Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,20,Mod(5,21)]
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, 5]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (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: | \(48.0515062768\) |
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 | 5.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.5 |
Dual form | 21.20.g.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | \(0.666667\pi\) | |||||||
\(3\) | 29524.5 | − | 17046.0i | 0.866025 | − | 0.500000i | ||||
\(4\) | −262144. | − | 454047.i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.84282e7 | + | 9.51504e7i | 0.453594 | + | 0.891209i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.81131e8 | − | 1.00655e9i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −1.54793e10 | − | 8.93700e9i | −0.866025 | − | 0.500000i | ||||
\(13\) | 7.60595e10i | 1.98926i | 0.103490 | + | 0.994631i | \(0.466999\pi\) | ||||
−0.103490 | + | 0.994631i | \(0.533001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.37439e11 | + | 2.38051e11i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.02386e12 | + | 5.91128e11i | 0.727919 | + | 0.420264i | 0.817660 | − | 0.575701i | \(-0.195271\pi\) |
−0.0897415 | + | 0.995965i | \(0.528604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.05175e12 | + | 1.98376e12i | 0.838428 | + | 0.545012i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.53674e12 | + | 1.65181e13i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.96238e13i | − | 1.00000i | ||||||
\(28\) | 3.05076e13 | − | 4.69318e13i | 0.545012 | − | 0.838428i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.39571e14 | + | 1.38317e14i | −1.62742 | + | 0.939590i | −0.642557 | + | 0.766238i | \(0.722126\pi\) |
−0.984860 | + | 0.173352i | \(0.944540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.09360e14 | −1.00000 | ||||||||
\(37\) | 7.90506e14 | − | 1.36920e15i | 0.999974 | − | 1.73201i | 0.493715 | − | 0.869624i | \(-0.335638\pi\) |
0.506258 | − | 0.862382i | \(-0.331028\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.29651e15 | + | 2.24562e15i | 0.994631 | + | 1.72275i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.01253e15 | 1.82434 | 0.912172 | − | 0.409807i | \(-0.134404\pi\) | ||||
0.912172 | + | 0.409807i | \(0.134404\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 9.37113e15i | 1.00000i | ||||||||
\(49\) | −6.70831e15 | + | 9.21593e15i | −0.588505 | + | 0.808493i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.45346e16 | − | 1.99385e16i | 1.72275 | − | 0.994631i | ||||
\(53\) | 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 | ||||||||
\(57\) | 4.03054e16 | 0.840528 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01134e17 | + | 5.83897e16i | 1.10730 | + | 0.639297i | 0.938127 | − | 0.346290i | \(-0.112559\pi\) |
0.169168 | + | 0.985587i | \(0.445892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.23917e17 | + | 6.54950e15i | 0.998606 | + | 0.0527804i | ||||
\(64\) | 1.44115e17 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.20587e17 | + | 3.82068e17i | 0.990535 | + | 1.71566i | 0.614139 | + | 0.789198i | \(0.289503\pi\) |
0.376396 | + | 0.926459i | \(0.377163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.43298e17 | + | 8.27332e16i | −0.284887 | + | 0.164480i | −0.635634 | − | 0.771991i | \(-0.719261\pi\) |
0.350747 | + | 0.936470i | \(0.385928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.63135e17 | + | 3.25126e17i | 0.866025 | + | 0.500000i | ||||
\(76\) | − | 6.19843e17i | − | 0.840528i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.31195e17 | + | 2.27236e17i | −0.123157 | + | 0.213314i | −0.921011 | − | 0.389537i | \(-0.872635\pi\) |
0.797854 | + | 0.602851i | \(0.205968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.75426e17 | − | 1.16987e18i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 1.00722e17 | − | 1.90567e18i | 0.0527804 | − | 0.998606i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.23710e18 | + | 3.68343e18i | −1.77285 | + | 0.902317i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.71548e18 | + | 8.16746e18i | −0.939590 | + | 1.62742i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.15735e19i | − | 1.54572i | −0.634575 | − | 0.772861i | \(-0.718825\pi\) | ||
