Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,33,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(136.219975799\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 2.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.2 |
Dual form | 21.33.h.a.11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −2.15234e7 | − | 3.72796e7i | −0.500000 | − | 0.866025i | ||||
\(4\) | −2.14748e9 | − | 3.71955e9i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.25760e13 | − | 6.57520e12i | 0.980232 | − | 0.197852i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.26510e14 | + | 1.60476e15i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −9.24421e16 | + | 1.60114e17i | −0.500000 | + | 0.866025i | ||||
\(13\) | 1.22181e17 | 0.183616 | 0.0918082 | − | 0.995777i | \(-0.470735\pi\) | ||||
0.0918082 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −9.22337e18 | + | 1.59753e19i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.91058e18 | − | 6.77332e18i | 0.0135576 | − | 0.0234825i | −0.859167 | − | 0.511695i | \(-0.829018\pi\) |
0.872725 | + | 0.488213i | \(0.162351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.46265e20 | − | 1.07290e21i | −0.661461 | − | 0.749980i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.16415e22 | − | 2.01637e22i | −0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.97664e22 | 1.00000 | ||||||||
\(28\) | −9.44132e22 | − | 1.07048e23i | −0.661461 | − | 0.749980i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.06862e23 | + | 1.22432e24i | 0.971734 | + | 1.68309i | 0.690317 | + | 0.723507i | \(0.257471\pi\) |
0.281417 | + | 0.959585i | \(0.409195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.95866e24 | 1.00000 | ||||||||
\(37\) | 1.07781e25 | − | 1.86682e25i | 0.873603 | − | 1.51313i | 0.0153605 | − | 0.999882i | \(-0.495110\pi\) |
0.858243 | − | 0.513244i | \(-0.171556\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.62975e24 | − | 4.55487e24i | −0.0918082 | − | 0.159016i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.72890e26 | 1.99752 | 0.998762 | − | 0.0497364i | \(-0.0158381\pi\) | ||||
0.998762 | + | 0.0497364i | \(0.0158381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 7.94072e26 | 1.00000 | ||||||||
\(49\) | 1.01796e27 | − | 4.28387e26i | 0.921709 | − | 0.387881i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.62383e26 | − | 4.54460e26i | −0.0918082 | − | 0.159016i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.36675e26 | −0.0271152 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.97705e28 | − | 3.42436e28i | 0.537949 | − | 0.931755i | −0.461066 | − | 0.887366i | \(-0.652533\pi\) |
0.999014 | − | 0.0443885i | \(-0.0141340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.96303e28 | + | 5.83687e28i | −0.318771 | + | 0.947832i | ||||
\(64\) | 7.92282e28 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.65665e27 | − | 4.60145e27i | −0.0161115 | − | 0.0279060i | 0.857857 | − | 0.513888i | \(-0.171795\pi\) |
−0.873969 | + | 0.485982i | \(0.838462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.83758e29 | − | 6.64688e29i | −0.590054 | − | 1.02200i | −0.994225 | − | 0.107320i | \(-0.965773\pi\) |
0.404171 | − | 0.914684i | \(-0.367560\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.01130e29 | + | 8.67982e29i | −0.500000 | + | 0.866025i | ||||
\(76\) | −3.35916e28 | −0.0271152 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.01348e30 | + | 1.75540e30i | −0.440334 | + | 0.762681i | −0.997714 | − | 0.0675768i | \(-0.978473\pi\) |
0.557380 | + | 0.830257i | \(0.311807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.71684e30 | − | 2.97366e30i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −1.95861e30 | + | 5.82371e30i | −0.318771 | + | 0.947832i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.98018e30 | − | 8.03367e29i | 0.179987 | − | 0.0363289i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.04281e31 | − | 5.27030e31i | 0.971734 | − | 1.68309i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21183e32 | 1.97285 | 0.986426 | − | 0.164204i | \(-0.0525057\pi\) | ||||
