804057 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.94499e21 | −1.17737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.18849e20 | −0.203117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.33333e21 | 1.66122 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.01856e21 | 1.13327 | 0.566634 | − | 0.823970i | \(-0.308245\pi\) | ||||
0.566634 | + | 0.823970i | \(0.308245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.29099e16 | 1.21007e−5 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.03672e21 | −2.17402 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.46527e20 | 0.228061 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.97710e20 | −0.310190 | −0.155095 | − | 0.987900i | \(-0.549568\pi\) | ||||
−0.155095 | + | 0.987900i | \(0.549568\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.56218e21 | −1.54424 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.97510e20 | 0.164976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.52857e20 | −0.277074 | −0.138537 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138537 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.68650e21 | 0.855128 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.87955e21 | −0.898089 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.19196e21 | −0.669883 | −0.334941 | − | 0.942239i | \(-0.608716\pi\) | ||||
−0.334941 | + | 0.942239i | \(0.608716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.41415e21 | −0.423505 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.89929e21 | −0.557410 | −0.278705 | − | 0.960377i | \(-0.589905\pi\) | ||||
−0.278705 | + | 0.960377i | \(0.589905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.42992e21 | 0.698906 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.45335e19 | 0.0238300 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.67902e16 | 1.01653e−5 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.40128e21 | 1.19201 | 0.596005 | − | 0.802981i | \(-0.296754\pi\) | ||||
0.596005 | + | 0.802981i | \(0.296754\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.29320e21 | −1.40526 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.30795e21 | 0.860909 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.32600e21 | 0.848601 | 0.424300 | − | 0.905521i | \(-0.360520\pi\) | ||||
0.424300 | + | 0.905521i | \(0.360520\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.95955e21 | −1.74088 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.66362e21 | 1.63428 | 0.817138 | − | 0.576443i | \(-0.195560\pi\) | ||||
0.817138 | + | 0.576443i | \(0.195560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.17053e17 | 2.81480e−5 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.03579e21 | −0.715832 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.50536e20 | 0.127298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.77725e21 | 0.402997 | 0.201499 | − | 0.979489i | \(-0.435419\pi\) | ||||
0.201499 | + | 0.979489i | \(0.435419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.76255e21 | −1.94860 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.17145e21 | −0.909790 | −0.454895 | − | 0.890545i | \(-0.650323\pi\) | ||||
−0.454895 | + | 0.890545i | \(0.650323\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.66366e21 | 1.21153 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.86266e17 | 6.00637e−5 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.58167e21 | 0.531337 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.10589e22 | −2.23269 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.88108e21 | 0.372558 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.71245e21 | 0.527035 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.96836e21 | −0.947114 | −0.473557 | − | 0.880763i | \(-0.657030\pi\) | ||||
−0.473557 | + | 0.880763i | \(0.657030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.67805e21 | 1.62310 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.14455e16 | 1.67818e−5 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.53109e21 | 0.455784 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.35254e21 | −1.29922 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.55056e21 | 0.789091 | 0.394546 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394546 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.43296e20 | 0.160527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.33403e21 | −1.55892 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.19877e21 | 0.688264 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.88401e16 | −9.46683e−6 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.78477e22 | 2.81859 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.12040e22 | 1.73683 | 0.868417 | − | 0.495834i | \(-0.165138\pi\) | ||||
0.868417 | + | 0.495834i | \(0.165138\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.56431e21 | −0.238048 | −0.119024 | − | 0.992891i | \(-0.537977\pi\) | ||||
−0.119024 | + | 0.992891i | \(0.537977\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.10134e22 | −1.64529 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.88737e21 | 0.570130 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38837e21 | 0.199913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.28199e16 | 1.17086e−5 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.31534e21 | 0.737831 | 0.368916 | − | 0.929463i | \(-0.379729\pi\) | ||||