0.634575 | − | 0.772861i | \(-0.281175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e18 | − | 8.66025e18i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.10657e19 | − | 1.21623e19i | −1.59082 | − | 0.918461i | −0.993166 | − | 0.116708i | \(-0.962766\pi\) |
−0.597655 | − | 0.801753i | \(-0.703901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −1.79910e19 | + | 1.03871e19i | −0.866025 | + | 0.500000i | ||||
\(109\) | 1.58738e19 | + | 2.74942e19i | 0.700049 | + | 1.21252i | 0.968449 | + | 0.249213i | \(0.0801720\pi\) |
−0.268399 | + | 0.963308i | \(0.586495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.38998e19i | − | 1.99995i | ||||||
\(112\) | −2.93066e19 | − | 1.54897e18i | −0.998606 | − | 0.0527804i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.65576e19 | + | 4.42005e19i | 1.72275 | + | 0.994631i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.05795e19 | + | 5.29653e19i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.25604e20 | + | 7.25177e19i | 1.62742 | + | 0.939590i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.92316e19 | 0.405043 | 0.202521 | − | 0.979278i | \(-0.435086\pi\) | ||||
0.202521 | + | 0.979278i | \(0.435086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.77517e20 | − | 1.02489e20i | 1.57993 | − | 0.912172i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.66217e18 | + | 1.26048e20i | −0.0443634 | + | 0.839357i | ||||
\(134\) | 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 | ||||||||
\(139\) | − | 3.87845e20i | − | 1.69831i | −0.528142 | − | 0.849156i | \(-0.677111\pi\) | ||
0.528142 | − | 0.849156i | \(-0.322889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.59740e20 | + | 2.76678e20i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.09649e19 | + | 3.86445e20i | −0.105414 | + | 0.994428i | ||||
\(148\) | −8.28905e20 | −1.99995 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.77389e19 | + | 3.07246e19i | 0.0353708 | + | 0.0612640i | 0.883169 | − | 0.469055i | \(-0.155405\pi\) |
−0.847798 | + | 0.530319i | \(0.822072\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.79744e20 | − | 1.17735e21i | 0.994631 | − | 1.72275i | ||||
\(157\) | −3.31927e20 | + | 1.91638e20i | −0.457084 | + | 0.263898i | −0.710817 | − | 0.703377i | \(-0.751675\pi\) |
0.253733 | + | 0.967274i | \(0.418341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.34847e20 | + | 4.06767e20i | −0.226466 | + | 0.392250i | −0.956758 | − | 0.290884i | \(-0.906050\pi\) |
0.730292 | + | 0.683135i | \(0.239384\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.32313e21 | −2.95716 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.19000e21 | − | 6.87045e20i | 0.727919 | − | 0.420264i | ||||
\(172\) | −1.57615e21 | − | 2.72997e21i | −0.912172 | − | 1.57993i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.10986e21 | + | 1.70737e21i | −0.545012 | + | 0.838428i | ||||
\(176\) | 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 | ||||||||
\(181\) | 1.59372e21i | 0.568152i | 0.958802 | + | 0.284076i | \(0.0916868\pi\) | ||||
−0.958802 | + | 0.284076i | \(0.908313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.98124e21 | 1.27859 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.77022e21 | − | 1.91891e21i | 0.891209 | − | 0.453594i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 4.25493e21 | − | 2.45658e21i | 0.866025 | − | 0.500000i | ||||
\(193\) | 3.42509e21 | + | 5.93243e21i | 0.663556 | + | 1.14931i | 0.979675 | + | 0.200592i | \(0.0642867\pi\) |
−0.316119 | + | 0.948719i | \(0.602380\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.94301e21 | + | 6.29984e20i | 0.994428 | + | 0.105414i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.60187e21 | + | 4.96629e21i | −1.24591 | + | 0.719329i | −0.970292 | − | 0.241937i | \(-0.922217\pi\) |
−0.275623 | + | 0.961266i | \(0.588884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.30255e22 | + | 7.52025e21i | 1.71566 | + | 0.990535i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.81061e22 | − | 1.04535e22i | −1.72275 | − | 0.994631i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.39936e22 | 1.99257 | 0.996283 | − | 0.0861410i | \(-0.0274536\pi\) | ||||