0.986426 | + | 0.164204i | \(0.0525057\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e31 | + | 8.66025e31i | −0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.30303e31 | + | 7.45307e31i | −0.268151 | + | 0.464450i | −0.968384 | − | 0.249463i | \(-0.919746\pi\) |
0.700234 | + | 0.713914i | \(0.253079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −1.71297e32 | − | 2.96695e32i | −0.500000 | − | 0.866025i | ||||
\(109\) | −2.22684e32 | − | 3.85700e32i | −0.560874 | − | 0.971462i | −0.997420 | − | 0.0717807i | \(-0.977132\pi\) |
0.436546 | − | 0.899682i | \(-0.356202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.27923e32 | −1.74721 | ||||||||
\(112\) | −1.95419e32 | + | 5.81058e32i | −0.318771 | + | 0.947832i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.13202e32 | + | 1.96072e32i | −0.0918082 | + | 0.159016i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.05569e33 | + | 1.82851e33i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.03595e33 | − | 5.25842e33i | 0.971734 | − | 1.68309i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.15599e33 | 1.56247 | 0.781233 | − | 0.624240i | \(-0.214591\pi\) | ||||
0.781233 | + | 0.624240i | \(0.214591\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.87351e33 | − | 1.01732e34i | −0.998762 | − | 1.72991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.28550e31 | − | 2.46360e32i | 0.00864355 | − | 0.0257007i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.79001e34 | −1.95166 | −0.975829 | − | 0.218537i | \(-0.929872\pi\) | ||||
−0.975829 | + | 0.218537i | \(0.929872\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.70911e34 | − | 2.96026e34i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.78800e34 | − | 2.87288e34i | −0.796770 | − | 0.604283i | ||||
\(148\) | −9.25831e34 | −1.74721 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.62428e34 | − | 6.27745e34i | −0.496125 | − | 0.859314i | 0.503865 | − | 0.863782i | \(-0.331911\pi\) |
−0.999990 | + | 0.00446863i | \(0.998578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.12947e34 | + | 1.95630e34i | −0.0918082 | + | 0.159016i | ||||
\(157\) | −1.35303e35 | − | 2.34352e35i | −0.992917 | − | 1.71978i | −0.599352 | − | 0.800485i | \(-0.704575\pi\) |
−0.393565 | − | 0.919297i | \(-0.628758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.77804e35 | − | 3.07966e35i | 0.716046 | − | 1.24023i | −0.246509 | − | 0.969141i | \(-0.579283\pi\) |
0.962555 | − | 0.271088i | \(-0.0873833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.27851e35 | −0.966285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.24638e33 | + | 1.25511e34i | 0.0135576 | + | 0.0234825i | ||||
\(172\) | −5.86027e35 | − | 1.01503e36i | −0.998762 | − | 1.72991i | ||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.11815e35 | − | 5.80308e35i | −0.661461 | − | 0.749980i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.42721e36 | −1.07555 | −0.537777 | − | 0.843087i | \(-0.680736\pi\) | ||||
−0.537777 | + | 0.843087i | \(0.680736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.70211e36 | −1.07590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.59847e36 | − | 5.24480e35i | 0.980232 | − | 0.197852i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −1.70526e36 | − | 2.95359e36i | −0.500000 | − | 0.866025i | ||||
\(193\) | 1.13971e36 | + | 1.97404e36i | 0.307524 | + | 0.532647i | 0.977820 | − | 0.209447i | \(-0.0671663\pi\) |
−0.670296 | + | 0.742094i | \(0.733833\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.77946e36 | − | 2.86640e36i | −0.796770 | − | 0.604283i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.22546e36 | + | 7.31872e36i | 0.698594 | + | 1.21000i | 0.968954 | + | 0.247241i | \(0.0795241\pi\) |
−0.270360 | + | 0.962759i | \(0.587143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.14360e35 | + | 1.98077e35i | −0.0161115 | + | 0.0279060i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.12692e36 | + | 1.95189e36i | −0.0918082 | + | 0.159016i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.03417e37 | 1.96571 | 0.982856 | − | 0.184373i | \(-0.0590256\pi\) | ||||