0.368916 | + | 0.929463i | \(0.379729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.48380e21 | −0.338546 | −0.169273 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169273 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.33842e22 | 1.79139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.01420e21 | 0.790473 | 0.395236 | − | 0.918580i | \(-0.370663\pi\) | ||||
0.395236 | + | 0.918580i | \(0.370663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.33653e21 | −0.559736 | −0.279868 | − | 0.960039i | \(-0.590291\pi\) | ||||
−0.279868 | + | 0.960039i | \(0.590291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.48140e21 | −0.314550 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.43681e21 | 0.801370 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.42679e20 | −0.0785861 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.64785e22 | 1.97914 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.92224e21 | −0.934616 | −0.467308 | − | 0.884095i | \(-0.654776\pi\) | ||||
−0.467308 | + | 0.884095i | \(0.654776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.79056e21 | −0.902815 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.10540e21 | −0.239678 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.30936e21 | −0.481934 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.80988e17 | −3.08718e−5 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.85422e22 | −3.08091 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.49187e21 | 1.00665 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.77976e21 | 0.498067 | 0.249034 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249034 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.47181e21 | −0.867422 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.38506e22 | −1.39352 | −0.696758 | − | 0.717306i | \(-0.745375\pi\) | ||||
−0.696758 | + | 0.717306i | \(0.745375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.13389e22 | −1.12104 | −0.560522 | − | 0.828140i | \(-0.689399\pi\) | ||||
−0.560522 | + | 0.828140i | \(0.689399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.38893e17 | −2.32103e−5 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.34506e22 | −1.28428 | −0.642142 | − | 0.766586i | \(-0.721954\pi\) | ||||
−0.642142 | + | 0.766586i | \(0.721954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.15281e21 | −0.483530 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.40324e21 | 0.590550 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.63321e21 | −0.691924 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.79524e21 | 0.159951 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.13091e21 | −0.361775 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.67838e17 | 2.30575e−5 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.71264e21 | 0.737315 | 0.368657 | − | 0.929565i | \(-0.379818\pi\) | ||||
0.368657 | + | 0.929565i | \(0.379818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.32093e21 | −0.442660 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.84288e22 | 1.50722 | 0.753611 | − | 0.657321i | \(-0.228310\pi\) | ||||
0.753611 | + | 0.657321i | \(0.228310\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.38696e21 | −0.513558 | −0.256779 | − | 0.966470i | \(-0.582661\pi\) | ||||
−0.256779 | + | 0.966470i | \(0.582661\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.21110e21 | 0.411960 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.26761e22 | 0.985279 | 0.492639 | − | 0.870234i | \(-0.336032\pi\) | ||||
0.492639 | + | 0.870234i | \(0.336032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.64747e17 | 2.78759e−5 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.90335e21 | 0.368477 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.63240e21 | 0.194521 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.40444e20 | 0.0174720 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.33890e21 | 0.310053 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.34650e21 | 0.516277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.76166e22 | −1.21755 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.28472e17 | −8.73274e−6 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.68524e21 | 0.313233 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.29670e21 | −0.0852676 | −0.0426338 | − | 0.999091i | \(-0.513575\pi\) | ||||
−0.0426338 | + | 0.999091i | \(0.513575\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.50114e21 | 0.0970942 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.26280e22 | −1.43966 | −0.719828 | − | 0.694153i | \(-0.755779\pi\) | ||||
−0.719828 | + | 0.694153i | \(0.755779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.27663e20 | 0.0205067 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.39581e22 | 1.47501 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.30762e17 | −3.82028e−5 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.37047e21 | 0.260412 | 0.130206 | − | 0.991487i | \(-0.458436\pi\) | ||||