0.996283 | + | 0.0861410i | \(0.0274536\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.47629e22 | − | 1.60969e22i | −1.57556 | − | 1.02418i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.82054e21 | + | 4.88531e21i | −0.164480 | + | 0.284887i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.84214e22i | 0.904537i | 0.891882 | + | 0.452269i | \(0.149385\pi\) | ||||
−0.891882 | + | 0.452269i | \(0.850615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.21684e22 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | −1.05658e22 | − | 1.83005e22i | −0.420264 | − | 0.727919i | ||||
\(229\) | −1.24485e22 | − | 7.18715e21i | −0.474985 | − | 0.274233i | 0.243339 | − | 0.969941i | \(-0.421757\pi\) |
−0.718324 | + | 0.695708i | \(0.755091\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | 8.94536e21i | 0.246314i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.33683e22 | + | 3.65857e22i | −1.48837 | + | 0.859310i | −0.999912 | − | 0.0132790i | \(-0.995773\pi\) |
−0.488456 | + | 0.872589i | \(0.662440\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.98832e22 | − | 2.30266e22i | −0.866025 | − | 0.500000i | ||||
\(244\) | − | 6.12260e22i | − | 1.27859i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.49609e22 | + | 7.78746e22i | −0.836015 | + | 1.44802i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −2.95102e22 | − | 5.79808e22i | −0.453594 | − | 0.891209i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.77789e22 | − | 6.54350e22i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68562e23 | + | 8.90921e21i | 1.99716 | + | 0.105558i | ||||
\(260\) | 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 | ||||||||
\(268\) | 1.15651e23 | − | 2.00314e23i | 0.990535 | − | 1.71566i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00409e23 | + | 1.15706e23i | 1.54422 | + | 0.891557i | 0.998565 | + | 0.0535483i | \(0.0170531\pi\) |
0.545657 | + | 0.838009i | \(0.316280\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.50884e23 | + | 2.32115e23i | −1.08417 | + | 1.66785i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11289e23 | + | 1.92758e23i | 0.696456 | + | 1.20630i | 0.969688 | + | 0.244348i | \(0.0785740\pi\) |
−0.273232 | + | 0.961948i | \(0.588093\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.21520e23i | 1.87918i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.26314e23 | − | 1.30662e23i | 1.15542 | − | 0.667082i | 0.205218 | − | 0.978716i | \(-0.434210\pi\) |
0.950202 | + | 0.311634i | \(0.100876\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.19536e23 | − | 2.07043e23i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.97281e23 | − | 3.41701e23i | −0.772861 | − | 1.33864i | ||||
\(292\) | 7.51294e22 | + | 4.33760e22i | 0.284887 | + | 0.164480i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | − | 3.40920e23i | − | 1.00000i | ||||||
\(301\) | 2.91176e23 | + | 5.72095e23i | 0.827512 | + | 1.62587i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.81438e23 | + | 1.62488e23i | −0.727919 | + | 0.420264i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.85262e23i | − | 1.61451i | −0.590200 | − | 0.807257i | \(-0.700951\pi\) | ||
0.590200 | − | 0.807257i | \(-0.299049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.29271e23 | −1.83692 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.95718e23 | − | 1.70733e23i | −0.579704 | − | 0.334692i | 0.181312 | − | 0.983426i | \(-0.441966\pi\) |
−0.761016 | + | 0.648734i | \(0.775299\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.37567e23 | 0.246314 | ||||||||
\(317\) | 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 | ||||||||
\(324\) | −3.54118e23 | + | 6.13350e23i | −0.500000 | + | 0.866025i | ||||
\(325\) | −1.25636e24 | + | 7.25360e23i | −1.72275 | + | 0.994631i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.37331e23 | + | 5.41168e23i | 1.21252 | + | 0.700049i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.32820e23 | − | 7.49666e23i | 0.498817 | − | 0.863976i | −0.501182 | − | 0.865342i | \(-0.667101\pi\) |
0.999999 | + | 0.00136580i | \(0.000434747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.18774e23 | − | 1.59136e24i | −0.999974 | − | 1.73201i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.91667e23 | + | 4.53827e23i | −0.891209 | + | 0.453594i | ||||