0.982856 | + | 0.184373i | \(0.0590256\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.10769e37 | + | 3.52357e37i | 1.28553 | + | 1.45756i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.65195e37 | + | 2.86126e37i | −0.590054 | + | 1.02200i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.75399e37 | 0.736349 | 0.368175 | − | 0.929757i | \(-0.379983\pi\) | ||||
0.368175 | + | 0.929757i | \(0.379983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.31440e37 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 7.23004e35 | + | 1.25228e36i | 0.0135576 | + | 0.0234825i | ||||
\(229\) | −2.14905e37 | + | 3.72226e37i | −0.375732 | + | 0.650787i | −0.990436 | − | 0.137971i | \(-0.955942\pi\) |
0.614704 | + | 0.788758i | \(0.289275\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.72540e37 | 0.880668 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.57310e37 | + | 1.65811e38i | 0.739231 | + | 1.28039i | 0.952842 | + | 0.303467i | \(0.0981441\pi\) |
−0.213611 | + | 0.976919i | \(0.568523\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.39044e37 | + | 1.28006e38i | −0.500000 | + | 0.866025i | ||||
\(244\) | −1.69828e38 | −1.07590 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.77800e35 | − | 8.27573e35i | 0.00248940 | − | 0.00431177i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 2.59261e38 | − | 5.23298e37i | 0.980232 | − | 0.197852i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.70141e38 | − | 2.94693e38i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.28360e38 | − | 6.79003e38i | 0.556959 | − | 1.65606i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.14102e37 | + | 1.97631e37i | −0.0161115 | + | 0.0279060i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.66940e38 | + | 6.35560e38i | −0.433598 | + | 0.751013i | −0.997180 | − | 0.0750466i | \(-0.976089\pi\) |
0.563582 | + | 0.826060i | \(0.309423\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.15616e38 | − | 1.31088e38i | −0.121455 | − | 0.137709i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.66328e38 | − | 1.67373e39i | −0.804356 | − | 1.39319i | −0.916725 | − | 0.399519i | \(-0.869177\pi\) |
0.112369 | − | 0.993667i | \(-0.464156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.61966e39 | −1.94347 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.54316e39 | − | 2.67283e39i | −0.911650 | − | 1.57902i | −0.811733 | − | 0.584028i | \(-0.801476\pi\) |
−0.0999165 | − | 0.994996i | \(-0.531858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18396e39 | + | 2.05067e39i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.60827e39 | − | 4.51766e39i | −0.986426 | − | 1.70854i | ||||
\(292\) | −1.64823e39 | + | 2.85481e39i | −0.590054 | + | 1.02200i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.30467e39 | 1.00000 | ||||||||
\(301\) | 8.88966e39 | − | 1.79431e39i | 1.95804 | − | 0.395214i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.21374e37 | + | 1.24946e38i | 0.0135576 | + | 0.0234825i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.43223e38 | −0.0230038 | −0.0115019 | − | 0.999934i | \(-0.503661\pi\) | ||||
−0.0115019 | + | 0.999934i | \(0.503661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.70463e39 | 0.536301 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.33486e37 | + | 5.77614e37i | −0.00392978 | + | 0.00680657i | −0.867984 | − | 0.496593i | \(-0.834584\pi\) |
0.864054 | + | 0.503399i | \(0.167918\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.70573e39 | 0.880668 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −7.37378e39 | + | 1.27718e40i | −0.500000 | + | 0.866025i | ||||
\(325\) | −1.42238e39 | − | 2.46363e39i | −0.0918082 | − | 0.159016i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.58582e39 | + | 1.66031e40i | −0.560874 | + | 0.971462i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.32351e40 | + | 2.29238e40i | −0.637498 | + | 1.10418i | 0.348482 | + | 0.937315i | \(0.386697\pi\) |
−0.985980 | + | 0.166863i | \(0.946636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.99720e40 | + | 3.45926e40i | 0.873603 | + | 1.51313i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.58677e40 | − | 5.22118e39i | 0.980232 | − | 0.197852i | ||||