0.130206 | + | 0.991487i | \(0.458436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.48204e22 | 1.45499 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.89460e21 | 0.397645 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.82543e22 | −1.03586 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.45383e22 | −0.811737 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.43423e22 | −1.33734 | −0.668672 | − | 0.743557i | \(-0.733137\pi\) | ||||
−0.668672 | + | 0.743557i | \(0.733137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.79628e22 | 0.971074 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.99230e22 | 1.05984 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.17671e22 | −0.616003 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.64776e22 | 0.848879 | 0.424439 | − | 0.905456i | \(-0.360471\pi\) | ||||
0.424439 | + | 0.905456i | \(0.360471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.99480e21 | −0.506736 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.09383e22 | −1.04477 | −0.522384 | − | 0.852710i | \(-0.674957\pi\) | ||||
−0.522384 | + | 0.852710i | \(0.674957\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.92110e21 | −0.388998 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.29235e17 | 1.59136e−5 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.36036e22 | 1.59868 | 0.799338 | − | 0.600881i | \(-0.205183\pi\) | ||||
0.799338 | + | 0.600881i | \(0.205183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.61770e21 | −0.122581 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.07762e22 | 1.41860 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.45292e22 | 1.56671 | 0.783357 | − | 0.621572i | \(-0.213506\pi\) | ||||
0.783357 | + | 0.621572i | \(0.213506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.85815e21 | −0.216993 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.73611e22 | 0.763375 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.85784e17 | −1.23708e−5 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.08910e22 | 1.74262 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.62525e22 | −0.681902 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03588e22 | 0.427913 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.34537e21 | −0.0547197 | −0.0273598 | − | 0.999626i | \(-0.508710\pi\) | ||||
−0.0273598 | + | 0.999626i | \(0.508710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.20718e22 | −1.28439 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.50334e21 | −0.0592807 | −0.0296403 | − | 0.999561i | \(-0.509436\pi\) | ||||
−0.0296403 | + | 0.999561i | \(0.509436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.54942e17 | 6.01620e−6 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.34434e21 | −0.319049 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.36133e22 | −1.64214 | −0.821068 | − | 0.570830i | \(-0.806622\pi\) | ||||
−0.821068 | + | 0.570830i | \(0.806622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.61799e22 | −1.34152 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.17093e22 | −1.88821 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.21986e21 | −0.115794 | −0.0578969 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578969 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.87473e22 | −0.663999 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.43587e17 | −8.49721e−6 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.25981e21 | −0.146359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.85010e22 | 1.64134 | 0.820670 | − | 0.571402i | \(-0.193600\pi\) | ||||
0.820670 | + | 0.571402i | \(0.193600\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.01939e22 | −1.33980 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.25689e21 | 0.106937 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.35543e22 | 1.73213 | 0.866065 | − | 0.499931i | \(-0.166641\pi\) | ||||
0.866065 | + | 0.499931i | \(0.166641\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.31110e22 | −1.69217 |
(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 | 16.16.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 144.16.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 2.16.a.a.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 64.16.a.a.1.1 | 1 | |||
8.5 | even | 2 | 64.16.a.k.1.1 | 1 | |||
12.11 | even | 2 | 18.16.a.e.1.1 | 1 | |||
20.3 | even | 4 | 50.16.b.a.49.2 | 2 | |||
20.7 | even | 4 | 50.16.b.a.49.1 | 2 | |||
20.19 | odd | 2 | 50.16.a.b.1.1 | 1 | |||
28.3 | even | 6 | 98.16.c.d.79.1 | 2 | |||
28.11 | odd | 6 | 98.16.c.a.79.1 | 2 | |||
28.19 | even | 6 | 98.16.c.d.67.1 | 2 | |||
28.23 | odd | 6 | 98.16.c.a.67.1 | 2 | |||
28.27 | even | 2 | 98.16.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.16.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
16.16.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
18.16.a.e.1.1 | 1 | 12.11 | even | 2 | |||
50.16.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
50.16.b.a.49.1 | 2 | 20.7 | even | 4 | |||
50.16.b.a.49.2 | 2 | 20.3 | even | 4 | |||
64.16.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
64.16.a.k.1.1 | 1 | 8.5 | even | 2 | |||
98.16.a.a.1.1 | 1 | 28.27 | even | 2 | |||
98.16.c.a.67.1 | 2 | 28.23 | odd | 6 | |||
98.16.c.a.79.1 | 2 | 28.11 | odd | 6 | |||
98.16.c.d.67.1 | 2 | 28.19 | even | 6 | |||
98.16.c.d.79.1 | 2 | 28.3 | even | 6 | |||
144.16.a.d.1.1 | 1 | 3.2 | odd | 2 |