\(337\) | 1.06890e24 | 1.03861 | 0.519305 | − | 0.854589i | \(-0.326191\pi\) | ||||
0.519305 | + | 0.854589i | \(0.326191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.20177e24 | − | 1.91987e23i | −0.987479 | − | 0.157753i | ||||
\(344\) | 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 | ||||||||
\(349\) | − | 1.51610e24i | − | 1.05654i | −0.849076 | − | 0.528270i | \(-0.822841\pi\) | ||
0.849076 | − | 0.528270i | \(-0.177159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.01376e24 | 1.98926 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 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 | ||||||||
\(361\) | −2.90345e23 | − | 5.02893e23i | −0.146756 | − | 0.254189i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.08503e24i | 1.00000i | ||||||||
\(364\) | 3.56961e24 | + | 2.32039e24i | 1.66785 | + | 1.08417i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.98463e24 | + | 2.30053e24i | −1.72211 | + | 0.994261i | −0.807562 | + | 0.589782i | \(0.799214\pi\) |
−0.914547 | + | 0.404479i | \(0.867453\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.94454e24 | 1.87918 | ||||||||
\(373\) | −6.38263e23 | + | 1.10550e24i | −0.236464 | + | 0.409568i | −0.959697 | − | 0.281036i | \(-0.909322\pi\) |
0.723233 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.06002e24 | 1.92931 | 0.964654 | − | 0.263520i | \(-0.0848835\pi\) | ||||
0.964654 | + | 0.263520i | \(0.0848835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15829e24 | − | 6.68742e23i | 0.350777 | − | 0.202521i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.49407e24 | − | 6.05190e24i | 0.912172 | − | 1.57993i | ||||
\(388\) | −5.25489e24 | + | 3.03391e24i | −1.33864 | + | 0.772861i | ||||
\(389\) | 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 | ||||||||
\(397\) | −3.95150e23 | − | 2.28140e23i | −0.0809567 | − | 0.0467404i | 0.458975 | − | 0.888449i | \(-0.348217\pi\) |
−0.539932 | + | 0.841709i | \(0.681550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.95192e24 | + | 3.83508e24i | 0.381258 | + | 0.749086i | ||||
\(400\) | −5.24288e24 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.05203e25 | − | 1.82217e25i | −1.86909 | − | 3.23736i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10693e25 | + | 6.39084e24i | −1.70902 | + | 0.986703i | −0.773242 | + | 0.634112i | \(0.781366\pi\) |
−0.935778 | + | 0.352591i | \(0.885301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.27531e25i | 1.83692i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.61119e24 | − | 1.14509e25i | −0.849156 | − | 1.47078i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.68847e24 | 0.549985 | 0.274993 | − | 0.961446i | \(-0.411325\pi\) | ||||
0.274993 | + | 0.961446i | \(0.411325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.58068e23 | + | 1.24506e25i | −0.0674848 | + | 1.27681i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 9.43249e24 | + | 5.44585e24i | 0.866025 | + | 0.500000i | ||||
\(433\) | − | 2.20683e25i | − | 1.98213i | −0.133365 | − | 0.991067i | \(-0.542578\pi\) | ||
0.133365 | − | 0.991067i | \(-0.457422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.32243e24 | − | 1.44149e25i | 0.700049 | − | 1.21252i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.08816e24 | − | 2.93765e24i | −0.401003 | − | 0.231519i | 0.285913 | − | 0.958255i | \(-0.407703\pi\) |
−0.686917 | + | 0.726736i | \(0.741036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.37787e24 | + | 1.21079e25i | 0.405923 | + | 0.913907i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | −2.44730e25 | + | 1.41295e25i | −1.73201 | + | 0.999974i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.97924e24 | + | 1.37126e25i | 0.453594 | + | 0.891209i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.04746e24 | + | 6.04753e23i | 0.0612640 | + | 0.0353708i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.26766e25 | − | 2.19566e25i | 0.682024 | − | 1.18130i | −0.292338 | − | 0.956315i | \(-0.594433\pi\) |
0.974362 | − | 0.224986i | \(-0.0722335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.04121e25 | 1.92084 | 0.960421 | − | 0.278552i | \(-0.0898545\pi\) | ||||
0.960421 | + | 0.278552i | \(0.0898545\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | − | 4.63476e25i | − | 1.98926i | ||||||