\(337\) | −1.85065e40 | −0.668723 | −0.334361 | − | 0.942445i | \(-0.608521\pi\) | ||||
−0.334361 | + | 0.942445i | \(0.608521\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.03444e40 | − | 2.06484e40i | 0.826746 | − | 0.562576i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.32145e40 | 1.92432 | 0.962159 | − | 0.272490i | \(-0.0878472\pi\) | ||||
0.962159 | + | 0.272490i | \(0.0878472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.74598e39 | 0.183616 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.15686e40 | + | 7.19990e40i | 0.499632 | + | 0.865389i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.08879e40 | 1.00000 | ||||||||
\(364\) | −1.15355e40 | − | 1.30793e40i | −0.121455 | − | 0.137709i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.21361e40 | − | 1.24943e41i | −0.666033 | − | 1.15360i | −0.979004 | − | 0.203840i | \(-0.934658\pi\) |
0.312971 | − | 0.949763i | \(-0.398676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.61375e41 | −1.94347 | ||||||||
\(373\) | 1.58690e39 | − | 2.74860e39i | 0.0113034 | − | 0.0195781i | −0.860318 | − | 0.509757i | \(-0.829735\pi\) |
0.871622 | + | 0.490179i | \(0.163069\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.75275e41 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.54021e41 | − | 2.66772e41i | −0.781233 | − | 1.35313i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.52835e41 | + | 4.37923e41i | −0.998762 | + | 1.72991i | ||||
\(388\) | −2.60239e41 | − | 4.50747e41i | −0.986426 | − | 1.70854i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.69470e41 | − | 6.39941e41i | 0.970356 | − | 1.68071i | 0.275877 | − | 0.961193i | \(-0.411032\pi\) |
0.694479 | − | 0.719513i | \(-0.255635\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.09675e40 | + | 2.21370e39i | −0.0265792 | + | 0.00536480i | ||||
\(400\) | 4.29497e41 | 1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.63654e40 | + | 1.49589e41i | 0.178426 | + | 0.309043i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.62140e41 | − | 8.00450e41i | −0.753703 | − | 1.30545i | −0.946016 | − | 0.324119i | \(-0.894932\pi\) |
0.192313 | − | 0.981334i | \(-0.438401\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.69627e41 | 0.536301 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.15738e41 | + | 1.41290e42i | 0.975829 | + | 1.69018i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.85857e42 | −1.90839 | −0.954194 | − | 0.299190i | \(-0.903284\pi\) | ||||
−0.954194 | + | 0.299190i | \(0.903284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.18886e41 | − | 1.24551e42i | 0.342965 | − | 1.01977i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −7.35716e41 | + | 1.27430e42i | −0.500000 | + | 0.866025i | ||||
\(433\) | 2.59382e42 | 1.69877 | 0.849383 | − | 0.527777i | \(-0.176974\pi\) | ||||
0.849383 | + | 0.527777i | \(0.176974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.56421e41 | + | 1.65657e42i | −0.560874 | + | 0.971462i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.75863e41 | − | 4.77809e41i | 0.144965 | − | 0.251086i | −0.784395 | − | 0.620261i | \(-0.787027\pi\) |
0.929360 | + | 0.369175i | \(0.120360\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.55692e41 | + | 2.03049e42i | −0.124939 | + | 0.992164i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 1.99270e42 | + | 3.45146e42i | 0.873603 | + | 1.51313i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.58094e42 | − | 5.20941e41i | 0.980232 | − | 0.197852i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.56014e42 | + | 2.70223e42i | −0.496125 | + | 0.859314i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.52910e42 | − | 6.11258e42i | 0.975000 | − | 1.68875i | 0.295063 | − | 0.955478i | \(-0.404659\pi\) |
0.679937 | − | 0.733271i | \(-0.262007\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.17477e42 | 1.38460 | 0.692301 | − | 0.721609i | \(-0.256597\pi\) | ||||
0.692301 | + | 0.721609i | \(0.256597\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(468\) | 9.72400e41 | 0.183616 | ||||||||