\(469\) | −2.56713e25 | + | 3.94919e25i | −1.07971 | + | 1.66098i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.53332e24 | + | 1.13160e25i | −0.263898 | + | 0.457084i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.25497e25i | 0.840528i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04140e26 | + | 6.01255e25i | 3.44541 | + | 1.98921i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.20650e25 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.06835e25 | − | 5.31453e25i | −0.902359 | − | 1.56293i | −0.824424 | − | 0.565972i | \(-0.808501\pi\) |
−0.0779343 | − | 0.996958i | \(-0.524832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.60128e25i | 0.452932i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.60404e25i | − | 1.87918i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.08933e25 | + | 3.61882e25i | −0.487586 | + | 0.844523i | −0.999898 | − | 0.0142759i | \(-0.995456\pi\) |
0.512312 | + | 0.858799i | \(0.328789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.27638e26 | + | 7.36920e25i | −2.56098 | + | 1.47858i | ||||
\(508\) | −1.02843e25 | − | 1.78130e25i | −0.202521 | − | 0.350777i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.48118e25 | − | 9.62825e24i | −0.275809 | − | 0.179287i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.34227e25 | − | 4.05693e25i | 0.420264 | − | 0.727919i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.30700e25 | − | 5.37340e25i | −1.57993 | − | 0.912172i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.66777e25 | − | 4.42699e25i | −1.14526 | − | 0.661214i | −0.197530 | − | 0.980297i | \(-0.563292\pi\) |
−0.947727 | + | 0.319083i | \(0.896625\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.66426e24 | + | 6.93278e25i | −0.0527804 | + | 0.998606i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.73077e25 | − | 6.46189e25i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.89783e25 | − | 3.00179e25i | 0.749086 | − | 0.381258i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.03584e25 | − | 3.52618e25i | 0.220480 | − | 0.381883i | −0.734474 | − | 0.678637i | \(-0.762571\pi\) |
0.954954 | + | 0.296754i | \(0.0959042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.71664e25 | + | 4.70537e25i | 0.284076 | + | 0.492034i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.22629e26 | 1.19596 | 0.597978 | − | 0.801513i | \(-0.295971\pi\) | ||||
0.597978 | + | 0.801513i | \(0.295971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.17544e26 | − | 6.78641e25i | 1.10730 | − | 0.639297i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.79751e25 | − | 1.47860e24i | −0.245970 | − | 0.0130005i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.76100e26 | + | 1.01671e26i | −1.47078 | + | 0.849156i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.57310e26i | 3.62910i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.86041e25 | − | 1.20922e26i | 0.545012 | − | 0.838428i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.15237e26 | − | 1.99596e26i | −0.747391 | − | 1.29452i | −0.949069 | − | 0.315067i | \(-0.897973\pi\) |
0.201678 | − | 0.979452i | \(-0.435360\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.37498e25 | − | 1.45059e26i | 0.500000 | − | 0.866025i | ||||
\(577\) | 2.89027e26 | − | 1.66870e26i | 1.69734 | − | 0.979959i | 0.749070 | − | 0.662491i | \(-0.230501\pi\) |
0.948269 | − | 0.317469i | \(-0.102833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.02248e26 | + | 1.16768e26i | 1.14931 | + | 0.663556i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 1.86203e26 | − | 8.27044e25i | 0.913907 | − | 0.405923i | ||||
\(589\) | −3.27051e26 | −1.57950 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.17293e26 | + | 3.76362e26i | 0.999974 | + | 1.73201i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.69311e26 | + | 2.93254e26i | −0.719329 | + | 1.24591i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.11996e26i | − | 1.24406i | −0.782994 | − | 0.622030i | \(-0.786308\pi\) | ||
0.782994 | − | 0.622030i | \(-0.213692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.12760e26 | 1.98107 | ||||||||
\(604\) | 9.30028e24 | − | 1.61086e25i | 0.0353708 | − | 0.0612640i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.32601e26 | − | 2.49762e26i | −1.56962 | − | 0.906222i | −0.996212 | − | 0.0869525i | \(-0.972287\pi\) |
−0.573409 | − | 0.819269i | \(-0.694379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.99985e26 | + | 3.46385e26i | 0.660881 | + | 1.14468i | 0.980384 | + | 0.197095i | \(0.0631507\pi\) |
−0.319503 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.04142e26 | + | 6.01263e25i | −0.313736 | + | 0.181135i | −0.648597 | − | 0.761132i | \(-0.724644\pi\) |
0.334861 | + | 0.942267i | \(0.391311\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.12763e26 | −1.98926 | ||||||||
\(625\) | −1.81899e26 | + | 3.15058e26i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.74025e26 | + | 1.00474e26i | 0.457084 | + | 0.263898i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.88321e26 | −1.97890 | −0.989450 | − | 0.144873i | \(-0.953723\pi\) | ||||
−0.989450 | + | 0.144873i | \(0.953723\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.08400e26 | − | 4.08995e26i | 1.72561 | − | 0.996283i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.00959e26 | − | 5.10231e26i | −1.60830 | − | 1.17069i | ||||
\(638\) | 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 | ||||||||
\(643\) | − | 8.31292e26i | − | 1.74482i | −0.488779 | − | 0.872408i | \(-0.662557\pi\) | ||
0.488779 | − | 0.872408i | \(-0.337443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.00550e27 | − | 5.31448e25i | −1.87656 | − | 0.0991839i | ||||
\(652\) | 2.46255e26 | 0.452932 | ||||||||
\(653\) | 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 | ||||||||
\(657\) | 1.92315e26i | 0.328959i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.48193e26 | − | 2.58764e26i | 0.723687 | − | 0.417821i | −0.0924209 | − | 0.995720i | \(-0.529461\pi\) |
0.816108 | + | 0.577899i | \(0.196127\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.14011e26 | + | 5.43883e26i | 0.452269 | + | 0.783352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.57491e26 | −1.16704 | −0.583521 | − | 0.812098i | \(-0.698325\pi\) | ||||
−0.583521 | + | 0.812098i | \(0.698325\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.54510e26 | − | 3.77882e26i | 0.866025 | − | 0.500000i | ||||
\(676\) | 1.13328e27 | + | 1.96290e27i | 1.47858 | + | 2.56098i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10122e27 | − | 5.60482e26i | 1.37756 | − | 0.701130i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −6.23901e26 | − | 3.60210e26i | −0.727919 | − | 0.420264i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.90048e26 | −0.548466 | ||||||||
\(688\) | −8.26356e26 | + | 1.43129e27i | −0.912172 | + | 1.57993i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.12985e27 | + | 6.52318e26i | 1.19668 | + | 0.690905i | 0.959814 | − | 0.280637i | \(-0.0905457\pi\) |
0.236868 | + | 0.971542i | \(0.423879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.06617e27 | + | 5.63513e25i | 0.998606 | + | 0.0527804i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.61874e27 | − | 9.34580e26i | 1.45580 | − | 0.840506i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.17157e27 | − | 2.02922e27i | 0.971916 | − | 1.68341i | 0.282156 | − | 0.959368i | \(-0.408950\pi\) |
0.689759 | − | 0.724039i | \(-0.257716\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.52482e26 | + | 2.64107e26i | 0.123157 | + | 0.213314i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.37072e26 | − | 2.59340e27i | 0.0969536 | − | 1.83436i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.24728e27 | + | 2.16035e27i | −0.859310 | + | 1.48837i | ||||
\(724\) | 7.23621e26 | − | 4.17783e26i | 0.492034 | − | 0.284076i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.89394e27i | 1.89197i | 0.324217 | + | 0.945983i | \(0.394899\pi\) | ||||
−0.324217 | + | 0.945983i | \(0.605101\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.57004e27 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.04366e27 | − | 1.80767e27i | −0.639297 | − | 1.10730i | ||||
\(733\) | −2.23012e27 | − | 1.28756e27i | −1.34846 | − | 0.778537i | −0.360433 | − | 0.932785i | \(-0.617371\pi\) |
−0.988032 | + | 0.154249i | \(0.950704\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.60254e26 | + | 1.31680e27i | 0.425438 | + | 0.736881i | 0.996461 | − | 0.0840533i | \(-0.0267866\pi\) |