\(469\) | −1.16798e41 | − | 1.32429e41i | −0.0213143 | − | 0.0241667i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.82435e42 | + | 1.00881e43i | −0.992917 | + | 1.71978i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.82100e41 | −0.0271152 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.31688e42 | − | 2.28091e42i | 0.160408 | − | 0.277835i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.06830e42 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.14159e42 | − | 1.58337e43i | −0.913185 | − | 1.58168i | −0.809538 | − | 0.587068i | \(-0.800282\pi\) |
−0.103647 | − | 0.994614i | \(-0.533051\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.53078e43 | −1.43209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.60786e43 | −1.94347 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.19381e43 | − | 2.06774e43i | 0.807841 | − | 1.39922i | −0.106515 | − | 0.994311i | \(-0.533969\pi\) |
0.914356 | − | 0.404910i | \(-0.132697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.20879e42 | + | 1.59501e43i | 0.483143 | + | 0.836827i | ||||
\(508\) | −1.53674e43 | − | 2.66171e43i | −0.781233 | − | 1.35313i | ||||
\(509\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.68717e43 | − | 1.91296e43i | −0.780595 | − | 0.885057i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.11933e41 | − | 5.40283e41i | 0.0135576 | − | 0.0234825i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.52265e43 | + | 4.36936e43i | −0.998762 | + | 1.72991i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.89818e43 | − | 5.01980e43i | 0.924909 | − | 1.60199i | 0.133202 | − | 0.991089i | \(-0.457474\pi\) |
0.791707 | − | 0.610901i | \(-0.209193\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.06176e43 | + | 3.15704e43i | −0.318771 | + | 0.947832i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.88045e43 | − | 3.25703e43i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.09428e42 | + | 2.20871e41i | −0.0265792 | + | 0.00536480i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.84312e43 | − | 8.38854e43i | 0.899434 | − | 1.55787i | 0.0712152 | − | 0.997461i | \(-0.477312\pi\) |
0.828219 | − | 0.560405i | \(-0.189354\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.07184e43 | + | 5.32059e43i | 0.537777 | + | 0.931456i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.05403e43 | 0.319750 | 0.159875 | − | 0.987137i | \(-0.448891\pi\) | ||||
0.159875 | + | 0.987137i | \(0.448891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.66352e43 | + | 6.34540e43i | 0.537949 | + | 0.931755i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.14730e43 | + | 6.38477e43i | −0.280731 | + | 0.834725i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.13899e43 | + | 1.40971e44i | 0.975829 | + | 1.69018i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.33421e43 | 0.366778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.54802e43 | − | 8.55812e43i | −0.661461 | − | 0.749980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.05755e44 | + | 1.83173e44i | 0.828176 | + | 1.43444i | 0.899468 | + | 0.436987i | \(0.143954\pi\) |
−0.0712925 | + | 0.997455i | \(0.522712\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.34057e43 | + | 1.27142e44i | −0.500000 | + | 0.866025i | ||||
\(577\) | −8.34478e43 | − | 1.44536e44i | −0.552843 | − | 0.957552i | −0.998068 | − | 0.0621333i | \(-0.980210\pi\) |
0.445225 | − | 0.895419i | \(-0.353124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.90609e43 | − | 8.49760e43i | 0.307524 | − | 0.532647i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −2.55115e43 | + | 2.02591e44i | −0.124939 | + | 0.992164i | ||||
\(589\) | 1.10569e43 | 0.0526976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.98821e44 | + | 3.44368e44i | 0.873603 | + | 1.51313i | ||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.81892e44 | − | 3.15047e44i | 0.698594 | − | 1.21000i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.46883e44 | 0.852118 | 0.426059 | − | 0.904695i | \(-0.359902\pi\) | ||||
0.426059 | + | 0.904695i | \(0.359902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.84564e42 | 0.0322231 | ||||||||