−0.571023 | + | 0.820934i | \(0.693453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.06561e27i | 1.67203i | ||||||||
\(742\) | 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 | ||||||||
\(751\) | 7.13011e26 | − | 1.23497e27i | 0.342387 | − | 0.593031i | −0.642489 | − | 0.766295i | \(-0.722098\pi\) |
0.984875 | + | 0.173264i | \(0.0554313\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.85961e27 | − | 1.20882e27i | −0.838428 | − | 0.545012i | ||||
\(757\) | 3.34562e26 | 0.148959 | 0.0744793 | − | 0.997223i | \(-0.476271\pi\) | ||||
0.0744793 | + | 0.997223i | \(0.476271\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.84735e27 | + | 2.84189e27i | −0.763071 | + | 1.17388i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.23081e27 | − | 1.28796e27i | −0.866025 | − | 0.500000i | ||||
\(769\) | − | 8.39780e26i | − | 0.322007i | −0.986954 | − | 0.161003i | \(-0.948527\pi\) | ||
0.986954 | − | 0.161003i | \(-0.0514730\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.79573e27 | − | 3.11030e27i | 0.663556 | − | 1.14931i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.56946e27 | − | 2.63818e27i | −1.62742 | − | 0.939590i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.12859e27 | − | 2.61027e27i | 1.78237 | − | 0.907164i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.27188e27 | − | 2.86355e27i | −0.405923 | − | 0.913907i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.18994e27 | + | 2.99642e27i | −1.59736 | + | 0.922236i | −0.605366 | + | 0.795947i | \(0.706973\pi\) |
−0.991994 | + | 0.126289i | \(0.959693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.44109e27 | + | 7.69220e27i | −1.27173 | + | 2.20270i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.50985e27 | + | 2.60377e27i | 1.24591 | + | 0.719329i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 7.88555e27i | − | 1.98107i | ||||||
\(805\) | 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 | ||||||||
\(811\) | − | 2.92108e27i | − | 0.675843i | −0.941174 | − | 0.337922i | \(-0.890276\pi\) | ||
0.941174 | − | 0.337922i | \(-0.109724\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.88932e27 | 1.78311 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.15601e27 | + | 3.55417e27i | 1.32797 | + | 0.766707i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.98152e26 | + | 9.42504e27i | −0.104994 | + | 1.98649i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.10110e27 | − | 3.63921e27i | −0.422812 | − | 0.732332i | 0.573401 | − | 0.819275i | \(-0.305624\pi\) |
−0.996213 | + | 0.0869425i | \(0.972290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.24939e27 | − | 3.60809e27i | 1.17373 | − | 0.677656i | 0.219178 | − | 0.975685i | \(-0.429663\pi\) |
0.954557 | + | 0.298029i | \(0.0963292\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.57149e27 | + | 3.79405e27i | 1.20630 | + | 0.696456i | ||||
\(832\) | 1.09613e28i | 1.98926i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.48063e27 | + | 9.49272e27i | 0.939590 | + | 1.62742i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.10326e27 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.28979e27 | − | 1.08942e28i | −0.996283 | − | 1.72561i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.52059e27 | − | 3.44640e26i | −0.998606 | − | 0.0527804i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.45454e27 | − | 7.71548e27i | 0.667082 | − | 1.15542i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.30743e28i | − | 1.87242i | −0.351444 | − | 0.936209i | \(-0.614309\pi\) | ||
0.351444 | − | 0.936209i | \(-0.385691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.12643e27 | + | 4.11445e27i | 0.954855 | + | 0.551286i | 0.894586 | − | 0.446897i | \(-0.147471\pi\) |
0.0602690 | + | 0.998182i | \(0.480804\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | − | 8.15045e27i | − | 1.00000i | ||||||
\(868\) | −8.17294e26 | + | 1.54632e28i | −0.0991839 | + | 1.87656i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.90599e28 | + | 1.67778e28i | −3.41289 | + | 1.97043i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.16492e28 | − | 6.72569e27i | −1.33864 | − | 0.772861i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.95755e27 | 0.328959 | ||||||||