\(604\) | −1.55662e44 | + | 2.69614e44i | −0.496125 | + | 0.859314i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.29972e44 | − | 5.71528e44i | 0.971533 | − | 1.68274i | 0.280601 | − | 0.959824i | \(-0.409466\pi\) |
0.690932 | − | 0.722920i | \(-0.257201\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.87605e44 | − | 6.71351e44i | −0.975038 | − | 1.68881i | −0.679811 | − | 0.733388i | \(-0.737938\pi\) |
−0.295227 | − | 0.955427i | \(-0.595395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.59678e44 | − | 6.22980e44i | −0.774218 | − | 1.34098i | −0.935233 | − | 0.354032i | \(-0.884810\pi\) |
0.161016 | − | 0.986952i | \(-0.448523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.70208e43 | 0.183616 | ||||||||
\(625\) | −2.71051e44 | + | 4.69473e44i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.81122e44 | + | 1.00653e45i | −0.992917 | + | 1.71978i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.15848e45 | −1.83408 | −0.917039 | − | 0.398798i | \(-0.869428\pi\) | ||||
−0.917039 | + | 0.398798i | \(0.869428\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.53054e44 | − | 1.13112e45i | −0.982856 | − | 1.70236i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.24376e44 | − | 5.23409e43i | 0.169241 | − | 0.0712214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.74213e44 | −0.555390 | −0.277695 | − | 0.960669i | \(-0.589571\pi\) | ||||
−0.277695 | + | 0.960669i | \(0.589571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.44692e44 | − | 1.91692e45i | 0.619522 | − | 1.84208i | ||||
\(652\) | −1.52733e45 | −1.43209 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.42222e45 | 1.18011 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20637e45 | + | 2.08949e45i | 0.908357 | + | 1.57332i | 0.816346 | + | 0.577563i | \(0.195996\pi\) |
0.0920114 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.92750e44 | − | 1.02667e45i | −0.368175 | − | 0.637697i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.41061e45 | 1.92571 | 0.962854 | − | 0.270022i | \(-0.0870310\pi\) | ||||
0.962854 | + | 0.270022i | \(0.0870310\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.28604e44 | − | 1.60839e45i | −0.500000 | − | 0.866025i | ||||
\(676\) | 9.18803e44 | + | 1.59141e45i | 0.483143 | + | 0.836827i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.94766e45 | − | 7.96804e44i | 1.93385 | − | 0.390333i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 3.11230e43 | − | 5.39065e43i | 0.0135576 | − | 0.0234825i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.85019e45 | 0.751464 | ||||||||
\(688\) | −2.51697e45 | + | 4.35951e45i | −0.998762 | + | 1.72991i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.06721e45 | + | 3.58052e45i | −0.765132 | + | 1.32525i | 0.175044 | + | 0.984561i | \(0.443993\pi\) |
−0.940177 | + | 0.340688i | \(0.889340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.05937e45 | + | 3.14992e45i | −0.318771 | + | 0.947832i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.42971e43 | − | 1.46007e44i | −0.0236880 | − | 0.0410287i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.98784e45 | + | 3.44305e45i | −0.487576 | + | 0.844507i | −0.999898 | − | 0.0142869i | \(-0.995452\pi\) |
0.512322 | + | 0.858794i | \(0.328786\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.87800e45 | − | 3.25279e45i | −0.440334 | − | 0.762681i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.11700e44 | + | 2.71084e45i | −0.170957 | + | 0.508323i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.12091e45 | − | 7.13762e45i | 0.739231 | − | 1.28039i | ||||
\(724\) | 3.06492e45 | + | 5.30860e45i | 0.537777 | + | 0.931456i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.21369e45 | 0.692010 | 0.346005 | − | 0.938233i | \(-0.387538\pi\) | ||||
0.346005 | + | 0.938233i | \(0.387538\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.36269e45 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 3.65526e45 | + | 6.33110e45i | 0.537949 | + | 0.931755i | ||||
\(733\) | 3.71231e45 | − | 6.42992e45i | 0.534541 | − | 0.925852i | −0.464644 | − | 0.885497i | \(-0.653818\pi\) |
0.999185 | − | 0.0403548i | \(-0.0128488\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.83528e45 | − | 8.37495e45i | −0.611098 | − | 1.05845i | −0.991056 | − | 0.133448i | \(-0.957395\pi\) |
0.379958 | − | 0.925004i | \(-0.375938\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.11354e43 | −0.00497880 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.41961e45 | − | 5.92294e45i | 0.333994 | − | 0.578494i | −0.649297 | − | 0.760535i | \(-0.724937\pi\) |
0.983291 | + | 0.182041i | \(0.0582703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.53100e45 | − | 8.53883e45i | −0.661461 | − | 0.749980i | ||||
\(757\) | −2.32391e46 | −1.99842 | −0.999208 | − | 0.0397813i | \(-0.987334\pi\) | ||||
−0.999208 | + | 0.0397813i | \(0.987334\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.79021e45 | − | 1.11004e46i | −0.741992 | − | 0.841289i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −7.32402e45 | + | 1.26856e46i | −0.500000 | + | 0.866025i | ||||
\(769\) | −2.97413e46 | −1.98856 | −0.994281 | − | 0.106798i | \(-0.965940\pi\) | ||||
−0.994281 | + | 0.106798i | \(0.965940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.89503e45 | − | 8.47845e45i | 0.307524 | − | 0.532647i | ||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.64579e46 | − | 2.85059e46i | 0.971734 | − | 1.68309i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.02280e46 | + | 6.10128e45i | −1.71267 | + | 0.345688i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.54540e45 | + | 2.02135e46i | −0.124939 | + | 0.992164i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.55652e45 | + | 1.48203e46i | 0.395095 | + | 0.684325i | 0.993113 | − | 0.117158i | \(-0.0373783\pi\) |
−0.598018 | + | 0.801482i | \(0.704045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.41559e45 | − | 4.18393e45i | 0.0987762 | − | 0.171085i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.81482e46 | − | 3.14336e46i | 0.698594 | − | 1.21000i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 9.82344e44 | 0.0322231 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.41952e46 | 1.83303 | 0.916513 | − | 0.400004i | \(-0.130991\pi\) | ||||
0.916513 | + | 0.400004i | \(0.130991\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.15912e46 | 0.867195 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.06716e45 | − | 1.84837e45i | 0.0270817 | − | 0.0469068i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.39846e45 | + | 7.13157e45i | −0.0585316 | + | 0.174037i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.67678e45 | − | 1.32966e46i | −0.173293 | − | 0.300153i | 0.766276 | − | 0.642511i | \(-0.222107\pi\) |
−0.939569 | + | 0.342359i | \(0.888774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.61366e46 | + | 6.25904e46i | 0.726231 | + | 1.25787i | 0.958465 | + | 0.285210i | \(0.0920632\pi\) |
−0.232234 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.15972e46 | + | 7.20485e46i | −0.804356 | + | 1.39319i | ||||
\(832\) | 9.68021e45 | 0.183616 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.63839e46 | + | 9.76597e46i | 0.971734 | + | 1.68309i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.26233e46 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.51582e46 | − | 1.12857e47i | −0.982856 | − | 1.70236i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.23673e46 | + | 6.65068e46i | −0.318771 | + | 0.947832i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.64280e46 | + | 1.15057e47i | −0.911650 | + | 1.57902i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.18058e46 | −0.277579 | −0.138790 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138790 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.65530e46 | − | 1.49914e47i | 0.984898 | − | 1.70589i | 0.342510 | − | 0.939514i | \(-0.388723\pi\) |
0.642388 | − | 0.766380i | \(-0.277944\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.01931e47 | 1.00000 | ||||||||
\(868\) | 6.43239e46 | − | 1.91260e47i | 0.619522 | − | 1.84208i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.24593e44 | − | 5.62211e44i | −0.00295834 | − | 0.00512400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.12277e47 | + | 1.94470e47i | −0.986426 | + | 1.70854i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.41902e47 | 1.18011 | ||||||||
\(877\) | −9.23396e46 | + | 1.59937e47i | −0.754040 | + | 1.30604i | 0.191809 | + | 0.981432i | \(0.438564\pi\) |
−0.945850 | + | 0.324604i | \(0.894769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66493e47 | −1.21906 | −0.609530 | − | 0.792763i | \(-0.708642\pi\) | ||||
−0.609530 | + | 0.792763i | \(0.708642\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.33113e47 | − | 4.70521e46i | 1.53158 | − | 0.309137i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.91414e46 | − | 1.02436e47i | −0.368175 | − | 0.637697i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −9.26510e46 | − | 1.60476e47i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.58226e47 | − | 2.92783e47i | −1.32128 | − | 1.49810i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.05473e47 | − | 3.55890e47i | −0.979577 | − | 1.69668i | −0.663919 | − | 0.747805i | \(-0.731108\pi\) |
−0.315659 | − | 0.948873i | \(-0.602226\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 3.10528e45 | − | 5.37850e45i | 0.0135576 | − | 0.0234825i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.84602e47 | 0.751464 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.23623e47 | + | 3.87326e47i | −0.863909 | + | 1.49634i | 0.00421644 | + | 0.999991i | \(0.498658\pi\) |
−0.868126 | + | 0.496344i | \(0.834675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.08265e45 | + | 5.33930e45i | 0.0115019 | + | 0.0199219i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.01894e47 | −1.74721 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.97360e46 | − | 1.38107e47i | −0.268151 | − | 0.464450i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.07921e45 | − | 8.57021e45i | 0.00338776 | − | 0.0269028i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.72662e47 | 1.62205 | 0.811027 | − | 0.585009i | \(-0.198909\pi\) | ||||
0.811027 | + | 0.585009i | \(0.198909\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.87109e45 | 0.00785955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −1.87377e47 | − | 3.24546e47i | −0.440334 | − | 0.762681i | ||||
\(949\) | −4.68881e46 | − | 8.12125e46i | −0.108344 | − | 0.187657i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.34735e47 | + | 1.27260e48i | −1.38853 | + | 2.40501i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.11162e47 | − | 7.12153e47i | 0.739231 | − | 1.28039i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.16909e48 | 1.99998 | 0.999989 | − | 0.00469250i | \(-0.00149367\pi\) | ||||
0.999989 | + | 0.00469250i | \(0.00149367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | 6.34834e47 | 1.00000 | ||||||||
\(973\) | −1.23463e48 | + | 2.49201e47i | −1.91308 | + | 0.386139i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.12287e46 | + | 1.06051e47i | −0.0918082 | + | 0.159016i | ||||
\(976\) | 3.64702e47 | + | 6.31682e47i | 0.537949 | + | 0.931755i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.25277e47 | 1.12175 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.10427e45 | −0.00497880 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.75119e47 | + | 1.16934e48i | 0.780193 | + | 1.35133i | 0.931829 | + | 0.362897i | \(0.118212\pi\) |
−0.151636 | + | 0.988436i | \(0.548454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.13945e48 | 1.27500 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.42742e47 | + | 1.63288e48i | 0.989168 | + | 1.71329i | 0.621704 | + | 0.783252i | \(0.286441\pi\) |
0.367465 | + | 0.930037i | \(0.380226\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.59730e47 | − | 1.48910e48i | 0.873603 | − | 1.51313i |
(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 | 21.33.h.a.2.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.33.h.a.2.1 | ✓ | 2 | |
7.4 | even | 3 | inner | 21.33.h.a.11.1 | yes | 2 | |
21.11 | odd | 6 | inner | 21.33.h.a.11.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.33.h.a.2.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.33.h.a.2.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.33.h.a.11.1 | yes | 2 | 7.4 | even | 3 | inner | |
21.33.h.a.11.1 | yes | 2 | 21.11 | odd | 6 | inner |