\(877\) | 7.38731e27 | − | 1.27952e28i | 0.812812 | − | 1.40783i | −0.0980766 | − | 0.995179i | \(-0.531269\pi\) |
0.910889 | − | 0.412653i | \(-0.135398\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.93667e28 | −1.99723 | −0.998617 | − | 0.0525783i | \(-0.983256\pi\) | ||||
−0.998617 | + | 0.0525783i | \(0.983256\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.89992e27 | + | 3.73291e27i | 0.183725 | + | 0.360978i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.36418e27 | − | 4.82906e27i | 0.783352 | − | 0.452269i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.81131e27 | − | 1.00655e28i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.83487e28 | + | 1.19274e28i | 1.52958 | + | 0.994290i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.49346e27 | − | 1.64432e28i | −0.758849 | − | 1.31437i | −0.943438 | − | 0.331549i | \(-0.892429\pi\) |
0.184589 | − | 0.982816i | \(-0.440905\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −5.53953e27 | + | 9.59476e27i | −0.420264 | + | 0.727919i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.53627e27i | 0.548466i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.36969e27 | − | 7.56852e27i | 0.308286 | − | 0.533966i | −0.669702 | − | 0.742630i | \(-0.733578\pi\) |
0.977987 | + | 0.208664i | \(0.0669114\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.16810e28 | − | 2.02320e28i | −0.807257 | − | 1.39821i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.01554e28 | 1.99995 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.44838e28 | + | 1.41357e28i | −1.59082 | + | 0.918461i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.23162e28 | + | 5.47039e27i | −0.768165 | + | 0.341190i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.83178e28i | 1.07485i | 0.843313 | + | 0.537423i | \(0.180602\pi\) | ||||
−0.843313 | + | 0.537423i | \(0.819398\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.16412e28 | −0.669384 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 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 | \(0.666667\pi\) | |||||||
\(948\) | 4.06161e27 | − | 2.34497e27i | 0.213314 | − | 0.123157i | ||||
\(949\) | −6.29264e27 | − | 1.08992e28i | −0.327193 | − | 0.566715i | ||||
\(950\) | 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 | ||||||||
\(961\) | 2.74276e28 | − | 4.75061e28i | 1.26566 | − | 2.19218i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.32232e28 | + | 1.91815e28i | 1.48837 | + | 0.859310i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.83031e28 | 1.66603 | 0.833014 | − | 0.553251i | \(-0.186613\pi\) | ||||
0.833014 | + | 0.553251i | \(0.186613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 2.41451e28i | 1.00000i | ||||||||
\(973\) | 3.69036e28 | − | 1.87826e28i | 1.51355 | − | 0.770344i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.47289e28 | + | 4.28318e28i | −0.994631 | + | 1.72275i | ||||
\(976\) | −2.77995e28 | + | 1.60500e28i | −1.10730 | + | 0.639297i | ||||
\(977\) | 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 | ||||||||
\(981\) | 3.68990e28 | 1.40010 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.71449e28 | 1.67203 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.57098e28 | + | 4.45307e28i | 0.885929 | + | 1.53447i | 0.844645 | + | 0.535326i | \(0.179811\pi\) |
0.0412835 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.95113e28i | − | 0.997633i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.08959e28 | + | 1.20643e28i | −0.679919 | + | 0.392552i | −0.799825 | − | 0.600234i | \(-0.795074\pi\) |
0.119905 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.42527e28 | − | 3.13228e28i | −1.73201 | − | 0.999974i |
(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 | 21.20.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.20.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.20.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.20.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.20.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.20.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.20.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.20.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |